层间弱粘贴复合材料层板的热弹性脱层

本文建立了一个层间弱粘贴复合材料层板热弹性脱层模型.该模型建立在两个描述层间弱粘贴的基本假设基础上.层间位移不连续由层间粘贴的物理关系来描述,表现为层间位移跳跃值与层间残余横向应力的关系;层间温度不连续由层间传热薄层来描述,并据此给出一个计算层间温度跳跃值的计算公式,表现为温度跳跃值与层间横向张开量之间的关系.在此假设基础上,根据平衡方程和静态传热方程导出了正交柱面弯曲层板热弹性脱层解.算例显示了层间弱粘贴对层板热弹性响应的影响.     

压电复合材料层板弱界面力-电-热多场耦合研究

压电复合材料层合结构界面缺陷的物理描述呈现出多场耦合现象。界面弹性场由位移跃变与横向应力的关系来描述;界面温度场由温度跃变与横向位移跃变的经验公式来描述;界面电场分别由电可导通假设、电不可导通假设和电半可导通假设来描述,获取了界面位移、温度和电势跃变的线性表达。基于这些界面假设,得到了柱面弯曲简支压电复合材料层板的力-电-热多场耦合解。算例表明,不同的界面电学假设对弹性场的影响有限,对电场的影响显著,其中电不可导通假设在各种载荷下均产生最大的界面电势跃变。算例提供的数值结果可作为后续研究比较之用。     

An accurate stress analysis model for angle-ply laminates with weakly bonded layers

Summary This paper presents a shear slip model suitable for the analysis of angle-ply composite laminated plates with weakly bonded layers. Being an extension of a relevant model that deals with perfectly bonded laminates, this study accounts further for the effects of shear slip by introducing appropriate interfacial bonding conditions. Accordingly, the model is based on a general five-degrees-of-freedom displacement field which includes certain general shape functions of the transverse co-ordinate. These are determined by means of appropriate three-dimensional elasticity considerations and include information relevant to the interfacial constitutive relations that account for weak bonding between layers. In dealing with weakly bonded angle-ply laminated plates in cylindrical bending, a closed form solution which is independent of the imposed boundary edge conditions is obtained. As a special case, the corresponding cross-ply laminated, weakly bonded plates solution is obtained by letting all the lamination angles involved to take 0° or 90° values. The high accuracy of the present model is shown by means of numerical comparisons with corresponding results based on an exact elasticity solution obtained for simply supported laminates. The effects of shear slip on the response of angle- and cross-ply laminated plates subjected to different edge boundary conditions are finally studied by means of corresponding numerical results that are obtained, presented and discussed.     

Progressive delamination growth analysis using discontinuous layered element

In this paper, a fracture mechanic approach is used to analyze delamination propagation between layers of composite laminates. A finite element method based on layer-wise theory is extended for the analysis of delamination growth. In this approach, delamination is modeled by jump discontinuity conditions at the interfaces. The layer-wise finite element is developed to calculate the strain energy release rates based on the virtual crack closure technique (VCCT). A procedure is proposed to handle the progressive delamination of laminates. Finally, analyses of the edge delamination propagation for several composite laminates are performed and the corresponding failure stresses are calculated. The predicted results are compared with the available experimental and numerical results. It is shown that the predicted failure stresses using this method are comparable with those obtained using interface elements.     

Stress field of a disclination dipole in hcp bicrystal with imperfect interface

In this paper, exact stress field solutions are derived for an interfacial disclination dipole in an hcp bicrystal with an imperfect interface described by the traction discontinuity, displacement discontinuity and slipping models. The solutions show that the stress variation is not necessarily monotonic with worsening imperfection and can exceed 100% of the stresses in bicrystals with perfect interfaces. A strong bias exists between the influence of the normal and shear traction jump parameters, and between the influence of the normal and tangential displacement jump parameters, on the interfacial stresses. The traction and displacement discontinuity models also predict very different dependence of the interfacial stresses on the jump parameters. These results suggest that imperfect interfaces may significantly raise the internal stresses and thus drastically alter the damage mechanisms (nucleation and propagation of dislocations/cracks, fatigue, etc.) as well as the mechanical properties (effective properties, failure modes, strength, etc.) of polycrystalline materials.     

A versatile interface model for thermal conduction phenomena and its numerical implementation by XFEM

A general interface model is presented for thermal conduction and characterized by two jump relations. The first one expresses that the temperature jump across an interface is proportional to the interfacial average of the normal heat flux while the second one states that the normal heat flux jump is proportional to the surface Laplacian of the interfacial average of the temperature. By varying the two scalar proportionality parameters, not only the Kapitza resistance and highly conducting interface models can be retrieved but also all the intermediate cases can be covered. The general interface model is numerically implemented by constructing its weak form and by using the level-set method and XFEM. The resulting numerical procedure, whose accuracy and robustness are thoroughly tested and discussed with the help of a benchmark problem, is shown to be efficient for solving the problem of thermal conduction in particulate composites with various imperfect interfaces.     

