Transverse ply cracking and its induced delaminations at the ø/90 interfaces in […/:øi/øm/90n]s laminates are theoretically investigated. Three cracked and delaminated model laminates, one five-layer model (FLM) laminate [SL/øm/902n/øm/SR]: and two three-layer model (TLM) laminates I and II, [øm//902n/øm/] and [SL/902n SR] are designed to examine constraining mechanisms of the constraining plies of the center 90-ply group on transverse crack induced delaminations, where SL\SL, SR, SL and SR are sublaminates [.../C] [øi…] […/øi/øm] and [øm/øi/…] respectively, A sublaminate!wise _rst!order shear laminate theory is used to analyze stress and strain elds in the three cracked and delaminated laminates loaded in tension [The extension sti] ness reduction of the constrained 89-plies and the strain energy release rate for a local delamination normalized by the square of the laminate strain are calculated as a function of delamination length and transverse crack spacing[ The constraining e]ects of the immediate neighboring plies and the remote plies are identi_ed by conducting comparisons between the three model laminates[It is seen for the examined laminates that the nearest neighboring ply group of the 89-plies primarily a]ects the sti]ness reduction and also the normalized strain energy release rate\whereas the in uences of the remote constraining layers are negligible

The local cyclic plasticity of the interface around a broken fiber in ductile matrix composites under the in-phase and out-of-phase thermomechanical fatigue (TMF) loads is analyzed by using the single-fiber shear-lag model. The elastic, perfectly-plastic shear stress-strain relation is used to model the thermomechanical behavior of the fiber/matrix interface. It is shown that the alternating plastic shearing of the interface takes place under an appropriate combination of mechanical stress and thermal load. In the stress versus temperature diagram the so-called cyclic plasticity zone is identified. A new parameter, i.e. the cyclic plasticity length, L s, is found which is smaller than the yield length, Ls, caused by monotonic loading. The closed-form solutions for L s, Ls, the fiber stress profiles and the cyclic plastic shear strain range, p, are obtained. L s and p increase for both the in-phase and out-of-phase TMF conditions as the mechanical load and/or thermal load increase. The in-phase condition produces a higher plastic shear strain range than the out-of-phase condition does. The solutions obtained may be used for modeling fiber/matrix debonding caused by the fiber breakage under TMF fatigue loading.

this paper, the two-dimensional electromechanical coupling problems that a piezoelectric patch of finite size bonded to an elastic substrate are considered. A subdivision model that the single physical piezoelectric layer is mathematically divided into a number of thinner layers is proposed to analyze the electromechanical responses of the structures. Within each virtual sub-layer of the piezoelectric patch the electric displacement and normal stress in the axial direction are assumed to be linear functions of the thickness coordinate. Hellinger-Reissner variational principle for elasticity is extended to the systems of piezoelectric multi-materials. The governing equations that comprise one-dimensional di erential equations and integro-differential equations are rigorously derived from the stationary conditions of the variational functional along with substitution of the assumed electromechanical fields. The subdivision model satisfies all mechanical and electric continuity conditions across the virtual interfaces and the physical interface of piezoelectrics/substrate. The numerical solutions of the governing equations are conducted, and the convergence of the subdivision model is demonstrated.

The elastic properties of symmetric laminates containing a cracked mid-layer are predicted by using the equivalent constraint model (ECM) proposed recently by the authors. In accordance with the ECM methodology the symmetric laminates subjected to an in-plane tension/shear load are subdivided into such sublaminates as the cracked centrallayer, two nearest laminae and two homogeneous layers smeared from the remaining plies (if applicable). The

In this paper, the two-dimensional electromechanical coupling problems that a piezoelectric patch of finite size bonded to an elastic substrate are considered. A subdivision model that the single physical piezoelectric layer is mathematically divided into a number of thinner layers is proposed to analyze the electromechanical responses of the structures. Within each virtual sub-layer of the piezoelectric patch the electric displacement and normal stress in the axial direction are assumed to be linear functions of the thickness coordinate. Hellinger-Reissner variational principle for elasticity is extended to the systems of piezoelectric multi-materials. The governing equations that comprise one-dimensional differential equations and integro-differential equations are rigorously derived from the stationary conditions of the variational functional along with substitution of the assumed electromechanical fields. The subdivision model satisfies all mechanical and electric continuity conditions across the virtual interfaces and the physical interface of piezoelectrics/substrate. The numerical solutions of the governing equations are conducted, and the convergence of the subdivision model is demonstrated.