In this study, a Jk-integral based computational method will be developed to conduct fracture analysis of fibrous composite laminates that possess variable fiber spacing. This study will be carried out for the fibrous composites exposed to not only thermal but also hygroscopic boundary condition, which results hygrothermal load. Formulation of the Jk-integral will be carried out by using the constitutive relations of plane orthotropic hygrothermoelasticity. One of the most important challenges of this study is to change Jk-integral formulation into domain independent form, because dealing with infinitely small domains in solving the integral would be frustrating. Developed form of Jk-integral will be merged to ANSYS, a finite element analysis software. Numerical results will be generated so as to assess the influence of variable fiber spacing on the modes I and II stress intensity factors, energy release rate, and the T-stress. For validation and comparison, some of the results are also obtained using Displacement Correlation Technique (DCT).

The main aim of this study is to utilize a Jk-integral based computational method in order to calculate crack tip parameters for orthotropic functionally graded materials (FGMs). The crack is subjected to mixed mode thermal loading. Mixed mode thermal fracture analysis requires the calculation of mode-I and mode-II stress intensity factors (KI ,KII ). In addition to stress intensity factors, energy release rate and T-stress are calculated by means of Jk-integral. Jk-integral is defined as a line integral over a vanishingly small curve. Since it is difficult to deal with a line integral on a vanishing curve , Jk-integral is converted to a domain independent form containing area and line integrals by the help of plane thermoelasticity constitutive relations. Steady-state temperature distribution profiles in FGMs and the components of the Jk-integral are computed by means of the finite element method. In both thermal and structural analyses, finite element models that possess graded isoparametric elements are created in the general purpose finite element analysis software ANSYS. In the formulation of Jk-integral, all required engineering material properties are assumed to possess continuous spatial variations through the functionally graded medium. The numerical results are compared to the results obtained from Displacement Correlation Technique (DCT). The domain independence of Jk-integral is also demonstrated. The results obtained in this study show the effects of crack location and material property gradation profiles on stress intensity factors, energy release rate and T-stress.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.

Apresenta-se um estudo, por meio do método dos elementos finitos, de problemas quase-estáticos de trincas em materiais anisotrópicos. Os fatores de intensidade de tensão em modo misto de carregamento foram determinados utilizando-se as metodologias da integral Jk, da correlação dos deslocamentos e da integral de fechamento de trinca modificada. Para a integral Jk, foi desenvolvida uma formulação baseada nas leis da conservação da elasto-estática e das integrais independentes do percurso. Na expressão, para a integral J2 levou-se em consideração o termo não singular da representação analítica do campo de tensões. Desta forma, foi obtida uma expressão analítica para a descontinuidade na densidade de energia de deformação, presente na integral J2. Com os valores da integral Jk, os fatores de intensidade de tensão puderam ser determinados diretamente. Com a mesma sistemática, desenvolvida para a integral J2, determinou-se a integral J1 para problemas envolvendo carregamento nas faces da trinca. Os resultados obtidos estão de acordo com os resultados presentes na literatura considerando ortotropia de material, ainda que para algumas configurações o mesmo é tratado como um caso de anisotropia geral. Assim como a integral J1 a integral J2 mostrou-se independente do contorno envolvendo a ponta da trinca. / A study is proposed based on crack quasi-static problems in anisotropic materials by the finite element method. The mixed-mode stress intensity factors were determined by the Jk integral, displacement correlation and modified crack closure integral methodologies. The Jk integral was derived from a conservation law of linear elasticity theory. In the formulation to obtain the J2 integral the non-singular term in the stress fields was considered. An analytical expression was obtained to discontinuity of the strain energy density in the crack faces, presented by J2 integral. A similar approach was applied to determine J1 integral in crack surface traction problems. The results confer with the results present in the literature considering orthotropic materials. In some configurations the problem is treated from general anisotropy theory. In the same way that J1 integral the path-independence property was established to J2 integral.