This paper employs the classical finite element method in simulation of crack propagation problems in a linear elastic and isotropic medium under mixed loading conditions. Two crack problems are considered; an inclined edge crack in a plate under tensile loading, and a shifted crack in a beam under three -point bending loading. The critical energy release rate criterion determines the threshold of propagation. The maximum tangential stress criterion determines the direction of crack propagation. Strain energy release rates are calculated using the virtual crack closure technique (VCCT). Deformation field is plane strain. The crack tip region is meshed with nonsingular 8-noded isoparametric quadrilateral elements. Realization of all numerical computations and demonstration of results are completely composed and written in MATLAB language. Results showed acceptable accuracy when compared with analytical ones, experimental work and those obtained by commercial ANSYS APDL program. KEY WORDSCrack propagation, virtual crack closure technique, mixed mode loading, crack path detection, maximum tangential stress criterion, and finite element method. Q8Eight-noded isoparametric quadrilateral element. ‫ܨܫܵ‬ Stress intensity factor. SM

This paper investigates numerically the enhancement of impact resistance of multiplayer steel armor to rigid and blunt projectiles. The monolithic armor always possesses higher ballistic resistance than the multilayer one of the same weight and areal density. In this work, the monolithic Weldox 460E steel armor is divided into three layers. The front and rear layers have the same thickness and they are thinner than the middle one. The thicker middle layer is prestressed by applying initial compressive strain. Then, the yield point of the middle layer is raised and the overall impact resistance of the prestressed multilayer armor is increased. The prestressed armor is impacted by a high-speed armor piercing (AP) blunt and rigid projectile. The impact resistance is macroscopically measured as the percentage reduction in the kinetic energy (KE) of the AP projectile. The percentage reductions in KE are calculated for the monolithic armor, equal and different thicknesses three layers armors with and without prestressing their middle layers. According to the presented computations, the maximum reduction in KE corresponds to the different thickness three layers armor having its thicker middle layer been prestressed.

Composite structures are distinguished by interfaces separating their different layers. These interfaces represent region of mismatches in mechanical and thermal properties of the adjacent layers. These regions are rich in cracks which are laying either on or sub-the interface in a direction parallel or perpendicular to it. In bi-material composites, interfacial crack is under mixed loading mode and stress intensity factor is a complex number even if the opening mode loading is applied. This paper solves for energy release rates and the magnitude of complex intensity factor of interfacial cracks using the classical stiffness finite element method. The path-independent integral is used to calculate the energy release rate during crack extension in the elastic plane strain deformation field. In this work, the crack tip region is meshed with fan-shaped non-singular four nodes isoparametric quadrilateral elements. In addition, a conical shape of function is employed in the numerical implementation of the equivalent energy domain integral. Realization of all numerical computations and demonstration of results are completely composed and written in MATLAB language. Meshing the computational domains and crack tip region are performed by a free downloadable program AUTOMESH-2D. Numerical results of stress intensity factor are found to be very close to the analytical and referenced values in both cases of bi-material and single layer systems. Furthermore, numerical values of-integral contours are very close to interfacial fracture energy measured experimentally between a hard film and a soft substrate.