Dynamic failure models

The shear failure model is based on the value of the equivalent plastic strain at element integration points; failure is assumed to occur when the damage parameter exceeds 1. The damage parameter, $\omega$, is defined as

where ${\overline{\epsilon }}_0^{pl}$ is any initial value of the equivalent plastic strain, $\mathrm{\Delta }{\overline{\epsilon }}^{pl}$ is an increment of the equivalent plastic strain, ${\overline{\epsilon }}_f^{pl}$ is the strain at failure, and the summation is performed over all increments in the analysis.

The strain at failure, ${\overline{\epsilon }}_f^{pl}$, is assumed to depend on the plastic strain rate, ${\dot{\overline{\epsilon }}}^{pl}$; a dimensionless pressure-deviatoric stress ratio, $p/q$ (where p is the pressure stress and q is the Mises stress); temperature; and predefined field variables. There are two ways to define the strain at failure, ${\overline{\epsilon }}_f^{pl}$. One is to use direct tabular data, where the dependencies are given in a tabular form. Alternatively, the analytical form proposed by Johnson and Cook can be invoked (see Johnson-Cook plasticity for more details).

When direct tabular data are used to define the shear failure model, the strain at failure, ${\overline{\epsilon }}_f^{pl}$, must be given as a tabular function of the equivalent plastic strain rate, the pressure-deviatoric stress ratio, temperature, and predefined field variables. This method requires the use of the Mises plasticity model.

For the Johnson-Cook shear failure model, you must specify the failure parameters, $d_1$–$d_5$ (see Johnson-Cook plasticity for more details on these parameters). The shear failure data must be calibrated at or below the transition temperature, ${\theta }_{\mathrm{transition}}$, defined in Johnson-Cook plasticity. This method requires the use of the Johnson-Cook plasticity model.

PLASTIC, HARDENING=ISOTROPIC
SHEAR FAILURE, TYPE=TABULAR

PLASTIC, HARDENING=JOHNSON COOK
SHEAR FAILURE, TYPE=JOHNSON COOK

When the shear failure criterion is met at an integration point, all the stress components will be set to zero and that material point fails. By default, if all of the material points at any one section of an element fail, the element is removed from the mesh; it is not necessary for all material points in the element to fail. For example, in a first-order reduced-integration solid element removal of the element takes place as soon as its only integration point fails. However, in a shell element all through-the-thickness integration points must fail before the element is removed from the mesh. In the case of second-order reduced-integration beam elements, failure of all integration points through the section at either of the two element integration locations along the beam axis leads, by default, to element removal. Similarly, in the modified triangular and tetrahedral solid elements failure at any one integration point leads, by default, to element removal. Element deletion is the default failure choice.

An alternative failure choice, where the element is not deleted, is to specify that when the shear failure criterion is met at a material point, the deviatoric stress components will be set to zero for that point and will remain zero for the rest of the calculation. The pressure stress is then required to remain compressive; that is, if a negative pressure stress is computed in a failed material point in an increment, it is reset to zero. This failure choice is not allowed when using plane stress, shell, membrane, beam, pipe, and truss elements because the structural constraints may be violated.

SHEAR FAILURE, ELEMENT DELETION=YES

SHEAR FAILURE, ELEMENT DELETION=NO

The shear failure model in Abaqus/Explicit is suitable for high-strain-rate dynamic problems where inertia is important. Improper use of the shear failure model may result in an incorrect simulation.

For quasi-static problems that may require element removal, the progressive damage and failure models (Progressive Damage and Failure) or the Gurson porous metal plasticity model (Porous metal plasticity) are recommended.

The Abaqus/Explicit tensile failure model uses the hydrostatic pressure stress as a failure measure to model dynamic spall or a pressure cutoff. The tensile failure criterion assumes that failure occurs when the pressure stress, p, becomes more tensile than the user-specified hydrostatic cutoff stress, ${\sigma }_{\mathrm{cutoff}}$. The hydrostatic cutoff stress may be a function of temperature and predefined field variables. There is no default value for this stress.

The tensile failure model can be used with either the Mises or the Johnson-Cook plasticity models or the equation of state material model.

PLASTIC
TENSILE FAILURE

EOS
TENSILE FAILURE

When the tensile failure criterion is met at an element integration point, the material point fails. Five failure choices are offered for the failed material points: the default choice, which includes element removal, and four different spall models. These failure choices are described below.

TENSILE FAILURE, ELEMENT DELETION=YES (default)

Spall models

An alternative failure choice that is based on spall (the crumbling of a material), rather than element removal, is also available. Four failure combinations are available in this category. When the tensile failure criterion is met at a material point, the deviatoric stress components may be unaffected or may be required to be zero, and the pressure stress may be limited by the hydrostatic cutoff stress or may be required to be compressive. Therefore, there are four possible failure combinations (see Figure 1, where “O” is the stress that would exist if the tensile failure model were not used).

Figure 1. Tensile failure choices.

These failure combinations are as follows:

• Ductile shear and ductile pressure: this choice corresponds to point 1 in Figure 1 and models the case in which the deviatoric stress components are unaffected and the pressure stress is limited by the hydrostatic cutoff stress; i.e., $p=max\left(-{\sigma }_{\mathrm{cutoff}},p\right)$.

  Input File Usage

  TENSILE FAILURE, ELEMENT DELETION=NO, 
  SHEAR=DUCTILE,  PRESSURE=DUCTILE

• Brittle shear and ductile pressure: this choice corresponds to point 2 in Figure 1 and models the case in which the deviatoric stress components are set to zero and remain zero for the rest of the calculation, and the pressure stress is limited by the hydrostatic cutoff stress; i.e., $p=max\left(-{\sigma }_{\mathrm{cutoff}},p\right)$.

  Input File Usage

  TENSILE FAILURE, ELEMENT DELETION=NO, 
  SHEAR=BRITTLE,  PRESSURE=DUCTILE

• Brittle shear and brittle pressure: this choice corresponds to point 3 in Figure 1 and models the case in which the deviatoric stress components are set to zero and remain zero for the rest of the calculation, and the pressure stress is required to be compressive; i.e., $p=max\left(0,p\right)$.

  Input File Usage

  TENSILE FAILURE, ELEMENT DELETION=NO, 
  SHEAR=BRITTLE,  PRESSURE=BRITTLE

• Ductile shear and brittle pressure: this choice corresponds to point 4 in Figure 1 and models the case in which the deviatoric stress components are unaffected and the pressure stress is required to be compressive; i.e., $p=max\left(0,p\right)$.

  Input File Usage

  TENSILE FAILURE, ELEMENT DELETION=NO, 
  SHEAR=DUCTILE,  PRESSURE=BRITTLE

There is no default failure combination for the spall models. If you choose not to use the element deletion model, you must specify the failure combination explicitly. If the material's deviatoric behavior is not defined (for example, the equation of state model without deviatoric behavior is used), the deviatoric part of the combination is meaningless and will be ignored. The spall models are not allowed when using plane stress, shell, membrane, beam, pipe, and truss elements.

The tensile failure model in Abaqus/Explicit is suitable for high-strain-rate dynamic problems in which inertia effects are important. Improper use of the tensile failure model may result in an incorrect simulation.