Internal material damping of polymer matrix composites under off-axis loading

The objective of this paper is to determine theoretically the material damping of short fibre-reinforced polymer matrix composites. The major damping mechanism in such composites is the viscoelastic behaviour of the polymer matrix. The analysis was carried out by developing a finite-element program which is capable of evaluating the stress and strain distribution of short fibre composites under axial loading (see Fig. 1a). Using the concept of balance of force we can express the modulusE _x along the loading direction as a function of the mechanical properties of the fibre and matrix materials, fibre aspect ratio,l/d, loading angle,, and fibre volume fraction,V _f. Then we apply the elastic-viscoelastic correspondence principle to replace all the mechanical properties of the composite, fibre and matrix materials such asE _x,E _f,E _m,G _m, by the corresponding complex moduli such asE _x +iE _x , andE _f +iE _f . After separation of the real and imaginary parts, we can expressE _' ^x/t' andE _x ^t" as functions of the fibre aspect ratio,l/d, loading angle,, stiffness ratio,E _f/E _m, fibre volume fraction,V _f, and damping properties of the fibre and matrix materials such as _f and _m. Numerical results of the composite storage modulus,E _x , loss modulus,E _x , and loss factor (damping), _C, are plotted as functions of parameters such asl/d,,V _f, and are discussed in terms of variations ofl/d,, andE _f/E _m, in detail. It is observed that for a given composite, there exist optimum values ofl/d and at whichE _x and _c are maximized. The results of this paper can be used to optimize the performance of composite structures.Nomenclature A _c,A _f,A _m cross-sectional area of composite, fibre and matrix, respectively - d fibre diameter - E _L longitudinal modulus of composite (along the fibre direction) (see Fig. 1a) - E _T transverse modulus of composite (see Fig. 1a) - E _x modulus of composite along thex-direction (see Fig. 1b) - E _f tensile modulus of fibre - E _m tensile modulus of matrix - G _m shear modulus of matrix - G _LT in-plane shear modulus of composite (see Fig. 1a) - l fibre length - m tip to tip distance between fibres - i (–1)^1/2 - R one-half of centre-to-centre fibre spacing - V _f fibre volume fraction - x distance along fibre from end of fibre - defined in Equation 22 - defined in Equation 3 - ^* defined in Equation 19 - _L extensional (longitudinal strain) of composite - _f, _m extensional (longitudinal strain) of fibre and matrix, respectively - _c, _f, _m extensional loss factor of composite, fibre and matrix respectively - G _m shear loss factor of matrix - angle between fibre and thex-direction - ¯ _c, ¯ _f, ¯ _m average longitudinal stress in composite, fibre and matrix, respectively - longitudinal stress in fibre - shear stress at fibre-matrix interface - defined in Equation 23     

含缺陷平纹机织复合材料拉伸力学行为数值模拟

基于平纹机织复合材料的细观结构单胞模型, 考虑其制备过程中产生的孔隙缺陷为随机分布的特征, 通过引入两参数Weibull分布函数, 应用Python语言实现了ABAQUS的二次开发, 并采用Linde等提出的失效准则, 建立了含孔隙缺陷平纹机织复合材料的渐进损伤模型, 利用有限元数值方法模拟了其拉伸应力-应变行为, 针对该模型, 讨论了孔隙缺陷对材料拉伸应力-应变行为的影响, 并阐述了该平纹机织复合材料单胞模型在经向拉伸载荷作用下其纤维束的损伤及演化过程。结果表明, 该模型给出的数值模拟结果与实验数据吻合较好, 证明了模型的有效性, 为该类材料的优化设计及其力学性能分析提供了一种有效方法。      

Experimental study and modeling of fatigue life prediction of plain weave carbon/polymer composite under constant amplitude loading

