Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics

A method for determining the in situ strength of fiber-reinforced laminas for three types of transverse loading including compression, tension and shear is presented. In the framework of this method, an analysis of local stresses that are responsible for the coalescence of matrix cracks is carried out by using a multi-fiber unit cell model and finite element method. The random distribution of fibers, fiber–matrix decohesion and matrix plastic deformations are taken into account in the micromechanical simulations. The present study also shows that the nonlinear hardening behavior of matrix reflects more realistically the influence of plastic deformations on the in situ transverse strength of lamina than the perfectly plastic behavior of matrix. The prediction of the in situ transverse strength is verified against the experimental data for a cross ply laminate subjected to uniaxial tension.     

缝合复合材料层合板拉伸疲劳损伤及其机理

对有、无缝合复合材料层合板的拉伸疲劳性能进行了试验研究,考察了0^\circ缝合对复合材料光滑板拉伸疲劳损伤扩展规律的影响. 通过有限元素法分析了有、无缝合复合材料层合板的应力状态分布情况,对缝合复合材料层合板的拉伸疲劳损伤及其扩展机理进行了分析. 研究表明,缝合改变了复合材料层合板拉伸疲劳损伤起始与扩展的机理,针脚附近的面内正应力\sigma_{x}与层间剪应力的集中对层合板拉伸疲劳损伤的发生与扩展有着重要的作用,自由边界处的层间集中应力对缝合板的疲劳性能也有影响. 自由边界处的层间集中应力是导致无缝合层合板疲劳损伤及其扩展的主要原因.      

复合材料层合板面内渐进损伤分析的CDM模型

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.      

复合材料层合板面内渐进损伤分析的CDM模型简

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.     

Stiffened Composite Panels with a Stress Concentrator Under in-Plane Compression

The in-plane compressive strength of a stiffened thin-skinned composite panel with a stress concentrator is examined. Two possible in-plane failure mechanisms are investigated. The first one is near-surface instability at the edge of the cutout, where high stress gradients are expected because of the stress concentration and the thickness heterogeneity of the laminated skin. Analytical 3D formulas allowing simple parametrical investigation of the phenomenon under consideration are derived. The second failure mechanism is fiber microbuckling in 0°-plies. An equivalent crack model is used to predict the compressive strength of a multidirectional composite laminate. How a stiffener affects the compressive strength of the thin-skinned panel with a hole is studied for both mechanisms. Experimental and predicted values of the critical load are in good agreement.     

Assessment of composite failure and ultimate strength without experiment on composite

This paper attempts to estimate the ultimate strength of a laminated composite only based on its con- stituent properties measured independently. Three important issues involved have been systematically addressed, i.e., stress calculation for the constituent fiber and matrix materials, failure detection for the lamina and laminate upon the internal stresses in their constituents, and input data determination of the constituents from monolithic measurements. There are three important factors to influence the accuracy of the strength prediction. One is the stress concentration factor （SCF） in the matrix. Another is matrix plasticity. The third is thermal residual stresses in the constituents. It is these three factors, however, that have not been sufficiently well realized in the composite community. One can easily find out the elastic and strength parameters of a great many laminae and laminates in the current literature. Unfortunately, necessary information to determine the SCF, the matrix plasticity, and the thermal residual stresses of the composites is rare or incomplete. A useful design methodology is demonstrated in the paper.     

Analysis of progressive fiber debonding in elastic laminates

The evolution of fiber debonding, and sliding, in fibrous laminates is modeled by a coupled micro/macro-mechanical analysis scheme. The laminates under consideration have a symmetric layup, and are subjected to mechanical loads. The individual plies are elastic, have a unidirectional reinforcement, and can suffer local damage at the fiber/matrix interface when the resolved normal and shear stresses exceed their ultimate magnitudes. The local fields in the plies are assumed to be periodic, and are approximated by the finite element method for overall loads and local resolved stresses that are in excess of the interface strength. Local effects in the individual plies are scaled up to the laminate analysis through stress transformation factors, which are a function of the elastic properties of the plies and their stacking configuration.The proposed analysis was implemented for a periodic array model of the laminas, and for in-plane loading of the laminate. The model predictions for a unidirectional steel/epoxy system subjected to transverse loading compare remarkably well with experimental measurements. This result, and several other examples given for axial and off-axis loading of SiC/CAS laminates, illustrate the model capabilities in predicting the overall strains in the presence of simultaneous, progressive debonding in the individual plies.     

