Size Effects in Manufacturing of Metallic Components

Size effects in manufacturing of metallic components

F. Vollertsen (1)a,*, D. Biermann b, H.N. Hansen (1)c, I.S. Jawahir (1)d, K. Kuzman (2)e

a Bremer Institut fuer angewandte Strahltechnik (BIAS), Bremen, Germanyb Institut fur spanende Fertigung (ISF), TU Dortmund, Germanyc Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmarkd Department of Mechanical Engineering, University of Kentucky, Lexington, KY, USAe University of Ljubljana, Ljubljana, Slovenia

CIRP Annals - Manufacturing Technology 58 (2009) 566–587

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CIRP Annals - Manufacturing Technology

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A R T I C L E I N F O

Keywords:

Forming

Machining

Size effects

A B S T R A C T

In manufacturing of metallic components, the size of the part plays an important role for the process

behaviour. This is due to so called size effects, which lead to changes in the process behaviour even if the

relationship between the main geometrical features is kept constant. The aim of this paper is to give a

systematic review on such effects and their potential use or remedy. First, the typology of size effects will

be explained, followed by a description of size effects on strength and tribology. The last three sections

describe size effects on formability, forming processes and cutting processes.

� 2009 CIRP.

1. Introduction

Rules for up- or down-scaling are extensively used in fluiddynamics, enabling experiments with smaller samples, which arecheaper and much easier to conduct than real size experiments.The theory of similarity describes the conditions which must besatisfied for a successful up- or down-scaling for that purpose.Pioneering work in this area was done by Pawelski [1,2], whoworked on the rules of similarity with respect to metal forming,reportedly the earliest [3,4]. It was shown that the rules ofsimilarity can help to design proper experiments, for example, forcompression testing with lubrication [5]. But, due to the complexnature of processes such as metal forming, Pawelski comes to theconclusion that it is often not possible to obey all necessary rules ofsimilarity when up- or down-scaling a process [6], while theresults of those limitations lead to so called size effects. A recentresearch work illustrates such effects in solid metal processingthrough simulation [7].

Microtechnology is very prominent field where size effectsplay an important role. Reviews on micro forming highlight theimportance of size effects in this field [8,9], where long-termbasic research is required to realise industrial applications [10].Also in the assembly of micro systems, size effects are one of theproblems to be solved [11]. Also, it is evident from the recentreview on micro machining [12] that no major effort has beenmade relating size effects, and no recent interdisciplinaryreview on size effects was reported since then. The aim of thispaper is to comprehensively review the work done with respectto size effects.

* Corresponding author.

0007-8506/$ – see front matter � 2009 CIRP.

doi:10.1016/j.cirp.2009.09.002

2. Basics

2.1. Definition

In order to establish the contents of this paper, size effects needto be defined first. This is done as proposed in [13] as follows.

Size effects are deviations from intensive or proportionalextrapolated extensive values of process characteristics whichoccur, when scaling the geometrical dimensions.

Size effects occur due to the fact that the ratio among alldecisive features cannot be kept constant according to the processrequirements [13].

Intensive variables are those which do not change with themass, for example, temperature, density, etc.

Extensive variables are those which change with mass, forexample, heat content, inertia force, etc.

Scaling means to reduce (down-scaling), or increase (up-scaling) all relevant length dimensions of the workpiece, the tools,and/or the processing parameters in a geometrically similar way,i.e., by a constant factor.

Geometrical dimensions might be workpiece, tool and/orgeometrical process dimension(s).

Size effects can be beneficial, neutral or detrimental. Despite thefact that such size effects can occur in all manufacturing processes,this paper is limited to metallic parts and those processes, whichare based on plastic deformation, i.e., metal forming andmachining. It is also emphasized by the definition that size effectsare of somewhat surprising nature at the first glance, as they occurdespite the fact that the length relationship between all geometricfeatures are held constant.

2.2. Typology

One early approach for a typology, e.g., a systematic order ofsize effects in manufacturing is given in [14]. An update was given

http://www.sciencedirect.com/science/journal/00078506

http://dx.doi.org/10.1016/j.cirp.2009.09.002

Fig. 1. Categories for size effects [13].

F. Vollertsen et al. / CIRP Annals - Manufacturing Technology 58 (2009) 566–587 567

in [7] by defining systematically the sources of the size effects. Thisapproach was recently revised [13], and the result is given inTable 1. The classification is made into three categories, which arein turn divided into subgroups.

The basic approach of the typology is to characterize the effectsusing the kind of value, which is held constant during scaling and isresponsible for the effect. Based on this, density, shape and (micro)structure effects can be distinguished, see Fig. 1.

Density effects occur, if the density – as an intensive variable –is held constant during scaling (up or down). Three different kindsof density can be distinguished, as the feature can be an interfacearea, a line or a point. For example, consider a constant defectdensity, e.g., pores, in a brittle material. In big samples, there willbe a large (absolute) number of such defects, resulting in low andconstant fracture strength. But, if one prepares very small samplesfrom the same material, some samples will contain no defect, whileothers will contain one, resulting in a considerable difference in thestrength and scatter in strength between the big and smallsamples. This effect is well known, and is described by the Weibulldistribution.

The category of shape effects comprise such effects thatoccur due to the fact that the volume of a part is proportional to thethird power of its size r3 while the surface goes with the secondpower r2. Changing the size r, while keeping the shape constant,would result in an inevitable change in the relation of surface tovolume by 1/r. All effects which are based on volume-related andsurface-related values are summarized here. The two subgroupsof this category, distinguished by these effects, were the volume-related values which are concurrent to surface-related ones (i.e.,shape balance effects), and those where the observed value is asum of volumes defined and surface defined sub values, while therelative amount of the two change due to scaling (shape sumeffects). One example of a shape balance effect is the size effectin handling, for example, the sticking effect described in [11].

Table 1Typology of size effects according to [13].

Category Subgroup Models

Density Interface area density

Line length density

Point defect density Weibull model

Shape Shape balance Relation between forces

Relation between heating and cooling

Relation between generation and effusion

Shape sum Surface grain model

Structure Characteristic length Strain gradient plasticity

Dislocation drain strengthening

Dislocation starvation effect

Microgeometry Lubricant pocket model

Composite model

Secondary artefact Texture model

This size effect, which makes it difficult to release small partsfrom grippers, is due to the change of the relation (the balance)between the surface-determined adhesion forces and the volume-determined gravitational forces.

The group of microstructure effects comprise such effectswhich occur due to the fact that it is (in practice) impossible toscale all structural values simultaneously by the same factor. Thisgroup can be subdivided into three categories, which distinguishbetween those effects, where it is physically not possible to changea characteristic length, where it is not practised to scale the microgeometry and where secondary artefacts occur while trying toscale in an appropriate way. One size effect of the characteristiclength type is the limited validity of the Hall–Petch relationship,described in [15]. The grain size is the three-dimensional feature,which is scaled down, while the diameter of dislocation loops is thecharacteristic length. As explained in [15], the Hall–Petch relation-ship is not valid in copper below a grain size of about 50 nm, asdislocation loops cannot be scaled down to such a grain size.Further details about the typology are given in [13].

3. Flow stress

3.1. Experimental findings

3.1.1. Methods for scaled strength determination

The measurement of the flow stress in scaled experiments, forexample, when the sheet thickness or rod diameter is reduced,can become very difficult in the micro range, as the handling ofthe small samples tends to introduce distortion and thereforeuniaxial stress conditions are difficult to guarantee. Furthermore,machines are necessary which allow the adaptation of the loadingparameters (e.g., speed) to the sample size. One solution for sucha machine, which can be used for different types of tests, wasdeveloped and described in [16].

As tensile tests might become difficult, plane-strain upsettingtests using stacked sheet metal samples were evaluated [17]. It wasseen from the results that the kind of sample type (loosely stackedsheets or glued sheet packages) strongly influenced the result,while the number of layers showed no significant influence on themeasured flow curve [17], if the same annealing condition isapplied to the material before the test.

Due to edge effects an increase of the flow stress withdecreasing sample width was sometimes observed. In order toexclude such effects, the bulge test was investigated for scaled flowstress determination. Picart et al. [18] used a hydraulic bulge testwith two different die diameters (20 mm and 50 mm, respec-tively), which were held constant during testing of different sheetthicknesses. They showed that there is a significant influence of thedie diameter on the measured flow stress [18]. Kurosaki usedscaled tool dimensions for hydraulic bulge tests on copper foilshaving a thickness between 5 mm and 1 mm [19]. He showed that

Examples for size effects

Scatter in flow stress

Yield strength of whiskers

Changing failure strength of brittle material

Adhesion to grippers in microtechnology

Stronger heating of large samples during forming

of gas Pore formation in large welds

Increase in flow stress with increasing size

Hardness decrease with increasing indentation depth

Strength increase due to dislocation pile up at a surface layer

Tensile strength of whiskers

Increase of friction with decreasing size

Increase of normalized cutting force with decreasing cutting depth

Decrease in flow stress with increasing size

Decrease in flow stress with increasing size, if grain size>

sheet thickness

F. Vollertsen et al. / CIRP Annals - Manufacturing Technology 58 (2009) 566–587568

for those experiments the Hall–Petch relationship was still valid. Anew method for the determination of flow curves for microspecimen, the Aero-Bulge test, was introduced by Hoffmann et al.[20]. Here the flow curve is measured by pneumatic bulging of thefoil, while the flow stress can be calculated from the appliedpressure and the shape of the sample as in hydraulic bulge tests. Itwas pointed out that the flow curve determination is much moreprecise than that from tensile tests.

Micro hardness tests can be used also as a measure for the flowstress, as it was shown by Chen et al., for a CuZn alloy, where arelationship between flow stress kf and hardness H like

k f ¼H

3(3.1)

was found [21]. The tests were made with a test load of 1 N. Otherresults for copper show that also for nano-indentation with loadsdown to 3 � 10�3 N, a good correlation can be found between thetensile strength of whiskers and the strength calculated fromhardness tests [22].

A method which is especially developed for thin samples suchas foils down to some mm in thickness is the bending andunloading test. Provided that the Young’s modulus of the materialis known, the strength at a certain strain can be determined justfrom the measurement of the curvature after unloading [23].Different strains can be achieved by mandrels having differentdiameters. Due to characteristic length effects (see Table 1)differences occurred between the results from tensile tests andfrom bending tests.

3.1.2. Influences on the mechanical strength

Size effects on the strength of metallic material (pure metalsand alloys) were investigated in a wide range of sizes, which covers6 orders of magnitude. It seems that neither the material itself(pure nickel, gold, aluminium; brass, aluminium alloys or highalloyed steel), nor the shape of the samples (sheet, wire orrectangular blocks) is of primary meaning for the results. The mostimportant feature is the size range [13].

In Fig. 2 an overview of the extent of different size effects isgiven. While the x-axis shows the range of the characteristic size(typically, the sheet thickness or the wire diameter, but alsoindentation depth) of the samples used for the particularinvestigation, the y-axis reflects the maximum relative importanceof the measured influence, the influence strength Ii. This influenceparameter is defined as [13]:

Ii ¼ðXmax � XminÞ=ðXmax þ XminÞðlmax � lminÞ=ðlmax þ lminÞ

(3.2)

while X are the measured values (flow stress, yield stress,coefficient of friction, etc.), l is the characteristic length, and‘min’ and ‘max’ denote the minimum and maximum values,respectively. The maximum relative importance Ii shows theimportance of the effects, as it accounts for the fact that thedifferences in mechanical strength could be small, but the range ofsizes might be also small, see e.g., [24], where a strong influence is

Fig. 2. Size range of appearance and influence strength of size effects on the strength

of materials (see [13] for details).

seen, while other investigations with wide ranges of sizes showonly little effects (see e.g., [19]).

It was surprising that the analysis shows almost always clearlyseparated fields for the most important size effects. A scientificexplanation for the reduction of the maximum effect strength withincreasing characteristic size cannot be offered here. It seems to beobvious that a certain effect shows certain strength and appears in acertain size span. Despite the fact that it is not fully unambiguous,Fig. 2 is a kind of map which would help to identify size effects fromexperimental findings. It also shows whether there is the probabilityfor an interaction of different effects. As the Hall–Petch effect occursin a similar size span like the surface grain effect, but is muchstronger, experiments concerning the surface grain effect mustcarefully exclude the occurrence of the Hall–Petch effect, normallyby working with a constant grain size. The interference with Hall–Petch might be the reason, why in some published work the surfacegrain effect was not detected despite the fact that a wide span from5 mm to 1 mm in sheet thickness was investigated [19]. Unfortu-nately, in that study the grain size was not constant for the varioussheet thicknesses, but decreased steadily.

The composite effect, the strain gradient plasticity and thesurface grain effect will be explained in more detail in Section 3.2.The dislocation starvation effect denotes a very strong effect whichis especially seen at the strength of whiskers, but not limited tothat. Whiskers are known as single crystals having no mobiledislocations. Due to this, the strength of real whiskers is very highand approaches the theoretical shear strength (see e.g., [25]). Onthe other hand, as shown in Fig. 3 (data from [22]), the strengthdrastically drops with increasing size. A similar effect was seen incompression tests on gold cylinders having a diameter from300 nm to 7.5 mm [26]. It can be explained by a dislocationstarvation model [26] which basically says that there is adislocation movement without dislocation multiplication insidethe sample. Dislocations have to be generated at the free surfaceand travel through the whole sample, leaving the lattice at the freesurface on the opposite side without any dislocation multi-plication, as the travel distance in small samples is smaller thanthat necessary for reproduction (which is about 1 mm for silver).As dislocation generation at free surfaces needs high stresses,the strength of samples being smaller than 1 mm increasessignificantly.

In some work (see e.g., [20,27–29]) on the surface grain effect itwas surprising that the strength increased with decreasing size, asopposed to what was observed from the surface grain effect, seeFig. 4. This effect, which occurs for samples having a thickness lessthan the grain size, is qualitatively explained by the texturegenerated during the preparation of the samples and the influenceof the individual grains on the measured strength [30,31]. Based onthis, it is called texture effect in this paper. It is assumed thatthe recrystallization leads to a grain orientation which shows ahigher strength than the average orientation in a polycrystal [28].While the data from Di Lorenzo et al. and Raulea et al. in Fig. 4have been measured by using a variation of the grain size byrecrystallization, the data by Gau et al., which were essentially

Fig. 3. Strength of Cu-whiskers as a function of their size (data from [22]).

Fig. 4. Influence of sheet thickness to grain size on the strength (yield strength Rp,

tensile strength Rm) for aluminium (data from [28,30,31]).

Fig. 6. Increase of hardness with penetration depth for sapphire. The sample was

exposed to water and tested under a water film (data from [39]).


generated from samples with different thickness, do not show thetexture effect.

The defect strength effect was observed in an investigation ofcomposite samples due to the fact that the severity of strengthdetermining defects was increasing with increasing sample size[32]. Despite the fact that the maximum relative importance andthe size range are nearly the same, the defect strength effect mustnot be mixed up with the well-known Weibull effect on thestrength of materials having statistically distributed defects. TheWeibull effect is based on the fact that the probability for theoccurrence of a large defect, which determines the strength,increases with the size of the part, as for a constant density ofdefects, the absolute number of defects in a volume V increaseswith V (see e.g., [33] p. 77).

The friction effect [34–37] is a typical microstructure effectfrom the micro geometry, especially the surface roughness. Asshown by [37], the coefficient of friction increases with decreasingsize, resulting in an increased influence of the friction on themeasured flow stress.

3.2. Description of size-dependent flow stress

3.2.1. Composite model

The influence of the processing steps in sample preparation weremeasured and empirically analysed by [38]. Samples from purealuminium (Al 99.999) were prepared by different methods (lasercutting, shear cutting, grinding) and partly ground prior to tensiletests. As shown in Fig. 5, the yield strength significantly increased inthe cutting process, while the influence increases with decreasingsample width. A similar effect was found by [20]. The differencebetween the samples of different width disappears with increasingstrain during tensile testing. The size effect was explained by thestrain hardening of the edges due to plastic deformation by thecutting process (in laser cutting, the shielding gas pressure isresponsible for that deformation). The thickness of the affected

Fig. 5. Technical stress–true strain curves of Al 99.999 after laser cutting (by

courtesy of [38]).

surface layer is almost constant, e.g., not dependent on the samplesize (e.g., width). An analysis, based on a rule of mixture (Tayloraveraging model) showed that the yield stress in the deformed edgeregions increased by a factor of up to 3.5 which results in thereported manufacturing-induced size effect (see [38]).

