Plane strain elastic-ideally plastic crack fields for mode I quasistatic growth at large scale yielding. II: Global analytical solutions for finite geometries
type: Item
instance of: scholarly article
title: Plane strain elastic-ideally plastic crack fields for mode I quasistatic growth at large scale yielding. II: Global analytical solutions for finite geometries
zbMATH Open document ID: 0754.73072
DOI: 10.1016/0022-5096(91)90011-C
author: Xing-Yu Chen
author: W. J. Drugan
published in: Journal of the Mechanics and Physics of Solids
publication date: 1993-01-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74C99
zbMATH DE Number: 90833
zbMATH Keywords: ductile materials
zbMATH Keywords: infinite series
zbMATH Keywords: incompressible elastic-ideally plastic Prandtl-Reuss-Mises material
zbMATH Keywords: material velocity
zbMATH Keywords: plastic dissipation corrections
MaRDI profile type: Publication
cites work: Plane strain elastic-ideally plastic crack fields for mode I quasistatic growth at large-scale yielding. I: A new family of analytical solutions
cites work: Q5801127
full work available at URL: 0022-5096(91)90011-c
OpenAlex ID: W2065352349
description: scientific article; zbMATH DE number 90833