Two Green’s function problems for rapid two-dimensional steady-state crack growth governed by fully coupled (dynamic) linear thermoelasticity are analyzed. In Problem A, normal and in-plane shear line loads move on the insulated surfaces of a semi-infinite crack growing at a subcritical speed. Problem B involves only normal line loads, but crack surface convection is allowed. Problem A involves, therefore, mixed traction/displacement boundary conditions, while Problem B also exhibits mixed thermal boundary conditions. Robust asymptotic forms based on exact solutions for related problems reduce Problems A and B to coupled sets of integral equations. Both sets exhibit both Cauchy and Abel operators, but are solved exactly. The solutions show that Mode II loading couples the tangential crack face separation and discontinuity in crack-face temperature changes, while crack surface convection enhances thermal response, especially at large distances. [S0021-8936(00)03101-9]

Issue Section:
Technical Papers
Keywords:
cracks, thermoelasticity, Green's function methods, integral equations
Topics:
Convection, Fracture (Materials), Thermoelasticity, Stress, Temperature, Steady state, Integral equations
1.
Noda
,
N.
,
Matsunaga
,
Y.
,
Tsuji
,
T.
, and
Nyuko
,
H.
,
1989
, “
Thermal Shock Problems of Elastic Bodies With a Crack
,”
J. Therm. Stresses
,
12
, pp.
369
–
384
.
2.
Freund, L. B., 1993, Dynamic Fracture Mechanics, Cambridge University Press, New York.
3.
Boley, B. A., and Weiner, J. H., 1985, Theory of Thermal Stresses, Krieger, Malabar, FL.
4.
Chadwick, P., 1960, “Thermoelasticity: The Dynamical Theory,” Progress in Solid Mechanics, Vol. 1, I. N. Sneddon and R. Hill, eds., North-Holland, Amsterdam.
5.
Brock
,
L. M.
,
1996
, “
Effects of Thermoelasticity and a von Mises Criterion in Rapid Steady-State Quasi-Brittle Fracture
,”
Int. J. Solids Struct.
,
33
, pp.
4131
–
4142
.
6.
Brock
,
L. M.
,
1999
, “
Rapid Crack Growth in a Thermoelastic Solid Under Mixed-Mode Thermomechanical Loading
,”
IMA J. Appl. Math.
,
62
, pp.
31
–
44
.
7.
Brock, L. M., 1999, “Effects of Crack Surface Convection for Rapid Crack Growth in a Thermoelastic Solid,” Int. J. Solids Struct., to appear.
8.
Brock
,
L. M.
, and
Georgiadis
,
H. G.
,
1997
, “
Steady-State Motion of a Line Mechanical/Heat Source Over a Half-Space: A Thermoelasodynamic Solution
,”
ASME J. Appl. Mech.
,
64
, pp.
562
–
567
.
9.
Brock
,
L. M.
, and
Georgiadis
,
H. G.
,
1999
, “
Convection Effects for Rapidly-Moving Mechanical Sources on a Half-Space Governed by Fully Coupled Thermoelasticity
,”
ASME J. Appl. Mech.
,
66
, pp.
347
–
351
.
10.
Ewalds, H. L., and Wanhill, R. J. H., 1985, Fracture Mechanics, Edward Arnold, London.
11.
Brock
,
L. M.
,
Rodgers
,
M.
, and
Georgiadis
,
H. G.
,
1996
, “
Dynamic Thermoelastic Effects for Half-Planes and Half-Spaces With Nearly-Planar Surfaces
,”
J. Elast.
,
44
, pp.
229
–
254
.
12.
Erdogan, F., 1976, “Mixed Boundary Value Problems in Mechanics,” Mechanics Today, Vol. 4, S. Nemat-Nasser, ed., Pergamon Press, New York.
13.
van der Pol, B., and Bremmer, H., 1950, Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge University Press, Cambridge, UK.
14.
Gradshteyn, I. S., and Ryzhik, I. M., 1980, Table of Integrals, Series and Products, Academic Press, New York.
15.
Brock
,
L. M.
,
1996
, “
Some Analytical Results for Heating due to Irregular Sliding Contact of Thermoelastic Solids
,”
Indian J. Pure Appl. Math.
,
27
, pp.
1257
–
1278
.
16.
Carrier, G. F., Krook, M., and Pearson, C. E., 1966, Functions of a Complex Variable, McGraw-Hill, New York.
17.
Sneddon, I. N., 1972, The Use of Integral Transforms, McGraw-Hill, New York.
18.
Abramowitz, M., and Stegun, I. A., 1970, Handbook of Mathematical Functions, Dover, New York.
19.
Muskhelishvili, N. I., 1975, Some Basic Problems in the Mathematical Theory of Elasticity, Noordhoff, Leyden.
20.
Stakgold, I., 1971, Boundary Value Problems of Mathematical Physics, Vol. 2, MacMillan, New York.
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