Mathematical Modeling For Thermo-mechanical Stress Field Associated With A Propagating Crack In Homogenous Isotropic Materials

The main objective of this research is to develop mathematical modeling of the thermosrnmechanical stress field associated with the propagating crack in homogeneous isentropic materialsrnby using a temperature field that can be replicated in real world application. In most of existingrnwork, the temperature field is obtained by assuming the heat flux to be singular at the crack tip. rnHowever, such assumption could lead to a theoretical solution practically generating a temperaturernfield where the heat flux singular at the crack tip is not attainable. The mechanical design ofrnengineering structure in accordance with preexisting flaws is analyzed based on mechanicalrnloading and mixed mode thermo-mechanical stress field by using asymptotic solution of the steadyrnstate 2D temperature field equation. The solution is developed for the mixed mode thermomechanicalrnloadingrnconditionrnwhenrntherncrackrnpropagatesrnatrnarnconstantrnvelocityrninrnhomogeneousrnrnisentropicrnrnmaterials using an asymptotic approach. The solution is obtained by simultaneouslyrnsolving equation of motion defined as a function of displacement potentials, and perturbationrntheory for the solution of two-dimensional steady state temperature field equation. The perturbedrntemperature field equation is used to derive the first three terms of thermo-mechanical stress fieldrnequations by superimposing with the mechanical loading equation for the steady state propagatingrncrack. The thermo-mechanical stress field developed by the superimposition and the developedrnstress fields evaluated for the crack tip introduce at the center single edge when the value of ��rnexpressed by the interval [−��, ��]. Around the crack tip from the crack tip plasticity approximationsrntheory with the distance �� = 0.002�� at �� = 0 from the crack tip the thermo-mechanical stressrnfield is zero. And the graph of stress intensity factors interpreted on the behalf of stress field sincernthe stress and stress intensity factors have direct relationships. As the temperature and the heat fluxrnincreases the principal thermo-mechanical stress field such as ������, ������ and ������ increases andrnsimilar trend is observed for the stress intensity factors that the material is overstressed tornpropagate the initial crack.

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