Perfect Plasticity Theory: State of the Art and Development Trends

Ivlev, D. D.

doi:10.1023/b:inam.0000015597.13365.69

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…The outcomes of these tests provided a foundation for plasticity theory, especially in connection with perfect plasticity, which is based on the assumed constancy of the flow stress of materials. 64) The hypothesis that after a large strain ideal plasticity sets in has been haunting the minds of researchers since Trescá's experiments. Among the first researchers who observed an anomalously weak strain hardening at large strains in torsion under high pressure was P. Bridgman.…”

Section: Perfect Plasticitymentioning

confidence: 99%

Some Unresolved Problems of High-Pressure Torsion

2023

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This overview highlights some salient features of one of the most popular severe plastic deformation techniques: high-pressure torsion (HPT). It focuses on the unresolved challenging problems of HPT. The problems selected touch upon some fundamental questions of mechanics of plasticity, fracture, and friction that are at the core of the HPT process. The scientific significance of these problems and the proposed pathways to resolving them are discussed. The article is meant to promote the use of HPT as a potent tool for studying plasticity at large strains theoretically and also as a practical method enabling novel micromanufacturing routes.

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Section: Perfect Plasticitymentioning

confidence: 99%

Some Unresolved Problems of High-Pressure Torsion

2023

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“…The modified Drucker-Prager cap model is formulated in terms of the two invariants of the stress tensor: the first invariant of the stress tensor, defined as J 1 , which is the trace of the stress tensor, and the square root of the second invariant of the deviatoric stress tensor ¢ J 2 , which reads where q is a failure envelope linear coefficient given by the tangent of the internal angle of friction b and a is the material cohesion. The failure surface is fixed in the plane (perfect plasticity condition [28]) and, therefore, it does not harden unless kinematic hardening occurs. The equation of the cap surface can be written as follows:…”

Section: Modified Drucker-prager Cap Modelmentioning

confidence: 99%

Computational modeling of the cold compaction of ceramic powders

Carlone

Palazzo

2006

Int Appl Mech

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A finite-element model of the cold compaction of ceramic powders by uniaxial pressing is developed and validated by comparison with experimental data. The mechanical behavior of processing powders is assumed according to the modified Drucker-Prager cap model. The frictional effects and the mechanical behavior of tools involved in the process are taken into account. The proposed model allows evaluation of the density distribution into the processed part, as well as stress and strain fields. Variations of the density distribution due to the unloading and the ejection of the part are evaluated Keywords: cold compaction, powder metallurgy, finite-element method, numerical modeling, DruckerPrager cap model Introduction.Manufacturing processes that allow obtaining near net-shape products using powders as raw material are referred to as powder metallurgy. The most relevant steps of powder metallurgy are the production of (pure or pre-alloyed) powders, the powder cold compaction process, and the sintering process. Sometimes, after these processes, the part is subjected to finishing processes, such as recompaction, resintering, heat treatment, and machining operations, to improve its geometrical and mechanical properties. The physical and chemical properties of processing powders are very important to achieve the desired mechanical properties of the final product.Metallic or ceramic powders can be obtained by several processes: mechanical processes, such as machining, sledging, grinding, granulating, shot blasting, and atomization; physical or physical-chemical processes, such as condensation and thermal decomposition; chemical processes, such as oxide reduction, solution precipitation, and corrosion; and electrolytic methods. The obtained powders are then subjected to mechanical and thermal treatments to improve density, to mix different kinds of powders, and to remove hardening effects and impurities.Cold compaction processes are used to shape powders into porous parts, called greens, whose mechanical resistance allows manipulating them during the sintering process. Typical processes of powder compaction are uniaxial pressing, isostatic pressing, high speed forming, extrusion forming, vibration forming, centrifugal forming, rolling forming, continuous forming, gravity forming, and mixture forming. The sintering process is heat treatment used to achieve stable cohesion of compacted powders. The sintering temperature is lower than the melting temperature of the main component of the powder mixture or of all different powders.The powder compaction process is very important to obtain a final product characterized by the desired mechanical and geometrical features. Indeed, plasticity phenomena, internal friction of a porous medium, and frictional effects between the die wall and the processing material may induce inhomogeneous density and residual stress distributions. As a consequence, during the sintering process, nonuniform shrinkage, local distortions, or cracks may occur. Nowadays, the powder metallurgy industry is base...

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“…They played a large role in optimizing the processes of manufacturing gun barrels and other products for the defense industry. These and many other studies concerned with plasticity theory, its current status and possible developments are addressed in the detailed review [63].…”

Section: Deformation Of a Viscoplastic Materials With Small Yield Strementioning

confidence: 99%

Deformation of a Bingham viscoplastic fluid in a plane confuser

et al. 2006

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A review is given to and comprehensive numerical-analytic study is carried out of the problem of steady Bingham viscoplastic flow in a plane confuser. The solution is constructed in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of an incompressible viscous material in a plane confuser) as the zero-order approximation. The numerical analysis is based on the modified accelerated-convergence method proposed earlier by the authors. The bifurcations of the deformation pattern occurring when the parameters reach some critical values are discussed and commented on. The asymptotic boundaries of the rigid zones that appear at infinity upon perturbation of the yield stress are determined Introduction. Recently, the journal Prikladnaya Mekhanika (International Applied Mechanics) has published review papers on solid mechanics and related subject areas [60, 63, 66, etc.], which is of practical interest for scientists who solve important problems based on recent achievements in mathematics and mechanics. This paper outlines and analyzes the theoretical results from solution of one specific problem.This problem describes the stationary deformation of a Bingham viscoplastic medium in a plane confuser. To solve it, we will use numerical and analytical methods. The solution will be found in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of a viscous incompressible medium in a flat-walled converging channel) as the zero-order approximation. We will determine and discuss the main characteristics of the process-asymptotic (first-order) quasi-rigid and deformed zones and analyze their behavior over a wide range of parameters. New mechanical effects will be revealed (bifurcations in the deformation pattern, shape and position of the asymptotic quasi-rigid zones, and the behavior of the velocity of the medium at their boundaries).Moreover, we will also perform a complete numerical and analytic study of the Jeffery-Hamel problem over the whole range of dimensionless parameters-the opening angle of the confuser and the Reynolds number. The numerical analysis is based on the modified accelerated-convergence method proposed by the authors.

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Perfect Plasticity Theory: State of the Art and Development Trends

Cited by 5 publications

References 2 publications

Some Unresolved Problems of High-Pressure Torsion

Some Unresolved Problems of High-Pressure Torsion

Computational modeling of the cold compaction of ceramic powders

Deformation of a Bingham viscoplastic fluid in a plane confuser

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