Prediccion Fatigue Traccion

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Predicting fracture and fatigue crack growth propertiesusing tensile properties

Bahram Farahmand a,*, Kamran Nikbin b

a Boeing Company, Huntington Beach, CA, USAb Department of Mechanical Engineering, Imperial College, London SW7 2AZ, United Kingdom

Received 3 January 2007; received in revised form 17 July 2007; accepted 12 October 2007

Abstract

The safe-life assessment of components requires information such as the plane stress ( Kc), plane strain (KIc), part-through fracture toughness (KIe), and the fatigue crack growth rate properties. A proposed parametric/theoreticalapproach, based on an extended Griffith theory is used to derive fracture toughness properties and generate fatigue crackgrowth rate data for a range of alloys. The simplicity of the concept is based on the use of basic, and in most cases avail-able, uniaxial stressstrain material properties data to derive material fracture toughness values. However since the meth-odology is in part based on an empirical relationship a wide ranging validation with actual data is required. This paper usessteel, aluminum and titanium based alloys from a pedigree database to quantify material properties sensitivity to the pre-

dictions for KIcand Kcand the subsequent estimation ofD

Kth threshold and the Paris constants, Cand n values. A sen-sitivity analysis using experimental scatter bounds show the range of da/dNpredictions can be achieved. It is found KIc/DKthratios designated as a has a range of 525 irrespective of tensile ductility, ef, and is insensitive to it. The value ofDKthfor all the alloys considered was found to be proportional to the final elongation, ef, and an empirical relationshipdescribing DKthas a function ofefwas established. Furthermore it is suggested that, with the knowledge of appropriatetensile properties and the estimated range of KIc/DKth ratios for the different alloys applying this method could be anappropriate tool that can be used to conservatively predict fracture and fatigue in similar alloy categories. Thus helpingto reduce costs and optimize the number of experimental tests needed for alloy characterizations. 2007 Elsevier Ltd. All rights reserved.

Keywords: Fracture toughness; Griffith theory; Virtual testing; Fatigue crack growth; Stressstrain curve; Uniaxial; Tensile elongation

1. Introduction

Deriving verifiable and stable materials properties data is of the utmost importance in both designing aswell as in residual life assessment modeling and predictions of industrial components. Many design and lifeassessment methods need verifiable fracture toughness and fatigue crack growth properties to implement in

0013-7944/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfracmech.2007.10.012

* Corresponding author.E-mail address:[email protected](B. Farahmand).

Available online at www.sciencedirect.com

Engineering Fracture Mechanics 75 (2008) 21442155

www.elsevier.com/locate/engfracmech
mailto:[email protected]:[email protected]


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the required calculations and to execute the relevant computer codes such as NASGRO [1]. Fracture testsunder the testing standard procedures require detailed specimen preparation, pre-fatiguing the notch, fatiguecrack growth rate measurements and interpretation of raw data, which all are costly and time consuming. Fur-thermore, in order that valid material property data is produced for each case specific material batch, typicallya substantial number of tests need to be performed. Therefore, any method that can improve and optimize thisprocess, and reduce the number of experimental tests, will help reduce number of tests an overall costs withoutcompromising any safety issues.

The proposed technique uses fundamental fracture-mechanics-based reasoning to establish a link betweenplastic damage and energy dissipation development in uniaxial stressstrain data and the materials fracturemechanics properties. The method uses the energy dissipated in the uniaxial failure to predict the fracturetoughness properties (Kcand KIc) parameters in a cracked geometry on the assumed basis that plastic damageis nearly the same in the uniaxial failure as it is locally at the crack tip. Further, it uses the predicted K

cand

KIcto derive the fatigue crack growth properties and derive the Paris constants for the material. In order toestablish and validate this methodology as an accepted industrial practice, calculations have been performedover a range of materials and specimen geometries [2]. However in order to be fully acceptable for differentclasses of materials a sensitivity exercise has been undertaken in this paper to validate the technique. In addi-tion the analysis should be used to attempt to understand the underlying physical reason for the observedrelationship between uniaxial stress/strain data and fracture properties of cracked components and in turnthe fracture properties with the Paris law fatigue properties. Several aluminums, titanium, and steels wereselected from the NASGRO[1] material database and the experimental Kcand KIc, da/dNversus DKvaria-tions were compared with the proposed analytical model. Based on this concept two computer codes, calledfracture toughness determination (FTD) and fatigue crack growth (FCG) were established in collaborationwith NASA[3]. The wide range of data compared using this method could then be used to widen the valida-

tion range.