Despite the fact that most examples for composite modelsdemonstrate a decrease in strength with increasing size, there arealso examples for the increase of strength. The hardness ofsapphire was shown to be dependent on the penetration depth, butnot as expected from the strain gradient theory with a decrease,but an increase of hardness was found with increasing indentationdepth, see Fig. 6 [39]. It was explained by a soft layer built in thesurface. It was also shown that the preparation of metallic sampleshas a strong influence on the measured dependence of hardness onthe indentation depth [39].

3.2.2. Passivation layer model

In the case of very thin hard layers, strong size effects can occureven if the measured strength is corrected with respect to theeffect described by the composite model (i.e., the strength of thehard layer was subtracted from the measured value of thecomposite). As shown in Fig. 7 the passivation layer leads to alarge increase in the strength. This influence was the strongest onewithin all effects reported here, see Fig. 2.

The increasing difference in the yield stress of passivatedcopper films compared to unpassivated ones is explained by adislocation blocking mechanism at the passivated surface [24]. Asthis is a short-range interaction between the passivation layer andthe dislocations inside the copper film, the difference betweenpassivated and unpassivated films disappears for film thicknessabove 1 mm. Over a half century ago, this effect was anticipated asexplanation for the strength of aluminium single and bi-crystals[40], but due to the size of their samples being some millimetres inthickness there is some doubt that the theory was applicable to thiscase.

Fig. 7. Strength of copper films having a thickness h of 0.34 mm up to 4.2 mm with

(‘passivated’) and without hard coatings (by courtesy of [24]).

Fig. 9. Transition from poly to single crystal [231].

Fig. 8. Change of flow stress with increasing share of surface grains; circles are values

measured from rod samples, rectangles are those from sheet samples (data from [53]).


3.2.3. Strain gradient model

One of the big disadvantages of conventional methods todescribe the local flow stress is that the models predict a uniformflow stress, which depends only on the (homogeneous) strain,strain rate, temperature, but does not account for any straingradients. Therefore, the description of processes having high localstrain gradients, such as the deformation at crack tips, theindentation of a cutting tool tip or the torsion of thin wires isextremely difficult, if not impossible. The description of the sizedependence of hardness on the indentation depth became thebenchmark for theories related to the strain gradient model. Nixet al. [41] give a good introduction to the development of the straingradient model by Ashby [42], Fleck and Hutchinson [43,44], whileBazant et al. published a comprehensive review on the develop-ment of the strain gradient models [45].

The basic approach of the strain gradient models is that theydefine two groups of dislocations, the geometrically necessarydislocations (GND) and the statistically stored dislocations (SSD).The SSD are those which are accounted for in conventional models.They are produced during plastic deformation and are storedhomogeneous when looking from a macro scale, but statisticallydistributed on the micro scale. Depending on the process, GND arenecessary to accommodate for strain gradients, the easiestexample is plastic bending of a sheet, where large deformationis introduced near the surface and no plastic deformation occurs inthe neutral layer. To accommodate such strain gradients, GND arestored in the lattice having a distribution according to the straingradient. The interaction width of the GND with mobile disloca-tions is described using length scales. For example, Zhao et al. [46]report length scales for six different materials (Al, Ag, Ni, Cu, a-TiAland g-TiAl, with length scales of 2.8 mm, 6.2 mm, 4.3 mm, 1.1 mm,74 nm and 49 nm, respectively), while [41] found length scales of12 mm and 5.8 mm for annealed and cold worked copper. Thedifferences between the values are not only due to the material,but also due to the different theories. As the mobile dislocationsinteract with GND and SSD in the same manner, and based on this,plastic deformation within materials having strain gradients canbe described properly.

To simulate micro forming with consideration of size effects,the theory of strain gradient plasticity was used in FE-simulationfor forming of thin sheet, improving the efficiency of thesimulation [47,48]. Further improvements were achieved bycombining a strain gradient elasto-plastic model and a surfacegrain model. It is concluded that the surface grain model helps todescribe the integral forces, while the – concurrently applied –strain gradient plasticity approach removes the sensitivity of themodel on the FEM element size [49].

Based on the Fleck–Hutchinson strain gradient plasticitytheory, a finite element method was used to predict the indentersize dependent hardness [50]. A nonlocal micromechanicaldamage model based on the strain gradient plasticity was usedfor FE-computation of plastic deformation to predict the failurebehaviour of a vessel steel [51].

3.2.4. Surface grain model

The surface grain model describes a size effect which is a typicalshape sum effect, as it occurs due to the fact that the measured flowstress of a sample is the sum of the share of volume grains andsurface grains. When changing the size of the sample whilekeeping the shape (and the grain size) constant, the share ofsurface grains increases, which results in decreasing flow stresswith decreasing sample size. Surface grains are those which have atleast one grain boundary on a free surface, volume grains are thosewhich are in contact with other grains at all its grain boundaries.

First systematic results with respect to micro forming weregiven by Geiger et al. [52], showing a strong influence of the samplesize on the flow stress. A systematic description of the effect wasproposed by Kals et al. [53] by defining a quantitative value for theshare of surface grains. An empirical formula for the flow stress independence on grain size and scaling factor was proposed [54], but

despite the fact that the calculated values correlated well withthe experimental ones, this model had the typical weakness ofempirical models as the influence of surface grains was onlyaccounted for by using experimental data. As the share of surfacegrains is dependent of the geometry of the cross-section, dif-ferences for the flow stress of flat and rod specimens are expected.It is shown qualitatively that such differences exist. If one plots thedata from [53], such as shown in Fig. 8, the clear influence of thesurface grains can be seen.

Using the size-dependent flow stress, a better correlationbetween experimental and numerical results can be achieved [53],which is also emphasized by other authors [55]. A model based onthe assumption of soft surface areas according to the surface graintheory was demonstrated to enhance the FEM simulation in bulkmetal forming [56]. It must be emphasized that the reduction inflow stress with decreasing size due to the surface grain effect mustbe carefully applied in calculations for forming processes. Inbending processes, the surface layers exhibit higher strains thanthe core layers, which led to the conclusion that the local flowstress, instead of a mean flow stress, should be used in FEMcalculations [57]. In the case of tool contact, the effect of the surfacegrains also disappears. Due to this, no surface grain effect isobserved in extrusion (nearly full contact at all surfaces), while inplane-strain upsetting only a smaller fraction of the surfacescompose free surfaces, thus, reducing the influence strength to lessthan 0.1, which can be seen from the results in Fig. 2 of [58].

3.2.5. Transition areas

There are two very important transition areas to be looked into inmodelling, as a change of the most important effect can occur there.The related effects for the first transition have been described in anearly paper by Armstrong [59], who additionally pointed out someeffects on scatter. If one starts with a large polycrystalline sample,the material might be described as homogeneous and continuum.For the strength of the material, the Hall–Petch relationship can beapplied. Reducing the size, for example, going from the right to theleft in Fig. 9, the first transition occurs, when a characteristic length

Fig. 10. Stress–strain curves from brass having different number of grains in cross-

section (by courtesy of [60]).

Fig. 11. Changes in COF determined by a double deflection stripe drawing test [74].


approaches the grain size. The material behaviour changes frompolycrystalline to single crystalline behaviour. A drop in flow stressand, due to readability not shown in Fig. 9, an increase in scatter canbe noted. Further reduction in the sample size will lead to a secondtransition area, where the material behaviour has to be described onan atomic level, and not as a single crystalline material. According toFig. 2, the first transition takes place at about 10 grains in the cross-section, which is consistent with the findings from [59] (‘less than20’). Other authors expect the transition for significantly less grains,as small as 2 [60] (see Fig. 10) or more grains of up to 50 [61].

A very comprehensive model by Justinger et al. [62,63] on thescatter leads to the conclusion that 50 grains should be in thedeformed volume. The deformed volume is for example the cross-section of a tensile sample or a ring element in the flange duringdeep drawing. If there are fewer grains in the relevant volume, thescatter will increase. The model is then based on the calculation ofthe Taylor factor, and it deduces the expected scatter for theprocess force. The earlier onset of scatter (below 50 grains in thecross-section) is not a contradiction to the noticeable reduction offorces at a lower number of grains along the thickness.

The second transition is expected, if the characteristic size ofthe objects approaches the characteristic length at which thevalidity of the dislocation theory has its limits. This will be atfeature sizes of some mm, being relevant for micro cutting, but lessrelevant for micro forming. According to Fig. 2, this is expected at adimension of 1–10 mm.

4. Tribology

4.1. Scalable friction tests

From the large variety of tests for the determination of thecoefficient of friction (COF), only a few were used in scalingexperiments. This is obviously due to the fact that many testsdemand the use of special equipment such as the Duncan–Shabeltest or the draw beam simulator, which cannot be directly used forscaled experiments, but would demand a large number of scaleddevices. Therefore, the high costs for the equipment prevent theapplication of many friction tests. Nearly all tests which are used inscaled experiments are based on the numerical identification of theCOF or the friction factor m. No comprehensive work using directmeasurement of friction forces in scaled experiments was found inthe literature. Only Mori et al. used a direct measurement of theCOF and, and gave an in-depth analysis of the results, but only twodifferent sizes, with contact areas of 13 mm2 and 75 mm2, wereused [64].

The ring-upsetting test, which uses the friction-dependentchange of the inner diameter when upsetting a ring-like sample, isone of the most frequently used tests in scaling experiments [65–67]. The identification of the COF or the fiction factor m is mostlydone by FEM simulation. Especially, Geiger and Engel et al. make

alternatively use of the double cup extrusion test [68–70] forscaled experiments.

For sheet metal forming, experiments conducted with scaleddeep drawing dies are used for the determination of the COF. In thereported work, either the COF is determined from the maximumforce in deep drawing [71], or it is identified by a numericalidentification based on an analytical model for a stripe drawingtest with twofold deflection [72,73].

4.2. Lubricated friction

4.2.1. Sheet metal forming

Generally, the COF appears to increase with decreasing size.According to Fig. 11, the COF decreases with increasing contactpressure up to a contact pressure of 5 MPa, above which the COF isalmost constant. For a scaling factor of 100, the COF increases by afactor of 2.4 (at a contact pressure of 5 MPa), which probably can beexplained by the lubricant pocket model (see below). Due to theimportance of the friction in sheet forming, the FEM simulation canbe significantly enhanced when using size-dependent COF [74].Especially if the non-uniform pressure distribution is taken intoaccount, very good results are derived for different dimensions ofthe workpiece [75].

The same order of magnitude and drop of the COF is measuredby the numerical identification from the maximum drawing force[71]. In contrast to the results shown in Fig. 11, only one COF,independent from the contact pressure is determined by thismethod. However, the increase of the COF from 0.05 to 0.13 forpunch diameters of 50 mm and 1 mm, respectively, correlated wellwith the other experiments.

Using the size-dependent COF, the change in the limitingdrawing ratio (LDR) in scaled experiments was interpreted [76]. Itwas seen that the COF is one of the decisive, but not the only factorfor the changes in drawability.

4.2.2. Bulk metal forming

One of the first investigations of scaling effects in bulk metalforming, which showed a considerable influence on the frictionbehaviour, was done by Pawelski et al. [77]. A reduction in thecoefficient of friction with increasing size was found [3]. The trendsobtained in lubricated friction experiments in bulk metal formingare the same as that in lubricated sheet metal forming, i.e., thecoefficient of friction [58] or the friction factor [68] increase withdecreasing size. All observations are explained by the lubricantpocket model, while a model by Engel et al. also accounts for thesurface texture [78].

Scaled plane-strain compression tests were used to evaluate thesize effect on the COF in bulk metal forming with the aim ofapplication on flat rolling [58]. Lubrication with oil was used for

Fig. 12. Size effect on the COF in bulk metal forming for plane-strain compression

tests (data from [58], OF-copper lubricated with drawing oil).

Fig. 13. Normalized punch force for scaled forward extrusion for a liquid and solid

lubricant (by courtesy of [70]).


the detection of size effects, while tests using a combination ofPTFE foil and boron-nitride gave standard results with a COF of 0.1.

As shown in Fig. 12, the COF increases by a factor of 3.8, whendecreasing the size from 4 mm to 0.5 mm. Also rolling experimentsshowed a similar trend, but due to some severe restrictions in thescaling possibilities the observed effect in rolling was much lesspronounced [58].

The double cup extrusion test is applied for the determinationof the friction factor m in scaled experiments, where the differencein sample size was only 4 [68] or 8 [79,80]. Nevertheless, asignificant increase in the friction factor from 0.01 to 0.05 wasdetected, which is equivalent to an influence strength (Eq. (3.2)) of1.1. The experiments were done using constant deformation rateinstead of constant sliding speed, but it was shown in [79] that theinfluence of the sliding velocity is rather small in the range of theapplied values.

Also, in upsetting tests of AA7075 a strong size effect wasobserved. Scaled experiments, with MoS2-grease as lubricant,showed an increase in the coefficient of friction from 0.03 to 0.09when the diameter of the samples is decreased from 6 mm to 1 mm[81].

4.2.3. Lubricant pocket model

The lubricant pocket model is the only one available model forthe explanation of size effects in lubricated friction. Pawelski et al.[77] were the first to offer a suggestion to explain experimentaldata using the basic feature of this theory, but without offering aquantitative description of this model. The basic feature of thismodel is the fact that lubricant is entrapped in pockets betweenthe surface of the workpiece and the tool. If these pockets are fullysealed by a surrounding uninterrupted direct contact of the twosurfaces, the lubricant cannot escape and a pressure can be builtup, which quickly achieves nearly the value of the local contactpressure between the die and workpiece [82]. This lubricant bearsa part of the load, to which the workpiece is exposed by the tool. Incontrast to the load-bearing direct contact between tool andworkpiece, there is essentially no shear stress transferred by theindirect load by the lubricant. At the free border of the macroscopiccontact area, the lubricant can pour out of the lubricant pockets, asthese have free surface parts, i.e., they are not fully sealed off.Therefore, the lubricant in open pockets will not bear any load,exhibiting the asperities of the workpiece to a higher pressure,which will flatten the asperities, increase the real contact area, i.e.,the integral sum of all contact increments between the surfaceasperities of the workpiece and the tool, and finally increase thefriction factor. A qualitative description is given in [10], and aquantitative explanation was given by Engel [83,84], starting fromthe Wanheim-Bay model. Due to the complex nature of thechanges of the real contact area, only an iterative numericalsolution of the model is possible. Based on the consideration ofopen and closed lubricant pockets, the sheet surface was improvedfor enhanced deep drawing behaviour [85].

There are some possibilities to validate the model. One is by thetype of lubricant. If it is true that the size effect is due to the loss of

lubricant in the open pockets at the boundary, the size effectshould not be visible with solid lubricant. As can be seen fromFig. 13, this is indeed the case.

A very comprehensive work for the validation of the model isgiven by Tiesler [79]. If it is true that the open pockets at the borderof the contact area are only dependent on the contact pressure andthe surface topology, the relative amount should change not onlywith a correct scaling of the samples, but also with a simplereduction in height, if double cup extrusion is considered. It wasshown that there was also a drastic increase in the friction factor, ifonly the height of the samples was reduced [79]. It seems alsoplausible that the surface will be flattened stronger, if there is alarger effective contact pressure, i.e., in the area where openlubricant pockets are dominant. Indeed, such a dependence of theflattening and other indicators for the validity of the model havebeen shown by Tiesler [79].

The lubricant pocket model describes a micro geometry sizeeffect. One could argue that the size effect would disappear, if thesurface roughness is scaled down equivalent to the sample size,which would be possible, at least to a certain extent. From thefindings of Bay et al. (see for example, [82,86]), it is expected not tobe the case: the entrapped lubricant is squeezed out during thesliding action, reducing the COF. If the surface structure is scaleddown at the same ratio as the sample size, a shape balance effect islikely to occur: the surface area is reduced by r2, while the volumeof the lubrication pockets is reduced by r3. Thus, there will be lesslubricant in the micro than in the macro part, leading to worselubrication and again to an increase of the COF. This effect is knownfrom the lubricated sliding behaviour of polished surfaces.

