David Gloaguen

Evolution of internal stresses in rolled Zr702α

Internal stresses due to anisotropic thermal and plastic properties were investigated in a rolled Zirconium-α. The thermal stresses induced by a cooling process were predicted using a self-consistent model and compared with experimental results obtained by X-ray diffraction. The study of the elastoplastic response during uniaxial loading was performed along the rolling and the transverse direction of the sheet, considering the influence of the texture and the thermal stresses on the mechanical behaviour. We used an elastoplastic self-consistent formulation and the predicted results are compared with mechanical tests. The role of twinning and slip on the development of internal stresses is also discussed.

Determination of single-crystal elasticity constants in a cubic phase within a multiphase alloy: X-ray diffraction measurements and inverse-scale transition modelling

The scope of this work is the determination of single-crystal elastic properties from X-ray diffraction stress analysis performed on multiphase polycrystals. An explicit three-scale multiphase inverse self-consistent model is developed in order to express the single-crystal elasticity constants of a cubic phase as a function of its X-ray elasticity constants. The model is verified in the case of single-phase materials. Finally, it is applied to a two-phase (α+β) titanium-based alloy (Ti-17) and, as a result, the Ti-17 β-phase single-crystal elasticity tensor is estimated.

Mesoscopic residual stresses of plastic origin in zirconium: interpretation of X-ray diffraction results

Complementary methods have been used to analyse residual stresses in a heat-treated Zr702 sheet which had undergone uniaxial plastic deformation: X-ray diffraction and self-consistent models. The elastoplastic self-consistent model has been used to simulate the experiments and exhibits agreement with experimental data. X-ray diffraction analysis in the rolling direction shows opposite stress values for {[10bar{1}4]} and {[20bar{2}2]} planes, respectively. The measured strains were generated by an anisotropic plastic deformation. The comparison between ∊ϕψ versus sin2ψ and simulations confirms that prismatic slip is the main active deformation mode. Plastic incompatibility stress in X-ray measurements should be taken into account in order to make a correct interpretation of the experimental data.

Intergranular Strain Evolution in Titanium During Tensile Loading: Neutron Diffraction and Polycrystalline Model

Intergranular strains due to tensile plastic deformation were investigated in a commercially pure Ti. Neutron diffraction has been used to characterize the evolution of residual elastic strain in grains with different crystallographic orientations. Experimental data have been obtained for the macroscopic stress–strain curve and the intergranular strain evolution in the longitudinal and transverse direction relative to the uniaxial loading axis. The elasto-plastic self-consistent (EPSC) approach was used to model the deformation behavior of the studied material. Comparison between the neutron measurements and the model predictions shows that in most cases the EPSC approach can predict the lattice strain evolution and capture the plastic anisotropy observed in the experiments.

Interpretation of X‐Ray Stress Measurement and Evaluation of Internal Residual Stresses in Rolled α‐Ti40 Using Self‐Consistent Models

Internal stresses due to anisotropic thermal and plastic properties were investigated in rolled α-titanium. The thermal stresses induced by a cooling process were predicted using a self-consistent model and compared with experimental results obtained by X-ray diffraction. A study of the elastoplastic response after uniaxial loading was performed along the rolling and the transverse direction of the sheet. Using an elastoplastic self-consistent model, the predicted results were compared with X-ray diffraction and mechanical tests. Theoretical and experimental results agree in their tendencies. The comparison between e Φψ versus sin 2 ψ and simulations confirms that prismatic slip is the main active deformation mode.

Determination of the Macroscopic Elastic Constants of a Phase Embedded in a Multiphase Polycrystal-Application to the β-Phase of a Ti-17 Titanium Based Alloy

A one-site elastic self-consistent model following the mathematical formalism introduced by Kroner and Eshelby (KE) has been developed in order to solve the case of multiphase materials. This model has been applied to duplex steels and aluminium - silicium carbide Metal Matrix Composites (MMC) in the aim to study the evolution of their stiffness at pseudomacroscopic scale. Simulations justify the usually implicit hypothesis of the identity of the elastic moduli of a given phase, at macroscopic and pseudomacroscopic scales. The implementation of KE model by this hypothesis yields a new implicit formulation for the stiffness of a given unknown phase embedded in a two-phases material. This original characterization method will be applied to the β-phase of Ti-17 alloy. The singular behaviour in terms of residual pseudomacrostress of each phase after uniaxial loadings will be deduced from these data.