2. Analysis to predict fracture toughness

It has been shown previously [4,5] that material residual strength capability curve (a plot of fracturestress versus half a crack length) can be generated through the Griffith theory for an elastic media. Thishas been extended to account for the presence of plastic deformation at the crack tip [6,7]. Energy absorp-tion rate at the crack tip process zone could be assumed to have a similar mode of deformation of uni-axial specimens. Hence the material stressstrain curve of a uniaxial specimen can reflect the local energydissipation profile within the process zone and can describe the fracture behavior of a cracked specimen aslong as the stress and strain distribution and the subsequent energy balance is satisfied. Similar ideas of a

process zone have been previously considered at high temperatures [6] whereby creep cracking within a

Nomenclature

c half crack lengthn strain hardening coeficient in Paris equationC material constant in the Paris equationr applied stressrT true stressrTU true stress at ultimaterUF stress between ultimate& fractureeT true strainePN plastic strain at neckingeTU, eTL, eTL true strain at ultimate, limit & fracturek, l, b thickness correctionsDK stress intensity factor

B. Farahmand, K. Nikbin / Engineering Fracture Mechanics 75 (2008) 21442155 2145


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process zone can be described by the creep uniaxial and failure behavior of uniaxial creep test taken as ananalogy for time independent stress/strain tensile test. In the present case the failure range in the processzone is due to the elastic/plastic loading in a uniaxial tensile test specimen whereas in the creep case thecriterion for the damage process is a time dependant elastic/plastic/creep phenomenon since it has beenshown that creep and plasticity can be treated is a self-similar manner using non-linear fracture mechanics

concepts [8,9].Thus in a tensile stress/strain test case the total energy per unit thickness absorbed in plastic strainingaround the crack tip, UP, can be therefore written as

UP UFUU 1

where UFand UUare the energy absorbed per unit thickness in plastic straining of the material beyond theultimate at the crack tip and below the ultimate stress near the crack tip, respectively (Fig. 1). The rate of en-ergy absorbed at the crack tip in terms ofUFand UU, described by Eq. (1), can be rewritten as

oUEUSUFUU=oc0 2where UE and US are the total available energy and energy necessary to create two new crack surfaces.

g1= oUF/ocandg2= oUU/ocare the rates at which energy is absorbed in plastic straining beyond the ultimatestress at the crack tip and below the ultimate stress near the crack tip, respectively. The extended Griffith equa-tion[6,7]in terms ofg1and g2can be rewritten as

pr2c

E 2T oUF

ocoUU

oc 3

where oUS/oc= 2T, the work done in creating two new crack surfaces (Tis the surface tension energy of mate-rial). Having fracture stress, r, and half critical crack length, c, on hand, the material fracture toughness canbe calculated. The derivation and definition of terms describing this relationship in Eq. (4) are available inreferences [6,7], where the true stress, rT, and strain, eT, values were calculated from the engineering stressstrain curve.

c Epr2l

f2Tg1g2g 4

Stress

Strain

Uniform

Deformation

Non-uniform

Deformation

UUUF

fU

U

f

Non-uniform

straining

Uniform

straining

A center crack in a wide plate

Areas associated with the uniform and

Non-uniform straining

Stress

Strain

Uniform

Deformation

Non-uniform

Deformation

UUUF

fU

U

f

Non-uniform

straining

Uniform

straining

Stress

Strain

Uniform

Deformation

Non-uniform

Deformation

UUUF

fU

U

f

Stress

Strain

Uniform

Deformation

Non-uniform

Deformation

UUUF

fU

U

f

Non-uniform

straining

Uniform

straining

Non-uniform

straining

Uniform

straining

A center crack in a wide plate





Fig. 1. Full uniaxial stressstrain curve and crack tip deformation process zone where the deformation and rupture occurs locally.

