A rate-dependent damage model for brittle materials based on the dominant crack

Abstract

A rate-dependent, continuum damage model is developed for brittle materials under dynamic loading. This model improves on the approach (ISOSCM) of [Addessio, F.L., Johnson, J.N., 1990. A constitutive model for the dynamic response of brittle materials. Journal of Applied Physics 67, 3275-3286] in several respects. (1) A new damage surface is found by applying the generalized Griffith instability criterion to the dominant crack (having the most unstable orientation), rather than by averaging the instability condition over all crack orientations as done previously. The new surface removes a discontinuity in the damage surface in ISOSCM when the pressure changes sign. (2) The strain due to crack opening is more consistent with crack mechanics, with only the tensile principal stresses contributing to the crack opening strain. This is achieved by incorporating a projection operator in the equation for the crack opening strain. One consequence of incorporating the projection operator is a prediction of shear dilatancy, which is not accounted for in ISOSCM. (3) The evolution of damage, which is based on the energy-release rate for the dominant crack, has a physical basis, whereas in the previous approach the damage growth rate was assumed to be an exponential function of the distance from the stress state to the damage surface without specific physical justification.An implicit algorithm has been developed so that a larger time step can be used than with the explicit algorithm used in ISOSCM. The numerical results of a silicon carbide (SiC) ceramic under several loading paths (hydrostatic tension/ compression, uniaxial strain, uniaxial stress, and shear) and strain rates are presented to illustrate the main features of the model.

A crack-mechanics based model for damage and plasticity of brittle materials under dynamic loading

“…The material is assumed to contain a large number of penny-shaped cracks with different sizes and orientations. As in previous work (Addessio and Johnson, 1990;Zuo et al, 2006), the size distribution of the cracks is assumed to remain isotropic (i.e., independent of the crack orientation) and exponential during loading. Under such assumptions, the probability density function (pdf) of the crack numbers can be written as (Addessio and Johnson, 1990) …”

“…When the principle stresses are of mixed signs, P + eliminates the contributions of the compressive principal stresses to the crack opening strain, making the formulation consistent with crack-mechanics (Yazdani and Schreyer, 1988Wen and Yazdani, 2008). The details of the definition for P + are described by Zuo et al (2006). In Eq.…”

“…Recently, based on the ISOSCM model, Zuo et al (2006) proposed a rate-dependent damage model, the Dominant Crack Algorithm (DCA), for the damage of brittle materials under dynamic loading. The DCA model improves the ISOSCM model in several aspects.…”

A constitutive equation for ceramic materials used in lightweight armors

“…The ability of the model to capture the response of ceramic to dynamic shock loading were demonstrated by the simulation of a dynamic plate impact experiment on alumina. Zuo et al [21] developed the Dominant Crack Model (DCA), a rate dependent, continuum damage model for the dynamic response of brittle materials. A damage surface is proposed by applying the general ized Griffith instability criterion to the dominant crack having the most unstable orientation.…”

Three dimensional K-T z stress fields around the embedded center elliptical crack front in elastic plates

“…However, three-dimensional (3D) embedded cracks often occur in piezoelectric ceramics and other brittle materials and result in catastrophic accidents [1][2][3][4]. Therefore, they are as important as surface cracks and through cracks in engineering structures.…”