Failure criteria for linear elastic materials with U-notches

Abstract

This paper provides a simple, albeit accurate, criterion for prediction of the rupture loads of brittle, or quasi-brittle, U-notched samples, where linear elastic fracture mechanics is not applicable because blunted notches do not exhibit stress singularities. Good agreement is found between numerical predictions and experimental results. The results of fracture tests from 18 different ceramic materials and a polymer (at −60 • C) are summarized and are used as a reference for checking the fracture criterion. Seven fracture criteria are reviewed and it is shown that all can be recast into the proposed criterion.

Fracture behaviour of notched round bars made of PMMA subjected to torsion at −60°C

“…Previous tests on three point bending tests had shown an almost linear elastic behaviour up to failure [27][28][29]. Therefore, a similar behaviour was expected on these torsion tests.…”

“…Therefore, proposed fracture criteria are based on critical values of some macroscopic stresses [1], critical virtual cracks [2][3][4][5], non-local averaged parameters [6], stress intensity factors [7][8][9][10][11][12], notch rounding approach [13,14], strain energy density (SED) [15][16][17][18][19][20][21], J-integral [22,23] and Cohesive Zone Models [24][25][26][27][28][29].…”

Effect of notch root radius on fracture toughness of polycrystalline cubic boron nitride

“…An extensive review of these criteria is given by Gomez et al [21]. In the case of PCBN the most useful estimate of the effect of notch root radius is given by considering the elastic stress σ yy at a small distance from the tip of an elliptical notch of minor axis 2b and major axis 2a.…”

Large plasticity induced crack initiation from U-notches in thin aluminum sheets under mixed mode loadin

“…Moreover, because EMC acts as a bridge between the linear elastic and elastic-plastic analyses, it is expected that it can basically be linked to various brittle fracture criteria, e.g. the maximum tangential stress (MTS) and mean stress (MS) (Ayatollahi & Torabi, 2010a, 2010bTorabi, 2013d;Ayatollahi et al, 2011aAyatollahi et al, , 2011bAliha & Ayatollahi 2013;Mirsayar et al 2014;Torabi et al, , 2014dTorabi & Amininejad, 2015aTorabi & Pirhadi 2015;Torabi & Abedinasab, 2015a criteria, the averaged strain energy density (ASED) criterion (Lazzarin & Zambardi, 2001;Berto & Lazzarin, 2014;Torabi et al, , 2015cBerto & Barati, 2011;Gomez et al, 2007Gomez et al, , 2009aGomez et al, , 2009bBerto et al, 2007Berto et al, , 2012Berto & Ayatollahi, 2011;Berto & Lazzarin, 2009;Aliha et al 2016), the cohesive zone model (CZM) (Gomez et al, 2000(Gomez et al, , 2006Gomez & Elices, 2003;Cendon 42 et al, 2015) and the finite fracture mechanics (FFM) (Sapora et al, 2013(Sapora et al, , 2015Cornetti et al, 2012Cornetti et al, , 2014Weißgraeber & Becker, 2013;Carpinteri et al, 2008) etc. under different in-plane loading conditions.…”