Crack paths and the problem of global directional stability

• Published in: International journal of fracture Vol. 141; no. 3-4; pp. 513 - 534
• Main Authors: PHAM, V.-B, BAHR, H.-A, BAHR, U, FETT, T, BALKE, H
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01.10.2006; Springer Nature B.V
• Subjects: Asymptotic properties; Axial stress; Computer simulation; Crack propagation; Crack tips; Differential equations; Directional stability; Disturbances; Edge cracks; Exact sciences and technology; Finite element method; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Griffith Irwin fracture; Mathematical analysis; Mathematical models; Path predictors; Perturbation methods; Physics; Series expansion; Solid mechanics; Stresses; Structural and continuum mechanics; Biaxial load; Modeling; Edge crack; Crack propagation; Finite element method; Crack path prediction, Global directional stability, Crack path stabílity; Edge effect; Series expansion; Crack length; Defect; Griffith crack; Crack tip; Asymptotic approximation; Principal stress; Integrodifferential equation; T-stress; T stress
• DOI: 10.1007/s10704-006-9010-0
• ISSN: 0376-9429

Crack paths of original Griffith crack and edge crack under biaxial remote mode-I loading after different local disturbances are calculated by using integro-differential equations of first-order perturbation and numerical simulation with FEM respectively.Considering the asymptotic behaviour for large crack lengths the problem of global directional stability is reinvestigated extending the work by Melin. For the Griffith crack, correct power functions for the asymptotic path with one or both crack tips growing have been determined. The well- known critical stress biaxiality ratio Rc = 1 for the global directional stability has been obtained independently whether the crack is disturbed by local imperfections in geometry or in loading. For an edge crack the calculated critical stress biaxiality ratio for the global directional stability Rc = 0.616, also irrespective of the local disturbances, corresponds to a positive T-stress and is considerably smaller than the value R > 0.95 estimated by Melin (2002). In general, cracks need not propagate asymptotically in the direction perpendicular to the largest principal stress (without crack). This is found to be due to the effect of the boundaries.Considering the initial crack growth exclusively, it is shown that the solution for crack path prediction in series expansion form as derived by Cotterell and Rice (1980) for traction-free crack faces (after correction of a misprint) is exact in the two first terms in all cases. Thus, for small crack growth the Cotterell and Rice solution is universal with respect to all loading and geometrical situations.