Use of Symbolic Manipulator Software in Teaching Classical Elasticity

The use of a symbolic manipulator in the graduate level Theory of Elasticity course is presented in this paper. A symbolic manipulator is capable of conducting mathematical procedures (integration, differentiation and solution of equations) which are used in solving elasticity problems. It is shown in this paper that a symbolic manipulator is a powerful tool to solve lengthy and mathematically tedious problems. This is illustrated by three examples which are solved using MACSYMA

Fracture Mechanics of Composites with Nonhomogeneous Interphases and Nondilute Fiber Volume Fractions

A linear elastic fracture mechanics model is developed for a periodic composite geometry with a single cracked layer under uniform longitudinal strain. The interface between the fiber and the matrix can be nonhomogeneous, homogeneous or perfect. Four fracture mechanics models are considered: 1. (1) dilute fiber volume fraction composite with nonhomogeneous interphases. 2. (2) periodic composite with nondilute fiber volume fraction. 3. (3) periodic composite with irregular fiber spacing near a matrix layer. 4. (4) hybrid composites with more than one type of fiber. The stress intensity factors at the crack tips and the interface stress fields are studied to understand the fracture mechanics of composites as a function of the relative elastic moduli of the fiber, the matrix and the interphase, and the global and local fiber volume fractions

Effect of Stacking Sequence on Micro-Cracking in a Cryogenically Cycled Carbon/Bismaleimide Composite

An apparatus was developed to thermally cycle coupon-sized mechanical test specimens to −196 °C. Using this device, IM7/5250-4 carbon/bismaleimide cross-ply ([0/90]2S and [90/0/90/0/90/0/90/0/90]) and quasi-isotropic ([0/45/−45/90]S) laminates were submerged in liquid nitrogen (LN2) and returned to room temperature 400 times. Ply-by-ply micro-crack density (transverse cracks), micro-crack span, laminate modulus, and laminate strength were measured as a function of thermal cycles. The composite micro-cracked extensively in the surface plies followed by sparse micro-cracking of the inner plies. The tensile strength of the two blocked lay-ups (lay-ups with adjacent plies of the same orientation) decreased by 8.5% after 400 cycles. Sectioning of the samples revealed that the micro-cracks in the surface plies spanned the full width of the sample while many of the micro-cracks observed on the edge of the inner plies did not extend to the center of the samples, implying that a rectangular specimen with exposed free edges may result in a significantly different micro-crack density than a sample without free edges