Fatigue Life Prediction Using Unified Mechanics Theory in Ti-6Al-4V Alloys

Abstract

Fatigue in any material is a result of continuous irreversible degradation process. Traditionally, fatigue life is predicted by extrapolating experimentally curve fitted empirical models. In the current study, unified mechanics theory is used to predict fatigue life of Ti-6Al-4V under monotonic tensile, compressive and cyclic load conditions. The unified mechanics theory is used to derive constitutive model for fatigue life prediction using a three-dimensional computational model. The proposed analytical and computational models have been used to predict the low cycle fatigue life of Ti-6Al-4V alloys. It is shown that the unified mechanics theory can be used to predict fatigue life of Ti-6Al-4V alloys by using simple predictive models that are based on fundamental equation of the material, which is based on thermodynamics associated with degradation of materials.

Dynamic Equilibrium Equations in Unified Mechanics Theory

“…In this study, we attempt to introduce second law of thermodynamics in the Lagrangian system, using the unified mechanics theory. In the unified mechanics theory [8][9][10], each material point in a dynamics problem is defined in the space-time-TSI coordinate system. Hence the material point shall be a function of (x, t, Φ).…”

“…In the recent past, Boltzmann's model for the irreversibility of dissipative processes has been unified with the laws of Newton [8], called unified mechanics theory [9]. In the unified mechanics' theory (UMT) [9], dissipation mechanisms are represented by the Thermodynamics State Index (TSI) [9,10] of the system. The TSI represents the thermodynamic state of a physical system, as a function of entropy generation.…”

“…Hence, the unified mechanics' theory (UMT) explicitly introduces a new linearly independent axis in addition to Newtonian coordinates, x, y, z, and time [9,10].This concept was introduced [8][9][10][11] based on Boltzmann's statistical relation of entropy with the probability of microstates within the system. Several published works can be seen in the literature, which address various types of dissipation processes, such as fatigue in metals [8,[10][11][12], electromigration and thermomigration in nanoelectronics [13][14][15], damage in eutectic Pb/Sn solder joints [16][17][18], micromechanics of thermally induced dislocation annihilation [19], damage evolution in a particle-filled polymer matrix composite [20], damage due to concurrent thermal and vibration loading in electronic packaging [21], damage due to nanoindentation [22], etc. The TSI, Φ represents an index called Thermodynamic State Index (TSI), as shown in Figure 1, which is a linearly independent axis, spanning between zero and one.…”

“…The TSI, Φ represents an index called Thermodynamic State Index (TSI), as shown in Figure 1, which is a linearly independent axis, spanning between zero and one. The coordinate system in the unified mechanics theory (UMT) is explained in the literature [9,10] as shown in Figure 1. Let us assume that there is a 5-year-old boy with a terminal illness and 100-year-old sick man.…”

“…Where, ΔS represents total change in entropy calculated from the thermodynamic fundamental equation of the system, during the time, Δt. The terms, m , Φ , and R represent the molar mass, critical TSI value [10], and gas constant, respectively. If there are 'n' independent dissipation mechanisms in a system, general representation of the second law of unified mechanics theory [9], can be given as follows,…”