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International audience; A simple three-dimensional thermomechanical model for friction stir welding (FSW) is presented. It is developed from the model proposed by Heurtier et al. (2006) based on a combination of fluid mechanics numerical and analytical velocity fields. Those velocity fields are introduced in a steady state thermal calculation to compute the temperature field during welding. They allow partial sliding between the shoulder and the workpiece, the amount of which is provided as an additional result of the model. The thermal calculation accounts for conduction and convection effects by means of the particular derivative. The complete thermomechanical history of the material during the process can then be accessed by temperature and strain rate contours. The numerical results are compared with a set of experimental test cases carried out on an instrumented laboratory device. The choices for modeling assumptions, especially tribological aspects, are discussed according to agreements or deviations observed between experimental and numerical results. The amount of sliding appears to be significantly influenced by the welding conditions (welding and tool rotational velocities), and physical interpretations are proposed for its evolution.

Commercial 304 austenitic stainless steel was deformed in compression at high temperatures (800 to 1 280°C) and at strain rates from 0.001 to 1 s - 1 . The critical and peak strains associated with dynamic recrystallization were determined based on changes in the work hardening rate as a function of the flow stress. The effect of the deformation variables (T, e) on these values is analyzed; it is shown that over a range of temperature corrected strain rate (Z=10 1 4 to 10 1 6 s - 1 , Q d e f =405 kJ/mol), the initiation of dynamic recrystallization is delayed. This retardation is attributed to the segregation of substitutional impurity elements, principally phosphorus, to the sub-boundaries of the newly-forming DRX grains.

Microstructural changes during high-temperature extrusion and torsion of an AZ91 alloy (Mg–9Al–1Zn, wt.%) were investigated. In the experimental domain studied, dynamic recrystallisation (DRX) occurs and the effect of temperature and strain rate on the resulting recrystallised grain size was investigated. Complete recrystallisation in torsion is associated with the development of a stress plateau after softening from the peak stress, which is systematically observed in the first steps of straining. The resulting grain size can be related to the value of the peak stress. It appears that the precipitation of the Mg 17 Al 12 phase does not affect significantly the torsion behaviour of the alloy in the experimental domain investigated here. This study supports the idea that very fine-scale microstructures (i.e. with a mean grain size smaller than 5 μm) can be easily produced by DRX during high-temperature extrusion of the AZ91 alloy.

Compression tests were carried out on two compositions of Cu–Sn bronze: Cu–9·2Sn and Cu–9·1Sn–0·26Zn (wt-%). The experiments were performed at temperatures from ambient up to 750°C and at nominal (initial) strain rates in the range 10-3 to 10-1 s-1. The measured data were converted into true stress–true strain curves; these displayed yield drops as well as single peaks (or maxima) at higher temperatures and lower strain rates. The mean rate sensitivity applicable to the curves was 0·25. Optical metallography indicated that dynamic recrystallisation of the ‘grain refinement’ type was taking place at the higher temperatures and proceeded by necklace formation. Electron backscattered diffraction measurements were also carried out; these revealed that twinning plays an important role in these materials. The present results show that the progress of recrystallisation is considerably slower than in OFHC copper and that the recrystallised grain size is appreciably finer. These observations, taken togethe...

International audience; Iron-aluminium alloys display promising physical and mechanical properties. In this study, the effects of strain, strain rate and temperature on an Fe-8% Al were investigated. Hot torsion tests were performed in the temperature range 900-1100 degrees C and strain rate range 0.1-10 s(-1). In this alloy, two types of dynamic recrystallization may operate during hot deformation: at high temperature and high strain rate, this alloy undergoes discontinuous dynamic recrystallization, whereas at lower temperature and strain rate, continuous dynamic recrystallization occurs.

