About Damage and Failure for Ductile Metals

Abaqus offers a variety of choices of damage initiation criteria for ductile metals, each associated with distinct types of material failure. They can be classified in the following categories:

• Damage initiation criteria for the fracture of metals, including ductile (tabular, Johnson-Cook, and Hosford-Coulomb) and shear.

• Damage initiation criteria for the necking instability of sheet metal. These include forming limit diagrams (FLD, FLSD, and MSFLD) intended to assess the formability of sheet metal and the Marciniak-Kuczynski (M-K) criterion (available only in Abaqus/Explicit) to numerically predict necking instability in sheet metal taking into account the deformation history.

These criteria are discussed in Damage Initiation for Ductile Metals. Each damage initiation criterion has an associated output variable to indicate whether the criterion has been met during the analysis. A value of 1.0 or higher indicates that the initiation criterion has been met.

More than one damage initiation criterion can be specified for a given material. If multiple damage initiation criteria are specified for the same material, they are treated independently. Once a particular initiation criterion is satisfied, the material stiffness is degraded according to the specified damage evolution law for that criterion; in the absence of a damage evolution law, however, the material stiffness is not degraded. A failure mechanism for which no damage evolution response is specified is said to be inactive. Abaqus will evaluate the initiation criterion for an inactive mechanism for output purposes only, but the mechanism will have no effect on the material response.

DAMAGE INITIATION, CRITERION=criterion 1

The damage evolution law describes the rate of degradation of the material stiffness once the corresponding initiation criterion has been reached. For damage in ductile metals Abaqus assumes that the degradation of the stiffness associated with each active failure mechanism can be modeled using a scalar damage variable, $d_i$ ($i\in N_{\mathrm{act}}$), where $N_{\mathrm{act}}$ represents the set of active mechanisms. At any given time during the analysis the stress tensor in the material is given by the scalar damage equation

where D is the overall damage variable and $\overline{\mathit{\sigma }}$ is the effective (or undamaged) stress tensor computed in the current increment. $\overline{\mathit{\sigma }}$ are the stresses that would exist in the material in the absence of damage. The material has lost its load-carrying capacity when $D=1$ . By default, an element is removed from the mesh on material failure.

The overall damage variable, D, captures the combined effect of all active mechanisms and is computed in terms of the individual damage variables, $d_i$, according to a user-specified rule.

Abaqus supports different models of damage evolution in ductile metals and provides controls associated with element deletion due to material failure, as described in Damage Evolution and Element Removal for Ductile Metals. All of the available models use a formulation intended to alleviate the strong mesh dependency of the results that can arise from strain localization effects during progressive damage.

DAMAGE EVOLUTION