Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under uniaxial and biaxial bending

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under static uniaxial and biaxial bending. Extensive three-dimensional elastic–plastic finite element analyses are performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial bending conditions, covering from small-scale to large-scale yielding. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6, corresponding to four specimen configurations, are investigated. The full stress field solutions are obtained in topological planes perpendicular to the crack fronts. The question of J–Q characterization is addressed by comparing these elastic–plastic crack-front stress fields with J–Q family of stress fields. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from the finite element analyses. Complete distributions of the J-integral and Q-factors for the wide range of geometry and loading conditions are obtained. Size requirements in terms of crack depth (for shallow cracks) or ligament size (for deep cracks) that are necessary to ensure J–Q characterization of crack front fields in surface cracked plates are also discussed.