Papers by Author: Frank Montheillet

Abstract: A simple mesoscale model was developed for discontinuous dynamic recrystallization. The material is described on a grain scale as a set of (variable) spherical grains. Each grain is characterized by two internal variables: its diameter and dislocation density (assumed homogeneous within the grain). Each grain is then considered in turn as an inclusion, embedded in a homogeneous equivalent matrix, the properties of which are obtained by averaging over all the grains. The model includes: (i) a grain boundary migration equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a dislocation-density evolution equation, such as the Yoshie–Laasraoui–Jonas or Kocks–Mecking relationship, involving strain hardening and dynamic recovery, and (iii) an equation governing the total number of grains in the system due to the nucleation of new grains. The model can be used to predict transient and steady-state flow stresses, recrystallized fractions, and grain-size distributions. The effect of the distribution of grain-boundary mobilities has been investigated.

Abstract: Due to the high rate of dynamic recovery associated with the large stacking fault energy of the bcc structure, classical "discontinuous" dynamic recrystallization, occurring by nucleation and growth of new grains is not observed in the β phase of titanium alloys. Instead, the following mechanisms take place: at low and moderate strains (ε < 1), the original flattened (compression) or sheared (torsion) grains are still recognizable, although their boundaries are strongly serrated. In this strain range, grain size (thickness) results from both the convection and the migration of grain boundaries. At intermediate strains, "geometric" dynamic recrystallization leading to "pinching off" events of the original grains is observed, whereas at larger strains (ε > 5), grain fragmentation occurs by the generation of new grain boundaries ("continuous" dynamic recrystallization). The associated flow stress often exhibits pronounced softening and the resulting (equiaxed) grain size can be much smaller than the initial one. It is worth to note that a very similar sequence of mechanisms takes place in ferritic steels, as well as in aluminium alloys, in spite of their different crystallographic structure. In this paper, the above mechanisms will be illustrated by a set of data pertaining to titanium alloys.

Abstract: The effect of the metallurgical state of austenite (undeformed vs. deformed vs. deformed + recrystallised) on the properties of the austenite to bainite transformation were investigated thanks to thermal (Gleeble simulations) and thermomechanical (hot torsion) treatments. No obvious influence of the state of austenite was found, using electron backscatter diffraction, on the resulting microtexture. Advantages and drawbacks of using misorientation angle histograms vs. axis-angle pair distribution are discussed regarding investigations of local variant selection. For an austenite grain size higher than about 50 µm, a strong effect of the transformation temperature was evidenced, bainite formed at lower temperature (530°C) exhibiting a microtexture close to that of lath martensite in the same steel.

Abstract: This experimental work deals with the influence of niobium additions to high purity nickel on dynamic recrystallization behavior during hot working. Various high-purity alloys were prepared (unalloyed Ni and Ni–0.01, 0.1, 1 and 10 wt % Nb) and deformed to high strains by hot torsion tests to characterize the rheological behavior within the range 800 – 1000°C at strain rates of 0.03, 0.1 and 0.3 s–1. Niobium additions strongly increased the flow stress. To quantify such behavior, the strain-hardening parameter h and dynamic-recovery parameter r in the Yoshie-Laasraoui-Jonas constitutive equation were determined from the initial part of the experimental stress-strain curves (i.e., at strains before the stress peak) in which dynamic recrystallization does not alter the mechanical behavior. A table showing the variation of h and r as a function of strain rate, temperature, and niobium content was compiled and used to fit a simple empirical model for predicting h and r from the deformation conditions and alloy composition. In addition, microstructures were determined by optical metallography and SEM/EBSD. Based on this work, it appears that niobium additions noticeably refine the steady-state grain size by considerably decreasing the kinetics of dynamic recrystallization in nickel.

Abstract: A simple mesoscale model was developed for discontinuous dynamic recrystallization. The material is described on a grain scale as a set of (variable) spherical grains. Each grain is characterized by two internal variables: its diameter and dislocation density (assumed homogeneous within the grain). Each grain is then considered in turn as an inclusion, embedded in a homogeneous equivalent matrix, the properties of which are obtained by averaging over all the grains. The model includes: (i) a grain boundary migration equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a dislocation-density evolution equation, such as the Yoshie–Laasraoui–Jonas or Kocks–Mecking relationship, involving strain hardening and dynamic recovery, and (iii) an equation governing the total number of grains in the system due to the nucleation of new grains. The model can be used to predict transient and steady-state flow stresses, recrystallized fractions, and grain-size distributions. A method to fit the model coefficients is also described. The application of the model to pure Ni is presented.

