Incremental forms of Schapery’s model: convergence and inversion to simulate strain controlled ramps

Schapery’s nonlinear viscoelastic model is written in incremental form, and three different approximations of nonlinearity functions in the time increment are systematically analysed with respect to the convergence rate. It is shown that secant slope is the best approximation of the time shift factor, leading to significantly higher convergence rate. This incremental form of the viscoelastic model, Zapas’ model for viscoplasticity, supplemented with terms accounting for damage effect is used to predict inelastic behaviour of material in stress controlled tests. Then the incremental formulation is inverted to simulate stress development in ramps where strain is the input parameter. A comparison with tests shows good ability of the model in inverted form to predict stress–strain response as long as the applied strain is increasing. However, in strain controlled ramps with unloading, the inverted model shows unrealistic hysteresis loops. This is believed to be a proof of the theoretically known incompatibility of the stress and strain controlled formulations for nonlinear materials. It also shows limitations of material models identified in stress controlled tests for use in strain controlled tests.     

Damage characterization of a cross-ply carbon fiber/epoxy laminate by an optical measurement of the displacement field

Using Electronic Speckle Pattern Interferometry (ESPI), full-field displacement measurement was performed on the edge of a cracked cross-ply graphite/epoxy laminate subjected to a tensile loading. The displacement jumps corresponding to cracks are clearly visible and can be used to determine the crack opening displacement (COD) values along the cracks. The main objective of this study is to determine if the application of successive loads of increasing magnitude may have modified the existing cracks and thereby changed the COD dependence on the applied stress. Moreover, we have tested the applicability of the assumed linear elastic COD behavior in the presence of very high stress concentration at the crack tips. The profile of the opening along the crack was also studied.     

Modeling the Effect of Helical Fiber Structure on Wood Fiber Composite Elastic Properties

The effect of the helical wood fiber structure on in-plane composite properties has been analyzed. The used analytical concentric cylinder model is valid for an arbitrary number of phases with monoclinic material properties in a global coordinate system. The wood fiber was modeled as a three concentric cylinder assembly with lumen in the middle followed by the S3, S2 and S1 layers. Due to its helical structure the fiber tends to rotate upon loading in axial direction. In most studies on the mechanical behavior of wood fiber composites this extension-twist coupling is overlooked since it is assumed that the fiber will be restricted from rotation within the composite. Therefore, two extreme cases, first modeling fiber then modeling composite were examined: (i) free rotation and (ii) no rotation of the cylinder assembly. It was found that longitudinal fiber modulus depending on the microfibril angle in S2 layer is very sensitive with respect to restrictions for fiber rotation. In-plane Poisson’s ratio was also shown to be greatly influenced. The results were compared to a model representing the fiber by its cell wall and using classical laminate theory to model the fiber. It was found that longitudinal fiber modulus correlates quite well with results obtained with the concentric cylinder model, whereas Poisson’s ratio gave unsatisfactory matching. Finally using typical thermoset resin properties the longitudinal modulus and Poisson’s ratio of an aligned softwood fiber composite with varying fiber content were calculated for various microfibril angles in the S2 layer.     

Mechanical Response of Thermoset Polymers under High Compressive Loads, 2

Summary: A nonlinear viscoelastic material model was used to describe the experimental behaviour of thin vinyl ester specimens subjected to compression in thickness direction. The stress‐dependent material functions in the model were found in creep and strain recovery tests on thick cylindrical specimens. The elastic and creep response of thin thermoset polymer specimens subjected to compressive loads was simulated while varying the geometry of the test set samples. The calculated increase in the apparent elastic modulus and decrease of the creep‐strain rate due to reduced thickness‐to‐width ratio is in a good qualitative correlation with experimental results for corresponding geometries. The constraint due to friction and interaction with the material outside the loaded surface area were identified as the cause for high apparent stiffness, which converges with decreasing thickness to an asymptotic value dependent on the modulus and Poisson's ratio of the material.

The shape of a 2 mm‐thick specimen under compression.     

Mechanical Response of Thermoset Polymers under High Compressive Loads, 1

Summary: The present study describes the mechanical response of thermoset polymers under high compressive loads. A well‐defined free radically cured vinyl ester resin has been used and studied in six different geometries in order to determine the dependence of apparent mechanical properties on the particular size and shape of a sample. The mechanical response in compression has also been compared to the response in tensile tests. Variation of the film thickness, boundary conditions and loading conditions reveal that there is a significant effect on the mechanical performance (apparent properties) of the polymer. When the thickness‐to‐width ratio of the sample is reduced in a compression test, the friction between the sample and the compression plates proves to be of great importance. The yield stress increases dramatically when the thickness of the sample is reduced, whereas it decreases when the friction between sample and the compression plate is reduced. The creep decreases when the thickness of the material is reduced and it decreases even more due to reaction of the material surrounding the compressed part of the sample. The described test conditions and observed phenomena will be subject to simulation in Part 2 of this study.