2146 B. Farahmand, K. Nikbin / Engineering Fracture Mechanics 75 (2008) 21442155


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where

g1rUFePNhFk 5and

g2 n

n1 rTUeTU 1 rT

rTU

n1" #h eTFeTL

eTUeT

eTU

eTL

n1=n1

" #b !Kvbr

ffiffiffiffiffipc

p 6

A fracture toughness determination (FTD) software has been developed[3] using this methodology. Thesoftware is able to generate the plane strain and stress fracture toughness and plots the variation of fracturetoughness, Kc, versus plate thickness, B.Fig. 2shows the sequence of tests that may be required to establishthe fracture toughness dependency with respect to the thickness and plate dimensions for a given material andheat treatment. The actual number of tests will be multiples of this depending on the accuracies needed. Alsoin some cases when adequate material thickness is not available for a valid KIctest, the JIctest (the methodshown inFig. 2) can be implemented to derive the KIc.

3. Analysis to predict fatigue crack growth rate curve

The testing procedures in the ASTM E1820 and E647 are currently used to obtain fracture toughness andfatigue crack growth rate properties, respectively, through physical testing. The proposed technique identifiesthe relevant parameters affecting the micro-mechanical behavior within a plastic process zone and relates it toplastic damage in uniaxial tensile tests. It then uses the data from the uniaxial stress/strain test to derive thematerials fracture toughness values.

Numerical and analytical methods and test indicators such as the elastic, plastic and necking regions in atensile test are used to predict these material properties. The Kcvalue can be obtained through the ExtendedGriffith theory which includes the effects of local plasticity on K. Using data derived from the analysis of awide range of tensile data it has been established[2]for aluminums that a relationship exists betweenKth(DKthfor R= 0) and the plane strain fracture toughness, KIc, which allowed values for a=KIc/DKthto be derivedfor a range of alloys. It should be noted that presently the method is dependant on experimental testing, albeituniaxial tests, to develop the model. Therefore, until an understanding of the micro-structural and the physicalproperties exists, the model cannot be said to be fully analytical. It is, however, a significant step towards

achieving a method to reduce and optimize a wide ranging materials testing program.

M(T)

C(T)

or

Thickness, B

Plane StrainPlane Stress

KIc

JIc

KcKc

C(T)

Kc

KIc

KIc is thickness, plate width, and crack

length independent Kc is thickness, plate width, and crack

length dependent

KIc = [(E/(1- 2

)JIc]0.5

C(T)

Kc

Kc

2

Fig. 2. Variation of fracture toughness versus the plate thickness (several fracture toughness tests are needed to establish the trend).



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4. Example of fracture toughness determination (FTD) for a range of alloys

Three sets of alloys of varying properties and ductilites were investigated in this exercise. These were alu-minum, titanium and steel alloys.Table 1shows the range of alloys used with available failure elongation andfracture properties. In all cases data on alloys with full stressstrain curves were unavailable to establish frac-

ture toughness through the proposed technique to identify theK

Ic/DK

threlationships needed for deriving thefatigue crack growth properties. As an example analysis for an aluminum alloy is presented to highlight theFTD methodology.Fig. 3shows typical examples of uniaxial tensile behavior for two aluminum alloys.

