- Email: [email protected]
Strength of joints produced by transient liquid phase bonding in the Cu–Sn system
Acta Materialia 53 (2005) 2019–2027 www.actamat-journals.com
Strength of joints produced by transient liquid phase bonding in the Cu–Sn system N.S. Bosco, F.W. Zok
*
Materials Department, University of California, Santa Barbara, CA 93106-5050, USA Received 24 February 2004; received in revised form 12 January 2005; accepted 12 January 2005
Abstract The paper focuses on the strength and toughness of joints produced by transient liquid phase (TLP) bonding in the Cu–Sn system. It is motivated by potential applications of TLP bonding in attachment of high-temperature wide bandgap devices to ceramic substrates. Model test specimens suitable for mechanical testing are developed, utilizing substrates of oxide dispersion strengthened copper. Three microstructural conditions are probed: a uniform layer of the d intermetallic phase (Cu41Sn11), a two-phase microstructure comprising the d-phase and a dispersion of ductile (Cu) particles, and a uniform Cu solid solution. Notched and unnotched bend tests are used to ascertain strength and toughness. The d-phase exhibits a reasonably high strength (300 MPa), but low toughp ness (5 MPa m). Addition of (Cu) particles increases both the strength and the toughness by about 30% (400 MPa and p 7 MPa m, respectively). These property enhancements are rationalized on the basis of existing models of ductile phase toughening. The conversion of the intermetallic to Cu solid solution leads to a decrease in strength (to 200 MPa), but an increase in toughness (to p 13 MPa m). The latter trends appear to be a consequence of the reduction in the flow stress of the joint material. Additionally, the conversion to (Cu) is accompanied by the formation of voids, predominantly near the prior boundary between the d-phase and the adjoining Cu. The voids likely diminish the joint properties, relative to the intrinsic values associated with the defect-free copper solid solution. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Copper; Intermetallic phases; Electron beam methods; Fracture; Toughness
1. Introduction Transient liquid phase (TLP) bonding is a potential joining technique for attachment of high-temperature wide bandgap devices to ceramic substrates [1,2]. It can be implemented through the use of Cu metallization layers on both the device and the substrate and a low melting point metal as an interlayer material to effect bonding. To minimize bonding times and temperatures, the interlayer material should have a low melting point, coupled with high solubility and diffu*
Corresponding author. Tel.: +1 805 893 8699; fax: +1 805 893 8486. E-mail address: [email protected] (F.W. Zok).
sivity in the adjoining Cu. From an examination of binary phase diagrams, two candidate interlayer materials emerge: Sn and In. Both have melting points below 300 C and solubility limits in Cu of about 10–15% at temperatures of 400–500 C (the expected bonding range). Additionally, when the bonding process is taken to completion to form a Cu solid solution across the entire joint, the solidus temperature approaches 800 C. In this state, the mechanical properties of the joint should be retained for extended periods at the targeted upper service temperatures of these devices (300 C). However, both metals also produce a number of intermediate phases with Cu, introducing potential problems in bond integrity and reliability.
1359-6454/$30.00 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.01.013
2020
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
The overall objective of the present study is to probe the mechanical properties of joints produced by TLP bonding in the Cu–Sn system. It builds on an earlier study, focused on the bonding conditions necessary to produce joints with essentially pore-free microstructures [3]. In order to measure joint properties, a model system is developed, utilizing oxide dispersion strengthened (ODS) Cu as a substrate material. Its selection is based on its capability to retain high strength (about 420 MPa [4]) following the elevated temperature excursion associated with bonding. This high strength allows mechanical testing of the joint up to fracture, without detectable deformation remote from the joint location. Furthermore, with the use of thin sacrificial layers of pure copper on the ODS Cu substrates, the resulting microstructures are virtually identical to the ones previously obtained through TLP bonding of pure Cu substrates. One specific objective of this work is to assess the role of the joint microstructure on mechanical properties. To this end, three sets of bonding conditions are used. The resulting microstructures include a uniform layer of the d intermetallic phase (Cu41Sn11), a two-phase microstructure comprising the d-phase and a dispersion of ductile (Cu) particles, and a uniform Cu solid solution. The expectation is that the integrity and reliability of the joints should improve as the amount of remnant intermetallic is reduced. But this comes at the expense of increased bonding times and temperatures. In practice, the trade-offs between property enhancements and manufacturing cost would need to be considered in selecting an appropriate bonding schedule. Effects of thermal history on the microstructure and properties of surrounding materials would also need to be addressed. In an attempt to determine the fracture toughness of these joints, bend tests are performed on standard edgenotched specimens. An assessment of the effects of the finite notch root radius on the validity of the fracture toughness measurements is made through a stress analysis of the notch tip region. The analysis is coupled with the strength measurements in both notched and unnotched configurations, as well as fractographic observations, to determine whether the notch can be legitimately treated as a sharp crack in calculating fracture toughness. It is demonstrated that, in two of the three joint types tested in the current study (specifically, those that contain the d-phase), the pre-existing flaws are sufficiently large in relation to the notch root radius such that the notches can indeed be treated as cracks.
2. Specimen fabrication and mechanical testing techniques The test specimens were prepared in the following way. ODS Cu rods, 32 mm in diameter and 25 mm long, were ground to an optically flat finish using 3 lm diamond
Fig. 1. Phase diagram for the Cu–Sn system. At the bonding temperature of 400 C, the terminal (most Cu-rich) intermetallic phase is d. For the subsequent heat treatment at 550 C, d is consumed in the formation of c, which, in turn, decomposes into d + (Cu) upon cooling.