4.3. Dry friction

Size effects in the friction behaviour for dry friction were onlyinvestigated for bulk metal forming. The results are at the momentnot unambiguous, as some authors find that there are no sizeeffects [65,64], while others state that the friction is eitherincreasing [87] or decreasing [67] when decreasing the samplesize. A very detailed analysis of the friction was done [64] toexplain the effects which were found in scaled forward extrusionexperiments using brass (Cu:Zn 70:30) by [88,89]. An experi-mental investigation of frictional behaviour in dry micro extrusionof pins with diameters ranging from 0.57 mm to 1.33 mm wasconducted in [89]. Based on the comparison of the experimentallymeasured ram force or the extruded pin length with FE-simulationor analytical models, it was found that the COF decreased when thesize of extruded pins decreased (Fig. 14), except the case ofnumerical identification of the COF from the pin length. A directmeasurement of the COF (unfortunately, only two values for each

Fig. 14. Change in friction behaviour (a: Coulombs law identified by FEM-

simulation; b: friction factor, identified by two different analytical models) in

extrusion (by coutresy of [89]).


varied parameter were used) using a flat ring on disk-experimentshowed that there is no statistically significant influence of thegrain size (32 mm and 211 mm), contact pressure (22 MPa and250 MPa) or contact area (13 mm2 and 75 mm2) [64]. Thedifferences which are shown in Fig. 14 were explained to bedue to the fact that for the two small samples there are less than 5grains across the diameter of the extruded pins. This results in anindividual behaviour of the particular pins which cannot bedescribed with the models used in numerical identification, asthese models assume a continuum material [64].

A numerical identification of the COF from scaled dry ringcompression tests for brass (Cu:Zn 85:15; inner diameter from0.5 mm to 4.25 mm) reveals an increase in friction with decreasingsize at least for coarse grained material [66], see Fig. 15. It wasexplained by a shape sum effect (see Table 1) from the importanceof the real contact area for the COF. It was argued that the softgrains at the edge of the ring compression samples show a fasterflattening than the harder grains in the middle of the contact area.As a result of this, the real contact area is larger for the soft edge

Fig. 15. COF determined by numerical identification from dry ring compression

tests; L: grain size; D0-values are slightly shifted on the x-axis to make the scatter in

COF visible (by courtesy of [66]).

grains. Additionally, the COF is proportional to the real contactarea. Decreasing the diameter d of the ring-shaped sampleincreases the relative amount of edge grains according to 1/d,which results in an increase in the relative real contact area, andtherefore an increase in friction [87].

Ring compression tests using magnesium alloy AZ31 at elevatedtemperatures (350–450 8C) show a decreasing friction factor withdecreasing size [67]. The effect was less pronounced at the highertemperatures. Unfortunately, until now there is no satisfactoryexplanation for this effect. A comparison of lubricated and dryfriction in flat rolling was done by van Putten et al. [58]. They showthe known effect of increasing COF in lubricated friction, while indry friction the COF is independent of the size.

Finally it seems that there might be different explanations forthe results, but it appears to be very doubtful that a general modelexplaining differences for the COF in dry friction can be found.Therefore, it can be concluded that a general size effect, asdescribed in lubricated friction, does not exist for dry friction.

5. Formability

5.1. Sheet formability in tension

Through tensile and bending tests it is found that: for T/D > 1(T: thickness, D: average grain diameter), the yield strength andtensile strength decrease with the decrease in T/D ratio; for T/D < 1, the yield strength and tensile strength increase with thedecrease in T/D ratio. The lower the T/D ratio, the worse is theformability [30].

Scaled tensile tests were performed to investigate the sizeeffects on flow curves and fracture strain for Cu foils [90], Al 99.0–99.5% [29] and for CuZn36 [91]. The experimental results show adecrease in the yield strength and the maximal true strain with adecrease of specimen thickness, see Fig. 16.

Numerical results in biaxial stretching of mild steel, annealedaluminium and annealed 70/30 brass show that limiting strainsdecreased as the ratio of thickness/grain size decreased [92].Simulations of uniaxial tension and three-point bending testsinvolved a study of different orientations of grains and showed thata decrease in sheet thickness leads to a decrease in formability [93].Tensile tests of metal foils (SE-Cu 58) show that strain to fracturedecreases with foil thickness as a result of increasing inhomo-geneity of the microstructure with decreasing the ratio of the foilthickness to grain size [94].

5.2. Forming in upsetting

The effects of specimen size and loading rate on the flow stressand failure behaviour of workpiece under compressive loads wereinvestigated. The influence of temperature changes at differentstrain rates within scaled experiments was discussed. It was foundout that for one Al and Ti alloy, the failure strain depends on both ageometrical and process variables [37,95], see Fig. 17.

Fig. 16. Engineering stress–strain diagram for copper foils and different processing

conditions presenting size dependence on fracture strains (by courtesy of [90]).

Fig. 17. Size- and time-dependent compressive deformability of (a) Ti-6-22-22S and

(b) Al7075-T6 (by courtesy of [95]).

Fig. 19. Influence of sheet thickness on forming-limit curve (from [97]).


5.3. Forming limit diagram (FLD)

It has been found experimentally that the level of FLD increaseswith sheet thickness s0 and strain hardening exponent n. Kellerand Brazier [96] have approximated this effect by

FLD0 ¼ nð1þ 0:72s0Þ for n � 0:2 (5.1)

FLD0 ¼ 0:2ð1þ 0:72s0Þ (5.2)

The results are plotted in Fig. 18. As shown in Fig. 19, Hasek andLange [97] experimentally confirmed the impact of sheet thicknesson the FLD for mild steel.

Fig. 18. Effect of sheet thickness on FLDs (from [96]).

A new flexible micro sheet metal forming process – microincremental forming – was investigated. The geometrically similarexperiments using different sheet thicknesses also provided lowerforming limits for thinner sheets [98]. FLDs obtained by bulge tests(Fig. 20) showed the decrease in formability with decreasing thesheet thickness [99]. Size effects on flow stress and the influence ofgrain dimension on material formability were investigatedthrough tensile tests and formability tests with specimens indifferent sizes. It has been found that finer grains have a positiveimpact on the position of FLD [31] as demonstrated in Fig. 21. This

Fig. 20. FLDs of fine grained (25–500 mm) SE-Cu 58 and Al 99.5 obtained by bulge

test (by courtesy of [99]).

Fig. 21. FLD at the varying of grain size (sheets from AA1050 with thickness 0.5 mm)

(from [31]).


was confirmed by other experiments, where the grain size washeld constant and the sheet thickness was varied between 500 mmand 25 mm. A significant decrease in the maximum strain (ate1 = e2) from 0.25 (at sheet thickness of 500 mm) to 0.05 (at 25 mm)was detected [100].

Deep drawing with different specimen thickness and differentratios of punch diameter/specimen thickness was carried out. Thelimiting drawing ratio (LDR) decreased with increasing ratio ofpunch diameter/specimen thickness [101].

Using dies with different diameters, bulging tests with sheets ofdifferent materials in different thickness were performed toinvestigate the effect of thickness on the restoration of bulgedspecimens [102]. It has been ascertained that the thinner the sheetmetal, the greater is the effect of buckling on the formation ofwrinkles.

The study of micro deep drawing sheets from Al 99.5 withthickness from 1 mm to 0.02 mm show that the LDR in micro deepdrawing is significantly smaller than in macro deep drawing [76],which is not only due to the changes in friction behaviour. Lee et al.pointed out the importance of the ratio of sheet thickness to grainsize. If this ratio drops below 10, a significant decrease in the LDRwas observed [103].

6. Forming

Forming operations cover bulk and sheet metal forming both incold conditions and at elevated temperatures. In [8], a compre-hensive description of the state-of-the-art in micro forming isgiven. Table 2 indicates the types of micro forming processes thathave been investigated with respect to size effects. In the followingsections size effects related to forming forces and stresses,processing windows and accuracy will be described. It is clearthat specific experimental work will be related to specific processand material conditions. However, the present section will useselected cases to illustrate the general findings in the literature.

6.1. Forming force and stresses

A very early work on the influence of the size of the workpiecein bulk metal forming was done in backward can extrusion [104]. It

Table 2Typical micro forming operations.

Cold Elevated temperature

Bulk Closed die forging Extrusion

Coining Embossing (laser assisted)

Extrusion

Upsetting

Wire bending

Sheet Deep drawing Bending (laser assisted)

Blanking

Bending

was shown that the maximum forming force can be determinedfrom

Fmax;2 ¼ m� Fmax;1k f ;2

k f ;1 � l(6.1)

where Fmax is the maximum force, kf is the flow stress, and l is thelength scale factor. The correction factor m was determined to liebetween 0.6 and 1.1 and is considered to be a quantitative measurefor the sum of different size effects. One of these effects was basedon the surface to volume effect (shape balance in Table 1), yieldingstronger heating of the material by the deformation work in case ofthe larger samples [104]. Grain size effects play obviously no role,as the sample size was above 20 mm.

6.1.1. Bulk

A general observation in micro cold forming operations inclosed dies is that a decrease in part dimensions will result in anincrease in punch pressure defined as punch force divided by cross-section area of punch [8]. This is explained by the increase infriction, and this has been confirmed by both experimental andnumerical investigations. As previously stated, the effect of grainsize relative to dimension also plays an important role. Extrusionexperiments with different die diameters were performed toinvestigate the friction behaviour. Three different coated dies wereused to reduce the friction, and consequently the extrusion force[88]. An implementation of processes at elevated temperaturesdecreased the necessary forming forces in the example casereported in [105]. Micro embossing with laser assistance has alsobeen carried out. The results show the potential advantages inreducing the forming force and the risk of tool fracture, when ahigh power laser was used [106].

6.1.2. Sheet

Two different size effects were observed in the analysis of themicro deep drawing process detailed in [107]. The maximumrelative punch forces were found to be independent of the scalingfactor (which describes the ratio of the actual punch diameter to areference punch diameter of 8 mm), but were dependent on thegrain size to sheet thickness ratio. The maximum punch forces ofthe bigger cups decrease with increasing velocity, while the punchforces for the smaller cups do not. A thermally coupled FE-simulation show that this could be partially related to the thermalinfluence caused by heat generated from plastic dissipation andfriction, in combination with the differences of the surface tovolume ratio for the different scaling factors. Investigations in[108] show that the design of micro deep-drawing processes (e.g.,force) is subject to a heavier influence of production-determineddeviations concerning the design contours of the tool than in thecase of conventional, large-sized parts. Therefore, these produc-tion-determined deviations from the ideal geometry need to betaken into account in the process design.

Investigations on the bending process were carried out in scaledexperiments. The influence of grain size and orientation on thebending force and strain distribution was investigated. It waspointed out that it is impossible to develop a universally applicableFEM model [109]. In [57] size effects on flow curve and bendingforce were investigated. These effects were explained in terms ofthe change in the grain size/specimen size ratio.

The effect of grain size and orientation of the specimen on theprocess force and strain distribution within micro blanking andbending tests was investigated. It was concluded that it isimpossible to develop a universally applicable FEM modelalthough significant work was subsequently undertaken on thissubject [110].

6.1.3. Scatter of forces

Another remarkable size effect is the general increase of scatterof forming forces when dimensions are decreased [10]. [111]reports on a decrease in the observed scatter of forces when using

Table 3Parameters investigated in [114].

Lower limit Upper limit

Temperature 20 8C 200 8CGrain size Fine (28 mm) Coarse (80 mm)

Punch velocity 3 mm/min 30 mm/min

Lubrication None Drawing oil

Pin diameter 0.5 mm 2.0 mm


ultrafine-grained copper compared to coarse grained material in abackward extrusion operation. A numerical mesoscopic model wasdeveloped, with which a size-dependent simulation can be realised[112]. Experimentally it was observed that increasing scatter of thegrain size results in increasing scatter of the forming force [113].

6.2. Processing windows

6.2.1. Extrusion

In [114] a full backward extrusion process was investigatedexperimentally using a full factorial design of experiments in a highconductivity copper (Cu-ETP). Five main parameters were investi-gated: temperature, grain size, punch velocity, lubrication and pindiameter (see Table 3 for details). Among these factors, thetemperature and the pin diameter were found to be the mostsignificant along side with the lubrication. In particular, theinteraction between temperature and pin diameter was investigatedwith fine grain size, no lubrication and punch velocity 3 mm/min.Experiments were performed with a max force of 200 N. This secondlevel interaction was the only one found to be significant at a 95%confidence level. Fig. 22 illustrates the obtained aspect ratios of a2.0 mm and a 0.5 mm pin diameter at 20 8C and 200 8C, respectively.

In [115] a comparison of processing windows between twodifferent material types is presented for a combined forwardextrusion and embossing process. A 1.5 mm billet is extrudeddown to 1 mm, and a pattern is embossed on the top surface of thecomponent. The component was successfully manufactured in asilver alloy using a two-step forming procedure in cold conditionsyielding forming loads of up to 15 kN. Furthermore, thecomponents were also realized in a bulk metallic glass(Mg60Cu30Y10, amorphous) in a one-step forming procedure atelevated temperatures (170 8C). The forming force was signifi-cantly lower than in the previous case, but the necessary forming

Fig. 22. Full backward extrusion. Effect on aspect ratio of pin diameter and

temperature (by courtesy of [114]).

time was considerably higher (approximately 1 min). This exampleillustrates the tremendous differences observed in processingwindows when changing the workpiece material from crystallineto amorphous.

6.2.2. Deep drawing

In [116] experiments at various punch speeds ranging from0.01 mm/s to 100 mm/s were performed on CuZn37 foils in as-delivered and annealed conditions (3 h/600 8C) with thicknessesranging from 300 mm down to 40 mm. The blank diameters werescaled corresponding to the thickness. Wall thickness distributionswere measured on the produced cups using a microscope. Theexperiments show that the punch velocity has only a small effecton the cup geometry. The cup geometry seems to be more affectedby the microstructure. Under annealed and coarse-grainedconditions, the thinning of the cup walls became more pronouncedfor smaller cups, although the flow stress curves of all annealedmaterials are nearly in the same range.

Micro deep drawing with different punch diameters wasexperimentally and numerically investigated [117]. The influencesof friction coefficient, deviations of transverse anisotropy anddeviation of tool geometry on the process were discussed. Scaleddeep drawing was carried out. The punch force acquired in FEM-simulation agreed closely with the experimental results. Thevelocity of the punch showed effect on the punch force only by thepunch diameter of 8 mm [118]. Size effects in sheet drawing weredetermined by means of multi-grain model based on crystalplasticity theories, which accounts for the interaction among theindividual grains [119].

6.2.3. Upsetting and coining

Micro coining of thin sheet metal in different thicknesses wasexperimentally investigated, using a FE-analysis [120]. Thedistribution of non-dimensional forming height in coining withmicro cavities was found to be different for different micro cavitydiameters. This effect was explained by relative sliding and, it wasshown that the law of similarity cannot be applied to this case[121].

6.3. Accuracy

6.3.1. Bending angle

Bending angle and spring-back angle have been the subject ofsignificant research during the last decade. The reason for this isthe obvious industrial interest in such processes. In [94] two sizeeffects related to bending processes are described. The first one iscaused by an increasing share of surface grains in the overallvolume when the workpiece dimensions are scaled down. Theresulting effect is a decrease in material strength. The second sizeeffect is caused by large strain gradients appearing when the foilthickness is decreased. This results in an increase in materialstrength. Experimental and numerical investigations in [94]indicate that the first effect is dominant down to a scaling factorof 0.2 (decrease in spring-back angle), and for lower scaling factors,the second effect is dominating (increase in spring-back angle), seealso Fig. 23. The same conclusions are presented in [99]. In anearlier work by the same authors free bending with different foilthicknesses were carried out. The correlations such as spring-backangle vs. thickness and spring-back angle vs. bending angle wereacquired [122]. Scaled free bending tests were carried out. Thespring-back angle increased when decreasing specimen thicknessor decreasing grain size [123].

Several other relevant results have been reported. In whatfollows, a few will be summarized. The size effects in sheet metalforming were investigated through tensile tests, bending andblanking processes. The effect of grain size was analysed [29].Bending tests were carried out using specimens with differentthicknesses. The effects of the ratio thickness/grain size on thetensile strength, microhardness and spring-back were analysed[124].

Fig. 23. Dependence of spring-back angle on the scaling factor. Bending angle 458(by courtesy of [94]).

Fig. 24. Variation of shear stress on shear plane when cutting (data from [140] and

for SAE 1112 steel from [139]).


Though scaled tensile test, air bending and punching, the sizeeffects were investigated [125]. The causes for the size effectsoccurring in tensile tests were analysed and transferred to the airbending and punching [126]. A model for FE-simulation of microbending process was described. The influence of punch radius, dieradius, specimen thickness, etc., on the final parts geometry wereinvestigated [127]. The spring-back behaviour of brass wasinvestigated by three-point bending with different thicknesses.The correlation between spring-back and the thickness/grain sizeratio was discussed [128]. The effects of grain size and specimensize on final bending angel within the V-bending were investi-gated. The larger the grains size, the lower the spring-back [129].

6.3.2. Surface appearance

Aiming at development of a similarity law for the spinningprocess, the correlations between surface quality and contactpressure, sliding velocity and strain were investigated [130]. In[61] an attempt to model the surface evolution due to contactloading was presented. With the help of the proposed model, theinfluence of grain size and orientation as well as strain rate havebeen verified and quantified.

