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Micromechanical modeling of processing-induced damage in Al–SiC metal matrix composites synthesized using the disintegrated melt deposition technique
Materials Research Bulletin, Vol. 34, No. 1, pp. 71–79, 1999 Copyright © 1999 Elsevier Science Ltd Printed in the USA. All rights reserved 0025-5408/99/$–see front matter
PII S0025-5408(98)00205-0
MICROMECHANICAL MODELING OF PROCESSING-INDUCED DAMAGE IN Al–SiC METAL MATRIX COMPOSITES SYNTHESIZED USING THE DISINTEGRATED MELT DEPOSITION TECHNIQUE
L.M. Tham, L. Su, L. Cheng, and M. Gupta* Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 (Refereed) (Received April 22, 1998; Accepted May 4, 1998)
ABSTRACT Porosity of a few percent by volume can often be found in particulatereinforced metal-matrix composites (MMCs) produced by any of the solid, liquid, or solid–liquid phase processes. Like the voids nucleated within the ductile matrix of the composite during loading, processing-induced voids also have an effect on the mechanical response of the composite. However, unlike nucleated voids, processing-induced voids affect the elastic and initial plastic behavior of the composite, as they are present from the onset of loading. In this study, an axisymmetric finite element model was used to investigate the influence of processing-induced voids on the deformation behavior of silicon carbide particulate-reinforced aluminum metal-matrix composites synthesized by the disintegrated melt deposition technique. A limited parametric analysis of the effect of reinforcement content on the deformation response of the composite is discussed. The numerical predictions are compared with experimental measurements. © 1999 Elsevier Science Ltd KEYWORDS: A. composites, D. mechanical properties INTRODUCTION Metal-matrix composites (MMCs) are a unique class of material with the ability to blend the properties of ceramics with those of metals or alloys. The incorporation of a hard and brittle
*To whom correspondence should be addressed. 71
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ceramic phase offers the potential for significant improvements in the mechanical performance of the composite over that of the monolithic metal or alloy. As a result, MMCs are increasingly being sought for a wide range of applications in the electronics, automotive, and aerospace industries. MMCs have been synthesized using a number of different techniques, including solid phase processes, liquid phase processes, and two-phase (solid–liquid) processes [1]. A novel processing method known as the disintegrated melt deposition (DMD) technique is currently being investigated and developed for the synthesis of near-net shape discontinuously reinforced MMCs [2]. The DMD processing method brings together the cost-effectiveness associated with liquid phase processes and the scientific innovativeness associated with spray processes [1–3]. Unlike the spray processes, the DMD technique employs higher superheat temperatures and lower impinging gas jets velocity, with the end product being only bulk composite material. Published experimental evidence [2,4] reveals that DMD-processed composites exhibit uniform distribution of the ceramic reinforcing phase and good interfacial integrity between the ceramic reinforcement and the metallic matrix. Porosity, of a few percent by volume, can often be found in the composites produced by the DMD technique [2,4]. These processing-induced voids, like those nucleated within the ductile matrix during loading [5], affect the mechanical response of the composites. However, unlike nucleated voids, which only affect composite response after void nucleation [6], processing-induced voids would be expected to affect the elastic and the initial plastic behavior of the composites because they are present from the onset of loading. Accordingly, this numerical study was undertaken with the objective of investigating quantitatively the influence of processing-induced voids on the deformation response of Al–SiC MMCs synthesized by the DMD technique. The present study also includes a limited parametric evaluation of the role of reinforcement volume fraction on the deformation behavior of these composites with the porous matrices. In addition, the numerical results obtained in this study were quantitatively compared with the experimental measurements of the composites reinforced with different volume fractions of the silicon carbide particulates.
