Frank Montheillet

An experimental study of the recrystallization mechanism during hot deformation of aluminium

Abstract Discontinuous dynamic recrystallization (involving nucleation and grain growth) is rarely observed in metals with high stacking fault energies, such as aluminium. In this metal, two other types of recrystallization have been observed: continuous dynamic recrystallization (CDRX, i.e. the transformation of subgrains into grains); and geometric dynamic recrystallization (due to the evolution of the initial grains). The main purpose of this work was to bring clearly into evidence and to better characterize CDRX. Uniaxial compression tests were carried out at 0.7 T m and 10 −2 s −1 on three types of polycrystalline aluminium: a pure aluminium (1199), a commercial purity aluminium (1200) and an Al-2.5wt.%Mg alloy (5052), and also on single crystals of pure aluminium. In addition, 1200 aluminium specimens were strained in torsion. The deformed microstructures were investigated at various strains using X-ray diffraction, optical microscopy, scanning electron microscopy and electron back-scattered diffraction. Observations of the single crystalline samples confirm that subgrain boundaries can effectively transform into grain boundaries, especially when the initial orientation is unstable. In the case of polycrystalline specimens, after separating the effects of the initial and new grain boundaries, it turns out that CDRX operates faster in the 1200 aluminium compared to the two other grades. Moreover, it appears that the strain path does not alter noticeably the CDRX kinetics.

A mechanical analysis of the plane strain channel-die compression test: friction effects in hot metal testing

An analytical model is first proposed for the determination of a friction-corrected flow stress in channel-die compression. A variational approach is then used for estimating the strain and strain-rate heterogeneities as well as the shape changes during deformation for two specimen geometries. The results are compared with finite element calculations. Results obtained from the two methods are in good agreement, except for the outer profiles of the deformed specimens. Finally, the various components of the powers involved in the deformation process are compared.

Plane strain compression of silicon-iron single crystals

Abstract Six different orientations of Fe-3 wt% Si single crystals have been deformed in plane strain compression (using a channel die) up to true strains of 0.5. The finite strain behaviours, i.e. the shape changes, lattice rotations and stress-strain curves, are compared with the predictions of the generalized Taylor analysis of partially constrained crystal deformation. The influence of the relative critical resolved shear stresses on the {110} and {112} 〈111〉 glide systems has been systematically examined. It is shown that for most crystals under multiple slip conditions the shape changes and lattice rotations are consistent with the hypothesis of glide on {112} being somewhat easier than on {110}. Comparison with previous work on b.c.c. crystals undergoing large strains leads to the suggestion that: (i) under conditions of single or colinear slip, glide on {110} is easier than on {112}; (ii) under conditions of intersecting 〈111〉 slip directions, glide on {112} is easier than on {110}. For silicon-iron, the critical resolved shear stresses on the {112} 〈111〉 systems, relative to those on the {110}〈111〉 systems are found to be 0.93 and 0.96 for the twinning and anti-twinning senses, respectively.

Yield surfaces of b.c.c. crystals for slip on the {110} 〈111〉 and {112} 〈111〉 systems

Abstract The single crystal yield surfaces (SCYS) for slip in b.c.c. metals on either {112} 〈111〉 or mixed slip on {112} 〈111〉 and {110} 〈111〉 have been derived. In particular, for the general case of mixed slip, the SCYS is described in terms of ξ, the ratio of the critical resolved shear stresses for slip on the {112} 〈111〉 and {110} 〈111〉 systems. All the possible types of yield vertices are tabulated and classified into crystallographically non-equivalent groups. It is confirmed that there is a limited range of ξ for mixed slip: √ 3 2 ⩽ξ⩽ 2 √3 . Within this range, there are only two different SCYS configurations, depending on whether ξ is greater or smaller than 5 3 √3 . Each of these configurations has 15 groups of vertices and 216 stress states (plus their negatives). The two yield surfaces only differ with respect to 3 of the groups of vertices (72 stress states). The evolution of these vertices near the critical ξ value of 5 3 √3 is described in detail. The mixed slip vertices activate 5, 6 or 8 slip systems depending on the basic group to which they belong. In the vast majority of cases, only 5 slip systems are activated so that, by allowing mixed {110}, {112} glide, the slip ambiguity problem characteristic of {110} 〈111〉 restricted glide is substantially reduced.

Recrystallization and grain growth in high purity austenitic stainless steels

Optimization of structural materials such as austenitic stainless steels, especially through the control of microstructure changes during hot processing, is an obvious industrial concern. Following primary recrystallization during annealing, the increase of the mean grain size affects mechanical properties such as yield strength, deep drawability, and also intergranular corrosion resistance. Despite the importance of this phenomenon, only very few investigations of the grain growth kinetics in austenitic stainless steels have been carried out to date. The aim of this work is to describe grain growth in high purity 18wt% Cr--12wt% Ni steels as compared with other 304 grade alloys.

The Refinement of Grain Structure in a High-Purity α-Iron Base Alloy under Multiaxial Compression

Multiaxial compression (MAC) is a severe plastic deformation (SPD) method that allows sequential uniaxial compression of prismatic samples to relatively large cumulative strains. The technique involves a change in loading direction (x to y to z to x…) between successive compression passes. A high-purity α-iron containing 60 mass ppm C was thus strained using passes of ε ∼ 0.4 at room temperature (0.16 Tm) and 450 °C (0.40 Tm) to total ε ranging from 1.4 to 2.9. Both optical and electron microscopy were used to characterise the deformed microstructures. Fragmentation of the initial grain structure occurs mainly in the form of a dense, homogeneous network of low angle boundaries (LAB) delimiting subgrains of about 1 3m. The original grains are easily distinguishable and maintain a relatively equiaxed appearance even at larger strains. At room temperature, high angle boundaries (HAB) are observed within some of the initial grains, and not necessarily close to the grain boundaries. These HAB may be open or closed, and tend to align themselves at approximately 45° to the orthogonal axes, suggesting the presence of microshear bands and thus a heterogeneous deformation. Such bands of localised strain criss-cross as a result of different slip systems being activated from one pass to another. When the temperature is increased to 450 °C, grain boundary migration becomes significant owing to the lack of impurities that could otherwise provide a pinning effect. The resultant subgrain structure is coarsened to about 4 3m. Besides, the enhancement of recovery at higher temperatures also appears to discourage the generation of HAB by dislocation accumulation processes.

Mesoscopic Modeling of Discontinuous Dynamic Recrystallization: Steady-State Grain Size Distributions

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.

A Physically Based Flow Rule for the Simulation of Ti-6Al-4V Forging in the α - β Range

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.

Variant Selection in Zr Alloys: How Many Variants Generated from one Beta Grain?

The elastic energy of a set of the twelve variants generated during the b ® a transformation of zirconium, with volume fractions fi, i=1..12, is derived with simplifying assumptions and the conditions on the fi to reach the energy minimum are established analytically. The minimum number of variants needed to reach this minimum is shown to be 6, and in this case, the variants have very specific volume fractions. Another result is that the maximum volume fraction of any variant is 1/3.

A Model of Discontinuous Dynamic Recrystallization and Its Application for Nickel Alloys

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.