In a numerical micromechanical study of void nucleation, a framework is used where constitutive relations are specified independently for the matrix, the void-nucleating particles and the interface. Plane strain analyses are carried out for a doubly periodic array of circular cylindrical particles. The particles are taken to be rigid and the elastic-plastic deformations of the matrix are described in terms of continuum crystalline plasticity, using a planar crystal model that allows for three slip systems. Comparison is made with void-nucleation predictions based on a corresponding flow theory of plasticity with isotropic hardening. The crystal model can give rise to shear localization at the particle-matrix interface and shear localization, which leads to large localized strains in the matrix, is found to inhibit decohesion. The role of the triaxiality of the stress state in determining whether decohesion or localization occurs first is investigated. A parameteric study is also carried out for a crystal matrix using two descriptions of the interface shear behaviour; one is periodic in the shear displacement across the interface, while the other allows for shear decohesion.

https://iopscience.iop.org/article/10.1088/0965-0393/1/2/001/pdf

Void nucleation by inclusion debonding in a crystal matrix

Numerical results are presented on the effects of fiber distribution and of fiber cross-sectional geometry on the deformation of a metal-matrix composite reinforced with continuous fibers. The geometrical variables analyzed include several periodic and random distributions of uni-directional cylindrical fibers with circular, hexagonal and square shapes. The model system chosen for the finite element analysis is a 6061-O aluminum alloy reinforced with boron fibers. It is shown that, for a reinforcement level of 46 vol.% boron fibers, tensile and shear deformation in orientations transverse to the fiber axes are markedly influenced by both the packing of fibers and their cross-sectional shape, although the deformation of the composite is insensitive to such geometrical effects for tensile loading in the direction of fiber alignment. The effect of fiber distribution on the constitutive response is relatively stronger than that of fiber shape. The geometrical effects of fiber distribution on deformation are significantly less pronounced for the 6061 aluminum-matrix composite with 20 vol.% boron fibers. Details of the evolution of plastic strains and hydrostatic stresses in the constrained matrix during far-field loading are discussed, and the influence of such constraint on the geometry dependence of deformation is examined. The scientific and practical implications of the results are also pinpointed.

Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape

Deformation and failure of metal-matrix composites, by the nucleation and growth of voids within the ductile matrix, are studied numerically and experimentally. The matrix material is modelled as an elastic-viscoplastic ductile porous solid to characterize the evolution of damage from void formation. The material systems chosen for parametric analyses and for quantitative comparisons between numerical analyses and experiments are aluminum alloys discontinuously reinforced with SiC. The brittle reinforcement phase, in the form of spheres, particulates with sharp corners, or cylindrical whiskers, is modelled as elastic or rigid, with the interfaces between the ductile matrix and the brittle reinforcement assumed to be perfectly bonded. The overall constitutive response of the composite and the evolution of matrix failure are analyzed using finite element models within the context of axisymmetric and plane strain formulations. Detailed parametric analyses of the effects of (i) reinforcement shape, (ii) reinforcement volume fraction, (iii) mechanical properties of the matrix, (iv) nucleation strain and volume fraction of void-nucleating particles, and (v) reinforcement distribution on the overall deformation and ductility of the composite are discussed. The numerical predictions of yield strength, strain hardening exponent and ductility for the composites with different volume fractions of SiC particulates are also compared with experimental measurements.

An analysis of the effects of matrix void growth on deformation and ductility in metal-ceramic composites

Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I: micromechanics-based formulation

The combined effects of thermal residual stresses anmd fiber spatial distribution on the deformation of a 6061 aluminum alloy containing a fixed concentration unidirectional boron fibers have been analyzed using detailed finite element models. The geometrical structure includes perfectly periodic, uniformly spaced fiber arrangements in square and hexagonal cells, as well as different cells in which either 30 or 60 fibers are randomly placed in the ductile matrix. The model involves an elastic-plastic matrix, elastic fibers, and mechanically bonded interfaces. The results indicate that both fiber packing and thermal residual stresses can have a significant effect on the stress-strain characteristics of the composite. The thermal residual stresses cause pronounced matrix yielding which also influences the apparent overall stiffness of the composite during the initial stages of subsequent far-field loading along the axial and transverse direction. Furthermore, the thermal residual stresses apparently elevate the flow stress of the composite during transverse tension. Such effects can be traced back to the level of constraint imposed on the matrix by local fiber spacing. The implications of the present results to the processing of the composites are also briefly addressed.

Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites

The tensile properties of aluminum matrix composites containing SiC whiskers or particulate were investigated analytically and compared to experimental results. Two finite-element models were constructed and used for elastoplastic analysis. In both models, the SiC fibers are represented as longitudinally aligned cylinders in a three-dimensional array. The cylinder ends are transversely aligned in one model and staggered in the other. Using the models, the sensitivity of the predicted composite properties to the deformation characteristics of the matrix alloy was examined, and the general behavior of the models was validated. It was determined that both models are necessary to predict the overall composite stress-strain response accurately. The analytic results accurately predict: the observed composite stress-strain behavior; the experimentally observed increase in Young’s modulus and the work-hardening rate with increasing fiber volume content and aspect ratio; and the decrease and subsequent increase in proportional limit as the SiC volume fraction is increased. The models also predict that the transverse material properties should be insensitive to fiber aspect ratio. In addition, the model predicts the location of initial yielding and the propagation of the plastic region. These results offer insights into the deformation mechanisms of short fiber-reinforced composites.

J. M. Papazian

Papers

Tensile properties of short fiber-reinforced SiC/Al composites: Part II. Finite-element analysis