Constitutive Equations of Crack Growth in Engineering Polymers.

A process zone (PZ) in a vicinity of crack front is commonly observed in structural materials including engineering polymers. Strain localization in form of plastic deformation, micro cracks, crazes, shear bands, micro cavitation and others constitute PZ. Formation of the micro defects is a material “defense” against high concentrations (singularities) of elastic crack tip fields. A strong interaction of micro defects with crack significantly modifies the elastic crack tip fields. It also affects the crack and PZ growth kinetics.  Crack and PZ are coupled and their evolution is considered as growth of a crack layer (CL). CL has been observed and characterized in amorphous, semi-crystalline and polycrystalline materials. The thermodynamic forces associated with crack and PZ evolution are defined as the conjugates to the corresponding CL growth rates in the expression for global entropy production due to CL propagation. The elastic energy release rates due to the crack and PZ “movements” in material space constitute the driving parts whereas the energy absorption by the new damage formed in CL “movements” are the resistive part of CL forces. The CL constitutive equations are formulated as relations between the crack and PZ growth rates and CL thermodynamic forces. These equations are employed to model CL propagation, the effect of PZ on crack growth resistance, variation of PZ size with crack advance leading to the commonly known R-curve behavior. It is also demonstrated how the crack-PZ interaction leads to a discontinuous (step-wise) CL growth under fixed load (creep conditions) observed experimentally. Assessment of a structural component lifetime in brittle fracture is briefly discussed.