Residual stresses in crystallizable materials

The phase transition rate in the crystallization of polymeric materials is of the same order as the rates of the heat exchange processes accompanying crystallization. Consequently, the boundary between phases becomes spatially dispersed. This excludes the possibility of using methods based on the front transition model proposed for metals to calculate residual stresses in plastics.148 It is possible to split the general problem and to find the temperature-conversion field independently. Then, assuming that the evolution of temperature T(x,t) and degree of crystallinity a(x,t) in time t and in space (x is the radius vector of an arbitrary point in a body) is known, we can analyze the mechanical problem.143 

Calculation of residual stresses in crystallizable materials is primarily based on the assumption that these materials can be treated as a two-component mixtures of initial and final products, as indicated in Eq. (2.97). In this case, the share of both components is determined by the degree of crystallinity a, which is changing in time. The initial product is a melt, for which a = 0 the final 

In order to derive the determining physical equation for the stress-deformation state of a two-component mixture, let us consider the expression for the change in the elastic potential energy during a continious transition from a liquid to a solid phase. Let this transition occur at time t = to and let the quantity of material that undergoes the transition be equal to the increase in the degree of crystallinity Act. The specific elastic potential characterizing the new state of the material up to the time of a new transition can be written as 

The detailed expressions for both components of the total elastic potential are as follows  

Let us consider the n step of the transformation Aan at time tn. Now, it is possible to write down the equation for the elastic potential of the material up to time tn+i, when the next transformation Aan+l occurs  

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