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Effect of SiC Volume Fraction and Particle Size on the Fatigue Resistance of a 2080 Al/SiCp Composite N. CHAWLA, C. ANDRES, J.W. JONES, and J.E. ALLISON The effect of SiC volume fraction and particle size on the fatigue behavior of 2080 Al was investigated. Matrix microstructure in the composite and the unreinforced alloy was held relatively constant by the introduction of a deformation stage prior to aging. It was found that increasing volume fraction and decreasing particle size resulted in an increase in fatigue resistance. Mechanisms responsible for this behavior are described in terms of load transfer from the matrix to the high stiffness reinforcement, increasing obstacles for dislocation motion in the form of S’ precipitates, and the decrease in strain localization with decreasing reinforcement interparticle spacing as a result of reduced particle size. Microplasticity was also observed in the composite, in the form of stress-strain hysteresis loops, and is related to stress concentrations at the poles of the reinforcement. Finally, intermetallic inclusions in the matrix acted as fatigue crack initiation sites. The effect of inclusion size and location on fatigue life of the composites is discussed.

I.

INTRODUCTION

METAL matrix composites (MMCs) offer several advantages over conventional monolithic metallic alloys.[1,2,3] These include improved strength and stiffness, while providing weight savings and higher operating temperatures. One important design criterion in these materials is fatigue resistance, particularly in automotive components, where high cycle fatigue resistance is often required. Monolithic aluminum alloys of the type Al-Cu-Mg (2024 or 2080), while low in density, have inadequate fatigue resistance for many applications. The addition of a high stiffness ceramic particulate reinforcement, such as SiC, to aluminum alloys can result in a substantial increase in fatigue resistance while maintaining cost at an acceptable level.[4,5] Two types of strengthening may occur in MMCs: direct and indirect.[4] Direct strengthening results from load transfer from the matrix to the reinforcement. Indirect strengthening results from the influence of reinforcement on matrix microstructure or deformation mode. One example of indirect strengthening is the thermally induced dislocations produced by the thermal mismatch between the reinforcement and the matrix, which ‘‘indirectly’’ strengthen the composite.[6,7] Since dislocations act as nucleating sites for precipitate formation during aging, the increased dislocation density in the composites also promotes accelerated aging in the matrix.[8] Thus, the intrinsic properties and microstructure of the matrix material may be significantly different than those of the unreinforced alloy, and separating N. CHAWLA, Postdoctoral Research Fellow, and J.W. JONES, Associate Dean for Undergraduate Education and Professor, are with the Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2136. C. ANDRES, formerly Postdoctoral Research Fellow, Department of Materials Science and Engineering, University of Michigan, is currently Research Associate in the Department of Physical Metallurgy, Darmstadt University of Technology, 64287 Darmstadt, Germany. J.E. ALLISON, Senior Staff Technical Scientist, is with the Ford Research Laboratory, Ford Motor Company, Dearborn, MI 48124. Manuscript submitted March 9, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A

indirect and direct strengthening mechanisms becomes a difficult task. For example, there remains controversy on whether the observed strengthening in the composites, over the unreinforced alloy, is due to load transfer to the reinforcement[9,10,11] or is simply a result of thermally induced dislocations that strengthen and increase the work hardening rate in the matrix.[12,13] A limited number of systematic experimental studies have been conducted to determine the effect of reinforcement volume fraction and particle size on the fatigue life of particle-reinforced MMCs.[14–17] While these studies conclude that, in general, increasing volume fraction and decreasing particle size improve fatigue resistance, the underlying mechanisms for these improvements remain unclear. Many investigators have found that when stress-controlled experiments are used to characterize fatigue, the fatigue lives of particle-reinforced MMCs are generally longer than those of unreinforced metals.[14–18] These improvements are most pronounced at lower stresses, in the high cycle fatigue regime, while at high stress, the differences between reinforced and unreinforced materials are reduced. Fatigue behavior also depends on test mode, i.e., stress or strain control. When total strain[19,20] or plastic strain[21] controlled testing is used, the fatigue resistance of particle-reinforced MMCs is observed to be inferior to that of a similar unreinforced alloy. This is because in monotonic loading, at a fixed strain, the composite undergoes a higher stress than the unreinforced material as a result of the higher work hardening in the composite.[4,12,13] Thus, for a given strain, the fatigue stress applied to the composite will be much closer to the ultimate tensile strength than that applied to the unreinforced alloy, so the fatigue life in the composite is lower. Holcomb[22] and Hall et al.[14] have reported that for peakaged Al alloy matrix composites, decreasing SiC particle size led to an increase in stress-controlled fatigue life. The lower fatigue strength of the composite containing coarse particles was attributed to the increased propensity for particle cracking as the particle size increased. A clear dependence of increased frequency of particle cracking with increasing size has been observed in fatigue[14,22] and in tenVOLUME 29A, NOVEMBER 1998—2843

