Cutting Rake Angle and Orientation Effects on Surface Residual Stresses in Bone

B. Klutzke1, W. Peter2, T. Schnieders11Department of Mechanical Engineering, Iowa State University2Department of Industrial and Manufacturing Systems Engineering, Iowa State University

Bone machining is an integral aspect of surgeries such as joint replacement. However, machining can result in residual stresses in the bone that may have long term effects on the service of the implant and bone. Although residual stresses in bone are required for the bone to grow, undesirable tensile residual stresses can lead to crack propagation and weakening of the bone. This study focuses on how rake angle and orientation of the bone will affect the resulting residual stresses. Based off of previous studies, results are expected to suggest that the greatest amount of tensile residual stresses will occur in the transverse cutting orientation. Other studies of residual stresses based on rake angle conducted on metals suggest that although positive rake angles provide a better surface finish, they induce more tensile stresses. Therefore, for applications where service life is important, negative rake angles are typically used. It has also been shown that tensile residual stresses decrease as rake angle becomes more negative, and increase with greater positive rake angles. Based on these observations, cutting bone either parallel or perpendicular to the osteons with a negative rake angle will provide the least amount of undesirable tensile residual stresses.

Keywords: Rake Angle, Bone Machining, Orientation, Residual Stress, Surface Effects

Introduction and Literature Review

Stress in the bone is critical for remodeling and regrowth of bone, an important aspect

of healing from total joint replacement surgeries [1]. However, unintentional residual

stresses imposed through machining bone can also lead to undesirable defects and

weaknesses in the bone. The purpose of this study is to combine bone machining with

measuring residual stresses in order to identify surface residual stresses in bone

machining. The study will focus on the effects of machining parameters on the surface

quality of bones. According to Yeager [2] and Childs [3], rake angle and orientation have

considerable influence on the surface morphology of machined bones. Previous studies

focused on measuring surface quality through cutting force, thrust force, and surface

roughness. However, none of the studies focused on the possibility of resulting residual

stresses.

The characterization of the structure of bone has clear impacts on expected results. In

the study conducted by Yeager et al. bone is characterized as both a ceramic material

due to its composition of calcium and phosphate based mineral and as a composite

material as it mimics the basic structure of unidirectional composites. This unidirectional

nature of bones creates differences in results based on the cutting orientation [2].

According to Yeager et al.’s study, the highest cutting force and surface roughness

results from cutting perpendicular to the osteons, due to a much higher transverse

modulus from the columns of osteons, resulting in higher thrust forces and increased

surface damage [2]. This study suggests that induced tensile stresses will most likely

occur in the transverse orientation of bone machining. However, surgeons will likely not

have an option in cutting orientation in the operating room, so the knowledge of existing

residual stresses in all orientations will be beneficial.

Yeager et al. also studied the effects of rake angles, which have been shown to be a

critical machining parameter in determining cutting forces, thrust forces, and surface

roughness [2]. General conclusions from the study compared zero, positive, and

negative degree angles. Zero degree rake angles produced the most severe surface

damage, preventing quantification of surface topography. Positive rake angles resulted

in high surface roughness and exhibited regions with near-surface damage. Negative

rake angles resulted in the lowest surface roughness but induced micro-buckling

through crushing osteons [2]. The simulations modeling performed by Childs and Arola

also suggested that rake angle plays a critical role in bone machining, especially

affecting the cutting force and thrust/cutting force ratio. Childs and Arola’s study found

that cutting edge radius is critical to forces and surface roughness [3]. Although cutting

edge radius will not be specifically studied, it is an important consideration in regards to

tool wear in order to avoid effects to the results.

Residual stresses are important in bone to encourage growth in recreating structure and

geometry. Therefore, multiple studies have focused on measuring and understanding

residual stresses in bone using non-destructive evaluation methods such as X-ray

Diffraction and polychromatic X-ray techniques [1]. These methods work well

specifically for crystalline materials, and since bone tissue has an anisotropic structure

consisting of crystalline hydroxyapatite, these methods can be applied to bone residual

stresses as well [1]. X-ray Diffraction is a simple and widely used method, but requires

sequential removing of a thin layer to obtain information from deeper portions of the

bone [4]. The polychromatic X-ray method uses various beams with a wide wavelength

range. This allows information at deeper levels to be obtained without removing layers

of material [1]. As an initial study, an X-ray Diffraction method will be used to determine

residual stresses in machined bone samples.

