Computational models for ductile and brittle fracture

Abstract

Computational models of dynamic ductile and brittle fracture are developed for wave propagation in one- and two-dimensional geometries. The model features have been taken mainly from detailed observations of samples partially fractured during impacts, but the functional forms are consistent with theoretical results where applicable. Basic features of the models are the nucleation and growth (hence, the acronym NAG for the models) of voids or cracks, and the stress relaxation resulting from the growing damage. The results of the calculations include number and sizes of cracks, voids, or fragments as a function of position in the material. The NAG analysis presents the nucleation law, determined from experiment, and two growth laws: both growth and nucleation are functions of stress and stress duration. Procedures for treating cracks with a range of sizes and orientation are presented with the method for computing the stress relaxation that accompanies growth of damage. Brittle fracture is essentially anisotropic in actuality and in the model: cracks nucleate and grow as a function of stress normal to their plane, and the stress relaxation is a function of crack opening in the direction of the stress. Criteria are presented for the coalescence of cracks to form fragments and for complete fragmentation. The computational models have been applied to one- and two-dimensional wave propagation problems. The NAG models have been shown to be applicable to several metals, a plastic, and a quartzite, to stress levels from just above threshold to ten times the threshold, and to load durations from 20 nsec to several microseconds. The damage has been computed for stress waves caused by impact, thermal radiation, and explosion.

Spall damage in aluminum alloy

“…It is assumed that the function that relates pressure specific volume and specific internal energy for the matrix material in the porous state is the same as that which relates these quantities for the matrix material in its nonporous state (Carroll and Holt, 1972 ;Seaman et al, 1976). With this assumption, the P-u model gives the pressure in the porous material as a function of specific volume, specific internal energy, and porosity.…”

“…The form of this function is determined by the pressure-specific volume-specific internal energy (PVE) function for the matrix material in its nonporous state. We use the following PVE relation for the porous material (Seaman et al, 1976) :…”

“…The specific internal energy for the matrix material is the same in the porous and nonporous conditions, and the specific internal energy of the porous material is that of the matrix material, that is, the surface energy of the pores is neglected. The PVE relation of the matrix material is given by (Seaman et al, 1976) …”

“…The literature on this subject is extensive. By investigating the behavior of dynamic damage and fracture in solids in detail, Curran and co-workers (Barber et al, 1972;Seaman et al, 1976 ;Curran et al, 1977Curran et al, ,1987 established computational models called NAG (nucleation and growth) models for ductile and brittle fracture. In their models, two internal state variables N (the number of microvoids or microcracks per unit volume) and R (the average size of a microvoid or microcrack) are introduced to describe the processes of dynamic damage and fracture in solids.…”

High-power laser shock-induced dynamic fracture of aluminum and microscopic observation of samples

“…In 1914, Hopkinson firstly observed the spall phenomenon [2] that there were planar separation of material parallel to the wave front when materials under dynamic loads. After the Second World War, driven by engineering and military applications, spall research gets widespread concern and has a great progress [3][4][5]. Since the 1970s, the concepts of damage accumulation and evolution have been proposed as being responsible for the dynamic fracture of ductile metals.…”