Analysis of weakly bonded oxygen in HfO<Subscript>2</Subscript>/SiO<Subscript>2</Subscript>/Si stacks by using HRBS and ARXPS

We have used transmission electron microscopy, high-resolution Rutherford backscattering spectrometry (HRBS), and angle-resolved X-ray photoelectron spectroscopy (ARXPS) to investigate the interfacial oxidized states of hafnium oxide/silicon oxide/Si gate oxide stacks. The atomic concentrations and profiles of HRBS analysis are similar before and after annealing; however, ARXPS shows a clear difference in bond status. These results imply that weakly bonded oxygen atoms existed in the stacks alongside the suboxides. In the as-deposited layers, dioxides are found at the interfaces and suboxides in the layers whereas after annealing suboxides are found at the interfaces and dioxides are found in the layers because of redistribution of bonds during annealing. The combination of HRBS and ARXPS analyses indicated that the main oxidized states transformed from the suboxides to the dioxides with no obvious quantitative difference in the content of oxygen atoms, suggesting that reactions of the weakly bonded oxygen atoms occurred with the suboxides within the layers.     

压电复合材料层板弱界面的四种力电热物理模型

基于对压电复合材料层合结构弱界面弹性场、电场、温度场的宏观和细观尺度分析, 构建了四种界面力-电-热模型, 分别为非耦合型、耦合型和混合型。依据这些界面模型, 得到了柱面弯曲简支压电复合材料层板的力-电-热多场耦合解。结果表明, 损伤界面的多场耦合物理描述介于宏观和细观尺度之间, 需要多尺度考虑, 且基于不同尺度的描述也可获得相似的规律。在热载和力载下, 不同的界面模型对弹性场影响趋同、差异甚小, 而对电场和温度场, 四种模型的影响各异、但规律相似; 在电载作用下, 不同的界面模型无论对弹性场还是电场, 都有显著的影响。     

Effect of Electric Field on the Response of Clamped-FreeMagnetostrictive/Piezoelectric/Magnetostrictive Laminates

This work deals with the response of clamped-free magnetostrictive/piezoelectric/magnetostrictive laminates under electric field both numerically and experimentally. The laminate is fabricated using two magnetostrictive Terfenol-D layers and a soft piezoelectric PZT layer. Easy axis of Terfenol-D layers is length direction, while the polarization of PZT layer is the thickness direction. The magnetostriction of the Terfenol-D layers bonded to the upper and lower surfaces of the PZT layer is first measured. Next, a nonlinear finite element analysis is employed to evaluate the second-order magnetoelastic constants in the Terfenol-D layers bonded to the PZT layer using measured data. The induced magnetic field and internal stresses for the laminates under electric field parallel to the poling are then calculated and discussed in detail. In addition, the induced magnetic field is measured, and test results are presented to validate the predictions.     

复合材料层板层间缺陷分析——剪切滑移

根据三维弹性平衡方程和层间剪切滑移条件,导出了一个复合材料层板层间剪切滑移模型。本文模型具有一般形式的二维板壳理论的位移场及其平衡方程,但因引入了能反映层板界面粘贴情况及板面条件的剪切变形函数,模型因而简单又精确。层板的弯曲问题和屈曲问题被考虑,层间弱粘贴的影响被讨论。数值结果与精确解比较,表明了本文模型的高精度。      

Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer

This paper deals with the thermoelasticity problem of bonded dissimilar half-planes with a functionally graded interlayer, weakened by a pair of two offset interfacial cracks. The material nonhomogeneity in the graded interlayer is represented by spatially varying thermoelastic moduli expressed in terms of exponential functions. The cracks are assumed to be thermally insulated disturbing a steady-state uniform heat flow, and the solution is obtained within the framework of linear plane thermoelasticity. The Fourier integral transform method is employed, and the formulation of the current nonisothermal crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stress fields in the bonded system. In the numerical results, parametric studies are conducted so that the variations in mixed-mode thermal stress intensity factors are presented as a function of offset crack distance for various geometric and material combinations of the dissimilar homogeneous media bonded through the thermoelastically graded interlayer, elaborating thermally induced singular interaction of the two neighboring interfacial cracks.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

In this paper, the free vibration analysis of simply‐supported and clamped composite laminates, especially thick laminates, is carried out. The three‐dimensional theory of elasticity is integrated into a layerwise model via differential quadrature discretization. All physical governing equations are satisfied, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in‐plane strains and stresses along the interfaces of composite laminates. Effects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution. Copyright © 2003 John Wiley & Sons, Ltd.     

Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone – Part I: Mechanical response

The problem of collinear cracks embedded in a layered half-plane is investigated. The medium consists of a surface layer and a semi-infinite substrate bonded through an interfacial zone with graded properties. The interfacial zone is treated as a nonhomogeneous layer and its elastic modulus is assumed to vary continuously in thickness direction. Three collinear cracks of different length exist, one in each one of the constituent materials perpendicular to the nominal interfaces. A system of singular integral equations applicable under both the mechanical and transient thermal loading conditions is derived. Part I of the paper addresses the details that lead to the derivation of the integral equations and the cracking behavior in the layered medium subjected to mechanical loading. As a result, the values of stress intensity factors are presented as functions of geometric and material parameters of the problem. In Part II, under the uncoupled, quasi-static thermoelastic condition, the response of collinear cracks to thermal shock loading is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bridging micromechanisms of Z-pin in mixed mode delamination

A numerical model for analyzing the bridging mechanisms of Z-pining in composite laminates is presented. Main failure modes of the Z-pin are: debonding between the Z-pin and matrix, split and rupture of the Z-pin material; these have been taken into account here. The cohesive zone model was utilized to simulate splitting and rupturing within the Z-pin. The interfacial contact between the Z-pin and matrix was assumed to be initially bonded, followed by debonding and frictional sliding. The present model is validated by mode I experiments; the mode II simulation is verified by similar Z-pin shear tests. It is observed that the shear bridging force component increases with the mode II ratio, while the mode I bridging response decreases slightly with the mode II ratio. An enhanced frictional zone is located near the delamination surface. The mode II bridging force in cross-ply laminates is higher than that in UD laminates, while the Z-pin is more likely to rupture in cross-ply laminates when the mode II ratio is relatively high. The presented model can be used to evaluate the Z-pin bridging response. The calculated bridging force is suitable for analyzing the mechanical performance of Z-pinned structures.     

A Point‐wise Approach to the Analysis of Complex Composite Structures Using Digital Image Correlation and Thermoelastic Stress Analysis

Thermoelastic stress analysis (TSA) and digital image correlation (DIC) are used to examine the stress and strain distributions around the geometric discontinuity in a composite double butt strap joint. A well‐known major limitation in conducting analysis using TSA is that it provides a metric that is only related to the sum of the principal stresses and cannot provide the component stresses/strains. The stress metric is related to the thermoelastic response by a combination of material properties known as the thermoelastic constant (coefficient of thermal expansion divided by density and specific heat). The thermoelastic constant is usually obtained by a calibration process. For calibration purposes when using orthotropic materials, it is necessary to obtain the thermoelastic constant in the principal material directions, as the principal stress directions for a general structure are unknown. Often, it is assumed that the principal stress directions are coincident with the principal material directions. Clearly, this assumption is not valid in complex stress systems, and therefore, a means of obtaining the thermoelastic constants in the principal stress directions is required. Such a region is that in the neighbourhood of the discontinuities in a bonded lap joint. A methodology is presented that employs a point‐wise manipulation of the thermoelastic constants from the material directions to the principal stress directions using full‐field DIC strain data obtained from the neighbourhood of the discontinuity. A comparison of stress metrics generated from the TSA and DIC data is conducted to provide an independent experimental validation of the two‐dimensional DIC analysis. The accuracy of a two‐dimensional plane strain finite element model representing the joint is assessed against the two experimental data sets. Excellent agreement is found between the experimental and numerical results in the adhesive layer; the adhesive is the only component of the joint where the material properties were not obtained experimentally. The reason for the discrepancy is discussed in the paper.     

Dynamic crack extension along the interface of materials that differ in their thermal properties: with and without thermal relaxation

Summary Moving surface stresses cause crack extension along the interface of perfectly bonded thermoelastic materials at a constant sub-critical speed. The materials differ only in their thermal properties, and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction as well as thermal relaxation with one or two relaxation times. A dynamic steady state of plane strain is assumed. The exact transform solution for a propagating displacement and temperature discontinuity is used to find solutions to the interface crack valid away from the crack edge for low extension speeds and solutions valid at the crack edge for high speeds. Results show that Fourier heat conduction dominates the former case, but solution behavior in the latter is dependent upon the particular thermal model. Thermal mismatch is seen to by itself cause a solution behavior similar to that for bonded dissimilar isothermal elastic solids. In particular, the two-relaxation time solution exhibits both oscillatory and non-oscillatory terms, and the interface temperature at the crack edge is finite.     

Variational multiscale approach to enforce perfect bond in multiple-point constraint applications when forming composite beams

Composite laminates that consist of two or more layers find widespread applications in a variety of engineering structures. In the computational modelling of composite laminates, the layers can be stacked together and connected conveniently at the nodes by using multiple-point constraints (MPCs). However, this type of modelling leads to weakening of the kinematic constraint conditions imposed by the bond between the juxtaposed layers and as a consequence, MPCs application at the nodes produces behaviour that is softer than the perfectly bonded composite beam behaviour. The work herein shows that when kinematic conditions for composite action are weakly imposed in the variational form, they can be enforced in the point-wise sense by proper selection of the interpolation field or otherwise reinforced by using variational multiscale approach without modifying the kinematic model. The originality of the approach presented herein is in the interpretation of the MPCs application as the solution in a superfluously extended space because of the weakening in the kinematic constraints. It is shown that the perfect bond between the composite beam layers can be recovered by excluding the identified fine-scale effect from the solution of the multiple point constraint application. The convergence characteristic of the finite element formulation is also improved by using the variational multi-scale approach. It is also shown that the fine-scale effects can be represented by using extra fictitious elements and springs, which offers a direct correction technique in modelling of composite beams that is especially useful when access to the numerical procedure is limited.