An Approximate Method for Determining the Temperatures Reached in Steady Motion Problems of Plane Plastic Strain

Bishop, Justin

doi:10.1093/qjmam/9.2.236

Cited by 66 publications

(8 citation statements)

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“…The stresses, a are related to the strain rate using equation (4) and retaining the mean pressure as a = -mp + p D E (12) &=Lu (13) Here the strain rate I? is defined as…”

Section: Coupled Thermal Plastic/viscoplastic Flow: Basic Equationsmentioning

confidence: 99%

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A general formulation for coupled thermal flow of metals using finite elements

Zienkiewicz

Oñae

Heinrich

1981

Numerical Meth Engineering

114

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SUMMARYA finite element formulation to deal with the flow of metals coupled with thermal effects is presented. The deformation process of the metal is treated using the visco-plastic flow approach and the solution technique for the coupled problem implies a simultaneous solution for velocities and temperatures. Some aspects of the numerical solution of the problem are given and in the last part of the paper some examples of steady-state extrusion and rolling problems showing the applicability of the method are shown.

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“…The stresses, a are related to the strain rate using equation (4) and retaining the mean pressure as a = -mp + p D E (12) &=Lu (13) Here the strain rate I? is defined as…”

Section: Coupled Thermal Plastic/viscoplastic Flow: Basic Equationsmentioning

confidence: 99%

“…and using the constitutive equation equation (12), and equation (21), the final system of equations for the coupled problem can now be written as…”

Section: Discretization Of the Thermal $Ow Equationsmentioning

confidence: 99%

A general formulation for coupled thermal flow of metals using finite elements

Zienkiewicz

Oñae

Heinrich

1981

Numerical Meth Engineering

114

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“…Recently, Zicke [11] developed an experimental technique for measuring the temperature distribution in the cross-section of hot forged pieces. To analyze heat transfer during heating and cooling as well as during deformation, finitedifference techniques have been used that predict the time-temperature history at various locations of a forging [12][13][14].…”

Section: Analysis Of Deformation and Heat Transfermentioning

confidence: 99%

“…For heat transfer analysis a finite-difference technique [6,16] was used to analyze heat conduction within forging as well as heat conduction to the dies. Since heat generation takes place during deformation, Bishop's approach [14] was used to include heat of deformation and friction. In this approach, the heat generation and heat transportation during a small time increment are regarded as taking place instantaneously and the time increment is then used for heat conduction.…”

Section: Analysis Of Deformation and Heat Transfermentioning

confidence: 99%

Forging Simulations and Properties Achievable for Large Waspaloy Forgings for Land-Based Gas Turbines

Shah

Monti

1981

Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation;

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This paper describes a computer simulation technique used to analyze the heat transfer and deformation encountered during various forging and heat treatment operations of a large Waspaloy forging for a land-based gas turbine. Using the same processing cycle on a sub-scale forging, it was possible to predict the property levels obtainable in the original forging. The subscale data are compared with the properties evaluated from a cut-up of a full-size forging showing good agreement. The tensile and stress rupture property levels achievable in the large forgings and the influence of processing variables on them are presented in this paper. Also presented are the data on the heat treat response for various section sizes.

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“…A theory that deals with viscoplasticity was described in Chap. 4. It was shown that the governing equations for deformation of viscoplastic materials are formally identical to those of plastic materials, except that the effective stress is a function of strain, strain-rate, and temperature.…”

Section: Introductionmentioning

confidence: 99%

Thermo-Viscoplastic Analysis

Kobayashi¹,

Oh²,

Altan³

1989

Metal Forming and the Finite-Element Method

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The main concern here is the analysis of plastic deformation processes in the warm and hot forming regimes. When deformation takes place at high temperatures, material properties can vary considerably with temperature. Heat is generated during a metal-forming process, and if dies are at a considerably lower temperature than the workpiece, the heat loss by conduction to the dies and by radiation and convection to the environment can result in severe temperature gradients within the workpiece. Thus, the consideration of temperature effects in the analysis of metal-forming problems is very important. Furthermore, at elevated temperatures, plastic deformation can induce phase transformations and alterations in grain structures that, in turn, can modify the flow stress of the workpiece material as well as other mechanical properties. Since materials at elevated temperatures are usually rate-sensitive, a complete analysis of hot forming requires two considerations—the effect of the rate-sensitivity of materials and the coupling of the metal flow and heat transfer analyses. A material behavior that exhibits rate sensitivity is called viscoplastic. A theory that deals with viscoplasticity was described in Chap. 4. It was shown that the governing equations for deformation of viscoplastic materials are formally identical to those of plastic materials, except that the effective stress is a function of strain, strain-rate, and temperature. The application of the finite-element method to the analysis of metal-forming processes using rigid-plastic materials leads to a simple extension of the method to rigid-viscoplastic materials. The importance of temperature calculations during a metal-forming process has been recognized for a long time. Until recently, the majority of the work had been based on procedures that uncouple the problem of heat transfer from the metal deformation problem. Several researchers have used the following approach. They determined the flow velocity fields in the problem either experimentally or by calculations, and they then used these fields to calculate heat generation. Examples of this approach are the works of Johnson and Kudo on extrusion, and of Tay et al. on machining. Another approach uses Bishop’s numerical method in which heat generation and transportation are considered to occur instantaneously for each time-step with conduction taking place during the time-step.

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An Approximate Method for Determining the Temperatures Reached in Steady Motion Problems of Plane Plastic Strain

Cited by 66 publications

References 0 publications

A general formulation for coupled thermal flow of metals using finite elements

A general formulation for coupled thermal flow of metals using finite elements

Forging Simulations and Properties Achievable for Large Waspaloy Forgings for Land-Based Gas Turbines

Thermo-Viscoplastic Analysis

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