Mixed-mode cohesive laws and the use of linear-elastic fracture mechanics

S Goutianos,M.D Thouless,B.F Sørensen

doi:10.1016/j.engfracmech.2021.107792

Abstract

Small-scale cohesive-zone models based on potential functions are expected to be consistent with the important features of linear-elastic fracture mechanics (LEFM). These include an inverse-square-root K-field ahead of a crack, with the normal and shear stresses being proportional to the mode-I and mode-II stress-intensity factors, KI and KII, the work done against crack-tip tractions being equal to KI2+KII2∕Ē, where Ē is the appropriate modulus, and failure being controlled by the toughness. The use of an LEFM model also implicitly implies that the partition of the crack-tip work into shear and normal components is given by a phase angle defined as ψK=tan−1KII∕KI. In this paper, we show that the partition of crack-tip work in a cohesive-zone model is consistent with LEFM if the normal and shear deformations across an interface are uncoupled. However, we also show that this is not the case for coupled cohesive laws, even if these are derived from a potential function. For coupled laws, LEFM cannot be used to predict the partition of work at the crack tip even when the small-scale requirements for LEFM conditions being met; furthermore, the partition of the work may depend on the loading path. This implies that LEFM cannot be used to predict mixed-mode fracture for interfaces that are described by coupled cohesive laws, and that have a phase-angle-dependent toughness.

Highlights

2 Cohesive-zone models, originating from the work of Hillerborg et al 3 (1976) and Needleman (1987), are widely used to simulate the initiation 4 and growth of cracks in problems ranging from the materials scale (Marshall 5 et al, 1985; Needleman, 1987; Tvergaard and Hutchinson, 1992; Reinoso 6 et al, 2017) to the structural scale, such as adhesive joints (Yang et al, 7 1999; Mohammed and Liechti, 2000; Sørensen et al, 2009) and wind turbine 8 blades (Overgaard and Lund, 2010)
The crack tip are uniquely defined by KI and KII, and independent of the cohesive length, provided this latter parameter is small enough. The implication of this is that any loading-path dependence that might exist for deformation of the crack tip potentially is inconsistent with the assumptions that underpin the use of linear-elastic fracture mechanics (LEFM). We investigate this specific issue within the broad framework of small-scale fracture that is generally taken to correspond to LEFM conditions
We explore in detail the difference between coupled and uncoupled laws, while ensuring that we are unambiguously within the range where LEFM is valid

Summary

Introduction

2 Cohesive-zone models, originating from the work of Hillerborg et al 3 (1976) and Needleman (1987), are widely used to simulate the initiation 4 and growth of cracks in problems ranging from the materials scale (Marshall 5 et al, 1985; Needleman, 1987; Tvergaard and Hutchinson, 1992; Reinoso 6 et al, 2017) to the structural scale, such as adhesive joints (Yang et al, 7 1999; Mohammed and Liechti, 2000; Sørensen et al, 2009) and wind turbine 8 blades (Overgaard and Lund, 2010) In these models, the fracture process 9 is described by a traction-separation relationship, known as a cohesive law, that comprises both a strength (peak traction) and a fracture energy (area under the traction-separation curve) (Dugdale, 1960; Barenblatt, 1962). There are what are termed as ”uncoupled” and ”coupled” 24 mixed-mode laws

Results

Discussion

Conclusion