MATERIALS PROCESSING AND TESTING Experiments and numerical simulations were carried out to study the effects of processinginduced voids on the stress–strain response of a model DMD-processed composite system of a commercially pure aluminum alloy AA1050 ($99.5wt%Al) reinforced with varying volume fractions of a-SiC particulates of 35 mm average size. An unreinforced alloy with a similar processing history was also included in this study, to allow a direct comparison of the quantitative predictions of the finite element model with the experimental observations. DMD-processed composites were synthesized by mixing the SiC particulates with a liquid aluminum matrix, aided by mechanical agitation. The resulting composite slurry was then disintegrated by jets of inert gas and subsequently deposited on a metallic substrate. The as-processed composites were then hot-extruded at 350°C using an extrusion ratio of 13:1. Results of chemical dissolution tests [2] showed that approximately 5 and 15 vol% of the SiC particulates were successfully incorporated. The volume fractions of the porosity were estimated from the measured densities and the results of the chemical dissolution tests [2,4] to be 0.9 and 0.8% in the composites reinforced by 5 and 15 vol% of the SiC particulates, respectively. Porosity in the unreinforced alloy was similarly estimated to be 0.05 vol%.
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TABLE 1 Tensile Properties of the Composite Samples Material
Process
UTS (MPa)
Ductility (%)
A1–5vol%SiC A1–15vol%SiC A1–22vol%SiCa
DMD 1 extrusion DMD 1 extrusion Spray codeposition 1 HACAb
104.4 6 5.1 120.3 6 7.9 110.0
17.3 6 8.6 8.9 6 2.4 8.0
a
Reference 7. HACA 5 hot-rolled to 50% 1 annealed for 30 min at 500°C cold-rolled to 50% 1 annealed for 30 min at 500°C. b
Microstructural characterization studies revealed a uniform distribution of the SiC particulates, good matrix-reinforcement interfacial integrity and limited amounts of porosity. Further details of the microstructural characteristics associated with MMCs processed using the DMD method can be found elsewhere [2,4]. For the experimental investigation of the mechanical response, round tension test specimens of 4 mm diameter and 20 mm gauge length were machined from the extruded composite rods. Uniaxial tensile tests were conducted in accordance with the ASTM test method E8M-91, using an automated servohydraulic testing machine with the crosshead speed set at 0.254 mm/min. The results of the tensile tests carried out on the reinforced specimens are shown in Table 1. The results reveal a strength and ductility combination that is superior to that reported by other investigators [7]. FINITE ELEMENT FORMULATION The stress–strain response of the composites was investigated by the finite element analysis of a unit cell. The composite material was idealized in terms of a periodic array of identical hexagonal cylindrical cells with the SiC reinforcement located in the center of each cell. Axisymmetric cylindrical cells, which can be regarded as approximations to the threedimensional array of the hexagonal cylindrical cells [8,9], were used in the calculations (see Fig. 1a). To simulate the uniaxial tensile test, the axisymmetric cylindrical cell was subjected to an overall stress parallel to the cylindrical axis. Based on symmetry and periodicity arguments, the lateral surface was required to remain a right circular cylinder with zero shear tractions and zero average normal tractions. The faces perpendicular to the direction of stressing were also required to remain planar with zero shear tractions and with the average normal stress equal to the applied stress. The reinforcement volume fraction was taken as the ratio of the reinforcement volume to the cell volume. The aspect ratio of the cell, the ratio of the height of the cylinder to its diameter, was taken to be the same as that of the reinforcement. The matrix material was assumed to be a rate-independent isotropically hardening elasticplastic solid characterized by the J2 flow theory of plasticity. The solutions were calculated incrementally with the stress increment related to the strain increment by s˙ ij 5
H
˙ kl E n 3 (1 1 n)s 22 e s ijs klε ε˙ ij 1 ε˙ kkd ij 2 11n 1 2 2n 2 [1 1 2⁄ 3 (1 1 n)(E/Et 2 1) 21]
