Papers by Author: Maxime Sauzay

Abstract: Two homogeneization approaches are used in order predict the cyclic elastic-plastic behaviour of 316L(N) polycrystals, either

Abstract: Slip localization is widely observed in metallic polycrystals after tensile deformation, cyclic deformation or pre-irradiation followed by tensile deformation. Such strong deformation localized in thin slip bands induces local stress concentrations in the quasi-elastic matrix around, at the intersections between slip bands (SBs) and grain boundaries (GBs) where microcrack initiation is often observed. Since the work of Stroh, such stress fields have been mostly modeled using the dislocation pile-up theory which leads to stress singularities similar to the LEFM ones. The Griffith criterion has then been widely applied, leading usually to strong underestimations of the macroscopic stress to GB crack initiation. In fact, slip band thickness is finite: 20nm-1000nm depending on material, temperature and loading conditions. Then, many slip planes are plastically activated through the thickness, and not only one single atomic plane. To evaluate more realistic stress fields, numerous crystalline finite element (FE) computations have been carried out using microstructure inputs (slip band aspect ratio, crystal and GB orientation...). A strong influence of slip band thickness close to the slip band corner has been highlighted, which is not accounted for by the pile-up theory. But far away, the thickness has a negligible effect and the predicted stress fields are close to the one predicted by the pile-up theory. Closed-form expressions are deduced from the numerous FE computation results allowing a straightforward prediction of GB stress fields. Slip band plasticity parameters, such as length and thickness, as well as crystal orientation, GB plane and remote stress are taken into account. The dependence with respect to the various parameters can be understood in the framework of matching expansions usually applied to cracks with V notches of finite thickness. As the exponent of the GB stress close-field is only about one-half of the pile-up or LEFM crack one, the Griffith criterion may not be used for GB microcrack prediction in case of finite thickness. That is why finite crack fracture mechanics is used together with both energy and stress criteria. Taking into account SB finite thickness, t>0, leads to predicted remote stresses to GB microcrack initiation three to six times lower than the ones predicted using the to pile-up theory, in agreement with experimental data.

Abstract: Austenitic Stainless Steels (SSs) are presently being investigated as appropriate candidates for structural components for the future Generation IV nuclear reactors. Austenitic SSs of different grades will operate at high temperature and suffer low stress loading for decades. At the laboratory, austenitic SSs have been subjected to creep tests at various stresses and temperatures between 500°C to 700°C, up to nearly 50·10³h. Interrupted creep tests show an acceleration of the reduction in cross-section only during the last 15% of creep lifetime which may be called macroscopic necking. The modeling of necking using a modified Norton power-law allows lifetime predictions in agreement with experimental data up to a few thousand hours only. And the experimental results show that, the extrapolation of the 'stress lifetime curves obtained at high stress leads to large overestimations of lifetimes at low stress. After FEGSEM observations, these overestimates are mainly due to additional intergranular cavitation along grain boundaries. The modeling of cavity growth by vacancy diffusion along grain boundaries coupled with continuous nucleation proposed by Riedel has been carried out. Lifetimes for long term creep are rather correctly predicted with respect to experimental lifetimes. The lifetime curves predicted by either the necking model or the creep cavity one cross each other, defining transition times of five to ten thousand hours for temperatures between 600°C and 700°C, in agreement with experimental curves.

Abstract: The cyclic behaviour of the steel EUROFER 97 during isothermal plastic strain-controlled tests was investigated at room temperature and at 550°C. Under these test conditions, the steel shows, after the first few cycles, a cyclic softening following a power-law function that continues up to failure. The rate of softening increases with temperature, being very pronounced at temperatures above 500°C. The evolution of the flow stress during cycling was studied by analyzing the so-called “back” and “friction” stresses obtained from the hysteresis loops measured along the entire test. From the analysis of the hysteresis loops and corroborated by electron microscopy observations, it can be concluded that the strong cyclic softening observed on these samples with a "tempered martensite" structure is produced by the softening exhibited by both stresses. However, the importance of each of these stresses on the softening depends on the applied strain amplitude and temperature. It was observed that, at low temperatures and applied strains, the friction stress shows the strongest influence on the cyclic softening. On the contrary, at higher temperatures and applied strains the back stress reveals the most important changes occurring in the interior of the material.

