A wedge fracture toughness test for intermediate toughness materials: Application to brazed joints

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Acta Materialia 56 (2008) 4593–4600 www.elsevier.com/locate/actamat

A wedge fracture toughness test for intermediate toughness materials: Application to brazed joints N.R. Philips *, M.Y. He, A.G. Evans Materials Department, University of California, Santa Barbara, CA 93106-5050, USA Received 19 February 2008; received in revised form 10 May 2008; accepted 11 May 2008 Available online 23 June 2008

Abstract A fracture toughness test for intermediate toughness materials is developed. The test configuration is a wedge-driven double cantilever beam, with design guided by analytical solutions for the energy release rate and compliance. Actual toughness measurements require finite element methods. To promote crack stability, a pre-cracking fixture is employed. The method is illustrated for a brazed joint. Measurements of the fracture resistance used both fractographic and compliance methods to ascertain crack length. The ensuing fracture resistance, CR  1 kJ m2, is significantly greater than that for the intermetallic constituents. Approximately half of the toughening is attributed to plastic stretch of the ductile phase within the eutectic. The remainder is attributed to dissipation within a plastic zone that forms in the primary c-Ni regions. A rationale for improving toughness is presented. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Fracture; Toughness; Finite element modeling; Brazing

1. Introduction Fully calibrated (beam and compact tension) tests are widely implemented for determining the toughness of ductile alloys [1,2]. Pre-cracks are introduced by fatigue. For brittle solids, bending methods are commonly used with chevron notches used to stabilize the cracks [3]. These methods are not well suited to materials of intermediate toughness (such as amorphous/nanograined alloys and brazed joints). Such materials are difficult to reproducibly pre-crack by fatigue. An alternative approach is preferred. The intent of this paper is to describe such a test and demonstrate its application to mode I toughness measurements on a brazed joint formed between stainless steel members. The test concept is depicted on Fig. 1. It consists of a truncated double cantilever beam (DCB), supported on a pivot and loaded with a wedge. This loading has the advantage that, for fixed opening displacement, the energy

*

Corresponding author. Tel.: +1 805 893 4362. E-mail address: [email protected] (N.R. Philips).

release rate decreases with increase in crack length [4], thereby facilitating pre-cracking and stable growth. Nevertheless, because overloads are needed to create a crack from a machined notch, ancillary loading assures that the pre-crack arrests well within the specimen [5]. This loading consists of a transverse compression along the lower portion of the specimen, introduced by means of an instrumented clamp. Brazing has experienced renewed interest for fabricating metallic sandwich panels and lattice materials [6,7], but because of testing difficulties, measurements of the toughness are sparse. To rectify this deficiency, the new test is implemented and demonstrated using a Ni-based braze alloy joint between 304 stainless steel. The toughness of such joints is compromised by residual intermetallic phases: an unavoidable consequence of the modifiers used to enhance fluidity and improve corrosion resistance [8]. The toughness test will be used to quantify the performance of these intermetallic-laden joints. To address the foregoing objectives, the paper is organized as follows. The test method and its analysis are described, followed by a description of the experimental

1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.05.017

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Test Load

b Load Point

2δ

h

Displacement Gage Point

t

a

d

Clamping Load

L

Fig. 1. Double cantilever beam specimen. The specimen is loaded with a 30° silicon nitride wedge and simply supported. Load line displacement (d) is determined with a clip gauge. For measurements on the braze joints, the specimen dimensions are: b = 6.35 mm, h = 4.76 mm, a = 2.54 mm, L = 9.17 mm, t = 1.27 mm, d = 3.81 mm.

setup. Then, measurements obtained on a brazed joint are presented. Finally, the mechanisms governing the toughness are discussed and a route for improved material performance is presented. 2. The toughness test The test specimen utilizes two cantilever arms (Fig. 1). To minimize shear and torsion, the fixture incorporates a midline groove along the base that allows pivoting. The load line deflection, d, is determined with a clip gauge in contact with the specimen at a location t below the load point. (A correction needed to account for rotation is discussed in Appendix A.) To accommodate the clip gauge and wedge, a slot is cut into the specimen. For pre-cracking, specimens are clamped prior to insertion of the wedge, at distance d from the load point. (Specific results are obtained using specimens having width h = 4.8 mm, thickness b = 6.4 mm and clip gage location t = 1.27 mm: the effective length is L = 9.2 mm (accounting for the groove and the slot). During pre-cracking, the clamps are located at d = 3.81 mm.) The strain energy release rate for this specimen in displacement control has been derived analytically as [4] Gwedge ¼

