損傷初始及擴(kuò)展

1、Damage in itiati on criterio n and damage evoluti on resp onseAbaqus/Sta ndard and Abaqus/Explicit offer a gen eral capability forpredict ing the on set of failure and a capability for modeli ngprogressive damage and failure of ductile metals. In the most generalcase this requires the specification

2、of the following:? the un damaged elastic-plastic resp onse of the material(“Classical metal plasticity,”Section 20.2.1 );? a damage in itiatio n criteri on (“ Damage in itiati on for ductilemetals, ”Section 21.2.2 ); and? a damageevolution response, including a choice of element removal (“ Damage e

3、volution and element removal for ductilemetals, ”Section 21.2.3 ).Damage initiation criterionDamage initiation criteria for the fracture of metals, including ductile and shear criteria.Damage in itiati on criteria for the n eck ing in stability of sheet metal. These include forming limit diagrams (F

4、LD, FLSD, and in ten ded to assess the formability of sheet metal and the Marci niak-Kucz yn ski (M-K) criteri on (available only in Abaqus/Explicit) to nu merically predict n eck ing in stability in sheet metal tak ing into acco unt the deformati on history.More than one damage initiationcriterion

5、can be specified for a givenmaterial. If multiple damageinitiationcriteria are specified for thesame material, they are treated in depe nden tly.Damage evoluti onThe damage evolutio n law describes the rate of degradati on of the material stiffness once the corresponding initiation criterion hasbee

6、n reached. For damage in ductile metals Abaqus assumes that the degradatio n of the stiff ness associated with each active failure mecha nism can be modeled using a scalar damagevariable, 巧 0 E 訶),whererepresents the set of activemecha ni sms. At any give n time duri ng the an alysis the stress ten

7、sor in the material is give n by the scalar damage equati on(7 = (1 - D)疔、where D is the overall damagevariable and & is the effectiveun damaged) stress ten sor computed in the curre nt in creme nt.arethe stresses that would exist in the material in the absenee of damageThe material has lost its loa

8、d-carryi ng capacity whe nBydefault, an element is removed from the mesh if all of the sectionpoints at any one in tegrati on locati on have lost their load-carry ingcapacity.In put FileUse the followi ng opti on immediately after the correspo nding*DAMAGEINITIATION option to specify the damage evol

9、uti on behavior: *DAMAGE EVOLUTIONAbaqus/CAE Usage:Property module: materialeditor:Mechanical Damage for DuctileMetals-criteri on:Suboptions- DamageEvoluti on1. Ductile criterio nThe ductile criteri on is a phe nomeno logical model for predict ing theon set of damage due to nu cleati on, growth, and

10、 coalesce nee of voids.The model assumes that the equivale nt plastic stra in at the on set of-p/idamage, D, is a function of stress triaxiality and strain rate:wherep/q is the stress triaxiality,p is the pressurestress, q is the Mises equivale nt stress, and尹 is theequivale nt plastic strain rate.

11、The criterio n for damage in itiati onis met when the following condition is satisfied:where 二門 is a state variable that in creases monotoni cally with plastic deformati on. At each in creme nt duri ng the an alysis the in creme ntal in crease inis computed asXd = -7r 0.r 衆(zhòng)“評(píng))2. Joh nson-Cook criter

12、i onThe Joh nson-Cook criterio n (available on ly in Abaqus/Explicit) is aspecial case of the ductile criteri on in which the equivale nt plasticstra in at the on set of damage,n, is assumed to be of the formPn = kA珂)_ w丿whereare failure parameters and is the referenee strainrate. This expression di

13、ffers from the original formula publishedby Johnson and Cook (1985) in the sign of the parameter旳.Thisdiffere nee is motivated by the fact that most materials experie nee a decrease in 仇 with in creas ing stress triaxiality;therefore, 心 in the above expressi on will usually take positivevalues. 0 is

