a matrix of a 50:50 mixture of phenol formaldehyde resin and polyvinyl butyral resin. Figure J-1 shows the scheme of cone formation in two-dimensional woven fabric composites during projectile impact. The yarns that the bullet directly contacts are called primary yarns; these yarns resist penetration and undergo deformation due to cone formation. The longitudinal compressive stress wave generated upon impact propagates outward along the yarn direction, forming a quasi-circular shape. The conical portion moves backward and stores kinetic energy by its motion.
Deformation of Yarns and Failure
When a PMC undergoes ballistic impact, the primary yarns deform and resist projectile penetration. The other yarns (called orthogonal yarns) also deform, but to a lesser extent due to primary yarn deformation; this process stores kinetic energy. During cone formation, strain is highest along the middle primary yarns in each layer of the composite. The highest overall strain is at the point of impact, and the strain falls off along the radial direction. After the cone forms, the top layers of the PMC are compressed, leading to an increase in the tensile strain of the yarns there. A linear relation between strain and depth along the thickness direction can be assumed; see Figure J-1. Once the strain is beyond the failure strain, sequential breakage will occur beginning at the top layer. This yarn failure absorbs additional kinetic energy.
Delamination and Matrix Cracks
During ballistic impact, transverse and longitudinal waves are formed. The geometry of the deformation influences the terminology used to describe the deformation:The waves that move out in the lateral direction (having both longitudinal and transverse polarization) from the point of impact are called transverse, and the waves propagating along the direction of the incident projectile are called longitudinal. A cone of deformation, quasi-lemniscate in shape, is formed due to transverse waves.7 As the longitudinal waves propagate along the yarns, attenuation occurs, leading to strain variations radially from the impact site in the target. The matrix has mechanical properties different from those of the yarns, but it must carry the same deformation lest delamination or slippage occur due to weak adhesion between the yarn and the matrix; there may be damage if the yarn strain is higher than the strain at failure in the matrix. As the material deforms, cracking and delamination will continue until total perforation occurs.8 Research has shown9 that initiation and propagation of delamination occur more frequently along the warp and fill directions than along other directions. Compared to conventional materials, composite materials contain numerous interfaces between the matrix and the fibers, providing multiple locations for cracking to occur. Energy absorption occurs through a combination of cracking, delamination, and shear banding (the latter is dependent on the plasticity of the matrix and possibly of the fibers). Typical shapes of delaminated regions after impact are shown in Figure J-2;10 the noncircular shape is attributed to the anisotropic nature of these materials (different paths of the stress waves, hence different distances that the stress information must travel).
During impact experiments on conventional carbon-fiber-reinforced plastic laminates, it was observed11 that a small area of the laminate was sheared off by the projectile
7Wu, E., and L.-C. Chang. 1995. Woven glass/epoxy laminates subject to projectile impact. International Journal of Impact Engineering 16(4): 607-619.
8Naik, N., and K. Reddy. 2002. Delaminated woven fabric composite plates under transverse quasi-static loading: experimental studies. Journal of Reinforced Plastics and Composites 21(10): 869-877.
9Wu, E., and L.-C. Chang. 1995. Woven glass/epoxy laminates subject to projectile impact. International Journal of Impact Engineering 16(4): 607-619.
10Naik, N. 2006. Ballistic impact behaviour of woven fabric composites: Formulation. International Journal of Impact Engineering 32(9): 1521-1552.
11Cantwell, W., and J. Morton. 1990. Impact perforation of carbon fibre reinforced plastic. Composites Science and Technology 38(2): 119-141.