Material fracture toughness as a function of part thickness was calculated for a range of aluminum alloysusing the FTD software[3]. Effect of plate width and crack length on fracture toughness (narrow and wideplates) was compared with the data from the NASGRO database[1]. Fig. 4 shows an example of fracturetoughness versus plate thickness for two aluminum alloys compared to NASGRO data. It should be noted

Table 1Tensile and fracture properties for a range of alloys used in the analysis ( Kunits in MPa

pm)

Materials KIc Kth KIc/Kth % Elongef

AISI 304, Ann Plt & Sht, Cast; 550F Air 137 5.5 25 25AISI 304, Ann Plt & Sht, Cast; 800F Air 91 6.4 14 25AISI 316, Ann Plt & Sht, Cast; 600F Air 137 5.46 25 25AISI 316, Ann Plt & Sht, Cast; 800F Air 91 7.3 12 25PH13-8Mo ( H1000; Plt, Forg, Extr) 91 4.55 20 1615-5PH (H1100; Rnd, C-R) 73 4.6 16 16Inconel 706 (Forg and extrusion) 85 12 7 27280 Maraging steel 64 2.73 23 11AF1410 100 3.1 32 124340 steel (Ftu = 1518 Mpa) 72.8 4 18 1317-4PH, H1100 (Ftu = 1035 Mpa) 82 3.6 23 162014-T6 (Plt & Sht, L-T) 24.5 2.5 10 107075-T7351 (Extr; L-T) 30 2.7 11 12Ti-55 ( Plt & Sht) 45.5 4.5 10 18Ti-70 ( Plt & Sht) 45.5 4.5 10 16Ti5Al2.5Sn 59 4.5 13 13Ti2.5Cu STA 45.5 4.6 9.9 15.52024-T3 (Clad, Plt & Sht, L-T) 30 2.6 12 10Ti8Al1Mo1V 50 3.1 13 132014-T6 (Plt & Sht, L-T) 30 2.6 12 11.52124-T851 27 2.7 10 86061-T651 (Plt; L-T & T-L) 24.6 3.2 8 147075-T7351 (Extr; L-T) 30 2.7 11 12

0

100

200

300

400

500

600

0 0.025 0.05 0.075 0.1 0.125 0.15

Stress,

MPa

Stress,

MPa

2014-T6 Aluminum -RT

(Longitudinal)

0

100

200

300

400

500

0 0.025 0.05 0.075 0.1 0.125

Strain, mm/mm Strain, mm/mm

2219-T87 Aluminum - RT

(Long Transverse)


(Longitudinal)


(Longitudinal)

2219-T87 Aluminum - RT

(Long Transverse)

Fig. 3. Typical full stressstrain curve for 2219-T87 and 2014-T6 aluminums.



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that the NASGRO curve for a single material are typically not based on numerous tests at different thicknessesthrough which a smooth curve passes, assuming a relationship betweenKcand thickness observed from multi-ple materials.

In all cases the FTD analysis assumes no net-section yielding across the specimen width under monotonicload. Note that the fracture toughness values, Kc, in the NASGRO material library are available via an empir-ical equation proposed by Vromen[10]as a function ofKIcand material yield value, which represent the lowerbound ofKcvalues for a given part thickness. Fig. 5shows the fracture toughness versus thickness data andthe curve fit plot obtained from NASGRO manual. This figure includes numerous test data which umbrellas

whole range of plate width and crack lengths, a. The estimated empirical NASGRO curve fit seems to repre-sents the typical values ofKc. The upper bound value of data shown inFig. 5must be associated with largercracks and wider plates. For this reason the FTD has the option of plotting the fracture toughness versusthickness variations for plates of different width. The narrow plate represents the fracture toughness associatedwith small cracks where the residual strength can be as high as 75% of material yield value. In Fig. 5it is seenthat a relatively good agreement of a factor of about two difference in KIc/Kcexists between the physical test-ing taken from the NASGRO best fit[1]and the present analysis shown inFig. 4.

5. Estimation of threshold Kth using predicted KIcvalues

Fig. 4shows that theKIcfrom NASGRO and predictions are close to each other for the aluminum data con-

sidered. Therefore ifKIcis not available through the ASTM testing standards, it can be derived conservatively

2014-T6 Aluminum Alloy

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90

Thickness - mm.

