Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29° from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.

Numerical simulations of fast crack growth in brittle solids

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

For a whisker-reinforced metal matrix composite, failure by decohesion of the fibre-matrix interface is analysed. The unit-cell model applied for the numerical analyses represents a periodic array of aligned fibres, where neighbouring fibres are somewhat shifted relative to one another. The debonding behaviour at the interface is represented in terms of a cohesive zone model that describes decohesion by normal separation as well as decohesion by tangential separation. The predicted failure initiates by void formation near the sharp edges at the fibre ends, and subsequently fibre pull-out is described. The effect of friction during pull-out is included in the model.

Effect of fibre debonding in a whisker-reinforced metal

Microstructure-sensitive computational modeling of fatigue crack formation

Numerical simulations of crack initiation which use a cohesive zone law to model a weak interface in the solid are often limited by the occurrence of an elastic snap-back instability. At the point of instability, quasi-static finite element computations are unable to converge to an equilibrium solution, which usually terminates the calculation and makes it impossible to follow the post-instability behaviour. In this paper, we show that such numerical difficulties can easily be avoided by introducing a small viscosity in the constitutive equations for the cohesive interface. Simple boundary value problems are used to develop guidelines for selecting appropriate values of viscosity in numerical simulations involving crack nucleation and growth. As a representative application, we model crack nucleation at the interface between an elastic thin film and an elastic–plastic substrate, which is subjected to contact loading.

https://iopscience.iop.org/article/10.1088/0965-0393/12/3/007/pdf

A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces

The effect of thermally induced residual stresses on the mechanical properties and ductility of AlSiC composites was investigated numerically. The predicted behavior in uniaxial loading was calculated with and without the inclusion of the residual stresses which result from the mismatch in thermal expansion between aluminum and SiC. In this analysis, void nucleation by interfacial debonding at the whiskers' ends was assumed to be the limiting failure mechanism. Two cases, both with a fiber volume fraction of 20% and fiber aspect ratio of 4, but with different fiber spacings, were considered. The residual stresses had a small effect on the predicted ductility of the composite, even when a relatively weak interface strength was assumed. The residual stresses are shown to redistribute as interfacial failure is approached. A close end-to-end fiber spacing gives a greater flow strength in compression than in tension and the residual stresses which arise during thermomechanical processing tend to enhance this effect.

An analysis of the effect of residual stresses on deformation and damage mechanisms in AlSiC composites

Neutron diffraction experiments were conducted on 15vol.% whisker and 20vol.% particulate reinforced aluminum/silicon carbide composites subjected to a rapid quench followed by various deformation histories. Corresponding numerical simulations were carried out using an axisymmetric unit cell model, with a phenomenological, isotropic hardening descriotion of matrix plasticity. Thermal expansion and the temperature dependence of material properties were accounted for. For the whisker reinforced matrix, quantitative agreement was generally found between the measured and calculated residual elastic strains. For the particulate reinforced matrix, the calculations tended to overestimate the magnitude of the residual strains parallel to the deformation axis, but very good agreement was obtained transverse to the deformation axis. For the silicon carbide reinforcement, both whisker and particulate, the variation of predicted residual elastic strains along the deformation axis was qualitatively consistent with the measurements, although quantitative agreement was often lacking. Measured and predicted residual strains perpendicular to the deformation axis for the silicon carbide typically were not in agreement. Parametric studies were carried out to ascertain the dependence of calculated flow strengths and residual strains on cell and reinforcement aspect ratio, and on reinforcement spacing and shape.

Thermally and mechanically induced residual strains in Al-SiC composites

The effects of fiber spacing, volume fraction and aspect ratio on the residual stresses in metal-matrix composites are analyzed numerically. The composite is modeled as a periodic array of cylindrical cells, each consisting of the matrix alloy with a whisker embedded in the ceter. Account is taken of thermoelasticity both in the fiber and in the matrix and of temperature-dependent plasticity in the aluminum matrix. A general formulation, valid for finite strains and rotations, is discussed. Quenching is simulated by imposing a temperature history obtained from a macroscopic solution of the heat equation for a cylindrical bar to the surface of a cell. The resulting residual stress fields are calculated. The results show that the side-to-side spacing of fibers is the most important microstructural parameter affecting the distribution of residual stress and plastic deformation in the matrix. The overall level of plastic deformation in the matrix, measured by the volume average of effective plastic strain, depends primarily on fiber volume fraction. The fiber aspect ratio has little effect, apparently because the residual fields become essentially independent of axial position a short distance from the fiber corner.

An analysis of residual stress formation in whisker-reinforced AlSiC composites

Finite Element Simulations of Fiber Pull-Out

An attempt is made to predict the creep behavior of thermally cycled Al-SiC composites using a continuum-based cell model. The model is found to predict most of the experimentally observed features of the creep behavior of the composites. The calculated stress exponent approaches unity at low applied stresses, and the thermally cycled creep rate is significantly greater than the isothermal creep rate that occurs when the composite is held at the maximum value of the periodic temperature history. 12 refs.

G.L. Povirk

Papers

An analysis of the effect of residual stresses on deformation and damage mechanisms in AlSiC composites

Thermally and mechanically induced residual strains in Al-SiC composites

An analysis of residual stress formation in whisker-reinforced AlSiC composites

Finite Element Simulations of Fiber Pull-Out

Analysis of creep in thermally cycled Al/SiC composites