A theoretical and computational framework for studying creep crack growth

Cocks

2021

Preprint

Self Cite

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 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 an effective traction and separation 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 * -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 ) is determined in terms of a dimensionless quantity Φ 0 (which is the ratio of geometric and material length scales), mode mixity χ and the deformation and damage coupling parameters. We demonstrate that the form of the 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.

Section: Theoretical Analysis Of Mixed Mode Creep Crackmentioning

confidence: 99%

“…In what follows, a range of traction-separation-rate laws are introduced for mixed mode conditions which generalise the models described by Elmukashfi and Cocks [38].…”

Section: γIn Nmentioning

confidence: 99%

Section: Kachanov Type Empirical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Cocks

2021

Preprint

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A modelling framework for coupled hydrogen diffusion and mechanical behaviour of engineering components

Tarleton

2020

Comput Mech

Self Cite

In this paper, we propose a finite element formulation for solving coupled mechanical/diffusion problems. In particular, we study hydrogen diffusion in metals and its impact on their mechanical behaviour (i.e. hydrogen embrittlement). The formulation can be used to model hydrogen diffusion through a material and its accumulation within different microstructural features of the material (dislocations, precipitates, interfaces, etc.). Further, the effect of hydrogen on the plastic response and cohesive strength of different interfaces can be incorporated. The formulation adopts a standard Galerkin method in the discretisation of both the diffusion and mechanical equilibrium equations. Thus, a displacement-based finite element formulation with chemical potential as an additional degree of freedom, rather than the concentration, is employed. Consequently, the diffusion equation can be expressed fundamentally in terms of the gradient in chemical potential, which reduces the continuity requirements on the shape functions to zero degree, C 0 , i.e. linear functions, compared to the C 1 continuity condition required when concentration is adopted. Additionally, a consistent interface element formulation can be achieved due to the continuity of the chemical potential across the interface-concentration can be discontinuous at an interface which can lead to numerical problems. As a result, the coding of the FE equations is more straightforward. The details of the physical problem, the finite element formulation and constitutive models are initially discussed. Numerical results for various example problems are then presented, in which the efficiency and accuracy of the proposed formulation are explored and a comparison with the concentration-based formulations is presented. Keywords Hydrogen embrittlement (HE) • Hydrogen enhanced local plasticity (HELP) • Hydrogen enhanced decohesion (HEDE) • Chemical potential • Galerkin method • Interface/cohesive model Nomenclature HEDE Hydrogen enhanced decohesion HELP Hydrogen enhanced local plasticity HE Hydrogen embrittlement HID Hydrogen induced decohesion α Number of trapping sites in a trap β L Number of interstitial sites per solvent atom B Elsiddig Elmukashfi

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

Cocks

2021

Int J Fract

Self Cite

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.