Constitutive modeling of fracture waves

Abstract

A fracture wave (FW) in a brittle material is a narrow transition region (border) of a continuous fracture zone, which may be associated with the damage accumulation process initiated by propagation of shock waves. In multidimensional structures the fracture wave may behave in an unusual way. The high-speed photography of penetration of a borosilicate (Pyrex) glass block [N. K. Bourne, L. Forde, and J. E. Field, Proc. SPIE 2869, 626 (1997)] shows a visible fracture zone with an apparent flat front although the projectile is a hemispherically nosed rod. A strain-rate-sensitive model is being developed and employed for analysis of the role of the complex stress state and kinetic description of the damage accumulation to describe the process of the impact. Numerical analysis is conducted with a one-dimensional wave propagation code employing the model and with the LS-DYNA2D hydrocode in which the model has been implemented. The analysis demonstrates that (i) the second (plastic) shock wave is superseded by quicker FW relaxing stress behind the elastic precursor, and (ii) the FW front flattening is apparently caused by the change in the acoustic directional properties. This change is associated with the phase-like transition due to the damage accumulation within the FW. In particular, the FW transition separates a highly anisotropic zone of material characterized acoustically by longitudinal and shear waves in front of the FW from a nearly isotropic region of the material characterized only by bulk waves behind the FW.

Deformation model for brittle materials and the structure of failure waves

“…In an intermediate state, an element of the medium can be treated as a mixture of components of the intact and "fully damaged" materials. According to [3], the order parameter ξ can be identified with the volume concentration of the "fully damaged" material in the mixture.…”

“…Moreover, the model takes into account the inelastic deformation of the material that accompanies continual failure. A similar small-strain model and numerical analyses of some problems in good agreement with experimental data [1] were proposed in [3].…”

“…The fracture of a brittle material under compressive stresses is characterized by the formation of numerous cracks and has a wave nature [1,2]. Theoretical investigation of the fracture waves is in its infancy [3,4], and no adequate mathematical model has been proposed for a qualitative analysis and numerical study of the processes mentioned above. In the present paper, constitutive differential equations based on the nonlinear theory of inelastic strains [5] are formulated in the form of a hyperbolic system in which each equation has divergent form.…”

Failure Fronts in Brittle Materials and Their Morphological Instabilities

“…The last conclusion shows an additional analogy between failure fronts and slow combustion fronts (but, of course, the mechanisms of destabilization are totally different). The morphological instability discussed here may shed some light on the appearance of corrugations on failure fronts and crack bifurcations as observed in experiments on static indentation of brittle materials, the appearance of radial cracks in dynamic experiments with penetration of projectiles through brittle materials, the appearance of corrugations on the disintegration fronts in Prince Ruppert drops (4), and the appearance of failure front waviness detected in numerical simulations (22 …”

“…This interpretation, however, requires further (numerical) studies of deeply nonlinear stage of the instability. Another appealing possibility of the instability applications is to the failure-front waviness that was detected in the numerical modeling of Resnyansky et al (22). These authors use a formally different, but conceptually close, model.…”