External Reference Samples for Residual Stress Analysis by X-Ray Diffraction

The GFAC (French Association for residual stress analysis) decided in 2007 to work on external reference samples for residual stress analysis by X-ray diffraction as defined in the XPA 09-285 and EN 15305-2009 standards. Seven materials are studied: ferritic steel, martensitic steel, aluminium alloy, titanium alloy, 2 types of Nickel-Chromium alloy and tungsten thin layers deposited on silicon wafers. The purpose of this external round robin campaign is threefold: (i) to give possibilities for each laboratory involved in the campaign test to obtain external reference samples for each material tested, (ii) to validate a common procedure for qualification of external samples and (iii) to commercialise validated external reference samples through the GFAC association. A common approach of X-Ray diffraction parameters, samples geometry and standard procedure has been chosen and adopted by each laboratory involved in these tests. No indication in terms of residual stress calculation method is given; the choice of the method (centroid, middle point, maximum of peak, fitting…) is the choice of the laboratory according to their X-ray diffraction set-ups, softwares and experience. Once all samples are analysed, values given by each laboratory are compared and analysed.

Influence of morphologic texture on stress analysis by X-ray and neutron diffraction in single-phase metallic materials

In this work, a study on the influence of morphologic texture on the residual stress determination by diffraction in metallic materials with cubic and hexagonal symmetry is proposed. To this end, elastic self-consistent model has been developed to properly take into account the morphologic texture. Extreme crystallites morphologies (sphere, disc and fibre) were studied, and coupled with the crystallographic texture to reflect the combined effect of morphologic and crystallographic texture in elasticity. In the case of morphologic texture, a stronger influence than the crystallographic texture on the estimated residual stresses (several tens of MPa difference) was observed. We propose a methodology through a scale transition model to take into account the influence of these different morphologies in the stress analysis by diffraction methods. The main purpose of this work was to make the best choice for lattice planes (hkl) used for residual or internal stress analysis, in elasticity, depending on the morphologic (and crystallographic) texture of the polycrystal, especially when the usual X-ray Elasticity Constants (XECs) are used instead of the stress factors.

X-ray measurement of residual stresses and texture development during a rolling sequence of zirconium alloy cladding tubes – influence of plastic anisotropy on mechanical behaviour

Texture and residual stress analysis using X-ray diffraction have been carried out on zirconium alloy cladding tubes after cold pilgering, an industrial mechanical process. The final rolling pass has been completely characterized by X-ray diffraction. An interpretation of the effect of intergranular stresses on the development of analysed stress has been made using a modified elastoplastic self-consistent model in order to account for the effect of the high intrinsic plastic anisotropy of hexagonal close-packed crystals. The contribution and magnitude of the first- and second-order residual stresses were correctly evaluated using information from the model. The main features of the rolling sequence were qualitatively reproduced by the simulations, considering prismatic slip as the main active deformation mode in this alloy under large strain.

Study of the Coefficients of Thermal Expansion of Phases Embedded in Multiphase Materials

The present paper describes a new approach developed in order to determine the nCoefficients of Thermal Expansion (CTE) of phases embedded in two-phase materials. The nprocedure is based on the coupling of numerical simulations with scale transition models and nexperiments. A three scales one-site thermo-elastic self-consistent model following the formalism nintroduced by Kroner and Eshelby (KE) was extended to multiphase materials. Preliminary nnumerical computations justify to identify the CTE of a given phase embedded in a two-phase nmaterial with the CTE of the corresponding pure single-phase. This additional assumption was nintroduced in KE model. The implementation yields an explicit formulation for the unknown CTE nof a phase embedded in a (a+f3) two-phases material. The application of this expression to the ncharacterization of f3 thermal expansion properties implies the measurement or knowledge of nseveral parameters. This approach was checked through the study of an Al-50%vol.-SiC-50%vol. nMMC. The CTE of Silicon Carbide were determined as a function of the temperature. Simulated nresults obtained show a very good agreement with experimental values available in the literature.