Mechanical performance of a thermoset polymer under high compressive loads.     

A constitutive model for non‐linear behavior of SMC accounting for linear viscoelasticity and micro‐damage

An approach for modeling sheet molding compound (SMC) composites as viscoelastic damageable material is presented. Continuum damage mechanics theory by Chow and Wang (Int. J. Fract., 33, 3 (1987)) was used in combination with linear viscoelasticity. The model was applied to a modern SMC composite material containing both hollow glass spheres for low density and toughening additive for improved impact resistance. Tensile tests and uniaxial creep test were employed to build the constitutive model. Validation was done by comparing test data with simulations of uniaxial creep on material with different degrees of damage. The model has good accuracy at moderate damage levels under controlled time‐dependent crack propagation. Tensile testing at two different fixed strain rates was simulated using quasi‐elastic method to calculate relaxation modulus. The model predicts the stress‐strain curve with good accuracy until the region is close to failure, where new mechanisms not accounted for are taking place. Finally, a simulation of a cyclic tensile test with increasing maximum strain per cycle was performed, and since both damage and viscoelasticity are included in the model, the slope change, accumulation of residual strain, and hysteresis in the stress‐strain, loading‐unloading curve are predicted. POLYM. COMPOS., 26:84–97, 2005. © 2004 Society of Plastics Engineers     

The fiber-matrix interface crack — A numerical analysis using Boundary Elements

The calculation of the energy release rate of a debonding interface crack between fiber and matrix in plane strain requires a knowledge of the stress state and displacements at the neighbourhood of the crack tip. Analytical solutions which involve interpenetrations of the free boundaries of the fiber and matrix have classically been used to predict the variation of the energy release rate with the debonding angle. In this paper a numerical study of this problem as a contact problem, using Boundary Elements, is carried out. The singular stress components are modelled by means of singular discontinuous elements, a particular contact algorithm, which is very appropriate for cases like that under consideration where the fiber is much stiffer than the matrix, having been proposed. The numerical procedure shows the appearance of a contact zone with physical meaning starting at a certain value of the debonding angle, which implies the presence of a pure mode II of fracture. The values of G found by BEM are compared with those predicted by the use of an analytical solution showing clear discrepancies when the contact zone starts to develop, BEM always predicting smaller values of the energy release rate, in accordance with the absence of mode I in the presence of a contact zone.     

Nonlinear Viscoelastic,Viscoplastic Characterization of Unidirectional GF/EP Composite

Viscoplastic strains of unidirectional continuous fiber composite (HEXCEL GF/EPprepreg system) are studied experimentally and theoretically. Creep and strainrecovery tests are used. Schapery's nonlinear viscoelastic viscoplasticconstitutive equations are used and generalized to describe inelastic behavior ofunidirectional composite under isothermal creep and strain recovery conditions. Themethodology to quantify the viscoplastic strains with respect to applied stress isproposed. Viscoplastic strains of composite are described by plastic shear strain inmaterial symmetry axis. Assumptions has been used and validated that the functiondescribing the stress and time dependence of viscoplastic strain can be presented asa product of two, time and correspondingly stress dependent, master curves.     

Numerical analysis of debond propagation in the single fibre fragmentation test

A numerical analysis, using the Boundary Element Method, of the stress state within the specimen in the single fibre fragmentation test is presented first. Thermal residual stresses and fibre–matrix interfacial friction along the debonding crack faces have been considered in the study. Special attention has been paid to the axial stresses along the fibre and the interfacial tractions and relative displacements in the neighbourhood closest to the debonding crack tips. In order to analyse the debond propagation, the associated Energy Release Rate has been evaluated from the near-tip elastic solution. Numerical results show that both the effects of thermal residual stresses and of fibre–matrix interfacial friction are opposed to the debond propagation. Additionally, the effect of the debond propagation on the load transfer through the interface has been studied, showing that fibre–matrix interfacial friction has a weak influence on the distance needed to re-establish the nominal axial load within the fragment.     

Contribution of wood fiber hygroexpansion to moisture induced thickness swelling of composite plates

One of the main drawbacks of wood fiber‐based composite materials is their propensity to swell due to moisture uptake. Because the wood fibers are usually the main contributor to hygroexpansion, it is of interest to quantify the hygroexpansion coefficient of wood fibers, to compare and rank different types of fibers. This investigation outlines an inverse method to estimate the transverse hygroexpansion coefficient of wood fibers based on measurements of moisture induced thickness swelling of composite plates. The model is based on composite micromechanics and laminate theory. Thickness swelling has been measured on polylactide matrix composites with either bleached reference fibers or crosslinked fibers. The crosslinking modification reduced the transverse hygroexpansion of the composites and the transverse coefficient of hygroexpansion of the fibers was reduced from 0.28 strain per relative humidity for reference fibers to 0.12 for cross‐linked fibers. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers