The creep behaviors of TA2 and R60702 at low and intermediate temperature were presented and discussed in this paper. Experimental results indicated that an apparent threshold stress exhibited in the creep deformation of R60702. Meanwhile, the primary creep phase was found as the main pattern in the room temperature creep behavior of TA2. Compared with exponential law, the power law has been proved to be a proper constitutive model in the description of primary creep phase. It also showed that θ projection method had its significant advantage in the evaluation of accelerated creep stage. Thus, a composite model which combined power law with θ projection method was applied in the creep curves evaluation at low and intermediate temperature. Based on the multiaxial creep deformation results, the model was modified and discussed. A linear relationship existed between composite model parameters and applied load. Finally, the creep life could be accurately predicted and the composite model method is suitable for application in low and intermediate temperature creep life analysis.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

The extended finite element method (XFEM) is now widely used in crack simulations and the direction of propagation of the XFEM crack in SS-304 has been quite interesting. This paper discusses the direction,θ(+ve in anti-clockwise direction), of the XFEM crack (under mode-I) propagation based on the von Mises stress-field around the crack-tip for static loading under the light water reactors (LWRs) conditions. The Mises core region from the crack-tip is chosen for β=〖90〗^o, the angle between the load and the initial crack. Experimental data for LWRs’environment is obtained and the simulations have been carried out applying three different static loads and results for the direction of the crack are calculated by measuring the stress-field around the crack-tip. It has been found that the direction of the XFEM varies inversely as the stress-field around the crack tip is increased. The computational results have been compared with the numerical results based on the minimum strain energy density criterion[S-criterion].