Y.-L. Shen

Mechanical Behavior of Particle Reinforced Metal Matrix Composites

Metal matrix composites provide significantly enhanced properties — like higher strength, stiffness and weight savings — in comparison to conventional monolithic materials. Particle reinforced MMCs are attractive due to their cost-effectiveness, isotropic properties, and their ability to be processed using similar technology used for monolithic materials. This review captures the salient features of experimental as well as analytical and computational characterization of the mechanical behavior of MMCs. The main focus is on wrought particulate reinforced light alloy matrix systems, with a particular emphasis on tensile, creep, and fatigue behavior.

Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers

Experimental and numerical results are presented on the evolution of stresses and the accompanying changes in the overall curvatures due to the patterning of silicon oxide lines on silicon wafers and subsequent thermal loading. The finite element analysis involves a generalized plane strain formulation, which is capable of predicting the wafer curvatures in directions parallel and perpendicular to the lines, for both the patterning and thermal cycling operations. The predictions compare reasonably well with systematic curvature measurements for several different geometrical combinations of the thickness, width and spacing of the patterned lines. The non‐uniform stress fields within the fine lines and the substrate are also analyzed. It is shown both experimentally and theoretically that certain geometries of patterned lines on the substrate induce dramatic shape changes and reversals of curvature in the direction perpendicular to the lines. The mechanistic origin of this effect is identified to be the Poisson effect arising from the anisotropic strain coupling in the patterned structure.

Coefficients of thermal expansion of metal-matrix composites for electronic packaging

Finite element analyses of the effective coefficient of thermal expansion (CTE) of metal-matrix composites are presented, with a focus on composites with potential for use in electronic packaging applications. The analyses are based on two-dimensional plane strain and axisymmetric unit-cell models. The brittle phase is characterized as an isotropic elastic solid with isotropic thermal expansion. The possibility of plastic deformation, described by an isotropic-hardening flow rule, is allowed for in the ductile phase. A wide range of reinforcement volume fractions is considered. The effects of phase geometry, phase contiguity, ductile phase material properties, processing-induced residual stresses, and brittle particle fracture are considered. The CTE is found to be much less sensitive to phase distribution effects than is the tensile stiffness. The results show that there is a significant dependence of the overall CTE on the phase contiguity (i.e., on whether the brittle or the ductile phase is continuous).

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pet Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed.

Correlation between tensile and indentation behavior of particle-reinforced metal matrix composites: an experimental and numerical study

The correlation between tensile and indentation behavior in particle-reinforced metal matrix com- posites (MMCs) was examined. The model composite system consists of a Al-Cu-Mg alloy matrix reinforced with SiC particles. The effects of particle size, particle volume fraction, and matrix aging characteristics on the interrelationship between tensile strength and macro-hardness were investigated. Experimental data indi- cated that, contrary to what has been documented for a variety of monolithic metals and alloys, a simple relationship between hardness and tensile strength does not exist for MMCs. While processing-induced par- ticle fracture greatly reduces the tensile strength, it does not significantly affect the deformation under inden- tation loading. Even in composites where processing-induced fracture was nonexistent (due to relatively small particle size), no unique correspondence between tensile strength and hardness was observed. At very low matrix strengths, the composites exhibited similar tensile strengths but the hardness increased with increasing particle concentration. Fractographic analyses showed that particle fracture caused by tensile testing is inde- pendent of matrix strength. The lack of unique strength-hardness correlation is not due to the particle fracture- induced weakening during the tensile test. It is proposed that, under indentation loading, enhanced matrix flow that contributes to a localized increase in particle concentration directly below the indenter results in a significant overestimation of the overall composite strength by the hardness test. Micromechanical modeling using the finite element method was used to illustrate the proposed mechanisms under indentation loading and to justify the experimental findings.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

On the correlation between hardness and tensile strength in particle reinforced metal matrix composites

The correlation between macrohardness and tensile strength of particle reinforced metal matrix composites was studied. Contrary to monolithic metals, a simple relationship between hardness and tensile strength was not found. The reinforcement fraction and matrix strength appear to play an important role in influencing the behavior of the composite under hardness and tensile loading conditions. The different loading modes of the tensile test compared to the hardness test, along with the local increase in particle concentration directly underneath the indenter during indentation, result in a significant overestimation of the tensile strength by the hardness test, especially when the matrix strength is relatively low.