paste. In the initial bonding attempts, the polished rods were coated with Sn and bonded in the manner described below. These bonds proved to be of poor mechanical integrity, because of entrainment of the alumina dispersoids (originally contained within the ODS Cu) into the liquid phase and banding of the dispersoids during subsequent solidification. Fracture invariably occurred along the dispersoid bands at low strength levels. To mitigate this problem, the procedure was modified, through addition of thin sacrificial layers of pure Cu. To this end, the polished ODS Cu rods were coated with 50 lm of Cu by electron beam deposition (EBD). To ensure adequate smoothness for bonding, the coated surfaces were polished. Moreover, to enhance adhesion between the deposited Cu and the underlying ODS Cu, the coated rods were annealed at 800 C for 5 min under flowing 5% H2 in Ar [5]. Following this treatment, the substrates were immediately placed back in the EBD chamber for deposition of a 10 lm thick Sn layer. The total Sn layer thickness, 20 lm (when matching pairs of coated rods are bonded), exceeds the minimum value of 12 lm, prescribed by results presented in a previous study [3]. Bonding was performed in a vacuum furnace at 2 · 106 torr. The temperature was ramped at a rate of 5 C/min. This low heating rate was chosen to minimize temperature gradients in the sample and to prevent temperature overshoots on approach to the targeted bonding temperature. Bonding was performed at 400 C for 4 h. These conditions produced a uniform layer of the d-phase, without remnant e, g or Sn, and without porosity (Fig. 3(a)). 1 The rods were sectioned by electrodis1 The d phase is metastable for extended periods at room temperature; its decomposition into e + (Cu) through the eutectoid reaction at 350 C is extremely sluggish. Indeed, subsequent heat treatments at 300 C for 24 h followed by both X-ray diffraction measurements and energy-dispersive spectroscopy in a scanning electron microscope revealed negligible amounts of e-phase.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
charge machining into unnotched bend specimens, 3 mm · 3 mm in cross-section, and notched beams, 3 mm · 6 mm in cross-section, with notches machined to half of the specimen depth along the joint (Fig. 2). The notch root radius was q = 160 lm. Following sectioning, some specimens were subject to further heat treatments to produce alternate microstructures. In one set, the beams were heated for an additional 30 min at 550 C. During this treatment, the d-phase is converted to c-phase (Fig. 1). Upon cooling, the c-phase undergoes a eutectoid reaction (at 520 C), resulting in a two-phase microstructure comprising a d-phase matrix and a dispersion of (Cu) particles (Fig. 3(b)). The volume fraction, f, of (Cu) particles was measured to be approximately 25%: consistent with a lever rule calculation from the phase diagram. Another set of specimens was heated for 20 h at 600 C. Through this treatment, the d-phase is consumed in the formation of (Cu) across the entire joint. However, this is accompanied by the formation of pores, predominantly at the boundary between the prior d-phase and the adjoin-
2021
Fig. 2. Schematic of the bonded rods and the sectioning procedure used to extract bend specimens.
Fig. 3. Optical micrographs of cross-sections through the three joint types: (a) following bonding at 400 C for 4 h; (b) with additional treatment of 550 C for 30 min; and (c) with additional treatment of 600 C for 20 h.
2022
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
ing Cu. These pores are believed to be a consequence of the Kirkendall effect: the diffusivity of Sn (with its low melting point) being significantly higher than that of Cu [6]. The unnotched beams were tested in four-point flexure, with inner and outer loading spans of 20 and 40 mm, respectively. The notched specimens were tested in three-point flexure, with the same outer loading span. All tests were preformed on an Instron 8562 test frame, equipped with a 900 N compression load cell, at a displacement rate of 0.01 mm/min. The fracture surfaces were subsequently examined in a scanning electron microscope (SEM).
3. Measurements and observations 3.1. Strength The measured strength values are summarized in Fig. 4. The d-phase exhibited a rather high unnotched strength (300 MPa), but a high degree of notch sensitivity: the notched/unnotched strength ratio (on a netsection basis) being about 0.5. The addition of the (Cu) particles to the d-phase produced a 30% increase in unnotched strength, to about 400 MPa. A similar relative increase was obtained in the notched strengths of the two joint types, from 140 to 190 MPa. The similarities in the strength elevations in the notched and unnotched configurations suggest an increase in toughness but with no change in the size of the strength-limiting flaws. This effect is attributable to ductile phase toughening by the (Cu) particles, as detailed later. Upon conversion of the microstructure to only (Cu), the unnotched strength decreased relative to that of the two-phase microstructure, by almost 50%. In contrast,
Fig. 4. Summary of notched and unnotched strength measurements. Net-section and remote stresses in the notched configuration are related to one another by a factor (1 c/b)2 = 0.25.
Fig. 5. Typical load–displacement curves for the notched test specimens. In joints containing d or d + (Cu), crack propagation occurs unstably at the load maximum. In contrast, in joints with only (Cu), it occurs stably across the entire cross-section, without precipitous load drops.
Fig. 6. Fracture surface of a d joint, showing combinations of transgranular (T) and intergranular (I) fracture.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
the corresponding notched strength increased by about 15%, reaching a level virtually identical to that of the unnotched (Cu) specimens (230 MPa). That is, the ratio of notched-to-unnotched strength was essentially unity. The diverging trends in notched and unnotched strengths coupled with the notch-insensitivity of the (Cu) joints suggest that the enhancement in toughness associated with the conversion of d to (Cu) is accompanied by a significant reduction in the flow stress of the joint material. Evidently, the latter reduction is sufficient to cause failure to occur by plastic yielding followed by ductile rupture. An additional pertinent feature of the (Cu) joints is the stable manner in which fracture occurred. That is, the load–displacement response varied smoothly as the crack propagated across the bond section. In contrast, the d-containing joints exhibited precipitous load drops at the onset of cracking (at the load maximum), in similarly notched configurations. These behaviors are illustrated in Fig. 5.
2023
3.2. Fractography SEM observations of the fracture surfaces revealed that fracture had occurred through the interlayers in all cases (not the sacrificial EBD Cu or the ODS Cu).
Fig. 8. Fracture surface of a (Cu) joint, showing predominantly ductile rupture, but accompanied by some brittle fracture facets.
Fig. 7. Fracture surface of a d + (Cu) joint, showing brittle fracture of the d-phase along with plastic stretching and chisel-point fracture of the embedded (Cu) particles.
Fig. 9. A typical bonding flaw (highlighted by the white line), found at the notch tip of a d joint.
