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This paper presents a stochastic fracture response and crack growth analysis of mixed-mode stress intensity factors (MSIFs) for edge cracked laminated composite beams subjected to uniaxial, uniform tensile, shear and combined stresses with random system properties. The randomness in material properties of the composite material, lamination angle, laminate thickness, the crack length and the crack angle are modeled as both input uncorrelated and correlated random variables. An extended finite element method (XFEM) through the so-called M-interaction approach combined with the second-order perturbation technique (SOPT) and Monte Carlo simulation (MCS) is used to obtain the statistics in terms of the mean and coefficient of variation (COV) of MSIFs for edge cracked laminated composite beams. The effect of crack propagation on the MSIFs in the presence of tensile, shear and combined stresses using a global tracking algorithm is also investigated. The results using the present approach are compared with the available published results. A good agreement is seen whenever alternative results are available.

Piezoelectric materials possess special characteristics of electromechanical coupling behavior and thus have found numerous applications such as transducers, sensors, actuators. Fracture of piezoelectric materials has drawn substantial attention of the research community and is being widely investigated for predicting their failure. Most of the research on piezoelectric materials is based on impermeable crack conditions. In the present study semi-permeable crack boundary conditions has been analyzed using the extended finite element method (XFEM). Combined Mechanical and Electrical loading with quasi-static crack growth has been considered on a pre-cracked rectangular plate with crack at its edge and center. Stress intensity factors have been evaluated by interaction integral approach using the asymptotic crack tip fields. Effect of presence of minor cracks and holes have been analyzed on the intensity factors of semi-permeable major crack.

This work is focused to investigate the effect of various discontinuities like cracks, inclusions and voids for an orthotropic plate, to evaluate the normalized mixed-mode stress intensity factors (NMMSIFs) by implementing the extended finite element method (XFEM) under uniaxial tensile loading though considering the various numerical examples. The NMMSIFs are investigated with the interaction of crack, single- and multi-inclusions/voids for an orthotropic plate. The effect of NMMSIFs is analyzed for an orthotropic plate with several orthotropy axis orientations by changing the position of single- and multi-inclusions/voids while aligned, above and away with respect to an edge crack of the plate and for the both side inclusions/voids aligned the center crack. It is also investigated for the effect of various shapes of inclusions/voids for an edge crack orthotropic plate under uniaxial tensile loading using XFEM.

Engineering components are susceptible to numerous fatigue fracture issues in the context of long-term service. The failure of a large number of components is often accompanied by the propagation process of fatigue cracks. The elastic-plastic finite element simulation analysis method was employed to deeply investigate the crack propagation mechanism of aluminum alloy materials under fatigue loading in this paper. First, a finite element model of the CT specimen was constructed based on the constitutive relationship of elastic-plastic materials. Additionally, the crack propagation rule was defined using the extended finite element method (XFEM). Subsequently, the validity and accuracy of the simulation model were verified through fatigue crack propagation experiments using a 6005A aluminum alloy CT specimen. Finally, the simulation model was further utilized to investigate the effects of different stress ratios and specimen thicknesses on the crack propagation behavior. The research findings demonstrated that the crack propagation simulation model established by the elastic-plastic material constitutive and the XFEM is capable of accurately simulating the crack propagation behavior of aluminum alloys under fatigue loading. In the validation CT model, the crack of the simulation model expanded from 13mm to 30mm after 160,000 cycles, and the expansion rate ranged from $2.5\times 10^{-5}$ to $3\times 10^{-3}$. The height and width of the plastic zone at a crack length of 16 mm were 3.1mm and 2.0mm, respectively, which are very close to the experimental results. Furthermore, the simulation model also reveals the significant role of plastic flow at the crack tip in the fatigue crack propagation process.