The following experimental procedure will be used to measure induced residual

stresses in bone based on multiple machining parameter combinations. Based on

previous studies, it is believed that negative rake angles will produce compressive

residual stresses, and the highest tensile residual stresses will occur with high surface

damage when cutting in the transverse orientation [2].

Materials and Methods

Sample Preparation

Samples for the bone machining will be acquired from bovine femurs. It is important that

throughout the preparation, the bones are preserved as well as possible. When not

using the samples, the bones should be refrigerated in an isotonic saline solution. If

long storage of the bone is required, they can be preserved at room temperature in a

solution of 50% water and 50% ethanol. This will limit the amount of mechanical

changes in the bone to less than 2% decline in Young’s modulus [5]. The bone will need

to be rehydrated before further cutting or testing is conducted. The bone will also need

to be kept hydrated during any cutting processes. This requires that the bones are

irrigated with saline during preparation and machine testing. For large cuts, a hacksaw

or jigsaw is suggested. Damage to the bone from overheating is still possible, but it

should only affect approximately 1 to 2 mm from the cut. This damaged area can be

removed by using wet sand paper, or simply avoided in the specimens that are being

tested [5]. For more precise cuts, a diamond-impregnated wire saw or wafering saw

should be used. Rotation speeds should be approximately 600-800 rpm or comparable

to rotation speeds for cutting aluminum [5][6].

The ability to produce uniform samples is crucial for accurate results, including

uniformity in size, density, orientation and cutting of the samples. Since bone

composition changes throughout the bone, it is important that all samples are taken

from the same section of bone. Bone samples should be cortical compact bone rather

than cancellous spongy bone, so the samples will all be taken from the middle portion of

the diaphysis. In order to obtain these samples, both ends of the femur will be cut off

and the bone marrow will be removed [1]. The selected portion of the bone will be sliced

into cross sections with a height of approximately 30 mm. The cross sections will then

be divided into four sections, each with a width of about 30 mm. Since bovine femurs

have a significantly greater diameter than human femurs, and human femurs are

greater than 30 mm, this will allow the four sections to be cut as relatively flat pieces.

The thickness of the samples will be dictated by the thickness of the cortical bones of

the femurs [1].

These dimensions for the samples were chosen based on standards set in Bone

Research Protocols and Mechanical Testing of Bone and the Bone-Implant Interface,

which were based off of ASTM standards for similar processes using metals [5][6]. The

requirements of the equipment being used were also taken into consideration in

determining sample size and will be discussed further in their respective sections.

Finally, previous studies were referenced, especially Yeager et al.’s Machining of

Cortical Bone and Tadano et al.’s Anisotropic Residual Stress Measurements in

Compact Bone [1][2]. This will allow the results to be compared to previous studies.

After the preparation of bone samples, the experiment will take place in two main

components, first machining the bone with varying machine parameters, and secondly

measuring the residual stresses in the bone using X-ray Diffraction.

Bone Machining

The first component of the experiment will conduct bone machining

on samples with varying orientations and rake angles, similar to the

study conducted by Yeager et al. [2]. Three orientations will be

tested, namely parallel, perpendicular, and transverse orientations,

shown respectively as a, b, and c in Figure 1. Rake angles tested

will consist of both positive and negative angles with 6 angles

between -30 and +30. Zero will not be tested due to the

conclusions from Yeager et al.’s study showing extensive damage

with no angle [2]. Based on these identified parameters, there will

be 18 unique combinations that will need to be tested. A power

calculation for a general full factorial design was conducted using

Minitab Software and the direction of a professional statistician. This accounted for a

design that has multiple varied parameters with more than 2 levels, and with runs

conducted for each combination of parameters [7].Equal variance is assumed between

sample combinations, and by using a sample size of 36, it was determined that

differences with a standard deviation of at least 2.99 can be detected between trials [8].

By running tests for each combination of parameters, a regression model can be

developed for each orientation.

