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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.

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Embedding fiber optic sensor (FOS) in fiber reinforced composites caused resin pockets and geometric disturbance of the reinforcing fibers around the optical fiber. The disturbance angle varied from 6.2 to 8.2 and the resin pocket area varied from 7 to 10 times the cross-sectional area of the sensor. These two act like defects and cause premature failure initiation. Failure initiation was hypothesized as due to transverse stress concentration. A static experimental study was conducted to evaluate the effect of an embedded optical fiber in unidirectional composite laminates. Inclination of FOS with respect to reinforcing fiber (loading direction) varied from 0 to 90 and the laminate thickness varied from 8 to 20 plies. The embedment had practically no loss of tensile modulus and about 10% loss of tensile strength while compression strength reduction was as large as 40%.

Clamped circular composite plates were analyzed for static equivalent impact loads. Three plate sizes-25.4, 38.1, and 50.8 mm radii-made of quasi-isotropic graphite/epoxy laminate were analyzed. The analysis was based on the minimum total potential energy method and used the von Karman strain-displacement equations. A step-by-step incremental transverse displacement procedure was used to calculate plate load and ply stresses. The ply failure region and modes (splitting and fiber break) were calculated using the Tsai-Wu and the maximum stress criteria, respectively. Reduced moduli were then used in the failed region in subsequent increments of analyses. The analysis predicted that the failure would initiate as splitting in the bottom-most ply and then progress to other plies. Larger radii plates had a lower splitting threshold (load or energy) and a higher first-fiber failure threshold. The size and shape of the ply damage regions were different for different plies. The bottom ply damage was the largest and elongated in its ply-fiber direction. Calculated splitting damage for a 25.4 mm radius plate agreed with reported test data. a a c A U ,AI c;,c 2 E Err,Eee F's G h N L R ,N d P r,B,z s u u V w W0 X,X r Y,Y'x,y,z Nomenclature = plate radius, m = contact radius, m = constants defined in Appendix = radial displacement constants = constants; C\ = C l w 2 0 /a 3 , C 2 = C 2 Wo/a 4 = modulus, Pa = lamina stiffness in r-6 system, N/m 2 = lamina strength parameters, defined in Appendix = shear modulus, Pa = plate thickness, m = number of layers = number of divisions in radial and circumferential directions, respectively = plate load, v N = load intensity, N/m 2 = polar coordinates, m, deg, m, respectively = average radius of a typical element (r=rj, see Appendix) = lamina shear strength, Pa = strain energy, N • m (J) = radial deflection, m = potential energy due to loading, N • m = transverse deflection, m = central, transverse deflection, m =iamina tensile and compressive strengths in fiber direction, Pa = lamina tensile and compressive strengths perpendicular to fiber direction, Pa = Cartesian coordinates, m a.= ply fiber angle 0 =2ir-a-6 A Jk = area of a typical element (see Appendix) e = in-plane strain 0 = tangential coordinate at the center of a typical element II = total potential energy, N • m v -Poisson ratio a = in-plane stress, N/m 2 Subscripts i,j,k = dummy subscripts, range of l-N L , l-N R , and 1-JV0, respectively I = longitudinal (fiber) direction t = transverse (fiber) direction r = radial direction 6 = circumferential direction

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