Fig. 1—Particle cracking in F-280 reinforcement prior to fatigue testing.

(a)

structural factor is the presence of intermetallic inclusions formed during processing. Li and Ellyin[25] observed that fatigue damage–induced degradation took place in the form of matrix cracking at large intermetallic particles, reinforcement defects, particle clusters, or large reinforcement particles with sharp edges surrounded by large reinforcementfree areas. This localized damage then led to initiation and extension of a short crack. Similar crack initiation sites were observed by Bonnen et al.[18] Levin and Karlsson[26] reported that cracks in a 6061/SiC/15p composite initiated near the particle/matrix interface, in regions of high volume fraction of reinforcement, or by fracturing of individual particles, which were stressed more highly than particles completely within the matrix. This study indicates that fatigue crack initiation and failure may be more likely to take place at defects at the surface of the specimen. The onset of fatigue crack initiation has also been studied in some whisker-reinforced MMCs. In a SiC whisker-reinforced Al matrix composite, Chen et al.[27] showed that in the low cycle regime, cracks originated early in fatigue life, at approximately 10 pct of total life. In the high cycle regime, on the other hand, crack initiation occurred quite late (after about 80 pct of the life of the specimen). Lukasek[28] observed the initiation of fatigue cracks in the high cycle regime, also at about 70 to 90 pct of total life, for spherical Si particles embedded in an Al matrix. Thus, it appears that in the low cycle regime, crack propagation was dominant, while at long lives, crack initiation was more important in determining fatigue life. The purpose of this study was to quantify the effect of volume fraction and size of reinforcement on fatigue behavior. In an attempt to minimize indirect strengthening effects, a thermomechanical treatment was used to maintain a constant precipitate structure in the matrix of the composite and the unreinforced alloy. The effect of intermetallic inclusions on the fatigue behavior of the composites vs the unreinforced alloy is also detailed.

II.

(b) Fig. 2—(a) Particle size and (b) aspect ratio distributions for the SiC particulate reinforcement, 25 mm (F-280), 7 mm (F-600), and 5 mm (F1000).

sion.[23] Couper and Xia[24] showed, further, that the size distribution of the reinforcement is also very important. By narrowing the range of particle distribution in a 15 pct Al2O3 reinforced 6061 T6 Al composite, the fatigue life was increased because the fracture of larger particles in the distribution was eliminated. In powder metallurgy composites, an additional micro-

2844—VOLUME 29A, NOVEMBER 1998

MATERIALS AND EXPERIMENTAL PROCEDURE

The composite examined in this study was consolidated via powder metallurgy processing and extruded (Alcoa Technical Center, Alcoa, PA). In the powder metallurgy processing route, powders of SiC and Al are blended and hot pressed to achieve consolidation of the Al matrix. Details of the powder metallurgy process for fabricating discontinuously reinforced MMCs can be found elsewhere.[29,30,31] A 2080 Al alloy (Al-3.6Cu-1.9Mg-0.2Zr, age hardenable) was reinforced with 10, 20, and 30 pct SiC particles. Of these, for 20 pct SiC composites, three separate composites were fabricated with varying particle size: 23 mm (F-280), 6mm (F-600), and 5 mm (F-1000). The similarity in particle size between F-1000 and F-600 was unintentional and may have been the result of particle fracture in F-600 during the extrusion and the rolling treatment described subsequently. Particle cracking in F-280 was also observed prior to fatigue testing (Figure 1). The particle size distribution for all three particle sizes is shown in Figure 2(a). Notice that F-1000 has the narrowest distribution, followed by F-600 and F-280. The aspect ratio of the par-

METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 3—Microstructures of 2080 Al alloy reinforced with (a) 0 pct SiC, (b) 10 pct SiC, (c) 20 pct SiC, and (d ) 30 pct SiC.

ticles, defined as the ratio of largest to smallest diameter for a given particle, Dmax/Dmin, is given in Figure 2(b). All particle distributions showed a mean aspect ratio of about 2. Figure 3 shows the reinforcement distribution in the composite compared with the microstructure of the unreinforced alloy. In the composite materials, some preferential alignment of the reinforcement particles along the extrusion axis was seen. The matrix microstructure also contained a distribution of Fe-Si rich intermetallic inclusions that were formed as a result of the powder process. A thermomechanical treatment (T8 treatment) developed by Krajewski et al.[32] was applied to the composite and the unreinforced alloy. The procedure consisted of a solution treatment at 493 5 2 7C for 2 hours followed by a water quench, cold rolling (5 pct reduction in thickness), and aging at 175 7C for 24 hours (peak aged). The rolling step was crucial since it provided a homogeneous distribution of dislocations that served as heterogeneous nucleation sites for precipitation, and resulted in nearly identical S’ precipitates in the microstructures of all the composites as well as the unreinforced alloy. Microstructures in the reinforced and unreinforced conditions were characterized via transmission electron microscopy (TEM). Foils were prepared by jet thinning using a nitric/methanol solution (1:4 ratio) at 220 7C and by ion milling using a working chamber cooled by liquid nitrogen. Tensile and fatigue samples were machined using lowstress grinding. The gage diameter of tensile specimens was 5.08 mm and that of fatigue samples was 4 mm. An extensometer with a gage length of 12.7 mm was used in all tests. Tensile tests were carried out at a strain rate of 1023 s21. Axial fatigue tests were carried out in stress control mode using a triangular waveform, R ratio (smin/smax) of


21, and a frequency of 30 Hz. All tests were conducted on a servohydraulic load frame. Surface replicas of the gage section of the specimen were taken throughout the fatigue tests to characterize the onset of crack initiation.

III.

RESULTS

The S’ precipitates (AlCu2Mg) that form in Al-Cu-Mg alloys have a needlelike morphology and are semicoherent.[33] These precipitates can nucleate heterogeneously, particularly at dislocations and grain boundaries.[34,35] As a result of the rolling step in the T8 process, the precipitates formed in both the unreinforced alloy in the composite were homogeneously distributed and identical in all materials (Figure 4). The precipitates were quite small with a spacing of approximately 30 nm. The effect of different heat treatments and matrix microstructures on fatigue behavior of 2080 Al/SiCp composites is reported separately.[32] Increasing amounts of reinforcement led to higher elastic modulus, yield strength, and ultimate strength, with a corresponding decrease in ductility (Table I). Similar trends have been reported by several investigators.[36–39] Smaller particle sizes for a given volume fraction of reinforcement resulted in higher strength levels. At the largest particle size (F-280), strength values were found to be substantially below that of the base alloy. Microscopic examination of tensile fracture surfaces showed significant particle fracture in the F-280 composite. This is attributed to the statistical nature of flaw-sensitive fracture in the ceramic reinforcement, i.e., the probability of a particle containing a strength-limiting flaw increases with increasing particle size.[14] The beneficial effects of increasing volume fraction and

VOLUME 29A, NOVEMBER 1998—2845

Fig. 4—T8 microstructures in (a) matrix of 2080 Al/SiCp composite and (b) unreinforced alloy (TEM, ^100& zone axis).

Table I.

