Constitutive Equations for Annealed and Explosively Shocked Iron for Application to High Strain Rates and Large Strains

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Scale effects in necking

“…For both shocked and unshocked materials the work hardening rate is independent of the strain rate [3]. This characteristic is a basic assumption of the constitutive equation proposed by Armstrong and Zerilli for body centred cubic metals at small strains, and fuelled the development of equation 4 for the flow stress,σ.…”

“…After comparing work hardening curves at different temperatures Goldthorpe found a small but steady divergence with increasing strain [3]. Further investigation then identified that as the temperature of a shocked material diverges from ambient it increasingly diverges from the unshocked data.…”

“…This equation features a thermally activated component, denoted by the inclusion of temperature, T , a straindependent component which includes the strain term, ε n f , and a constant, C 1 , which refers to the athermal resistances of the material [3]. The remaining variables C 2 , C 3 , C 4 , C 5 and n are additional experimental constants andε relates to the strain rate.…”

“…Armstrong and Zerilli based their model for body centred cubic metals on two characteristics that are well established at small strains; strain hardening being independent of both strain rate and temperature [3]. This model represents the original formulation from which the basic forms of the modified constitutive equations were developed.…”

“…To address this Goldthorpe introduced a shear modulus correction factor since it is well published that the temperature dependence of the shear modulus influences work hardening. (5) is the definition of the Goldthorpe modified-Armstrong-Zerilli constitutive model, featuring temperature dependence [3]. This model is used to predict isothermal stress-strain curves for body centred cubic metals when combined with measurements of the evolution of the neck radius of curvature with strain.…”