Thermomechanical analysis of elastic–plastic fibrous composites comprising an inhomogeneous interphase

An analytical approach is presented to investigate thermomechanical response of composites consisting of a transversely isotropic fiber, an inhomogeneous interphase and an elastic–plastic matrix. Using the existing cubic variation to describe the continuous change of the material properties of the interphase and dividing the interphase into a number of subdomains, the continuously varying material properties of the interphase are approximated by the constant ones of these subdomains, and the deformations and stresses of the interphase are described with the same formulae as those of transversely isotropic fibers. The analytical expressions of elastic–plastic deformations and stresses of the matrix are obtained from the basic equations of axisymmetric problems in elasticity, the assumption of generalized plane strain, the linear strain–hardening stress–plastic strain relation, Tresca’s yield condition, the associated flow rule and impressibility of plastic deformation. The boundary conditions of the composites and the continuities of the radial displacement and stress between different components are used to determine all the unknown constants and the obtained analytical solution is applied to thermomechanical analysis of the composites. The effects of the inhomogeneity of the interphase, and the plasticity and material properties of the matrix on the thermomechanical response of the composites are investigated.     

A method for the assessment of hyperstatic cracked structures in the elastic–plastic regime

This paper presents a methodology for the assessment of hyperstatic cracked structures constituted of high toughness materials which therefore break under Elastic–Plastic conditions. The method presented combines calculations based on Strength of Materials and Elastic–Plastic fracture mechanics to calculate the crack driving force applied to the cracked section by making its movements and those of the rest of the structure compatible. The application of the proposed assessment procedure is illustrated through the resolution of a practical example. The results of an experimental test, with the same geometrical configuration as the practical example, are also provided.     

Critical excitation for elastic–plastic structures via statistical equivalent linearization

Since earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method for single-degree-of-freedom (SDOF) elastic–plastic structures is proposed. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and related simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except elastic–plastic time-history response analysis. Statistical equivalent linearization is utilized to estimate the elastic–plastic stochastic peak responses approximately. The critical excitations are obtained for two examples and compared with the corresponding recorded earthquake ground motions.     

Analysis of shear-deformable composite beams in postbuckling

The nonlinear response of composite beams modeled according to higher-order shear deformation theories in postbuckling is investigated. The beam ends are restrained from axial movement, and as a result the contribution of the midplane stretching is considered. The equations of motion and the boundary conditions are derived using Hamilton’s principle. The shear deformation effect on the critical buckling load and static postbuckling response is introduced using classical, first-order, and higher-order shear deformation theories. This paper presents an exact solution for the static postbuckling response of a symmetrically laminated simply supported shear-deformable composite beam. The shear effect is shown to have a significant contribution to both the buckling and postbuckling behaviors. Results of this analysis show that classical and first-order theories underestimate the amplitude of buckling while all higher-order theories, considered in this study, yield very close results for the static postbuckling response.     

Drawing behaviour of metal–composite sandwich structures

The drawing behaviour of metal–composite sandwich structures is investigated as a function of the constituent material properties and the process variables of blank preheat temperature and blank-holder force. Materials include three grades of aluminium alloy as the skin layer material and two types of reinforced polypropylene composite as the core layer material. Blank-holder force has a significant effect on the failure mode of the metal–composite system with lower forces resulting in wrinkling as the dominate mode and higher forces resulting in splitting and fracture. Increasing preheat temperature decreases the failure in the composite core however it will increase the severity of wrinkling in the outer flange and sidewall.     

