SAM

Classical and sequential limit analysis revisited

LEBLOND, Jean-Baptiste — Mon, 01 Jan 2018 00:00:00 GMT

Classical and sequential limit analysis revisited LEBLOND, Jean-Baptiste; REMMAL, Almahdi; MORIN, Léo; KONDO, Djimedo Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.

Modeling and simulation of laser shock waves in elasto-plastic 1D layered specimens

LAPOSTOLLE, Lucas — Sat, 01 Jan 2022 00:00:00 GMT

Modeling and simulation of laser shock waves in elasto-plastic 1D layered specimens LAPOSTOLLE, Lucas; MORIN, Léo; BERTHE, Laurent; CASTELNAU, Olivier; DERRIEN, Katell The aim of this paper is to study the effect of microstructure heterogeneity upon elasto-plastic wave propagation generated during laser shot peening. We consider a simplified elasto-plastic laminate specimen subjected to uniaxial strain. The microstructure is composed of two phases alternating periodically and perfectly bonded together. The associated PDE system is solved using a high-resolution Godunov scheme, allowing to study the wave propagation in the heterogeneous structure. It is found that, even for a small mechanical contrast between the two phases, the considered laminate microstructure has a significant effect on the distribution of plastic strain. In addition, an elasto-plastic homogenization of the laminate has been carried out, and the resulting Homogeneous Equivalent Medium (HEM) has been used to decrease the computation time of the wave propagation. The HEM-based model is able to reproduce accurately the full-field solution in terms of distribution of mean plastic strain within the specimen and its fluctuation between the two phases.

Analysis of shear ductile damage in forming processes using a micromechanical model with void shape effects

TAJDARY, Pouya — Sat, 07 May 2022 00:00:00 GMT

Analysis of shear ductile damage in forming processes using a micromechanical model with void shape effects TAJDARY, Pouya; MORIN, Léo; ROMERO-RESENDIZ, Liliana; GORJI, Maysam B.; BRAHAM, Chedly; GONZALEZ, Gonzalo The aim of this work is to investigate and predict ductile failure in forming processes. Experimental results of deep drawing and corrugation processing on aluminum alloys suggest that in some cases failure can be due to shear-dominated loadings. In order to simulate numerically failure during forming, we use the micromechanical Madou–Leblond model, which permits to account for void shape effects that are important under shear loadings. In the case of deep drawing, the model is able to reproduce failure either due to bottom or shear cracks, depending on the processing conditions. In the case of corrugation processing, the model reproduces accurately the occurrence of failure as well as the crack shape. Comparisons with the GTN model show the importance of void shape effects upon failure.

Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming

TAJDARY, Pouya — Fri, 01 Sep 2023 00:00:00 GMT

Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming TAJDARY, Pouya; DORHMI, Khaoula; MORIN, Léo; DERRIEN, Katell; HADJEM-HAMOUCHE, Zehoua; BRAHAM, Chedly; CHEVALIER, Jean-Pierre; CHEVALIER, Jean-Pierre The aim of this work is to investigate the damage mechanisms and stiffness loss in Fe-TiB metal-matrix composites during plastic deformation. First, experimental results of interrupted tensile tests are performed to quantify the evolution of damage, using SEM observations, as well as the decrease of Young’s modulus as a function of the tensile strain. The experimental results are then used to calibrate a two-step homogenization model for metal-matrix composites in which the nucleation and growth of voids modify incrementally the overall elastic properties. The model is finally applied to the numerical prediction of stiffness loss in a problem of metal forming based on Nakazima tests. Overall, the stiffness loss predicted before the onset of coalescence is moderate and its distribution is homogeneous, emphasizing that Fe-TiB metal-matrix composites could be used in applications requiring metal forming.

Experimental study and micromechanical modelling of the effective elastic properties of Fe–TiB2 composites

DORHMI, Khaoula — Fri, 01 Jan 2021 00:00:00 GMT

Experimental study and micromechanical modelling of the effective elastic properties of Fe–TiB2 composites DORHMI, Khaoula; HADJEM-HAMOUCHE, Zehoua; MORIN, Léo; BONNET, Frédéric; CHEVALIER, Jean-Pierre; DERRIEN, Katell The aim of this paper is to investigate the effective properties of Fe–TiB2 composites obtained after hot or cold rolling. The elastic moduli of both hot and cold rolled composites are measured experimentally using several methods. Microstructure analyses based on SEM observations are performed to characterize the distribution of particles and cracks, and are then used to generate 3D representative microstructures using the RSA method. This allows the numerical determination of the overall elastic behavior of Fe–TiB2 composites using full-field FFT-based simulations. In addition, Young’s moduli of the hot rolled Fe–TiB2 composites are also determined analytically using the mean-field homogenization scheme of Mori–Tanaka. The elastic properties determined experimentally, analytically and numerically are in a good agreement. Overall, a significant improvement of the specific stiffness in comparison to standard steels is achieved irrespective of the processing conditions

A FFT-based numerical scheme for the transient conductivity of heterogeneous materials with non-periodic boundary conditions