FTD (Wide Plate)

FTD (narrow Plate)

NASGRO

2219-T87 Aluminum Alloy

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90

Thickness (mm)

FractureToughne

ss-MPa(m)0.5

FractureToughness-MPa(m)0.5

FTD (Wide Plate)

FTD (Narrow Plate)

NASGRO

Fig. 4. Example of fracture toughness versus plate thickness for two aluminum alloys compared to NASGRO data[1].

Fig. 5. Measured fracture toughness versus thickness for several crack length of 2219-T87 aluminum[1].



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through this analysis by using data from the stressstrain curve. Studying the threshold values of more thanhundred tests from different metallic alloys, the quantity Kth was found to be related to the material planestrain fracture toughness, where KIc. = aKth.Fig. 6shows the NASGRO value ofKthfor several aluminum,titanium and steel alloys.

FromFigs. 6 and 7it can be seen that the NASGRO value ofKthis material dependent and have varying

ranges for aluminum, titanium and steel alloys. From the experimentalK

th values inFig. 6mean values ofDKth= 2.5 MPapm for aluminum alloys, DKth= 4 MPapm for the titanium alloys and DKth= 5 MPapmfor steels are found. The scatter for the steels are seen to be highest (because of different types of steel withwide range of tensile properties) and for Al the lowest.

Looking at the stressstrain curves for several aluminums, the final elongation for most aluminums fallbetween 8% and 12% with KIcvalues range from 20 to 27 MPa

pm. This is one reason for aluminums alloys

having the minimum amount of scatter as indicated inFig. 6when compared with the steel. The range ofa foraluminums and titanium falls approximately between 8 and 14 and 9 and 16, respectively (see Fig. 7). Therange ofa for variety of steels is shown inFig. 8and their lower and upper values are 5 and 25, respectively.

To understand the physical relationship that may exist between tensile elongation and fracture behavior thecorrelations between them have been established for the different alloys shown in Table 1. It should be notedthatTable 1has narrow range of ductility due to the lack of available Kth and efvalues for more ductile or

brittle alloys. However it is important to understand that the failure elongation values presented are withina practical range for engineering alloys. Invariably any material outside this range could render the alloy eithervery brittle or too ductile.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 20 40 60 80 100

Number of Materials

Kth(Mpam

0.5)

Steel Titanium Aluminum

Fig. 6. NASGROKthvalues for a range of steel, Al and Ti alloys.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0 10 20 30 40 50 60 70

Number of Tests

KIc/Kth()

Titanium

Aluminum

Fig. 7. aValues for a range of Al and Ti alloys.



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Fig. 9shows the relationship between tensile elongation and Kthfor the data of different alloys. In addition,Fig. 10shows the relationship ofa to tensile elongation for the different alloys in Table 1. It can be observed

that fairly good correlation for these properties with respect to tensile elongation exist inFig. 9which shows alinear relation betweenKthand tensile elongation (taken from standard gauge lengths[1]). This suggests thatthis relationship is material independent within the range examined. It should be noted that a necking ratio atfailure could be a less geometry dependent than elongation. However as data for necking is not always avail-able it would be difficult to make direct comparisons at this stage. InFig. 10the relationship betweenaandfailure elongation is investigated. Given the range of failure strains of a factor of over three the best fit equa-tion shown inFig. 10gives a very good indication that a is relatively insensitive to failure elongation. As anengineering method it can be used to identify an a lower limit even though there is a scatter of a factor of 3 in

0

5

10

15

20

25

30

0 20 40 60 80 100

Number of tests

KIc/K

th

()

Steel

Fig. 8. Predicteda values for a range of steel alloys containing a wide scatters.

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

5.0 10.0 15.0 20.0 25.0 30.0

elongation%

Kth(MPam

0.5)

. Steel

Aluminum

TitaniumBest fit

Kth = - 0.6337 + 0.3143

Fig. 9. Relationship ofKthdata and tensile elongation fromTable 1.