Ed2 ða=hÞ4 h

F 1 ða=h; L=hÞ

ð1Þ

r2trans ða  dÞF 2 ða=hÞ ð3Þ E where rtrans is the transverse stress and F2(a/h) = 8/p. The fidelity of this estimate is assessed by extracting Gtrans from the net energy release rate upon pre-cracking

Gtrans ¼ 

2

where a is the crack length, E is Young’s modulus and F1 is a non-dimensional function summarized in Appendix B. The corresponding compliance is [4] d 1 ¼ /ða=h; L=hÞ P Eb

tests. ABAQUS standard has been implemented for this purpose, using the procedures described in the manual [11]. The function F1 is plotted as a function of a/h in Fig. 2a, where it is compared with the analytic estimate. There are two discrepancies: (i) at small crack extensions the energy release rate is somewhat smaller, attributed to the reduced width of the beam above the braze seam, where it was cut away to accommodate the wedge; (ii) a divergence near the end of the specimen arises because the through-thickness stress, r22, becomes significant relative to the bending stress, r11 (Fig. 3). Therefore, as the crack approaches the edge, the substantial energy stored through r22 is released later in the fracture process than r11, delaying the drop-off of the energy release rate. The corresponding comparison between the analytic estimate of the compliance and the FE results is presented in Fig. 2b. The deviation for longer cracks arises for the foregoing reason. The energy release rate due to the transverse clamp is estimated using an analytic solution for tractions applied to the crack flanks of a semi-infinite specimen [2]

ð2Þ

where the compliance function, /, has the analytic form given in Appendix B. These formulas have the limitation that they are restricted to thin, slender beams [9,10]; i.e. the method neglects the shear and through-thickness stresses induced by the wedge. Because of this limitation, the finite element (FE) method has been used to re-evaluate F1 and / for the specific geometry (L/h = 1.93) used in the following

ðK wedge þ K trans Þ E sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!2 Ed2 r2trans ða  dÞ F2  ¼ F 1 E ða=hÞ4 h

Gtotal 

ð4Þ

such that F 2 ða=hÞ ¼

pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi2 E Gwedge  Gtotal r2trans a½1  ðd=hÞðh=aÞ ð5Þ

The FE calculations are plotted Fig. 4. Note that imposing the clamp lowers the energy release rate and increases the slope; both serve to increase the tendency for crack arrest.

0.30

4595

a Finite Element

0.25 0.20 0.15

Analytical

0.10 0.05 0

b 200

Analytical

100

Finite Element 0

0.5

1.0

1.5

2.0

Energy Release Rate F2 (a h, L h)

Compliance Function

(a/h, L/h)

Energy Release Rate F1(a/h,L/h)

N.R. Philips et al. / Acta Materialia 56 (2008) 4593–4600

4

c

Finite Element

3

Analytical

2

1 0.8

1.1

1.4

1.7

Crack Length, (a/h)

Crack Length (a/h)

Fig. 2. Energy release rate and compliance functions for the test configuration: (a) comparison of the analytic estimate of the energy release rate function (F1) for a wedge-loaded DCB specimen [4] with the present FE results. (b) Comparison of compliance function / obtained analytically with FE results. Agreement degrades as the crack approaches the end of the specimen. (c) The calculated function (F2) for transverse clamping. The analytical solution is 8/p.

1.5 Normal Stress

11

1.03 1.0 0.8 0.6 0.4 0.2 0 -0.2 -0.34

Normal Stress22

Energy Release Rate (kJ / m2)

2 h/E

1.0

Gtotal G wedge 0.5 50 MPa

100MPa

0 0.5

1.0

1.5

2.0

Crack Length, a/h Fig. 3. Contours of stress in the DCB specimen. The through-thickness stresses (a) are comparable to the bending stresses (b) used in the analytical calculation. The discrepancy between the FE and analytical result for F1 arises because the through-thickness stresses are neglected in the analytical formulation.