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FIG. 1 (a) Approximation of a hexagonal unit cell of the 3-D periodic array by the axisymmetric unit cell [9], and (b) finite element discretization of the axisymmetric unit cell. where sij is the stress, sij is the stress deviator, εij is the strain, se 5 (3sijsij/2)1/2, E is Young’s modulus, n is the Poisson ratio, and Et is the tangent modulus of the tensile stress–strain curve at the current value of se. The last term in the above equation was taken to be zero for an elastic increment. In our analyses, the reinforcements were taken to be rigid and the matrix material was assumed to be perfectly bonded to the reinforcements. For the small reinforcement volume fractions considered here, the idealization of the stiff elastic reinforcement as rigid has only a very small effect on the computed composite stress-strain curves [8]. The ABAQUS code was employed using 8-noded biquadratic elements to solve the boundary value problem formulated above. The finite element discretization of the unit cell used is shown in Figure 1b and consists of a spherical particle embedded in the center of the circular cylindrical cell. Convergence studies were conducted for the low and high reinforcement volume fractions to ensure that the element meshes were sufficiently refined. The stress–strain curves were computed incrementally using strain increments dictated by the convergence rate. The maximum strain increment was limited to 0.2ε0, where ε0 denotes the yield strain of the matrix in tension. When the composite was undamaged, which in this study referred to a matrix that was free of processing-induced voids, the tensile stress–strain curve was calculated using the axisymmetric cell model with the reinforcement particle surrounded by a shell of fully dense matrix material, the properties of which are given by the unreinforced matrix material. However, in the case of a damaged composite, the axisymmetric cell model was modified by replacing the shell of fully dense matrix material with one that was porous. The material properties of this porous outer shell were calculated using the axisymmetric cell model with a shell of fully dense matrix material surrounding a spherical void. The void volume fraction was taken to be the ratio of the void volume to the cell volume. The finite element mesh used was similar to that shown in Figure 1b except that the fully fixed boundary conditions at the matrixreinforcement interface, imposed to simulate a rigid particle, were made free to simulate the void. Throughout this study, the reinforcement particles and the processing-induced voids
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FIG. 2 Finite element predictions of the effect of reinforcement content on the stress–strain curves of Al–SiC composites (so denotes the matrix yield stress).
were assumed to be uniformly distributed throughout the matrix and not clustered. It should be noted that the present analysis focuses only on the effects of the processing-induced voids and does not consider the coalescence of the voids or the interactions between the reinforcement particles and the voids. NUMERICAL RESULTS The influence of processing-induced voids on the deformation response of the Al–SiC composites was investigated by hypothesizing that these voids were the sole damage mechanism and that other failure mechanisms were presumed to play a negligible role. For the calculations reported here, the stress-strain curve for the unreinforced aluminum alloy was used as input for the numerical analyses and taken to be fully dense. The reinforcement volume fractions were taken to be 5 and 15%. The void volume fractions were taken to be 0.9 and 0.8% for the composites with reinforcement volume fractions of 5 and 15%, respectively. It should be noted that the values of the reinforcement and void volume fractions were experimentally determined (see previous section). All the stress–strain curves presented are curves of true stress versus logarithmic strain. Effect of Reinforcement Content. The effect of reinforcement content on the deformation response of the composite with the porous matrix was analyzed by considering two different
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TABLE 2 Results of the Finite Element Analysis Material
Porosity (vol%)
Ec/Ema
nb
A1–5vol%SiC A1–5vol%SiC A1–15vol%SiC A1–15vol%SiC
0.0 0.9 0.0 0.8
1.12 1.08 1.43 1.38
0.092 0.098 0.102 0.109
a
Ec/Em denotes the ratio of the composite to matrix Young’s modulus. b n denotes the strain-hardening exponent.
SiC volume fractions of 5 and 15%. The effects of the increasing reinforcement volume fraction on the computed stress–strain curves are plotted in Figure 2. The dotted lines show the results for the composites with the porous matrix. For comparison purposes, the solid lines show the corresponding results for the composites where the matrix remains fully dense throughout deformation. The numerically predicted elastic moduli and strain-hardening exponents of the different composites are summarized in Table 2. The results show that for a constant level of matrix porosity, the elastic modulus and overall flow strength increase with increasing reinforcement volume fraction. However, when porosity levels in the matrix are increased for a fixed reinforcement content, both elastic
FIG. 3 Numerical predictions and experimental results for the Al–5vol%SiC composite.