2024
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
The d-phase exhibited a combination of transgranular and intergranular fracture, without evidence of appreciable plasticity (Fig. 6). The d-phase within the d + (Cu) joints fractured in a similarly brittle manner. In contrast, the (Cu) particles embedded within the dphase exhibited significant plastic stretching, with most displaying chisel point fracture (Fig. 7). This feature exemplifies the targeted ductile phase toughening associated with the two-phase microstructure. The (Cu) fracture surfaces exhibited predominantly ductile dimpling (Fig. 8). However, there was evidence of brittle faceted features, likely a consequence of the pre-existing pores. Notwithstanding, the extensive dimpling coupled with the notch-insensitivity of strength re-affirms the assertion that fracture occurs through local yielding of the (Cu), at stresses dictated by the flow stress of the (Cu). In the two microstructures containing the d-phase, the tensile side of the fracture plane was found to contain irregularly shaped bonding defects, typically no greater than about 100 lm. The rounded topography of these defects suggests that they are a result of remnant porosity. One such example is shown in Fig. 9. In this example, the defect extends about 70 lm into the material beyond the notch tip.
4. Analysis of notched strength The preceding results for notched strength have been analyzed, with the objective of obtaining estimates of fracture toughness. For the case of the (Cu) joints, the lack of notch sensitivity in strength precludes use of standard LEFM solutions for stress intensity factors in calculating fracture toughness. As a consequence, an estimate of toughness was obtained from the associated work of fracture [7] coupled with the Irwin relation. The procedure is facilitated by the stable crack growth across the cross-section (Fig. 5). Such measurements yield a fracture energy of 1700 ± 200 J/m2 and a corresponding fracture toughness (usingp a YoungÕs modulus of 110 GPa) of Kc 13 MPa m. The high notch sensitivity of the d-containing joints suggests that the fracture toughness might be obtained from the peak load in the notched bend tests, predicated on the assumption that the notch acts as a sharp crack. An assessment of this assumption is made in the following way. First, an estimate is made of the minimum size of a pre-existing flaw at the tip of a circular notch beyond which the notch can be treated as a sharp crack. Second, the measured notched and unnotched strengths are used to infer the size of the strength-limiting flaw and the result then compared with the preceding minimum value. The analysis follows. The analysis is based on the configuration shown schematically in Fig. 10. It consists of a notched beam
Fig. 10. A schematic showing a flaw at the tip of a rounded notch in a three-point bend specimen. An analysis of this loading configuration yields the results plotted in Fig. 11.
of a homogeneous linear elastic material. 2 A preexisting sharp flaw of length a resides at the tip of a rounded notch, with root radius q and length c. The notched beam is subjected to a remote bending stress, r1. The effect of notch root radius on the notched strength is assessed by considering two limiting cases, wherein the pre-existing flaw is either much smaller or much larger than q. An analogous approach has been used previously in the analysis of cracks emanating from circular holes [8]. In case I, a q and thus the stress intensity factor for the flaw is pffiffiffiffiffiffi K ¼ 1:12rL pa; ð1Þ where the numerical coefficient 1.12 is the free surface correction factor and rL is the maximum local stress at the notch tip. In turn, the local stress is given by [9] 2K nom rL ¼ pffiffiffiffiffiffi ; pq
ð2Þ
where Knom is the nominal stress intensity factor at the tip of a sharp crack with the same length as that of the notch and subject to the same loading conditions pffiffiffiffiffi ð3Þ K nom ¼ r1 pcF ðc=bÞ; where F(c/b) is the usual finite crack correction factor (tabulated, for example, in [10]). Combining Eqs. (1)– (3) yields the result in non-dimensional form pffiffiffiffiffiffiffiffi K pffiffiffiffiffi ¼ 2:24 a=qF ðc=bÞ: ð4Þ r1 pc 2
The assumption that the layer is elastically homogeneous is justified on the basis of YoungÕs modulus measurements, made by depth-sensing nanoindentation. Specifically, the moduli of the EBD Cu, the ODS Cu and the solid solution (Cu) were all found to lie in the range 110 ± 8 GPa: consistent with the expected value for Cu. The pertinent value for the d-phase was only slightly lower: 95 ± 5 GPa. The degree of elastic mismatch is deemed to be inconsequential.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
In case II, q a c. Here the stress intensity factor is independent of q and given by K pffiffiffiffiffi ¼ F ðc=bÞ: r1 pc
ð5Þ
The stress intensity factors for the two limiting cases for c/b = 0.5 are plotted in Fig. 11(a). Accordingly, the intersection of the two provides an estimate of the critical value of ac/q; for a < ac, fracture is controlled by the stress concentration (Eq. (4)), whereas for a > ac, fracture is controlled by the nominal stress intensity factor (Eq. (5)). From the preceding treatment, the critical value is ac/q 0.2 for c/b = 0.5. For q = 160 lm (the value in the present experiments), the critical flaw size is ac 30 lm. As a preliminary assessment, it is noted that ac is less than the size of the flaws found on the fracture surfaces (by a factor of about 2–3), suggesting that the finite notch root radius can be neglected in the determi-
2025
nation of the fracture toughness. A more critical assessment of this conclusion follows. Further insights are obtained from a comparison of the notched and unnotched strengths, subject to the two preceding limiting cases. In case I, wherein a < ac, fracture occurs in the notched configuration when the local stress exceeds a critical value: rL ¼
Kc pffiffiffiffiffiffi ; 1:12 pa
ð6Þ
where Kc is the fracture toughness. In turn, the local stress rL can be expressed in terms of the remote stress, via Eqs. (2) and (3), yielding a remote notched strength of h pffiffiffiffiffiffiffiffi i1 Kc pffiffiffiffiffiffi 2 c=qF ðc=bÞ : rN ¼ ð7Þ 1:12 pa Recognizing that the unnotched strength rU is similarly related to fracture toughness, via rU ¼
Kc pffiffiffiffiffiffi 1:12 pa
ð8Þ
and assuming that the same flaws are present in both the notched and unnotched specimens, the ratio of notched to unnotched strength (from Eqs. (7) and (8)) becomes: i1 rN h pffiffiffiffiffiffiffiffiffiffiffi ¼ 2 ðc=qÞF ðc=bÞ : ð9Þ rU For the current test configuration, rN/rU = 0.082, independent of flaw size. In case II, wherein ac < a c, the ratio of notchedto-unnotched strength can be expressed analogously in terms of the fracture toughness, through combination of Eqs. (5) and (8), yielding: rN 1:12 pffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffi q=c a=q: ð10Þ ¼ rU F ðc=bÞ
Fig. 11. Effects of normalized flaw size, a/q, on (a) the stress intensity factor and (b) the ratio of notched to unnotched strength. For a notch length c/b = 0.5, the transition in the pertinent solutions occurs at a critical flaw size ac/q 0.2. The present experimental results and observations reside in the domain a/q > ac/q.
