Combination of fracture and damage mechanics for numerical failure analysis

Abstract A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J -integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.

[1]  T. Belytschko,et al.  Localization limiters in transient problems , 1988 .

[2]  M. Stern.  Families of consistent conforming elements with singular derivative fields , 1979 .

[3]  E. Becker,et al.  A conforming crack tip element with quadratic variation in the singular fields , 1978 .

[4]  S. Murakami,et al.  Mechanical Modeling of Material Damage , 1988 .

[5]  R. MacNeal,et al.  Finite Elements: Their Design and Performance , 1993 .

[6]  A. H. England.  A Crack Between Dissimilar Media , 1965 .

[7]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

[8]  J. Rice,et al.  Elementary engineering fracture mechanics , 1974 .

[9]  Toshihisa Nishioka,et al.  The use of the dynamic J integral (J′) in finite-element simulation of mode I and mixed-mode dynamic crack propagation , 1990 .

[10]  D. Borst,et al.  Uncoupled numerical method for fracture analysis , 1997 .

[11]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[12]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[13]  J. Rots.  Smeared and discrete representations of localized fracture , 1991 .

[14]  E. Oñate,et al.  A plastic-damage model for concrete , 1989 .

[15]  René de Borst,et al.  A generalisation of J 2 -flow theory for polar continua , 1993 .

[16]  R. Barsoum.  On the use of isoparametric finite elements in linear fracture mechanics , 1976 .

[17]  J. Z. Zhu,et al.  The finite element method , 1977 .

[18]  D. Borst,et al.  Fundamental issues in finite element analyses of localization of deformation , 1993 .

[19]  Gene H. Golub,et al.  Matrix computations , 1983 .

[20]  J. Chaboche.  Continuum Damage Mechanics: Part I—General Concepts , 1988 .

[21]  W. C. Cooley,et al.  Mechanics of Brittle Fracture , 1982 .

[22]  L. J. Sluys,et al.  Wave propagation, localisation and dispersion in softening solids : proefschrift , 1992 .

[23]  Hans Muhlhaus,et al.  Application of Cosserat theory in numerical solutions of limit load problems , 1989 .

[24]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .

[25]  Jean-Louis Chaboche,et al.  Continuous damage mechanics — A tool to describe phenomena before crack initiation☆ , 1981 .

[26]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories , 1993 .

[27]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

[28]  van Jcw Jos Vroonhoven,et al.  Dynamic crack propagation in brittle materials : analyses based on fracture and damage mechanics , 1996 .

[29]  M. H. Aliabadi.  Localized Damage, Computer-Aided Assessment and Control , 1990 .

[30]  P. Feenstra.  Computational aspects of biaxial stress in plain and reinforced concrete : proefschrift , 1993 .

[31]  J. Chaboche.  Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth , 1988 .

[32]  Z. Bažant,et al.  Stability Of Structures , 1991 .

[33]  H.E.J.G. Schlangen,et al.  Experimental and numerical analysis of fracture processes in concrete : proefschrift , 1993 .

[34]  A. Needleman.  Material rate dependence and mesh sensitivity in localization problems , 1988 .

[35]  S. Atluri,et al.  Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics , 1983 .

[36]  J. Lemaître.  How to use damage mechanics , 1984 .