SCHOOL OF MECHANICAL ENGINEERING SEMINAR Monday, June 18, 2012 at 15:00 Wolfson Building of Mechanical Engineering, Room 206

M.Sc. student of Prof. Leslie Banks-Sills, School of Mechanical Engineering, Tel-Aviv University

The arms industry is one of the largest in the world today. One of its challenges is to improve the defense against ballistic impact. Today there are many companies and factories that specialize in ballistic protection in cars, helicopters, other building applications and personal protective vests. Protection is achieved not only by the prevention of bullet penetration but also by the absorption of the high momentum of the bullet. Therefore, armor contains two layers. The first layer is generally made from a very hard ceramic material that shatters and blunts the projectile to prevent its penetration. The back layer is made of a ductile material that absorbs the remaining kinetic energy of the projectile. Another important factor in the design of armor is its weight. Lightweight armor will improve mobility and reduce energy consumption during transportation.

In recent years, there have been two main methods for investigating the ballistic behavior of targets: experiments and analysis using finite element software. As ballistic experiments are very costly, numerical analysis in this field has it advantages. By performing numerical finite element analysis, it is possible to save costs and perform preliminary design of the armor. In addition, ballistic computerized analysis enables greater understanding of the failure process. As compared to experiments, it is much simpler and faster to change the initial and boundary conditions of the problem to observe the effect on the results. However, it should be noted that there are many inaccuracies in numerical analysis. The main reason stems from the fact that empirical models do not always simulate properly the behavior of the real material. Therefore, it is always important to calibrate the simulations according to experimental data.

The present study deals with 3D finite element modeling using Abaqus Explicit (2010) Software. The investigation includes ballistic impact of a projectile on a boron carbide ceramic tile backed by an aluminum substrate. The projectile is made of steel and copper. The JH-2 model by Johnson and Holmquist (1994, 1999) was used to describe the mechanical behavior of the boron carbide. This model describes the mechanical behavior and failure of ceramics under extreme conditions of high strain, high strain rates and high pressures. The metals were described by the Johnson and Cook model (1983, 1985). This model characterizes the plastic behavior and failure of metals subjected to a wide range of strains, strain rates, temperatures and pressures. The Differential Efficiency Factor was used to calibrate the models based on experimental results. Then, several analyses were performed to evaluate the influence of internal pressure within the boron carbide on the ballistic resistance of the target. Numerical simulations were performed on a target subjected to a single and two successive impacts.

An improvement of the ballistic resistance was observed for a boron carbide tile subjected to internal pressure supported by an aluminum substrate. This occurred for both a single and double impact. It seems that even small internal pressures appear to improve the resistance against ballistic impact of the target.

M.Sc. student of Prof. Leslie Banks-Sills, School of Mechanical Engineering, Tel-Aviv University

This investigation deals with a delamination in an interface between two composite materials. Those materials are fiber-reinforced composites, that may be treated effectively as anisotropic. A delamination may occur during manufacture or service. The use of composite materials is growing, because of their high strength but low weight, in all fields of industry. Therefore, there is a need to investigate cracks or delaminations in structures, predict their propagation, and the circumstances of their failure.

This research focuses on a delamination between two layers of a fiber-reinforced composite material. The upper composite has fibers in the 900 direction, and the lower composite is a 00/900 weave. The upper material is transversely isotropic, whereas the lower material is tetragonal. The delamination in this case may be treated as a crack in an interface. The behavior of the stress and displacement fields near the delamination front was investigated. The first term of the asymptotic displacement and stress fields was determined analytically under plane deformation conditions, using the Stroh and Lekhnitskii formalisms.

Two different methods are extended for this case in calculating stress intensity factors. With the first method, displacement extrapolation, stress intensity factors are calculated directly from the delamination face displacements. The values of the displacements are determined at the nodes by means of a finite element analysis. The second method, the path independent three-dimensional M-integral, is an energy based method. With this method, both the analytic asymptotic fields and the actual fields, which were obtained from finite element analysis, are used. This two methods are independent of each other; therefore, they can be used for validation of the results obtained in this investigation. A three-dimensional numerical approach has been taken when analyzing this delamination.

Finally, several problems are considered in order to examine the accuracy of both methods. Three test cases are analyzed, with accurate results obtained by means of the M-integral. The displacement extrapolation method is not as accurate as the M-integral, and has been used to check the results obtained by the M-integral. In addition, three problems of a central crack in a symmetric balanced composite, made from three layers, subjected to different loading conditions are solved. The loadings include tension, in-plane and out-of-plane shear. In all cases, stress intensity factors, Griffith's energy and phase angles are obtained along the delamination front.

The Behavior of Ceramics Subjected to Dynamic Impact

Gil Noivirt