Figure 1: Orientations of Bone

Sample requirements for machining are minimal since the vice for the cutting machinery

can be adjusted within the needed specification. The only other concern is that the

sample is large enough that the experimental machined effects can be isolated from the

sample preparation cuts. The sample size will be approximately 30 x 30 mm and the

cutting from sample preparation should only affect 2mm on the edges [5]. Since the cut

made on the sample will only be approximately 3 mm deep and 3 mm wide, similar to

the cuts made in Yeager et al.’s study, there will be plenty of space on the sample piece

to keep the effects of the different cutting processes separated [2].

The samples will be loaded individually in the designated orientation into the adjustable

vice of either the chosen shaper or mill. Uncoated carbide tool inserts will be used and

adjusted for the designated rake angle [2]. Both a shaper and a mill will allow constant

parameters such as cutting speed and cut depth to be kept steady, while accurately

controlling and changing the varied parameters, such as the orientation and designated

rake angle. They will also provide a controlled, simple, and linear cutting motion. Bone

must remain hydrated with saline solution during all experimental machining of the

bone. It is also crucial to avoid any other surface defects during machining that may

affect the induced residual stresses from the intended cut [9]. During sample machining,

time, cutting force, and thrust force will all be measured in order to provide a

comparison to Yeager et al.’s previous study and identify correlations between these

forces and residual stresses [2].

X-ray Diffraction

The second component of the study will measure residual stresses in the machined

bone samples using X-ray Diffraction. X-ray Diffraction is a very common method of

measuring residual stresses in crystalline materials, as it provides non-destructive and

accurate results [10]. As previously discussed, bone tissue is made up of

hydroxyapatite, which is a crystalline material [1]. Therefore residual stresses in bone

can be measured using an X-ray Diffraction method by identifying changes in the lattice

structure of crystalline materials. By comparing lattice patterns of machined bone to the

lattice patterns of powdered bone, which should have no residual stresses, differences

in the structure can be identified and correlated to residual stresses [1]. Sample

requirements for X-ray Diffraction require that a suitable flat region of 500 μm is

available that is 1-2 mm away from the edge to avoid effects from sample preparation,

the sample is able to fit on the sample stage to allow tilt of the machine, and there is

homogeneity throughout the bone samples. It is also important to avoid any extra

surface modification, such as secondary abrasion, corrosion, or etching. Finally,

temperature should be kept relatively constant to avoid thermal expansion and changes

in residual strength [9].

Each sample will be loaded and secured onto the sample base of an X-ray

Diffractometer. The sample will be aligned with the goniometer, in order to allow rotation

around the analyzed point [9]. The sample will then be exposed to an X-ray beam which

will interact with the crystal lattice in order to create diffraction patterns. By comparing

the collected diffraction patterns to a baseline of powdered bone from the same sample

source, a shift in inter-planer spacing of lattice patterns can be detected, suggesting

induced strain within the material [1]. By using Bragg’s law shown in Equation 1, the

precise measurement of the inter-planer spacing can be determined.

2d∗sin (θ )=nλ Equation 1

In this equation, d represents the inter-

planer spacing, θ represents the angle of

diffraction, and λ represents the

wavelength of the incident radiation. These

components are shown in Figure 2. When

the Bragg condition is satisfied, n will be an integer and visible peaks will be present

since the scattered rays from different planes will be in phase [11].

When d is determined for both the sample and the powdered reference, the strain can

be calculated simply as shown in equation 2, where dn represents the inter-planer

spacing for the sample, and d0 represents the inter-planer spacing for the powdered

reference [11].

ϵ=(dn−d0 )d0

Equation 2

Residual stresses can then be determined with Hooke’s law and an estimate of Young’s

modulus [11]. Estimations for Young’s modulus are approximately 11-21 GPa for

longitudinal cortical bone, and 5-13 GPa for transverse cortical bone [12]. Hooke’s Law

is shown in equation 3, where σ represents stress, E represents Young’s modulus, and

ϵ represents strain [11].

Figure 2: Bragg's Law

σ=Eϵ Equation 3

These calculations are all conducted through software programs connected to X-ray

Diffraction machines. The above equations are only a simple representation of the

calculations conducted through the software. This will allow an accurate read out of

residual stresses for all tested samples.

