Plane strain elastic-ideally plastic crack fields for mode I quasistatic growth at large scale yielding. II: Global analytical solutions for finite geometries (Q1198746)

This paper continues the effort begun in the authors part I [J. Mech. Phys. Solids 37, No. 1, 1-26 (1989; Zbl 0666.73068)] to extend the theoretical foundations for understanding and quantitatively describing stable plane strain tensile crack growth to large-scale yielding and general yielding situations in ductile materials. We first confirm the veracity and physical appropriateness of Part I's infinite series (in distance, \(r\), from the crack tip) global representation of the growing crack stress field in extensions of ``centered fan'' plastic regions in isotropic, incompressible elastic-ideally plastic Prandtl-Reuss-Mises material. This is accomplished both by showing that this series almost always possesses a physically significant radius of convergence, and by calculating higher-order (in \(r\)) material velocity and plastic dissipation corrections. We then propound a method for employing this stress field representation to construct approximate global analytical solutions for crack growth in finite geometries at general yielding.