Elastic-Plastic and Fully Plastic Analysis of Crack Initiation, Stable Growth, and Instability in Flawed Cylinders

Abstract

In this paper a procedure has been developed for examining crack initiation, stable growth, and instability in flawed cylinders. Elastic and fully plastic solutions are presented for cylinders containing axial and circumferential cracks located at the inner surface. In the case of an axial crack the loading is due to internal pressure and a plane-strain analysis is carried out. The circumferentially cracked cylinder is loaded by remote uniform tension and is treated as an axisymmetric problem. The solutions are based on the deformation theory of plasticity and employ a special incompressible finite-element method. Solutions cover a broad range of values for the wall thickness to radius ratio, crack length to wall thickness ratio a/b, and strain-hardening exponent n. The relevant crack parameters such as the J-integral, crack mouth opening displacement, and load-point displacement are suitably normalized and tabulated. Accuracy of the elastic solutions is assessed by a comparison with available literature solutions and some other consistency checks. By appropriately combining the elastic and fully plastic solutions developed, simple estimation formulas are derived through which the relevant crack parameters can be readily computed in the entire range of elastic-plastic deformation. Corresponding results for some illustrative problems are compared with detailed finite-element calculations based on both flow and deformation theories of plasticity. Example J-integral crack driving force diagrams are presented for materials like A533B and 304 stainless steel. Since equilibrium of crack growth requires that applied J equal the material resistance, a superposition of the material JR-curve on such diagrams yields complete information regarding crack initiation, amount of stable growth, instability, and the overall deformation behavior. Finally, the instability of crack growth under J-controlled growth conditions is examined along the lines of the tearing modulus, TJ, approach. J versus TJ stability diagrams are presented for both axial and circumferential cracks covering a broad range of practical problems of interest. Instability develops when the applied tearing modulus exceeds the material resistance to crack growth. Effects of material properties, flaw size, and cylinder dimensions, including system compliance, on the crack growth and instability phenomenon are investigated in some detail.