An efficient method of analysis of heat transfer during plane strain upsetting of a viscoplastic strip

Alexandrov, Sergei; Lang, Lihui

doi:10.1002/zamm.201700313

Cited by 2 publications

(1 citation statement)

References 32 publications

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“…In the case of pressure-independent plasticity, the singularity in solution behavior may significantly affect the temperature field near the singular surface [30]. This effect is due to the plastic work rate, which is involved in the heat conduction equation.…”

Section: Discussionmentioning

confidence: 99%

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

et al. 2019

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The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

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Section: Discussionmentioning

confidence: 99%

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

et al. 2019

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Effect of Strain Hardening Laws on Solution Behavior Near Frictional Interfaces in Metal Forming Processes: A Simple Analytical Example

2020

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The main objective of the present paper is to compare, by means of a problem leading to a closed-form solution, the qualitative behavior of solutions based on three strain hardening laws: Swift’s law, Ludwik’s law, and Voce’s law. The boundary value problem involves the maximum friction law as one of the boundary conditions. Such features of the solutions as nonexistence and singularity are emphasized. An important feature of Swift’s and Ludwik’s laws is that the equivalent stress approaches infinity as the equivalent strain approaches infinity. On the contrary, Voce’s law involves saturation stress as one of the constitutive parameters. This qualitative difference in the equivalent stress behavior as the equivalent strain approaches infinity results in the qualitative difference in solutions’ behavior. In particular, Swift’s and Ludwik’s hardening laws are compatible with the regime of sticking independently of other conditions. In the case of Voce’s law, the solution under sticking conditions may break down. Moreover, Voce’s law predicts intensive strain levels near the friction surface at sliding, and the other strain hardening laws do not. Thin layers of intensive plastic deformation often occur near frictional interfaces in metal forming processes. Voce’s law predicts the occurrence of such layers without any additional assumptions.

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An efficient method of analysis of heat transfer during plane strain upsetting of a viscoplastic strip

Cited by 2 publications

References 32 publications

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

Effect of Strain Hardening Laws on Solution Behavior Near Frictional Interfaces in Metal Forming Processes: A Simple Analytical Example

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