The F2 ascertained from these results, plotted on Fig. 2c, exceeds the analytic estimate by 20% within the range relevant to crack arrest upon pre-cracking.

Fig. 4. Energy release rates calculated for a specimen under an applied displacement of 15 lm, with and without orthogonal clamping. Note the sharper decline when the clamp is applied.

Equating the total energy release rate to the mode I toughness, C, allows a lower bound estimate to be made of the transverse stress needed to arrest the pre-crack at a specified length. Incorporating toughness estimates for the brazed joints (elaborated below), C  1 kJ m2, sug-

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3. Materials and methods The test method has been applied to 304 stainless steel, brazed using a quaternary Ni-based alloy, as described elsewhere [12]. Nicrobraze 31 was selected due to its high strength, corrosion resistance and the ability to join complex, thin structures effectively. Specimens were prepared by wire electrical discharge machining (EDM), then bright annealing at 1000 °C in high vacuum (103 Pa) to remove the recast surface layer. With a fixed gap width of 135 lm, the joints were brazed for 2 h at 1100 °C in a resistively heated vacuum furnace. Heating and cooling rates were 10 °C min2. Following brazing, some specimens were polished for metallurgical examination and machined into mechanical test specimens. Polishing was carried out according to standard metallographic procedures. Samples were tested on a servohydraulic test frame with displacement control. A Si3N4 wedge with a 15° half angle (h), lubricated with graphite, was used to generate the opening displacement. A clip gauge measures the crack opening displacement. After calibration, the gauge was determined to be accurate to within 0.25 lm over the duration of a test. A hardened steel transverse clamp was attached near the base with the imposed force monitored using a load cell. The system was instrumented with a crosshead load cell and displacement measurement at the actuator. Toughness testing was conducted without the transverse clamp. Metallographic examination of the polished surface was conducted immediately after pre-cracking both to measure the surface crack length and to record fracture processes. Specimens were heat tinted at 600 °C for 15 min to delineate the pre-crack front. Following testing, the fracture surfaces were exposed for optical and scanning electron fractography. An electron microscope equipped with a focused ion beam (FIB) was used to further investigate bridging phenomena. For this purpose, the fracture surface was covered with a protective platinum film prior to crosssectioning with the FIB. Nanoindentation performed on the c-Ni phase, conducted using a cube-corner diamond indenter at a maximum load of 15 mN, was used to asses the hardness, H = 4 GPa: indicative of a yield strength, r0  1.3 GPa [13]. 4. Results 4.1. Pre-cracking Pre-cracking was conducted by wedge loading with the clamp activated. The foregoing analysis indicates that,

for the crack to arrest, the clamping stress should be about 50 MPa. In practice, cracks were found to arrest for clamping stresses greater than 37 MPa. The initiation of a crack from the notch was evident from the load-opening displacement traces (Fig. 5a) as a sudden load drop, accompanied by a corresponding displacement jump and acoustic emission. The nonlinearity prior to abrupt crack propagation is associated with formation of a tunneling crack (rather than plasticity) that increases the compliance. Heat tint fractography of the ensuing pre-crack profile (Fig. 6) revealed that, in order to realize an acceptable crack configuration, the transverse stress needed to be maintained within an intermediate range: 37–47 MPa. At larger loads, the cracks tunnel excessively; while at smaller loads they become non-planar. In practice, test results were discarded if the pre-crack length varied by more than 12% across the width. A tendency for the cracks to bow slightly near the surface rendered the surface measurements inaccurate. By polishing prior to pre-cracking, plastic deformation along the crack was highlighted by shear bands. Using these bands as a conservative estimate for the extent of plasticity, we conclude that, beyond a small (<200 lm) process zone, the specimen remained elastic throughout the pre-cracking procedure.