Abstract: Cyclic slip irreversibility is one of the most important features of fatigue processes in ductile metals because it induces surface relief evolutions during cycling which are mainly responsible for crack initiation. The reversible and irreversible parts of the slip within persistent slip bands (PSBs) in polycrystalline nickel are measured directly after half-cycle deformation and one full cycle on specimen surfaces once more well-polished after 60% of fatigue life using atomic force microscopy (AFM) and different techniques of scanning electron microscopy as electron channelling contrast imaging and electron backscattered diffraction. Using AFM measures on the same slip steps after half-cycle and full cycle, the cyclic slip irreversibility factor is directly evaluated and discussed with respect to the literature.

Abstract: Slip localization is often observed in metallic polycrystals after cyclic deformation (persistent slip bands) or pre-irradiation followed by tensile deformation (channels). To evaluate its influence on surface relief formation and grain boundary microcrack nucleation, crystalline finite element (FE) computations are carried out using microstructure inputs (slip band aspect ratio/spacing). Slip bands (low critical resolved shear stress (CRSS)) are embedded in small elastic aggregates. Slip band aspect ratio and neighboring grain orientations influence strongly the surface slips. But only a weak effect of slip band CRSS, spacing and grain boundary orientation is observed. Analytical formulae are deduced which allow an easy prediction of the surface and bulk slips. The computed slips are in agreement with experimental measures (AFM/TEM measures on pre-irradiated austenitic stainless steels and nickel, copper and precipitate-strengthened alloy subjected to cyclic loading). Grain boundary normal stresses are computed for various materials and loading conditions. A square root dependence with respect to the distance to the slip band corner is found similarly to the pile-up stress field. But the equivalent stress intensity factor is considerably lower. Analytical formulae are proposed for predicting the grain boundary normal stress field depending on the microstructure lengths. Finally, an energy balance criterion is applied using the equivalent elastic energy release rate and the surface/grain boundary energies. The predicted macroscopic stresses for microcrack nucleation are compared to the experimental ones.

Abstract: This numerical study focuses on the recent observations of Man et al. [4] showing welloriented grains presenting no Persistent Slip Marking even if PSMs are observed in 86% of the surface grains in 316L austenitic stainless steel cycled at room temperature up to 60% of fatigue life. Scanning Electron Microscopy (SEM) permits us to build Finite Element (FE) meshes of the observed aggregates and to assign to the modelled grains the crystallographic orientations measured by Electron Back Scattering Diffraction (EBSD). Then, 3D FE computations using crystalline elasticity allow the evaluation of mean grain stress tensors and resolved shear stresses. The results could explain qualitatively the anomalous behaviour of the studied well-oriented grains which is partly due to the particular orientations and shapes of the neighbour grains. This study highlights the influence of crystalline elasticity and neighbour grains in microplasticity and crack nucleation.

Abstract: In the work presented here an elastic-plastic crystalline finite element method is used to simulate the cyclic behavior of 316L austenitic stainless steel single crystals and polycrystal. The evolution of the back stress on each slip system is described using a non linear kinematics hardening law to account for the hardening induced by long range dislocation interactions. As the contribution of short range interactions is assumed to be negligible, the value of the friction stress is kept constant. Three dimensional finite element calculations are performed to simulate the cyclic stress strain curves in the case of a single crystal oriented for multiple slips, as well as for the case of the polycristal. Simulations are compared to experimental data. They seem to be satisfactory for low strain values (
εp\2 <10-3) whereas, for
εp\2 >10-3, they underestimate the hardening observed experimentally.

Abstract: Under fatigue loading, the number of cycles to failure and its associated scatter increase when the loading level decreases. The High-Cycle Fatigue (HCF) regime is thus characterized by a large scatter in the number of cycles to failure [1]. Cracks initiation represents an important part of the lifetime of the structures. A stochastic method is used to study the fatigue crack initiation prediction in the 316L austenitic stainless steel. The present work proposes to show that this scatter can be attributed to the random orientation of individual grains, which influences the crack initiation localization. The stresses in grains are determined by finite element computations (FEM [2]), using a configuration representative of a polycrystalline aggregate. This approach takes into account the crystallographic orientations of the grains in the aggregate as well as the deformation incompatibilities between neighbouring grains due to crystalline anisotropic elasticity and elasticplasticity [3]. Then, the scatter of the number of cycles to crack initiation is derived from the FEM stress fields using two fatigue crack initiation criteria: an usual one, Mura’s criterion [4] and a more recent one [5], based on Discrete Dislocation Dynamics (DDD) simulations and taking into account plastic slips, cross slip and stress tensor components.