Analytical modeling and finite element simulation of the plastic collapse of sandwich beams with pin-reinforced foam cores

Analytical predictions are presented for the plastic collapse strength of lightweight sandwich beams having pin-reinforced foam cores that are loaded in 3-point bending. Both polymer and aluminum foam cores are considered, whilst the facesheet and the pins are made of either composite or metal. Four different failure modes are account for: metal facesheet yield or composite facesheet microbuckling, facesheet wrinkling, plastic shear of the core, and facesheet indentation beneath the loading rollers. A micromechanics-based model is developed and combined with the homogenization approach to calculate the effective properties of pin-reinforced foam cores. To calculate the elastic buckling strength of pin reinforcements, the pin-reinforced foam core is treated as assemblies of simply supported columns resting upon an elastic foundation. Minimum mass design of the sandwich is then obtained as a function of the prescribed structural load index, subjected to the constraint that none of the above failure modes occurs. Collapse mechanism maps are constructed and compared with the failure maps of foam-cored sandwich beams without pin reinforcements. Finite element simulations are carried out to verify the analytical model and to study the performance and failure mechanisms of the sandwich subject to loading types other than 3-point bending. The results demonstrate that the weaker the foam is, the more optimal the pin-reinforced foam core becomes, and that sandwich beams with pin-reinforced polymer foam cores are structurally more efficient than foam- or truss-cored sandwich beams.     

Non-linear dynamic response of a thin laminate subject to non-uniform thermal field

Non-linear dynamics behavior of a thin isotropic laminate in a simply supported boundary condition is studied for its response with both mechanical and thermal loads in effect. The thermal effects of both the in-plane and transverse non-uniform temperature variations in steady-state are considered. The equation of motion for the laminate deflection is reduced to the Duffing equation in a decoupled modal form by means of a generalized Galerkin's method. The stress field as a function of deflection and temperature variation is also obtained in a plane stress condition for its non-linear elastic behavior with von Karman strain field.For an exemplary laminated microstructure used as a printed wiring board, it is found that a high rise of the in-plane temperature increases the resonance frequency and could significantly increase the stresses of the lamina. The through thickness temperature variation has no significant effect on the deflection. Failure analysis is also made based on the composite failure criteria for a laminate to identify the critical mechanical and thermal loads.     

Compressive failure of fiber composites under multi-axial loading

This paper examines the compressive strength of a fiber reinforced lamina under multi-axial stress states. An equilibrium analysis is carried out in which a kinked band of rotated fibers, described by two angles, is sandwiched between two regions in which the fibers are nominally straight. Proportional multi-axial stress states are examined. The analysis includes the possibility of bifurcation from the current equilibrium state. The compressive strength of the lamina is contingent upon either attaining a load maximum in the equilibrium response or satisfaction of a bifurcation condition, whichever occurs first. The results show that for uniaxial loading a non-zero kink band angle β produces the minimum limit load. For multi-axial loading, different proportional loading paths show regimes of bifurcation dominated and limit load dominated behavior. The present results are able to capture the beneficial effect of transverse compression in raising the composite compressive strength as observed in experiments.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

缝纫复合材料层合板面内弹性模量分析

基于对缝纫孔附近局部细观结构的分析,提出了一种预测缝纫复合材料层合板面内力学性能的理论模型．从分析缝孔单胞的纤维弯曲几何特征入手,最终得到单向板及层合板的弹性常数．通过有限元分析研究了缝纫参数对复合材料层合板面内等效模量的影响．研究结果表明,缝纫造成单向板及层合板面内材料性质的不均匀,随着缝纫密度和缝纫线直径的增加,层合板的等效模量逐渐降低．     

考虑内部损伤影响的层合板最终强度预测

层合板强度分析若只考虑面内失效而忽略自由边界处的分层失效,往往会高估强度值,得不到合理的预测结果.该文提出了一种层合板强度的数值分析方法,综合考虑了层合板的面内失效(基体失效和纤维断裂)以及层间分层失效.采用有限元方法对层合板进行结构分析得到板的应力响应,结合面内失效判据和分层失效判据对层合板各个单层进行失效判断,采用刚度退化和逐步失效方法求得层合板的最终失效强度.与以往方法相比,该文模型和方法考虑的因素更全面.数值算例表明该方法预测得到的最终失效载荷和分层起始载荷和已有文献实验结果一致.     

Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires

Previous atomistic simulations and experiments have shown an increased Young's modulus and yield strength of fivefold twinned (FT) face-centered cubic metal nanowires (NWs) when compared to single crystalline (SC) NWs of the same orientation. Here we report the results of atomistic simulations of SC and FT Ag, Al, Au, Cu and Ni NWs with diameters between 2 and 50 nm under tension and compression. The simulations show that the differences in Young's modulus between SC and FT NWs are correlated with the elastic anisotropy of the metal, with Al showing a decreased Young's modulus. We develop a simple analytical model based on disclination theory and constraint anisotropic elasticity to explain the trend in the difference of Young's modulus between SC and FT NWs. Taking into account the role of surface stresses and the elastic properties of twin boundaries allows to account for the observed size effect in Young's modulus. The model furthermore explains the different relative yield strengths in tension and compression as well as the material and loading dependent failure mechanisms in FTNWs.     

