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# A theoretical and computational investigation of mixed mode creep crack growth along an interface

journal contribution
posted on 2024-02-08, 16:16 authored by Elsiddig Elmukashfi, Alan CF Cocks

In this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the $$C^{*}$$ C ∗ -integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function ($$C_{k}$$ C k ) is determined in terms of a dimensionless quantity $$\phi _{0}$$ ϕ 0 (which is the ratio of geometric and material length scales), mode mixity $$\chi$$ χ and the deformation and damage coupling parameters. We demonstrate that the form of the $$C_{k}$$ C k -function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions.

## Funding

### Transferability of small-specimen data to large-scale component fracture assessment

Engineering and Physical Sciences Research Council

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## Author affiliation

School of Engineering, University of Leicester

## Version

• VoR (Version of Record)

## Published in

International Journal of Fracture

229

2

125 - 159

## Publisher

Springer Science and Business Media LLC

0376-9429

1573-2673

2021

2024-02-08

en

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