A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading

A fracture mechanics based failure criterion for unidirectional composites under combined loading has been developed. The predictions from this criterion have been compared with experimental data obtained from combined compression–torsion loading of glass and carbon fiber reinforced polymer composites of 50% fiber volume fraction. The specimens were loaded under rotation control and displacement control in a proportional manner. Comparison of the Budiansky–Fleck kinking model, specialized to a solid circular cylinder, and the new failure model against experimental data suggests that the Budiansky–Fleck model predictions do not capture the variation of compressive strength as a function of shear stress for glass fiber composites. This is because these composites fail predominantly by compressive splitting. The Budiansky–Fleck model predictions are appropriate for composites that fail by compressive kinking. The new model predictions capture the experimental results for glass composites where the compression strength is initially unaffected by shear stress but undergoes a drastic reduction when a critical value of shear stress is reached.     

Structural first failure times under non-Gaussian stochastic behavior

An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed.In the method,a power series that constants can be obtained from response moments (skewness,kurtosis,etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process,then mean up-crossing rates,mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated,and finally,the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent.An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Ganssian model.     

The role of texture in tension–compression asymmetry in polycrystalline NiTi

The purpose of the present study is to thoroughly understand the stress–strain behavior of polycrystalline NiTi deformed under tension versus compression. To do this, a micro-mechanical model is used which incorporates single crystal constitutive relationships and experimentally measured polycrystalline texture into the self-consistent formulation. For the first time it is quantitatively demonstrated that texture measurements coupled with a micro-mechanical model can accurately predict tension/compression asymmetry in NiTi shape memory alloys. The predicted critical transformation stress levels and transformation stress–strain slopes under both tensile and compressive loading are consistent with experimental results. For textured polycrystalline NiTi deformed under tension it is demonstrated that the martensite evolution is very abrupt, consistent with the Luders type deformation experimentally observed. The abrupt transformation under tension is attributed to the fact that the majority of the grains are oriented along the [111] crystallographic direction, which is soft under tensile loading. Since single crystals of the [111] orientation are hard under compression it is also demonstrated that under compression the martensite in textured polycrystalline NiTi evolves relatively slower.     

Modeling of particle–resin suspension impregnation in compression resin transfer molding of particle-filled,continuous fiber reinforced composites

A particle–resin suspension impregnation model is used for analyzing the mold filling process in compression resin transfer molding (CRTM) of particle-filled, continuous fiber composites. The model is based on Darcy flow coupled with particle filtration and is applicable to two-dimensional impregnation through isotropic/anisotropic fiber preforms. Comparisons with simple analytical solutions and experimental results from the literature were made to validate the numerical solution. Simulations showed that CRTM was advantageous over resin transfer molding (RTM) for smaller non-homogeneity in composite microstructure, when particle filtration was high. Limits on certain process parameters were observed beyond which molding pressures in CRTM became comparable with those in RTM. The preform anisotropy was effective in the particle distribution profile. The choice of inlet gate configuration in CRTM was found influential in the particle distribution homogeneity and molding pressures. The developed modeling tool can be extended to analyze any composite liquid molding process involving particle fillers.     

Effects of fibrous fillers on friction and wear properties of polytetrafluoroethylene composites under dry or wet conditions

The friction and wear behavior and mechanism as well as the mechanical properties of polytetrafluoroethylene （PTFE） composites filled with potassium titanate whiskers （PTW） and short carbon fibers （CF） under dry, wet and alkaline conditions were investigated. Experiments indicated that owing to appropriate cooling and boundary lubricating effects, the filled PTFE composites showed much lower frictional coefficient and better wear resistance under alkaline than dry and wet sliding conditions. The wear resistance of carbon-fiber-filled PTFE was much better than that of potassium titanate-whisker-filled PTFE composites in water. Results also showed that the transfer film on counterpart rings was significantly hindered by water and alkali. Hydrophilic-filler-reinforced PTFE composites yield higher wear rate when sliding under water.     

The elastic–plastic behaviour of foam under shock loading

An experimental investigation of the elastic–plastic nature of shock wave propagation in foams was undertaken. The study involved experimental blast wave and shock tube loading of three foams, two polyurethane open-cell foams and a low-density polyethylene closed-cell foam. Evidence of precursor waves was observed in all three foam samples under various compressive wave loadings. Experiments with an impermeable membrane are used to determine if the precursor wave in an open-cell foam is a result of gas filtration or an elastic response of the foam. The differences between quasi-static and shock compression of foams is discussed in terms of their compressive strain histories and the implications for the energy absorption capacity of foam in both loading scenarios. Through a comparison of shock tube and blast wave loading techniques, suggestions are made concerning the accurate measurements of the principal shock Hugoniot in foams.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

Fibre-reinforced composites with fibre-bending stiffness under azimuthal shear – Comparison of simulation results with analytical solutions

In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy potential. In the present contribution a comparison of the numerical solution by means of the multi-field finite element approach against the analytical solution is presented for the azimuthal shear deformation of a tube-like structure. To this end, the general deformation pattern and especially the distribution of the stress and couple stress tensor are taken into account. We find that, although the analytical solution is derived subject to the assumption of small deformations, whereas the numerical solution is based on the finite strain counterpart of the theory, the simulation results are quasi identical, which verifies the numerical framework proposed.     

The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer–matrix composites

The interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (non-linear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.     

