A three-dimensional micromechanical model based on the assumptions of simplified unit cell method (SUCM) is presented to obtain the closed-form solution for overall behavior of a unidirectional polymer matrix composite. The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. The Schapery single integral viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix. The presented analytical formulation is able to predict the effective response of the composite in any combination of normal and shear loading conditions. In particular, the effective creep response of the material in the off-axis loading is investigated. Prediction of the presented analytical model for the creep response of glassy amorphous polymer PMMA material shows good agreement with available experimental data. Furthermore, the predicted overall creep behavior of 10 and 908 off-axis coupons of graphite/epoxy composite demonstrate close agreement with experimental and other numerical results available in the literature. The overall creep-recovery of the graphite/epoxy composite in various off-axis loading conditions for several stress levels is also presented.
The Dynamic Relaxation (DR) technique together with finite difference discritization is used to study the bending behavior of Mindlin composite plate including geometric nonlinearity. The overall behavior of the unidirectional composite is obtained from a three-dimensional (3D) micromechanical model, in any combination of normal and shear loading conditions, based on the assumptions of Simplified Unit Cell Method (SUCM). The composite system consists of nonlinear viscoelastic matrix reinforced by transversely isotropic elastic fibers. A recursive formulation for the hereditary integral of the Schapery viscoelastic constitutive equation in multiaxial stress state is used to model the nonlinear viscoelastic matrix material in the material level. The creep tests data is used for verification of the predicted response of the current approach. Under uniform lateral pressure, the laminated plate deformation with clamped and hinged edged constraints is predicted for various time steps.
The geometrically nonlinear laminated annular plate structure with nonlinear viscoelastic orthotropic composite is considered using the dynamic relaxation (DR) method for the first time in the present study. The DR technique in conjunction with the finite difference discretization is used to study the behavior of a Mindlin plate. The plate is made of nonlinear viscoelastic orthotropic material expressed by the Schapery single integral model. A recursive-iterative formulation is implemented for the hereditary integral of the material. Under uniform lateral pressure and clamped and hinged edged constraints, the unsymmetrical laminated sector plate deformation is predicted in different times. The present results are compared with the elastic finite element (FE) generated numerical results. The correlations are very satisfactory. The load-center deflections for linear and nonlinear viscoelastic material plate along the symmetrical radial line for elastic and viscoelastic plate are illustrated. The dimensionless deflection results for up to 480 min are predicted to show the creep behavior of the material. Finally, the dimensionless stress couple results are obtained after 8 h creep time for a graphite/epoxy composite plate.
In this work, the thermomechanical viscoelastic response of a high temperature polymer matrix composite system made up of T650-35 graphite fibers embedded in PMR-15 resin is studied through a micromechanical model based on the assumptions of simplified unit cell method within a temperature range of 250–300℃ corresponding to aerospace engine applications. The advantage of this particular micromechanical model lies in its ability to give closed-form expressions for the effective viscoelastic response of unidirectional composites as well as each of their constituents. Using the experimental data of the creep behavior of thermostable PMR-15 polyimide, the micromechanical model is first calibrated to account for the effect of temperature. The resulting elastic and viscoelastic responses are found to be in good agreement with the existing experimental data. The validated model is then used to predict the behavior of the composite material under different combinations of thermal and mechanical loadings. The results clearly demonstrate the importance of accounting for the viscoelastic effect of the matrix material as the temperature increases. Current works on modeling temperature-dependent viscoelastic behavior of polymer matrix composites are mainly based on the assumption of thermorheologically simple material. However, through the present approach where the matrix is modeled as a thermorheologically complex material, the effect of temperature on the elastic and viscoelastic response of the composite system can be individually investigated.
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