Junqian Zhang

Analysis of multiple matrix cracking in [±θm/90n]s composite laminates. Part 1: In-plane stiffness properties

Abstract In previous work Fan and Zhang1 have proposed the equivalent constraint model (ECM) to predict the effect of matrix cracking on the in-plane stiffness properties of [±θm/90n]s composite laminates loaded in tension. The model is based on a two-dimensional shear-lag analysis where out-of-plane shear stresses in the constraining ±θ layers are assumed to vary linearly. In the present paper this shear-lag model is further developed to allow partial variation of shear stresses across the thickness of the constraining layers. The effect of non-uniform matrix cracking on the stiffness properties is also examined. Predictions of the new model compare favourably with experimental results for various multiply laminates and the discrepancy is less than that given by other theoretical models.

Analysis and design of a cylindrical magneto-rheological fluid brake

Abstract A magneto-rheological (MR) fluid brake is a device to transmit torque by the shear force of an MR fluid. An MR rotary brake has the property that its braking torque changes quickly in response to an external magnetic field strength. In this paper, the design method of the cylindrical MR fluid brake is investigated theoretically. The equation of the torque transmitted by the MR fluid within the brake is derived to provide the theoretical foundation in the cylindrical design of the brake. Based on this equation, after mathematical manipulation, the calculations of the volume, thickness and width of the annular MR fluid within the cylindrical MR fluids brake are yielded.

Analysis of multiple matrix cracking in [±θm/90n]s composite laminates. Part 2: Development of transverse ply cracks

Abstract In this paper the progressive transverse ply cracking in [± θ m /90 n ] s composite laminates is investigated theoretically. A general and simple expression for the energy release rate due to transverse matrix cracking is obtained using the potential energy approach in classical fracture mechanics and the assumption of a through-the-thickness flaw; thermal residual stresses are taken into account. The laminate resistance to crack multiplication is examined for both uniform and nonuniform crack spacing by substituting the measured applied stress/crack density data into corresponding energy release rate expressions. The resistance curve concept is employed to predict crack growth with increasing applied load. The results indicate that the assumption of uniform cracking and a resistance curve concept is a convenient and acceptable method for modelling crack initiation and multiplication in composite laminates.

In-situ damage evolution and micro/macro transition for laminated composites

In this paper, a theoretical formulation for the development of matrix cracking damage in composite laminates is presented. To describe the constraint effects on any layer k, an in-situ damage effective function, Λij(k), is introduced. An equivalent constraint model and a micro/macroscopic damage analysis are then developed to express Λij(k) explicitly in terms of constraint stiffness and thickness ratio as well as a damage state variable, D(k). The reduction of E, G and v in the in-situ damage state and a constrained damage evolution law incorporating residual curing strain are then derived through Λij(k) and dΛij(k)dD(k), respectively. A series of experimental results are correlated and some phenomena, such as the effects of the lamina thickness on damage initiation, damage evolution, and energy dissipation, are predicted and explained.

Delaminations induced by constrained transverse cracking in symmetric composite laminates

Abstract Transverse ply cracking and its induced delaminations at the φ/90° interfaces in [. . . /φi/φm/90n] s laminates are theoretically investigated. Three cracked and delaminated model laminates, one five-layer model (FLM) laminate [SL/φm/902n/φm/SR] T and two three-layer model (TLM) laminates I and II, [φm/902n/φm] T and [S′L/902n/S′R] T, are designed to examine constraining mechanisms of the constraining plies of the center 90°-ply group on transverse crack induced delaminations, where SL, SR, S′L and S′R are sublaminates [. . ./φi] T, [φi/. . .] T, [. . ./φi/φm] T and [φm/φi/. . .] T, respectively. A sublaminate-wise first-order shear laminate theory is used to analyze stress and strain fields in the three cracked and delaminated laminates loaded in tension. The extension stiffness reduction of the constrained 90°-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 effects of the immediate neighboring plies and the remote plies are identified by conducting comparisons between the three model laminates. It is seen for the examined laminates that the nearest neighboring ply group of the 90°-plies primarily affects the stiffness reduction and also the normalized strain energy release rate, whereas the influences of the remote constraining layers are negligible.

