Evolution Equation of Creep Damage Under Stress Variation

Design and assessment of structural components at elevated temperature are very significant for ensuring the safety. Lear damage accumulation (summation of creep time fraction) is widely used to predict creep rupture time under stress and temperature variation. Life prediction of creep under stress variation by creep damage mechanics of Kachanov-Rabotnov concides with that of linear damage accumulation model. However, creep rupture time under stress variation is essentially the nonlinear problem. A modified evolution equation of creep damage by Kachanob-Rabotnov is formulated by memory effect of the previous stress. The evolution equation of creep damage consists of tow terms as follows:(1) the power damage law of Kachanov-Rabotnov, (2) acceleration anad deceleration by memory effect of the previous stress. The memory effect of the previous stress gradually disappears under the present stress. Additional internal state variable describing this effect is defined and the evolution equation is formulated in order to approach the present stress value from previous stress. The evolution equation of creep damage can be extended to the multiaxial state of stress with isotropic creep damage (scalar) and anisotropic creep damage (2

nd

symmetric tensor) proposed by Murakami and Ohno. Creep constitutive equation (McVetty type) for damaged material is formulated by the conventional creep damage theory. The model is lacking in the representation of the transient creep after increased stress. Micrographs of specimen ruptured under constant stress and stress variation are observed and creep damage mechanisms are discussed. After material constants are identified by describing creep curves at constant uniaxial stress, the validity of the proposed theory is discussed by the theoretical predictions with the corresponding experiments on tough pitch copper under nonsteady uniaxial stress at 250°C. The prediction of creep rupture time by the present theory is fairly good with the experiment results under stress variation.