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FIG. 4 Numerical predictions and experimental results for the Al–15vol%SiC composite. modulus and overall flow strength are reduced. Table 2 also shows that the composite strain-hardening exponents do not appear to be affected significantly by the presence of the processing-induced voids. Unlike nucleated voids which only affect composite response after void nucleation (at a plastic strain of around 0.02, i.e., no voids initially [6]), processinginduced voids, because they are present from the onset of tensile loading, cause the elastic and initial plastic behavior of the composites with the porous matrix to differ from those of the composites with the fully dense matrix. The small increase in the overall flow strength of the composites for an increase in the volume fraction of rigid spheres from 5 to 15% should also be noted. Numerical Predictions vs. Experiments. The computed stress–strain curves for the Alalloy composites reinforced with 5 and 15 vol% of SiC are plotted in Figures 3 and 4, respectively, along with the corresponding experimental measurements. It can be seen that for the Al–5vol%SiC composite (Fig. 3), the elastic part of the experimental stress–strain curve is predicted reasonably well by the numerical model. Beyond this point, however, the model predictions overestimate slightly the experimental response. In the case of the Al– 15vol%SiC composite (Fig. 4), an appreciable overestimation of the experimental stress– strain curve by the computational model is observed over the elastic and initial plastic strain ranges. The overestimation in Figures 3 and 4 can be attributed to the coupled influence of (i) the occurrence of other failure mechanisms, including brittle fracture of the reinforcements and nucleation, growth and coalescence of voids in the matrix [5,6,10]. This hypothesis is supported by the typical scanning electron micrograph of the fracture surface of the
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FIG. 5 Scanning electron micrograph of the fracture surface of the Al–15vol%SiC composite showing failure mechanisms associated with SiC particulates. Al–15vol%SiC composite (Fig. 5), which shows evidence of reinforcement cracking and void formation, and (ii) the assumptions of the finite element formulation, which include the spherical reinforcements and voids, uniform distribution of the reinforcements and voids, perfect bonding between the matrix and the reinforcements, absence of interaction between the reinforcements and voids, and coalescence of the voids. It can also be seen that the magnitude of the overestimation of the experimental measurements by the numerical model increases with increasing reinforcement content. This trend is consistent with the experimental results of Finot and co-workers [11], who have reported that the fraction of broken reinforcement particles increases with increasing reinforcement content. Quantitative modeling of the effects of the other failure mechanisms on the composite response, although beyond the scope of the present analysis, is expected to lead to a better match with the experimental results. Further work is continuing in this area. It may further be noted that the degree to which the different failure mechanisms influence the deformation of the composites is strongly dependent on a variety of factors [5], including processing and consolidation procedures. These factors determine the levels of the processing-induced voids, to which the composites are subjected prior to mechanical loading. Hence, the effects of processinginduced voids on the mechanical response of the Al–SiC composites could conceivably be greater in composites with higher levels of these voids. CONCLUSIONS The primary conclusions that can be derived from the finite element formulation used in the present study are as follows: 1. 2.
Processing-induced voids affect the elastic and initial plastic behavior of the composites. An increase in the volume fraction of the processing-induced voids leads to a degradation in composite elastic modulus and overall flow strength.
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The presence of processing-induced voids within the limits of 0.9 vol% does not affect the strain hardening rate of the composites investigated in the present study. For low volume fractions of processing-induced voids, the effects of reinforcement cracking and nucleation, growth and coalescence of voids in the matrix cannot be ignored. ACKNOWLEDGMENTS
TLM would like to thank NUS for financially supporting this investigation through the provision of a research scholarship. In addition, the authors would like to acknowledge with gratitude the guidance of Prof. Gang Bao and Ms. Bo Fan. REFERENCES 1. 2. 3. 4. 5.
6. 7. 8. 9. 10. 11.
