Dynamic fracture and spallation in ductile solids

Abstract

A mathematical model of ductile hole growth under the application of a mean tensile stress is developed and applied to the problem of spallation in solids. The object is to describe dynamic ductile fracture under a wide range of tensile loading conditions. The mathematical model presented here describes both plate-impact spallation (as observed by postshot examination and time-resolved pressure measurements) and explosively produced spallation (as observed by dynamic x-radiographic techniques) in copper. It is found to be inapplicable to ductile fracture of expanding rings, even in the absence of possible adiabatic shear banding and classical necking instabilities, because of the fact that the mean tensile stress (void growth) and the deviatoric stress (homogeneous plastic shear strain) are not independent. A phenomenological model of void growth under uniaxial stress conditions is developed independently and applied to the numerical finite-difference solution of fracture in an expanding ring. The initial porosity in a material element is a random variable following Poisson statistics and the assumption that all the void radii are equal. The necessary theoretical generalizations and supporting experimental measurements to improve our understanding of fracture and fragmentation in expanding rings are discussed.

The shock and spall response of three industrially important hexagonal close-packed metals: magnesium, titanium and zirconium

“…It should be noted that the contributing factors for materials spalling have been studied for decades [21][22][23][24][25][26][27] and the phenomenon of spall was documented by Hopkinson [28]. Nevertheless, unlike FCC and BCC metals where the shock response has been reviewed [29,30], no such review exists for HCP metals.…”

Spall damage in aluminum alloy

“…The second term I;,(a)& denotes the influence of the material viscosity, which describes the effect of the rate sensitivity and is one of the major features differing from the quasi-static growth of voids. Other researchers' studies, such as Curran et al (1987), Johnson (1981) and Cortes (1992), have resulted in the same fact. The third term F,(a) is the total effects of the applied external stress, the change of the void surface energy, work-hardening and the yield stress in the solid surrounding the void on the void growth.…”

“…Johnson (1981) once numerically analyzed the change of temperature at expanding pore wall for copper-like material, and showed that if all the plastic work went into heat, the temperature at the expanding pore wall could be a substantial fraction of the melting temperature. Cortes (1992) investigated the thermal softening of the matrix material.…”

“…They suggested that the effect of elastic compressibility in the matrix material is small, and can go immediately to the case of fully plastic deformation around the void. Johnson (1981) applied Carroll and Holt's approach to void growth in a viscoplastic medium. Cochran and Banner (1977) studied spallation in uranium using a simple theoretical model.…”

Shock and spall behaviors of a high specific strength steel: Effects of impact stress and microstructure

“…50,51 Subsequent void growth has also been extensively investigated over the past several decades, and substantial micromechanical models have been proposed for understanding the quasi-static void growth 44,52,53 or the dynamic void growth under extreme loading conditions. 39,[54][55][56][57][58][59][60][61][62] Moreover, a few modeling papers have suggested that the porosity achieved at the peak tensile stress is typically low (<1%), and the void coalescence is achieved long after the peak tensile stress. [63][64][65] Thus, it was proposed that the void coalescence behavior has no perceivable influence on the pull-back velocity and spall strength.…”