Product: ABAQUS/Explicit
Ductile and shear damage initiation criteria are tested for the following material models: Mises plasticity, Hill plasticity, Drucker-Prager plasticity, and equation of state with Johnson-Cook plasticity.
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. 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 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 set using the *SECTION CONTROLS, MAX DEGRADATION option. The default failure choice (i.e., element deletion) is used in all tests in this subsection.
Material degradation starts when the equivalent plastic strain reaches the specified damage initiation criterion. The damage variable evolves according to the evolution law specified in terms of the plastic displacement or energy dissipation. The element is deleted from the mesh once all the integration points at any one section of an element fail; the element output variable STATUS will then be set to zero.
Ductile criterion, Mises plasticity.
Ductile criterion, Hill plasticity.
Ductile criterion, Drucker-Prager plasticity.
Ductile criterion, equation of state with Johnson-Cook plasticity.
Shear criterion, Mises plasticity.
Shear criterion, Hill plasticity.
Shear criterion, Drucker-Prager plasticity.
Shear criterion, equation of state with Johnson-Cook plasticity.
The FLD and FLSD damage initiation criteria are tested on elements with a plane stress formulation for the following material models: Mises plasticity, Hill plasticity, Drucker-Prager plasticity, and Johnson-Cook plasticity.
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. 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.
For the FLD criterion material degradation starts when the maximum in-plane principal strain reaches the major limit strain according to the specified forming limit curve. For the FLSD criterion material degradation starts when the maximum in-plane principal stress reaches the major limit stress according to the specified forming limit stress curve. The damage variable evolves according to the evolution law specified in terms of the plastic displacement or energy dissipation.
FLD criterion, Mises plasticity.
FLD criterion, Hill plasticity.
FLD criterion, Drucker-Prager plasticity.
FLD criterion, Johnson-Cook plasticity.
FLSD criterion, Mises plasticity.
FLSD criterion, Hill plasticity.
FLSD criterion, Drucker-Prager plasticity.
FLSD criterion, Johnson-Cook plasticity.
A set of single elements with a plane stress formulation is loaded under equibiaxial tension to test the M-K damage initiation criterion for different element types. 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.
To demonstrate the capability of the M-K analysis in predicting forming limit diagrams, parametric studies are also 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: 
, with 
, 
, and 
. 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.
Material degradation starts when the ratio of the deformation in the groove relative to the nominal deformation reaches the specified critical value. The damage variable evolves according to the evolution rule specified in terms of the plastic displacement or energy dissipation.
Figure 2.2.20–1 shows the FLD curves predicted with the M-K analyses for the three sets of parametric studies described above, along with a typical loading path involved in each study. The predicted FLD curve with no prestrain matches the analytical criterion suggested by Hill (1952) in the left side of the FLD curve (drawing region). The 10% plane strain prestrain shifts the FLD curve upward and, thus, increases the forming limit in both the drawing region and the stretching region. The 10% equibiaxial prestrain moves the FLD curve downward and to the right; therefore, the forming limit is increased in some regions while lowered in others. These results suggest that the FLDs strongly depend on the loading paths prior to reaching the localization point.
M-K criterion; Mises plasticity; SC8R, S4R, S4RS, CPS4R, M3D4R, and M3D4 elements.
Template file for parametric study with zero prestrain.
Script file for parametric study with zero prestrain.
Template file for parametric study with uniaxial prestrain.
Script file for parametric study with uniaxial prestrain.
Template file for parametric study with biaxial prestrain.
Script file for parametric study with biaxial prestrain.
The nondefault degradation behavior is tested by using the *SECTION CONTROLS, ELEMENT DELETION=NO option.
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.
For elements with two-dimensional and three-dimensional stress states, only the deviatoric and tensile hydrostatic response of the material are degraded once the damage initiation criterion is met; the compressive hydrostatic response is not degraded. For elements with one-dimensional stress states, the stress component is degraded only when it is positive. All elements remain active when element deletion is not used.
The maximum and multiplicative rules for computing the overall damage variable from each individual damage variable contribution are tested by using the *DAMAGE EVOLUTION, DEGRADATION=MAXIMUM option or the *DAMAGE EVOLUTION, DEGRADATION=MULTIPLICATIVE option. The field and temperature dependence of the damage initiation criteria and the damage evolution rules are also tested.
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.