1500

(a) Precracking

1000

Load (N)

gests that clamping stresses of about 50 MPa are needed. In practice, as elaborated below, at these stress levels, the precrack extends somewhat further than predicted by Fig. 4. The discrepancy is caused by inertia induced in the separating beams, once the crack becomes dynamic, resulting in overshoot. Pre-cracking trials are needed to allow for this effect.

500

0

0

5

10

15

20

Displacement (b) Wedge Loading 300 225

Load (N)

4596

150 75 0

0

5

10

15

20

25

Displacement Fig. 5. Load/displacement traces obtained on the braze joint. (a) Precrack formation is marked by a jump in crack opening, accompanied by an acoustic emission. (b) Displacement of the pre-cracked specimen during toughness measurements.

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ments of the bending behind the crack font, conducted in conjunction with determinations of the wedge-opening displacements, offer a more reliable alternative. 4.3. Toughness measurements

A typical load/displacement response for a wedgeloaded, pre-cracked specimen with the clamping force removed is presented in Fig. 5b. The curve is linear up to a load maximum and then decreases continuously (while the crack extends) with increase in displacement. The linear portion of the loading curve has been used to calibrate the compliance upon noting that the load applied to the wedge, Pwedge, is related to the force P at the load point by   l cosðhÞ þ sinðhÞ P wedge ¼ 2P ð6Þ cosðhÞ  l sinðhÞ where l is the coefficient of friction between the Si3N4 wedge and the specimen. The effective l is ascertained by comparing the measured slope with that obtained from Fig. 2b at the a/h obtained from the post facto heat tint measurement of the crack length. Small levels of friction emerged, l = 0.03 ± 0.02, consistent with that expected for hard surfaces lubricated with graphite [14]. Hereafter, this friction coefficient is used to determine the crack length during crack extension (from the measured load and crack opening), in conjunction with (6) and Fig. 2b. Attempts at using the unloading compliance to assess the crack length were unsuccessful because of the erratic behavior caused by stick/slip friction at the wedge. Strain gage measure-

Fracture Resistamce (kJ/m2 )

4.2. Compliance calibration

1.5

a

1.0

0.5

0

Fracture Resistance (kJ/m2)

Fig. 6. Fracture surface of the braze joint. Pre-cracked samples were heated to 600 °C, resulting in the tinted fracture surface seen here. Also present are two large defects where the substrate was not fully wetted by the braze.

Measurements of the type presented in Fig. 5b have been used to determine the initiation and propagation levels of the mode I toughness. The initiation toughness estimates are based on the crack opening displacement at the load maximum and the crack length ascertained post facto from the fractographic measurement of the heat-tinted region. A series of four measurements have been conducted. These measurements gave a mode I initiation toughness, C0 = 930 ± 80 J m2 (the corresponding toughness of the 304 stainless steel is 672 kJ m2) [15]. The authors are unaware of any prior measurements of the toughness of brazed joints in steel systems that could be used for comparison. Moreover, we have yet to identify a ‘‘standard bond” having known toughness (as well as amenability to fabrication into the present configuration) that could be used to check the fidelity of the results. The propagation toughness was ascertained as a function of crack extension, Da, from the load and crack opening by using the compliance, (2). The results are plotted in Fig. 7. Note that the measurements for all of the specimens are within a relatively narrow range, CR  1 kJ m2, with a

b

1.5

1.0

0.5

0 0

1

2

Crack Extension

Fig. 7. (a) Fracture resistance as a function of crack extension for a single sample: the result found by compliance calibration () is compared with that obtained by direct fractographic measurement of the crack length (M). (b) The superposition of results for several specimens.