Design, optimization and manufacturing of wood–plastic composite pallet

This paper presents the application of an innovative method of optimization to the design of an I-shape profile used in a wood–plastic composite (WPC) pallet. The pallet was made via assembling three WPC extruded profiles manufactured in the extrusion process. The middle profile was considered to be I-shaped, a design which known to have a high load bearing capability. However, due to the characteristics of WPC products, a delicate design and thus optimization is highly required. A multi-objective-optimization program of micro-genetic algorithm was developed in Visual Basic environment to accomplish the optimization task. By specifying the dimensional variables of the profile section and applying finite elements analysis on the profile and then using the optimization program, an optimal profile section was obtained. The objective was to withstand the maximum load while yielding the minimum deflection and mass. The optimized design was used to manufacture a die and then the product was produced to validate the design. The comparison of simulations and experimental results indicted that the given design method is reasonably reliable. The final mass of the produced pallet was less than 20 kg whereas its strength against bending and distributed smooth restraint loading were greater than 500 kg and 2000 kg, respectively.     

On the thermal problem for composite beams using a finite element semi-discretisation

The paper deals with steady state thermo-elastic problems in beam-like structures and it is composed of three theoretical sections. The first part presents a two-dimensional finite element procedure to compute the temperature distribution within a beam cross section subjected to prescribed boundary conditions. It allows the beam cross section to be modelled taking into account any kind of thermal anisotropy or inhomogeneity.

The second part is devoted to the structural thermo-elastic problem in a beam having arbitrary non-homogeneous, anisotropic material properties over the cross section but constant along the axis; the extension of a well-known semi-discretisation procedure to take into account anisotropic thermal expansion coefficients is presented. In this way it is possible to compute strains and stresses related to temperature distributions on the cross section computed, using the method outlined in the first part of the paper.

The third part describes the procedure to evaluate thermal equivalent loads suitable for a three dimensional frame analysis.

Some examples are presented and the results are compared either with their theoretical counterparts or with numerical results obtained from a full three-dimensional finite element analysis.     

Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis

Bending behaviour of one-dimensional structures is an important consideration in the design of structural components. In the present study a multiscale analysis of the deflection and stress behaviour of carbon nanotube (CNT) reinforced polymer composite beams is presented. The micromechanics models used in the study include straight CNTs aligned in one direction, randomly oriented CNTs and a two parameter model of agglomeration. The effects of volume fraction of CNTs and the nanotube diameter are investigated on the beam deflection and comparisons are made with carbon fibre reinforced composites. The main purpose of the study is to observe the stiffening effect of CNTs when used in structural applications such as beams.     

Studies of elastic and elastic–plastic J integral for mixed mode cracked plate under biaxial loading

Analyses of I–II mixed mode central cracked plate by finite element method are performed in this paper, and some different phenomena are found. First for I–II mixed mode crack, the distribution of J integral along crack tip thickness depends on biaxiality factors because of the existence of vertex (corner) singularity, which is unlike that for mode I or mode II crack. Then J integrals at middle layer keep constant for any cracked plates with different inclined angles β when the biaxiality ratio is equal to 1 or ?1, which implies that the inclined angle or the extent of I–II mixed mode has no effect on the J integral for positive or negative equal axial loading conditions. And the decreasing trend of J integral with the inclined angle β for biaxiality ratio λ being between?1 and 1 is just opposite with that for biaxiality ratio λ being larger than 1 and smaller than ?1. Finally, proposed h₁ (a/W, n, λ, β) of cracked plate with different inclined angles under different biaxial loading are calculated.     

Perturbed solution of free non-linear vibrations of composite beams

The aim of this study is to characterize the free non-linear vibration behavior of composite beams by using polynomial finite element method with shape functions based on Legendre polynomials or sinusoidal functions. The beams are subjected to different boundary conditions. Non-linear frequencies and modes shapes are obtained using asymptotic linearization method applied on the fundamental vibrating mode. The different composite beams are subjected to different layer dispositions. The nature of the interface between layers is of no object in this study. Navier–Bernoulli hypothesis on the transverse sections is adopted. The study concerns the influence of geometrical non-linearities of the free dynamical behavior. The analysis is performed thus by considering the influence of the vibration amplitude on the modal frequencies of the structure. The solutions are obtained by numerical simulation and by semi-analytical method using asymptotic linearization applied in the real temporal modal space. The numerical values are compared to the different ones obtained in literature.     

