In this paper a review is given about the fracture mechanical investig
ation of the thermal crack initiation and propagation in one of the se
gments or in the material interface of two- and three-dimensional self
-stressed bimaterial structures. The resulting boundary value problems
of the stationary thermoelasticity for uncracked and cracked 2-D and
3-D two-phase compounds are solved by means of Muskhelishvili's method
of complex potentials as well as of the finite element method. In the
case of 2-D bimaterial specimens orthogonal sets of principal stress
trajectories could be obtained in the corresponding cross sections, ch
aracterizing the self-stress fields in the associated two-phase compou
nds. Further, by applying an appropriate crack growth criterion based
on the numerical calculation of the total energy release rate of a qua
sistatic mixed-mode crack extension the further development of thermal
crack paths starting at the intersection line of the material interfa
ce with the external stress-free surface of 2-D and 3-D bi materials c
ould be predicted. In case of the disk-like two-phase compounds the th
eoretically predicted crack paths show a very good agreement with resu
lts gained by associated cooling experiments. Several specimen geometr
ies consisting of different material combinations and subjected to uni
form as well as non-uniform temperature distributions have been invest
igated by applying the relevant methods of fracture mechanics. Thereby
it could be stated that thermal cracks propagating in one segment of
a bimaterial only obey the rule G(II) = 0, whereas for interface crack
s a mixed-mode propagation is always existent where the Gn values play
an important role. Moreover, by applying the proposed crack growth cr
iterion the possible crack kinking direction theta of an interface cr
ack tip out of the interface could be predicted under the consideratio
n, of the finite thickness of an interlayer (interphase). Furthermore.
the influences of three-dimensional effects on the thermal crack prop
agation in axialsymmetrical bimaterial structures have been studied by
means of this crack growth criterion as well as by using the finite e
lement method. The numerical results show some remarkable differences
between. 2-D and 3-D bimaterials concerning the ther mal crack paths a
s well as the associated fracture mechanical parameters.