1

10

100

5 10 15 20 25 30

elongation %

KIc/Kth

()

SteelAluminumTitaniumBest Fit

= 16.348 -0.0685 f

Fig. 10. Relationship ofaversus tensile elongation for data in Table 1.



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a. This scatter can be reduced if individual alloys are considered. For example the Al and Ti alloys exhibit a

lower range than the maximum seen in the steel. Hence correlations inFigs. 9 and 10suggest that the tensileelongation could be an important factor in trying to understanding the physical fracture properties in thesealloys as well as them being used as a practical engineering tool to improving predictions for fatigue andfracture.

Using the best fit equations shown in theFigs. 9 and 10 it would possible to get a material independentmean values ofa and Kth using available tensile ductility. The best fit equations give

Kth 0:63370:3143ef 7a16:3480:0685ef 8

Eq.(7)gives a very good indication of a linear relationship between Kth and ef. This will allow FCG to useestimated Kthfrom Eq.(7)to generate the total da/dNcurve.

6. Fatigue crack growth rate (FCG) estimation

Typically in a test a complete fatigue crack growth rate curve contains three regions. The primary and ter-tiary regions (Fig. 11) are sensitive to the stress ratio, Rand material micro-structural dependence. The sec-ondary region is not and is invariably described by the Paris equation, where Cand nare material constantsand DKis the stress intensity factor range (Eq. (9))

da=dN CDKn 9Appropriate material properties taken from experimental tests of the aluminum alloys are then introduced foruse in the deterministic analyses. The method later was extended to other aerospace alloys. The methodology

used to generate the fatigue crack growth curve for the threshold and Paris regions are described below. Aswas mentioned earlier the DKvalue in the accelerated region is related to the critical value of the stress inten-sity factor, Kc, and is plate thickness and width dependent. Moreover, from the derivation ofKIcby the ex-tended Griffith theory, the lower portion of fatigue crack growth rate curve, Kth, can be estimated for the stressratio,R = 0. Because of the difficulty of obtaining full stressstrain curves for several materials, it was decidedto use the value ofKIcfrom the NASGRO database for calculating the Kthvalue.

7. Analysis to predict steady state paris region for FCG

To estimate the Paris region it is possible to do it by using the FTD code where full uniaxial data are avail-able or from a pedigree fatigue data set. It can be shown that for estimating the Paris region the two quantities

Kc&KIcmust be available. These two quantities will be helpful to establish two points in the Paris region. The

Accelerated Region

(Thickness dependent)

K

da/dN

(1)

(2)

Kth

K K

Paris Region

Threshold

Region

Accelerated Region


K

da/dN

(1)

(2)

Kth

K K

Accelerated Region


K

da/dN

(1)

(2)

Kth

K K

Paris Region

Threshold

Region

Fig. 11. Three regions of the da/dNcurve (threshold, Paris and accelerated regions).



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two points inFig. 11(the lower and upper points of Paris region corresponding to points 1 and 2) have uniqueproperties which are common among many aluminum alloys. The lower point in the steady crack growth rateregion, just before getting into the threshold zone of the fatigue curves (point 1 ofFig. 11), has a materialindependent property so that the ratio of the stress intensity factor, KL, at the mean lower bound pointand the threshold value, Kth, (DKL/DKth for R= 0) is1.125 for the crack growth rate per cycle,

da

/dN

2.54E-6 mm/cycle (1.0E7 in./cycle) in aluminum. In the upper region of the da

/dN

curve (at theend of the steady crack growth Paris region, point 2 ofFig. 11), the ratio of the upper bound stress intensityfactor, KU, and its critical value, Kc, (DKU/Kcfor R = 0) is found to be0.9 for the da/dN0.127 mm/cycle(0.005 in./cycle). Having the two quantities Kcand KIcavailable (either through the extended Griffith theoryor NASGRO database) the two points in the Paris region can be generated. Hence, theCand n of Eq.(9)canbe determined.