GEBT: A general-purpose nonlinear analysis tool for composite beams

Geometrically Exact Beam Theory (GEBT), a general-purpose tool for nonlinear analysis of composite slender structures, is developed to meet the design challenges associated with future engineering systems featuring highly-flexible slender structures made of composites. GEBT is based on the mixed formulation of the geometric exact beam theory which can capture all geometric nonlinearities due to large deflections and rotations, subject to the strains being small. Coupled with Variational Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis, GEBT can effectively analyze geometric nonlinear behavior of slender structures having arbitrary cross-sections made of arbitrary materials.     

A numerical method for the analysis of longitudinal elastic–plastic stress wave propagation

A numerical method for the analysis of one-dimensional propagation of elastic–plastic stress waves in cylindrical bars is proposed. The method is based on the division of the bar into elements of finite length and the solution of the equations of motion for these elements. Numerical results are presented for semi-infinite bars and a finite bar fixed at one end.     

Formulation and numerical treatment of incompressibility constraints in large strain elastic–plastic analysis

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate‐independent finite strain analysis of solids undergoing large elastic‐isochoric plastic deformations. The formulation relies on the introduction of a mixed‐variant metric deformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure which can be additively decomposed into the exact isochoric (deviatoric) and volumetric (spheric) strain measures. This fact may be seen as the basic idea in the formulation of appropriate mixed finite elements which guarantee the accurate computation of isochoric strains. The mixed‐variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response whereas the plastic material behavior is assumed to be governed by a generalized J₂ yield criterion and rate‐independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on higher‐order Padé approximations. To be able to take into account the plastic incompressibility constraint a modified mixed variational principle is considered which leads to a quasi‐displacement finite element procedure. Finally, the numerical solution of finite strain elastic‐plastic problems is presented to demonstrate the efficiency and the accuracy of the algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Postbuckling and free vibrations of composite beams

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse deformations of a composite laminated beam accounting for the midplane stretching are derived. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial–integral–differential equation governing the transverse deformations. We find out that the governing equation for the postbuckling of symmetric or asymmetric composite beams has the same form as that of beams made of an isotropic material. Composite beams with fixed–fixed, fixed–hinged, and hinged–hinged boundary conditions are considered. A closed-form solution for the postbuckling deformation is obtained as a function of the applied axial load, which is beyond the critical buckling load. To study the vibrations that take place in the vicinity of a buckled equilibrium position, we exactly solved the linear vibration problem around the first buckled configuration. Solving the resulting eigen-value problem results in the natural frequencies and their associated mode shapes. Both the static response represented by the postbuckling analysis and the dynamic response represented by the free vibration analysis in the postbuckling domain strongly depend on the lay-up of the laminate. Variations of the beam’s midspan rise and the fundamental natural frequency of the postbuckling domain vibrations with the applied axial load are presented for a variety of lay-up laminates. The ratio of the axial stiffness to the bending stiffness was found to be a crucial parameter in the analysis. This control parameter, through the selection of the appropriate lay-up, can be manipulated to help design and optimize the static and dynamic behavior of composite beams.     

FEM analysis of dynamic flexural behaviour of composite sandwich beams with foam core

The dynamic flexural behaviour of sandwich beams, with composite face-sheets and a foam core, was analysed by developing a 3D finite-element model. To model the core behaviour, a crushable foam model was used. The Hou criteria were used to predict the failure of the face-sheets. Dynamic bending tests were performed to validate the numerical model. The comparison between numerical and experimental results in terms of contact-force histories, peak-force values, absorbed energy, and maximum displacement of both face-sheets was satisfactory. It was revealed that the collapse of the foam core under the impact region favoured the failure of the upper face-sheet.     

