Hardening (metallurgy)

Abstract: Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Abstract: The kinetics of glide at constant structure and the kinetics of structure evolution are correlated on the basis of various experimental observations in pure f.c.c. mono- and polycrystals. Two regimes of behavior are identified. In the initial regime, the Cottrell-Stokes law is satisfied, hardening is athermal, and a single structure parameter is adequate. With increasing importance of dynamic recovery, be it at large strains or at high temperatures, all of these simple assumptions break down. However, the proportionality between the flow stress and the square-root of the dislocation density holds, to a good approximation, over the entire regime; mild deviations arc primarily ascribed to differences between the various experimental techniques used. A phenomenological model is proposed, which incorporates the rate of dynamic recovery into the flow kinetics. It has been successful in matching many experimental data quantitatively.

Abstract: Metals have been mankind's most essential materials for thousands of years; however, their use is affected by ecological and economical concerns Alloys with higher strength and ductility could alleviate some of these concerns by reducing weight and improving energy efficiency However, most metallurgical mechanisms for increasing strength lead to ductility loss, an effect referred to as the strength-ductility trade-off Here we present a metastability-engineering strategy in which we design nanostructured, bulk high-entropy alloys with multiple compositionally equivalent high-entropy phases High-entropy alloys were originally proposed to benefit from phase stabilization through entropy maximization Yet here, motivated by recent work that relaxes the strict restrictions on high-entropy alloy compositions by demonstrating the weakness of this connection, the concept is overturned We decrease phase stability to achieve two key benefits: interface hardening due to a dual-phase microstructure (resulting from reduced thermal stability of the high-temperature phase); and transformation-induced hardening (resulting from the reduced mechanical stability of the room-temperature phase) This combines the best of two worlds: extensive hardening due to the decreased phase stability known from advanced steels and massive solid-solution strengthening of high-entropy alloys In our transformation-induced plasticity-assisted, dual-phase high-entropy alloy (TRIP-DP-HEA), these two contributions lead respectively to enhanced trans-grain and inter-grain slip resistance, and hence, increased strength Moreover, the increased strain hardening capacity that is enabled by dislocation hardening of the stable phase and transformation-induced hardening of the metastable phase produces increased ductility This combined increase in strength and ductility distinguishes the TRIP-DP-HEA alloy from other recently developed structural materials This metastability-engineering strategy should thus usefully guide design in the near-infinite compositional space of high-entropy alloys

Abstract: A new rate dependent constitutive model is developed for polycrystals subjected to arbitrarily large strains. The model is used to predict deformation textures and large-strain strain hardening behavior following various stress-strain histories for single phase f.c.c. aggregates that deform by crystallographic slip. Examples involving uniaxial and plane strain tension and compression are presented which illustrate how texture influences polycrystalline strain hardening, in particular these examples demonstrate both textural strengthening and softening effects. Input to the model includes the description of single crystal strain hardening and latent hardening along with strain rate sensitivity, all properties described on the individual slip system level. The constitutive formulation used for the individual grains is essentially that developed by Peirce et al . [6, Acta metall . 31, 1951 (1983)] to solve rate dependent boundary value problems for finitely deformed single crystals. Inclusion of rate dependence is shown to overcome the long standing problem of nonuniqueness in the choice of active slip systems which is inherent in the rate independent theory. Because the slipping rates on all slip systems within each grain are unique in the rate dependent theory, the lattice rotations and thus the textures that develop are unique. In addition, the model makes it possible to study how strain rate sensitivity on the slip system, and single grain, levels is manifested in polycrystalline strain rate sensitivity. The model is also used to predict “constant offset plastic strain yield surfaces” for materials that are nearly rate insensitive—these calculations describe the development of rounded “yield surface vertices” and the resulting softening of material stiffness to a change in loading path that vertices imply. For our rate dependent solid this reduction in stiffness occurs after small but finite loading increments. Finally the model is used to carry out an imperfection-based sheet necking analysis both for isotropic and strongly textured sheets. The results show that larger strain hardening rates, and strain rate sensitivity, on the slip system level both increase the failure strains, as expected, but also demonstrate a strong influence of texture on localized necking.

Abstract: SUMMARY AN ANALYSIS is presented which relates the critical value of tensile stress (a,) for unstable cleavage fracture to the fracture toughness (K,,) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic*lastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress a,, exceeds a, over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K,, with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensiiication. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.