Tensile Properties of Reinforced and Unreinforced 2080 Al

30 pct, F-1000 20 pct, F-1000 10 pct, F-1000 20 pct, F-600 20 pct, F-280 Unreinforced

Yield Strength (MPa)

Ultimate Strength (MPa)

Elastic Modulus (GPa)

Strain to Failure (Pct)

575 539 528 522 457 490

639 593 574 563 478 525

119 107 89 106 95 75

2.27 3.14 6.34 2.88 1.02 9.0

Fig. 5—Effect of SiC reinforcement volume fraction on fatigue life (constant SiC particle size, F-1000).

decreasing particle size were observed in fatigue as well. Figure 5 shows stress amplitude vs cycles to failure for the unreinforced and composite materials with varying reinforcement volume fractions. Increasing SiC volume fraction resulted in higher fatigue strength (taken as the highest stress at which a specimen survived 107 cycles), (Table II). 2846—VOLUME 29A, NOVEMBER 1998

Table II. Effect of Reinforcement Volume Fraction (F-1000 Particle Size) on Fatigue Properties of 2080 Al

30 pct SiC 20 pct SiC 10 pct SiC Unreinforced

Approximate Fatigue Strength (107 Cycles), sfat (MPa)

Yield Strength (0.2 Pct Offset), s0.2 (MPa)

Fatigue Ratio (sfat /s0.2 )

250 230 210 140

575 539 528 490

0.43 0.42 0.40 0.28

In particular, the highest volume fractions, 30 pct, showed a pronounced improvement in fatigue strength compared to the matrix alloy. The fatigue ratio, taken as the ratio of fatigue strength to yield strength, was fairly constant for all composites and significantly higher than that of the 2080 Al alloy. The stress vs cycles curves also showed an apparent convergence in fatigue lives of the composite and the unreinforced alloy at high stresses, which may be attributed to the lower ductility in the composite materials, i.e., ‘‘ductility exhaustion.’’ At high plastic strains (i.e., short lives), the cyclic ductility of a material limits the amount of plastic strain and, thus, the number of cycles that can be accumulated prior to fracture. Therefore, at high stresses, although the plastic strains are lower in the composite material, so too is the cyclic ductility and the resistance to cyclic strains. The presence of intermetallic inclusions, believed to originate in the starting Al powder or during processing, is the likely cause of a somewhat larger than average scatter in fatigue life, especially at lower stresses. The high degree of scatter in fatigue life is probably due to the variation in size of large iron-rich intermetallic inclusions at the surface (sometimes greater than 100 mm). The inclusions (Figure 6(a)), as well as particle clusters (Figure 6(b)) acted as crack nucleation sites for fatigue failure, as has been docMETALLURGICAL AND MATERIALS TRANSACTIONS A

(a)

(b) Fig. 6—SEM micrograph of (a) intermetallic inclusion and (b) particle cluster, that served as a fatigue failure initiation site. Fatigue initiation and fast fracture regions are marked I and F, respectively.


VOLUME 29A, NOVEMBER 1998—2847

Fig. 7—SEM micrographs of (a) fatigue initiation region and (b) fast fracture region. A larger fraction of decohered or fracture particles is observed in the fast fracture region.

umented by several other investigators.[14,26,40,41] Two distinct fracture morphologies were observed: an initiation region (marked I) and a fast fracture region (marked F). Higher magnifications of these two regions (Figure 7) show that the fracture region around the initiation site did not have as many fractured or decohered particles (Figure 7(a)) as the fast fracture region (Figure 7(b)). Crack initiation during fatigue was monitored by taking surface replicas of the specimen gage section. A crack length of 10 mm was taken as the threshold for the detection of a crack at a given number of cycles, Ni. In the composite, crack initiation occurred early in fatigue life in the low cycle (high stress) regime (Figure 8). In the high cycle regime, crack initiation occurred quite late in life, indicating that initiation dominated in the high cycle regime, while propagation dominated in the low cycle regime. Surface replicas and scanning electron microscopy (SEM) fractography showed that a more torturous path for crack growth was observed in the composite, due to the closely spaced reinforcing particles, than in the unreinforced material. An example of this is shown in Figure 9. The effect of particle size on fatigue life in composites with a constant volume fraction of 20 pct SiC is shown in Figure 10. In general, decreasing the particle size led to slightly higher fatigue strengths, although the incremental increase between the finer particle sizes (F-600 and F-1000) was not as significant as that from F-280 to F-600 (Table III). The latter was due to the relatively similar average particle sizes and distributions between F-600 and F-1000. F-280 reinforcement showed little improvement over the unreinforced alloy due to cracking of the large particles prior to fatigue. In general, cracking, caused by the rolling treatment prior to fatigue, was observed predominantly in the highest particle size reinforcement, but not in the finer particles, i.e., F-600 and F-1000.