14、 the non dime nsional temperature defi ned as,11 0for nielt3. Shear criterio nThe shear criterio n is a phe nomeno logical model for predict ing theon set of damage due to shear band localizatio n.The model assumes that-pfthe equivale nt plastic stra in at the on set of damage,冒,is afun cti on of th

15、e shear stress ratio and stra in rate:Here =(J + 丘“”粘心 is the shear stress ratio,弘心 is themaximumshear stress, and 韶 is a material parameter. A typical value of 宀 for alumi num is= 0.3 (Hooputra et al., 2004). Thecriterion for damage initiation is met when the following conditionis satisfied:4. Form

16、ing limit diagram (FLD) criteri onThe forming limit diagram (FLD) is a useful con cept in troduced byKeeler and Backofen (1964) to determine the amount of deformation that a material can withsta nd prior to the on set of n eck ing in stability.The maximumstrai nsthat a sheet material can sustai n pr

17、ior to the on setof necking are referred to as the forming limit strains. A FLD is a plot of the forming limitstrainsin the space of principal(in-plane)logarithmic stra ins. In the discussi on that follows major and mi nor limit strai ns refer to the maximum and minimum values of the in-planeprincip

18、allimit strains , respectively.The major limit strain is usually represented on the vertical axis and the minor strain on the horizontal axis, as illustrated inFigure21.2.2 1. The line connecting the states at which deformationbecomesunstable is referred to as the forming limit curve (FLC). The FLC

19、gives a sense of the formability of a sheet of material. Strains computed nu merically by Abaqus can be compared to a FLC to determ ine the feasibility of the forming process un der an alysis.Figure 21.2.2 1 Formi ng limit diagram (FLD).FLCThe FLD damage initiationcriterion requires the specificatio

20、n of theFLC in tabular form by giving the major prin cipal stra in at damageinitiation as a tabular function of the minor principal strain and,opti on ally, temperature and predefi ned fieldvariables,/J. The damage initiation criterion forthe FLD is give n by the con diti on=1, where thevariable匸 fl

21、d is a fun ctio n of the curre nt deformati on state andis defined as the ratio of the current major principal strain,“呃切,to the major limit strain on the FLC evaluated at the current valuesof the minor principalstrain, min&r; temperature, 0; and predefinedfield variables,fi:* iiiMjor宀卜 1 J _ -1IJJ

22、For example, for the deformati on state give n by point A inFigure21.2.2 1 the damage in itiati on criterio n is evaluatedas *卜1-jiki 5. Forming limit stress diagram (FLSD) criteri onWhe n stra in-based FLCs are con verted into stress-based FLCs, theresultingstress-based curves have been shown to be

23、 minimally affectedby cha nges to the stra in path (Stought on, 2000); that is, differe ntstrain-basedFLCs, corresponding to differentstrain paths, are mapped onto a sin gle stress-based FLC. This property makes forming limit stress diagrams (FLSDs) an attractive alter native to FLDs for the predict

24、 ion of n eck ing in stability un der arbitrary load ing. However, the appare nt in depe ndence of the stress-based limit curves on the strain path may simply reflect the small sen sitivity of the yield stress to cha nges in plastic deformati on. This topic is still un der discussi on in the researc

25、h com mun ity.A FLSD is the stress coun terpart of the FLD, with the major and mi nor prin cipal in-pla ne stresses corresp onding to the on set of n eck ing localization plotted on the vertical and horizontal axes, respectively.Damage evoluti onFigure 21.2.3 1 illustrates the characteristic stress-

26、strain behavior of a material un derg oing damage. In the con text of an elastic-plastic material with isotropic harde ning, the damage mani fests itself in two forms: softening of the yield stress and degradation of the elasticity.The solid curve in the figure represe nts the damaged stress-stra in response, while the dashed curve is the response in the absenee of damage. As discussed later, the damagedresponse depends on the element dimensions such that mesh depe ndency of the results is mini mized.Figure 21.2.3 1 Stress-str