Thermal expansion of metal-ceramic composites : a three-dimensional analysis

Abstract The thermal expansion response of macroscopically isotropic metal–ceramic composites is studied through micromechanical modeling. Three-dimensional finite element analyses are carried out for the entire range of phase concentration from pure metal to pure ceramic, using the aluminum–silicon carbide composite as a model system. Particular attention is devoted to the effects of phase connectivity, since other geometrical factors such as the phase shape and particle distribution play a negligible role in affecting the overall coefficient of thermal expansion (CTE) of the composite. Three types of phase connectivity, i.e. metal-matrix, ceramic-matrix and interpenetrating (where both phases form a continuous network in space), are considered. It is found that for fixed phase concentrations, the composite CTE depends strongly on the phase connectivity, with the metal- and ceramic-matrix cases showing the highest and lowest CTE values, respectively. The numerical results are compared with analytical predictions. The combined effects of phase connectivity and metal plasticity are examined by numerically varying the thermal history. The correlation between the constrained metal yielding and the composite CTE is identified. The three-dimensional analysis allows the thermal deformation behavior of interpenetrating composites to be examined in a realistic manner. The results presented in this paper are important in the design and characterization of composites in applications such as electronic packaging and functionally graded materials.

Thermal expansion of metals reinforced with ceramic particles and microcellular foams

The thermal expansion of three isotropic metal-matrix composites, reinforced with SiC particles or microcellular foam, is measured between 25 °C and 325 °C. All three composites show initial co-efficient of thermal expansion (CTE) values in agreement with the Turner model predictions, and near Schapery’s lower elastic bound for CTE. At higher temperatures, the CTE of foam-reinforced Al decreases, while that of the two particle-reinforced composites increases. These observations are interpreted as resulting from the presence of a very small fraction of microscopic voids within the infiltrated composites. This interpretation is confirmed with finite-element simulations of the influence of voids, cracks, and reinforcement convexity in two-dimensional (2-D) composites featuring an interconnected reinforcement of SiC surrounding isolated Al phase regions, thermally cycled from an elevated processing temperature and deforming in generalized plane strain.

Stress evolution in passivated thin films of Cu on silica substrates

have been measured uponthermal cycling. Very high stresses have been found, approaching 1 GPa in thethinnest (40 nm) films. Strengthening beyond yield occurs upon both cooling andheating, indicative of strong strain hardening in the Cu. The hardening continuesdown to at least 77 K. The yielding behavior of the Cu films has been characterizedby a kinematic constitutive law, with exceptional strain hardening and a conventionaltemperature-dependent yield strength. The physical basis for this behavior is ascribedto confined shear bands in the Cu that induce large back stress. Transmission electronmicroscopy reveals aligned dislocations, which seemingly dictate the inelasticdeformations in the shear bands.I. INTRODUCTIONThe residual stresses that arise in thin metal layerscan be extremely large.

Thermal cycling and stress relaxation response of Si-Al and Si-Al-SiO2 layered thin films

Abstract The deformation of Si-Al and Si-Al-SiO 2 multi-layered thin films in response to controlled sequences of constant- and variable-amplitude thermal cycling and isothermal exposures has been studied experimentally by recourse to in situ measurements of curvature changes which made use of the laser scanning technique. In an attempt to systematically isolate salient mechanistic features, a select set of companion experiments have also been conducted on the Si-SiO 2 bi-layer system. In some cases, the layered solids have been subjected to as many as 14 thermal cycles between 20 and 450°C to examine the stability of thermally induced deformation. It is found that the variation of curvature with temperature reaches saturation after the first thermal cycle for the Si-Al bi-layer system. The presence of the SiO 2 passivation layer, however, drastically alters the plastic deformation characteristics of the Al layer with the result that: (i) sharp transitions arise in the variation of curvature with temperature during constant-amplitude thermal cycling; (ii) as many as 12 thermal cycles are needed to attain saturation in the curvature-temperature hysteresis loops; (iii) the extent of stress relaxation is significantly reduced during isothermal hold periods in the heating or the cooling phase of the thermal cycle; and (iv) the effects of certain types of variable-amplitude thermal cycling on elastoplastic deformation are essentially suppressed. An elastoplastic analysis, presented by Suresh et al. ( J. Mech. Phys. Solids 42 , 979, 1994) for multi-layer systems, has been used to interpret some of the experimental results obtained in this paper. The predictions of this analysis for curvature changes during thermal cycling (without isothermal hold periods) are found to capture many trends experimentally observed in the Si-Al and Si-Al-SiO 2 layered systems. It is seen, however, that continuum analyses based upon assumptions of steady-state, power-law creep response for the thin Al film fail to capture the measured effects of the passivation layer on creep relaxation even at saturation.