Inelastic Constitutive Properties and shear Localization in Tennessee Marble

Shear bands and faults are ubiquitous features of brittle rock deformation at a variety of length scales. Despite the prevalence of these features, understandhg of their inception remains rudimentary. Laboratory experiments suggest a casual association of localization of deformation (faulting) with peak stress, but more detailed examination reveals that localization can precede or follow the peak. Rudnicki and Rice (1975, hereafter abbreviated as RR) have suggested a the- ory of the inception of localization as a bifurcation or nonuniqueness of the so- lution for homogeneous deformation. They predict a strong dependence of local- ization on deformation state. In particular, they predict that localization can occur prepeak for deformation states near deviatoric pure shear and does not occur until well after peak for axisymmetric compression. This prediction is roughly in ac- cord with the true triaxial experiments of Mogi (1967, 1971). More recently, Ord et al. (1991) and Wwersik et al. (1991) have reported observations of localization prior to peak stress in plane strain experiments. The predictions of RR depend strongly on the constitutive properties of the rock and detailed comparison has been impeded by inadequate knowledge of those properties. Even the idealized constitutive model used by RR requires knowledge of the evolution of the constitutive properties with inelastic deformation that is not readily obtainable from the typical axisymmetric compression test. Although it is conceptually advantageous to consider inelastic deformation at fixed mean stress, the mean stress changes throughout the axisymmetric compression test. In this paper, we present a synthesis of a number of axisymmetric compres- sion tests to extract a detailed implementation of the constitutive framework used by RR. The resulting constitutive relation is then used to -predict the response for plane strain. Conditions for localization of deformation derived by RR are evalu- ated for both plane strain and axisymmetric compression

Microstructural Shear Localization in Plastic Deformation of Amorphous Solids

The shear-transformation-zone (STZ) theory of plastic deformation predicts that sufficiently soft, non-crystalline solids are linearly unstable against forming periodic arrays of microstructural shear bands. A limited nonlinear analysis indicates that this instability may be the mechanism responsible for strain softening in both constant-stress and constant-strain-rate experiments. The analysis presented here pertains only to one-dimensional banding patterns in two-dimensional systems, and only to very low temperatures. It uses the rudimentary form of the STZ theory in which there is only a single kind of zone rather than a distribution of them with a range of transformation rates. Nevertheless, the results are in qualitative agreement with essential features of the available experimental data. The nonlinear theory also implies that harder materials, which do not undergo a microstructural instability, may form isolated shear bands in weak regions or, perhaps, at points of concentrated stress.Comment: 32 pages, 6 figure

The analytic solution of near-tip stress fields for perfectly plastic pressure-sensitive material under plane stress condition

Different from dense metals, many engineering materials exhibit pressure-sensitive yielding and plastic volumetric deformation. Adopting a yield criterion that contains a linear combination of the Mises stress and the hydrostatic stress, the analytic solutions of plane-stress mode I perfectly-plastic near-tip stress fields for pressuresensitive materials are derived. Also, the relevant characteristic fields are presented. This perfectly plastic solution, containing a pressure sensitivity parameter μ, is shown to correspond to the limit of low-hardening solutions, and when μ=0 it reduces to the perfectly plastic solution of near-tip fields for the Mises material given by Hutchinson [1]. The effects of material pressure sensitivity on the near-tip fields are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42771/1/10704_2004_Article_BF00034180.pd

Plastic Flow in Two-Dimensional Solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t. Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of $\pm \pi/4$ with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to metastable, structurally disordered states. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/index-e.htm

Influences of non-singular stresses on plane-stress near-tip fields for pressure-sensitive materials and applications to transformation toughened ceramics

In this paper, we investigate the effects of the non-singular stress ( T stress) on the mode I near-tip fields for elastic perfectly plastic pressure-sensitive materials under plane-stress and small-scale yielding conditions. The T stress is the normal stress parallel to the crack faces. The yield criterion for pressure-sensitive materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by the normality flow rule. The results of our finite element computations based on a two-parameter boundary layer formulation show that the total angular span of the plastic sectors of the near-tip fields increases with increasing T stress for materials with moderately large pressure sensitivity. The T stress also has significant effects on the sizes and shapes of the plastic zones. The height of the plastic zone increases substantially as the T stress increases, especially for materials with large pressure sensitivity. When the plastic strains are considered to be finite as for transformation toughened ceramics, the results of our finite element computations indicate that the phase transformation zones for strong transformation ceramics with large pressure sensitivity can be approximated by those for elastic-plastic materials with no limit on plastic strains. When the T stress and the stress intensity factor K are prescribed in the two-parameter boundary layer formulation to simulate the crack-tip constraint condition for a single-edge notch bend specimen of zirconia ceramics, our finite element computation shows a spear shape of the phase transformation zone which agrees well with the corresponding experimental observation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42782/1/10704_2004_Article_BF00018779.pd