H.J. McQueen

Constitutive analysis in hot working

Constitutive equations including an Arrhenius term have been commonly applied to steels with the objective of calculating hot rolling and forging forces. The function relating stress and strain rate is generally the hyperbolic-sine since the power and exponential laws lose linearity at high and low stresses, respectively. In austenitic steels, the equations have been used primarily for the peak stress (strain) associated with dynamic recrystallization (DRX) but also for the critical and steady state stresses (strains) for nucleation and first wave completion of DRX. Since the peak strain is raised by the presence of solutes and fine particles, the stress is raised more than by simple strain hardening increase, thus causing a marked rise in activation energy in alloy steels. In contrast, large carbides, inclusions or segregates, if hard, may lower the peak strain as a result of particle stimulated nucleation. Due to the linear relation between stress and strain at the peak, flow curves can be calculated from the constitutive data with only one additional constant. Maximum pass stresses can also be calculated from a sinh constitutive equation determined in multistage torsion simulations of rolling schedules. Comparison is made between carbon, micro-alloyed, tool and stainless steels and to ferritic steels which usually do not exhibit DRX. Parallels to the effects of impurities and dispersoids on the constitutive equations for Al alloys are briefly discussed.

Hot working characteristics of steels in austenitic state

The behavior of C, HSLA, tool and stainless steels in the austenitic condition during industrial hot forming is reviewed. In the constitutive relations, it is primarily the activation energy which rises with alloy additions. Strain hardening is reduced mainly by dynamic recovery as indicated by its stress dependence and confirmed microscopically in the austenitic stainless steels. Dynamic recrystallization provides additional softening, possible grain refinement and enhanced ductility. After deformation, the metal undergoes static recovery and static recrystallization at longer times to provide grain refinement and stress reduction in any following stage. With rapid cooling, it is possible to retain either hot-work substructures in elongated grains or fine new grains which strengthen the product directly or through refined ferrite.

The production and utility of recovered dislocation substructures

The production of dislocation substructures by cold working and recovery, fatigue, creep and hot working are reviewed. The relationships of subgrain size and dislocation density to the causal parameters of strain, strain rate, strain amplitude, temperature, stress and time (as applicable) are presented for each process. The importance of dislocation mechanisms such as climb, cross-glide, annihilation and subboundary formation are explained. The relative capabilities and limitations of each mode of creation with respect to both external processing and internal mechanisms are explored. The effects of the metals stacking fault energy, of solid solution and of particle dispersion on structure and behavior are presented. The properties of the different kinds of substructures for room temperature and creep service are examined. The need for modification of the Petch relationship between yield strength and subgrain size is explored. The thermal stability is shown to be an important factor for creep service. It is concluded that the most suitable modes of substructure preparation are either cold working and recovery or hot working both from the view point of fitting into current industrial practice and from that of dependable, useful service properties.

Comparative hot workability of 7012 and 7075 alloys after different pretreatments

Hot torsion tests, in the range 250–450 °C and 0.05–5.0 s−1, were performed on AlZnMgCu alloys (7012 and 7075), which had been direct chill cast, homogenized and precipitation treated to give fine, well-dispersed precipitates. Additional tests were conducted on material that had been extruded, solution treated or precipitation treated at deformation temperature. The peak flow stress was related to the strain rate by the hyperbolic sine equation; the activation energy for precipitated alloys was close to that of the bulk self-diffusion of pure aluminium. For solution-treated metal, the peak stress was very high at low temperatures due to dynamic precipitation; as a consequence, the activation energy was about 50% higher than that of precipitated alloys. The ductility was almost independent of temperature in the investigated range, but decreased with rising strain rate. The ductility of the extruded alloys was almost double that of the as-cast material, with the exception of the solution-treated material where, at low temperature, the ductility of the extruded alloy was lower. The original grains were elongated with precipitates on the boundaries. The dynamically recovered subgrains exhibited sub-boundaries with a high density of fine precipitates and an interior network of dislocations also tied to precipitates.

Dynamic recovery: sufficient mechanism in the hot deformation of Al (<99.99)

Abstract A recent OIM study of the substructure in hot compressed Al has observed an increase in the fraction of boundaries both of 15–20° and above 20° as strain rises from 0.9 to 1.5. This was interpreted as evidence of continuous dynamic recrystallization being the mechanism for the steady state deformation. However, when the original grain boundaries and transition boundaries between deformation bands are discounted, the fraction of 15–20° boundaries is reduced to less than 20% and would be much lower if subboundaries less than 0.5° visible in TEM were taken into account. The present authors argue that dynamic recovery maintains the subgrains of constant size, low misorientation and equiaxed to produce a steady state and can permit a limited number of discrete segments with higher misorientation notably as temperature falls. Moreover, continuous dynamic recrystallization is not appropriate terminology because it is far from reaching the completion observed in other instances of continuous recrystallization.