The Bending of Elastic Circular Ring of Non-homogeneous and Variable Cross Section under the Actions of Arbitrary Loads

On the basis of the stepped reduction method suggested in[1],we investigatethe problem of the bending of elastic circular ring of non-homogeneous andvariable cross section under the actions of arbitrary loads.The general solutionof this problem is obtained so that it can be used for the calculations of strengthand rigidity of practical problems such as arch,tunnel etc.In order to examineresults of this paper and explain the application of this new method,an exampleis brought out at the end of this paper.Circular ring and arch are commonly used structures in engineering.Timo-shenko,S.,Barber,J.R.,Tsumura Rimitsu et al.have studied theseproblems of bending,but,so far as we know,it has been solely restricted to thegeneral solution of homogeneous uniform cross section ring.The only knownsolution for the problems with variable cross section ones has been solelyrestricted to the solution of special case of flexural rigidity in linear functionof coordinates.On account of fundamental equations of the non-homoge     

The effect of microstructural morphology on the elastic,inelastic, and degradation behaviors of aluminum–alumina composites

Micromechanical models with idealized and simplified shapes of inhomogeneities have been widely used to obtain the average (macroscopic) mechanical response of different composite materials. The main purpose of this study is to examine whether the composites with irregular shapes of inhomogeneities, such as in the aluminum–alumina (Al–Al₂O₃) composites, can be approximated by considering idealized and simplified shapes of inhomogeneities in determining their overall macroscopic mechanical responses. We study the effects of microstructural characteristics, on mechanical behavior (elastic, inelastic, and degradation) of the constituents, and shapes and distributions of the pores and inclusions (inhomogeneities), and thermal stresses on the overall mechanical properties and response of the Al–Al₂O₃ composites. Microstructures of a composite with 20% alumina volume content are constructed from the microstructural images of the composite obtained by scanning electron microscopy (SEM). The SEM images of the composite are converted to finite element (FE) meshes, which are used to determine the overall mechanical response of the Al–Al₂O₃ composite. We also construct micromechanics model by considering circular shapes of the inhomogeneities, while maintaining the same volume contents and locations of the inhomogeneities as the ones in the micromechanics model with actual shapes of inhomogeneities. The macroscopic elastic and inelastic responses and stress fields in the constituents from the micromechanics models with actual and circular shapes of inhomogeneities are compared and discussed.     

Homogenization of aligned “fuzzy fiber” composites

The aim of this work is to study composites in which carbon fibers coated with radially aligned carbon nanotubes are embedded in a matrix. The effective properties of these composites are identified using the asymptotic expansion homogenization method in two steps. Homogenization is performed in different coordinate systems, the cylindrical and the Cartesian, and a numerical example are presented.     

The monotonicity and critical periods of periodic waves?of?the �� 6 field model

In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the ?? ⁶ field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.     

Dual-phase steel sheets under cyclic tension–compression to large strains: Experiments and crystal plasticity modeling

In this work, we develop a physically-based crystal plasticity model for the prediction of cyclic tension–compression deformation of multi-phase materials, specifically dual-phase (DP) steels. The model is elasto–plastic in nature and integrates a hardening law based on statistically stored dislocation density, localized hardening due to geometrically necessary dislocations (GNDs), slip-system-level kinematic backstresses, and annihilation of dislocations. The model further features a two level homogenization scheme where the first level is the overall response of a two-phase polycrystalline aggregate and the second level is the homogenized response of the martensite polycrystalline regions. The model is applied to simulate a cyclic tension–compression–tension deformation behavior of DP590 steel sheets. From experiments, we observe that the material exhibits a typical decreasing hardening rate during forward loading, followed by a linear and then a non-linear unloading upon the load reversal, the Bauschinger effect, and changes in hardening rate during strain reversals. To predict these effects, we identify the model parameters using a portion of the measured data and validate and verify them using the remaining data. The developed model is capable of predicting all the particular features of the cyclic deformation of DP590 steel, with great accuracy. From the predictions, we infer and discuss the effects of GNDs, the backstresses, dislocation annihilation, and the two-level homogenization scheme on capturing the cyclic deformation behavior of the material.     

Is it really chaos? The complexity of transient dynamics of double pendula

Nonlinear Dynamics - In this paper, we re-examine the dynamics of double pendulum in numerical simulations and experimental observations. Typical types of behaviors of the parametrically excited...     

Multiple cracking of fiber/matrix composites—Analysis of normal extension

This paper is concerned with the fracture of a fiber embedded in a matrix of finite radius. There is a periodic array of cracks in the fiber along the central axis of the medium. The paper accounts for the cases of axial extension and residual temperature change of the composite medium. Fourier and Hankel transforms are used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the problem, is conducted. Numerical solutions for the crack tip field and the stress in the fiber are obtained for various values such as crack radius, crack spacing and fiber volume fraction.     

Micromechanical analysis of the finite elastic–viscoplastic response of multiphase composites

Nonlinear thermoelastic–viscoplastic constitutive equations for large deformations with isotropic and directional hardening, are incorporated into a micromechanical finite strain analysis. As a result of this analysis, which is based on the homogenization technique for periodic microstructures, a global thermoinelastic constitutive law is established that governs the overall response of multiphase materials under finite deformations. This constitutive law is expressed in terms of the instantaneous effective mechanical and thermal stress tangent tensors together with the instantaneous global inelastic stress tensor that represents the viscoplastic effects. Results for a thermoinelastic matrix reinforced by a hyperelastic compressible material are given that illustrate the response of fibrous and particulate composites to various types of loading.     

The Solution of Elastostatic Problems and the Principles of Minimum Potential Energy,Minimum Complementary Work,under Fuzzy Boundary Conditions

A Solution of elastostatic problem is defined on the basis of set theory andextended to the cases with fuzzy boundary conditions.Extension is alsogiven for the principles of minimum potential energy and minimum comple-mentary work with fuzzy boundary conditions.A quasisolution of an elasto-static problem is defined as an approximate solution with boundary conditionsmost close to the original.And the existance of quasisolution of an elasto-static problem can be proved on the basis of certain assumptions and thetheorem of minimum elementary potential energy.