An improved description of copper‐ and iron‐cylinder impact (Taylor) test results has been obtained through the use of dislocation‐mechanics‐based constitutive relations in the Lagrangian material dynamics computer program EPIC‐2. The effects of strain hardening, strain‐rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive beha...

/pdf/dislocation-mechanics-based-constitutive-relations-for-2fq9j5sid1.pdf

Dislocation-mechanics-based constitutive relations for material dynamics calculations

A new model of metal plasticity and fracture with pressure and Lode dependence

Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.

Computational methods in Lagrangian and Eulerian hydrocodes

Smoothed Particle Hydrodynamics: Some recent improvements and applications

The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids. This criterion has been extensively used in rock and soil mechanics as it correctly accounts for the effects of hydrostatic pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes are the equivalent strain to fracture $${\bar \varepsilon_f}$$
 , the stress triaxiality η, and the normalized Lode angle parameter $${\bar \theta}$$
 . For a proportional loading, the fracture surface is shown to be an asymmetric function of $${\bar \theta}$$
 . A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality, which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie (1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic. Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.

Application of extended Mohr–Coulomb criterion to ductile fracture

Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures

An improved computational constitutive model for brittle materials is presented. It is applicable for brittle materials subjected to large strains, high strain rates and high pressures, and is well‐suited for computations in both Lagrangian and Eulerian codes. The equivalent strength is dependent on the intact strength, fractured strength, strain rate, pressure, and damage. The pressure includes the effect of bulking, which is introduced through the transfer of internal energy from decreased shear and deviator stresses to potential internal energy associated with increased hydrostatic pressure. Examples are presented to illustrate the model.

An improved computational constitutive model for brittle materials

This article presents an analysis of the response of boron carbide (B4C) to severe loading conditions that produce large strains, high strain rates, and high pressures. Experimental data from the literature are used to determine and/or estimate constants for the JH-2 constitutive model for brittle materials. Because B4C is a very strong material, it is not always possible to determine the constants explicitly. Instead they must sometimes be inferred from the limited experimental data that are available. The process of determining constants provides insight into the constitutive behavior for some loading conditions, but it also raises questions regarding the response under other loading conditions. Several Lagrangian finite element and Eulerian finite difference computations are provided to illustrate responses for a variety of impact and penetration problems.

Response of boron carbide subjected to large strains, high strain rates, and high pressures

This article presents an analysis of the response of silicon carbide to high velocity impact. This includes a wide range of loading conditions that produce large strains, high strain rates, and high pressures. Experimental data from the literature are used to determine constants for the Johnson–Holmquist constitutive model for brittle materials (JH-1). It is possible to directly determine the strength and pressure response of the intact material from test data in the literature. After the ceramic has failed, however, there are not adequate experimental data to directly determine the response of the failed material. Instead, the response is inferred from a comparison of computational results to ballistic penetration test results. After the constants have been obtained for the JH-1 model, a wide range of computational results are compared to experimental data in the literature. Generally, the computational results are in good agreement with the experimental results. Included are computational results that m...

Response of silicon carbide to high velocity impact

This paper examines the usefulness of cylinder‐impact test data to determine constants for various computational constitutive models. The Johnson–Cook and Zerilli–Armstrong constitutive models are evaluated by comparing model predictions to tension, torsion, and cylinder‐impact test data. Then the cylinder‐impact test data are used to determine constitutive model constants for various forms of these models. Under bounded conditions of strains and strain rates, this approach can produce useful results. It can also produce very erroneous results if not used properly.

Gordon R. Johnson

Papers

Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures

An improved computational constitutive model for brittle materials

Response of boron carbide subjected to large strains, high strain rates, and high pressures

Response of silicon carbide to high velocity impact

Evaluation of cylinder‐impact test data for constitutive model constants