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

It is shown by an analysis similar to that for the spinodal decomposition of a supersaturated solution that an array of dislocations, modelled by parallel screw dislocations, of uniform density, is unstable; the dislocations move to form a structure having a modulated dislocation density. It is suggested that the instability grows ultimately into a dislocation cell structure and that the cell size is given by the dominant wavelength of the density modulation. This wavelength λm is found to be proportional to ρ−1/2 and furthermore the wavelength is given by λm ≈ Kc·ρ−1/2=rc, where Kc is a constant, ρ is the dislocation density and rc is defined as a dislocation‐dislocation interaction distance. Data in the literature relating to cell size are shown to support this result. Restrictions on the applicability of the analysis are discussed.

Dislocation Cell Formation in Metals

The deformation behaviour of intermetallic superlattice compounds

Dynamic Recrystallization of Minerals

Over the past 15 years important advances have been made in the experimental study of the microstructural changes occurring during the non-linear steady-state creep of single phase crystalline matter at elevated temperatures. Curiously, although the results of these painstaking studies have gone a long way toward elucidating the mechanism of this phenomenon, they have been largely ignored in favour of some simple dislocation mechanisms that are not only inconsistent with these observations, but are also unable to describe correctly the known phenomenology. This review concentrates primarily on the recent experiments on microstructural alterations occurring during creep; however, it also surveys the many mechanistic models that attempt to describe this phenomenon, and finds them all deficient.

Steady-state creep of single-phase crystalline matter at high temperature

Study of CuAu I by transmission electron microscopy

The thin foil transmission electron microscope technique has been used to study the ordering of CuAu I. At low annealing temperatures ordered plate-like CuAu I nuclei are formed which are coherent with the disordered matrix and parallel to the (101) planes. At higher annealing temperatures short range strain accommodations in the form of microtwinning occur at first and later long range accommodations in the form of coarse twin lamellae. The latter result from the accommodations to strains set up by the growth of ordered lattice domains whose nucleation centers had different c-axis orientations. The orientation of the twin planes is (101) and the twins appear to be nucleated by other twins or on free surfaces and not by dislocations. The ordered domains become disordered at the twin interfaces but remain intact within the lamellae. The increase in mechanical strength upon ordering is related to the coherency strains between ordered nuclei and disordered matrix and the decline of the mechanical strength is due to the elimination of coherency strains by twinning.

S Weissmann

Papers

Study of CuAu I by transmission electron microscopy

Study of CuAu I by Transmission Electron Microscopy

Mechanical properties of age-hardened titanium-aluminum alloys

Substructure formation in iron during creep at 600°c

Fatigue studies of metal crystals