Abstract: A simple analytical model is proposed for estimating grain boundary mobility during dynamic recrystallization in metallic alloys. The combined effects of solutes (solute drag) and second phase particles (Zener pinning) on mobility are considered. The approach is based on (and is consistent with) a recently published mesoscale model of discontinuous dynamic recrystallization. The dependence of grain boundary mobility on solute concentration and particle size is summarized in the form of two-dimensional maps.

Abstract: The thermo-mechanical simulation of Friction Stir Welding focuses the interest of the welding scientific and technical community. However, literature reporting material flow modeling is rather poor. The present work is based on the model developed by Heurtier [2004] and aims at improving this thermo-fluid simulation developed by means of fluid mechanics numerical and analytical velocity fields combined together. These various velocity fields are investigated separately and especially according to the power dissipated during the flow. Boundary conditions are considered through a new approach based on the kinematic analysis of the thread of the pin. An equilibrium is established between the vertical motion of the bulk material dragged in the depth of the metal sheet, and its partial circulation around the pin. The analyses of the obtained velocity fields enable the understanding of the welded zone asymmetry and highlights the bulk material mixing between the welded coupons in the depth of the sheet. A regression is performed on the relative sliding velocity of the aluminium according to the surface of the tool: shoulder and pin. Two dimension flow lines in the depth of the metal sheet are then obtained and successfully compared with the results obtained by Colegrove (2004) [1].

Abstract: The aim of this work is to study the flow instabilities occurring during hot forging of titanium alloy blades. In this view, the viscoplastic deformation behaviour of Ti-6Al-4V alloy is investigated by means of torsion tests under isothermal hot working conditions at temperatures ranging from 800 to 1020 °C and strain rates of 0.01, 0.1 and 1s−1. The thermomechanical processing is performed up to a true strain of 10. The flow stress data are analysed in terms of strain rate and temperature sensitivities. A constitutive equation that relates not only the dependence of the flow stress on strain, strain rate and temperature, but also for the fraction of each phase α and β is proposed. Two mechanical models are compared : the uniform strain rate model (Taylor) and the uniform plastic energy model (IsoW). The usual strain rate sensitivity and activation energy values of Ti-6Al-4V alloy are obtained by fitting the experimental data. Furthermore, specific values of strain rate sensitivities and activation energies are calculated for the α and β phases providing thus a constitutive law based on the physics of the α / β phase diagram. The flow stress is then related to strain by an empirical equation taking into account the flow softening observed after a true strain of 0.5 and the steady state flow reached after a true strain of 4. Comparison of the calculated and measured flow stresses shows that the constitutive equation predicts the experimental results with a reasonable accuracy. The above constitutive equation is then used for simulating forging processes by the finite element method. The calculations exhibit the localisation of deformation produced by shearing effects in the form of the classical X shape.

Abstract: The present work deals with the influence of niobium in solid solution on the dynamic recrystallization of pure nickel. High-purity nickel and two model nickel-niobium alloys were deformed to large strains via torsion at temperatures between 800 and 1000°C. Niobium additions considerably increased the flow stress, while they lowered the strain-rate sensitivity and increased the apparent activation energy. EBSD of the steady-state microstructures revealed strong grain refinement. Substructure development was favored, whereas thermal twinning was reduced by niobium. More generally, discontinuous recrystallization kinetics were considerably decreased.

Abstract: Thermomechanical processing involving severe plastic deformation (SPD) is a popular approach to ultrafine grain formation in bulk samples. In the present study, two grades of highpurity α-iron were deformed within the ferritic domain in cold and warm torsion to large strains (>> 1). Examination of the deformed samples using orientation imaging microscopy revealed a highly fragmented, lamellar structure aligned almost parallel to the direction of shear. Between 37 and 54 % of boundaries detected are high angle ones (HAB). Some of these HAB are associated with the original grain boundaries. However, a good number are believed to originate from dislocation accumulation processes, during which the misorientation angle across certain strain-induced low angle boundaries (LAB) rises with increasing strain. The resultant microstructure is composed of ultrafine crystallites on the order of 1 – 2 1m. In fact, localised regions of equiaxed grains on the micron scale were observed within samples deformed between room temperature and 300 °C. Nonetheless, other areas remain relatively unfragmented despite persistent straining until failure. At higher temperatures, the microstructure is more homogeneous, but the average grain size is coarsened. Optimal grain refinement thus appears to be a compromise between several competing factors: large strains at relatively low temperatures for high dislocation density, higher temperatures to enable sufficient dynamic recovery, and low grain boundary mobility that is aided by low temperatures and/or pinning by solute atoms or second phase particles. Furthermore, the development of a torsion texture composed of a single ideal orientation at large strains is unfavourable towards the generation of HAB.