IV.

DISCUSSION

To fully understand fatigue mechanisms in this composite, it is instructive to discuss the increase in modulus and yield strength of the composite over the unreinforced alloy. The increase in modulus has been explained analytically 2848—VOLUME 29A, NOVEMBER 1998

and by the finite element method in References 23 and 42 through 44. The explanation for the increase in yield strength in the composite, on the other hand, is not as straightforward. Arsenault[12] has attributed the increase in strength to the high dislocation density that arises from thermal mismatch between the composite constituents. Others have suggested that much of the strengthening comes from load transfer from the matrix to the reinforcement.[5,9,11,44] Nardone and Prewo[9,11] have used a modified shear-lag type of analysis, due to the small aspect ratio of the SiC particles or ‘‘platelets,’’ to show that load transfer from the matrix to the particles exists. Using this analysis, the composite yield strength, scy, is given by[9]

scy 5 smy

~

Vp (S 1 4) 4

!

1 Vm

where smy is the unreinforced matrix yield strength, S is the aspect ratio of the reinforcement particle (taken from Figure 2(b)), and Vp and Vm are the volume fraction of particles and matrix, respectively. A comparison of experimental and predicted yield strengths is shown in Table IV. The matrix yield strength was taken to be the same as the unreinforced yield strength, given the same microstructure due to the T8 treatment. Relatively good agreement is observed for the finest particle sizes, i.e., F-1000 and F-600. However, the modified shear-lag model only takes into consideration the aspect ratio and not the particle size. Thus, for F-600 and F-280, although the aspect ratios are identical, the larger particle size in F-280 results in large matrix-rich regions and the yield strength in this composite is much lower than the predicted value. That the modified shear-lag theory accurately predicts composite yield strength for a range of SiC volume fraction levels and matrix yield strength indicates that load transfer is occurring in the composites. This is further proved by the substantial improvements in composite modulus relative to the unreinforced alloy, since a material with higher modulus should have more efficient load transfer to the reinforcement and a lower stress being applied to the matrix. This study shows that increasing volume fraction of SiC particles leads to improvements in fatigue resistance. Figure METALLURGICAL AND MATERIALS TRANSACTIONS A

occurs in the T8 matrix due to small precipitate size and spacing.[4,18] While the precipitates are deformable, the SiC particles are nondeformable, acting as obstacles to dislocation motion. A combination of nondeformable particles in a matrix of shearable precipitates can result in a beneficial change in the deformation mechanisms. According to Parker,[45] this condition occurs when the microstructure consists of nondeformable particles with a particle spacing of around 1 mm. The interpaticle spacing, l, for SiC particles in the present study is taken as the average center-to-center spacing between two particles less the particle diameter and is given by[47]

l'd Fig. 8—Fatigue ratio (cycles to crack initiation to cycles to failure) vs cycles for the composite with 20 pct SiCp, F-1000 reinforcement.