STRAIN ENERGY RELEASE RATE ASSOCIATED WITH LOCAL DELAMINATION IN CRACKED COMPOSITE LAMINATES

In the present paper the total strain energy release rate GT associated with delaminations that initiate from a matrix crack in a symmetric composite laminate is calculated using the potential energy approach in elastic fracture mechanics and a two-dimensional finite element analysis. Two laminate stacking sequences, [02904]s and [±25904]s, are examined with a matrix crack in the 90° plies and delaminations growing uniformly from the matrix crack tip in the 090 and − 2590 interfaces, respectively. The finite element analysis indicates that the Gl component (opening mode delamination) is reduced to zero for delamination length greater than one ply thickness; the shear mode (Mode II) dominates the growth of delamination. The total GT increases with increasing delamination length, but eventually approaches a constant asymptotic value, which is close to the GT result calculated from the analytical model. Finally, the analytical and numerical calculations show that G for local delamination decreases notably with increasing matrix cracking.

Effects of matrix cracking and hygrothermal stresses on the strain energy release rate for edge delamination in composite laminates

Abstract A simple theoretical model based upon the equivalent constraint model1,2 and a sublaminate approach3 is used to determine the strain energy release rate, Ged, in [± ϑ m 90 n ] s carbon/epoxy laminates loaded in tension. The analysis provides closed-form expressions for the reduced stiffness due to edge delamination and matrix cracking and the total strain energy release rate. The parameters controlling the behaviour are identified. The effect of laminate stacking sequence, matrix crack density and hygrothermal stresses on Ged is examined. Results show that the available energy for edge delamination is increased notably due to transverse ply cracking. Also, residual thermal stresses increase substantially the strain energy release rate and this effect is magnified by the presence of matrix cracking. Finally, predictions for the edge delamination onset strain are in acceptable agreement with experimental measurements.

A coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate: Part I, development of governing equations

Abstract This two-part contribution presents a novel and efficient method to analyze the two-dimensional (2-D) electromechanical fields of a piezoelectric layer bonded to an elastic substrate, which takes into account the fully coupled electromechanical behavior. In Part I, Hellinger–Reissner variational principle for elasticity is extended to electromechanical problems of the bimaterial, and is utilized to obtain the governing equations for the problems concerned. The 2-D electromechanical field quantities in the piezoelectric layer are expanded in the thickness-coordinate with seven one-dimensional (1-D) unknown functions. Such an expansion satisfies exactly the mechanical equilibrium equations, Gauss law, the constitutive equations, two of the three displacement–strain relations as well as one of the two electric field-electric potential relations. For the substrate the fundamental solutions of a half-plane subjected to a vertical or horizontal concentrated force on the surface are used. Two differential equations and two singular integro-differential equations of four unknown functions, the axial force, N , the moment, M , the average and the first moment of electric displacement, D 0 and D 1 , as well as the associated boundary conditions have been derived rigorously from the stationary conditions of Hellinger–Reissner variational functional. In contrast to the thin film/substrate theory that ignores the interfacial normal stress the present one can predict both the interfacial shear and normal stresses, the latter one is believed to control the delamination initiation.

A coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate: Part II, numerical solution and applications

This two-part contribution presents a novel and efficient method to analyze the two-dimensional (2-D) electromechanical fields of a piezoelectric layer bonded to an elastic substrate, which takes into account the fully coupled electric and mechanical behaviors. In Part I, we have obtained a system of governing integro-differential equations for the structure via a variational principle. This part presents a numerical solution algorithm of the integro-differential equations and the numerical results of some applications. A numerical algorithm for solving the system of four integro-differential equations with strongly singular kernels is developed. The convergence of the numerical algorithm is discussed. The numerical results suggest that the fully coupled electromechanical analysis is helpful for a better understanding of the performance of the piezoelectric sensor and actuator. The interfacial normal stress is much higher than the interfacial shear stress, suggesting that the interfacial normal stress causes a delamination initiation.

Cyclically thermomechanical plasticity analysis for a broken fiber in ductile matrix composites using shear lag model

Abstract 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, Δγp, are obtained. L−s and Δγp 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.