Note that the KIcvalue is used to estimate the Kthvalue. The above assumptions used for establishing theParis region is also applicable to Titanium and Steel alloys. The total predicted fatigue crack growth curve canthen be plotted using Eq.(10), where the fracture parameters and constants are taken from the estimatedKIc,Kc,Kth, and the Paris constantsCandnvalues. For any other range ofR-ratios the Newman closure equation,f, [11]can be used to establish the full fatigue crack growth rate curve when R5 0

dadN

C1fn

DKn

1DKth

DK p

1Rn 1 DK1RKc q 10

In all cases the constants pand q of Eq.(10)were taken as 0.5 and 1, respectively.

8. Comparison of predicted bounds with experimental fatigue crack growth data

The computer program[3] which can run the simulations of the model and also on the world wide web(www.alphastarcorp.com) was made available in order to verify a number of test cases. The input of datacan be treated as deterministic data or as probabilistic bounds of the data. Based on the above-mentionedassumptions (construction of accelerated, Paris, and threshold regions), the fatigue crack growth curves for

three alloys are established and then compared with fatigue crack growth test data in NASGRO database.The use of statistical methods give further confidence to the methodology and is therefore crucial to any

sensitivity analysis that would be needed in design and life estimation methods. In obtaining material prop-erties through physical or virtual testing, it is always expected to observe some amount of scatter on fracturetoughness and fatigue crack growth values due to material variations that can vary through heat lots when thematerial is processed. Lesser amount of variability can also be observed in test coupons that have beenmachined from a given plate of a given manufacturer by a specified heat lot. Figs. 7 and 8 give the rangeof scatter that could exist in the parametera for the different alloys. It should be noted that in the present casethe comparison is made with a wide variation of alloys of different ductilities. It is expected that in case specific

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1 10 100

K - MPa (m)0.5

da/dN-mm/cycle

NASGRO

Alpha=8

Alpha=14

Fig. 12. FCG and NASGRO da/dNcurves for 6061-T62 aluminum.

http://www.alphastarcorp.com/http://www.alphastarcorp.com/


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single alloy conditions the scatter in a will be much less. However for the present example the upper lowerbounds will be considered.

Hence using the upper and lower bounds for alpha (a) for each alloy taken from Figs. 7 and 8the Pariscurve can be constructed and compared with experimental mean data from NASGRO[1].Figs. 1214showthe predicted bounds of fatigue crack growth curves for the Al, Ti and the steel family of alloys shown in Table1. The mean experimental data in all cases were compared with the upper and lower bound cases ofa. It can beseen that in the Paris region there is good agreement between the da/dNdata provided by the FCG and theNASGRO database. In the threshold region the predictions give the widest variation in the analysis whichassumes a fixed KIc. The increase in variation of a in the steel by a factor of 4 gives the biggest differencein the fatigue prediction as shown Fig. 14. For life assessment analysis of structural components it will beappropriate to use the lower bound da/dNdata corresponding to the upper bounda values. The upper boundvalues ofa (lowerKthvalue) can provide conservative life assessment. It may be possible to avoid unnecessaryconservatism by tuning the threshold value to the material ductility using the correlations shown inFigs. 9 and10in order to obtain better agreement with the test data.

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1 10 100

K- MPa (m)0.5

da/dN-m

m/cycle

NASGRO

Alpha=9

Alpha=16

Fig. 13. FCG and NASGRO da/dNcurves for Ti2.5 Cu Titanium.

Table 2Mean fatigue data form NASGRO fatigue database

Material KIc(MPap

m) Kth(MPap

m) C n

6061-T62 Al 25.5 2.7 5.5E10 2.8Ti2.5CuSTA 45.5 4.6 1.4E10 2.9Inconel 706 80.1 10.9 2.9E7 4.0

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1 10 100 1000

K - MPa (m)0.5

da/dN-mm/cycle

NASGRO

Alpha=7

Alpha=25

Fig. 14. FCG and NASGRO da/dNcurves for Inconel 706 steel.