Recent advances in hot working: Fundamental dynamic softening mechanisms

ConclusionsThe fundamental mechanisms responsible for the low rate of strain hardening during high temperature deformation and for a steady state of flow at high strains have been confirmed to be:I.Dynamic recovery, which limits the accumulation of dislocations through annihilation and which operates at all strains in all metals; andII.Dynamic recrystallization, which eliminates dislocations through the migration of grain boundaries and which only operates beyond a critical strain when the dislocation density becomes high enough to give rise to the nucleation and growth of new grains.These softening processes are retarded by the presence of solute atoms and second phase particles which reduce the mobility of both dislocations and high angle boundaries. These effects have some similarities to those observed under cold working and annealing but there is a strong dynamic element introduced by straining at the elevated temperature. As a result of the high strains imposed there is much more microstructural change than during creep loading.Industrial hot forming processes generally involve several stages of deformation separated by intervals during which static recovery or recrystallization take place. The interaction between dynamic and static softening processes under industrial conditions will be the subject of a sequel paper. This work will also consider the trends in hot ductility; the latter depends on the retardation of grain boundary cracking by dynamic recovery and recrystallization. Finally, since the effects of alloying in hot working have been treated only in a general way, the behavior of specific materials and their thermomechanical processing will be reviewed in the third and fourth papers of this-series.

Flow stress, dynamic restoration, strain hardening and ductility in hot working of 316 steel

Abstract From the determination of flow stress σ in torsion tests over the range 900–1200°C, 0.1–5.0 s−1, in both as-cast and worked 316 stainless steel, the dependence on temperature and strain rate is shown to fit the sinh and Arrhenius functions. Through evolution of the strain-hardening rate θ, changes in slope of the θ-σ curves and extrapolation to the θ=0 axis permits determination of the saturation stress σs∗, the constants for the Kocks-Mecking equations and the critical strain for dynamic recrystallization, which could be compared with σp and ϵp at the peak in the flow curve. The ductility mounts as temperature rises, the strain-rate falls and the cast structure becomes homogenized. The relationships between grain size, substructure, hot ductility, and stress are discussed. The above hot properties are compared with those of 304 and 317 which have less and more molybdenum respectively.

Geometric dynamic recrystallization in hot torsion of Al5Mg0.6Mn (AA5083)

Abstract Geometric dynamic recrystallization (GDRX) is a process in which a refined and nearly equiaxed grain structure is formed, because grain boundaries which have become serrated during formation of subgrains in the course of hot deformation recombine as serrations pinch off or as the grains thin down. GDRX was first found in aluminium and more recently in AlMg solid solution. In the present work the question was addressed whether GDRX occurs also in an industrial Al alloy (5083) containing particles. Specimens were deformed in torsion from 473 to 773 K at equivalent (surface) strain rates between 10−3 and 4 s−1 to strains up to 3.6. Under these conditions the egg tray model predicts that GDRX will occur. This is indeed found from observations of the grain structure with light and electron microscopy. The results indicate that GDRX occurs not only by recombination of opposite boundaries of the thinned grain but also by pinching off of serrations. The size of the GDRX grains is about two to three times the subgrain size. The close similarity to Al5Mg means that the particles in the alloy do not prevent the small-scale grain boundary migration which is necessary to form the serrations. Static recrystallization after hot deformation destroys the DRX structure, if the specimen is not cooled fast enough.

New formula for calculating flow curves from high temperature constitutive data for 300 austenitic steels

Abstract The high temperature flow curves for 301, 304 and 317 stainless steels can be calculated up to the peak stress σ p and peak strain ϵ p by : σ/σ p =[(ϵ/ϵ p exp (1−1ϵ/ϵ p )] c . The values of σ p may be derived from the sinh-Arrhenius constitutive equation for which the constants have already been published based on torsion tests. ϵ p is shown to be linearly related to σ p for each alloy. The values of the shape constant c are shown to have averages of 0.203 for 301, 0.216 for 304 and 0.200 for 317 with average errors of less than 2.6%. The value of c decreases only slightly with rising strain rate and declining temperature. An average value of 0.204 (including 316 with c = 0.193 previously published) may be employed for all the steels without significant increase in the error.

Dynamic restoration mechanisms in Al-5.8 At. Pct Mg deformed to large strains in the solute drag regime

An Al-5.8 at. pct Mg (5.2 wt pct Mg) alloy was deformed in torsion within the solute drag regime to various strains, up to the failure strain of 10.8. Optical microscopy (OM) and transmission electron microscopy (TEM) were used to analyze the evolution of the microstructure and to determine the dynamic restoration mechanism. Transmission electron microscopy revealed that subgrain formation is sluggish but that subgrains eventually (ε ≈ 1) fill the grains. The “steady-state” subgrain size (λ ≈ 6 μm) and misorientation angle (θ ≈ 1.6 deg) are reached by ε ≈ 2. These observations confirm that subgrains eventually form during deformation in the solute drag regime, though they do not appear to significantly influence the strength. At low strains, nearly all of the boundaries form by dislocation reaction and are low angle (θ < 10 deg). At a strain of 10.8, however, the boundary misorientation histogram is bimodal, with nearly 25 pct of the boundaries having high angles due to their ancestry in the original grain boundaries. This is consistent with OM observations of the elongation and thinning of the original grains as they spiral around the torsion axis. No evidence was found fordiscontinuous dynamic recrystallization, a repeating process in which strain-free grains nucleate, grow, deform, and give rise to new nuclei. It is concluded that dynamic recovery in the solute drag regime gives rise togeometric dynamic recrystallization in a manner very similar to that already established for pure aluminum, suggesting that geometric dynamic recrystallization may occur generally in materials with a high stacking-fault energy (SFE) deformed to large strains.