Constitutive equations are reviewed and discussed in the context of extrusion. It is concluded that mainly because extrusion converts directly from cast to finished product a steady state equation is adequate for use in extrusion problems and that the Zener-Hollomon type of formulation is both convenient and defined for a number of aluminium alloys. Experimental work is presented to show that if the data are correctly interpreted by suitably allowing for temperature rise, then testing in either torsion or compression yields identical equations. The physical interpretation of the various constants is discussed. Evidence is presented that differing homogenisation treatments produce differing equations and the effects of heating and cooling rates are considered. The implications are discussed in some detail. Constitutive equations are quantified for 26 aluminium alloys.

Constitutive equations for use in prediction of flow stress during extrusion of aluminium alloys

On dislocation accumulation and work hardening in Hadfield steel

The 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; and




II.

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.

Recent advances in hot working: Fundamental dynamic softening mechanisms

Specimens of Type 304 stainless steel have been deformed in torsion at temperatures of 950–1150°C and annealed for different times before quenching or continuing the deformation. The kinetics of static recrystallization and the recrystallized grain size have been determined by quantitative metallography. Increasing strain and decreasing original grain size both reduce recrystallization time and recrystallized grain size. Increasing strain rate and decreasing temperature of deformation have a similar, but smaller effect. Annealing temperature also strongly influences recrystallization time (activation energy 425 kJ mol−1), but not recrystallized grain size. The effects of all the experimental variables are described in terms of simple parametric relationships. The kinetics of static restoration have been determined both from hardness tests on quenched specimens and from interrupted torsion tests. The extent of restoration is related in a non-linear manner to fraction recrystallized. This arises par...

Static recrystallization and restoration after hot deformation of Type 304 stainless steel

Kinetics of pearlite spheroidisation during static annealing and during hot deformation

Hot torsion tests have been carried out on aluminum, stainless steel, and silicon steel specimens using a wide range of gage length: radius ratios and bore diameters. For stainless steel, which dynamically recrystallises, a higher strain to maximum stress was found for specimens with a gage length : radius ratio A new effective radius is proposed for calculation of strains, strain rates, and shear stresses from torque-twist data for solid and tubular specimens.

Barraclough

Papers

Effect of Specimen Geometry on Hot Torsion Test Results for Solid and Tubular Specimens