D.J. Lloyd, Int. Mater. Rev. 39, 1 (1994). M. Gupta, M.O. Lai, and C.Y. Soo, Mater. Res. Bull. 30, 1525 (1995). E.J. Lavernia and Y. Wu, Spray Atomization and Deposition, Wiley and Sons, New York (1996). M. Gupta, M.O. Lai, and C.Y. Soo, Mater. Sci. Eng. A 210, 114 (1996). A. Needleman, S.R. Nutt, S. Suresh, and V. Tvergaard, in Fundamentals of Metal-Matrix Composites, eds. S. Suresh, A. Mortensen, and A. Needleman, p. 233, Butterworth-Heinemann, Boston (1993). J. Llorca, A. Needleman, and S. Suresh, Acta Metall. Mater. 39, 2317 (1991). A.R.E. Singer and S. Ozbek, Powder Metall. 28, 72 (1985). T. Christman, A. Needleman, and S. Suresh, Acta Metall. Mater. 37, 3029 (1989). G. Bao, J.W. Hutchinson, and R.M. McMeeking, Acta Metall. Mater. 39, 1871 (1991). G. Bao, Acta Metall. Mater. 40, 2547 (1992). M. Finot, Y.L. Shen, A. Needleman, and S. Suresh, Metall. Mater. Trans. A 25A, 2403 (1994).
PII S0025-5408(98)00205-0
MICROMECHANICAL MODELING OF PROCESSING-INDUCED DAMAGE IN Al–SiC METAL MATRIX COMPOSITES SYNTHESIZED USING THE DISINTEGRATED MELT DEPOSITION TECHNIQUE
L.M. Tham, L. Su, L. Cheng, and M. Gupta* Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 (Refereed) (Received April 22, 1998; Accepted May 4, 1998)
ABSTRACT Porosity of a few percent by volume can often be found in particulatereinforced metal-matrix composites (MMCs) produced by any of the solid, liquid, or solid–liquid phase processes. Like the voids nucleated within the ductile matrix of the composite during loading, processing-induced voids also have an effect on the mechanical response of the composite. However, unlike nucleated voids, processing-induced voids affect the elastic and initial plastic behavior of the composite, as they are present from the onset of loading. In this study, an axisymmetric finite element model was used to investigate the influence of processing-induced voids on the deformation behavior of silicon carbide particulate-reinforced aluminum metal-matrix composites synthesized by the disintegrated melt deposition technique. A limited parametric analysis of the effect of reinforcement content on the deformation response of the composite is discussed. The numerical predictions are compared with experimental measurements. © 1999 Elsevier Science Ltd KEYWORDS: A. composites, D. mechanical properties INTRODUCTION Metal-matrix composites (MMCs) are a unique class of material with the ability to blend the properties of ceramics with those of metals or alloys. The incorporation of a hard and brittle
*To whom correspondence should be addressed. 71
72
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Vol. 34, No. 1
ceramic phase offers the potential for significant improvements in the mechanical performance of the composite over that of the monolithic metal or alloy. As a result, MMCs are increasingly being sought for a wide range of applications in the electronics, automotive, and aerospace industries. MMCs have been synthesized using a number of different techniques, including solid phase processes, liquid phase processes, and two-phase (solid–liquid) processes [1]. A novel processing method known as the disintegrated melt deposition (DMD) technique is currently being investigated and developed for the synthesis of near-net shape discontinuously reinforced MMCs [2]. The DMD processing method brings together the cost-effectiveness associated with liquid phase processes and the scientific innovativeness associated with spray processes [1–3]. Unlike the spray processes, the DMD technique employs higher superheat temperatures and lower impinging gas jets velocity, with the end product being only bulk composite material. Published experimental evidence [2,4] reveals that DMD-processed composites exhibit uniform distribution of the ceramic reinforcing phase and good interfacial integrity between the ceramic reinforcement and the metallic matrix. Porosity, of a few percent by volume, can often be found in the composites produced by the DMD technique [2,4]. These processing-induced voids, like those nucleated within the ductile matrix during loading [5], affect the mechanical response of the composites. However, unlike nucleated voids, which only affect composite response after void nucleation [6], processing-induced voids would be expected to affect the elastic and the initial plastic behavior of the composites because they are present from the onset of loading. Accordingly, this numerical study was undertaken with the objective of investigating quantitatively the influence of processing-induced voids on the deformation response of Al–SiC MMCs synthesized by the DMD technique. The present study also includes a limited parametric evaluation of the role of reinforcement volume fraction on the deformation behavior of these composites with the porous matrices. In addition, the numerical results obtained in this study were quantitatively compared with the experimental measurements of the composites reinforced with different volume fractions of the silicon carbide particulates.