6.3.3. Shape accuracy

Shape accuracy is an important quality parameter in microforming processes since net shape processes are the ultimate goalalso in micro forming.

A very impressive example of the influence of a size effect onthe shape accuracy was shown in [64]. The occurrence of curvedsamples was assumed to be an effect of inhomogeneousdeformation in the coarse-grained samples, while the fine-grainedones did not show the curvature even in multiple repeatedexperiments. It was reported in [89] that using the same smallestextrusion die which reduces the diameter from 0.76 mm to0.57 mm (marked with ‘0.76:0.57 mm’), specimens with 32 mmgrain size resulted in all straight pins, while 60% of pins with anoriginal grain size of 211 mm showed an uncontrolled curvature inthe final extruded pins. These results indicate that the size,orientation, and distributions of grains play an important part inthe extrusion process. A more detailed analysis of local hardnessand microstructure of deformed pins to illustrate the size effect canbe found in [131]. The importance of the local flow behaviour ofindividual grains for the shape accuracy is shown by Geißdorferet al., who did backward extrusion in the micro range using a partlytransparent tool. The homogeneity of material flow decreased withincreasing ratios of grain size to extruded wall thickness [132,133].

6.3.4. Downscaled equipment

In the pursuit of achieving the desired accuracy, efforts havebeen made to downscale the manufacturing equipment in order topursue a higher absolute precision. The main reasons are thedecrease in heat deformation of machine tools with the decrease intheir sizes, decrease in vibration amplitudes and decrease in spaceand energy consumption [134].

A micro superplastic backward extrusion machine was devel-oped, with which microgear shafts of 10–50 mm were fabricated[135].

A laser-assisted micro forming setup was developed, on whichthe semi-hot embossing experiments were carried out. The risk of afracture of the tool is lower and the quality of specimen is better[136].

In [137] and [138] a modular approach to the realisation of ahigh precision, flexible press for micro forming is described.

7. Cutting

7.1. General

Generally, in literature the term size effect in metal cutting isunderstood as the non-linear increase of the specific cutting energywith decreasing the undeformed chip thickness. Backer et al. [139]were among the first to determine the energy consumed indeforming a unit volume of a ductile material (SAE 1112 steel), anddevelop a relationship between the shear energy per cubic volumeand the specimen size. They showed the decreasing trend in shearenergy per unit volume for three major manufacturing processes:grinding, micromilling, and turning (see Fig. 24). It is to be notedthat after over four decades, Taniguchi [140] confirmed thisrelationship through his extensive research showing the sizeeffects observed in a range of processes including tensile test, theresults are also plotted in Fig. 24. Shaw [141], in a recent analysis ofsize effects revisited his earlier explanation and describes theorigin of size effects as resulting from a short-range inhomogene-ities present in all commercial engineering metals.

7.2. Orthogonal cutting

7.2.1. Early work on experimental flow fields and strain-hardening

models

Palmer and Oxley [142] showed the flow around the roundedcutting edge using cine filming techniques for chip formation at alow cutting speed. They showed the existence of a shear zoneand developed a slip-line model for chip formation and thematerial flow around this rounded cutting edge by considering thestrain-hardening property of the work material. Their model andthe experimental observations correlated better compared with

Fig. 25. Experimental flow field obtained using cine filming method for material

flow around the rounded cutting edge (from [142]).


previous rigid-plastic shear plane models. An experimentallyobserved flow field is shown in Fig. 25.

Based on his earlier work on the use of a centered fan slip-linemodel for machining with a restricted contact tool [143], Johnsondeveloped an admissible slip-line field for cutting with a doubleedge tool representing the rounded cutting edge. An interestingfeature of this early work is that Johnson [144] was able to show arange of solutions for the plastic flow of the work material alongthe machined surface at varying velocities. Contemporary experi-mental work by Nakayama et al. [145] shows the ‘microchip’formation at the asperity on the tool flank resulting in a plasticallydeformed, interrupted machined surface in cutting of a softmaterial with a hard tool. Larsen-Basse and Oxley [146] subse-quently showed that the size effects are a consequence of materialstrengthening due to the increase of strain rate in the primarydeformation zone when the undeformed chip thickness decreases.In a pioneering analytical work using plane-strain slip-line modelsand the associated hodographs (velocity diagrams) for the stressand velocity fields, Challen and Oxley [147] from single and doubleedge chords representing the rounded cutting edge show theexistence of three specific regimes: (a) rubbing, (b) wear, and (c)cutting. This work shows an analytical formulation with the use ofsimilarity mechanics involving a non-dimensionalized parameterof the ratio of undeformed chip thickness to tool edge radius.Kopalinsky and Oxley [148] show the size effect as resulting fromthe strain rate and temperature-dependent flow stress propertiesof the work material. In a further work, Kopalinsky et al. [149]show the generation of tensile stresses on the machined surfacedue to the severe plastic deformation.

7.2.2. Ploughing effects and force models

An early work by Masuko [150] reports the effects of cuttingedge radius through a cutting force analysis. Albrecht [151]developed a ploughing force model to explain the size effect. Bydividing the tool–chip–work contact region of the cutting tool intofour sections, he developed a force relationship for the cuttingprocess involving a rounded cutting edge tool (see Fig. 26). He

Fig. 26. Integrated force diagram for machining with and rounded edge tool under

ploughing conditions (from [151]).

showed an experimental method to separate the ploughing forcefrom the cutting force. He also correlated the ploughing force withthe chip curl and the residual stresses generated in machining.

Armarego and Brown [152], using their experimental resultsfrom machining of aluminium alloy 50-St-5 and steel 1022with HSS rectangular tool show that specific cutting energyreduces as the undeformed chip thickness reduces, and afterreaching a certain value, it increases exponentially withfurther reduction in undeformed chip thickness, for 1022 steel.Shaw argues in the discussion of this paper that circular andrectangular tools might differ in the way the force, and hence thespecific cutting energy, is generated in machining, and thatthe formation of a small built-up edge may have caused thisvariation from the conventionally observed trends of continuousincrease of specific cutting energy when the undeformed chipthickness reduces.

Nakayama and Tamura [145] developed a force-based analysisto describe the size effects in cutting at small depths, and feedsand demonstrated it experimentally by showing that the sizeeffect is attributed to the subsurface plastic work, implying thesurface integrity in terms of subsurface metallurgical andmicrostructural changes. Khaet and Vasilyuk [153], through aseries of experimental work with a range of work and toolmaterials, showed the optimum value of the ratio of undeformedchip thickness and tool edge radius to provide the maximum tooledge strength.

Abdelmoneim and Scrutton [154] showed the existence ofplastic recovery behind the cutting tool in machining with anegative rake tool and attributed this to the intending action of thecutting tool edge. In their subsequent work, Abdelmoneim andScrutton [155] developed a theory for cutting with a roundedcutting edge tool by assuming the existence of a stable built-upedge ahead of the cutting tool, and show the dependence of thespecific cutting pressure on the ratio of undeformed chip thicknessto edge radius. Taminiau and Dautzenberg [156], through a seriesof analytical and experimental work verified the model byAbdelmoneim and Scrutton [155] in high precision cutting byplotting the specific cutting and thrust force against the ratio ofundeformed chip thickness and tool edge radius.

Lucca and Seo [157] conducted an experimental study oforthogonal cutting of Al6061-T6 alloy to examine the dissipation ofmechanical energy in cutting at small depths of cut, and show thetransition from cutting to ploughing and report the significanteffects of tool edge radius in cutting. In a subsequent work [158],they show the significant effect of cutting edge geometry on thecutting force components and the plastically deformed machinedlayer.

More recently, Arsecularatne [159] used Oxley’s predictivemachining theory [160] to investigate the ploughing force, andseparated the cutting force from the ploughing force, and used itin the calculation of tool–chip interface stress distributions.Dinesh shows that if the flow stress of a material is dependenton a strain gradient parameter, size effects should be expectedwhen machining this material, i.e., increasing specific cuttingforce with decreasing undeformed chip thickness, which isalso related to indentation size effects [161]. A further cuttingmodel accounting for the edge radius size effect is given byBissacco et al. [162].

7.2.3. Chip formation

Clos et al. [163] experimentally investigated the strainlocalisation in cutting as an adiabatic shear banding mechanism.In orthogonal cutting experiments, a change in the chip formingprocess from continuous to segmented chip formation withincreasing undeformed chip thickness was found [164].

A changing chip formation was also found when scaling theundeformed section of cut in turning processes with large cornerradii. The changed chip formation mechanisms were accounted forthe higher specific cutting forces. A model for the description ofchip formation is currently under development [165].

Fig. 28. Variation of specific cutting energy with uncut chip thickness at 240 m/min

(from [174]).


7.2.4. Cutting edge radius

The cutting force and feed force in hard turning by differentratios of rb/h (cutting edge radius/undeformed chip thickness)were experimentally investigated [166]. In addition, scaling effectsof the process parameters, e.g., undeformed chip thickness h andcutting edge radius rb on the chip formation, cutting force andsurface quality in hard turning was investigated [167]. It was foundout that cutting force and feed force rise rapidly with increasingcutting edge radius. In further investigations, a scaling of thecutting edge radius and the undeformed chip thickness inorthogonal machining was carried out. Chip formation, degreeof segmentation and shear band width are affected by the scaling ofthe cutting edge radius [168]. The influence of a scaling of cuttingedge radius or chamfer and depth of cut on the burr formation inorthogonal machining was investigated by [169]. Throughexperiments and a FE-simulation, non-linear influence of the sizeof a cutting edge chamfer on the temperature, the mean stress inthe burr shear zone and on the size of the hydrostatic bowl werefound.

7.2.5. Analytical and numerical models and experimental validation

(a) A
nalytical models and experimental validation
There has been significant effort to model the micromachiningprocess using various analytical modelling methods includingmolecular dynamic modelling, multi-scale modelling and mechan-istic modelling. A good summary of these modelling methods aregiven in a recent CIRP keynote paper by Dornfeld et al. in 2006[170].

Manjunathaiah and Endres [171] developed a new model fororthogonal machining with an edge radius tool. This modelconsisted of a geometry model and a force model. They show thatthe increase in specific cutting energy with edge radius issubstantially due to the energy expended in shearing the chipdue to the apparent more negative effective rake angle. They alsoattribute this increase, and hence the size effect, to increases instrain and strain rate. This work was extended to an extensiveexperimental study of orthogonal machining of zinc involving arange of edge radius tools [172]. They tested the two traditionallyknown methods for extracting the ploughing force: extrapolationmethod, and dwell method, and show that neither of these twomethods yields to a consistent material behaviour.

Joshi and Melkote [173] modelled the primary deformationzone through a simple parallel-sided configuration using the straingradient plasticity theory, and explained the occurrence of sizeeffects in machining. By extending this work to include thesecondary shear zone, in a subsequent work, Liu and Melkote [174]compared the variation of maximum temperature (see Fig. 27), andcompared the specific cutting energy developed with straingradient model and without strain gradient model (see Fig. 28).This paper shows two material strengthening factors: (i) thedecrease in the secondary deformation zone cutting temperature,and (ii) strain gradient strengthening. This work also shows the

Fig. 27. Variation of maximum temperature in the primary and secondary shear

zones at 200 m/min cutting speed (PSZ: primary shear zone; SSZ: secondary shear

zone) (from [174]).

relative contributions of these two factors to the increase inspecific cutting energy when the undeformed chip thickness isreduced. Also shown is an analysis of the finite element orthogonalcutting model which performs simulations on Aluminium 5083-H116, which has a small strain rate hardening exponent, thusminimizing strain rate effects.

(b) S
lip-line models and experimental validation
Early work on the use of slip-line models for orthogonal cuttingat small depth of cut and for the polishing processes shows thematerial flow around the rounded cutting edge using single anddouble edge chords [147] to represent a range of frictionalconditions and tool edge radius. Account is also taken oflubrication conditions. Based on their earlier slip-line model fornegative rake angle cutting [175], Abebe and Appl [176] developeda new model for the ploughing abrasive process using ‘‘effectiveplanes’’ to represent the three-dimensional machining processthrough slip-line and upper bound models.

More recent work by Fang [177] involves a rounded cuttingedge and multiple cutting edge chords, and this work is based onthe extended application of the universal slip-line model devel-oped for machining with a restricted contact tool [178]. Morerecently, Wang and Jawahir [179,180] show an admissible slip-linemodel with the corresponding hodograph for machining with arestricted contact grooved tool having a rounded cutting edgerepresented by double cutting edge chords, BS and SN – see Fig. 29.

The non-linear system of slip-line model is based on the fiveslip-line angles u1, u2, C, h1, h2 and their five equations:

f 1 ¼ mb � F 0x � F 0y ¼ 0

f 2 ¼ M0 þ F 0x � CC1 � F 0y � CC2 ¼ 0

f 3 ¼ h2 � ðX f�g f � Y f�b f Þ2 þ ðX f�b f þ Y f�g f Þ2 ¼ 0

f 4 ¼ h02 � ðXl�hl � Yl�hlÞ2 þ ðXl�gl þ Yl�glÞ2 ¼ 0

f 5 ¼ Ru þt2

2

� �sinðg2 þ hgÞ �

GW 0

2¼ 0

8>>>>>>>><>>>>>>>>:

(7.1)

The non-dimensionalized (similarity mechanics-based) resul-tant force (F) developed is shown as

F*

kt1w¼ F*

A3A2

kt1wþ F*

A2A1

kt1wþ F*

I1A1

kt1wþ F*

I1C1

kt1wþ F*

C1D1

kt1wþ F*

D1B1

kt1wþ F*

B1B2

kt1w

þ F*

B2M1

kt1wþ F*

M1M2

kt1wþ F*

M2N

kt1w(7.2)

The ploughing force P was derived as

P*

kt1w¼ F*

B1B2

kt1wþ F*

B2M1

kt1wþ F*

M1M2

kt1wþ F*

M2N

kt1w(7.3)

where k is the shear flow stress and w is the width of cut. Thismodel predicts cutting forces, chip thickness, chip up-curl radius,temperatures and flow stresses at the primary shear zone and atthe tool–chip interface, etc. Predictive modelling of size effectsusing the above slip-line model for machining with a roundedcutting edge tool shows the effects of cutting edge radius on

Fig. 29. Extended slip-line model and hodograph for machining with a rounded

edge restricted contact grooved tool (from [180]).


stresses, strains, strain rates and temperatures developed incutting along with cutting forces, chip curl radius, chip thickness,etc., with experimental validation [181].

(c) N
umerical models
During the past decade, there has been a surge in numericalmodelling of orthogonal cutting to predict the various machiningparameters including the size effects in finish machining at smallcutting depths (undeformed chip thickness). A finite elementmethod was developed to predict the temperature and the stressdistribution in micro machining [182]. The influence of the cuttingedge radius was considered in this model and the results confirmthat the cutting edge radius is one of the major causes of the sizeeffects. Ozel and Altan [183] show the effect of edge radius onforces and stresses developed in machining. Yen et al. [184] in afollow-up work, used a range of tool edge configurations includingchamfer and hone radius conditions and simulated the materialflow by calculating the stresses, strains and temperatures. Theyshowed the ploughing effect and related the edge radius with theresulting force, temperature and stress conditions.

Using a thermal elastic–viscoplastic finite element model, Eeet al. [185] predicted the residual stresses induced by machiningwhen using edge radius tools. Simoneau et al. [186,187], Liu and

Melkote [188] studied the size effects influenced by the tool edgeradius in microcutting of A15083-H116 alloy using the ABAQUSfinite element software with strain gradient plasticity formulation.Weber et al. [189] used a thermo-mechanically coupled finiteelement method to study the problem of size effects in normalizedsteel AISI 1045 and annealed AISI 02 using the ABAQUS/Explicithaving a provision for modelling the viscoplastic behaviour of thework materials with a range of dimensionless similarity mechanicsparameters representing the material law in the model. They showthe effects of cutting speed and the cutting edge radius on sizeeffects.

Size effects in metal cutting concerning the cutting force androughness were experimentally investigated. A FEM-simulationincluding the use of similarity mechanics to establish theparametric influence of various factors was attempted [190].Hochrainer et al. [191] carried out a 2D FE-simulation oforthogonal cutting using similarity mechanics approach, andinvestigated the correlation between normalized specific cuttingforce and similarity number as well as relative sharpness. Sizeeffects influenced by the specific cutting force are described interms of strain hardening, heat distribution in front of the cuttingtool and by non-linear increase in the plastically deformed surfacelayer. Machining with multiple passes requires the effect ofprevious pass in the newly generated surface layer which influencethe specific cutting force and the depth of plastic deformation[192]. Also, experimental and numerical investigations to deter-mine the influence of the friction coefficient on the specific cuttingforce were carried out. A linear dependence of the specific cuttingforce on the friction coefficient was shown, which leads to anintensification of the size effect for higher friction components[193].

