Papers by Keyword: Self-Consistent Model

Abstract: The main objective of this work is to apply the Principal Component Analysis (PCA) to the key parameters of a micromechanical model, namely the shape parameter of inclusion (grain) (ratio =a/b) and γ viscoplastic parameter in view of a better simulation. In this work, the sensitivity of the model to parameters and γ is evaluated on the stabilized global stress during cyclic Tension-Compression (TC) loadings and out-of-phase Tension–Torsion, with a sinusoidal waveform and a phase lag of 90 between the two sinusoidal signals TT90 loadings. Indeed several values ​​of and γ are pulled thanks to these loading, we use later the PCA in order to choose the couple (, γ) adequate to launch our simulation. The model used is expressed as part of the self-consistent approach and time-dependent plasticity. Based on the Eshelby tensor, this model considers that the elastic behavior is compressible. For a polycrystalline structure, the grains are deformed by crystallographic sliding located in the most favorably oriented systems and which support a strong constrained stress.

Abstract: The main objective of this work is to study the grain shape effect (aspect ratio α = a / b) and the viscoplastic parameter γ on the evolution of the kinematic and isotropic hardening of FCC type metallic materials, under uniaxial cyclic Tension-Compression ‘‘TC’ and to interpret these results. These parameters of shape and viscoplastic were developed and introduced by Abdul-Latif and Radi, indeed in this study we use their model. Expressed within the framework of a self-consistent approach, the rate-dependent inelastic strain is examined at the crystallographic slip system level describing a constitutive model for FCC metallic polycrystals, whereas the elastic strain is determined at the granular level. Based on the Eshelby’s tensor, the elastic behavior is assumed to be compressible. For a polycrystalline structure, the grains deform plastically by crystallographic slip located at the most favorably oriented systems supporting a high resolved shear stress . The approach considers that the inclusion (grain) form is ellipsoidal of half axes defining by a, b and c such as a ≠b= c. Several numerical tests are carried out highlighting the role of shape and viscoplastic parameter on the evolution of kinematic and isotropic hardening. A general comparison between the and effect on the overall hardening of the polycrystal shows that this work hardening is more sensitive to the parameter (for given ) compared to (for given). Keywords: Grain shape effect, Ellipsoidal inclusion, Viscoplastic parameter effect, Kinematic and isotropic hardening, Uniaxial cyclic ‘‘TC‘‘, Self-consistent model.

Abstract: The effect of interlamellar spacing on monotonic behavior of C70 pearlitic steel was investigated. Tensile tests under X-ray diffraction coupled with self-consistent model have been used to identify the role of interlamellar spacing on the ferrite plasticity parameters and residual stresses. It has been established that yielding of pearlite is controlled by ferrite critical shear stresses ( τc 0α) which is higher for the smaller interlamellar spacing. Moreover, the residual stress level in ferrite is higher for the largest interlamellar spacing under the same imposed total strain. Lattice strains, measured by synchrotron X-ray diffraction, show an elastic and plastic anisotropy of ferrite crystallites and high stresses in cementite which confirm the self-consistent model calculation. Keywords: Pearlitic steel, X-ray diffraction, Synchrotron radiation, Self-consistent model, Critical shear stress, Lattice strains.

Abstract: To get a quantitative estimate of residual stresses in polycrystals from XRD measurements, a micromechanical modeling is required, except in particular cases. The most widely used method is only valid for homogeneous and isotropic samples. We present here the possibility to determine residual stresses by coupling measurements with the portable INEL^TM Xsolo equipement with a self-consistent polycrystalline model. This methodology may take into account texture and intergranular stresses induced by thermomechanical treatments. One example obtained for titanium subjected to tensile loading illustrates the methodology.

Abstract: A new theoretical approach is developed to simulate the elastoplastic behaviour in cubic alloys during various strain-path changes. The polycristal is considered as a composite consisting of hard dislocation walls of high local dislocation density which are separated by soft regions of low local dislocation density. The improved elasto-plastic self-consistent method is applied to deduce the global behaviour of the aggregate. The model is tested by simulating the macroscopic behavior and the development of intergranular strains during different complex loads.

Abstract: A two-level homogenization approach is adopted in order to predict the stress state of deformed polycrystals in correlation with the microstructure. This study is devoted to complex loading paths behaviour of cubic material. A mechanical description of the grain is developed through a micro-meso transition based on elastoplastic Kröner’s model. The meso-macro transition using a self-consistent approach is applied to deduce the global behaviour. Mechanical tests and neutron diffraction measurements are used to validate and assess the model.

Abstract: This work investigates, by diffraction methods, the morphological texture influence on the residual stress analysis in polycrystals having cubic or hexagonal symmetries. Different extreme crystallite morphologies (sphere, disc and fiber, with their principal axes aligned along common directions) were considered in the present study. In a second part, crystallographic textures were accounted for, also, enabling to reflect the combined effect of the simultaneous occurrence of morphological and crystallographic textures. A stronger influence of morphological texture than that of the crystallographic texture in terms of stresses was observed. The main purpose of this work is to make the best choice of lattice planes (hkl) used for residual stress analysis, in elasticity, depending on the morphological (and crystallographic) texture of the polycristal.

Abstract: The aim of the present work is to study effects occurring during elatoplastic deformation and unloading of Al/SiCp metal–matrix composite material. We have measured lattice strains for both phases independently using two separated diffraction peaks (the 111 reflections of Al and SiC) during in situ tensile testing. Lattice strains were measured in the direction parallel to the applied load. The results were compared with an elastoplastic model in order to find parameters determining the plastic deformation of Al matrix (critical resolved shear stress and hardening parameter). We have found that during initial deformation relaxation of the thermal stresses occurs in both phases. Afterwards, the distribution of strains measured during the in situ test and unloading of the sample agree very well with self-consistent model prediction.

Abstract: Time of flight neutron diffraction method was applied to measure elastic lattice strains in austenitic steel during "in situ" tensile test. Comparing experimental data with self-consistent model, the critical resolved shear stress and hardening parameters were determined for polycrystalline grains. The result allowed us to determine the main component of the stress localization tensor, relating the rate of grain stress with the applied macrostress rate. The evolution of concentration tensor in function of the applied macrostress was analyzed. Finally, the load transfer between grains during yielding of the sample was studied.

Abstract: ray diffraction method is used to determine the stress field in polycrystalline materials. The measurement of peak shifts enables the determination of the macrostresses and the plastic incompatibility stresses (intergranular stresses). In the interpretation of the experimental results self-consistent model of elatoplastic deformation is used. In the present work, the plastic incompatibility stresses and the elastic energy stored in cold rolled brass and ferritic steel were determinate. The results are discussed and presented in Euler space.