Results

Good measurements of residual stress are expected, since using X-ray Diffraction

methods have been used, just not in relation to bone machining [1][4][13]. This

experiment is an extension of Yeager et al.’s experiment on machining bone [2].

Therefore, it is expected to find similar results in regards to machining parameters. The

effects of orientation are likely to remain the same, with much higher thrust forces and

the largest range in surface quality when cutting transverse to the osteons. More crack

tips and divots will result in more undesirable tensile residual stresses [2]. In Yeager et

al.’s study, positive rake angles resulted in higher surface roughness, creating bone

fractures near the surface of the bone. Crack propagation initiated from the surface

defects suggests the presence of tensile residual stresses. Negative rake angles

resulted in less surface roughness than positive rake angles. Although there was the

presence of micro-buckling from crushing osteons, there was no identified sub-surface

damage. These findings suggest that negative rake angles may result in compressive

instead of tensile residual stresses [2]. Using the resulting data, tool geometry can be

proposed based on a desirable rake angle to use. It will also allow surgeons to pick a

rake angle based on the amount of desired roughness on the machined bone to allow

for bone integration with mesh or an implant.

Expected results can also be inferred from studies correlating rake angle to residual

stresses in machining metals. According to Lo’s study, tensile stress in the cutting

direction on the work piece surface will increase as the tool rake angle increases [14].

Dahlman et al.’s study found that greater negative rake angles resulted in larger

induced compressive stresses, and a larger area of the piece affected under the surface

[15]. Miguelez et al. showed that tensile residual stresses decrease as rake angles take

larger negative values. He also suggested that positive rake angles generally provide

machined surfaces with higher quality than negative rake angles, and are therefore

often chosen for finishing operations. However, when quality requires a long service life,

aspects such as residual stresses are more important, and therefore negative rake

angle tools are often used for these applications [16].

Discussion

Although there are no accessible studies that directly related the effect of bone

machining to degenerative diseases, there are studies that dealt with the correlation of

degenerative diseases like osteoporosis and osteoarthritis with bone machining. Both F.

R. Ong et Al. [17] and S. Hloch et. Al. [18] discuss the importance of the mechanical

behavior exhibited by cancellous bone and cortical bone under the effects of metabolic

and degenerative disease. Cancellous bone has a more porous structure, and therefore

a greater surface area, than that of cortical bone. It is this feature that causes

degenerative diseases to affect cancellous bone in a more accelerated rate [18].

The effectiveness of a surgical operation involving bone machining depends on the

selection and effective technique of bone cutting [18]. These two factors, among others,

influence both the quality and the biological potential of the generated surface.

According to Hloch et al. the most common reason for subsequent implantation failure is

a result of an aseptic loosening of the endoprosthesis. However, long term success also

lies in the used surgical techniques, the method of cutting and machining of the bones,

and their properties [17] [18].

The physical makeup of bone creates a natural defense against fracture in the

transverse direction through the use of crack deflection [19]. In particular, cortical bone,

comprised of osteons, are capable of deflecting a propagating crack up to 90o. This

defense is capable of reducing the driving force of crack advancement up to 50% when

compared to an undeflected crack [20]. Additionally, it has been shown in the work of

Ritchie et al [21], Yeager et al. [2] and Childs et al. [3] that size and orientation of

osteons have an influence on the mechanical properties of bone. Raetz hypothesizes

that smaller, more densely packed osteons will yield higher fracture toughness values

[19].

Osteoporosis results from the loss of bone tissue and therefore becoming less dense

and more likely to fracture. It is therefore hypothesized that bone machining with

positive rake angles would be correlated to the advancement of degenerative diseases.

As discussed earlier, positive rake angles create more surface roughness by creating

fractures in the bone. This is more likely to cause tensile residual stresses which will

lead to crack propagation.

Conclusions

Expected results of this study have been inferred from both studies relating to bone and

to metal. The bone studies have focused on both machining effects from rake angle and

orientation, as well as measuring residual stresses in bone. However, no study has

been conducted to measure residual stresses based on bone machining parameters.

Therefore, results were inferred based on surface quality results from machining. By

studying the effects of rake angle on residual stresses in metal, conclusions were

identified that supported the inferred results for bone. These conclusions suggested

that:

1) Cutting in the transverse direction to the osteons will result in the most tensile

residual forces.