The two strength ratios, defined by Eqs. (9) and (10), are plotted against a/q in Fig. 11(b). This ratio is constant up to the critical value, ac/q, but subsequently increases with a/q. Also shown in Fig. 11(b) is the range of strength ratios that had been obtained experimentally for both the d and the d + (Cu) joints. The latter clearly fall in the domain a > ac, re-affirming the earlier conclusion that the notch root radius can be neglected in calculating the fracture toughness. As a further check on this conclusion, the preceding analysis has been combined with the measured strength ratios to infer the size of the strength-limiting flaws. Upon re-arranging Eq. (10), the latter flaw size is 2 rN F ðc=bÞ a=c ¼ : ð11Þ rU 1:12 Combining this result with the pertinent measured values yields flaw sizes of 70 ± 7 and 77 ± 8 lm for the d and d + (Cu) microstructures, respectively. These
2026
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
values are in broad agreement with the measured flaw sizes on the fracture surfaces (Fig. 9). Furthermore, they are considerably larger than the critical value, ac 30 lm, beyond which the notch can be treated as a sharp crack. Having ascertained that the finite notch root radius can be neglected, the fracture toughness values of the two d-containing joints werepcalculated via Eq. (5). They are Kc 4.6 and 6.7 MPa m for the d and d + (Cu) joints, respectively. Both are considerably lower p than the value for the (Cu) joints (Kc 13 MPa m), obtained from the work of fracture measurements.
to the observed elevations in both strength and toughness. The conversion of the joint microstructure to (Cu) yields improvements in toughness, but reductions in unnotched strength: a consequence of the reduced flow stress of the (Cu) relative to that of the d-phase. An additional consequence is the production of voids, which are likely deleterious to both strength and toughness. It is surmised that heat treatment conditions that yield the targeted (Cu) joints without forming voids, using either shorter times or lower temperatures for annealing, might be viable.
5. Discussion
6. Conclusions
The fracture toughness of the d-phase is low, but consistent with values for other intermetallic compounds. Nevertheless, with the rather small flaws produced during bonding (<100 lm), the strength (300 MPa) appears to be at a reasonably high level, possibly acceptable for the targeted applications in power electronic devices. The addition of the (Cu) particles to the d-phase enhances both the strength and the toughness by an appreciable amount (about 30%). The toughness enhancement can be rationalized on the basis of existing models of ductile phase toughening in the following way. Assuming steady-state fracture conditions, the fracture energy Gd attributable to the ductile particles can be determined from the matrix toughness Go and the composite toughness Gc via [11–13]:
The strength and toughness of joints produced by TLP bonding in the Cu–Sn system depend sensitively on the terminal microstructure, as dictated by the thermal history. The d-phase appears to be rather strong but brittle. Improvements in both strength and toughness can be obtained through conversion of the d-phase to the d + (Cu) microstructure. From a practical viewpoint, this property enhancement comes at the expense of an additional heat treatment, at a somewhat higher temperature than that used for bonding. Its acceptability would depend on the high temperature stability of the components to be bonded. Conversion of the microstructure to (Cu) has mixed consequences: increasing the toughness, but decreasing the unnotched strength. It would be desirable in situations where large flaws are introduced either during processing or subsequently in service. Otherwise, the expense of the extended heat treatment and the effect of the treatment on the microstructure of the components may not be justifiable.
Gd ¼ Gc ð1 f ÞGo ;
ð12Þ
where Go and Gc are obtained from the corresponding Kc values via the Irwin relation. For the d + (Cu) system, Gd 320 J/m2. Moreover, the ductile phase toughening contribution should scale in accordance with [11–13]: Gd ¼ ary fR;
Acknowledgments
ð13Þ
where ry is the yield strength of the ductile particles; R is the average particle radius and a is non-dimensional coefficient that depends on the hardening characteristics and ductility of the particles, but is typically of order unity. Nanoindentation measurements on the (Cu) particles give a yield stress of approximately 800 MPa (taken to be 1/3 of the hardness). The effective particle radius has been measured to be 1 lm and the volume fraction of particles is f = 0.25. Combining these results with Eq. (13) yields a 1.5. This falls well within the range of reported values for other composite systems. Specifically, it coincides closely with the value of 2 obtained for the Al2O3/Al system [11], wherein the metal reinforcements fracture in a similar chisel-point fashion. This correlation reaffirms that the main role of the (Cu) particles is in classical ductile phase toughening, leading
Funding for this work was provided by DARPA, through a sub-contract from Rockwell International (B8U410685).
References [1] [2] [3] [4]
Lee CC, Chen YC. Thin Solid Films 1996;286:213. Hou MM, Eager TW. J Electron Pack 1992;114:443. Bosco NS, Zok FW. Acta Mater 2004;52:2965. Metals handbook vol. 2 properties and selection: nonferrous alloys and special-purpose materials. 10th ed. New York: ASM International; 1990. p. 283. [5] Samal PK. In: Cieslak MJ, Perepezko JH, Kang S, Glicksman M, editors. The metal science of joining. The Minerals, Metals and Materials Society; 1992. p. 295. [6] Porter DA, Easterling KE. Phase transformation in metals and alloys. London: Chapman & Hall; 1993 [chapter 2].
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027 [7] [8] [9] [10]
Tattersall HG, Tappin G. J Mater Sci 1996;1:296. Dowling NE. Fatigue Eng Mater Struct 1979;2:129. Creager M, Paris PC. Int J Fract Mech 1967;3:247. Tada H. The stress analysis of cracks handbook. 2nd ed. St. Louis: Paris Productions Incorporated; 1985.
2027
[11] Sigl SL, Mataga PA, Dalgleish BJ, McMeeking RM, Evans AG. Acta Metall Mater 1988;36:945. [12] Bannister M, Shercliff H, Bao G, Zok F, Ashby MF. Acta Metall Mater 1992;40:1531. [13] Mataga PA. Acta Metall Mater 1989;37:3349.
