Pressurization of a Solidifying Sphere

1972 ◽  
Vol 39 (1) ◽  
pp. 71-77 ◽  
Author(s):  
K. H. Hsiao ◽  
J. E. Cox ◽  
P. G. Hedgcoxe ◽  
L. C. Witte
Keyword(s):  
Aluminum Alloy ◽  
Approximate Solution ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Steady State ◽  
Heat Conduction Problem ◽  
Solid Shell ◽  
Stress Distributions ◽  
Dimensionless Form ◽  
Molten Material

The pressurization in a solidifying sphere of molten material (initially at a uniform melting temperature) immersed in an infinite cooling medium is presented. The steady-state approximate solution applied to the heat-conduction problem with change of phase (the Stefan problem) provides the temperature distribution in the shell and rate of solidification, which can be employed in the evaluation of the pressurization stress and thermal stress distributions in the solid shell. Stress distributions are evaluated and plotted in dimensionless form. Additional results are presented for the specific case of aluminum alloy.

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.

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