Outeiro [194] measured experimentally and established theeffect of cutting edge radius on the thermo-mechanical conditionsdeveloped in metal cutting. In particular, he found that increasingthe ratio of undeformed chip thickness to cutting edge radius (h/rb)leads to an increase in the temperature developed in the cuttingzone, and a greater part of this heat is conducted into theworkpiece and the tool, this resulting in high temperatures andthermally affected layers being produced on the machined surface.This usually induces higher residual stresses on the machinessurface, or causes a phase change in the material [195].Wanigarathne et al. [196] developed a finite element methodfor studying the effects of cutting temperatures and the coolingeffects in finish machining of AISI 1045 steel with multi-layercoated tools having a rounded cutting edge under conditionsproducing size effects. They extended the Johnson–Cook model toincorporate the changes studied.

s ¼ ðAþ Beypn Þ � ½1þ C lnð ˙eyp� þ 10�3 e�100 ˙eyp�

Þ�ð1� T�mÞ (7.4)

where A, B, C are the material constants, e the strain and T is thetemperature.

They showed the effects of cutting speed, coating thickness,coating thermal conductivity, cutting edge radius, tool–chipinterface friction, etc., on the resulting machining performance.Fig. 30 shows the simulated results, and the temperature fieldsdeveloped are correlated with the higher residual stresses and thesize effects produced.

(d) E
xperimental findings
Subbiah [197] attributes the size effect to a component of thecutting force, which remains constant with decreasing unde-formed chip thickness. By machining with very large rake angles(up to 708) the shear influences in the chip could be minimized andthe constant cutting force component could be isolated. Chipformation with these high rake angles occurs mainly by ductilefracture or ductile tearing ahead of the cutting edge. The value ofthe constant force component is in the range of the force of ductilefracture and crack formation. This work is consistent with the

Fig. 30. Simulated cutting temperature profiles along the contact regions of the

cutting tool in machining of AISI 1045 steel with coated and uncoated tools (from

[181]) (yc ¼ 300 m=min and a = 0.25 mm/rev).

Fig. 31. Apparent undeformed area of cut in finish turning (not to scale) [204].

Fig. 32. Effect of cutting edge radius on apparent area of cut [204].


theory of Atkins [198] which attributes the size effect to the energywhich is needed for the formation of a new surface by ductilefracture. This energy is independent from the cutting force, andtherefore, responsible for the size effect. The increasing of specificcutting force with decreasing of cross-section of undeformed chipwas observed and analysed [199].

7.3. Turning operations

Shawky and Elbestawi [200] developed a mechanistic cuttingforce model for turning which included the effects of ploughingforce. The comprehensive CIRP collaborative work on modelling ofmachining operations presents the shortcomings of all currentmodels in accurately predicting the edge effects in turning [201].Redetzky et al. [202] presented a generic predictive model for chipflow and cutting forces which combined a geometric model and aforce model. This model included the cutting edge effect andconsidered the size effects.

Significant effects that could be attributed indirectly to the sizeeffect phenomenon can be seen in some complex machiningoperations such as contour turning. In an experimental study ofcontour turning of two aluminium alloys (6061-B and 2011-T3),Balaji and Jawahir [203] observed that there are drastic changes inmachining performance measures such as cutting forces, chip-flowand chip formation, and surface roughness induced by thecontinuously varying geometry due to the complex geometry ofthe contour shape. Balaji and Jawahir [203] tested two cutting tools(a flat-faced polycrystalline diamond tool (PCD) and a grooved CVDdiamond-coated carbide tool (DCG)). In contour turning, there arecontinuous changes in the effective depth of cut and effective feedalong the contour, which leads to drastic changes in the effectivemechanics of the machining operation. The significant changes ineffective depth of cut and feed also lead to continuously varyingsize effect conditions along the contour. In this particular study, theflat-faced PCD tool was relatively up-sharp with no significanthone to its cutting edge, whereas the diamond-coated grooved tool(DCG) has an edge-hone to provide edge strength and stability tothe cutting edge. The changing effective geometry of the cuttingconditions and the cutting edge impose size effects in the surfacesgenerated. Surface roughness was measured at discrete locationsalong the contour profile for the finish machining case. Aninteresting observation was that the diamond-coated grooved toollargely produced a rougher surface when machining the 6061-Balloy, but ended up being far superior to the PCD tool whenmachining 2011-T3 alloy. The role of size effect in influencingdifferent surface texture when machining different alloys withdifferent tools remains an interesting area for future study of thefundamental mechanics of material removal.

More recent comprehensive analysis of the cutting edge radiuseffects in turning includes development of a new model forpredicting the apparent area of contact in the cutting edgeregion [204]. A typical apparent undeformed area of cut (view on

tool reference plane Pr) is shown in Fig. 31 for a finish turningprocess.

According to the position of the given point S (S = A, B, C, D, E) onthe circular cutting edge, the entire undeformed area of cut can bedivided into four regions:Region 1: ABJ, Region 2: BEIJ, Region 3: ECFI, and Region 4: CFD.

The total apparent area of cut for each region is calculated byadding the apparent area of cut generated from the roundedcutting edge and the apparent area of cut generated from the rakeface together. Based on the mathematical derivation, the effect ofcutting edge radius on the apparent area of cut can be calculatedand 3D visualized (Fig. 32). This theoretical work was followed byan experimental validation process for specific cutting energyversus the ratio of feed and cutting edge radius. An interestingsimilarity was observed in the pattern of apparent contact regionsfor all four edge radius tool groups considered. Also, an analysis ofmachined surface quality was done. Three patterns of machinedsurfaces named as acceptable, marginal and unacceptable (Fig. 33)were observed in all tests.

All machined surfaces from DLC insert are found to beacceptable. But for Diamond tool inserts, all machined surfacefor the ratio of feed/edge radius smaller than 0.8 are eitherMarginal or Unacceptable. As a result, DLC inserts generate muchmore acceptable machined surfaces than diamond inserts. Thisindicates the complex tribological interactions that are takingplace in the cutting regions of these tools.

7.4. Drilling operations

Using the drills with and without web thinning, the influence ofthe chisel edge length on the cutting torque and feed force was

Fig. 33. Machined surface patterns [204].

Fig. 34. Measured (continuous line) and simulated (dotted line) cutting force

progressions for different tool diameters (material: AISI P20, cutting speed:

yc ¼ 35 m=min, feed per tooth fz = 0.01 � d, depth of cut: ap = 0.04 � d) [218].


investigated. It was found that a downscaling of the tool diameterleads to a non-linear increase of the specific feed force [205].Furthermore, a non-linear scaling effect on the related feed forcewas observed in drilling tests by downscaling of drill diameter.With a proposed 3D-FE-model, the experimentally determinedscaling effects are well predicted [206].

Based on the interaction between the cutting mechanisms inshearing and ploughing, a new analytical approach was developedto determine the minimum undeformed chip thickness and topredict the observed non-linear size effect in specific cuttingenergy (Fig. 24). Also, a 3D-FE-model was developed, andsuccessfully validated to predict chip formation, feed force, cuttingtorque and temperature in drilling [207,208].

Lugscheider et al. [209] developed a FE-model to simulate thecontact between a drill and specimen in micro drilling. The effect ofPVD hard coatings geometry on the micro drills was discussed. Theinfluence of a scaling of the coating thickness on microdrilling toolswas investigated in [210]. The thickness of the coating influencesthe bending and torsional stiffness, and therefore the dynamicbehaviour of the tools.

Dix et al. [211] studied the Burr formation and the temperaturedistribution in drilling processes with scaled tool diameter. Theyfound the existence of size effects in the burr formation processwhere they showed that the burr height and the burr type do notchange linearly with the tool diameter, but, the maximumtemperature varies non-linearly with the tool diameter.

Paris et al. [131] developed a new cutting force model forundeformed chip thickness close to zero, called as ‘‘fractionalModel’’ for drilling and milling, and validated it experimentally andagainst the traditionally known exponential function. Theyshowed that the accuracy of this proposed new model wassuperior to those obtained by the exponential function.

7.5. Milling operations

Ko [212] developed a model to predict cutting forces for endmilling by considering the size effect through the use ofinstantaneous cutting coefficients and validated it experimentally.The values of the cutting force components are determinedempirically or semi-empirically. Wang and Zheng [213] proposedan analytical force model with dual shearing and ploughingmechanisms for end milling.

Other significant FEM work includes work by Vogler et al. [214]where the authors developed a cutting force model for microendmilling, and by incorporating the minimum chip thicknessconcept, they were able to predict the effect of cutting edgeradius on cutting forces. Finite element simulations wereperformed to calibrate the various machining parameters formicromilling force model. Their model incorporated the metal-lurgical microstructural features.

Bissacco et al. [215] investigated size effects on the surfacegeneration when downscaling the tool diameter in millingprocesses. Size effects occur when the ratio of cutting edge radiusto undeformed chip thickness be-comes critical.

Weinert et al. [216,217] also studied the influence of the cuttingedge radius to the process. When scaling the undeformed chipthickness subject to the tool diameter, the cutting edge radius has amajor influence to the process because it cannot be scaled down inthe same range as tool diameter. A small undeformed chipthickness, in combination with a big cutting edge radius, prevents awell-defined cutting of the material and leads to ploughing effects.

The influence of a downscaling of tool diameter and chipthickness on the cutting forces in micromilling was experimentallyinvestigated by Biermann et al. [218]. Non-linear rising specificcutting forces with decreasing chip thickness were found. Ageometric simulation was used to calculate the cutting forces,which matched well with the experimental results (Fig. 34).

Bissacco et al. [162] presented a theoretical model for cuttingforce prediction in micro milling by taking into account the sizeeffect related to the decreasing ratio between undeformed chipthickness and cutting edge radius. This model is based on a revisedimplementation of the Unified Mechanics of Cutting. Thecomparison of measured and predicted cutting forces showed agood agreement. A recent analytical modelling work showsaccurate prediction of cutting forces and their experimentalvalidation in milling of 316L stainless steel and TiAl6V4 alloy atsmall undeformed chip thickness [131].

An important factor in downscaled milling processes are thetools. A decreasing tool size, related to the tool diameter, leads toan increasing deviation of the tool geometry from the tool design[219]. Another size effect which occurs is the increasing tooldeflection with decreasing tool radius caused by the cubicallydecreasing section modulus subject to the diameter of the tools.Investigations show contour deviations of machined webs up to30 mm when machining with a 0.4-mm tool with a length of 4 mm,while the parts machined with a 2-mm tool show almost nodeviations of the desired contour [216]. This behaviour wasconfirmed by Uhlmann et al. [220] who examined the scaling inmilling of tungsten–copper composites. A size effect was found inthe tool displacement which showed a non-linear dependency onthe tool diameter.

Furthermore, size effects on process force, speed, tool drift,surface roughness and natural frequencies of the tool wereinvestigated in scaled milling of tungsten copper composites.

Fig. 35. Influence of the size of the tungsten particles on the chip formation

(material: WCu 60/40, tungsten particle size dk = 3 mm (left) and dk = 30 mm (right),

cutting speed yc ¼ 0:01, uncut chip thickness h = 100 mm) (by courtesy of [222]).


A non-linear behaviour of the process when using tool diametersbelow 1 mm was detected [221]. In further investigations, theinfluence of a scaling of the size of the tungsten particles and thepercentage of tungsten in the WCu specimen on the process wasalso determined. An increase in cutting forces with decreasingtungsten particle size was observed while a higher percentage oftungsten leads to higher cutting forces. In quasistatic chippingtests, a scaling of the tungsten particle size also leads to a change inchip formation (Fig. 35) [222].

Another important factor, which has to be taken into accountwhen downscaling the tool diameter, is the dynamic behaviour ofthe milling process. Biermann and Kahnis [223] investigated thedynamic behaviour by analysing the tool tip motion. They foundout that at low depths of cut only a few experiments showed theoccurrence of chatter. But, also in the experiments where theprocess was stable, differences in the vibration amplitude and themean tool tip displacement were noted. A decreasing tool diameterleads to increasing vibration amplitude and tool tip displacement.An example for a surface where chatter occurs during themachining process can be seen in Fig. 36.

Lai et al. [224] developed a model to predict cutting forces andthe chip formation in micro milling, which considers size effect,cutting edge radius and minimum chip thickness. The model isbased on a modified Johnson–Cook approach using strain gradientplasticity. As a result, the simulation was able to determine theminimum undeformed chip thickness. Also, the proposed modelcould explain material strengthening behaviours which are foundto be the main causes for the size effect. The increasing specificshear energy when machining at undeformed chip thicknesssmaller than the minimum undeformed chip thickness was largelydue to ploughing effects.

7.6. Grinding operations

Size effects in grinding, i.e., the increase in the specific energyand the average specific grain energy with decreasing chipthickness, were investigated in early work by Kannappan andMalkin [225] and by Malkin [226], and more recently, Brinksmeierand Giwerzew [227] discussed about a possible application for acontrolled strengthening of workpiece subsurface via work-hardening. Therefore, an advanced grinding process of abrasivematerial removal, in combination with plastic deformation, hasbeen designed, which could be used successfully for a controlled

Fig. 36. SEM picture of a machined slot with tool vibrations (cutting parameters:

d = 0.5 mm, yc ¼ 60 m=min, ap = 0.05 mm, fz = 0.007 mm, material: X6CrNiMoTi17-

12-2) [223].

strengthening of workpiece subsurface. Lowering the cuttingspeed at constant chip thickness additionally increases the specificgrinding energy because of microploughing effects [228]. Heinzeland Bleil [229] showed the promising possibility of using sizeeffects involving the increased specific grinding energy in surfacelayer work-hardening of metallic parts by showing their effects onthe resulting compressive residual stresses.

7.7. Size effects and surface integrity

In recent times, there has been a great interest in studies onsurface integrity developed on the machined surface and subsur-face, particularly in view of its influence on the life and functionalperformance of machined components. Over the years, significanteffort has been made by the research community in developingquantitative understanding of the surface integrity issues andtheir controlling factors. Among all well-known surface integrityparameters such as surface finish; macrostructure (10� or less) –macrocracks, macroetch indications, etc.; microstructure –microcracks, plastic deformation, phase transformation, inter-granular attack, pits, tears, laps, protrusions, built-up edge,melted and redeposited layers, selective etching, etc.; micro-hardness, the machining-induced residual stresses have beenshown to significantly influence the functional performance of themachined component, particularly the fatigue life. Numerouspublications have reported on current and past attempts todevelop analytical means to predict the residual stresses inmachining in terms of machining parameters (cutting conditions),tool geometry and the work material property, and to deviseexperimental methods to measure residual stresses in 2D and 3Dmachining processes. The impact of scaling down the machiningoperation to micro and even nanolevel machining and the effectsof reduced feeds and depths of cut producing large specific cuttingenergy are still being established. How the size effects will affectthe surface integrity and the resulting product life including theoverall performance of the machined component has thereforebecome a major research topic in the research circle. A recentpaper by Outeiro et al. [230] discusses some interesting newresearch directions while the newly formed CIRP Working Groupon ‘Surface Integrity and Functional Performance of Components’has embarked on paving the way for international cooperativeresearch in this area.

8. Conclusions

It is shown by this review that size effects have a stronginfluence on production processes. The knowledge about sizeeffects is essential for a proper process control. The main featuresof size effects, which can be divided into three groups of density,shape and structure effects, are:

1. T
he flow stress of material is influenced by different types of sizeeffects, which are dominant in different size scales. Both anincrease and decrease in strength can be observed withincreasing size, while the effects are well understood. Theextent of the effects increases with decreasing size.
2. In
tribology, all size effects observed in lubricated friction can beexplained by the lubricant pocket model. Size effects in dryfriction seem to be questionable.
3. T
he formability decreases with decreasing size, making microforming processes more difficult to control. This is especiallytrue, if the grain size to thickness ratio increases.
4. S
ize effects in forming generate effects on the forming forces andthe accuracy of the parts, including spring-back and shapedistortions.
5. T
he most important effect in machining is the increase of thenormalized cutting force with decreasing undeformed chipthickness. Despite the fact that the effect itself seems to bealways the same (e.g., increase of normalized force) it is ofdifferent nature depending on the experimental conditions. A


wide variety of different models can be applied to explain theseeffects.

6. I
n forming and in cutting a shape balance effect, e.g., the balancebetween volume heating by deformation and cooling via thesurface plays an important role.
Acknowledgements

The authors like to thank the following scientists forcontributing actively to this paper.

