Physics of residual stresses in uniform materials

There are two possibilities first, nonuniform or multicomponent polymer materials. Internal stresses may appear due to differences in the properties of various parts of an article and the existence of phase boundaries. Second, uniform materials, which seem quite homogeneous, can be amorphous or polycrystalline.The physics of the development of residual stresses in such materials will be discussed in this section. 

Residual (or inherent) stresses are self-balancing stresses that exist throughout the volume of a body in the absence of external forces. The appearance and growth of residual stresses in non-loaded articles are typical of materials prepared by the reactive processing. A general source 

One further reason for the development of residual stresses should be mentioned. This is the heterogeneity of the final state of a material which may occur even if the initial reactive mixture was homogeneous. This phenomenon is related to the differing diffusion rates of the various components of the reactive mass during a chemical reaction. This localized distribution of concentrations can be frozen upon solidification of the material. 

The primary reason for the appearance of inherent stresses is inhomogeneity of the temperature and conversion fields within an article. Therefore calculations of the T(z,t) and a(z,t) functions, which were discussed in Section 2.3, are the basis for estimating residual stresses. It is generally necessary to consider functions of all three coordinate directions. In many cases, it is important to know the final stress distribution and its change in time this is why time t enters the functions T(z,t) and a(z,t) as an independent argument. 

In the majority of practical important situations, it is reasonable to neglect heat output due to deformations and its possible influence temperature and reaction rate. This simplifies the problem and splits it into two independent parts first, calculation of the temperature and conversion fields, and second, estimation of the stresses from previously determined temperature and conversion 

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