Many engineering components, such as power plant steam pipes, aero-engine turbine discs, etc, operate under severe loading/temperature conditions for the majority of their service life. As a result, cracks can initiate and subsequently propagate over time due to creep. Damage mechanics is a robust method for the prediction of behaviour of components subjected to high temperature creep conditions and in particular, the Liu and Murakami model has proven to be a useful tool for the prediction of creep crack growth under such conditions. Previous methods for obtaining the constant of multiaxiality required for the use of such models, i.e. α, have relied upon the steady load testing of specimens designed to give a specific multiaxial stress-state, such as notched bars, and the failure time obtained. A series of results from finite element (FE) analyses based on the same geometry and loading/temperature conditions as the experiment, each performed with a different α-value, are then interpolated in order to identify the α-value which results in the same failure time, tf , as that of the experimental test. However, the stress-state present within such a specimen geometry (and therefore the α-value obtained) does not reflect the multiaxial severity of the stress state ahead of a crack tip. Therefore, for the application of the Liu and Murakami model to crack tip (i.e., creep crack growth) conditions, it follows that the α-value should be obtained from a multiaxial stress-state of equal severity to that to which it is to be applied, i.e. a crack tip. Therefore compact tension (CT) specimen creep crack growth data has been used in order to obtain the α-value. The process for the α-value determination is similar to that discussed for the notched bar, except that the interpolation of the time to failure is replaced with an interpolation of the time to a given crack length, ta . The resulting FE predictions based on CT and thumbnail crack specimen geometries, for a 316 stainless steel, are shown to be accurate in comparison to experimental results.
Hyde, C. J., Sun, W., & Hyde, T. (2010). A novel method for obtaining the multiaxiality constant for damage mechanics which is appropriate to crack tip conditions. Journal of Energy and Power Engineering, https://doi.org/10.1115/PVP2011-57166