M. Arentoft and N. Bay (Denmark); E. Brinksmeier; U. Engel, M.Geiger, P. Groche, G. Hirt, H. Hoffmann, F. Klocke, K. Lange, L.W.Meyer, R. Kopp, V. Schulze, and K. Weinert (Germany); P. Jenssen(The Nederlands); J. Cao, D.A. Lucca, S. Melkote, and A.K. Balaji(USA).

Furthermore, special thanks are devoted to the DeutscheForschungsgemeinschaft for financial support of many of thereported work, especially within the SPP 1138 and Dr.-Ing. ZhenyuHu for the preparation of the initial literature survey.

References

[1] Pawelksi O, (1993) Ahnlichkeitstheorie in der Umformtechnik.Dahl W, KoppR, Pawelski O, (Eds.) Umform-technik, Plastomechanik und Werkstoffkunde,Springer Berlin. p. 158–176.

[2] Pawelski H, Pawelski O (2000) Technische Plastomechanik. Stahleisen Dus-seldorf.

[3] Pawelski O (1964) Beitrag zur Ahnlichkeitstheorie der Umformtechnik. Archivfur das Eisenhuttenwesen 35(1):27–36.

[4] Kopp R, Wiegels H (1998) Einfuhrung in die Umformtechnik. AugustinusBuchhandlung, Aachen.

[5] Gunasekera JS, Havanek J, Littlejohn MH (1982) The Effect of Specimen Sizeon Stress–Strain Behaviour in Compression. Transactions of the ASME104:274–279.

[6] Pawelski O (1992) Ways and Limits of the Theory of Similarity in Applicationto Problems of Physics and Metal Forming. Journal of Materials ProcessingTechnology 34:19–30.

[7] Vollertsen F, (2003) Size Effects in Manufacturing.Vollertsen F, Hollmann F,(Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 1–9.

[8] Geiger M, Kleiner M, Eckstein R, Tiesler N, Engel U (2001) Microforming.Annals of the CIRP 50(2):445–462.

[9] Vollertsen F, Schulze Niehoff H, Hu Z (2006) State of the Art in Micro Forming.Journal of Machine Tools and Manufacture 46(11):1172–1179.

[10] Engel U, Eckstein R (2002) Microforming—From Basic Research to its Realiza-tion. Journal of Materials Processing Technology 125–126:35–44.

[11] Van Brussel H, Peirs J, Reynaerts D, Delchambre A, Reinhart G, Roth N, WeckM, Zussmann E (2000) Assembly of Microsystems. Annals of CIRP 49(2):451–472.

[12] Masuzawa T (2000) State-of-the-Art on Micromachining. Annals of CIRP49(2):473–488.

[13] Vollertsen F (2008) Categories of Size Effects. Production Engineering2(4):377–383.

[14] Geiger M, Vollertsen F, Kals R (1996) Fundamentals on the Manufacturing ofSheet Metal Microparts. CIRP Annals 45:277–282.

[15] Arzt E (1998) Size Effects in Materials Due to Microstructural and Dimen-sional Constraints: A Comparative Review. Acta Materialia 46(16):5611–5626.

[16] Schulze Niehoff H, Vollertsen F (2007) Versatile Micro Forming Press. inVollertsen F, Yuan S, (Eds.) Proceedings of the 2nd International Conference onNew Forming Technology. BIAS-Verlag, Bremen, pp. 167–176.

[17] Kopp R, van Putten K, (2003) Flow Curve Determination of Micro Strip WithAid of the Plane Strain Compression Test.Vollertsen F, Hollmann F, (Eds.)Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 73–79.

[18] Picart P, Michel JF (1999) Effects of Size and Texture on the ConstitutiveBehaviour for Very Small Components in Sheet Metal Forming. AdvancedTechnology of Plasticity 2:895–900.

[19] Kurosaki Y (1993) Thickness Dependence of Equi-Biaxial Yield Stress andLimit Strain in Electronic Copper Sheets and Foils. Proceedings of the Inter-national Conference on Technology of Plasticity, 1893–1898.

[20] Hoffmann H, Hong S (2006) Tensile Test of Very Thin Sheet Metal andDetermination of Flow Stress Considering the Scaling Effect. Annals of theCIRP 55(1):263–266.

[21] Chen FK, Tsai JW (2006) A Study of Size Effect in Micro-Forming With Micro-Hardness Tests. Journal of Materials Processing Technology 177(1–3):146–149.

[22] Manika I, Maniks J (2006) Size Effects in Micro- and Nanoscale Indentation.Acta Materialia 54(8):2049–2056.

[23] Stolken JS, Evans AG (1998) A Microbend Test Method for Measuring thePlasticity Length Scale. Acta Materialia 46:5109–5115.

[24] Xiang Y, Vlassak JJ (2006) Bauschinger and Size Effects in Thin-Film Plasticity.Acta Materialia 54(20):5449–5460.

[25] Brenner SS (1956) Tensile Strength of Whiskers. Journal of Applied Physics27(12):1484–1491.

[26] Greer JR, Oliver WC, Nix WD (2005) Size Dependence of Mechanical Proper-ties of Gold at the Micron Scale in the Absence of Strain Gradients. ActaMaterialia 53(6):1821–1830.

[27] Raulea LV, Govaert LE, Baaijens FPT (1999) Grain and Specimen Size Effects inProcessing Metal Sheets. Advanced Technology of Plasticity 2:939–944.

[28] Raulea LV, Goijaets AM, Govaert LE, Baaijens FPT (1999) Size Effects in theProcessing of Thin Metal Sheets. Proceedings of the SheMet’99, 521–528.

[29] Raulea LV, Goijaets AM, Govaert LE, Baaijens FPT (2001) Size Effects in theProcessing of Thin Metal Sheets. Journal of Materials Processing Technology115(1). 22: 44–48.

[30] Gau J-T, Principe C, Wang J (2007) An Experimental Study on Size Effects onFlow Stress and Formability of Aluminium and Brass for Microforming.Journal of Materials Processing Technology 184(1–3):42–46.

[31] Di Lorenzo R, Beccari S, Micari F (2003) An Experimental Investigation onMicro Sheet Forming. Proceedings of the 1st International CIRP Seminar onMicro and Nano Technology, Copenhagen, 73–76.

[32] Carrillo JG, Cantwell WJ (2007) Scaling Effects in the Tensile Behaviour ofFiber-Metal Laminates. Composites Science and Technology 67:1684–1693.

[33] Vollertsen F, Vogler S (1989) Werkstoffeigenschaften und Mikrostruktur.Hanser Munich.

[34] Kruger L, Meyer LW, Halle Th, (2003) Size Effects at Flow Stress BehaviourUnder Compressive Loading.Vollertsen F, Hollmann F, (Eds.) Strahltechnik,vol. 24. BIAS-Verlag, Bremen. p. 65–71.

[35] Kruger L, Meyer LW, Halle T, Herzig N (2004) Size Effects on Flow StressBehaviour of Tool Steel 40CrMnMo7 at High Loading Rates. Proceedings of the6th Mesomechanics, Patras (Greece), 420–425.

[36] Meyer LW, Herzig N, Kruger L (2005) Size Effects on Flow Stress and Failure ofTi-6-22-22S and Al7075 Over a Wide Range of Strain Rates. Proceedings of the11th ICF International Conference on Fracture Turin (Italy) (on CD), .

[37] Herzig N, Meyer LW, Halle T (2006) Time and Size Dependencies of Flow andFailure Behaviour of Metallic Materials: An Experimental Study, MESO.International Conference for Mesomechanics, vol. 8, 972-8953-07-025–32.

[38] Janssen PJM (2007) First-Order Size Effects in the Mechanics of MiniaturisedComponents, PhD thesis, Eindhoven University of Technology.

[39] Bull SJ (2003) On the Origins and Mechanisms of the Indentation Size Effects.Zeitschrift Fur Metallkunde 94:787–792.

[40] Fleischer RL, Chalmers B (1958) Size effects in the Deformation of Aluminium.Transactions of the Metallurgical Society AIME 212:265–274.

[41] Nix WD, Gao H (1998) Indentation Size Effects in Crystalline Materials: A Lawfor Strain Gradient Plasticity. Journal of the Mechanics and Physics of Solids46(3):411–425.

[42] Ashby MF (1970) The Deformation of Plastically Non-Homogeneous Materi-als. Philosophical Magazines 21:399–424.

[43] Fleck NA, Hutchinson JW (1997) Strain Gradient Plasticity. Advances inApplied Mechanics 33:295–361.

[44] Fleck NA, Hutchinson JW (2001) A Reformulation of Strain Gradient Plasticity.Journal of the Mechanics and Physics of Solids 49:2245–2271.

[45] Bazant ZP, Guo Z (2002) Size Effect and Asymptotic Matching Approxima-tions in Straingradient Theories of Micro-Scale Plasticity. International Journalof Solids and Structures 39:5633–5657.

[46] Zhao M, Slaughter WS, Li M, Mao SX (2003) Material-Length-Scale-ControlledNanoindentation Size Effects DUE TO Strain-Gradient Plasticity. Acta Materi-alia 51:4461–4469.

[47] Michel JF, Picart P (2002) Modelling the Constitutive Behaviour of Thin MetalSheet Using Strain Gradient Theory. Journal of Materials Processing Technology125(126):164–169.

[48] Michel JF, Picart P (2002) Modeling and FE Simulation for Thin Sheet MetalForming Using Strain Plasticity Gradient. ICTP International Conference onTechnology of Plasticity 7:1045–1050.

[49] Pernin N, Chambert J, Picard P (2005) Modelling of Micro-Forming byPlasticity Gradient and Surface Layer Methods. ESAFORM International ESA-FORM Conference on Material Forming 8:109–112.

[50] Shu JY, Fleck NA (1998) The Prediction of a Size Effect in Micro-Indentation.International Journal of Solids and Structures 35(13):1363–1383.

[51] Yuan U, Chen J, Krompholz K, Wittmann FH (2003) Investigations of SizeEffects in Tensile Tests Based on a Nonlocal Micro-Mechanical DamageModel. Computational Materials Science 26:230–243.

[52] Geiger M, Engel U, Vollertsen F, Kals R, Messner A (1994) Metal Forming ofMicro Parts for Electronics. Production Engineering II(1):15–18.

[53] Kals R, Pucher HJ, Vollertsen F (1995) Effects of Specimen Size and Geometry inMetal Forming. in Hashmi SJ, (Ed.) Proceedings of the 2nd International Con-ference on Advances in Materials and Processing Technologies, vol. III1288–1297.

[54] Picart P, Ghouati O, Gelin JC (1998) Characterization and Modelisation ofMetal Forming for Micro Components. Proceedings of the first ESAFORMConference, 33–36.

[55] Peng L, Liu F, Ni J, Lai X (2007) Size Effects in Thin Sheet Metal Forming andits Elastic–Plastic Constitutive Model. Materials & Design 28(5):1731–1736.

[56] Engel U, Meßner A, Geiger M (1996) Advanced Concept for the FE-Simulationof Metal Forming Processes for the Production of Microparts, AdvancedTechnology of Plasticity. in Altan T, (Ed.) Proceedings of the 5th ICTP, vol.II903–907.

[57] Kals R, Vollertsen F, Geiger M, (1996) Scaling Effects in Sheet Metal For-ming.Kals HJJ, Shirvani B, Singh UP, Geiger M, (Eds.) Sheet Metal, vol. II.University of Twente Enschede. p. 65–75.

[58] van Putten K, Franzke M, Hirt G (2007) Size Effect on Friction and Yielding inWire Flat Rolling. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2ndInternational Conference on New Forming Technology. BIAS-Verlag, Bremen,pp. 583–592.

[59] Armstrong RW (1961) On Size Effect in Polycrystal Plasticity. Journal ofMechanics and Physics of Solids 9:196–199.

[60] Cao J, Krishnan N, Wang Z, Lu H, Liu WK, Swanson A (2004) Microforming –Experimental Investigation of the Extrusion Process for Micropins and itsNumerical Simulation Using RKEM. ASME Journal of Manufacturing Scienceand Engineering 126:642–652.


[61] Groche P, Schafer R, Henning M (2007) Finite Element Calculation of SurfaceEvolution Considering Grain Size and Crystallographic Texture Effects. inAzushima A, (Ed.) Proceedings of the 3rd International Conference on Tribologyin Manufacturing Processes ICTMP, vol. 09. Yokohama National University, pp.219–226.

[62] Justinger H, Hirt G (2007) Scaling Effects in the Miniaturization of the DeepDrawing Process. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2ndInternational Conference on New Forming Technology. BIAS-Verlag, Bremen,pp. 665–674.

[63] Justinger H, Hirt G (2009) Estimation of Grain Size and Grain OrientationInfluence in Microforming Processes by Taylor Factor Considerations. Journalof Material Processing Technology 209:2111–2121.

[64] Mori L, Krishnan N, Cao J, Espinosa H (2007) Study of the Size Effects andFriction Conditions in Micro-Extrusion. Part II. Size Effect in Dynamic Frictionfor Brass–Steel Pairs. ASME Journal of Manufacturing Science and Engineering129(4):677–689.

[65] Messner A, Engel U, Kals R, Vollertsen F (1994) Size Effect in the FE-Simula-tion of Micro-Forming Processes. Journal of Materials Processing Technology45(1–4):371–376.

[66] Geiger M, Messner A, Engel U, Kals R, Vollertsen F (1995) Design of Micro-Forming Processes: Fundamentals, Material Data and Friction Behaviour.International Cold Forging Congress 9:155–164.

[67] Behrens B-A, Doege E, Hundertmark A, (2003) Modelling of Size-Effects inBulk Metal Forming Processes.Vollertsen F, Hollmann F, (Eds.) Strahltechnik,vol. 24. BIAS-Verlag, Bremen. p. 49–56.

[68] Tiesler N, Engel U, Geiger M (1999) Forming of Microparts – Effects ofMiniaturization on Friction. Advanced Technology of Plasticity 2:889–894.

[69] Engel U, Tiesler N, Eckstein R (2001) Microparts – A Challenge for FormingTechnology, ICIT. International Conference on Industrial Tools 3:31–39.

[70] Geiger M, Tiesler N, Engel U (2003) Cold Forging of Microparts. ProductionEngineering Research and Development 10(1):19–22.

[71] Hu Z, Schulze Niehoff H, Vollertsen F (2007) Tribological Size Effects in DeepDrawing. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2nd InternationalConference on New Forming Technology. BIAS-Verlag, Bremen, pp. 573–582.

[72] Hu Z, Schulze Niehoff H, Vollertsen F, (2003) Determination of the FrictionCoefficients in Deep Drawing.Vollertsen F, Hollmann F, (Eds.) Strahltechnik,vol. 24. BIAS-Verlag, Bremen. p. 27–34.

[73] Hu Z, Vollertsen F (2004) Scaled Friction Test Integrated in Deep Drawing.Proceedings of the 2nd International Conference on Tribology in ManufacturingProcesses, 561–568.

[74] Vollertsen F, Hu Z (2006) Tribological Size Effects in Sheet Metal FormingMeasured by a Strip Drawing Test. Annals of the CIRP 55(1):291–294.

[75] Vollertsen F, Hu Z (2008) Determination of Size-Dependent Friction Func-tions in Sheet Metal Forming with Respect to the Distribution of the ContactPressure. Production Engineering 2(4):345–350.

[76] Vollertsen F, Hu Z (2007) On the Drawing Limit in Micro Deep Drawing.Journal Technology of Plasticity 1–2(32):1–11.

[77] Pawelski O, Lueg W (1961) Versuche und Berechnungen uber das Ziehen undEinstoßen von Rundsta-ben. Stahl und Eisen 81(25):1729–1739.

[78] Engel U, Messner A, Tiesler N (1998) Cold Forging of Microparts – Effect ofMiniaturisation on Friction. in Chenot JL, et al. (Eds.) Proceedings of the 1stESAFORM Conference on Materials Forming77–80.

[79] Tiesler N, Engel U (2000) Microforming – Effects of Miniaturization, MetalForming. International Conference on Metal Forming, vol. 8, 355–360.

[80] Tiesler N (2002) Microforming – Size Effects in Friction and Their Influence onExtrusion Processes. Wire 52:34–38.

[81] Herzig N, Meyer LW (2006) Material Characterisation at High Strain Rateswith Special Emphasis on Miniaturization and Size Dependencies. in KleinerM, Tekkaya E, (Eds.) Proceedings of the International Conference on High SpeedForming (2nd ICHSF)13–22.

[82] Bech JI, Bay N, Eriksen M (1998) A Study of Mechanisms of Liquid Lubricationin Metal Forming. Annals of CIRP 47(1):221–226.

