Progressive damage and failure of ductile metals

This verification test consists of a set of single-element models subjected to biaxial tension; an exception is the truss and beam elements, which are loaded by uniaxial tension. For each material model only those element types supported for that model are used. The ductile criterion is specified in terms of the plastic strain at the onset of damage as a tabular function of the stress triaxiality and the equivalent plastic strain rate. In Abaqus/Explicit the ductile criterion can also be defined as a tabular function of Lode angle. The Johnson-Cook criterion (available only in Abaqus/Explicit) is specified in terms of failure parameters $d_1$ – $d_5$ , the reference strain rate ${\dot{\epsilon }}_0$ , the melting temperature, and the transition temperature. The shear criterion is specified in terms of the plastic strain at the onset of damage as a tabular function of the shear stress ratio and the equivalent plastic strain rate. The Hosford-Coulomb criterion (available only in Abaqus/Standard) is specified in terms of failure parameters $a$ , $b$ , $c$ , and $n$ . The damage evolution law (available only in Abaqus/Explicit) is specified in terms of the equivalent plastic displacement or in terms of the fracture energy dissipation. A maximum degradation of 0.75 is set. The default failure choice (i.e., element deletion) is used in all tests in this subsection.

The tests for initial conditions on the damage initiation measures do not subject the elements to any deformation. Instead, these tests verify only that the specified initial conditions are output without any modifications.

This verification test consists of a set of single-element models subjected to equibiaxial tension. The FLD criterion is specified in terms of the maximum in-plane principal strain at damage initiation as a tabular function of the minimum in-plane principal strain. The FLSD criterion is specified in terms of the maximum in-plane principal limit stress as a tabular function of the minimum in-plane principal stress. In Abaqus/Explicit input files the damage evolution law is specified in terms of the equivalent plastic displacement or in terms of the fracture energy dissipation. A maximum degradation of 0.75 is used. The default failure choice (i.e., element deletion) is used in all tests in this subsection.

First, a set of single elements with plane stress formulation is loaded under equibiaxial tension to test the M-K damage initiation criterion for different element types. The material properties for this test correspond to a steel alloy modeled with rate-dependent Mises plasticity. The initial imperfection size is defined as a tabular function of the angular direction. The M-K criterion is specified in terms of the limit ratio of the deformation in the groove (thickness imperfection) relative to the nominal deformation outside the groove.

In addition, to demonstrate the capability of the M-K analysis in predicting forming limit diagrams for an aluminum alloy, a set of parametric studies are performed to evaluate the effect of strain paths on the FLDs using S4R elements. In these studies an aluminum alloy (AA 5754–O) is modeled using isotropic Mises plasticity with Nadai hardening: ${\sigma }_y=C{\left({\epsilon }^{pl}+{\epsilon }_0\right)}^n$, with $C=446.3$MPa, $n=0.292$, and ${\epsilon }_0=0.0039$. The initial imperfection size is assumed to be 0.9999 in these studies. The number of virtual imperfections is set to 100. A set of analyses are performed with the ratio between the major and minor principal strain parameterized and kept constant throughout each individual analysis, which generates the FLD curve without prestrain. To evaluate the effect of the loading paths on the FLDs, two more sets of studies are performed in which the material is initially prestrained (either with plane strain or equibiaxial loading) and subsequently subjected to the same type of proportional loading as in the case without prestrain.

A set of single elements with a plane stress formulation is loaded under equibiaxial tension to test the MSFLD damage initiation criterion for different element types. The MSFLD criterion is specified in terms of the maximum in-plane principal strain at damage initiation as a tabular function of the minimum in-plane principal strain (FLD definition) or in terms of the equivalent plastic strain at damage initiation as a tabular function of the ratio of principal strain rates (MSFLD definition).

To demonstrate the capability of the MSFLD criterion in predicting failure for nonlinear strain paths, a number of numerical simulations of two-step forming processes have been carried out in Abaqus/Explicit using the MSFLD criterion as well as the M-K criterion. Each of the two forming steps follows a linear path with constant principal strain rate ratio $\alpha$, but there can be a jump in the value of $\alpha$ from the first step to second step; therefore, the overall deformation path is not linear. Based on the value of $\alpha$ throughout the first step and the value of equivalent plastic strain at the end of the first step, these simulations are grouped into five sets: within each set, individual simulations differ only in the value of $\alpha$ during the second step. The same material model described in the last section (AA 5754–O) has also been used here.

The test for initial conditions on the damage initiation measure does not subject the elements to any deformation. Instead, this test verifies only that the specified initial conditions are output without any modifications.

The ductile initiation criterion is used on a set of single-element models, subjected to plane strain compression followed by plane strain tension for the elements with two-dimensional and three-dimensional stress states. The truss elements are loaded in uniaxial compression followed by uniaxial tension.

This verification test consists of six elements, each associated with a different material. For each of the first five materials, only one initiation criterion with its corresponding evolution rule is specified; for the material assigned to the sixth element, all five initiation criteria with their corresponding evolution rules are specified. In this way the individual contribution to the overall damage variable (in the sixth element) can be obtained explicitly from the damage variables of the first five elements.