The theory of the invariant representation for tensor functions in first illustrated by providing a general form of the Hill (1948) orthotropic yield criterion. It is then applied to derive a quadratic yield equation for the case of prismatic monoclinic symmetry, which is induced by simple shear deformation. This new criterion can in turn be approximated by an orthotropic one by choosing the ‘best’ symmetry axes. The above equations are then used to derive the angular dependences of the uniaxial yield stress and strain rate ratio in the plane of a prismatic monoclinic sheet. Finally, it is shown on an example that they are able to predict the axial stresses occurring during torsion testing with a fairly good accuracy.

Two complementary analytical approaches and the finite difference method are proposed for modeling asymmetric rolling (ASR) of metal sheet. The first analytical model is an upper bound method based on a uniform strain field depending on one single optimization parameter, viz. the entry velocity of the sheet. Its results can be straightforwardly used for practical applications. The second model uses a more refined analytical velocity field based on the classical parabolic estimation of the material flow lines in rolling. It involves an additional optimization parameter associated with the precise form of the velocity field. Local values of strain, strain rate and self‐heating temperature are easily calculated, as well as the rolling force. Finally, the finite difference method is applied to compute heat transfers between the rolls and the sheet. In conclusion, the respective advantages of the three methods are discussed.

As far as only volume changes are considered, the analysis of void growth during plastic straining of a material can be reduced to the two simple cases of (i) a cylindrical cavity submitted to axial and axisymmetric radial remote loads and (ii) a spherical cavity submitted to remote uniform mean stress. The latter are investigated for materials exhibiting either a power law or a linear stress-strain rate relationship. The influence of strain hardening is also considered in the case of spherical geometry. Finally, inertia effects are investigated. It is shown that both the linear strain rate dependence and inertia effects are likely to decrease void growth rate and thus to improve ductility at high strain rate.

Publication suite à la confèrence : 8th Int. Conf. on Mechanical and Physical Behaviour of Materials Under Dynamic Loading (Dijon 2006); International audience; A new experimental torsion test is developed to achieve intermediate strain rates. The gauge length of the classical torsion bar (27 mm) is reduced within the range 0 to 5 mm. Analytical predictions with simple constitutive equation show that strain rates achieve the magnitude of 250 s - 1. A finite difference analysis is proposed to simulate the test with more evolved constitutive equations. A comparison between experimental and numerical results shows a good agreement.

International audience; The "Iso-W" approach recently proposed to generate simple flow rules for two phase materials is extended to nonlinear viscoplastic constituents and generalized, which produces three families of models. Comparison with the Hashin-Shtrikman bounds leads to select the variant assuming strain rate compatibility and stress equilibrium. The Iso-W assumption is in fairly well agreement with the Mori-Tanaka and self-consistent models for mixtures of both linear and nonlinear materials.

International audience; The dieless wire drawing process is analyzed in detail by using a simple slice method. A thermomechanical analysis first shows that the stability of the process depends on the slope of the curve giving the load applied to the wire as a function of the area reduction. It turns out that material parameters have a relatively large influence on the process, whereas the two process parameters having the main influence are the maximum strain rate reached at the end of the heating zone, and the maximum temperature of the wire. The former has to be limited to ensure stability, whereas the latter must remain within a very small range (typically 1 degrees C). When these two conditions are fulfilled, relatively large and constant area reductions can be achieved by the dieless wire drawing process.

The influence of carbon in solid solution on the stress-strain curves of ?-iron was investigated using model alloys prepared from high purity iron. Uniaxial compression tests were carried out within the ferritic domain at temperatures between 700 and 880 ?C. Oscillating stress-strain curves observed at high temperatures and low strain rates indicate that discontinuous dynamic recrystallization takes place. The macroscopic strain rate sensitivities m and apparent activation energies Q associated with the flow stress are not significantly modified by carbon additions. By contrast, the mesoscopic parameters h and r associated with strain hardening and dynamic recovery, respectively, are strongly dependent on the carbon content. Finally, an estimation of the grain boundary mobilities during dynamic recrystallization was carried out from the above rheological data.

Polycrystal yield surfaces were calculated by the Bishop and Hill method for a series of idealized cube textures. The textures were specified in terms of a rotationally symmetric gaussian distribution of misorientations with scatter widths increasing from 0° (single crystal) to 45°. The corresponding polycrystal yield surfaces were determined for a sample containing up to 400 such grains; the yield surfaces are described in terms of equilibrated stress and strain rate components expressed in a five-dimensional orthonormal reference frame. The effect of increasing the scatter width on the π plane and shear stress cross-sections is illustrated. The yield stress and strain rate ratios were also calculated for these samples and the dependence on scatter width is presented.

The specific problems involved by high strain rate tension tests are first examined, as well as the various parameters describing ductility. Some experimental data relative to a high purity copper then illustrate the typical increase of dynamic ductility with strain rate. Finally, the main factors which are expected to determine ductility are reviewed. It is concluded that the dominant factor is the increase of stability with strain rate, which in turn may result from the occurrence of a linear flow rule and/or from inertia effects.

Analytical yield surfaces have been fitted and compared to the crystallographic yield surfaces pertaining to a series of idealized cube textures. The textures were specified in terms of a rotationally symmetric gaussian distribution of misorientations with scatter widths increasing from 0° (single crystal) to 45°. The analytical yield surfaces are based on a series of quadratic and non-quadratic yield functions. Both π -plane and shear stress cross-sections were prepared, together with plots of the yield stress and strain rate ratios. Comparison with the corresponding crystallographic plots (presented in Part I) indicates that, whereas a quadratic ( n = 2) representation is generally acceptable, a better fit is obtained with an exponent n = 1.7. The cross-sections pertaining to the latter yield surface are also in better agreement with experimentally determined yield loci taken from the literature. Finally, the n = 1.7 criterion is employed to predict the strain rate ratios ( R -values) expected in metals containing common texture components; these estimates are seen to be in good qualitative, and frequently quantitative, agreement with experimental observations.

Etude dans le domaine de vitesse de deformation de 10 −4 a 2×10 3 s −1 . On montre que la ductilite est essentiellement determinee par la stabilite de l'elongation, qui elle-meme resulte des valeurs des coefficients d'ecrouissage et de sensibilite a la vitesse

Impact tension tests were carried out on two grades of high purity copper at room temperature and in the strain rate range 1000–3500 8-1. At a constant true strain ɛ, a linear stress-strain rate relationship σ = σo + βɛ is exhibited. σo depends on ɛ according to the same power law for the two coppers; β is a decreasing function of ɛ and is smaller for the CuC1 grade. The data are interpreted on the basis of a model involving a transition regime between the thermally activated and the viscous glide controlled domains. Microstructural investigations are presented to discuss the results. It is concluded that only fine details of the microstructure can differ between the quasistatic and the dynamic strain rate range.

In a series of torsion tests, we have analysed the behaviour of commercial purity. aluminium_(99.5 % Al) during a strain rate change. The strain rate range 5 x 10 -3 s -1 to 0.15 s -1 for temperatures between 0.7 and 0.8 T f (400°C, 450°C and 500°C) has been explored. It is often assumed that p m , density of mobile dislocations, remains constant during a rate change. This assumption is in conflict with our observations and it is concluded that p m must decrease during the increase of the strain rate. It is nevertheless possible to obtain activation areas determined at constant structure, using the extrapolation of the parameter . The activation areas measured at the maximum of the flow curves are between 400 and 900 b 2 . They vary linearly with 1/σ but are strongly temperature dependent.

The strain rates and stresses developed within and around an elliptical (resp. spheroidal) inclusion embedded in a viscous matrix are determined for a prescribed plane (resp. axially symmetric) strain at infinity. An exact solution is derived for a linearly viscous matrix, providing analytical expressions for the strain rates and stresses within the whole material. In the more general case of a power-law viscous matrix, a variational approach based on the above velocity field is proposed. The inclusion strain rate ratios obtained in this way are compared with finite element results and experimental data from the literature. Finally, the induced stress concentrations at the inclusion-matrix interface are described in detail and discussed in connection with the problem of damage initiation.