Date of Award

Spring 2005

Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)


Mechanical Engineering

First Advisor

I. Joga Rao

Second Advisor

Rong-Yaw Chen

Third Advisor

E. S. Geskin

Fourth Advisor

Kwabena A. Narh

Fifth Advisor

Michael R. Booty


Nickel based single crystal Superalloys are finding wide spread use in high temperature gas turbines and other similar applications because of their superior high-temperature strength and creep properties as compared to the other materials. This is due to two factors: solid solution and precipitation strengthening of the gamma (γ) and gamma prime (γ') phases, and the elimination of grain boundaries. Creep of Nickel based single crystal Superalloys are caused by two primary mechanisms, dislocation creep and diffusion creep. Several factors that affect the creep life of Nickel based single crystal Superalloys are the specific microstructure, stress, temperature and rafting. Also, the creep behavior is highly anisotropic, with the degree of anisotropy varying with temperature.

This research is focused on developing a continuum model to simulate the creep response of Nickel based single crystal Superalloys that includes the influence of microstructure, anisotropy and recognizes the fact that these materials are inelastic and dissipate energy. A framework, built on the idea of evolving of natural configurations, utilizing the maximization of the rate of dissipation, has been used to formulate the model. The specific model is constructed by specifying forms of the stored energy and the rate of dissipation. The reduced energy-dissipation equation is used to obtain the constitutive relations for the stress and the maximization of the rate of the dissipation is used to obtain equations for the evolution of the underlying natural configurations through a rate equation for the inelastic strain.

The material constants for the model are obtained by comparing predictions of the model with experimental data. Solving the required boundary value problem is complicated due to the anisotropic material behavior. Two coordinate systems need to be introduced to solve the problem, since all the constitutive equations are developed in the crystal coordinate system while the stress and strain are usually measured in the specimen coordinate system. Transformation from the crystal coordinate system and specimen coordinate system is required. This is being done by introducing two 4th order tensors.

The main material parameters required to solve the equations are the components of the viscosity tensor, k. A parametric study is required to decide the viscosity tensor k, for a FCC material k has three independent components. We determine functional forms for these three components as a function of inelastic strain, temperature and stress. The specific forms are different for the low and high temperature regimes, because the underlying creep mechanisms are different. Simulation results, creep curves and strain vs. strain rate curve, clearly indicate the difference between the low and high temperature regimes. The parameters chosen fit the experimental data adequately.

This model was implemented into a Finite Element software ABAQUS by using a User-Defined Material Subroutine, UMAT. The Finite Element simulation results also showed a reasonable fit with the experimental data.