Estimation of the Zone of Failure Extent in Quasi-Brittle Specimens with Different Crack-Tip Constraint Conditions from Stress Field

Abstract

A multi-parameter fracture mechanics concept based on the Williams power series is applied on novel cracked specimen geometries utilizing combined boundary conditions of the wedge splitting and the three-point bending test. Crack tip stress fields for various configurations (causing different constraint conditions at the crack tip and thus also different fracture process zone extents) are numerically investigated and subsequently analytically reconstructed using developed procedure. An importance of using higher order terms of the Williams series is demonstrated.

Evaluation of Crack Tip Stress Field Using Combination of Advanced Implementation of Over-Deterministic Method and FE Analysis

“…Over-Deterministic Method is the computational technique (based on linear least-squares formulation) which is used to obtain the coefficients of higher-order terms of the series [2]. Displacements of selected nodes of FE model serves as inputs -variety of this nodal selection is the subject of previous papers [5] and results of some other studies [3] serve as point of interest for continuation in this field of research.…”

“…The Williams power series is utilized in the relevant research in order to describe the crack-tip stress field in nonlinearly fracturing materials [3], [4] (the authors are focused on quasi-brittle materials). It has been proven in previous works [3], [5] that the knowledge of several initial terms of Williams series (definitely more than the classical one or two) is needed for reconstruction of the fields for proper fracture analysis in the case of these materials. The fields must be described accurately enough not only in the crack-tip vicinity, as is the case of brittle materials.…”

“…Former studies of the authors' research team were aimed on a proper selection of nodal results for their utilization within ODM [2]. The obtained approximations of stress/deformation fields by the mentioned method were investigated in detail and influence of variations of boundary conditions (leading to different constraint conditions at the crack tip stress fields) was investigated [5], [6]. Subsequently, an analytical backward reconstruction of the stress field from the determined terms of series was shown in [5].…”

“…The obtained approximations of stress/deformation fields by the mentioned method were investigated in detail and influence of variations of boundary conditions (leading to different constraint conditions at the crack tip stress fields) was investigated [5], [6]. Subsequently, an analytical backward reconstruction of the stress field from the determined terms of series was shown in [5]. However, the adopted way of ODM application in the referred works was substantially time-demanding and labour-intensive.…”

Numerical study and pilot evaluation of experimental data measured on specimen loaded by bending and wedge splitting forces

“…In the paper, the numerical support (calibration and compliance curves) for evaluation of the experimentally obtain data is shown/introduced. The pilot numerical study of the selected shape of specimens by using Williams expansion was introduced in [22,25,28,30]. The values of stress intensity factor (SIF), T-stress and crack opening displacement (COD, see Fig.…”