[83] Engel U (2004) Tribology in Microforming. Proceedings of the 2nd InternationalConference on Tribology in Manufacturing Processes, 549–559.

[84] Engel U (2006) Tribology in Microforming. Wear 260(3):265–273.[85] Nilsson MS, Olsson DD, Petrushina I, Andreasen JL, Bay N, Christensen E, Bjerrum

NJ (2004) Development of Strategic Surface Topographies for Lubricationin Sheet Forming of Stainless Steel. Proceedings of the InternationalConference on Tribology in Manufacturing Processes, ICTMP2004, Nyborg,Denmark, 275–284.

[86] Sørensen CG, Andreasen JL, Bech J, Bay N, Engel U, Neudecker T (1999) A BasicStudy of the Influence of Surface Topography on Mechanisms of LiquidLubrication in Metal Forming. Annals of the CIRP 48(1):203–208.

[87] Geiger M, Messner A, Engel U (1997) Production of Microparts – Size Effectsin Bulk Metal Forming, Similarity Theory. Production Engineering 4(1):55–58.

[88] Krishnan N, Cao J, Kinsey. Dohda K (2005) Microforming: Study of FrictionConditions and the Impact of Low Friction/High-Strength Die Coatings on theExtrusion of Micropins. MED 16(1):331–340.

[89] Krishnan N, Cao J, Dohda K (2007) Study of the Size Effect on Friction Conditionsin Micro-Extrusion. Part 1. Micro-Extrusion Experiments and Analysis. ASMEJournal of Manufacturing Science and Engineering 129(4):669–676.

[90] Simons G, Weippert C, Dual J, Villain J (2006) Size Effects in Tensile Testing ofThin Cold Rolled and Annealed Cu Foils. Materials Science and Engineering A416(1–2):290–299.

[91] Michel JF, Picart P (2003) Size Effects on the Constitutive Behaviour for Brassin Sheet Metal Forming. Journal of Materials Processing Technology 141:439–446.

[92] Yamaguchi K, Mellor P (1976) Thickness and Grain Size Dependence of LimitStrains in Sheet Metal Stretching. International Journal of Mechanical Sciences18(2):85–90.

[93] Fulop T, Brekelmans WAM, Geers MGD (2006) Size Effects From GrainStatistics in Ultra-Thin Metal Sheets. Journal of Materials Processing Technol-ogy 174(1–3):233–238.

[94] Diehl A, Engel U, Geiger M (2008) Mechanical Properties and BendingBehaviour of Metal Foils. Proceedings of the IMechE Part B Jounal of EngineeringManufacture 222:83–91.

[95] Meyer LW, Herzig N (2005) Großeinflusse beim Fließ-, Verfestigungs- undVersagenverhalten metalischer Werkstoffe, 2. Kolloquium Prozessskalierung.Bremen 147–156.

[96] Keeler SP, Brazier WG (1977) Relationship Between Laboratory MaterialCharacterisation and Press-Shop Formability. Proceedings of the Microalloying,vol. 75, Union Carbide, New York, pp. 517–530.

[97] Hasek V, Lange K (1980) Forming-Limit Diagram and Its Applications in Deep-Drawing and Stretch-Forming Processes. Werkstattstechnik Zeitschrift FurIndustrielle Fertigung 70:577–580. (in German).

[98] Tanaka S, Nakamura T, Hayakawa K (2002) Miniature Incremental Forming ofMillimeter-Sized Thin Shell Structures. Advanced Technology of Plasticity1:403–408.

[99] Diehl A, Geissdorfer S, Engel U (2007) Investigation of Size DependentMechanical Properties of Metal Foils in Micro Sheet Metal Forming Processes.Proceedings of the 2nd ICOMM, Clemson University: Proceedings of the 2ndInternational Conference on Micromanufacturing, Greenville, USA, 156–161.

[100] Diehl A, Staud D, Engel U (2008) Investigation of the Mechanical Behaviour ofThin Metal Sheets Using the Hydraulic Bulge Test. Proceedings of the 4thInternational Conference Multi-Material Micro Manufacture (4M), Cardiff Sept,vol. 9–11, 195–198.

[101] Saotome Y, Kaga H (1990) Micro Deep Drawability of Very Thin Sheet Steels.Advanced Technology of Plasticity 3:1341–1346.

[102] Yamaguchi K, Sagrado R, Takakura N, Lizuka T (2002) Effect of Thickness onthe Restoration Behavior of Sheet Metals Subjected to Bulge Deformation,ICTP. International Conference on Technology of Plasticity 7:997–1002.

[103] Lee RS, Chen CH, Gau J-T (2008) Effect of Thickness to Grain Size Ratioon Drawability for Micro Deep Drawing of AISI 304 Stainless Steel. inYang DY, Kim YH, Park CH, (Eds.) Proceedings of the 9th ICTP. . paper MD 1-2(on CD).

[104] Kast D (1969) Modellgesetzmaßigkeiten beim Ruckwartsfließpressen geome-trisch ahnlicher Napfe, Dissertation, Giradet Essen.

[105] Arentoft M, Bruschi S, Ghiotti A, Paldau NA, Holstein IV (2008) Microformingof Light Weight Metals in Warm Conditions. in Engel U, Rosochowski A, (Eds.)Proceedings of the 11th ESAFORM Conference MS08-1 (on CD).

[106] Wulfsberg JP, Hilpert S-E, Ostendorf A, Samm K, (2003) Fundamentals ofLaser-Assisted Microforming.Vollertsen F, Hollmann F, (Eds.) Strahltechnik,vol. 24. BIAS-Verlag, Bremen. p. 89–98.

[107] Justinger H, Hirt G (2007) Analysis of Size-Effects in the Miniaturized DeepDrawing Process. Key Engineering Materials 344:791–798.

[108] Witulski N, Hirt G, Justiger H.. (2004) Validation of FEM-Simulation forMicro Deep Drawing Process Modeling. Proceeding of the 8th InternationalConference on Numerical Methods in Industrial Forming Process, 0-7354-0188-8.

[109] Eckstein R, Engel U (2000) Behavior of the Grain Structure in Micro SheetMetal Working, Metal Forming. International Conference on Metal Forming8:453–459.

[110] Geiger M, Eckstein R, Engel U (2001) Study of Micro Sheet Metal WorkingProcesses, Production Engineering. Research and Development 8(1):55–58.

[111] Geißdorfer S, Rosochowski A, Olejnik L, Engel U, Richert M (2008) Micro-Extrusion of Ultrafine Grained Copper. International Journal of Material Form-ing . (available on-line).

[112] Geiger M, Geißdorfer S, Engel U (2007) Mesoscopic Model – AdvancedSimulation of Microforming Processes. Production Engineering ResearchDevelopment 1(1):79–84.

[113] Geißdorfer S, Engel U, Geiger M, (2003) Mesoscopic Model – SimulativeApproach to the Scatter of Process Factors in Microforming.Vollertsen F,Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 81–88.

[114] Eichenhuller B, Engel U, Geissdorfer S (2008) Process Parameter Interactionin Microforming. International Journal of Material Forming . (available on-line).

[115] Arentoft M, Paldan NA, Eriksen RS, Gastaldi T, Wert J, Eldrup M (2007) BulkForming of Industrial Micro Components in Conventional Metals and BulkMetallic Glasses. Proceedings of the10th ESAFORM Conference on MaterialForming, 665–670.

[116] Justinger H, Hirt G, Witulski N (2005) Analysis of Cup Geometry and Tem-perature Conditions in the Miniaturized Deep Drawing Process. AdvancedTechnology of Plasticity 459–460.

[117] Justinger H, Witulski N, Hirt G (2004) Experimental and Numerical Inves-tigation of Miniaturisation in Deep Drawing. Proceedings of the 10th Inter-national Conference on Metal Forming, Metal Forming, pp. 693–698.

[118] Hirt G, Justinger H, Witulski N, (2003) Analysis of Size Effects in Micro SheetForming.Vollertsen F, Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag,Bremen. p. 27–34.

[119] Richelsen AB, van der Giessen E (2001) Size Effects in Sheet Drawing.Proceedings of the 9th International Conference on Sheet Metal, Leuven, 263–270.

[120] Hirt G, Rattay B (2001) Coining of Sheet Metal to Produce Thin Plates withMicro Channel Structures, SheMet. Proceedings of the 9th International Con-ference on Sheet Metal, vol. 9, 119–126.

[121] Ike H, Plancak M (1999) Controlling Metal Flow of Surface Microgeometry inCoining Process. Advanced Technology of Plasticity 2:907–912.

[122] Diehl A, Engel U, Geiger M (2005) Investigation of the Spring-Back in MetalFoil Forming. Proceeding of the 24th IDDRG Conference, Besancon, France, .

[123] Diehl A, Engel U, Geiger M (2005) Spring-Back Behaviour of Thin Metal Foilsin Free Bending Processes. Multi-Material Micro Manufacture 147–150.


[124] Cavaliere P, Gabrielli F, Frantini L (2000) Bending of Very Thin Sheets: TheInfluence of Thickness on Material Characterisation. in PietrzykMetal Form-ing405–410.

[125] Kals R (1998) Fundamentals on the Miniaturization of Sheet Metal WorkingProcesses. Meisenbach-Verlag, Bamberg.

[126] Kals RTA, Eckstein R (2000) Miniaturization in Metal Sheet Working. Journalof Material Processing Technology 103:95–101.

[127] Pucher HJ, Kals R, Buchner M, Glasmacher M (1996) Simulation of MicroBending Process for Metal Forming of Component Leads. Proceedings of theFirst Plan Pacific Microelectronics Symposium, Honolulu, 37–44.

[128] Gau J-T, Principe C, Yu M (2007) Springback Behavior of Brass in Micro SheetForming. Journal of Materials Processing Technology 191:7–10.

[129] Kocanda A, Prejs T (2000) The Effect of Miniaturisation on the Final Geometryof the Bent Products, Metal Forming. International Conference on MetalForming 8:375–378.

[130] Groche P, Schafer R, (2003) Analysis of the Geometrical Tolerances andSurface Roughness of the Spinning Process.Vollertsen F, Hollmann F, (Eds.)Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 35–42.

[131] Paris H, Brissaud D, Gouskov A (2007) A More Realistic Cutting Force Model atUncut Chip Thickness Close to Zero. Annals of the CIRP 56(1):415–418.

[132] Geißdorfer S, Engel U, Geiger M (2008) A Novel Approach for In-Situ Obser-vation of Local Deformation Behaviour at Micro Scale. in Yang DY, Kim YH,Park CH, (Eds.) Proceedings of the 9th ICTP. . paper MD 1-5 (on CD).

[133] Geißdorfer S, Engel U (2009) Mesoskopisches Modell zur Abbildung vonGroßeneffekten mit Methoden der FE-Simulation fur die Kaltmassivumfor-mung. in Vollertsen F, (Ed.) Großeneinflusse bei Fertigungsprozessen. BIAS-Verlag, Bremen, pp. 155–180.

[134] Alting L, Kimura F, Hansen HN, Bissacco G (2003) Micro Engineering. Annals ofCIRP 52(2):635–658.

[135] Saotome Y, Iwazaki H (2001) Superplastic Backward Microextrusion ofMicroparts for Micro-Electro-Mechanical Systems. Journal of Materials Pro-cessing Technologies 119:307–311.

[136] Wulfsberg JP, Terzi M (2005) Investigation and Application of Size Effect inthe Laser Assisted Forging of Microparts With Transparent Tools. AdvancedTechnology of Plasticity 453–454.

[137] Hansen HN, Eriksson T, Arentoft M, Paldan N (2006) Design Rules forMicrofactory Solutions. Proceedings of the 5th International Workshop onMicrofactories, Besancon, France, .

[138] Paldan NA, Arentoft M, Eriksen RS (2007) Production Equipment and Pro-cesses for Bulk Formed Micro Components. Proceedings of the 10th ESAFORM,April, Saragoza, Spain, .

[139] Backer WR, Marshall ER, Shaw MC (1952) The Size Effect in Metal Cutting.Transactions of the ASME 74:61–72.

[140] Taniguchi N (1994) The State-of-the-Art of Nanotechnology for ProcessingUltra-Precision and Ultra-Fine Products. Precision Engineering 16(1):5–24.

[141] Shaw MC (2003) The Size Effects in Metal Cutting. Sadhana 28(5):875–896.[142] Palmer WB, Oxley PLB (1959) Mechanics of Orthogonal Machining. Proceed-

ings of the Institute of Mechanical Engineers 173(24):623–636.[143] Johnson W (1962) Some Slip-Line Fields for Swaging or Expanding Indenting,

Extruding and Machining for Tools With Curved Dies. International Journal ofMechanical Sciences 4:323–347.

[144] Johnson W (1967) Cutting With Tools Having a Rounded Edge – SomeTheoretical Considerations. Annals of the CIRP 14:315–319.

[145] Nakayama K, Tamura K (1968) Size Effect in Metal Cutting Force. ASMETransactions-Journal of Engineering for Industry 90(1):119–126.

[146] Larsen-Basse J, Oxley PLB (1973) Effect of Strain-Rate Sensitivity on ScalePhenomenon in Chip Formation. Proceedings of the 13th MTDR Conference,209–216.

[147] Challen JM, Oxley PLB (1984) Slip-Line Fields for Explaining the Mechanics ofPolishing and Related Processes. International Journal of Mechanical Sciences26(6–8):403–418.

[148] Kopalinski E, Oxley PLB (1984) Size Effect in Metal Removal Processes.Proceedings of the Mechanical Properties at High Rate of Strain, Oxford, UnitedKingdom, 389–396.

[149] Kopalinski E, Oxley PLB, Young HT (1990) A Strain-Hardening Slip Line FieldAnalysis of the Plastic Deformation Observed in a Model Asperity InteractionExperiment. International Journal of Mechanics and Physical Solids 38(6):765–785.

[150] Masuko M (1953) Fundamental Research on the Metal Cutting. 1. A NewAnalysis of Cutting Force. Transactions of the Society of Mechanical Engineers(Japan) 19:32–39.

[151] Albrecht P (1960) New Developments in the Theory of the Metal CuttingProcesses. ASME Transactions Journal of Engineering for Industry ;(Novem-ber)348–358.

[152] Armarego EJA, Brown RH (1961) On the Size Effect in Metal Cutting. Inter-national Journal of Production Research 1(3):75–99.

[153] Khaet GL, Vasilyuk GD (1970) Effect of a Rounded Cutting-Edge on CementedCarbide Tools. Russian Engineering Journal 4:81–84.

[154] Abdelmoneim MEs, Scrutton RS (1973) Post-Machining Plastic Recovery andthe Law of Abrasive Wear. Wear 24:1–13.

[155] Abdelmoneim MEs, Scrutton RS (1974) Tool Edge Roundness and StableBuild-Up Formation in Finish Machining, ASME Transactions. Journal ofEngineering for Industry ;(November)1258–1267.

[156] Taminiau DA, Dautzenberg JH (1991) Bluntness of the Tool and ProcessForces in High Precision Cutting. Annals of the CIRP 40(1):65–68.

[157] Lucca DA, Seo ZW (1993) Effect of Tool Edge Geometry on Energy Dissipationin Ultraprecision Machining. Annals of the CIRP 42(1):83–86.

[158] Lucca DA, Seo ZW (1994) Aspects of Surface Generation in OrthogonalUltraprecision Machining. Annals of the CIRP 43(1):43–46.

[159] Arsecularatne JA (1997) On Tool–Chip Interface Stress Distributions, Plough-ing Force and Size Effect in Machining. International Journal of machine toolsand manufacture 37(7):885.

[160] Oxley PLB (1989) Mechanics of Machining: An Analytical Approach to AssessingMachinability. Ellis Horwood, Chichester, United Kingdom.

[161] Dinesh D, Swaminathan S, Chandrasekar S, Farris TN (2001) An Intrinsic Size-Effect in Machining Due to The Strain Gradient. ASME/MED-IMECE 12:197–204.

[162] Bissacco G, Hansen HN, Slunsky J (2008) Modelling the Cutting Edge RadiusSize Effect for Force Prediction in Micro Milling. Annals of the CIRP 57:113–116.

[163] Clos R, Schreppel U, Veit P, (2003) Chipformation and Strain Localization in100Cr6.Vollertsen F, Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag,Bremen. p. 161–168.

[164] Clos R, Radoch S, Schreppel U, Veit P, et al, (2007) Size Effect at ChipFormation in 100Cr6. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2ndInternational Conference on New Forming Technology. BIAS-Verlag, Bremen, pp.511–519.