2) Positive rake angles will result in significant tensile residual stresses, whereas

negative rake angles will result in more desirable compressive residual stresses.

3) Tensile residual stresses will increase as the tool rake angle becomes more

positive.

4) Greater negative rake angles will result in larger compressive residual forces that

will impact a deeper portion of the cutting sample.

5) Tensile residual stresses will decrease with larger negative rake angles.

6) Although positive rank angles are often used for finishing metals since they

provide good surface qualities, negative rake angles are generally used for

applications that require a longer service life.

References

[1] Tadano, S. and Todoh, M. Anisotropic Residual Stress Measurements in Compact Bone Using Polychromatic X-ray Diffraction. IUTAM Symposium on Synthesis in Bio Solid Mechanics. 1999.

[2] Yeager, C., Nazari, A. and Arola, D. Machining of Cortical Bone: Surface Texture, Surface Integrity, and Cutting Forces. Machining Science and Technology, 12:1 (2008), 100 — 118

[3] Childs, T. H. C. and Arola, D. ‘Machining of Cortical Bone: Simulations of Chip Formation Mechanics Using Metal Machining Models', Machining Science and Technology, 15: 2 (2011), 206 — 230

[4] Tadano, Shigeru and Okoshi, Taro: Residual stress in bone structure and tissue of rabbit’s tibiofibula. Bio-Medical Materials and Engineering, p. 11-21. January 2006.

[5] An, Yuehuei H., and Robert A. Draughn, eds. Mechanical Testing of Bone and the Bone-implant Interface. Boca Raton: CRC, 2000. Print.

[6] Ralston, S. and Helfrich, Miep H. Bone Research Protocols. London: Humana Press, 2012.

[7] Morris, Max. Design of Experiments: An Introduction Based on Linear Models. Boca Raton: CRC, 2011. Print.

[8] Minitab Inc. (2010). Software. <www. minitab.com>

[9] Prevey, Paul S. X-ray Diffraction Residual Stress Techniques. Lambda Research, Inc.

[10] Clark, C, and Dutrow, B. Single-crystal X-ray Diffraction. Geochemical Instrumentation and Analysis. December 15, 2013.

[11] Fitzpatrick, M.E. et al. Determination of Residual Stresses by X-ray Diffraction - Issue 2. National Physical Laboratory. Sept. 2005.

[12] "Mechanical Properties of Bone." Dissemination of IT for the Promotion of Materials Science. University of Cambridge, 2013. Web. 28 Apr. 2014. <http://www.doitpoms.ac.uk/tlplib/bones/bone_mechanical.php>.

[13] Yamada, Satoshi and Tadano, Shigeru. Effects of growth on residual stress distribution along the radial depth of cortical cylinders from bovine femurs. Journal of Biomechanics, Vol. 46, Issue 13. September 2013.

[14] Lo, Ship-Peng. An analysis of cutting under different rake angles using the finite element method. Journal of Materials Processing Technology, p. 143-151. 2000.

[15] Dahlman, Patrik, et al. The influence of rake angle, cutting feed and cutting depth on residual stresses in hard turning. Journal of Materials Processing Technology. Vol. 147, Issue 2, p. 181-184. 10 April 2004.

[16] Miguelez, M. H. et al. Residual Stresses in Orthogonal Cutting of Metals: The Effect of Thermomechanical Coupling Parameters and of Friction. J Therm Stresses, 32(2009) p. 1-20.

[17] Hloch, S. et al. Advances in (Un)Conventional Engineering of Biomaterials and Nursing Care. DAAAM International Scientific Book (2013) p. 297-316.

[18] Ong, F. R. et al. Evaluation of bone strength: correlation between measurements of bone mineral density and drilling force. IMechE 214 (2000) p. 385-399.

[19] Raetz, M. Osteon Size Effect on the Dynamic Fracture Toughness of Bone. SEM Annual Conference (2010) p. 167-168.

[20] Nalla, R.K. et al: Mechanistic fracture criteria for the failure of human cortical bone. Nat, Mater. v 2, p164 (2003)

[21] Ritchie, R.O. et. al: A fracture mechanics and mechanistic approach to the failure of cortical bone. Fatigue and Fracture of Engineering materials and Structures. 28,4. (2005).