Strength of joints produced by transient liquid phase bonding in the Cu–Sn system N.S. Bosco, F.W. Zok
*
Materials Department, University of California, Santa Barbara, CA 93106-5050, USA Received 24 February 2004; received in revised form 12 January 2005; accepted 12 January 2005
Abstract The paper focuses on the strength and toughness of joints produced by transient liquid phase (TLP) bonding in the Cu–Sn system. It is motivated by potential applications of TLP bonding in attachment of high-temperature wide bandgap devices to ceramic substrates. Model test specimens suitable for mechanical testing are developed, utilizing substrates of oxide dispersion strengthened copper. Three microstructural conditions are probed: a uniform layer of the d intermetallic phase (Cu41Sn11), a two-phase microstructure comprising the d-phase and a dispersion of ductile (Cu) particles, and a uniform Cu solid solution. Notched and unnotched bend tests are used to ascertain strength and toughness. The d-phase exhibits a reasonably high strength (300 MPa), but low toughp ness (5 MPa m). Addition of (Cu) particles increases both the strength and the toughness by about 30% (400 MPa and p 7 MPa m, respectively). These property enhancements are rationalized on the basis of existing models of ductile phase toughening. The conversion of the intermetallic to Cu solid solution leads to a decrease in strength (to 200 MPa), but an increase in toughness (to p 13 MPa m). The latter trends appear to be a consequence of the reduction in the flow stress of the joint material. Additionally, the conversion to (Cu) is accompanied by the formation of voids, predominantly near the prior boundary between the d-phase and the adjoining Cu. The voids likely diminish the joint properties, relative to the intrinsic values associated with the defect-free copper solid solution. 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Copper; Intermetallic phases; Electron beam methods; Fracture; Toughness
1. Introduction Transient liquid phase (TLP) bonding is a potential joining technique for attachment of high-temperature wide bandgap devices to ceramic substrates [1,2]. It can be implemented through the use of Cu metallization layers on both the device and the substrate and a low melting point metal as an interlayer material to effect bonding. To minimize bonding times and temperatures, the interlayer material should have a low melting point, coupled with high solubility and diffu*
Corresponding author. Tel.: +1 805 893 8699; fax: +1 805 893 8486. E-mail address: [email protected] (F.W. Zok).
sivity in the adjoining Cu. From an examination of binary phase diagrams, two candidate interlayer materials emerge: Sn and In. Both have melting points below 300 C and solubility limits in Cu of about 10–15% at temperatures of 400–500 C (the expected bonding range). Additionally, when the bonding process is taken to completion to form a Cu solid solution across the entire joint, the solidus temperature approaches 800 C. In this state, the mechanical properties of the joint should be retained for extended periods at the targeted upper service temperatures of these devices (300 C). However, both metals also produce a number of intermediate phases with Cu, introducing potential problems in bond integrity and reliability.
1359-6454/$30.00 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.01.013
2020
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
The overall objective of the present study is to probe the mechanical properties of joints produced by TLP bonding in the Cu–Sn system. It builds on an earlier study, focused on the bonding conditions necessary to produce joints with essentially pore-free microstructures [3]. In order to measure joint properties, a model system is developed, utilizing oxide dispersion strengthened (ODS) Cu as a substrate material. Its selection is based on its capability to retain high strength (about 420 MPa [4]) following the elevated temperature excursion associated with bonding. This high strength allows mechanical testing of the joint up to fracture, without detectable deformation remote from the joint location. Furthermore, with the use of thin sacrificial layers of pure copper on the ODS Cu substrates, the resulting microstructures are virtually identical to the ones previously obtained through TLP bonding of pure Cu substrates. One specific objective of this work is to assess the role of the joint microstructure on mechanical properties. To this end, three sets of bonding conditions are used. The resulting microstructures include a uniform layer of the d intermetallic phase (Cu41Sn11), a two-phase microstructure comprising the d-phase and a dispersion of ductile (Cu) particles, and a uniform Cu solid solution. The expectation is that the integrity and reliability of the joints should improve as the amount of remnant intermetallic is reduced. But this comes at the expense of increased bonding times and temperatures. In practice, the trade-offs between property enhancements and manufacturing cost would need to be considered in selecting an appropriate bonding schedule. Effects of thermal history on the microstructure and properties of surrounding materials would also need to be addressed. In an attempt to determine the fracture toughness of these joints, bend tests are performed on standard edgenotched specimens. An assessment of the effects of the finite notch root radius on the validity of the fracture toughness measurements is made through a stress analysis of the notch tip region. The analysis is coupled with the strength measurements in both notched and unnotched configurations, as well as fractographic observations, to determine whether the notch can be legitimately treated as a sharp crack in calculating fracture toughness. It is demonstrated that, in two of the three joint types tested in the current study (specifically, those that contain the d-phase), the pre-existing flaws are sufficiently large in relation to the notch root radius such that the notches can indeed be treated as cracks.
2. Specimen fabrication and mechanical testing techniques The test specimens were prepared in the following way. ODS Cu rods, 32 mm in diameter and 25 mm long, were ground to an optically flat finish using 3 lm diamond
Fig. 1. Phase diagram for the Cu–Sn system. At the bonding temperature of 400 C, the terminal (most Cu-rich) intermetallic phase is d. For the subsequent heat treatment at 550 C, d is consumed in the formation of c, which, in turn, decomposes into d + (Cu) upon cooling.