AMADOU SANOKO, Abdoul Magid — Wed, 01 Jan 2025 00:00:00 GMT

A FFT-based numerical scheme for the transient conductivity of heterogeneous materials with non-periodic boundary conditions AMADOU SANOKO, Abdoul Magid; ESSONGUE, Simon; GELEBART, Lionel; LAPOSTOLLE, Lucas; MORIN, Léo; JOSEPH, Paux The aim of this work is to develop FFT-based solvers for transient diffusion in heterogeneous materials subjected to non-periodic (Dirichlet/Neumann) boundary conditions. We focus on a problem of thermal conductivity and derive a theta-method which includes an implicit solver for transient thermal conductivity in heterogeneous materials. The method is based on a fixed-point iterative solution of an auxiliary problem obtained by a Galerkin discretization using an approximation space based on mixed sine–cosine series. The solution field is decomposed as a known term verifying the boundary conditions and a fluctuation (unknown) term described by appropriate sine–cosine series. The solution of the auxiliary problem involves discrete sine–cosine transforms, of type I and III, which makes the solver rely on the computational complexity of fast Fourier transforms. The method is applied to the prediction of transient thermal fields in a composite material subjected to non periodic boundary conditions.

Reconstruction of heterogeneous surface residual-stresses in metallic materials from X-ray diffraction measurements

MORIN, Léo — Fri, 01 Jan 2021 00:00:00 GMT

Reconstruction of heterogeneous surface residual-stresses in metallic materials from X-ray diffraction measurements MORIN, Léo; BRAHAM, Chedly; TAJDARY, Pouya; SEDDIK, Raoudha; GONZALEZ, Gonzalo The aim of this paper is to provide spatially resolved distributions of residual stresses. X-ray diffraction measurements provide an intrinsic average of the residual stress due to the diffracted volume analyzed during the measurement. When the irradiated area is higher than the characteristic length of stress gradients, strong averaging effects are observed. A spatial deconvolution technique is developed to reconstruct the local residual stress field, based on the inversion of a linear system constructed from the average datasets. The method is first applied to the reconstruction of residual stresses in two reference cases inducing heterogeneous plastic strains (laser shot peening and repetitive corrugation and straightening processing), in which the average datasets are constructed from the local stress profiles determined numerically by the finite element method. In both processes, a very good agreement is observed between the reference stress profiles and the reconstructed ones. Finally, the method is applied to experimental X-ray diffraction measurements on a specimen processed by repetitive corrugation and straightening in similar conditions than the numerical simulations. A strong averaging effect is observed on the collected data and a good agreement is observed between the local stress profile reconstructed from the experimental measurements and that predicted numerically.

Fast numerical estimation of residual stresses induced by laser shock peening

DERRIEN, Katell — Tue, 01 Nov 2022 00:00:00 GMT

Fast numerical estimation of residual stresses induced by laser shock peening DERRIEN, Katell; BERTHE, Laurent; LAPOSTOLLE, Lucas; CASTELNAU, Olivier; MORIN, Léo The aim of this paper is to develop a model allowing a fast first approximate estimation of the elastic–plastic stress wave propagation caused by a laser impact and the resulting residual stress field. We start by modeling the stress wave propagation, adopting a 1D uniaxial modeling, reducing the behavior of the specimen to the axis of the laser impact, excluding any edge effects caused by the edges of the laser spot. The plastic strain field resulting from this propagation can in turn be used to compute the residual stresses, by making use of an analytic modeling in the case of an infinite planar plate. The accuracy of the 1D model is assessed by comparing it to finite elements simulations, acting as a reference solution, for several materials and laser spot diameters. The results show that the stress wave propagation from the 1D model is close to identical to the reference solution. The residual plastic and stress fields from the finite elements model present a uniaxial distribution on a large portion of the laser spot, except for the very edge and spot center. The comparison between the 1D model and the reference solution shows a good match, indicating that the 1D model can be used for a fast approximation the mechanical fields created by a laser impact for laser spot diameters larger than 2 mm.

A model of porous plastic single crystals based on fractal slip lines distribution

PAUX, Joseph — Sat, 01 Oct 2022 00:00:00 GMT

A model of porous plastic single crystals based on fractal slip lines distribution PAUX, Joseph; MORIN, Léo; BRENNER, Renald The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.

Identification of constitutive equations at very high strain rates using shock wave produced by laser

SEDDIK, Raoudha — Fri, 01 Jan 2021 00:00:00 GMT

Identification of constitutive equations at very high strain rates using shock wave produced by laser SEDDIK, Raoudha; RONDEPIERRE, Alexandre; PRABHAKARAN, Subramaniyan; MORIN, Léo; FAVIER, Véronique; PALIN-LUC, Thierry; BERTHE, Laurent A method coupling experiments and simulations, is developed to characterize the yield stress and strain hardening of several metals loaded at 10⁶ s−ⁱ and < 25 ns, typically involved during Laser Shock Peening. It was applied to four materials: pure aluminum, 2024-T3 and 7175-T7351 aluminum alloys and Ti6Al4V-ELI titanium alloy. Thin foils have been irradiated with high-power laser to induce high-pressure shock wave. Plastic deformation is activated through the thickness up to the rear free-surface of the foils. These experiments have been simulated using three material constitutive equations: Elastic–Perfectly Plastic model considering static yield stress, Johnson–Cook model without strain hardening and Johnson–Cook model with strain hardening. The material parameters of Johnson–Cook law were identified by comparison of the experimental and calculated velocity profiles of the rear-free surface. Results are shown and discussed.