Numerical Analysis of Surface Crack in Functionally Graded Coating Using Extended Finite Element Method

Abstract

Temperature distribution in structural elements in practical cases usually changes in two or three directions. Based on such facts, aiming at more effectiveness, a functionally graded material (FGM) coating, whose properties change in two directions called bi-directional FGM was introduced. This thesis aimed to model and investigate a mode I surface cracked coating-substrate problem with a bi-directional coating bonded to a homogeneous substrate under linear thermal loading and uniform stress. Sequentially Coupled three-dimensional thermoelastic analysis was used to investigate the stresses and the stress intensity factor (SIF) at various crack geometry dimensions under thermomechanical loads. The extended finite element method was utilized to model the problem in ABAQUS software. FORTRAN user subroutines for the FGM properties were developed and implemented into the ABAQUS package. The thermomechanical stress and stress intensity factor was solved by considering different parameters i.e., gradient index, cack aspect ratio, crack length, and temperature gradient. The applied remote stress was 100 MPa with maximum values of temperature employed ranging from 400 ℃ to 800 ℃. Thermo-mechanical stress field was evaluated and extracted from the crack tip for radian value and the stress intensity factor along the crack front was calculated for the crack with those parameters. The numerical results showed that the stress intensity factor was affected by the gradient. The maximum value of stress intensity value decreased from value for n = q = 0 to value for n = q = 1 by 52.56% for a/c = 0.7 and by 63.84% for aspect ratio a/c = 1. The decrease showed that the maximum stress intensity factor value of functionally graded coating was reduced compared to the same crack geometry and loading in a homogeneous material. For linear bidirectional coating types (n = q = 1) mode I stress intensity factors were obtained maximum at the symmetry surface while it was at free surface for homogeneous material coating. The crack stress intensity factor was also affected by thermal the loading and the gradient index that Maximum Stress intensity factor increased from value for n = q = 1 to value for n = q = 2 by 22.97% at 400 ℃ while by 23.6% at temperature 800 ℃. The results generally showed that the crack stress intensity factor can be minimized by controlling the loading and the gradient index for the crack in functionally graded coating.