About determining the coefficient η for J-integral for SEN(B) specimens

Abstract

The general formula proposed by Landes and Begeley [1], which has been modified for years, among which more or less complicated approaches can be distinguished for determining the J-integral in laboratory conditions. One of them is the ASTM standard [2], according to which the energy required to calculate the J-integral should be decomposed into elastic and plastic parts, and thus the factor η depending on the shape of the specimen used in laboratory tests. Some approaches, e.g. the Polish standard [3], indicate that the J-integral should be calculated without decomposing into elastic and plastic parts. The normative documents mentioned do not usually mention the dependence of the η factor on the geometrical dimensions of the specimen (except for the shape of the specimen) or the dependence on the material characteristics. As shown in [4-7], the value of the coefficient η depends on the crack length and the material characteristics, however, the influence of material constants is usually discussed in a strictly defined range. It should be noted that papers [4-7] are based on the decomposition of the coefficient η value into elastic and plastic parts. The hybrid method presented in [8] for assessing selected parameters of fracture mechanics, referring to EPRI procedures [9], allows to evaluate them without the need for tedious numerical calculations, however, unlike EPRI procedures, it does not introduce the need to decompose these parameters into elastic and plastic components. In view of this fact, in this study it was decided to assess on the basis of numerical calculations carried out for the dominance of plane strain, the effect of crack length and material constants (expressed in yield strength and strain hardening exponent in R-O law) on the value of the coefficient η which is required to estimate the value of the J-integral in accordance with by Landes and Begeley [1]. The discussion presented in [10] was the inspiration to undertake this topic. In this paper, based on a comprehensive numerical analysis of SEN(B) specimens dominated by a plane strain state, for four different crack lengths and sixteen hypothetical elastic-plastic materials (characterized by different yield strength and different level of stain hardening exponent), the values of the J-integral were estimated, the impact of the crack length and material constants on the value of J-integral was assessed, an analysis of the P=f(u) curves and discussion on the effect of crack length and material constants on the value of the factor η were presented. Using the approach given in [4-7], simplification was made in the analysis and the value of the coefficient η was determined for each analysed specimen. The analysis showed a strong dependence of the coefficient η on the crack length and the strain hardening exponent n. It turned out that the coefficient η does not depend on the yield strength of the specimen material. The results were summarized in tabular form and approximated using the Table Curve 3D program. The measurable effect of the paper is a summary of numerical results – values of the coefficient η for 64 SEN(B) specimens and a new form of the function η=f(a/W, n) which was proposed, and which allowing to take into account in the process of determining the J-integral by the factor η the geometry of the specimen (relative crack length a/W) and material characteristics (n – strain hardening exponent in R-O law).