损伤初始及扩展

.Damage initiation criterion and damage evolution responseAbaqus/Standard and Abaqus/Explicit offer a general capability for predicting the onset of failure and a capability for modeling progressive damage and failure of ductile metals. In the most general case this requires the specification of the following: the undamaged elastic-plastic response of the material (“Classical metal plasticity,”Section 20.2.1); a damage initiation criterion (“Damage initiation for ductile metals,”Section 21.2.2); and a damage evolution response, including a choice of element removal (“Damage evolution and element removal for ductile metals,”Section 21.2.3).Damage initiation criterion Damage initiation criteria for the fracture of metals, including ductile and shear criteria. 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.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.Damage evolutionThe 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,(), whererepresents the set of active mechanisms. At any given time during the analysis the stress tensor in the material is given by the scalar damage equationwhereDis the overall damage variable andis the effective (or undamaged) stress tensor computed in the current increment.are the stresses that would exist in the material in the absence of damage. The material has lost its load-carrying capacity when. By default, an element is removed from the mesh if all of the section points at any one integration location have lost their load-carrying capacity.InputFileUsage:Use the following option immediately after the corresponding*DAMAGE INITIATIONoption to specify the damage evolution behavior:*DAMAGE EVOLUTIONAbaqus/CAEUsage:Propertymodule: material editor:MechanicalDamage for Ductile Metalscriterion:SuboptionsDamage Evolution1. Ductile criterionThe ductile criterion is a phenomenological model for predicting the onset of damage due to nucleation, growth, and coalescence of voids. The model assumes that the equivalent plastic strain at the onset of damage, is a function of stress triaxiality and strain rate:whereis the stress triaxiality,pis the pressure stress,qis the Mises equivalent stress, andis the equivalent plastic strain rate. The criterion for damage initiation is met when the following condition is satisfied:whereis a state variable that increases monotonically with plastic deformation. At each increment during the analysis the incremental increase inis computed as2. Johnson-Cook criterionThe Johnson-Cook criterion (available only in Abaqus/Explicit) is a special case of the ductile criterion in which the equivalent plastic strain at the onset of damage, is assumed to be of the formwhereare failure parameters andis the reference strain rate. This expression differs from the original formula published byJohnson and Cook (1985)in the sign of the parameter. This difference is motivated by the fact that most materials experience a decrease inwith increasing stress triaxiality; therefore,in the above expression will usually take positive values.is the nondimensional temperature defined as3. Shear criterionThe shear criterion is a phenomenological model for predicting the onset of damage due to shear band localization. The model assumes that the equivalent plastic strain at the onset of damage, is a function of the shear stress ratio and strain rate:Hereis the shear stress ratio,is the maximum shear stress, andis a material parameter. A typical value offor aluminum is= 0.3 (Hooputra et al., 2004). The criterion for damage initiation is met when the following condition is satisfied:4. Forming limit diagram (FLD) criterionThe forming limit diagram (FLD) is a useful concept introduced by Keeler and Backofen (1964) to determine the amount of deformation that a material can withstand prior to the onset of necking instability. The maximum strains that a sheet material can sustain prior to the onset of necking are referred to as the forming limit strains. A FLD is a plot of the forming limit strains in the space of principal (in-plane) logarithmic strains. In the discussion that followsmajorandminorlimit strains refer to the maximum and minimum values of the in-plane principal limit strains, respectively. The major limit strain is usually represented on the vertical axis and the minor strain on the horizontal axis, as illustrated inFigure 21.2.21. The line connecting the states at which deformation becomes unstable is referred to as the forming limit curve (FLC). The FLC gives a sense of the formability of a sheet of material. Strains computed numerically by Abaqus can be compared to a FLC to determine the feasibility of the forming process under analysis.Figure 21.2.21Forming limit diagram (FLD).The FLD damage initiation criterion requires the specification of the FLC in tabular form by giving the major principal strain at damage initiation as a tabular function of the minor principal strain and, optionally, temperature and predefined field variables,. The damage initiation criterion for the FLD is given by the condition, where the variableis a function of the current deformation state and is defined as the ratio of the current major principal strain, to the major limit strain on the FLC evaluated at the current values of the minor principal strain,; temperature,; and predefined field variables,:For example, for the deformation state given by point A inFigure 21.2.21the damage initiation criterion is evaluated as5. Forming limit stress diagram (FLSD) criterionWhen strain-based FLCs are converted into stress-based FLCs, the resulting stress-based curves have been shown to be minimally affected by changes to the strain path (Stoughton, 2000); that is, different strain-based FLCs, corresponding to different strain paths, are mapped onto a single stress-based FLC. This property makes forming limit stress diagrams (FLSDs) an attractive alternative to FLDs for the prediction of necking instability under arbitrary loading. However, the apparent independence of the stress-based limit curves on the strain path may simply reflect the small sensitivity of the yield stress to changes in plastic deformation. This topic is still under discussion in the research community.A FLSD is the stress counterpart of the FLD, with the major and minor principal in-plane stresses corresponding to the onset of necking localization plotted on the vertical and horizontal axes, respectively.Damage evolutionFigure 21.2.31illustrates the characteristic stress-strain behavior of a material undergoing damage. In the context of an elastic-plastic material with isotropic hardening, the damage manifests itself in two forms: softening of the yield stress and degradation of the elasticity. The solid curve in the figure represents the damaged stress-strain response, while the dashed curve is the response in the absence of damage. As discussed later, the damaged response depends on the element dimensions such that mesh dependency of the results is minimized.Figure 21.2.31Stress-strain curve with progressive damage degradation.In the figureandare the yield stress and equivalent plastic strain at the onset of damage, andis the equivalent plastic strain at failure; that is, when the overall damage variable reaches the value. The overall damage variable,D, captures the combined effect of all active damage mechanisms and is computed in terms of the individual damage variables, as discussed later in this section (see“Evaluating overall damage when multiple criteria are active”).The value of the equivalent plastic strain at failure, depends on the characteristic length of the element and cannot be used as a material parameter for the specification of the damage evolution law. Instead, the damage evolution law is specified in terms of equivalent plastic displacement, or in terms of fracture energy dissipation,; these concepts are defined next.