[165] Denkena B, Boehnke D, Kohler J (2007) Influence of the Rake Angle on theChip Formation in Form Turning Process. in Vollertsen F, Yuan S, (Eds.)Proceedings of the 2nd International Conference on New Forming Technology.BIAS-Verlag, Bremen, pp. 521–530.

[166] Denkena B, Becker JC, Jivishov V, (2003) Scaling Effects on Chip Formationand Forces in Hard Turning.Vollertsen F, Hollmann F, (Eds.) Strahltechnik, vol.24. BIAS-Verlag, Bremen. p. 113–119.

[167] Denkena B, Becker JC, Jivishov V (2005) Scaling Effects on Chip Formation,Forces and Surface Layer in Hard Turning. 8th CIRP International Workshop onModeling of Machining Operations, Mai 10/11, Chemnitz, 87–91.

[168] Denkena B, Clos R, Veit P, Jivishov V, Meyer R (2007) Influence of the CuttingEdge Geometry on the Chip Formation in Machining. in Vollertsen F, Yuan S,(Eds.) Proceedings of the 2nd International Conference on New Forming Tech-nology. BIAS-Verlag, Bremen, pp. 491–498.

[169] Stoll A, Leopold J, Neugebauer R (2006) Hybrid Methods for Analyzing BurrFormation in 2D-Orthogonal Cutting. Proceedings of the 9th CIRP Workshop onModeling of Machining Operations, 441–448.

[170] Dornfeld DA, Min S, Takeyuchi Y (2006) Recent Advances in MechanicalMicromachining. Annals of the CIRP 55(2):745–768.

[171] Manjunathaiah J, Endres WJ (2000) A New Model and Analysis of OrthogonalMachining With an Edge-Radiused Tool. Journal of Manufacturing Science andEngineering 122:384–390.

[172] Schimmel RJ, Endres WJ, Stevenson R (2002) Application of an InternallyConsistent Material Model to Determine the Effect of Tool Edge Geometry inOrthogonal Machining. Journal of Manufacturing Science and Engineering124:536–543.

[173] Joshi SS, Melkote SN (2004) An Explanation for the Size-Effect in MachiningUsing Strain Gradient Plasticity. Journal of Manufacturing Science and Engi-neering 126:679–684.

[174] Liu K, Melkote SN (2006) Material Strengthening Mechanisms and TheirContribution to Size Effect in Micro-Cutting. Journal of Manufacturing Scienceand Engineering 128(3):730–738.

[175] Abebe M, Appl FC (1981) A Slip-Line Solution for Negative Rake AngleCutting. Proceedings of the 9th North American Manufacturing Research Con-ference, University Park, PA, 341–348.

[176] Abebe M, Appl FC (1988) Theoretical Analysis of the Basic Mechanics ofAbrasive Processes. Part II. Model of the Ploughing Process. Wear 126:267–283.

[177] Fang N (2003) Slip-Line Modeling of Machining With a Rounded-Edge Tool.Journal of the Mechanics and Physics of Solids 51:715–762.

[178] Fang N, Jawahir IS, Oxley PLB (2001) A Universal Slip-Line Model With Non-Unique Solutions for Machining With Curled Chip Formation and a RestrictedContact Tool. International Journal of Mechanical Science 43:557–580.

[179] Jawahir IS, Wang X (2007) Development of Hybrid Predictive Models andOptimization Techniques for Machining Operations. Journal of MaterialsProcessing Technology 185:46–59.

[180] Wang X, Jawahir IS (2007) Recent Advances in Plasticity Applications inMetal Machining: Slip-Line Models for Machining With Rounded CuttingEdge Restricted Contact Grooved Tools. International Journal of Machining andMachinability of Materials 2(1):347–360.

[181] Wang X, Jawahir IS (2009) Predictive Modelling and Validation of Size Effectsin Orthogonal Cutting With Rounded Cutting Edge Tools Using the ExtendedUniversal Slip-Line Model. International Journal of Mechanical Sciences.

[182] Kim KW, Lee WY, Sin H (1999) A Finite Element Analysis for the Character-istics of Temperature and Stress in Micro-Machining Considering the SizeEffects. International Journal of Machine Tools & Manufacture 39:1507–1524.

[183] Ozel T, Altan T (2000) Determination of Workpiece Flow Stress and Friction atthe Chip–Tool Contact for High-Speed Cutting. International Journal ofMachine Tools & Manufacture 40:133–152.

[184] Yen Y, Jain A, Altan T (2004) A Finite Element Analysis of OrthogonalMachining Using Different Tool Edge Geometries. Journal of Materials Proces-sing Technology 146(1):72–81.

[185] Ee KC, Dillon OW, Jawahir IS (2005) Finite Element Modeling of ResidualStresses in Machining Induced by Cutting Tool with a Finite Edge Radius.International Journal of Mechanical Sciences 47:1611–1628.

[186] Simoneau A, Ng E, Elbestawi MA (2006) The Effect of Microstructure on ChipFormation and Surface Defects in Microscale, Mesoscale, and MacroscaleCutting of Steel. Annals of the CIRP 55(1):97–102.

[187] Simoneau A, Ng E, Elbestawi MA (2006) Chip Formation During MicroscaleCutting of a Medium Carbon Steel. International Journal of Machine Tools andManufacture 46:467–481.

[188] Liu K, Melkote SN (2007) Finite Element Analysis of the Influence of Tool EdgeRadius on Size Effect in Orthogonal Micro-Cutting Process. InternationalJournal of Mechanical Sciences 49:650–660.

[189] Weber M, Hockrainer T, Gumbsch P, Autenrieth H, Delonnoy L, Schulze V,Lohe D, Kotsschen-Reuther J, Fleischer J (2007) Investigation of Size Effects inMachining With Geometrically Defined Cutting Edges. Machining Science andTechnology 11:447–473.


[190] Kotschenreuther J, Delonnoy L, Hochrainer T, Schmidt J, Fleischer J, Schulze V,Lohe D, Gumbsch P, (2003) Modelling Simulation and Experimental Tests forProcess Scaling of Cutting Processes With Geometrically Defined Edge.Vol-lertsen F, Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p.

121–136.[191] Hochrainer T, Delonnoy L, Kotschenreuther J, Schulze V, Lohe D, Gumbsch P,

Fleischer J (2005) An Integrated Approach to the Modeling of Size-Effects inMachining With Geometrically Defined Cutting Edges. Proceedings of the 8thCIRP International Workshop on Modeling of Machining Operations, 123–130.

[192] Kotschenreuther J, Autenrieth H, Weber MJ, Fleischer J, Schulze V, Lohe D,Gumbsch P (2007) Influence of Multiple Machining Steps on the SpecificCutting Force and Surface Characteristics in Micro Cutting. in Vollertsen F,Yuan S, (Eds.) Proceedings of the 2nd International Conference on New FormingTechnology. BIAS-Verlag, Bremen, pp. 551–562.

[193] Autenrieth H, Weber M, Kotschenreuther JJ, Schulze V, Lohe D, Gumbsch P,Fleischer J (2007) Influence of Friction and Process Parameters on the SpecificCutting Force and Surface Characteristics in Micro Cutting. Proceedings of the10th CIRP Workshop on Modeling of Machining Operations, 539–546.

[194] Outeiro JC (2007) Influence of Tool Sharpness on the Thermal and MechanicalPhenomena Generated During Machining Operations. Journal of Machiningand Machinability of Materials 2(3–4):413–432.

[195] Outeiro JC, Dias AM, Jawahir IS (2006) On the Effects of Residual StressesInduced by Coated and Uncoated Cutting Tools With Finite Edge Radii inTurning Operations. Annals of the CIRP 55(1):111–116.

[196] Wanigarathne PC, Dillon OW, Jawahir IS (2009) A Finite Element Study of SizeEffects in Finish Machining With Coated Edge Radius Tools. InternationalJournal of Mechanical Sciences.

[197] Subbiah S, Melkote SN (2006) The Constant Force Component Due to MaterialSeparation and Its Contribution to the Size Effect in Specific Cutting Energy.Journal of Manufacturing Science and Engineering 128:811–815.

[198] Atkins AG (2003) Modelling Metal Cutting Using Modern Ductile FractureMechanics: Quantitative Explanations for Some Longstanding Problems.International Journal of Mechanical Sciences 45:373–396.

[199] Kotschenreuther J, Delonnoy L, Hochrainer T, Schmidt J, Fleischer J, Schulze V,Lohe D, Gumbsch P (2004) Influences of Process Scaling in Metal Cutting withGeometrically Defined Cutting Edges. in Brinksmeier E, Corbett J, Evans CJ,Hocken R, Kiyono S, Weck M, Kim S-WPeggs G, McKeownBurke T, (Eds.)Proceedings of the 4th Euspen173–174.

[200] Shawky AM, Elbestawi MA (1997) An Enhanced Dynamic Model in TurningIncluding the Effect of Ploughing Force. ASME J Manufacturing Science andEngineering 119(1):10–20.

[201] van Luttervelt CA, Childs THC, Jawahir IS, Klocke F, Venuvinod PK (1998)Present Situation and Future Trends in Modeling of Machining Operations.Annals of the CIRP 47(2):587–626.

[202] Redetzky M, Balaji AK, Jawahir IS (1999) Predictive Modelling of CuttingForces and Chip Flow in Machining With Nose Radius Tools. Proceedings of the2nd CIRP International Workshop on Modelling of Machining Operations, Jan-uary, Nantes, France, 160–180.

[203] Balaji AK, Jawahir IS (2001) A Machining Performance Study in Dry ContourTurning of Aluminum Alloys With Flat-Faced and Grooved Diamond Tools.Machining Science and Technonogy 5(2):269–289.

[204] Chen S, Jawahir IS (2008) The Influence of Cutting Edge Radius on SurfaceIntegrity and Size Effects in Dry Turning of Automotive Aluminum Alloy A356with Diamond Tools. Proceedings of the 11th CIRP Conference on Modeling ofMachining Operations, Gaithersburg, MD, USA, 247–254.

[205] Klocke F, Gerschwiler K, Risse K, (2003) Modelling of Dimensional Influencesin Drilling and Threading – Scaling Effects in Drilling of Steel.Vollertsen F,Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 169–176.

[206] Klocke F, Lung D, Gerschwiler K, Abouridouane M, et al, (2006) 3D Modelingand Scaling Effects in Drilling. Proceedings of the 9th CIRP Workshop onModeling of Machining Operations, 263–269.

[207] Klocke F, Lung D, Gerschwiler K, Abouriduane M (2007) Size Effects of theCutting Edge Rounding on the Minimum Uncut Chip Thickness and 3D FEModeling in Drilling. Proceedings of the 10th CIRP Workshop on Modelling ofMachining Operations, 197–205.

[208] Klocke F, Gerschwiler K, Abouriduane M (2007) Size Effects of the Tool EdgeRadius on Specific Cutting Energy and Chip Formation in Drilling. in Vol-lertsen F, Yuan S, (Eds.) Proceedings of the 2nd International Conference on NewForming Technology. BIAS-Verlag, Bremen, pp. 499–509.

[209] Lugscheider E, Papenfuß-Janzen N, Hurevich V, (2003) Simulation ofGeometrical Influences of PVD Hard Coatings on the Micro Drills.Vollert-sen F, Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen .

p. 153–159.

[210] Bobzin K, Nickel R, Parkot D, Hurevich V (2007) Theoretical Study of theInfluence of a PVD Hard Coating on the Dynamic Properties of the MicroDrilling Process. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2nd Inter-national Conference on New Forming Technology. BIAS-Verlag, Bremen, pp.531–538.

[211] Dix M, Leopold J, Neugebauer R (2007) Modelling, Simulations and Experi-mental Verification of Size Effects in Burr Formation. in Vollertsen F, Yuan S,(Eds.) Proceedings of the 2nd International Conference on New Forming Tech-nology. BIAS-Verlag, Bremen, pp. 471–480.

[212] Ko JH, Yun W, Cho D, Ehmann KF (2002) Development of Virtual MachiningSystem. Part 1. Approximation of the Size Effect for Cutting Force Prediction.International Journal of Machine Tools & Manufacture 42:1595–1605.

[213] Junz Wang J-J, Zheng CW (2002) An Analytical Force Model With Shearingand Ploughing Mechanisms in End Milling. International Journal of MachineTools and Manufacture 42:761–771.

[214] Vogler MP, DeVor RE, Kapoor SG (2004) On the Modelling and Analysis ofMachining Performance in Micro-Endmilling. Part II. Cutting Force Predic-tion. Journal of Manufacturing Science and Engineering 126:694–705.

[215] Bissacco G, Hansen HN, Chiffre L (2006) Size Effects on Surface Generation inMicro Milling of Hardened Tool Steel. Annals of the CIRP 55(1):593–596.

[216] Kahnis P, Weinert K (2006) Analysis of Tool Influences on High-Precision-Micromilling of Steel Work-Pieces. Proceedings of the 6th euspen InternationalConference, Baden bei Wien, 0-9553082-0-8128–131.

[217] Weinert K, Kahnis P (2007) Analysis of Tool Influences on DownscaledMilling Processes. in Vollertsen F, Yuan S, (Eds.) Proceedings of the 2ndInternational Conference on New Forming Technology. BIAS-Verlag, Bremen,pp. 481–490.

[218] Biermann D, Kahnis P, Surmann T (2007) Analysis and Simulation of CuttingForces in Downscaled Milling Processes. Proceedings of the 10th CIRP Inter-national Workshop on Modeling of Machining Operations, Reggio Calabria, 493–499.

[219] Weinert K, Kahnis P, Koehler W, (2003) Investigation of Scaling Effects onModelling and Simulation of Scaled Milling Processes.Vollertsen F, HollmannF, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 107–112.

[220] Uhlmann E, Graf vd, Schulenburg M (2007) Scaling of the Milling Process ofTungsten–Copper-Composites – Experimental and Numerical Research. inVollertsen F, Yuan S, (Eds.) Proceedings of the 2nd International Conference onNew Forming Technology. BIAS-Verlag, Bremen, pp. 541–550.

[221] Uhlmann E, Schauer K, Jerzembeck S, (2003) Modelling of Scaling Effectsduring the Scaling of the Chipping Process of a W–Cu-Particle CompoundMaterial.Vollertsen F, Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag,Bremen. p. 177–184.

[222] Graf vd, Schulenburg M, Uhlmann E (2008) Scaling Effects in Milling Opera-tions of Tungsten–Copper-Composites. Proceedings of the International Con-ference on Mechanical and Manufacturing Engineering, Johor Bahru, Malaysia.(in print).

[223] Biermann D, Kahnis P (2008) Influence of a Downscaling of the Tool Diameteron the Dynamic Behaviour of Micromilling Processes. in Byrne G, O’Donnel G,(Eds.) Proceedings of the 3rd CIRP International Conference High PerformanceCutting (HPC)978-1-905254-32-3169–178.

[224] Lai X, Li H, Li C, Lin Z, Ni J (2008) Modelling and Analysis of Micro Scale MillingConsidering Size Effect, Micro Cutter Edge Radius and Minimum Chip Thick-ness. International Journal of Machine Tools & Manufacture 48:1–14.

[225] Kannappan S, Malkin S (1972) Effects of Grain Size and Operating Parameterson the Mechanics of Grinding. Trans ASME – J Eng For Industry 94:833–842.

[226] Malkin S (1975) Specific Energy and Mechanisms in Abrasive Processes.Proceedings of the 3rd NAMRC (North American Manufacturing Research Con-ference), Carnegie Press, 453–465.

[227] Brinksmeier E, Giwerzew A, (2003) Characterization of the Size Effect and ItsInfluence on the Workpiece Residual Stresses in Grinding.Vollertsen F,Hollmann F, (Eds.) Strahltechnik, vol. 24. BIAS-Verlag, Bremen. p. 137–144.

[228] Brinksmeier E, Bleil N (2007) Using the Size Effect of Specific Energy inGrinding for Work Hardening. International Journal of Manufacturing Tech-nology and Management 259–269. 12/1/2/3.

[229] Heinzel C, Bleil N (2007) The Use of the Size Effect in Grinding for Work-Hardening. Annals of the CIRP 56(1):327–330.

[230] Outeiro JC, Kandibanda R, Pina JC, Dillon OW, Jawahir IS (2008) Size Effects inMachining and its Influence on Product Sustainability. Proceedings of the15the CIRP Conference on Life Cycle Engineering, Sydney, Australia, March,658–663.

[231] Vollertsen F (2001) in Buschow J, Kopp R, et al. (Eds.) Metal Forming:Microparts, Encyclopaedia of Materials: Science and Technology. Elsevier,Amsterdam, pp. 5424–5427.

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Size Effects in Manufacturing of Metallic Components