MATERIALS PROCESSING AND TESTING Experiments and numerical simulations were carried out to study the effects of processinginduced voids on the stress–strain response of a model DMD-processed composite system of a commercially pure aluminum alloy AA1050 ($99.5wt%Al) reinforced with varying volume fractions of a-SiC particulates of 35 mm average size. An unreinforced alloy with a similar processing history was also included in this study, to allow a direct comparison of the quantitative predictions of the finite element model with the experimental observations. DMD-processed composites were synthesized by mixing the SiC particulates with a liquid aluminum matrix, aided by mechanical agitation. The resulting composite slurry was then disintegrated by jets of inert gas and subsequently deposited on a metallic substrate. The as-processed composites were then hot-extruded at 350°C using an extrusion ratio of 13:1. Results of chemical dissolution tests [2] showed that approximately 5 and 15 vol% of the SiC particulates were successfully incorporated. The volume fractions of the porosity were estimated from the measured densities and the results of the chemical dissolution tests [2,4] to be 0.9 and 0.8% in the composites reinforced by 5 and 15 vol% of the SiC particulates, respectively. Porosity in the unreinforced alloy was similarly estimated to be 0.05 vol%.
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TABLE 1 Tensile Properties of the Composite Samples Material
Process
UTS (MPa)
Ductility (%)
A1–5vol%SiC A1–15vol%SiC A1–22vol%SiCa
DMD 1 extrusion DMD 1 extrusion Spray codeposition 1 HACAb
104.4 6 5.1 120.3 6 7.9 110.0
17.3 6 8.6 8.9 6 2.4 8.0
a
Reference 7. HACA 5 hot-rolled to 50% 1 annealed for 30 min at 500°C cold-rolled to 50% 1 annealed for 30 min at 500°C. b
Microstructural characterization studies revealed a uniform distribution of the SiC particulates, good matrix-reinforcement interfacial integrity and limited amounts of porosity. Further details of the microstructural characteristics associated with MMCs processed using the DMD method can be found elsewhere [2,4]. For the experimental investigation of the mechanical response, round tension test specimens of 4 mm diameter and 20 mm gauge length were machined from the extruded composite rods. Uniaxial tensile tests were conducted in accordance with the ASTM test method E8M-91, using an automated servohydraulic testing machine with the crosshead speed set at 0.254 mm/min. The results of the tensile tests carried out on the reinforced specimens are shown in Table 1. The results reveal a strength and ductility combination that is superior to that reported by other investigators [7]. FINITE ELEMENT FORMULATION The stress–strain response of the composites was investigated by the finite element analysis of a unit cell. The composite material was idealized in terms of a periodic array of identical hexagonal cylindrical cells with the SiC reinforcement located in the center of each cell. Axisymmetric cylindrical cells, which can be regarded as approximations to the threedimensional array of the hexagonal cylindrical cells [8,9], were used in the calculations (see Fig. 1a). To simulate the uniaxial tensile test, the axisymmetric cylindrical cell was subjected to an overall stress parallel to the cylindrical axis. Based on symmetry and periodicity arguments, the lateral surface was required to remain a right circular cylinder with zero shear tractions and zero average normal tractions. The faces perpendicular to the direction of stressing were also required to remain planar with zero shear tractions and with the average normal stress equal to the applied stress. The reinforcement volume fraction was taken as the ratio of the reinforcement volume to the cell volume. The aspect ratio of the cell, the ratio of the height of the cylinder to its diameter, was taken to be the same as that of the reinforcement. The matrix material was assumed to be a rate-independent isotropically hardening elasticplastic solid characterized by the J2 flow theory of plasticity. The solutions were calculated incrementally with the stress increment related to the strain increment by s˙ ij 5
H
˙ kl E n 3 (1 1 n)s 22 e s ijs klε ε˙ ij 1 ε˙ kkd ij 2 11n 1 2 2n 2 [1 1 2⁄ 3 (1 1 n)(E/Et 2 1) 21]
J