paste. In the initial bonding attempts, the polished rods were coated with Sn and bonded in the manner described below. These bonds proved to be of poor mechanical integrity, because of entrainment of the alumina dispersoids (originally contained within the ODS Cu) into the liquid phase and banding of the dispersoids during subsequent solidification. Fracture invariably occurred along the dispersoid bands at low strength levels. To mitigate this problem, the procedure was modified, through addition of thin sacrificial layers of pure Cu. To this end, the polished ODS Cu rods were coated with 50 lm of Cu by electron beam deposition (EBD). To ensure adequate smoothness for bonding, the coated surfaces were polished. Moreover, to enhance adhesion between the deposited Cu and the underlying ODS Cu, the coated rods were annealed at 800 C for 5 min under flowing 5% H2 in Ar [5]. Following this treatment, the substrates were immediately placed back in the EBD chamber for deposition of a 10 lm thick Sn layer. The total Sn layer thickness, 20 lm (when matching pairs of coated rods are bonded), exceeds the minimum value of 12 lm, prescribed by results presented in a previous study [3]. Bonding was performed in a vacuum furnace at 2 · 106 torr. The temperature was ramped at a rate of 5 C/min. This low heating rate was chosen to minimize temperature gradients in the sample and to prevent temperature overshoots on approach to the targeted bonding temperature. Bonding was performed at 400 C for 4 h. These conditions produced a uniform layer of the d-phase, without remnant e, g or Sn, and without porosity (Fig. 3(a)). 1 The rods were sectioned by electrodis1 The d phase is metastable for extended periods at room temperature; its decomposition into e + (Cu) through the eutectoid reaction at 350 C is extremely sluggish. Indeed, subsequent heat treatments at 300 C for 24 h followed by both X-ray diffraction measurements and energy-dispersive spectroscopy in a scanning electron microscope revealed negligible amounts of e-phase.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
charge machining into unnotched bend specimens, 3 mm · 3 mm in cross-section, and notched beams, 3 mm · 6 mm in cross-section, with notches machined to half of the specimen depth along the joint (Fig. 2). The notch root radius was q = 160 lm. Following sectioning, some specimens were subject to further heat treatments to produce alternate microstructures. In one set, the beams were heated for an additional 30 min at 550 C. During this treatment, the d-phase is converted to c-phase (Fig. 1). Upon cooling, the c-phase undergoes a eutectoid reaction (at 520 C), resulting in a two-phase microstructure comprising a d-phase matrix and a dispersion of (Cu) particles (Fig. 3(b)). The volume fraction, f, of (Cu) particles was measured to be approximately 25%: consistent with a lever rule calculation from the phase diagram. Another set of specimens was heated for 20 h at 600 C. Through this treatment, the d-phase is consumed in the formation of (Cu) across the entire joint. However, this is accompanied by the formation of pores, predominantly at the boundary between the prior d-phase and the adjoin-
2021
Fig. 2. Schematic of the bonded rods and the sectioning procedure used to extract bend specimens.
Fig. 3. Optical micrographs of cross-sections through the three joint types: (a) following bonding at 400 C for 4 h; (b) with additional treatment of 550 C for 30 min; and (c) with additional treatment of 600 C for 20 h.
2022
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
ing Cu. These pores are believed to be a consequence of the Kirkendall effect: the diffusivity of Sn (with its low melting point) being significantly higher than that of Cu [6]. The unnotched beams were tested in four-point flexure, with inner and outer loading spans of 20 and 40 mm, respectively. The notched specimens were tested in three-point flexure, with the same outer loading span. All tests were preformed on an Instron 8562 test frame, equipped with a 900 N compression load cell, at a displacement rate of 0.01 mm/min. The fracture surfaces were subsequently examined in a scanning electron microscope (SEM).
3. Measurements and observations 3.1. Strength The measured strength values are summarized in Fig. 4. The d-phase exhibited a rather high unnotched strength (300 MPa), but a high degree of notch sensitivity: the notched/unnotched strength ratio (on a netsection basis) being about 0.5. The addition of the (Cu) particles to the d-phase produced a 30% increase in unnotched strength, to about 400 MPa. A similar relative increase was obtained in the notched strengths of the two joint types, from 140 to 190 MPa. The similarities in the strength elevations in the notched and unnotched configurations suggest an increase in toughness but with no change in the size of the strength-limiting flaws. This effect is attributable to ductile phase toughening by the (Cu) particles, as detailed later. Upon conversion of the microstructure to only (Cu), the unnotched strength decreased relative to that of the two-phase microstructure, by almost 50%. In contrast,
Fig. 4. Summary of notched and unnotched strength measurements. Net-section and remote stresses in the notched configuration are related to one another by a factor (1 c/b)2 = 0.25.
Fig. 5. Typical load–displacement curves for the notched test specimens. In joints containing d or d + (Cu), crack propagation occurs unstably at the load maximum. In contrast, in joints with only (Cu), it occurs stably across the entire cross-section, without precipitous load drops.
Fig. 6. Fracture surface of a d joint, showing combinations of transgranular (T) and intergranular (I) fracture.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
the corresponding notched strength increased by about 15%, reaching a level virtually identical to that of the unnotched (Cu) specimens (230 MPa). That is, the ratio of notched-to-unnotched strength was essentially unity. The diverging trends in notched and unnotched strengths coupled with the notch-insensitivity of the (Cu) joints suggest that the enhancement in toughness associated with the conversion of d to (Cu) is accompanied by a significant reduction in the flow stress of the joint material. Evidently, the latter reduction is sufficient to cause failure to occur by plastic yielding followed by ductile rupture. An additional pertinent feature of the (Cu) joints is the stable manner in which fracture occurred. That is, the load–displacement response varied smoothly as the crack propagated across the bond section. In contrast, the d-containing joints exhibited precipitous load drops at the onset of cracking (at the load maximum), in similarly notched configurations. These behaviors are illustrated in Fig. 5.
2023
3.2. Fractography SEM observations of the fracture surfaces revealed that fracture had occurred through the interlayers in all cases (not the sacrificial EBD Cu or the ODS Cu).
Fig. 8. Fracture surface of a (Cu) joint, showing predominantly ductile rupture, but accompanied by some brittle fracture facets.
Fig. 7. Fracture surface of a d + (Cu) joint, showing brittle fracture of the d-phase along with plastic stretching and chisel-point fracture of the embedded (Cu) particles.
Fig. 9. A typical bonding flaw (highlighted by the white line), found at the notch tip of a d joint.
