Strain localization in ductile crystals deforming by single slip was analyzed. The plastic flow is modeled as rate-in-sensitive; and localization, viewed as a bifurcation from a homogeneous deformation mode to one which is concentrated in a narrow ''shear band'', is found to be possible only when the plastic hardening modulus for the slip system has fallen to a certain critical value, h/sub cr/, where h/sub cr/ is sensitive to the precise form of the constitutive law governing incremental shear. The general form of this constitutive law is developed. Incorporated within it is the possibility of deviations from the Schmid rule of a critical resolved shear stress. It is shown that h/sub cr/ may in fact be positive when there are deviations from the Schmid rule. It is suggested that micromechanical processes such as ''cross-slip'' in crystals provide specific cases for which stresses other than the Schmid stress may influence plastic response and, further, there is an experimental association of localization with the onset of large amounts of cross-slip. The specific form of h/sub cr/ is given for a constitutive model that corresponds to the non-Schmid effects in cross-slip, and a dislocation model of the process is developed from which anmore » estimate of the magnitude of the parameters involved is made. The work supports the notion that localization can occur with positive strainhardening, h/sub cr/ greater than 0, and the often-invoked notions of the attainment of an ideally plastic or strain softening state for localization may be unnecessary. 6 figures.« less

http://esag.harvard.edu/rice/066_AsaroRice_SingleCryst_JMPS77.pdf

Strain localization in ductile single crystals

All available literature on the constitution of Ti−Al is reviewed. Based on a critical evaluation of these data the phase diagram for this system is assessed.

Reassessment of the binary Aluminum-Titanium phase diagram

The Al-B-Nb-Ti system

Investigations made by the authors and collaborators into the microstructural aspects of adiabatic shear localization are critically reviewed. The materials analyzed are low-carbon steels, 304 stainless steel, monocrystalline Fe-Ni-Cr, Ti and its alloys, Al-Li alloys, Zircaloy, copper, and Al/SiCp composites. The principal findings are the following: (a) there is a strain-rate-dependent critical strain for the development of shear bands; (b) deformed bands and white-etching bands correspond to different stages of deformation; (c) different slip activities occur in different stages of band development; (d) grain refinement and amorphization occur in shear bands; (e) loss of stress-carrying capability is more closely associated with microdefects rather than with localization of strain; (f) both crystalline rotation and slip play important roles; and (g) band development and band structures are material dependent. Additionally, avenues for new research directions are suggested.

/pdf/shear-localization-in-dynamic-deformation-microstructural-4u091fjk2m.pdf

Shear Localization in Dynamic Deformation: Microstructural Evolution

The effect of SiC volume fraction and particle size on the fatigue behavior of 2080 Al was investigated. Matrix microstructure in the composite and the unreinforced alloy was held relatively constant by the introduction of a deformation stage prior to aging. It was found that increasing volume fraction and decreasing particle size resulted in an increase in fatigue resistance. Mechanisms responsible for this behavior are described in terms of load transfer from the matrix to the high stiffness reinforcement, increasing obstacles for dislocation motion in the form of S’ precipitates, and the decrease in strain localization with decreasing reinforcement interparticle spacing as a result of reduced particle size. Microplasticity was also observed in the composite, in the form of stress-strain hysteresis loops, and is related to stress concentrations at the poles of the reinforcement. Finally, intermetallic inclusions in the matrix acted as fatigue crack initiation sites. The effect of inclusion size and location on fatigue life of the composites is discussed.

G Lütjering

Papers

Mechanical properties of age-hardened titanium-aluminum alloys