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FIG. 1 (a) Approximation of a hexagonal unit cell of the 3-D periodic array by the axisymmetric unit cell [9], and (b) finite element discretization of the axisymmetric unit cell. where sij is the stress, sij is the stress deviator, εij is the strain, se 5 (3sijsij/2)1/2, E is Young’s modulus, n is the Poisson ratio, and Et is the tangent modulus of the tensile stress–strain curve at the current value of se. The last term in the above equation was taken to be zero for an elastic increment. In our analyses, the reinforcements were taken to be rigid and the matrix material was assumed to be perfectly bonded to the reinforcements. For the small reinforcement volume fractions considered here, the idealization of the stiff elastic reinforcement as rigid has only a very small effect on the computed composite stress-strain curves [8]. The ABAQUS code was employed using 8-noded biquadratic elements to solve the boundary value problem formulated above. The finite element discretization of the unit cell used is shown in Figure 1b and consists of a spherical particle embedded in the center of the circular cylindrical cell. Convergence studies were conducted for the low and high reinforcement volume fractions to ensure that the element meshes were sufficiently refined. The stress–strain curves were computed incrementally using strain increments dictated by the convergence rate. The maximum strain increment was limited to 0.2ε0, where ε0 denotes the yield strain of the matrix in tension. When the composite was undamaged, which in this study referred to a matrix that was free of processing-induced voids, the tensile stress–strain curve was calculated using the axisymmetric cell model with the reinforcement particle surrounded by a shell of fully dense matrix material, the properties of which are given by the unreinforced matrix material. However, in the case of a damaged composite, the axisymmetric cell model was modified by replacing the shell of fully dense matrix material with one that was porous. The material properties of this porous outer shell were calculated using the axisymmetric cell model with a shell of fully dense matrix material surrounding a spherical void. The void volume fraction was taken to be the ratio of the void volume to the cell volume. The finite element mesh used was similar to that shown in Figure 1b except that the fully fixed boundary conditions at the matrixreinforcement interface, imposed to simulate a rigid particle, were made free to simulate the void. Throughout this study, the reinforcement particles and the processing-induced voids
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FIG. 2 Finite element predictions of the effect of reinforcement content on the stress–strain curves of Al–SiC composites (so denotes the matrix yield stress).
were assumed to be uniformly distributed throughout the matrix and not clustered. It should be noted that the present analysis focuses only on the effects of the processing-induced voids and does not consider the coalescence of the voids or the interactions between the reinforcement particles and the voids. NUMERICAL RESULTS The influence of processing-induced voids on the deformation response of the Al–SiC composites was investigated by hypothesizing that these voids were the sole damage mechanism and that other failure mechanisms were presumed to play a negligible role. For the calculations reported here, the stress-strain curve for the unreinforced aluminum alloy was used as input for the numerical analyses and taken to be fully dense. The reinforcement volume fractions were taken to be 5 and 15%. The void volume fractions were taken to be 0.9 and 0.8% for the composites with reinforcement volume fractions of 5 and 15%, respectively. It should be noted that the values of the reinforcement and void volume fractions were experimentally determined (see previous section). All the stress–strain curves presented are curves of true stress versus logarithmic strain. Effect of Reinforcement Content. The effect of reinforcement content on the deformation response of the composite with the porous matrix was analyzed by considering two different
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TABLE 2 Results of the Finite Element Analysis Material
Porosity (vol%)
Ec/Ema
nb
A1–5vol%SiC A1–5vol%SiC A1–15vol%SiC A1–15vol%SiC
0.0 0.9 0.0 0.8
1.12 1.08 1.43 1.38
0.092 0.098 0.102 0.109
a
Ec/Em denotes the ratio of the composite to matrix Young’s modulus. b n denotes the strain-hardening exponent.
SiC volume fractions of 5 and 15%. The effects of the increasing reinforcement volume fraction on the computed stress–strain curves are plotted in Figure 2. The dotted lines show the results for the composites with the porous matrix. For comparison purposes, the solid lines show the corresponding results for the composites where the matrix remains fully dense throughout deformation. The numerically predicted elastic moduli and strain-hardening exponents of the different composites are summarized in Table 2. The results show that for a constant level of matrix porosity, the elastic modulus and overall flow strength increase with increasing reinforcement volume fraction. However, when porosity levels in the matrix are increased for a fixed reinforcement content, both elastic
FIG. 3 Numerical predictions and experimental results for the Al–5vol%SiC composite.