11 shows a plot of fatigue strength vs volume fraction for the three particle sizes. The fatigue strength increases with volume fraction because of the significant amount of the load being transferred to the stiffer particulate reinforcement and overall lower total strains for a given fatigue stress, as described in the previous paragraph. With decreasing particle size, for a given volume fraction, the fatigue strength of the composites also increased. The increase in fatigue strength was particularly significant when comparing the smaller particle sizes, i.e., F-600 and F-1000, to the coarsest particle size, F-280. We attribute this to fracture of the coarser particles that may have taken place during rolling, prior to fatigue testing. Optical microscopy revealed that the cracked particles had cracks that were unfilled by the matrix during rolling. The effect of the cracked particles is reflected in the slightly lower modulus and lower load-carrying capability in the F-280 composites with a given reinforcement volume fraction. The particle sizes of F-600 and F-1000 are relatively small so cracking can be ruled out as a mechanism for decrease in fatigue strength. Moreover, no cracked particles were found on fatigued fracture surfaces. The finer particles sizes are also quite similar (7 and 5 mm, respectively), yielding similar fatigue lives, while the broader size distribution in the F-280 may have contributed to its lower fatigue strength. Although reinforcement size is generally given as an average value, Couper and Xia[24] showed that by narrowing the range of particle distribution in a 15 pct Al2O3 reinforced 6061 T6 Al composite, the fatigue life increased because the fracture of larger particles in the distribution was eliminated. In our study, a narrower distribution in the F-1000 and F-600, coupled with particle cracking in F-280, provided the large magnitude improvement in fatigue life for the finer particle sizes. Another contributing factor for increase in fatigue strength may be related to the nature of slip in the matrix with increasing reinforcement particle volume fraction and size. If precipitates in the matrix are sheared by moving dislocations, strain localization reminiscent of persistent slip bands can occur since the precipitates are unable to resist any further deformation.[45,46] The concentration of slip deformation is likely to result in nucleation of small cracks in the matrix. It is likely that precipitate shearing METALLURGICAL AND MATERIALS TRANSACTIONS A

@~ ! # 1 2f

1/3

21

where d is the particle diameter and f is the volume fraction of particles. Table V shows the calculated values for interparticle spacing. Notice that at the highest volume fractions and smallest particle sizes, the interparticle spacing reaches the critical value of about 1 mm. Thus, with decreasing interparticle spacing up to the critical spacing, the fine precipitates give strength to the matrix, while the larger SiC particles prevent the formation of reversible slip bands when the particles are spaced closely enough. Parker[45] also suggests that the nondeformable particles can act to stabilize the cell structure in the matrix at low strains, while with increasing strain, a sharpening of the cell wall structure takes place with slight misorientation across the cell walls. The duplex particle microstructures have also shown beneficial effects in titanium alloys[48] as well as in aluminum alloys.[49] In our composites, the fortuitous combination of closely spaced SiC particles, at large volume fractions and small particle sizes, and fine precipitates in the matrix may serve as an indirect strengthening mechanisms. Another indirect mechanism relates to the distribution of intermetallic inclusions in the matrix of the composite and in the unreinforced alloy. Depending on the size of the inclusion, the stress concentration varied from specimen to specimen leading to scatter in fatigue life. Fractography of failed fatigue specimens showed that most specimens failed at an inclusion located at the surface of the specimen (Figure 12(a)). This is consistent with the observation in Reference 26, which showed that the stress concentration at an inclusion is greater when it is located at or near the surface than in the interior of a stressed volume. Furthermore, it has been shown that with the addition of SiC particles, the stress concentration on the inclusion is much lower, because a much larger fraction of the load is carried by the high stiffness reinforcement.[50] Thus, the stress enhancement in the unreinforced alloy is much greater than that of the composite, and the effect of an inclusion is much greater in the unreinforced material. It is also interesting to note that the size distribution of intermetallic inclusions in the composite is a function of reinforcement volume fraction. Figure 12(b) shows the size of inclusions for a given failed specimen, as a function of volume fraction. At the highest volume fraction, i.e., 30 pct, the size of the fatigue strength-limiting inclusions is much smaller than that for unreinforced or lower volume fracVOLUME 29A, NOVEMBER 1998—2849

(a) Fig. 9—Crack propagation in (a) unreinforced 2080 Al and (b) 2080 Al reinforced with 20 pct, F-1000 SiC particles. Continued on next page.

tions. We attribute this to the brittle inclusions being more likely to be fractured, with increasing volume fraction of particles, during the extrusion and rolling processes. Thus, the addition of the SiC particles served yet another indirect strengthening effect, by decreasing the size of the inclusions in the matrix and increasing the fatigue life of the composite. The presence of SiC reinforcement particles in the 2080 Al matrix also affects the onset of plasticity in the composites. In monotonic tension, an initial deviation from linearity in the stress-strain curves, termed here as the proportional limit stress, spl, was observed at stresses much lower than the macroscopic (e.g., 0.2 pct offset) yield stress. The origin of the proportional limit in MMCs was first documented by Corbin and Wilkinson,[51] who used load/unload sequences as well as incremental cyclic hysteresis loop measurements to determine the onset of detectable plastic strain. In this study, we define this threshold as a 1 pct deviation from linearity, in the elastic regime of the monotonic stress-strain curve.[52] Figure 13 shows the effect of reinforcement volume fraction on proportional limit, yield strength, and fatigue strength (taken as the stress for fatigue runout at 107 cycles). While the 0.2 pct offset yield strength and fatigue strength increase with volume fraction, the onset of plasticity, spl, shows the opposite trend. 2850—VOLUME 29A, NOVEMBER 1998

