Zihui Xia

A unified periodical boundary conditions for representative volume elements of composites and applications

Abstract An explicit unified form of boundary conditions for a periodic representative volume element (RVE) is presented which satisfies the periodicity conditions, and is suitable for any combination of multiaxial loads. Starting from a simple 2-D example, we demonstrate that the “homogeneous boundary conditions” are not only over-constrained but they may also violate the boundary traction periodicity conditions. Subsequently, the proposed method is applied to: (a) the simultaneous prediction of nine elastic constants of a unidirectional laminate by applying multiaxial loads to a cubic unit cell model; (b) the prediction of in-plane elastic moduli for [± θ ] n angle-ply laminates. To facilitate the analysis, a meso/micro rhombohedral RVE model has been developed for the [± θ ] n angle-ply laminates. The results obtained are in good agreement with the available theoretical and experimental results.

A rate-independent constitutive model for transient non-proportional loading

Abstract A comprehensive yet relatively simple rate-independent constitutive model is presented. Most experimental observations such as strain amplitude effect, cross-hardening effect, erasure of memory property, etc., are simulated by the model. It is applicable to arbitrary complex non-proportional loading paths including cyclic loading. The material constants are comparatively few, and the procedure to determine them is outlined. The predictions of the model are compared to various experimental results and the agreement is found to be fairly good.

A meso/micro-mechanical model for damage progression in glass-fiber/epoxy cross-ply laminates by finite-element analysis

Abstract A three-dimensional multi-cell meso/micro-mechanical finite-element model has been developed for the prediction of the overall mechanical behavior of a [0,903,0]T glass-fiber/epoxy laminate, and for the study of damage mechanisms in fiber-reinforced polymer laminates. The epoxy matrix is represented by a non-linear viscoelastic constitutive model, which was incorporated into the finite-element analysis code, ADINA, through the user-defined subroutine. In addition, a damage criterion for the epoxy matrix is introduced into the finite-element model. Numerical results from the finite-element analysis are compared with experimental data, and it is found that both the predicted overall stress/strain response and the prediction of the initiation and propagation of the damage are in good agreement with the experimental results.

Evolution of Residual Stresses Induced during Curing Processing Using a Viscoelastic Micromechanical Model

The effect of viscoelasticity of matrix material on the evolution of processing- induced residual stresses in [0/90] glass fiber/epoxy cross-ply laminate has been investigated by a finite element micromechanical model. The micromechanical model is based on a periodic array of continuous fibers embedded in an epoxy matrix. The epoxy matrix is represented by a nonlinear viscoelastic model. The finite element residual stress analysis indicates that a higher cooling rate results in higher initial residual stresses in the laminate. However, the residual stress relaxes with time and tends to an asymptotic small value independent of the cooling rate. The effect of free edge surface on the generation of residual stresses is also investigated, and it is found that they are significantly different from those in the interior region. Although the coefficients of thermal expansion (CTE) for the individual constituents (glass fiber and epoxy matrix) are constant, the CTE for composite, on the other hand, is initially time-dependent due to the mismatch constraint and approaches an asymptotic value after a long stress relaxation period.

A constitutive model with capability to simulate complex multiaxial ratcheting behaviour of materials

An elasto-plastic constitutive model developed by the authors has been further extended and implemented into a user-supplied material model in conjunction with a commercial Finite Element Model (FEM) code, ADINA. As benchmark problems, comprehensive experimental data by Jiang and Sehitoglu (1994a,b) are compared with the numerical predictions of the model as implemented in the ADINA code. It is clearly shown that this material model has a capability to simulate the complex multiaxial and multi-step ratcheting behaviour of metals and alloys.

Mechanical behavior of Al2O3-particle-reinforced 6061 aluminum alloy under uniaxial and multiaxial cyclic loading

Abstract Uniaxial and biaxial (proportional and non-proportional) strain-controlled tests were conducted to obtain mechanical properties of 6061 aluminum alloy reinforced with Al 2 O 3 particles with 0.1 and 0.2 volume fractions. Thin-walled specimens were heat-treated in three groups, i.e. fully annealed (T0), solution and precipitation (T6) and as-extruded (F). The results indicaie that this composite material essentially has isotropic elasto-plastic properties similar to those of the matrix constituent, the aluminum alloy. It is rate-insensitive at room temperature. Under cyclic loading the composite strain-hardens during almost the entire cyclic life and it does not show a stable state for specimens prepared under F and T0 conditions. For T6 heat-treatment, cyclic hardening occurs only during the ftrst few cycles and thereafter the response is stable until failure. More strain hardening was observed under biaxial non-proportional cyclic loading in comparison with proportional cyclic loading. A fall in the elastic modulus is observed during cyclic loading with a relatively larger cyclic plastic strain, especially in biaxial cyclic loading in specimens with T0 and F conditions. Mechanisms of damage caused by the biaxial stress state are discussed on the basis of microscopic observations.