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The effect of the upper/lower bound aon the prediction of threshold and Paris region, mainlyCandn, werecompared with the NASGRO data[1]. The details are shown inTables 2 and 3. For those cases where the fullstressstrain curves were available (Table 2), the range of predicted values ofKth, Cand n were falling wellwithin the mean of the parameters obtained through experimental data shown inTable 3.

9. Conclusion

A parametric analysis has been carried out to quantify the effects of static tensile properties on the predic-tion of fracture and fatigue properties of three different classes of alloys, namely Al, Ti and steel alloys which

had different tensile failure strains. The proposed analytical/empirical approach, using an extended Griffithmethod to evaluate the energy dissipation at the crack tip using simple stress/strain data, can provide a usefultool for engineers to derive fracture toughness and fatigue crack growth data for classical metal alloys used inthe aerospace industry where only a few or no test data are available. Two methods have been developed thatcan estimate material fracture allowables; (1) facture toughness determination (FTD), which can estimatematerial fracture toughness and also generates the fracture toughness versus part thickness and (2) fatiguecrack growth rate (FCG) that can generate the whole regions of d a/dNcurve. It has been shown that the pre-dictions compare well with the test data of the same materials and geometries used in ASTM testing standardsfor fracture toughness and fatigue crack growth. In addition, a sensitivity analysis using the variation in theempirically derived parametera =KIc/Kthwas carried out to see the effects of material variability on the pre-diction of fatigue crack growth of the alloys considered. It has been found that, for the range considered, ahas

a lower bound with respect to failure elongation and the fatigue threshold and da/dNpredictions can vary byat most a factor of three using the upper/lower bounds of the parametera which is found to exhibit a range of525 for the present set of alloys. It has also been found that Kthis, within the range of experimental scatterand specimen sizes, directly proportional to material tensile elongation and could be used as a material inde-pendent property for the range of alloys investigated. These effects need further investigations in order tounderstand the physical reasons for the correlations between tensile ductility and fracture properties and tovalidate these relationships for a wider range of alloys.

References

[1] Fatigue Crack Growth Computer Program NASGRO 4.0, JSC, SRI, ESA, and FAA, January 2002.[2] Farahmand B. Virtual testing versus physical testing for material characterization. In: 45th AIAA/ASME/ASCE/AHS/ASC, April

1922, Palm Springs, California; 2003.[3] Virtual Testing NASA/LaRC Contract # NAS-01067, NASA Langley Research Center, Alpha STAR Corporation and Boeing

Aerospace Company.[4] Griffith AA. The phenomenon of rupture and flow in solids. Philos Trans R Soc London, Ser A 1920;221.[5] Tetelman AS, McEvily Jr AJ. Fracture of structural materials. John Wiley and Sons; 1967.[6] Farahmand B. Fatigue and fracture mechanics of high risk parts. Chapman and Hall; 1997 [chapter 5].[7] Farahmand B. Fracture mechanics of metals, composites, welds, and bolted joints. Kluwer Acadamic Publisher; 2000. now Springer-

Verlag Publishers [chapter 5].[8] Nikbin KM, Smith DJ, Webster GA. Prediction of creep crack growth from uniaxial data. Proc R Soc London, Ser A

1984;396:18397.[9] Rice JR, Rosengren GF. Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 1968;16:1.

[10] Vroman GA. Material thickness effect on critical stress intensity factor. Monograph #16, TRW Space and Technology Group; 1983[February].

[11] Newman Jr JC. A crack opening stress equation for fatigue crack growth. Int J Fract 1984;24(3).

Table 3Range of prediction, lower and upper alpha (a) values (MPa

pm)

Material Predicted KIc Predicted Kth-range Predicted C Predicted n

6061-T62 Al 26.9 1.93.4 2.6E84.7E7 3.24.2Ti2.5CuSTA 43 2.74.8 3.0E81.1E7 3.14.1Inconel 706 77.5 3.011.0 4.6E

111.5E

7 2.84.5


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