2024
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
The d-phase exhibited a combination of transgranular and intergranular fracture, without evidence of appreciable plasticity (Fig. 6). The d-phase within the d + (Cu) joints fractured in a similarly brittle manner. In contrast, the (Cu) particles embedded within the dphase exhibited significant plastic stretching, with most displaying chisel point fracture (Fig. 7). This feature exemplifies the targeted ductile phase toughening associated with the two-phase microstructure. The (Cu) fracture surfaces exhibited predominantly ductile dimpling (Fig. 8). However, there was evidence of brittle faceted features, likely a consequence of the pre-existing pores. Notwithstanding, the extensive dimpling coupled with the notch-insensitivity of strength re-affirms the assertion that fracture occurs through local yielding of the (Cu), at stresses dictated by the flow stress of the (Cu). In the two microstructures containing the d-phase, the tensile side of the fracture plane was found to contain irregularly shaped bonding defects, typically no greater than about 100 lm. The rounded topography of these defects suggests that they are a result of remnant porosity. One such example is shown in Fig. 9. In this example, the defect extends about 70 lm into the material beyond the notch tip.
4. Analysis of notched strength The preceding results for notched strength have been analyzed, with the objective of obtaining estimates of fracture toughness. For the case of the (Cu) joints, the lack of notch sensitivity in strength precludes use of standard LEFM solutions for stress intensity factors in calculating fracture toughness. As a consequence, an estimate of toughness was obtained from the associated work of fracture [7] coupled with the Irwin relation. The procedure is facilitated by the stable crack growth across the cross-section (Fig. 5). Such measurements yield a fracture energy of 1700 ± 200 J/m2 and a corresponding fracture toughness (usingp a YoungÕs modulus of 110 GPa) of Kc 13 MPa m. The high notch sensitivity of the d-containing joints suggests that the fracture toughness might be obtained from the peak load in the notched bend tests, predicated on the assumption that the notch acts as a sharp crack. An assessment of this assumption is made in the following way. First, an estimate is made of the minimum size of a pre-existing flaw at the tip of a circular notch beyond which the notch can be treated as a sharp crack. Second, the measured notched and unnotched strengths are used to infer the size of the strength-limiting flaw and the result then compared with the preceding minimum value. The analysis follows. The analysis is based on the configuration shown schematically in Fig. 10. It consists of a notched beam
Fig. 10. A schematic showing a flaw at the tip of a rounded notch in a three-point bend specimen. An analysis of this loading configuration yields the results plotted in Fig. 11.
of a homogeneous linear elastic material. 2 A preexisting sharp flaw of length a resides at the tip of a rounded notch, with root radius q and length c. The notched beam is subjected to a remote bending stress, r1. The effect of notch root radius on the notched strength is assessed by considering two limiting cases, wherein the pre-existing flaw is either much smaller or much larger than q. An analogous approach has been used previously in the analysis of cracks emanating from circular holes [8]. In case I, a q and thus the stress intensity factor for the flaw is pffiffiffiffiffiffi K ¼ 1:12rL pa; ð1Þ where the numerical coefficient 1.12 is the free surface correction factor and rL is the maximum local stress at the notch tip. In turn, the local stress is given by [9] 2K nom rL ¼ pffiffiffiffiffiffi ; pq
ð2Þ
where Knom is the nominal stress intensity factor at the tip of a sharp crack with the same length as that of the notch and subject to the same loading conditions pffiffiffiffiffi ð3Þ K nom ¼ r1 pcF ðc=bÞ; where F(c/b) is the usual finite crack correction factor (tabulated, for example, in [10]). Combining Eqs. (1)– (3) yields the result in non-dimensional form pffiffiffiffiffiffiffiffi K pffiffiffiffiffi ¼ 2:24 a=qF ðc=bÞ: ð4Þ r1 pc 2
The assumption that the layer is elastically homogeneous is justified on the basis of YoungÕs modulus measurements, made by depth-sensing nanoindentation. Specifically, the moduli of the EBD Cu, the ODS Cu and the solid solution (Cu) were all found to lie in the range 110 ± 8 GPa: consistent with the expected value for Cu. The pertinent value for the d-phase was only slightly lower: 95 ± 5 GPa. The degree of elastic mismatch is deemed to be inconsequential.
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
In case II, q a c. Here the stress intensity factor is independent of q and given by K pffiffiffiffiffi ¼ F ðc=bÞ: r1 pc
ð5Þ
The stress intensity factors for the two limiting cases for c/b = 0.5 are plotted in Fig. 11(a). Accordingly, the intersection of the two provides an estimate of the critical value of ac/q; for a < ac, fracture is controlled by the stress concentration (Eq. (4)), whereas for a > ac, fracture is controlled by the nominal stress intensity factor (Eq. (5)). From the preceding treatment, the critical value is ac/q 0.2 for c/b = 0.5. For q = 160 lm (the value in the present experiments), the critical flaw size is ac 30 lm. As a preliminary assessment, it is noted that ac is less than the size of the flaws found on the fracture surfaces (by a factor of about 2–3), suggesting that the finite notch root radius can be neglected in the determi-
2025
nation of the fracture toughness. A more critical assessment of this conclusion follows. Further insights are obtained from a comparison of the notched and unnotched strengths, subject to the two preceding limiting cases. In case I, wherein a < ac, fracture occurs in the notched configuration when the local stress exceeds a critical value: rL ¼
Kc pffiffiffiffiffiffi ; 1:12 pa
ð6Þ
where Kc is the fracture toughness. In turn, the local stress rL can be expressed in terms of the remote stress, via Eqs. (2) and (3), yielding a remote notched strength of h pffiffiffiffiffiffiffiffi i1 Kc pffiffiffiffiffiffi 2 c=qF ðc=bÞ : rN ¼ ð7Þ 1:12 pa Recognizing that the unnotched strength rU is similarly related to fracture toughness, via rU ¼
Kc pffiffiffiffiffiffi 1:12 pa
ð8Þ
and assuming that the same flaws are present in both the notched and unnotched specimens, the ratio of notched to unnotched strength (from Eqs. (7) and (8)) becomes: i1 rN h pffiffiffiffiffiffiffiffiffiffiffi ¼ 2 ðc=qÞF ðc=bÞ : ð9Þ rU For the current test configuration, rN/rU = 0.082, independent of flaw size. In case II, wherein ac < a c, the ratio of notchedto-unnotched strength can be expressed analogously in terms of the fracture toughness, through combination of Eqs. (5) and (8), yielding: rN 1:12 pffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffi q=c a=q: ð10Þ ¼ rU F ðc=bÞ
Fig. 11. Effects of normalized flaw size, a/q, on (a) the stress intensity factor and (b) the ratio of notched to unnotched strength. For a notch length c/b = 0.5, the transition in the pertinent solutions occurs at a critical flaw size ac/q 0.2. The present experimental results and observations reside in the domain a/q > ac/q.
