MSFLD Damage

The model works on the basis of equivalent plastic strain and assumes that the forming limit curve represents the sum of the highest attainable equivalent plastic strains. The approach requires transforming the original forming limit curve (without predeformation effects) from the space of major versus minor strains to the space of equivalent plastic strain, ${\bar{ε}}^{p l}$ , versus ratio of principal strain rates, $α = {\dot{ε}}_{\min o r} / {\dot{ε}}_{m a j o r}$ .

For linear strain paths, assuming plastic incompressibility and neglecting elastic strains:

α = ε_{\min o r} / ε_{m a j o r} a n d {\bar{ε}}^{p l} = ε_{m a j o r} \sqrt{\frac{4}{3}} (1 + α + α^{2})

According to the MSFLD criterion, the onset of localized necking occurs when the sequence of deformation states intersects the forming limit curve, as discussed below. It is emphasized that for linear deformation paths both FLD and MSFLD representations are identical and give rise to the same predictions. For arbitrary loading, however, the MSFLD representation takes into account the effects of the history of deformation through the use of the accumulated equivalent plastic strain.

For the specification of the MSFLD damage initiation criterion in Abaqus, you can directly provide the equivalent plastic strain at damage initiation as a tabular function of $α$ and, optionally, equivalent plastic strain rate, and temperature, ${\bar{ε}}_{M S F L D}^{p l} (α, {\overset{\dot{¯}}{ε}}^{p l}, θ)$ . Alternatively, you can specify the curve in the traditional FLD format (in the space of major and minor strains) by providing a tabular function of the form $ε_{m a j o r} (ε_{\min o r}, {\overset{\dot{¯}}{ε}}^{p l}, θ)$ . In this case Abaqus will automatically transform the data into the ${\bar{ε}}^{p l} - α$ format.

Let $ω_{M S F L D}$ represent the ratio of the current equivalent plastic strain, ${\bar{ε}}^{p l}$ , to the equivalent plastic strain on the limit curve evaluated at the current values of $α$ ; strain rate, ${\overset{\dot{¯}}{ε}}^{p l}$ ; and temperature, $θ$ :

ω_{M S F L D} = \frac{{\bar{ε}}^{p l}}{{\bar{ε}}_{M S F L D}^{p l} (α, {\overset{\dot{¯}}{ε}}^{p l}, θ)} .

The MSFLD criterion for necking instability is met when the condition $α = {\dot{ε}}_{\min o r} / {\dot{ε}}_{m a j o r}$ is satisfied.

Damage due to bending deformation cannot be evaluated using this model.

In the table below, damage parameters that are followed by MSFLD or FLD apply only to that type of damage definition.


Input Data	Description
Definition	Select MSFLD to enter data in the form of equivalent plastic strains and ratios of minor to major strain rates, or select FLD to enter data in the form of major and minor principal strains and the equivalent plastic strain and to have data transformed into the Müschenborn-Sonne form.
Omega	Omega is used to filter the ratio of principal strains rates, preventing the ratio from jumping to a higher value due to sudden changes in the strain direction (deformation path); the default value is $ω = 1$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specify material parameters that depend on field variables. Field columns appear in the data table for each field variable you add. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Plastic Strain at Initiation (MSFLD)	Equivalent plastic strain at initiation of localized necking.
Ratio of Principal Strain (MSFLD)	Ratio of minor to major principal strains, $α$ .
Major Principal Strain (FLD)	Major principal strain at damage initiation.
Minor Principal Strain (FLD)	Minor principal strain at damage initiation.
Plastic Strain Rate	Equivalent plastic strain rate.
Use damage evolution	Damage evolution defines how the material degrades after one or more damage initiation criteria are met. Select the check box, and specify settings in the Damage Evolution group box; these settings are described in Damage Evolution.