The decrease in proportional limit with increasing volume fraction can be attributed to microplasticity effects in the composite; i.e., upon the application of a far-field stress, the matrix begins to plastically deform in a localized and inhomogeneous manner. Goodier showed that for inclusions in an elastic medium, the localized deformation in the matrix takes place due to a stress concentration at the ‘‘poles’’ of the reinforcement.[53] Finite element studies of an elastic reinforcement in an elastic-plastic matrix have also shown this.[54,55] The stress concentration at the poles of the reinforcement is further magnified by the angular nature of the SiC particles[56] and may occur inhomogeneously in unyielded particle-free regions where there is little plastic constraint.[51] The relative volume of localized deformation in the composite increases with an increase in volume fraction of reinforcing particles because of a lower volume of matrix with larger number of particles, which results in the earlier onset of plasticity, i.e., a lower spl. While the decrease in matrix volume results in the earlier onset of plasticity, it also increases the work hardening rate of the composite, so the macroscopic yield strength of the composite increases with volume fraction of reinforcement. The residual stress in the composite also contributes to the early onset of microplasticity. Upon cooling, the Al matrix expands a greatly deal more than SiC, so the residual stress is tensile in the matrix and compressive in the parMETALLURGICAL AND MATERIALS TRANSACTIONS A

(b) Fig. 9—Continued. Crack propagation in (a) unreinforced 2080 Al and (b) 2080 Al reinforced with 20 pct, F-1000 SiC particles.

Table III. Effect of Reinforcement Size (20 Percent Reinforcement Volume Fraction) on Fatigue Properties of 2080 Al

F-1000 F-600 F-280 Unreinforced

Fig. 10—Effect of reinforcement particle size on fatigue life (constant volume fraction, 20 pct).

ticle. Thus, a lower far-field applied stress is required to obtain yielding in the composites. In some cases, a plastic zone will form around the particles upon cooling, because the residual stress at the interface is highest, and is high enough for yielding of the Al to take place. In our case, the 2080 Al alloy is rolled and age hardened and air cooled METALLURGICAL AND MATERIALS TRANSACTIONS A

Approximate Fatigue Strength (107 Cycles), sfat (MPa)

Yield Stress (0.2 Pct Offset), s0.2 (MPa)

Fatigue Ratio (sfat /s0.2 )

230 220 150 140

539 522 457 490

0.42 0.42 0.33 0.28

to room temperature. We can calculate the thermal residual stress in the matrix to determine whether yielding will occur upon cooling. Assuming a spherical SiC particle in an Al matrix shell, the radial stress can be given by[57] sr 5 Da DT

@

#

0.5 (1 1 nm ) 1 (1 2 2nm )Vp (1 2 2np ) 1 Em (1 1 Vp ) Ep

21

where Da is the difference in the coefficient of thermal expansion between the particle and matrix; DT is the temperature difference upon cooling (taken here as 150 K); and nm, np, Vm, Vp, Em, and Ep are the Poisson ratios, volume VOLUME 29A, NOVEMBER 1998—2851

Table IV.

Experimental and Predicted Yield Strength Values for the Composites

Strength (MPa)

Yield Strength (MPa)

Modified Shear Lag Prediction of Yield

30 Pct, F-1000 20 Pct, F-1000 10 Pct, F-1000 20 Pct, F-600 20 Pct, F-280 Unreinforced

575 539 528 522 457 490

561 537 514 533 531 —

(a)

Fig. 11—Fatigue strength vs volume fraction of reinforcement for all three particle sizes.

