Int J Fract DOI 10.1007/s10704-017-0230-2 IUTAM BALTIMORE A theoretical and computational framework for studying creep crack growth Elsiddig Elmukashfi · Alan C. F. Cocks Received: 12 March 2017 / Accepted: 29 June 2017 © The Author(s) 2017. This article is an open access publication Abstract In this study, crack growth under steady state creep conditions is analysed. A theoretical frame- work is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type dam- age and micromechanical based interface models are used. Using the path independency property of the C ∗ -integral and dimensional analysis, analytical mod- els are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A com- putational framework is then implemented using the Finite Element method. The analytical models are cali- brated against detailed Finite Element models. The the- oretical framework gives the fundamental form of the model and only a single quantity ˆ C k needs to be deter- mined from the Finite Element analysis in terms of a dimensionless quantity φ 0 , which is the ratio of geo- metric and material length scales. Further, the validity of the framework is examined by investigating the crack E. Elmukashfi (B ) · A. C. F. Cocks Department of Engineering Science, University of Oxford, Park Road, OX1 3PJ Oxford, UK e-mail: elsiddig.elmukashfi@eng.ox.ac.uk A. C. F. Cocks e-mail: [email protected] growth response in the limits of small and large φ 0 , for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments. Keywords Creep · Crack · C*-integral · Damage zone model · Traction-separation rate law (TSRL) · Double cantilever beam (DCB) · Dimensionless analysis Nomenclature 2 l The spacing between two adjacent pores β A material parameter of the exponen- tial damage law δ c n The critical normal displacement jump in the damage zone at the crack tip δ f n The normal displacement jump at fail- ure in the crack tip δ i The displacement jump vector across the damage zone (i = 1, 2, 3) ˙ δ 0 The separation rate at the reference traction T 0 ˙ δ m n The maximum normal displacement jump rate vector in the crack tip ˙ δ i The displacement jump rate vector across the damage zone (i = 1, 2, 3) ˙ ε 0 The strain-rate at the reference stress σ 0 123
A theoretical and computational framework for studying creep crack growth
Jun 04, 2023
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