PREDICTIVE APPROACH TO FAILURE OF COMPOSITE LAMINATES WITH EQUIVALENT CONSTRAINT MODEL

<正>This work established a new analytical model based upon the equivalent constraint model(ECM)to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading,by taking into account the effect of matrix cracking.The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate.Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates,is introduced for the construction of the failure criterion. The effects of lamina properties,lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper.A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems.The theory predictions demonstrated great match with the experimental observations investigated in this study.     

Evaluation of Failure Behavior of Transversely Loaded Unidirectional Model Composites

A leading reason for the limited use of laminated composite materials in primary structural applications is that the failure initiates in the ply oriented transverse to the direction of the applied load at a much lower strain level than that which would cause the ultimate failure of the laminate. Previous studies indicate that transverse failure is manifested as either cavitation-induced failure of the matrix system or fiber-matrix debonding. The mechanism causing the failure initiation event is not decidedly known and depends on the local stress field of the constrained matrix that is a function of fiber spacing. In the present study a model composite system using a transparent matrix is employed in a cruciform-shaped specimen to evaluate the viability of several transverse failure theories. The cruciform-shaped specimen utilizes a low strain-to-failure 828/D230 RT cured epoxy and stainless steel wires arranged such that a fiber is placed at the intersection of face diagonals of four remaining fibers located at corners of a square. The transverse failure mechanism is observed in-situ via the reflected light method and recorded utilizing high resolution, high magnification microscope cameras. A parametric study is conducted using three dimensional finite element models to analyze the stress state in the cruciform specimen as a function of fiber spacing. The result of the 3-D FE models in conjunction with experimental observations are used to evaluate the transverse failure theories suggested in the literature. In addition this data will be used to develop a comprehensive failure criterion for transversely loaded multi-fiber composites that encompasses the dependence on fiber spacing.     

Compressive failure strengths and modes of woven S2-glass reinforced polyester due to quasi-static and dynamic loading

The failure strengths and modes of the woven S2-glass reinforced polyester thick laminate are characterized through a comprehensive set of experiments. Compression strength tests in different directions were performed, and optical and scanning electron microscopy studies of the fractured specimen surfaces were conducted. The failure modes are complex involving a combination of failure mechanisms. The failure stresses and strains in the ply lay-up direction were higher than those in the plane of the lamina. The material's dynamic response was determined using both the split Hopkinson pressure bar and the direct disk impact techniques. The material was found to be significantly strain rate sensitive.     

Compressive response and failure of balsa wood

Balsa wood is a natural cellular material with excellent stiffness-to-weight and strength-to-weight ratios as well as superior energy absorption characteristics. These properties are derived from the microstructure, which consists of long slender cells (tracheids) with approximately hexagonal crosssections that are arranged axially. Parenchyma are a second type of cells that are radially arranged in groups that periodically penetrate the tracheids (rays). Under compression in the axial direction the material exhibits a linearly elastic regime that terminates by the initiation of failure in the form of localized kinking. Subsequently, under displacement-controlled compression, a stress plateau is traced associated with the gradual spreading of crushing of the cells through the material. The material is less stiff and weaker in the tangential and radial directions. Compression in these directions crushes the tracheids laterally but results in a monotonically increasing response typical of lateral crushing of elastic honeycombs. The elastic and inelastic properties in the three directions have been established experimentally as a function of the wood density. The microstructure and its deformation modes under compression have been characterized using scanning electron microscopy. In the axial direction it was observed that in the majority of the tests, failure initiated by kinking in the axial–tangential plane. The local misalignment of tracheids in zones penetrated by rays ranged from 4° to 10° and axial compression results in shear in these zones. Measurement of the shear response and the shear strength in the planes of interest enabled estimation of the kinking stress using the Argon–Budiansky kinking model. The material strength predicted in this manner has been found to provide a bounding estimate of the axial strength for a broad range of wood densities. The energy absorption characteristics of the wood have also been measured and the specific energy absorption was found to be comparable to that of metallic honeycombs of the same relative density.     

STAGS computational procedure for progressive failure analysis of laminated composite structures

Non-linear analyses are difficult simulations to perform and place increased demands not only on the computational systems but also on the analyst. The number of possible problems and/or difficulties increases significantly compared to those for linear elastic analyses. Combined material and geometric non-linearities challenge the analyst and the solution algorithms. Progressive failure and damage propagation for composite structures result in even more complexities due to the discrete, abrupt changes in local material stiffness. Analysts need to interrogate the computed solutions carefully based on their understanding of structural mechanics, material behavior, computational procedures and non-linear phenomena to distill correct physics from such simulations. This paper describes the computational strategy incorporated into the STAGS non-linear finite element analysis code with special emphasis on progressive failure analysis of laminated composite structures. Results for selected laminated composite structures are used to demonstrate the PFA capability.