The two strength ratios, defined by Eqs. (9) and (10), are plotted against a/q in Fig. 11(b). This ratio is constant up to the critical value, ac/q, but subsequently increases with a/q. Also shown in Fig. 11(b) is the range of strength ratios that had been obtained experimentally for both the d and the d + (Cu) joints. The latter clearly fall in the domain a > ac, re-affirming the earlier conclusion that the notch root radius can be neglected in calculating the fracture toughness. As a further check on this conclusion, the preceding analysis has been combined with the measured strength ratios to infer the size of the strength-limiting flaws. Upon re-arranging Eq. (10), the latter flaw size is 2 rN F ðc=bÞ a=c ¼ : ð11Þ rU 1:12 Combining this result with the pertinent measured values yields flaw sizes of 70 ± 7 and 77 ± 8 lm for the d and d + (Cu) microstructures, respectively. These
2026
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027
values are in broad agreement with the measured flaw sizes on the fracture surfaces (Fig. 9). Furthermore, they are considerably larger than the critical value, ac 30 lm, beyond which the notch can be treated as a sharp crack. Having ascertained that the finite notch root radius can be neglected, the fracture toughness values of the two d-containing joints werepcalculated via Eq. (5). They are Kc 4.6 and 6.7 MPa m for the d and d + (Cu) joints, respectively. Both are considerably lower p than the value for the (Cu) joints (Kc 13 MPa m), obtained from the work of fracture measurements.
to the observed elevations in both strength and toughness. The conversion of the joint microstructure to (Cu) yields improvements in toughness, but reductions in unnotched strength: a consequence of the reduced flow stress of the (Cu) relative to that of the d-phase. An additional consequence is the production of voids, which are likely deleterious to both strength and toughness. It is surmised that heat treatment conditions that yield the targeted (Cu) joints without forming voids, using either shorter times or lower temperatures for annealing, might be viable.
5. Discussion
6. Conclusions
The fracture toughness of the d-phase is low, but consistent with values for other intermetallic compounds. Nevertheless, with the rather small flaws produced during bonding (<100 lm), the strength (300 MPa) appears to be at a reasonably high level, possibly acceptable for the targeted applications in power electronic devices. The addition of the (Cu) particles to the d-phase enhances both the strength and the toughness by an appreciable amount (about 30%). The toughness enhancement can be rationalized on the basis of existing models of ductile phase toughening in the following way. Assuming steady-state fracture conditions, the fracture energy Gd attributable to the ductile particles can be determined from the matrix toughness Go and the composite toughness Gc via [11–13]:
The strength and toughness of joints produced by TLP bonding in the Cu–Sn system depend sensitively on the terminal microstructure, as dictated by the thermal history. The d-phase appears to be rather strong but brittle. Improvements in both strength and toughness can be obtained through conversion of the d-phase to the d + (Cu) microstructure. From a practical viewpoint, this property enhancement comes at the expense of an additional heat treatment, at a somewhat higher temperature than that used for bonding. Its acceptability would depend on the high temperature stability of the components to be bonded. Conversion of the microstructure to (Cu) has mixed consequences: increasing the toughness, but decreasing the unnotched strength. It would be desirable in situations where large flaws are introduced either during processing or subsequently in service. Otherwise, the expense of the extended heat treatment and the effect of the treatment on the microstructure of the components may not be justifiable.
Gd ¼ Gc ð1 f ÞGo ;
ð12Þ
where Go and Gc are obtained from the corresponding Kc values via the Irwin relation. For the d + (Cu) system, Gd 320 J/m2. Moreover, the ductile phase toughening contribution should scale in accordance with [11–13]: Gd ¼ ary fR;
Acknowledgments
ð13Þ
where ry is the yield strength of the ductile particles; R is the average particle radius and a is non-dimensional coefficient that depends on the hardening characteristics and ductility of the particles, but is typically of order unity. Nanoindentation measurements on the (Cu) particles give a yield stress of approximately 800 MPa (taken to be 1/3 of the hardness). The effective particle radius has been measured to be 1 lm and the volume fraction of particles is f = 0.25. Combining these results with Eq. (13) yields a 1.5. This falls well within the range of reported values for other composite systems. Specifically, it coincides closely with the value of 2 obtained for the Al2O3/Al system [11], wherein the metal reinforcements fracture in a similar chisel-point fashion. This correlation reaffirms that the main role of the (Cu) particles is in classical ductile phase toughening, leading
Funding for this work was provided by DARPA, through a sub-contract from Rockwell International (B8U410685).
References [1] [2] [3] [4]
Lee CC, Chen YC. Thin Solid Films 1996;286:213. Hou MM, Eager TW. J Electron Pack 1992;114:443. Bosco NS, Zok FW. Acta Mater 2004;52:2965. Metals handbook vol. 2 properties and selection: nonferrous alloys and special-purpose materials. 10th ed. New York: ASM International; 1990. p. 283. [5] Samal PK. In: Cieslak MJ, Perepezko JH, Kang S, Glicksman M, editors. The metal science of joining. The Minerals, Metals and Materials Society; 1992. p. 295. [6] Porter DA, Easterling KE. Phase transformation in metals and alloys. London: Chapman & Hall; 1993 [chapter 2].
N.S. Bosco, F.W. Zok / Acta Materialia 53 (2005) 2019–2027 [7] [8] [9] [10]
Tattersall HG, Tappin G. J Mater Sci 1996;1:296. Dowling NE. Fatigue Eng Mater Struct 1979;2:129. Creager M, Paris PC. Int J Fract Mech 1967;3:247. Tada H. The stress analysis of cracks handbook. 2nd ed. St. Louis: Paris Productions Incorporated; 1985.
2027
[11] Sigl SL, Mataga PA, Dalgleish BJ, McMeeking RM, Evans AG. Acta Metall Mater 1988;36:945. [12] Bannister M, Shercliff H, Bao G, Zok F, Ashby MF. Acta Metall Mater 1992;40:1531. [13] Mataga PA. Acta Metall Mater 1989;37:3349.