Micro/meso-scale damage analysis of three-dimensional orthogonal woven composites based on sub-repeating unit cells

The mechanical responses including damage mechanisms for surface and interior parts of three-dimensional orthogonal woven composite have been analyzed by the multi-scale finite element method. Based on fabric architecture and fiber volume fraction in the three-dimensional orthogonal woven composite, the meso-scale repeating unit cells model and micro-scale repeating unit cell model are established. The periodic boundary conditions are applied to the micro-repeating unit cell and meso-repeating unit cell models. Appropriate failure criteria and a post-damage constitutive model are used to simulate the failures of fiber/fiber-bundles and resin in the micro/meso-scale repeating unit cells. A new elastic material model with damage propagation is defined with the user-defined material subroutine in commercial finite element software package ABAQUS/Standard. Mechanical behaviors including initiation and propagation of damage in micro/meso repeating unit cells under different loadings have been simulated with the user-defined material subroutine and the ABAQUS/Standard. The simulation results are compared with the experimental observations and they are in good agreement.

Interface crack between two different viscoelastic media

The plane (including antiplane) problem of an interfacial crack between different viscoelastic (including viscoelastic and elastic) media is considered. By using the Laplace transform method, the viscoelastic problem is reduced to an associated elastic one. The corresponding elastic analysis results in the viscoelastic solutions in the transformed field. The crack tip fields and fracture parameters of the viscoelastic interface crack are derived through an approximate Laplace inverse transform method. As an example, numerical calculations for an interfacial crack between viscoelastic and elastic materials are carried out. It is shown that the simple formulae of the crack line (and tip) fields and fracture parameter (energy release rate) of the viscoelastic interface crack, derived by the approximate method, are quite accurate. When the bimaterial is subject to a remote uniform and constant tensile loading, the normal stress along the crack line (including tip) is almost time independent. In contrast, the relative crack surface displacements and crack energy release rate do change with time, and are very much dependent on the creep compliance of the viscoelastic material. The tendencies of the crack advancing along the interface, and kinking out of the interface, are estimated and discussed.

Analysis of Al/Al2O3 metal matrix composites under biaxial cyclic loading using a digital image based finite element method

Abstract This paper examines the use of a twodimensional digital image based finite element method to predict the global behaviour of multiphase material systems. Micrographic images are digitised and meshed for implementation into the general purpose finite element code ADINA. The global cyclic response of the composite can be effectively modelled by using an appropriate constitutive relationship to describe the cyclic elastic–plastic behaviour of the matrix phase. The main advantage of the digital image based method is that the actual microstructural details including particle size, shape, and distribution are inherently captured in the analysis. The predicted global stress–strain responses of aluminium alloy 6061-T0/Al2O3particulate metal matrix composites under uniaxial and biaxial loading conditions (monotonic and cyclic) are found to correlate accurately with experimental results. When compared with predictions based on existing unit cell models, a noticeable improvement is observed. The effect of the representative lengthscale (field of view) used in the analysis was found to be quite important in determining an accurate global response. A statistical analysis using uniformly derived lineal fraction measurements was also performed to demonstrate the correlation between the particle morphology in a particular field of view and the measured global response. Preliminary results indicate that this analysis technique may provide a possible method for determining the appropriate lengthscale for which global analysis applies.

Nonlinear Viscoelastic Constitutive Model for Thermoset Polymers

A nonlinear viscoelastic constitutive model, in differential form, is presented based on the deformation characteristics of thermoset polymers under complex loadings. This rheological model includes a criterion to delineate loading and unloading in multiaxial stress states, and different moduli for loading and unloading behaviors. The material constants and functions of this model are calibrated in accordance with a well-defined procedure. The model predictions are compared with the experimental data of an epoxy polymer subjected to uniaxial and biaxial stress states with monotonic and cyclic loading. The agreement is very good for various loading regimes. The constitutive model is further implemented in a finite element code and the residual stresses arising from the curing process of polymer reinforced composites is determined for two different epoxy resins.