Analytical stress around mode II crack parallel to principle axis in orthotropic composite plate

Stress analyses for orthotropic composite materials containing a through crack under remote shear loads (Mode II) are conducted. By employing the complex theory, a harmonic differential equation was established for the orthotropic plates with axes normal to the three orthogonal planes of material symmetry. An analytical complex function was introduced by following the Westergaard approach. Stress around a mode II crack in the orthotropic composite plate is deduced to have an analytical form. In addition, the analytical solution for a mode II crack was examined in the case of isotropic materials. It demonstrated that the analytical solution obtained is correct for the mode II cracked orthotropic composite plates.     

Dynamic models for low-velocity impact damage of composite sandwich panels – Part B: Damage initiation

Equivalent single and multi degree-of-freedom systems are used to predict low-velocity impact damage of composite sandwich panels by rigid projectiles. The composite sandwich panels are symmetric and consist of orthotropic laminate facesheets and a core with constant crushing resistance. The transient deformation response of the sandwich panels subjected to impact were predicted in a previous paper, and analytical solutions for the impact force and velocity at damage initiation in sandwich panels are presented in this second paper. Several damage initiation modes are considered, including tensile and shear fracture of the top facesheet, core shear failure, and tensile failure of back facesheet. The impact failure modes are similar to static indentation failure modes, but inertial resistance and high strain rate material properties of the facesheets and core influence impact damage loads. Predicted damage initiation loads and impact velocities compare well with experimental results.     

粘弹性复合材料夹芯板的稳态响应分析

芯材采用Kelvin粘弹性本构模型,推导了复合材料夹芯板的动力学方程,运用模态正交原理,以Navier完备解形式求解了四边简支正交对称铺层层合板的稳态响应,并给出了固有频率和结构损耗因子的解析解。通过固有频率的有限元解对比验证了数值计算的可靠性。分析了芯材剪切模量和芯材厚度对结构固有频率和损耗因子的影响。探讨了稳态响应的收敛性,并得到结构稳态响应振幅与频率的关系,分析了芯材损耗因子对结构稳态响应的影响。结果表明：芯材剪切模量存在最佳设计值;结构首阶模态特性主导结构的稳态动态响应。     

Buckling of shear deformable laminated composite plates

A shear deformable finite element is developed for the buckling analysis of laminated composite plates. The finite element formulation is based on Mindlin's theory in which shear correction factors are derived from the exact expressions for orthotropic materials. A variety of problems on uniaxial and shear bucklings of laminated composite plates are solved. The effects of material properties, plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle on the buckling loads of symmetrically and antisymmetrically laminated composite plates are investigated. Optimal lamination arrangements of layers for maximizing the buckling loads of the plates are determined.     

Closing of wedged crack in orthotropic viscoelastic composite

Quasi-static crack closing in a linear viscoelastic orthotropic composite with a crack which is opened by the wedge of constant width is analyzed. The use of superposition allows us to develop exact equations for predicting free crack length as a function of time. These equations are solved numerically using operator continued fractions method. As an example of the proposed approach some results for the composite of silicate glass fibers and epoxy resin binder are presented.     

Vibration and damping analysis of a three-layered composite annular plate with a viscoelastic mid-layer

The natural frequencies and modal loss factors of the three-layered annular plate with a viscoelastic core layer and two polar orthotropic laminated face layers are considered. The discrete layer annular finite element is employed to derive the equations of motion for the three-layered annular plate. The viscoelastic material in the central layer is assumed to be incompressible, and the extensional and shear moduli are described by the complex quantities. Complex eigenvalued problems are then solved, and the frequencies and modal loss factors of the composite plate are extracted. The results of the symmetric and non-symmetric composite annular plates are both presented. The effects of material properties, radius to thickness ratio, stacking sequences and thickness of face layers, and thickness of the viscoelastic core layer are discussed.     

Analytical solution for orthotropic composite plate containing a mode I crack along principle axis

Analytical stress analyses are presented for orthotropic composite materials containing a through crack under uniaxial normal loads (mode I). A harmonic differential equation has been established for the orthotropic plates with axes normal to the three orthogonal planes of material symmetry by introducing new complex variables. The complex theory was employed to find stress functions to satisfy the equilibrium equation, compatibility equation and boundary condition at infinite and crack surfaces. An analytical solution was examined in the case of isotropic materials. It is demonstrated that the analytical solution obtained is correct for the orthotropic composite plates.     

