A constitutive equation of cyclic strain softening for materials with low internal stress levels was derived from the rate equation. The study showed that cyclic strain softening is associated with stress relaxation and that the two phenomena are parallel over a high stress and low temperature range where thermally activated plastic flow in the two processes can be approximated with activation over a single energy barrier. The constitutive parameters were identical in both processes, leading to the recommendation that stress relaxation can be employed to determine the experimental variables for the understanding of the cyclic softening process.
The kinetics study is based on the energetically favourable crack propagation mechanism of double kink nucleation and its subsequent sideways spreading. The analysis was carried out on linearly elastic solids for the case when kink spreading is the rate controlling mechanism. The kink spread distribution is described by a differential equation that is identical with the mass and heat transport equations. The solutions of the differential equation represent the distribution function and the crack propagation velocity as a function of the bond breaking energy AG, the work W contributed by the applied stress, and of the temperature. When W ~> AGI2 the crack velocity increases exponentially with increasing work, decreases steeply with decreasing work, and reduces to zero when W~AG[2. The theory represents well the behavior of ceramic materials and some metals in Region I and at the threshold region of stress corrosion cracking. It is of special interest for stress corrosion cracking designs that the threshold stress intensity is independent of the temperature under the conditions of the present investigation.
Constitutive equations of cyclic strain and stress softening for materials with low internal stress levels are derived from the rate theory. The study shows that over the high stress and low temperature range where the description of plastic flow in cyclic softening can be approximated with activation over a single energy barrier, cyclic strain softening is well related to stress relaxation process while cyclic stress softening is related to creep process. The material structural characteristics for cyclic strain softening, cyclic stress softening and stress relaxation are identical. Subsequently, it is shown that cyclic stress and strain softening within the high stress and low temperature range can be evaluated from the constitutive equations using the material structural characteristics measured from a simple stress relaxation test.
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