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FIG. 4 Numerical predictions and experimental results for the Al–15vol%SiC composite. modulus and overall flow strength are reduced. Table 2 also shows that the composite strain-hardening exponents do not appear to be affected significantly by the presence of the processing-induced voids. Unlike nucleated voids which only affect composite response after void nucleation (at a plastic strain of around 0.02, i.e., no voids initially [6]), processinginduced voids, because they are present from the onset of tensile loading, cause the elastic and initial plastic behavior of the composites with the porous matrix to differ from those of the composites with the fully dense matrix. The small increase in the overall flow strength of the composites for an increase in the volume fraction of rigid spheres from 5 to 15% should also be noted. Numerical Predictions vs. Experiments. The computed stress–strain curves for the Alalloy composites reinforced with 5 and 15 vol% of SiC are plotted in Figures 3 and 4, respectively, along with the corresponding experimental measurements. It can be seen that for the Al–5vol%SiC composite (Fig. 3), the elastic part of the experimental stress–strain curve is predicted reasonably well by the numerical model. Beyond this point, however, the model predictions overestimate slightly the experimental response. In the case of the Al– 15vol%SiC composite (Fig. 4), an appreciable overestimation of the experimental stress– strain curve by the computational model is observed over the elastic and initial plastic strain ranges. The overestimation in Figures 3 and 4 can be attributed to the coupled influence of (i) the occurrence of other failure mechanisms, including brittle fracture of the reinforcements and nucleation, growth and coalescence of voids in the matrix [5,6,10]. This hypothesis is supported by the typical scanning electron micrograph of the fracture surface of the
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FIG. 5 Scanning electron micrograph of the fracture surface of the Al–15vol%SiC composite showing failure mechanisms associated with SiC particulates. Al–15vol%SiC composite (Fig. 5), which shows evidence of reinforcement cracking and void formation, and (ii) the assumptions of the finite element formulation, which include the spherical reinforcements and voids, uniform distribution of the reinforcements and voids, perfect bonding between the matrix and the reinforcements, absence of interaction between the reinforcements and voids, and coalescence of the voids. It can also be seen that the magnitude of the overestimation of the experimental measurements by the numerical model increases with increasing reinforcement content. This trend is consistent with the experimental results of Finot and co-workers [11], who have reported that the fraction of broken reinforcement particles increases with increasing reinforcement content. Quantitative modeling of the effects of the other failure mechanisms on the composite response, although beyond the scope of the present analysis, is expected to lead to a better match with the experimental results. Further work is continuing in this area. It may further be noted that the degree to which the different failure mechanisms influence the deformation of the composites is strongly dependent on a variety of factors [5], including processing and consolidation procedures. These factors determine the levels of the processing-induced voids, to which the composites are subjected prior to mechanical loading. Hence, the effects of processinginduced voids on the mechanical response of the Al–SiC composites could conceivably be greater in composites with higher levels of these voids. CONCLUSIONS The primary conclusions that can be derived from the finite element formulation used in the present study are as follows: 1. 2.
Processing-induced voids affect the elastic and initial plastic behavior of the composites. An increase in the volume fraction of the processing-induced voids leads to a degradation in composite elastic modulus and overall flow strength.
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3. 4.
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The presence of processing-induced voids within the limits of 0.9 vol% does not affect the strain hardening rate of the composites investigated in the present study. For low volume fractions of processing-induced voids, the effects of reinforcement cracking and nucleation, growth and coalescence of voids in the matrix cannot be ignored. ACKNOWLEDGMENTS
TLM would like to thank NUS for financially supporting this investigation through the provision of a research scholarship. In addition, the authors would like to acknowledge with gratitude the guidance of Prof. Gang Bao and Ms. Bo Fan. REFERENCES 1. 2. 3. 4. 5.
6. 7. 8. 9. 10. 11.
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