Analytical and finite element modelling of roughness induced crack closure

Relations between microstructure, precipitation, age-formability and damage tolerance of Al–Cu–Mg–Li (Mn, Zr, Sc) alloys for age forming

“…Alloy 4 in particular is characterized by a combination of the highest Li content and large grain size: both factors may be expected to cause increasing slip heterogeneity. The relationships between surface roughness, closure levels and FCG performance were further investigated and confirmed by qualitative assessment of the fracture surfaces using 3D Talysurf profilometry, which clearly showed that the higher closure observed in the alloys with coarse grains (such as alloy 4) is associated with rougher fracture surfaces [29].…”

“…These, in turn depend on the propensity for shear band formation, crystallographic texture and grain size. In recent work on experimental determination and micromechanical modelling, RICC shear strains causing asperity contact are considered to arise explicitly from residual plastic deformation in the wake of a propagating crack [12]. The crack closure and resulting reduction in K have been analysed both for a 2D situation (profile of crack is unchanged along the crack front direction) [12] and a 3D situation in which the crack surface has ridges both parallel and normal to the crack [29].…”

“…In this analysis closure is given by [29]: where a* is the crack propagation distance since the last asperity tip, R is the load ratio (minimum over maximum applied stress), o σ is the yield strength, r p is the plastic zone size, ν is the Poisson ratio, θ and Φ are the angles defining the deflections parallel to crack growth direction and crack front, respectively, and λ and β are fitting parameters (linked to the physical length scales of plastic deformation at the crack tip), FE modelling suggests a reasonable value for λ to be the order of 0.4 [12]. In the 2D analysis closure is given by: A full analysis shows that crack closure levels rise monotonically with asperity sizes, and hence grain size, although these effects saturate when asperity size significantly exceeds the active plastic zone size, and a detailed analysis of relations between grain size, surface roughness and FCG resistance was presented elsewhere [12]. The reduction in FCG resistance with increasing ageing temperature can be understood within the context of these crack closure models, as S phase formed at higher ageing temperatures (Fig.…”

“…The addition of Li in selected alloys was made to take advantage of the associated improved fatigue crack growth resistance but Li contents were limited to 1.6 wt% to limit formation of δ' (Al 3 Li) precipitates which are associated with reduced toughness. An analytical model of roughness induced crack closure (RICC) has been developed to provide a semi-quantitative relation between fatigue crack growth (FCG) and microstructural features [12]. As underaged alloys generally show a better FCG resistance, alloy design aims at slowing down the precipitation process in these alloys compared to 2024.…”

“…In recent work on experimental determination and micromechanical modelling, RICC shear strains causing asperity contact are considered to arise explicitly from residual plastic deformation in the wake of a propagating crack [12]. The crack closure and resulting reduction in K have been analysed both for a 2D situation (profile of crack is unchanged along the crack front direction) [12] and a 3D situation in which the crack surface has ridges both parallel and normal to the crack [29]. In the latter the model includes a 3 dimensional representation of the crack surface with mode II and mode III contributions to the crack closure, as illustrated in Fig 9, which also illustrates the surface parameters included in the model.…”