Numerical aspects of non-local modeling of the damage evolution in elastic–plastic materials

The design of mechanical systems in modern industrial plants requires reliable and efficient methods to predict the behavior of structural materials. For complex loading conditions, the behavior of the structural materials is determined by damage evolution, strain rate and temperature. The subject of the article is the modeling of the damage evolution in elastic–plastic materials of structural components, which are utilized at various temperatures. To achieve this goal, a hybrid model of steel cracking is applied. The hybrid model uses a finite element simulation combined with an experimental test realized in the macroscale. By using the hybrid model, the modeling of the damage evolution affords possibilities of determining macroscopic effects of the steel micro-defects. An essence of solving the predicting behavior of structural materials with micro-defects consists in time integration procedures for constitutive equations. In the article a semi-implicit time integration procedure is presented. The semi-implicit time integration procedure is suitable for the inelastic materials (compressible or incompressible) with the combined kinematic–isotropic hardening behavior. Its numerical solutions are stable, namely without the oscillatory behavior. By spatial averaging over a representative volume (RV), the homogenization technique (HT) is used for the defining of non-local variables in the constitutive equations. Evolutionary algorithms (EAs) based on local selections are applied to perform the homogenization technique. Within the framework of the large strain theory, the non-local continuum satisfies the objectivity requirements. Limitations on applicability of the -integral approach to construct crack growth resistance curves are also presented.     

Internal stress and adhesion of amorphous Ni–Cu–P alloy on aluminum

This study investigated the effect of saccharin on the internal stress and the adhesion of amorphous Ni–Cu–P deposited on aluminum. An amorphous Ni–Cu–P deposit with slight compressive stress can be produced when one adds 8–10 g/l saccharin into the Ni–Cu–P deposition solution. The stress relief mechanism was investigated. The addition of saccharin restrains the coalescence of the islands within Ni–Cu–P nodules and reverses the internal stress of the electroless Ni–Cu–P deposit from tensile to compressive. The adhesion strength of the Si/Ti/Al/Ni–Cu–P multilayer specimen obtained with 10 g/l saccharin is around 35 to 45 MPa, and the fracture occurs at the silicon substrate after the pull test. The shear strength of the Ti/Al/Ni–Cu–P bump (100×100 μm) on Si is 132.9±12.7 g, and the fracture occurs at the Ni–Cu–P deposit after the shear test. Moreover, the inhibition of coalescence of the fine islands within Ni–Cu–P nodules increases the brightness and the hardness of the deposit.     

On the importance of cross-sectional warping in solid composite beams

The relative importance of the cross-sectional warping components in composite beams is studied and demonstrated using an exact solution for solid orthotropic beam of arbitrary cross-sectional geometry that undergoes a bending moment. In light of the effort required for warping modeling in general numerical schemes of composite beams, the present study contributes to the understanding of the importance of modeling the in-plane and the out-of-plane warping components.     

Flexural behaviour of glue-laminated fibre composite sandwich beams

This study involved experimental investigation onto the flexural behaviour of glue-laminated fibre composite sandwich beams with a view of using this material for structural beams. Composite sandwich beams with 1, 2, 3, and 4 composite sandwich panels glued together were subjected to 4-point static bending test in the flatwise and edgewise positions to evaluate their stiffness and strength properties. The results showed that the composite sandwich beams in the edgewise position failed with 25% higher bending strength but have 7% lower bending stiffness than beams in the flatwise position. The results however indicated that the bending stiffness of flatwise specimens converges to that of the edgewise specimens with increasing laminations. More importantly, the specimens in the edgewise position failed with greater ductility due to progressive failure of the fibre composite skins while the specimens in the flatwise position failed in a brittle manner due to debonding between the skin and core. Wrapping the glue-laminated sandwich beams with one layer of tri-axial glass fibres did not prove to be effective. Overall, it has been demonstrated that the glue-laminated sandwich beams exhibited better performance than the individual composite sandwich beams.