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under distributed normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. Bimaterial formulation of a crack problem is shown to converge to the mono-material formulation, derived independently, in the limiting case when both materials are the same.     

Plane problem of macro-microcrack interaction taking account of crack closure

The fracture stability of a macrocrack under the tensile and shear loading in the presence of a system of microcracks is analysed. Interaction of cracks leads to full or partial closure of the crack edges. The boundary problem is formulated and a solution is obtained by the small parameter method. Domains where microcracks are closed, and regions where microcracks cause full or partial closure of the macrocrack are found. The influence of crack contact on the stress intensity coefficient is analysed under the friction free assumption.     

On higher order parameters in cracked composite plates under far‐field pure shear

This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress‐based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non‐zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non‐singular term, ie, the T‐stress. Unlike the isotropic materials, in which the T‐stress is zero under pure shear, it is found that the T‐stress is non‐zero for the case of anisotropic materials, being the only material‐dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T‐stress on stresses near the crack tip in composite plates under pure shear loads.     

A New Incremental Formulation in the Time Domain for Crack Initiation in an Orthotropic Linearly Viscoelastic Solid

The problem of predicting the crack growth initiation in a linearlyviscoelastic material is investigated. A new incremental fractureequations relating viscoelastic stress intensity factors (VSIFs) toviscoelastic opening displacement intensity factors (VODIFs) areestablished. Crack growth initiation is studied in detail by means of acomputational approach based on a modified path independent integral. Itis found that the mechanical and kinematical fields around the crack tipcan be determined using an incremental formulation based on a discretespectrum representation of the viscoelastic compliance functions; thusthe difficulty of computer storage requirements is avoided. Numericalresults are obtained for predicting the time at which propagationinitiates and these are compared with the analytical solution.     

A systematic analysis and design approach for single-span FRP deck/stringer bridges

There is a concern with worldwide deterioration of highway bridges, particularly reinforced concrete. The advantages of fiber reinforced plastic (FRP) composites over conventional materials motivate their use in highway bridges for rehabilitation and replacement of structures. In this paper, a systematic approach for analysis and design of all FRP deck/stringer bridges is presented. The analyses of structural components cover: (1) constituent materials and ply properties, (2) laminated panel engineering properties, (3) stringer stiffness properties, and (4) apparent stiffnesses for composite cellular decks and their equivalent orthotropic material properties. To verify the accuracy of orthotropic material properties, an actual deck is experimentally tested and analyzed by a finite element model. For design analysis of FRP deck/stringer bridge systems, an approximate series solution for orthotropic plates, including first-order shear deformation, is applied to develop simplified design equations, which account for load distribution factors under various loading cases. An FRP deck fabricated by bonding side-by-side box beams is transversely attached to FRP wide-flange beams and tested as a deck/stringer bridge system. The bridge systems are tested under static loads for various load conditions, and the experimental results are correlated with those by an approximate series solution and a finite element model. The present simplified design analysis procedures can be used to develop new efficient FRP sections and to design FRP highway bridge decks and deck/stringer systems, as shown by an illustrative design example.     

A Probabilistic Method to Predict Fatigue Crack Initiation

A probabilistic method to predict macrocrack initiation due to fatigue damage is presented in this paper. Acoustic non-linearity is used to quantify pre-macrocrack initiation damage. This data is then used in a probabilistic analysis of fatigue damage. The probabilistic fatigue damage analysis consists of a suitably chosen damage evolution equation to model accumulated damage coupled with a procedure to calculate the probability of macrocrack initiation. The probability of macrocrack initiation is evaluated using the Monte Carlo Method with Importance Sampling. Numerical results for the probabilistic assessment of fatigue damage for a sample problem are presented and compared with experimental results.     

