Plastic Flow of Rock Under a Pointed Punch in Plane Strain

1968 ◽  
Vol 35 (1) ◽  
pp. 95-101 ◽  
Author(s):  
P. R. Paslay ◽  
J. B. Cheatham ◽  
C. W. G. Fulcher
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Yield Surface ◽  
Work Hardening ◽  
Deformation Rate ◽  
Plasticity Theory ◽  
Surface Work ◽  
Rate Vector ◽  
The Mean ◽  
Elastic Strains

Solutions are presented for the plane-strain plastic flow of rock under a pointed punch for two cases. In the first problem the indentation of a half space by a pointed punch is considered, and in the second the influence of a previous indentation on the formation of the next indentation is evaluated. The plasticity theory used in this analysis was developed by the authors earlier for rock mechanics applications. This theory incorporates a yield surface which is dependent on the mean normal stress and normality of the deformation rate vector to the yield surface. Work-hardening and elastic strains are neglected in the theory. These solutions furnish the analytical basis for some elementary experiments which may help to evaluate the theory.

Analysis of the Plastic Flow of Rock Under a Lubricated Punch

1968 ◽  
Vol 35 (1) ◽  
pp. 87-94 ◽  
Author(s):  
J. B. Cheatham ◽  
P. R. Paslay ◽  
C. W. G. Fulcher
Keyword(s):  
Plastic Flow ◽  
Yield Surface ◽  
Deformation Rate ◽  
Specific Problem ◽  
Three Dimensional ◽  
Plasticity Theory ◽  
Plane Flow ◽  
Perfectly Plastic ◽  
Isotropic Rock ◽  
Rate Vector

A general three-dimensional plasticity theory is presented for describing the plastic flow of homogeneous, isotropic rock. Normality of the deformation-rate vector to the yield surface is incorporated into the stress-deformation rate law used in the theory. The rock is assumed to be perfectly plastic or nonwork-hardening with a dependence of the yield strength on the hydrostatic component of stress. A particular type of yield surface, which is representative of the behavior of rock, is assumed in an application of the theory. The specific problem considered is the solution for the incipient plane flow under a flat lubricated punch.

Small deformation rate-independent plasticity based on a postulate of maximum dissipation

2020 ◽  
pp. 429-433
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Linear Programming ◽  
Plastic Flow ◽  
Yield Surface ◽  
Deformation Rate ◽  
Optimization Problem ◽  
Flow Direction ◽  
Small Deformation ◽  
Complementarity Conditions ◽  
Programming Theory ◽  
Plastic Dissipation

This chapter introduces the concept of maximum dissipation. The elastic set is introduced, and the plastic dissipation is maximized over the elastic set using classical methods from linear programming theory. The plastic flow direction is seen to be generally normal to the yield surface when the plastic dissipation is maximized. The Kuhn-Tucker complementarity conditions are seen in this context to arise from the postulated optimization problem, and the elastic set is seen to be necessarily convex. The concept of maximum dissipation is applied to a Mises material and the models of the earlier chapters are seen to be recovered.

An examination of the neutral loading condition in plasticity theory

1988 ◽  
Vol 23 (2) ◽  
pp. 47-60
Author(s):  
D W A Rees
Keyword(s):  
Plastic Flow ◽  
Work Hardening ◽  
Kinematic Hardening ◽  
Stress Path ◽  
Plasticity Theory ◽  
Elastic Response ◽  
Isotropic Hardening ◽  
Initial Loading ◽  
Classical Plasticity ◽  
Elastic Loading

An examination is made of a number of neutral loading experiments according to classical plasticity theory. For work hardening materials the question as to whether plastic deformation occurs during neutral loading depends strongly upon the deformation produced from initial loading. Initial elastic loading with a subsequent stress path that follows the boundary of the initial vield surface is truly neutral with a wholly elastic response. However, when plastic strain is produced from initial loading then plastic flow is produced from a subsequent stress path that follows the boundary of a surface that is an isotropic expansion of the initial yield surface. Since this violates the assumption of isotropic hardening the usefulness and limitations of the rule of kinematic hardening are examined. It is further shown that the results from recent experiments are particularly relevant to the appraisal of modern developments to plasticity theory. Neutral loading without work hardening will produce plastic flow. It is shown that the corresponding Prandtl—Reuss theoretical solutions are representative of observed behaviour for both severely pre-strained materials and for others that do not harden appreciably. The concept is introduced of lower and upper bounds on the deformation that can be expected from neutral loading. These correspond to the extreme purely elastic and non-work-hardening solutions, respectively.

scholarly journals The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure

1947 ◽  
Vol 191 (1026) ◽  
pp. 278-303 ◽  
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Region ◽  
Strain Diagram ◽  
Combined Stresses ◽  
Usual Theory ◽  
Plastic Components ◽  
Longitudinal Extension ◽  
Elastic Strains

In certain problems of plastic flow, for example, a thick tube expanded by internal pressure, it is important to consider changes in the elastic strain of material which is flowing plastically in order to deduce the correct stress distribution and deformation. The usual plastic theory which neglects elastic strains in the plastic region may lead to considerable errors in certain cases. In this paper we review the theory of the deformation of a material under combined stresses which involves both elastic and plastic components of strain. The relationship between stress and strain is represented on a plane diagram, the reduced stress-strain diagram, which facilitates discrimination between the elastic and plastic components of strain and aids considerably the solution of certain problems. The diagram can also be used to express the relationships governing the dissipation of energy during plastic flow under combined stresses. The theory is applied to the deformation of a long thick tube under internal pressure with zero longitudinal extension. The solution is compared with that based on the usual theory which neglects elastic strains in the plastic region, revealing an error which reaches a maxi­mum of over 60% in the longitudinal stress distribution. The significance of the differences between the two solutions is discussed in detail.

Surface work-hardening of back-up rolls

Metallurgist ◽  
1982 ◽  
Vol 26 (1) ◽  
pp. 32-33
Author(s):  
A. Yu. Firkovich ◽  
A. M. Tsun ◽  
A. I. Dobronravov ◽  
V. A. Brovkin ◽  
O. N. Shcherbakov
Keyword(s):  
Work Hardening ◽  
Surface Work

Effects of Crystallographic Texture on Plastic Flow Localization

2007 ◽  
Vol 340-341 ◽  
pp. 211-216
Author(s):  
Mitsutoshi Kuroda
Keyword(s):  
Shear Band ◽  
Plane Strain ◽  
Plastic Flow ◽  
Texture Component ◽  
Three Dimensional ◽  
Cube Texture ◽  
Shear Band Formation ◽  
Flow Localization ◽  
Band Formation ◽  
Plastic Flow Localization

In this study, effects of typical texture components observed in rolled aluminum alloy sheets (i.e. Copper, Brass, S, Cube and Goss texture components) on plastic flow localization are studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic-viscoplastic continuum slip constitutive relation. First, forming limits of thin sheet set by sheet necking are predicted using a Marciniak–Kuczynski (M–K-) type approach. It is shown that only the Cube texture component yields forming limits higher than that for a random texture in the biaxial stretch range. Next, three-dimensional shear band analyses are performed, using a three-dimensional version of M–K-type model, but the overall deformation mode is restricted to a plane strain state. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. It is concluded that the Cube texture component is said to be a shear band free texture, while some texture components exhibit significantly low resistance to shear band formation. Finally, shear band developments in plane strain pure bending of sheet specimens with the typical textures are studied.

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