The influence of film-substrate modulus difference

The general behavior of a long straight dislocation parallel to an interface between two isotropic elastic materials is well established. A configurational force acts on the dislocation due to its proximity to the interface. The direction of the force is normal to the interface, a direct consequence of the invariance of the conhguration under translation in any direction within the interface. The magnitude of the force varies with the inverse of the distance from the interface and, hnally, whether the force is attractive or repulsive depends on the relative magnitudes of the elastic constants of the two materials. For a screw dislocation, the force exerted by the interface 

The complete solution for the case of a screw dislocation in a configuration consisting of a layer of uniform thickness bonded to a substrate has been provided by Chou (1966). The critical thickness analysis proceeds by calculating the work Wd r]) that must be done to insert a dislocation into the material at a distance rj from the interface, and then comparing the result to the work that is done by the background mismatch stress 

To this level of accuracy, the work of formation of the dislocation is 

When ky = 0, it is evident that this result reduces to the appropriate limit for a homogeneous material given in (6.44). Furthermore, if /ig /if (/is /tf)i then the work required to form a dislocation anywhere in the film is increased (decreased) from the corresponding result for a homogeneous material, as 

For the dislocation to be strain-relieving, it must satisfy the condition that )rab 0. There is no loss of generality in assuming that 7m 0 and fe 0 separately if the signs are actually opposite to these in any particular situation, then 7m and b can be understood as magnitudes. 

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