Three-dimensional analysis for rectangular 1–3 piezoelectric fiber-reinforced composite laminates with the interdigitated: electrodes under electromechanical loadings

In this paper, an exact analysis for the rectangular composite laminated plate consisting of 1–3 piezoelectric fiber-reinforced composite layer and orthotropic elastic composite layer subjected to the electric field with the interdigitated electrode (IDE) and arbitrary loads is presented without any simplification. The solution of the derived governing differential equations is obtained through the power series expansion and Fourier expansion methods. An illustrative analysis is carried out to investigate the influence of the stiffness anisotropy, free-strain anisotropy and electric field on the shear curvature of the laminated plate with 1–3 active fiber-reinforced composite layer. The numerical results show that, the magnitude of shear curvature gradually increases as the stiffness anisotropy and the free-strain anisotropy increase, and increasing the electrical field also leads to an increase in shear curvature. Results presented here can be used to assess various approximate theories and enhance the understanding of the static and dynamic response behavior of the 1–3 piezoelectric composite structures.     

Dynamic stress intensity factor due to concentrated loads on a propagating semi-infinite crack in orthotropic materials

The elastodynamic response of an infinite orthotropic material with a semi-infinite crack propagating at constant speed under the action of concentrated loads on the crack faces is examined. Solution for the stress intensity factor history around the crack tip is found for the loading modes I and II. Laplace and Fourier transforms along with the Wiener-Hopf technique are employed to solve the equations of motion. The asymptotic expression for the stress near the crack tip is analyzed which lead to a closed-form solution of the dynamic stress intensity factor. It is found that the stress intensity factor for the propagating crack is proportional to the stress intensity factor for a stationary crack by a factor similar to the universal function k(v) from the isotropic case. Results are presented for orthotropic materials as well as for the isotropic case.     

Analysis of hybrid beams composed of GFRP profiles and polymer concrete

In this paper, a numerical approach for the analysis of a new type of hybrid composite beams is presented. Such beams are composed of composite materials that resist shear and tensile stresses, and polymer concrete acommodating compression stresses.The beams offer an optimized configuration in terms of stiffness and strength, with much potential for mechanical and civil engineering structures.The current numerical model is based on a finite element formulation for layered shell-like structures. The model accounts for a polymer concrete material model, orthotropic material model, and considers the analysis of geometric and material nonlinearities. The first-order shear deformation theory is used in order to describe the shell deformation under a total Lagrangian formulation. The model is validated experimentally and a close agreement with experimental results makes this model an attractive solution method for this type of composite hybrid beams.     

Modelling creep behaviour of orthotropic composites by the coincident element method

In this paper, the coincident method proposed previously is applied to model the four-point-bending creep experiments conducted at the Cooperative Research Centre for Advanced Composite Structures (CRC-ACS) on carbon-epoxy composite laminates. A parameter identification methodology is first developed to determine the elastic and viscoelastic material models to be used for a coincident element. Simulations are then conducted to model the flexural creep response of the composite laminates under different loading and temperature conditions. The predicted results are in reasonably good agreement with those obtained by experiments. It is demonstrated that the coincident element method is a relatively simple and useful tool for modelling orthotropic and viscoelastic response of laminated composites by using a finite element package that only supports isotropic viscoelastic material models.     

Buckling Analysis of Composite Sandwich Plates with Flexible Core Using Improved High-Order Theory

A new improved high-order theory is presented for global and local buckling analysis of sandwich plates with soft orthotropic core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. Overall buckling loads, as well as wrinkling loads, are obtained for various sandwich plates. Effect of geometrical parameters and material properties of face sheets and core are studied on the overall buckling and face wrinkling of sandwich plates.     

Viscoelastic crack growth process in wood timbers: An approach by the finite element method for mode I fracture

In this paper the effects of viscoelastic characteristics in wood timbers, on the creep crack growth process are studied through a new finite element approach in the time domain. In order to take into account the linear viscoelastic orthotropic behavior, we present an incremental formulation based on a rheological representation of creep tensor components. By using a relationship between stress and crack opening intensity factors, the general approach of path independent integrals is extended in order to calculate energy release rate and local fracture characteristics. Afterwards, fracture parameters are computed through a coupling process with the incremental viscoelastic behavior. The numerical algorithm is presented and validated through numerical as well as experimental examples.