Abstract
Abstract This article presents the results of analytical and numerical research focused on the numerical determination of selected fracture mechanics parameters for beams containing a crack in the state of four-point bending with the dominance of a plane strain state. Based on the numerical results, the influence of the specimen geometry and material characteristic on selected fracture parameters is discussed. By analogy to the already known solutions, new hybrid formulas were presented, which allow to estimate the J integral, crack tip opening displacement, and load line displacement. In addition, the study verified the Shih formula connecting the crack tip opening displacement and J integral, taking into account the influence of in-plane constraints on the value of the proportionality coefficient denoted as d n in the analysis. This article also presents the development of Landes and Begley’s idea, which allows to experimentally determine the J integral as a measure of the energy causing the crack growth. The innovative element is taking into account the influence of in-plane constraints on the value of the η coefficient, which is the proportionality coefficient between the J integral and energy A. The last sections of this article are the assessment of the stress distribution in front of the crack tip and the selected measures of in- and out-of-plane constraints, which can be successfully used in the estimation of the real fracture toughness with the use of appropriate fracture criteria.
Highlights
This article presents the results of analytical and numerical research focused on the numerical determination of selected fracture mechanics parameters for beams containing a crack in the state of four-point bending with the dominance of a plane strain state
Based on the analysis presented in ref. [10], for the considered geometry, to simplify the search for the value of the J integral, the crack tip opening displacement and the load line displacement as a function of the increasing external load, material characteristics, and specimen geometry, the following empirical expressions can be proposed to calculate the aforementioned fracture parameters: J=α⋅σ
The geometrical constraints depending on the geometry of the structural element and the material characteristics affect the level of stresses in front of the crack tip [8,9], as well as the values directly related to the parameters of the mechanical fields around the crack tip, as mentioned earlier
Summary
Abstract: This article presents the results of analytical and numerical research focused on the numerical determination of selected fracture mechanics parameters for beams containing a crack in the state of four-point bending with the dominance of a plane strain state. The analysis of all three parameters, the J integral, the crack tip opening displacement, and the load line displacement, was carried out in terms of the dependence of these parameters on the material characteristics (expressed by the strain hardening exponent n and yield stress σ0) and the geometry of the SEN(4PB) specimen, which was expressed in terms of the relative crack length a/W (Figures 4–6). The main quantities assessed during the numerical calculations were the J integral (which is treated as the crack driving force), the crack tip opening displacement δT, and the load line displacement, denoted by vLL These values were assessed as a function of the external load P normalized by the limit load P0. The increase in the material strength (expressed as yield point σ0) is accompanied by an increase in the value of the J integral, crack tip opening displacement δT, and load line displacement vLL at the same level of external load (Figures 4–6c)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
