Constraint evaluation and effects on selected fracture parameters for single-edge notched beam under four-point bending

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.

Keywords

• j integral
• crack tip opening displacement
• load line displacement
• limit load
• constraints
• stress distributions
• q stress
• in-plane constraints