The effects of bridging in a 3D composite on buckling, postbuckling and growth of delamination

Abstract

Buckling and postbuckling solutions to circular delamination constrained by transversal restoring forces, which occur extensively in stitched or woven composites with three-dimensional (3D) reinforcement, are obtained by using von Karman's geometrically nonlinear thin plate theory by means of Taylor's series expansion. The through-thickness tows are assumed to provide continuous and linear restoring tractions, opposing the de¯ection of the annular delaminated region adjacent to a penny-shaped crack. When the end of the delaminated layer is clamped, and the de¯ection is permitted in the positive direction of the z-axis only, there exists a characteristic delamination radius a à for initial buckling. In the case that the initial delamination radius a 0 exceeds a à , it will consist of waves whose sizes decrease gradually, as they are apart from the delamination center with larger distances, and will usually not span the whole crack region. Therefore, buckling pro®les can be divided into two types:(1) lacking contact phenomena between the delaminated layer and the base plate; (2) having contact surfaces inside the delamination region. In this paper, growth laws of buckling, postbuckling and growth of delamination at lacking contact surface are discussed. The corresponding stability of the delamination growth under ®xed boundary load is studied, and the dependence of stable scope upon the fracture toughness of the composite and the elastic constant of bridging ®ber is summarized. It follows from the analysis that bridging can increase the load-bearing capacity of composite structure, improve its mechanical performances and restrain the growth of delamination. IntroductionOwing to their low weight and high strength, composite materials have been widely used in automobile, construction, and weight-sensitive aeronautical and astronautical industries [1±7]. However, composites delaminate on occasion due to imperfections in production technology and under high impact. This phenomenon generally causes unexpected degradation of structure strength. In order to exert larger potential of composite materials, two tasks must be accomplished ®rst: the analysis of the nature of buckling, postbuckling and growth of delamination, and the design of some effective methods for the repair of the composite structure by increasing its load-bearing capacity and decreasing its susceptibility to delaminations. In recent years, the ®rst aspect has been widely researched, and many useful results obtained have greatly contributed to engineering design, [2±7]. The second aspect however, has not caused much attention so far, [1,8,9]. It is well known that the through-thickness tows in 3D composites can bridge the delamination cracks and prevent buckling of the adjacent delaminated layers; therefore, while the ®bers do not eliminate delaminations, they do minimize the loss of strength under subsequent compression. It is, therefore, required to take into account the effects of bridging. Cox [1] researched initial buckling of one-dimensional delamin...

Construction of a physical-mathematical model of oscillations of the unbalanced vibrator of the pneumatic sorting table

“…The amplitude of the deflection of the center of the plate in the direction of action of the pulse, in accordance with (3), ( 4) and (10), is:…”

“…The results obtained in [9] concern only the continuous movement of the plate from the base, which is provided for in the statement of the problem. Article [10] considered the possibility of using the theory of plates with continuous contact from the base to calculate the strength of hard asphalt concrete road surfaces.…”

“…In them, in addition to direct problems of mechanics, several inverse problems of identification of external dynamic loads based on the results of experimental measurement of deflections or deformations of the hard surface are solved. The problems are reduced to the numerical solution of integral equations, with separate regularization, but study [10] does not concern round plates.…”