A Numerical Analysis of Selected Elastic-Plastic Fracture Parameters for DEN(T) Plates under Plane Strain Conditions

Abstract

This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The J-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author's previous studies and simulations in the field of elastic-plastic fracture mechanics [4-6, 16, 17, 31].

The Characteristics of Selected Triaxiality Measures of the Stresses for a C(T) Specimen Dominated by the Plane Strain State

“…It can therefore be said that for a given material specification, the maximum value of successive normal components of the stress tensor is very slightly sensitive to the change in crack length. This confirms the conclusions given in the previous paper [25,26]. The analysis of Fig.6 also proves the fact that the maximum value of the average stresses  m , is generally equal to the maximum stress value in the thickness direction, denoted by  xx and is equal to 3.00 0 , 3.15 0 and 3.10 0 for specimens characterized by relative crack length a/W equal to 0.05, 0.20 and 0.70, respectively.…”

“…The above-mentioned statements indicate the fact that in the considered external loads range, the level of maximum stresses opening the fracture surfaces and their normalized location relative to the crack tip do not depend on the relative crack length, which confirms the conclusions given in [25,26]. As the numerical analysis has shown, the stresses that open the fracture surfaces should be identified with the maximum principal stresses.…”

“…Consideration of the distribution of normal components of the stress tensor presented in Fig.6 as a function of the normalized distance from the crack tip denoted by  is required to determine the maximum stress values opening the crack surfaces  zz and their normalized position relative to the crack tip, which is required to estimating the real fracture toughness using the selected fracture criteria -e.g. papers [18,25,26]. As it can be seen, the increase in external load is accompanied by a slight reduction in the normalized distance of the maximum stresses opening the crack surfaces to the crack tip -for the considered material characteristics, this value is around =1.00.…”

“…The paper presents an abbreviated characterization of the selected measures of the stress triaxiality for a compact specimen dominated by a plane strain state. Apart from short theoretical deliberations devoted to the description of stress fields near the crack tip, based on the results presented in [20,21], the basic measures of in-plane constraints used to assess the actual fracture toughness (Q stresses [13,14], maximum crack opening stresses [25,26]), are discussed, as well as the formulas allowing to estimate the selected measures of stress triaxiality, which are discussed in [27,[30][31][32][33].…”

“…The influence of the yield stress  0 (a), strain hardening exponent n (b) and relative crack length a/W (c) on the maximum crack opening stress ( o = 22_max / 0 ) for compact specimens -results for the whole spectrum of external load -based on [20,21]. Similar sets of in-plane constraints measurements for many other basic geometries used in the studies of fracture mechanics can be found in [22][23][24][25][26]. In addition to theoretical considerations, assessing the impact of external load, geometry or material characteristics, the simplified approximation formulas were also given in these papers, so that the estimation of the measurement of in-plane constraints was possible without the need to perform the FEM calculations.…”