An analysis of fracture under biaxial loading using the non‐singular T‐stress

Abstract

Finite element analysis using a two‐dimensional modified‐boundary‐layer approach wasused to model the effects of biaxial loading on crack tip stress fields. Loadings wereapplied corresponding to an elastic KI field, non‐singular T‐stress and a biaxial stress.For through‐thickness cracks the T‐stress inherent in the specimen geometry isaugmented by the external biaxial stress. For surface‐notched specimens the biaxialstress acts out of the crack plane. This effect was modelled with generalized plane strainelements. Results were analysed using the Anderson‐Dodds approach for cleavage andthe Beremin model in the ductile regime. Biaxial loading is predicted to have a largeeffect on the toughness of a through‐thickness crack but little effect on a surface crack.Experimental results from a previous series of large‐scale biaxial fracture tests aregenerally consistent with these predictions.

On modelling cracks in orthotropic plates under biaxial loading: synthesis and summary

“…As a result, such unconformity with experimental data stipulates the interest of researchers to the problem. This is supported by numerous publications on the subject 2–5 …”

An Energy Gradient Fracture Criterion Based on Virtual Crack Vector Model with Application to T-Stress Problem

“…Griffith formula can be obtained directly by substituting k=0 and =90 0 into Eq.8 and 9: (10) in which G I is the ERR of mode I crack under simple tension. The critical stress of mode I crack can be defined by letting G I =G IC in Eq.10 as: (11) in which IC and G IC are the critical stress and the critical ERR of mode I crack respectively.…”

“…It had been found that there were strong biaxial effects on brittle fracture, which could not be taken into account by the singular criterions. Therefore extensive investigations of fracture criterion take both singular and nonsingular stress terms into consideration [4][5][6][7][8][9][10][11] (nonsingular criterions for short). It had been revealed that nonsingular stress terms, especially the constant term of ox , often known as the T-stress, had significant influence on both fracture initiation and propagation [5][6][7][8][9][10][11].…”

A New Stress Field Model for Semiclosed Crack under Compression considering the Influence of T -Stress

“…In the past, only the singular stress term in the expansion is adopted by scholars when studying the stress field at the crack tip [14,15], ignoring the nonsingular term and the higher-order term. However, numerous studies [16][17][18] have shown that T-stress has a significant effect on the tip stress field, which can be summarized as follows: when r approaches to 0, the singular stress term in the expansion plays the main controlling role, and as the r gradually increases, the value of the singular stress term decreases rapidly while the proportion of nonsingular stress term gradually increases. It reveals that the nonsingular stress term cannot be ignored in particular under this condition.…”