Constitutive laws of plastic deformation and fracture. - Wu, Xijia. (University of Ottawa (Canada), 1992)
Environment assisted fatigue involves plastic deformation and degrading chemical reactions, which occur in a localized region ahead of the crack tip. Basically, transgranular crack growth proceeds by alternating slip processes. In this study, a transgranular fatigue crack growth rate model is developed on the basis of restricted slip reversibility (RSR), where transgranular fatigue crack growth rate is related to plastic deformation accommodation ahead of the crack tip (the product of the cyclic plastic strain range and the plastic zone size). The model is shown to take the form of the Paris equation with a power law exponent of 3 at positive R values. Fatigue crack growth behavior of a 8090 aluminum-lithium alloy has been examined by a series of tests using compact tension (C(T)) specimens with the load axis (a) parallel to the rolling direction (LT specimen), (b) inclined at 15$\sp\circ$ (L + 15$\sp\circ$), (c) inclined at 30$\sp\circ$ (L + 30$\sp\circ$), (d) inclined at 45$\sp\circ$ (L + 45$\sp\circ$) to the rolling direction. It has been found that in the LT, L + 15$\sp\circ$ and L + 30$\sp\circ$ specimens macroscopic cracks propagate along the plane normal to the rolling direction regardless of the deviation of loading directions and the fatigue crack in the L + 45$\sp\circ$ specimen propagates along the plane of specimen symmetry. Fatigue crack growth rate has been found to vary with the specimen orientation with the LT direction exhibiting the best fatigue crack growth resistance. These phenomena are discussed in terms of the crystallographic texture and the highly planar slip behavior of this ally. A revised RSR model is developed for the description of transgranular fatigue crack growth in aluminum-lithium alloys, where the effect of texture is related to a geometric factor for the favorable slip planes. Extension of the RSR model to environment assisted fatigue is also discussed. It is recognized that environmental effects contribute to crack propagation by the formation and rupture of an embrittlement zone in front of the crack tip. By incorporating a corrosion damage zone into the RSR model, fatigue crack growth rate in a deleterious environment is shown to be consists of two components: (i) mechanical fatigue which occurs by partially reversible slip and (ii) environmental enhancement of crack growth that results from the rupture of the embrittlement zone and is directly related to the characteristic dimension of this corrosion damage zone. In addition, fracture kinetics analysis is extended to crack growth behavior which exhibits the positive-negative temperature dependence. A constitutive law is derived from the general rate equation for a two-barrier consecutive system which represents stress corrosion cracking. The transition condition of the positive-negative temperature dependence is discussed and defined in terms of microstructural characteristic quantities (activation energy and work factor) and loading constraints (stress intensity factor and temperature). For the description of plastic deformation, a set of evolutionary rate equations is developed from deformation kinetics theory. Corresponding constitutive equations are derived for the dislocation glide mechanism, glide-plus-climb mechanism and diffusional flow. The operational equations are solved from the governing differential rate equation to determine deformation responses under different loading constraints.
Keywords: Engineering, Mechanical.