SYMPOSIA PAPER Published: 01 January 2003

Plane Stress Mixed Mode Crack-Tip Stress Fields Characterized by a Triaxial Stress Parameter and a Plastic Deformation Extent Based Characteristic Length


Residual strength assessment in aircraft fuselage structures requires that a general criterion for mixed-mode fracture of ductile materials be developed. An understanding of mixed-mode crack-tip stress fields is essential to define viable fracture parameters and perform accurate fracture analysis. In the present study, a self-similar family of mixed-mode crack-tip stress fields proposed by the present authors is studied in detail for plane stress problems under conditions ranging from small scale yielding to large scale yielding. Analytical and numerical studies indicate that stress and plastic strain in the crack tip region can be characterized by a plastic strain extent based characteristic length, Lp, and the crack tip region stress triaxiality constraint parameter, Am, defined as the ratio of mean stress over effective stress (σme). Results from all cases indicate that the proposed, self-similar family of mixed-mode crack-tip stress fields accurately represents the stress fields for both SSY models and actual fracture specimen geometry. The crack tip stress fields are shown to belong to a family of solutions parameterized by Am and Lp when the distance from crack tip, r, is measured in terms of its normalized value by the characteristic length scale, r/Lp. Specifically, in the tensile fracture dominated crack growth direction (locally Mode I direction), it is found that stress triaxiality takes its maximum value. This condition will promote the nucleation of micro-voids from large particles, resulting in Mode I dimpled fracture. In the shear dominated crack growth direction fracture (locally Mode II direction), corresponding to the direction of maximum Lp, it is shown that the effective and shear stresses reach their maximum values. This condition promotes the formation of an intense slip-band, resulting in Mode II fracture.

Author Information

Ma, F
Pratt & Whitney, East Hartford, CT
Sutton, MA
University of South Carolina, Columbia, SC
Deng, X
University of South Carolina, Columbia, SC
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Developed by Committee: E08
Pages: 233–269
DOI: 10.1520/STP11079S
ISBN-EB: 978-0-8031-5472-8
ISBN-13: 978-0-8031-2899-6