Evaluation of Fracture Behavior pf Functionally Graded Material Using Computational Methods

Abstract

newline Fracture behavior in functionally graded materials (FGMs) is complex and newlinechallenging to predict due to the continuous variation in their material newlinecomposition. Predicting failure and improving material design require newlineunderstanding fracture dynamics in FGMs. The constant changes in material newlineproperties can influence how cracks initiate and propagate. Because of variations newlinein material toughness over the gradient, cracks propagate differently than in newlinehomogeneous materials. newlineThe primary objective of this research is to design a functionally graded newlinematerial (FGM) beam with spatially varying mechanical properties along both newlinethe thickness and length directions by employing the dummy thermal load newlinetechnique. This approach allows for the simulation of continuous material newlinegradation in a computationally efficient manner. The second objective is to newlinevalidate the numerical model of the FGM beam using experimental data available newlinein the literature [27], ensuring the reliability and accuracy of the developed newlinesimulation framework. The third objective focuses on conducting a detailed newlineparametric study involving various crack lengths to evaluate the corresponding newlinevalues of the dimensionless h function, which characterizes the plastic newlinecomponent of the J-integral in the context of fracture mechanics. Lastly, the newlinefourth objective is to investigate the extended finite element method (XFEM) for newlineisotropic materials, and subsequently apply this understanding to analyse crack newlinepropagation behavior in the functionally graded beam under different loading and newlinecrack configurations. newlineThis study presents the fracture behavior of a functionally graded material newline(FGM) beam using a Single Edge Notch (SEN) specimen. Initially, the FGM newlinebeam is modelled by considering dummy thermal loads wherein the temperature newlineloads are used to assign the varying material properties to create the FGM beam. newlineAfter that, a through crack and part through crack are incorporated in the FGM newlinebeam to conduct the three-point bending test for observing the influence of newlinevarying crack length on stress intensity factors and J-integral. The results show newlinethe effect of localization through crack and part-through crack on stress intensity newlinefactor and J-integral, wherein the fracture parameters increase as the crack length newlineincreases. The individual contribution of fracture parameters in the elastic and newlineplastic regions is evaluated, and the elastic and plastic values of J-integral are newlineestimated from the total values of J-integral. Also, the plastic influence function, newlinei.e., h function values, which is dependent on the geometry of the components, newlinematerial properties, and crack size, is estimated. newlineAlso, the study is to determine the crack initiation angle and stress field at newlineand around the crack tip during initial crack propagation in a cracked beam of a newlinefunctionally graded material (FGM). The distribution of stresses developed in the newlinevaried elastic modulus directions is determined numerically using the extended newlinefinite element method (XFEM). A complete numerical analysis has been newlineperformed using a finite element model to evaluate the level of crack angle and newlinestructural stresses in the crack tip zone, crack growth zone and crack propagation newlinezone. An XFEM subroutine file was used to develop the enrichment function newlinemodel to simulate the crack growth process during the numerical analysis. It was newlineseen that high crack initiation angle arises in large initial crack length and that as newlinethe initial crack length a increases the crack initiation angle and#1012; also increases. newlineIn the crack tip region, the axial stresses are tensile and exhibit tensile behaviour newlinealong the elastic modulus ratio direction up to a depth of more than 45% of the newlineheight of FGM beam. In contrast, the shear stresses were found to be significantly newlinevolatile. The results display that the stresses produced at the outer surface region newlineof the crack zones are affected by the expansion of the crack tip zone. During the newlinecrack growth process, the bending effect created is principally responsible for the newlinedistribution of stresses in the crack zone. newlineCrack propagation angles and crack propagation paths for the FGM beam newlineloaded in three-point bending and four-point bending loading conditions are newlineobtained to conduct a comparison study. An initial crack/defect is incorporated newlinein the FGM beam at the bottom mid location, and the beam is considered a simply newlinesupported beam. The same boundary conditions are applied to it. A detailed newlinecomparison of crack propagation paths is made between the three and four-point newlinebending loading conditions. In case of three-point bending loading, only mode I newlinecondition of failure is occurring. In contrast, in case of four-point bending newlineloading, all three modes of failure, i.e., mode I, II and III, are occurring, also called newlinemixed-mode failure condition.