scholarly journals On Transient Thermal Stresses in an Infinite Thin Plate

1960 ◽  
Vol 12 (2) ◽  
pp. 69-73
Author(s):  
W. Derski
Keyword(s):  
Thin Plate ◽  
Thermal Stresses ◽  
Thermoelastic Stress ◽  
Additional Term ◽  
Elastic Solid ◽  
Rate Of Change ◽  
Stress And Strain ◽  
Infinite Extent ◽  
Transient Thermal ◽  
Strain Tensors

The presence of a non-steady state of temperature in an elastic solid gives rise to an additional term in the generalised Hooke's Law connecting the stress and strain tensors and terms involving the time rate of change of the dilatation. This time-dependent dilatation may produce so-called thermoelastic stress waves. The present note is concerned with the effects produced by these additional terms in a simple situation, in which the elastic solid is regarded as a thin plate of infinite extent. The distribution of temperature in the plate is produced by a point heat source of Dirac type.

X.—The Dynamic Stresses Produced in Elastic Bodies by Uneven Heating

1959 ◽  
Vol 65 (2) ◽  
pp. 143-176 ◽  
Author(s):  
G. Eason ◽  
I. N. Sneddon
Keyword(s):  
Additional Term ◽  
Elastic Solid ◽  
Rate Of Change ◽  
Stress And Strain ◽  
Heat Sources ◽  
Dynamic Stresses ◽  
Elastic Bodies ◽  
Infinite Extent ◽  
Uneven Heating ◽  
Strain Tensors

SynopsisThe presence of a non-uniform distribution of temperature in an elastic solid gives rise to an additional term in the generalized Hooke's Law connecting the stress and strain tensors and to a term involving the time rate of change of the dilatation in the equation governing the conduction of heat in the solid. The present paper is concerned with the effects produced by these additional terms in two simple situations. In the first, the elastic solid is regarded as being of infinite extent and the distribution of temperature in the solid is produced by heat sources whose strength may vary with time. In the second, the solid is supposed to be semi-infinite and to be deformed by prescribed variations in the temperature of the bounding plane and by heat sources within itself.

On Transient Thermal Stresses in Viscoelastic Materials With Temperature-Dependent Properties

1961 ◽  
Vol 28 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Rokuro Muki ◽  
Eli Sternberg
Keyword(s):  
Thermal Stresses ◽  
Constitutive Law ◽  
Time Dependent ◽  
Temperature Dependent ◽  
Infinite Extent ◽  
Temperature Dependent Properties ◽  
Transient Thermal ◽  
Temperature Time ◽  
Symmetric Temperature ◽  
Actual Test

This paper deals with the quasi-static analysis of transient thermal stresses in the linear theory of viscoelastic solids with temperature-dependent properties. The underlying constitutive law rests on the temperature-time equivalence hypothesis. Following an exposition of the theoretical framework exact solutions to two specific problems are deduced: The first concerns the thermal stresses in a slab of infinite extent, generated by a temperature field that depends arbitrarily on the thickness co-ordinate and time; the second application concerns the stresses produced in a sphere by an arbitrary time-dependent radially symmetric temperature distribution. The numerical illustrations of the results obtained include a quantitative study based on actual test data for a polymethyl methacrylate.

scholarly journals Thermal Stresses in Chemically Hardening Elastic Media With Application to the Molding Process

1974 ◽  
Vol 41 (3) ◽  
pp. 647-651 ◽  
Author(s):  
Myron Levitsky ◽  
Bernard W. Shaffer
Keyword(s):  
Residual Stress ◽  
Chemical Reaction ◽  
Thermal Stresses ◽  
Stress Component ◽  
Elastic Solid ◽  
Molding Process ◽  
Hardening Process ◽  
Exothermic Chemical Reaction ◽  
Component Parallel

A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

Sign in / Sign up

Export Citation Format

Share Document