Near Crack Line Elastic‐Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

Abstract

By using the crack line analysis method, this paper carries out an elastic‐plastic analysis for mode I cracks under plane stress condition in an elastic perfectly plastic solid and obtains the general form of matching equations of the elastic stress field and the plastic stress field near the crack line in rectangular coordinate form. The analysis in rectangular coordinates in this paper avoids the conversion from rectangular coordinates into polar coordinates in the existing analysis and greatly simplifies the power series forms of the elastic stress field and plastic stress field near the crack line during the solving process. Furthermore, by focusing on a new problem, i.e., the center‐cracked plate with finite width under unidirectional uniform tension, this paper obtains the elastic stress field, plastic stress field, and the length of the elastic‐plastic boundary near the crack line by using the general form of the solution. When the dimensions of the plate tend to be infinite, the results of this paper are consistent with those obtained for an infinite plate with a mode I crack. Furthermore, the variation curves of the length of the elastic‐plastic boundary are also delineated in different sized center‐cracked plates, and the results are compared with those obtained under the small‐scale yielding conditions. The solving process and the results in this paper abandon the small‐scale yielding conditions completely. The method used in this paper not only makes the solving process simpler during the elastic‐plastic analysis near the crack line but also enriches the crack line analysis method.