Q.H. Zuo

Modeling anisotropic damage in an encapsulated ceramic under ballistic impact

This paper presents a study of anisotropic damage and cracking in a hot isostatically pressed assembly of titanium alloy encapsulated AD-995 ceramic under ballistic impact using the statistical crack mechanics approach. Anisotropy of crack growth in the ceramic is illustrated numerically by examining the growth in crack sizes along three orientations. Comparisons with the experimental measurements of the predicted backsurface profile and the damage (cracking) in the ceramic suggest that the model predictions are consistent with the experimental data. Numerical simulation also indicates that a prestress of roughly 2kbar (200MPa) compensates for about 1% of initial porosity in the ceramic. A comparison is made to the Rajendran–Grove ceramic model in EPIC which assumes an isotropic crack distribution.

An implicit algorithm for a rate-dependent ductile failure model

An implicit numerical algorithm has been developed for a rate-dependent model for damage and failure of ductile materials under high-rate dynamic loading [F. L. Addessio and J. N. Johnson, J. Appl. Phys. 74, 1640 (1993)]. Over each time step, the algorithm first implicitly determines the equilibrium state on a Gurson surface, and then calculates the final state by solving viscous relaxation equations, also implicitly. Numerical examples are given to demonstrate the key features of the algorithm. Compared to the explicit algorithm used previously, the current algorithm allows significantly larger time steps that can be used in the analysis. As the viscosity of the material vanishes, the results of the rate-dependent model are shown here to converge to that of the corresponding rate-independent model, a result not achieved with the explicit algorithm.

Elastic waves and damage quantification in brittle material with evolving damage

This paper presents an analysis of the elastic wave propagation in brittle materials containing a distribution of microcracks. The crack-size distribution is assumed to be isotropic and exponential. The evolution of the mean crack size is described by a rate-dependent damage model based on the mechanics of microcracks. The analysis shows that the elastic wave speeds of a brittle material are sensitive to the change in the mean size of the distributed cracks in the material. The dependence of the wave speeds on the applied strain can also be used to validate the damage model. An example of a brittle ceramic under uniaxial-strain tension is presented to show quantitatively the changes in the longitudinal and shear wave speeds as functions of the applied strain. Explicit relations between the wave speeds and the mean crack size in the material are given.

Stability and well-posedness of a rate-dependent strain-softening plasticity model

This paper presents an investigation of the stability and well-posedness of a simple rate-dependent model for strain-softening materials. The model contains key features found in several advanced constitutive models that are currently used for damage and failure of materials. The stability and well-posedness of the model are studied by examining the behaviour of dynamic perturbations to the steady-state solution of a simple shear problem. It is shown that the introduction of strain-rate dependency makes the problem well-posed as dynamic perturbations with all wave lengths remain bounded for finite times. The effect of viscosity on the rate of growth of dynamic perturbations of different wave lengths is shown. It is found that the rate of growth for perturbations with short wave length is severely retarded by the material viscosity.

Modified formulation of a rate-dependent damage model for ductile materials

A modification to the rate-dependent damage and failure model developed by Addessio and Johnson [J. Appl. Phys. 74, 1640 (1993)] for ductile materials under high-rate loading is presented. In the current formulation the equilibrium stress, which is used to calculate the plastic strain rate and damage in the material, is defined as the orthogonal projection of the final stress onto an equilibrium yield surface, instead of being a projection of the trial stress onto the yield surface as is done in the original formulation. The modification makes the current formulation fully consistent with the viscoplasticity theory. An implicit algorithm is also presented for the modified model and numerical results of copper under uniaxial strain loading are given to show the features of the model and the algorithm. Comparisons with the results of the original formulation are also presented.

Crack-mechanics based brittle damage model including nonlinear equation of state and porosity growth

A three-dimensional rate-dependent model has been developed for damage and failure of brittle materials under impact. The model extends a recently developed, crack-mechanics based damage model [Zuo et al., Int. J. Solids Struct. 43, 3350 (2006)] to high rate problems by incorporating a nonlinear equation of state (EOS) and porosity growth. The pressure-volume response developed by Addessio and Johnson for ceramics under impact [J. Appl. Phys. 67, 3275 (1990)] was adapted to the current model. The model has been numerically implemented and the responses of a ceramic (silicon carbide) under various loading paths are shown. These responses are compared with those predicted by the existing model (having a linear equation of state) to illustrate the effects of nonlinear EOS and porosity.

Upper bound on wave speeds in anisotropic materials based on elastic projection operators

An upper bound on the speeds of waves propagating along an arbitrary direction in an elastic material with general anisotropy has been developed from an additive decomposition of the acoustic tensor. Several examples of materials with different elastic symmetries (cubic, tetragonal) are presented. A validation is provided by comparing the upper bounds for copper and tin crystals with numerical solutions of the eigenvalue problems.