Prediction of Impact Force and Duration Due to Low-Velocity Impact on Circular Composite Laminates

Two simple and improved models — energy-balance and spring-mass — were developed to calculate impact force and duration during low-velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was a transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. In the energy-balance model, a balance equation was derived by equating the kinetic energy of the impactor to the sum of the strain energies due to contact, bending, transverse shear, and membrane deformations at maximum deflection. The resulting equation was solved using the Newton-Raphson numerical technique. The energy-balance model yields only the maximum force; hence a less simple spring-mass model is presented to calculate the force history. In the spring-mass model, the impactor and the plate were represented by two rigid masses and their deformations were represented by springs. Springs define the elastic contact and plate deformation characteristics. Equations of equilibrium of the resulting two degree-of-freedom system, subjected to an initial velocity, were obtained from Newton’s second law of motion. The two coupled nonlinear differential equations were solved using Adam’s numerical integration technique. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data.