Thermally activated dislocation glide past obstacles

1 Thermally activated dislocation glide past obstacles 

Consider once again the specific phenomenon treated in Section 7.5, namely, a thin film bonded to a relatively thick substrate subject to a periodic fluctuation in temperature that varies over time between some initial relative temperature, T = T — To, where To is a reference temperature, and a higher temperature T = Tmax- The material is again assumed to be isotropic and to exhibit elastic-plastic behavior in this temperature range. The initial state at the time t 0 is characterized by an initial value of the biaxial stress cr(t), and all components of plastic strain are assumed to be zero initially. 

In the present discussion, it will be assumed that the plastic response is dominated by the thermally activated glide of crystal dislocations past discrete obstacles in the lattice. With reference to (7.78), the plastic rate equation proposed by Frost and Ashby (1982) has the form 

As noted in Section 7.6, the effective stress and equivalent biaxial strain for equi-biaxial tension of an isotropic film are ctm = a and = 2 eP. The condition that the total rate of strain parallel to the interface is zero implies that F t) + e t) + e t) = 0 or 

For a prescribed history T t) of temperature for t 0, relative to an initial absolute reference temperature Tq, and an initial value of stress ct(0) = (To, (7.82) is an ordinary differential equation for stress history. The 

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