An Analysis of the Plane-Strain Compression of Viscoplastic Materials

1997 ◽  
Vol 64 (2) ◽  
pp. 420-424 ◽  
Author(s):  
M. J. Adams ◽  
B. J. Briscoe ◽  
G. M. Corfield ◽  
C. J. Lawrence ◽  
T. D. Papathanasiou
Keyword(s):  
Plane Strain ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Plane Strain Compression ◽  
Flow Rule ◽  
Strain Fields ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Calculated Stress ◽  
Associated Flow Rule

A theoretical analysis for the plane-strain compression of viscoplastic materials with a Tresca wall boundary condition is described. The analysis is based upon the incorporation of a viscoplastic associated flow rule into the cycloidal solution originally developed for rigid-perfectly plastic materials. The evolution of the calculated stress field suggests that the influence of strain rate hardening is similar to that reported previously for strain hardening. The calculated strain fields are elliptical in form and are consistent with those measured for a viscoplastic paste. Previous analyses of the compression of viscoplastic materials have employed the lubrication approximation for fluid flows with a resulting kinematic inconsistency in the predicted velocity fields.

Examples of nonlinear homogenization involving degenerate energies. I. Plane strain

2005 ◽  
Vol 461 (2063) ◽  
pp. 3681-3703 ◽  
Author(s):  
Isaac V Chenchiah ◽  
Kaushik Bhattacharya
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Plane Strain ◽  
Stress And Strain ◽  
Strain Fields ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Nonlinear Homogenization

The study of polycrystals of shape-memory alloys and rigid-perfectly plastic materials gives rise to problems of nonlinear homogenization involving degenerate energies. This paper presents a characterization of the stress and strain fields in a class of problems in plane strain, and uses it to study examples including checkerboards and hexagonal microstructures. Consequences for shape-memory alloys and rigid-perfectly plastic materials are discussed.

scholarly journals Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nelli Aleksandrova
Keyword(s):  
Structural Steel ◽  
Yield Criterion ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Open Hole ◽  
Practical Engineering ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Material Compressibility

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies.

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part II: Applications

1986 ◽  
Vol 108 (4) ◽  
pp. 307-316 ◽  
Author(s):  
Betzalel Avitzur ◽  
Waclaw Pachla
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Metal Cutting ◽  
Failure Modes ◽  
Plastic Material ◽  
Rotational Velocity ◽  
Optimization Procedure ◽  
Velocity Fields ◽  
Perfectly Plastic ◽  
Strip Drawing

Following Part I which investigated an upper bound approach to plane strain deformation of a rigid, perfectly plastic material, this Part II considers the same approach as applied to actual forming operations. The processes of drawing and extrusion, of metal cutting and of rolling are analyzed, and explicit equations are developed to calculate the surfaces of velocity discontinuity (shear boundaries), velocity discontinuities, and the upper bound on power for these processes. Both the simple, unielement velocity fields as well as the more complex multielement fields are explored. The upper bound solution is shown to be a function of the independent (input) and pseudoindependent (assumed) process parameters as minimized by an optimization procedure. Rules concerning the assumption of pseudoindependent parameters are presented and the optimization procedure is discussed. Final conclusions lead the way for the application of upper bound analyses to such industrial processes as sheet and strip drawing, extrusion, forging, rolling, leveling, ironing and machining, and to the investigation of such flow failure modes as central bursting, piping and end splitting (alligatoring).

Constraints on Moving Strong Discontinuity Surfaces in Dynamic Plane-Stress or Plane-Strain Deformations of Stable Elastic-Ideally Plastic Materials

1990 ◽  
Vol 57 (3) ◽  
pp. 569-576 ◽  
Author(s):  
Yinong Shen ◽  
W. J. Drugan
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Yield Condition ◽  
Strong Discontinuity ◽  
Dynamic Crack Propagation ◽  
Small Displacement ◽  
Flow Rule ◽  
Dynamic Crack ◽  
Plastic Materials ◽  
Discontinuity Surfaces

For dynamic deformations of compressible elastic-ideally plastic materials in the practically important cases of plane stress and plane strain, we investigate the possible existence of propagating surfaces of strong discontinuity (across which components of stress, strain, or material velocity jump) within a small-displacement-gradient formulation. For each case, an explicit proof of the impossibility of such a propagating surface (except at an elastic wave speed) is achieved for isotropic materials satisfying a Huber-Mises yield condition and associated flow rule, and we show that our method of proof can be generalized to a large class of anisotropic materials. Nevertheless, we demonstrate that moving surfaces of strong discontinuity cannot be ruled out for all stable (i.e., satisfying the maximum plastic work inequality) materials, as in the case of a material whose yield surface contains a linear portion. A clear knowledge of the conditions under which dynamically propagating strong discontinuity surfaces can and cannot exist is crucial to the attainment of correct and complete solutions to such practical elastic-plastic problems as dynamic crack propagation, impact and rapidly moving load problems, high-speed forming, cutting, and other manufacturing processes.

scholarly journals Characteristic parameters of soil failure criteria for plane strain conditions – experimental and semi-theoretical study

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Justyna Sławińska-Budzich
Keyword(s):  
Plane Strain ◽  
Theoretical Study ◽  
Friction Angle ◽  
Failure Criteria ◽  
Flow Rule ◽  
Characteristic Parameters ◽  
True Triaxial ◽  
Soil Failure ◽  
Confining Pressures ◽  
Associated Flow Rule

Abstract The paper concerns the characteristic parameters of the selected isotropic failure criteria, i.e. Mohr–Coulomb, Drucker–Prager, Matsuoka–Nakai and Lade–Duncan. The parameters are determined directly from the failure criteria and stress measurements or by semi-theoretical approach, assuming that the soil obeys the associated flow rule and using the plane strain condition. In the latter case, the parameters can be expressed as functions of the plane strain internal friction angle, which is determined from measurements. The principal stress tensor components, corresponding to the soil peak strength and necessary to obtain the failure criteria parameters, are measured in a series of true triaxial, plane strain tests, on coarse Skarpa sand samples of different initial relative density, subjected to various confining pressures.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

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