Table V. Interparticle Spacing as a Function of Particle Size for Various Volume Fractions of SiC Particle Size (mm)

10 Pct SiCp (mm)

Interparticle Spacing 20 Pct SiCp (mm)

30 Pct SiCp (mm)

5.2 (F-1000) 6.4 (F-600) 23.3 (F-280)

3.69 4.54 16.54

1.85 2.29 8.32

0.965 1.188 4.32

fractions, and elastic moduli of the matrix and particle, respectively. The calculated residual stress in the matrix at 30 pct SiC is 289 MPa, well below the yield strength of the matrix (490 MPa, Table I), so plastic deformation after aging is not likely to take place. In the unreinforced alloy, the residual stresses are negligible and the stress concentration effect from microplasticity at the reinforcement poles does not exist, so the proportional limit is higher than that of the composites. In fatigue, Chawla et al.[52] have shown that plastic strain amplitude depends on the level of cyclic stress relative to spl. Below spl of the unreinforced alloy but above spl of the composites, a higher plastic strain was observed in the composites, due to microplasticity effects described previously. At a stress level above spl of both materials, but lower than sy of the composite, more plasticity and a larger loop area were observed in the unreinforced alloy. The total strain, on the other hand, is dominated by the elastic modulus of the material. Thus, regardless of stress level, the composite will have a lower total strain than the unreinforced alloy, since the load is transferred to the high stiffness SiC particles. With increasing volume fraction of 2852—VOLUME 29A, NOVEMBER 1998

(b) Fig. 12—(a) Frequency of fatigue failures categorized by inclusion location in the specimen and (b) distribution of inclusion size as a function of reinforcement volume fraction in failed fatigued samples.

Fig. 13—0.2 pct offset yield strength, proportional limit, and fatigue strength with increasing SiC volume fraction.

particles, then, the amount of microplastic deformation in the composites increases, so that at stresses in the vicinity of spl, the plastic strain amplitude is higher, but higher load transfer to the reinforcement also takes place, resulting in METALLURGICAL AND MATERIALS TRANSACTIONS A

a lower total strain amplitude. It is interesting to note that despite the higher plastic strain generated during fatigue, the composites have a higher fatigue strength than the unreinforced alloy. Thus, it is believed that the lower total strain in the composites, and not plastic strain, seems to be responsible for higher fatigue strength. V.

CONCLUSIONS

By obtaining nearly identical microstructures in the matrix of the composites as that of the unreinforced alloy, several conclusions can be made regarding the fatigue behavior of 2080 Al/SiCp composites. 1. Increasing SiCp volume fraction resulted in increased fatigue life in the composites. The higher fatigue strength of the composites was due largely to lower total strain as a result of load transfer to the high modulus reinforcement. 2. A decrease in SiC particle size also resulted in increased fatigue life. At the coarsest particle size, F-280, particle cracking from the rolling treatment contributed to substantially lower fatigue lives. With an increase in volume fraction and decrease in reinforcement particle size, the interparticle spacing (between SiC particles) reached a critical value that made slip motion difficult. 3. The addition of SiC particles reduced the effective stress concentration on intermetallic inclusions in the matrix of the composite, increasing the fatigue life over the unreinforced alloy, where the inclusions had a higher stress concentration. 4. Increasing SiCp volume fraction also resulted in smaller inclusion sizes in the composite. This was attributed to breaking of the brittle inclusions by the reinforcing particles during extrusion and rolling processes before testing. The lower inclusion size in composites with higher reinforcement loading may have indirectly contributed to higher fatigue lives in these composites. 5. With increasing reinforcement volume fraction, yield strength and fatigue strength increased, but the proportional limit decreased. The decrease in proportional limit is believed to be caused by stress concentrations at the poles of the reinforcement. With an increase in volume fraction, the number of sites for stress concentration increases, and the total amount of microplasticity also increases.

4.

5.

6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19.

20. 21. 22. 23. 24.

25. 26. 27. 28. 29. 30.

ACKNOWLEDGMENTS The authors are grateful to Dr. Warren Hunt, Jr. for supplying the materials used in this study. NC, CA, and JWJ acknowledge the support of Ford Motor Co. NC thanks Professor K.K. Chawla for useful discussions and comments on the manuscript.

31. 32. 33. 34. 35.

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