Stability of a frictional, cohesive layer on a viscous substratum: validity of asymptotic solution and influence of material properties

This study deals with the stability of a stratified structure composed of a cohesive and frictional overburden, a viscous substratum, and a rigid basement. That structure should be seen as a prototype for various salt tectonics and lithospheric plates stability analyses. The destabilizing factors are the density contrast, the tectonic compressive stress, and the possible erosion and deposition at the top surface. The overburden stiffness, a nonlinear function of in situ stress, has a stabilizing role. Two solutions are extracted from the variational formulation of the stability problem previously proposed [Leroy and Triantafyllidis, 1996]: the first is analytical and is obtained by disregarding gravity, and the second is numerical and is based on the finite element method. The latter is used to assess the validity of the previously presented asymptotic solution. It is shown that the asymptotic solution is accurate even for values of the small parameter, defined as the perturbation wavenumber times the overburden thickness, as large as 0.4. Furthermore, the possibility for the cohesive material in the overburden to accommodate part of the deformation by slip along a population of small pervasive faults is accounted for by the introduction of a deformation theory of plasticity. Stability predictions based on this theory indicate that structural modes, such as folding, and localized faulting modes are triggered for similar stress magnitudes. The parametric study presented includes the previously undetected influences of the stress gradient with depth and of the work hardening properties of the competent overburden. The role of erosion and deposition in destabilizing shallow overburdens, regardless of the magnitude of the tectonic stress, is also established. The stability predictions are then applied to a folded section through the Campos basin, offshore Brazil, revealing that the deformation theory of plasticity is necessary to explain the buckling that occurred during the Albian

Formability analysis of pre-strained AA5754-O sheet metal using Yld96 plasticity theory: Role of amount and direction of uni-axial pre-strain

Automotive industries are very much interested in formability of different pre-strained aluminum alloy sheets in the context of multistage stamping to fabricate complex components. In the present work, different uni-axial pre-strains of 6.4% and 12.2% were induced in AA5754-O aluminum alloy both along rolling direction (RD) and transverse direction (TD). The true stress-strain response, limiting dome height (LDH) and strain based forming limit diagram (ε-FLD) of as received and all pre-strained materials were evaluated experimentally. The anisotropy constitutive material model was developed using the Yld96 plasticity theory in-conjunction with the Hollomon isotropic hardening law to predict the yield strength evolution of the pre-strained materials. Also, it was found that the limiting strains in ε-FLD shifted significantly depending on the amount and direction of uni-axial pre-strain. Hence, the limiting strains of the as-received materials were transposed into stress space to estimate the stress based forming limit diagram (σ-FLD) using the anisotropy constitutive material model. Further, the dynamic shifts of ε-FLDs of four different pre-strained materials were predicted by successfully decoupling the σ-FLD of as-received materials within root mean square error of 0.008. Finite element models of both uni-axial pre-straining and subsequent LDH tests were developed, and the forming behavior of the pre-strained materials were predicted implementing the Yld96 plasticity model and estimated σ-FLD. It was found that LDH was significantly influenced by the amount of pre-strain, and the maximum thinning location shifted close to pole in the case of 12.2% pre-strained materials. However, the effect of uni-axial pre-strain direction on both LDH and maximum thinning location in AA5754-O material was very negligible