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shallow tearing modulus. Moreover, the initiation toughness levels are essentially the same as those obtained from direct measurements of the crack length. 5. Observations Optical microscopy observations made on the polished side surface of the specimens revealed the crack trajectory within the braze region (Fig. 8a). Three distinct phases are present: an austenitic c-Ni, present both as large primary grains and in the finer eutectic; an intermetallic silicide; and an intermetallic phosphide [12]. Evidently, the crack extends through the intermetallic region. Locally, it is also attracted to the ductile domains of primary c-Ni (due to their lower modulus [16]) and, therein propagates parallel to the interface occasionally blunting into the

c-Ni. Where this happens, slip bands are evident in the ductile phase, indicative of a contribution to the toughness from the plastic zone. Characterization of the fracture surfaces reveals a continuous plane of brittle cracking through the intermetallic, interspersed with islands of c-Ni alloy (Fig. 9a). Closer inspection reveals substantial plastic deformation within the secondary c-Ni in the eutectic (Fig. 9b). The extent of the ductile stretch is manifest as chisel point deformation and necking; fully constrained domains would display rupture by void formation and coalescence. The stretch is accommodated by the formation of a channel in the alloy adjacent the intermetallic, as indicated in Fig. 9b. Cross-sectioning by FIB revealed that the normalized plastic stretch is uc/R  1.8 (2R is the width of the bridging ligament). These features are remarkably similar to those presented in the literature for ductile phase

Eutectic Bridging Zone 2R

h

Plastic Zone

Fig. 8. Fracture process and microstructure. (a) The three phases present are: (i) the ductile c-Ni, present as both large, scalloped primary grains and within the fine eutectic; (ii) the ternary phosphide, present as the second component of the eutectic; (iii) the quaternary silicide, which forms irregular grains adjacent to both the primary c-Ni and the eutectic. Note the significant plastic deformation that occurs as the crack approaches the primary c-Ni. (b) A schematic representation of the active toughening mechanisms. The secondary c-Ni domains bridge the advancing crack front, while the primary c-Ni forms a plastic wake.

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about half the measured toughness. The remaining toughening is attributed to the dissipation occurring in the plastic wake in the primary c-Ni as the crack propagates adjacent to the interface (Fig. 8). The ductile stretch toughening could be enhanced by pursuing two possibilities: (1) elongation of the large primary c-Ni cells by solidification control to span the braze joint and (2) coarsening of the primary c-Ni at the expense of the dispersed secondary c-Ni in the eutectic to encourage percolation across the joint. 7. Concluding remarks

Fig. 9. Fractography of a brazed specimen. (a) Islands of ductile c-Ni protrude into the fracture plane. (b) The deformations of the secondary cNi domains, as evidenced by the cruciform chisel point stretch and the depression at the interface with the intermetallic.

A fracture toughness test for intermediate toughness materials has been described. It is based on a wedge-driven DCB, and its design is guided by analytical solutions for the energy release rate and compliance. Actual toughness measurements utilize FE solutions. To promote crack stability, a pre-cracking fixture is employed. Measurements of the fracture resistance were conducted using both fractographic and compliance methods to ascertain crack length. The test has been applied to joints in 304 stainless steel brazed with Nicrobraze 31. The joints were found to have fracture resistance, CR  1 kJ m2, significantly greater than that for the intermetallic constituents. Approximately half of the toughening is attributed to plastic stretch of the ductile phase within the eutectic. The remainder is attributed to dissipation within a plastic zone that forms in the primary c-Ni regions where the crack is attracted to (and parallels) the interface. The braze joint toughness should thus be sensitive to changes in processing parameters. Experimental work to improve toughness by microstructural control is well under way. Acknowledgement

toughened brittle solids [17–20], suggesting that this contribution to the toughness might be interpreted using the analysis applicable to these materials [21].

Appendix A. Opening displacement correction factor

6. Toughness interpretation The steady-state toughening imparted by plastic stretch of the ductile phase within the eutectic is given by [21] DCss ¼ r0 fRv

The authors would like to thank Dr. Craig A Steeves for helpful discussions and insightful comments.

ð7Þ

where v is a work-of-rupture parameter affected by the extent of the plastic stretch and can be approximated as [21] uc v ¼ 2:5 ð8Þ R Inserting the measured stretch, uc/R  1.8 indicates that v = 4.5. The area fraction of the ductile particles is f  0.15, with average width 2R  1.0 lm (Fig. 9b). Incorporating the estimate of the yield strength of the ductile phase ascertained from the foregoing hardness measurements (r0  1.3 GPa), the contribution to the toughness from plastic stretch is predicted to be DCss  450 J m2:

The crack opening displacement at the load point, d, is calculated from the measured displacement, d*, at the gage point. A correction determined from the FE calculations is presented in Table A.1 as k = d*/d. Note that the correction decreases with crack extension as expected. Appendix B. Analytic formulae The function characterizing the energy release rate upon point loading is given by [4] Table A.1 Displacement gage correction factor a/h

0.73

0.88

1.03

1.18

1.33

1.48

1.64

1.79

1.94

k

0.50

0.57

0.63

0.67

0.72

0.76

0.79

0.82

0.84

4600

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pffiffiffih  2 bþsin2 b sinh b cosh bsin b cos bi a2 3 a sinh þ sinh2 bsin2 b sinh2 bsin2 b    2    F I ða; bÞ ¼ 2 sinh b cosh bþsin b cos b sinh bþsin b sinh b cosh bsin b cos b 2a3 þ 6a2 þ 6a þ 3 2 2 2 2 2 2 sinh bsin b sinh bsin b sinh bsin b where p ffiffiffi a 4 a¼ 6 ; h

  ffiffiffi L  a p 4 b¼ 6 h

The corresponding compliance function is " ! 2 3 2 sinhðbÞ coshðbÞ þ sinðbÞ cosðbÞ ffiffiffi 2a þ 6a /¼p 2 2 4 6 sinhðbÞ  sinðbÞ ! 2 2 sinhðbÞ þ sinðbÞ þ6a 2 2 sinhðbÞ  sinðbÞ !# sinhðbÞ coshðbÞ  sinðbÞ cosðbÞ þ3 2 2 sinhðbÞ  sinðbÞ References [1] ASTM E1820, Annual book of ASTM standards, vol. 03.01. West Conshohocken, PA: ASTM International; 2001. [2] Tada H, Paris P, Irwin G. The stress analysis of cracks handbook. 2nd ed. Paris Productions Inc.; 1985. [3] ASTM C1421-01b, Annual book of ASTM standards, vol. 15.01. West Conshohocken, PA: ASTM International; 2007. [4] Kanninen MF. Int J Fract 1973;9(1):83–92. [5] Gilman JJ. J Appl Phys 1960;31(12):2208–18.

[6] Cote F, Deshpande VS, Fleck NA, Evans AG. Mater Sci Eng A – Struct Mater Proper Microstruct Process 2004;380(1–2):272–80. [7] Zok FW, Waltner SA, Wei Z, Rathbun HJ, McMeeking RM, Evans AG. Int J Solid Struct 2004;41(22–23):6249–71. [8] Lugscheider E, Partz KD. Weld J 1983;62(6):S160–4. [9] Gehlen PC, Popelar CH, Kanninen MF. Int J Fract 1979;15(3):281–94. [10] Shahani AR, Forqani M. Int J Solid Struct 2004;41(14):3793–807. [11] ABAQUS, Hibbitt, Karlsson and Sorensen; 2000. [12] Philips NR, Levi CG, Evans AG. Metall Mater Trans A 2008;39(1):142–9. [13] Tabor D. Brit J Appl Phys 1956;7(5):159–66. [14] Bhushan B. Principles and applications of tribology. New York: John Wiley; 1999. [15] Mills WJ. Int Mater Rev 1997;42(2):45–82. [16] Ritchie RO, Cannon RM, Dalgleish BJ, Dauskardt RH, McNaney JM. Mater Sci Eng A – Struct Mater Propert Microstruct Process 1993;166(1–2):221–35. [17] Deve HE, Evans AG, Odette GR, Mehrabian R, Emiliani ML, Hecht RJ. Acta Metall Mater 1990;38(8):1491–502. [18] Mendiratta MG, Lewandowski JJ, Dimiduk DM. Metall Trans A – Phys Metall Mater Sci 1991;22(7):1573–83. [19] Flinn BD, Lo CS, Zok FW, Evans AG. J Am Ceram Soc 1993;76(2): 369–75. [20] Heredia FE, He MY, Lucas GE, Evans AG, Deve HE, Konitzer D. Acta Metall Mater 1993;41(2):505–11. [21] Ashby MF, Blunt FJ, Bannister M. Acta Metall 1989;37(7):1847–57.