For fiber-reinforced composites, the anisotropy and the tension-compression asymmetry have very important influence on fatigue performance. The quasi-static and fatigue mechanical behavior of plain weave laminates of carbon/polymer composites were experimentally investigated in this paper. The quasi-static and stress-controlled fatigue tests were carried out on the servo-hydraulic material testing machine. Fracture failure surfaces were observed in micro-mechanism with scanning electron microscopy. A phenomenological and nonlinear constant life diagram (CLD) model was developed based on quasi-static strength and S–N curve data-sets of different stress ratios. The relationship between six parameters of the proposed model and the failure cycles was studied. The fatigue experimental results showed that the fatigue failure type changed from tensile mode to compressive mode at nearby stress ratio R = ?0.2. A satisfactory agreement between the predicted value of cycle life and experimental data was observed. The results indicated that the fatigue performance was adequately described by the Basquin S–N formulation and proposed CLD.     

Survival of actively cooled microvascular polymer matrix composites under sustained thermomechanical loading

Exposure to high heat can cause polymer matrix composites (PMC) to fail under mechanical loads easily sustained at room temperature. However, heat is removed and temperature reduced in PMCs by active cooling through an internal vascular network. Here we compare structural survival of PMCs under thermomechanical loading with and without active cooling. Microchannels are incorporated into autoclave-cured carbon fiber/epoxy composites using sacrificial fibers. Time-to-failure, material temperature, and heat removal rates are measured during simultaneous heating on one face (5–75 kW/m²) and compressive loading (100–250 MPa). The effects of applied compressive load, heat flux, channel spacing, coolant flow rate, and channel distance from the heated surface are examined. Actively cooled composites containing 0.33% channel volume fraction survive without structural failure for longer than 30 min under 200 MPa compressive loading and 60 kW/m² heat flux. In dramatic comparison, non-cooled composites fail in less than a minute under the same loading conditions.     

An analytical method for plain weave fabric composites

A two-dimensional closed-form analytical method has been developed for the thermoelastic analysis of two-dimensional orthogonal plain weave fabric laminae. Strand undulation and continuity in both the warp and fill directions, actual strand cross-section and weave geometry, strand fibre volume fraction and possible gap between the two adjacent strands have been considered in the analysis. Good correlation is observed between the predicted thermoelastic properties and experimental results.     

Interlaminar fracture characterization for plain weave fabric composites

For the analysis of laminated composite plates under transverse loading and drilling of composites, all the elastic, strength and fracture properties of the composite plates are essential. Interlaminar critical strain energy release rate properties in mode I, mode II, mixed mode I/II and mode III have been evaluated for two types of plain weave fabric E-glass/epoxy laminates. The double cantilever beam test and the end notch flexure test have been used for mode I and mode II loading. The mixed mode bending test and split cantilever beam test have been used for mixed mode I/II and mode III loading. It is observed that the plain weave fabric composite with lesser strand width has higher interlaminar fracture properties compared to the plain weave fabric composite with more strand width. Further, crack length versus crack growth resistance plots have been presented for mode III loading. In general, it is observed that total fracture resistance is significantly higher than the critical strain energy release rate.     

Creep of polymer composites

A model incorporating a modified thermal activation theory is presented to model and predict creep of polymer composites. Results are presented of the successful application of this model to predict creep of a unidirectional, continuous-carbon-fiber-reinforced polymer composite (AS4/3501-6) and its epoxy matrix, over a wide range of stress (10–80% of ultimate tensile strength) and temperature (295–433 K). From an analysis of model parameters, it is concluded that the reinforcing carbon fibers do not alter the creep mechanism but do alter the creep behavior of the epoxy matrix, resulting in reductions in creep rate and in the magnitude of creep.     

Micromechanical modeling of interface damage of metal matrix composites subjected to off-axis loading

A three dimensional micromechanics based analytical model is presented to investigate the effects of initiation and propagation of interface damage on the elastoplastic behavior of unidirectional SiC/Ti metal matrix composites (MMCs) subjected to off-axis loading. Manufacturing process thermal residual stress (RS) is also included in the model. The selected representative volume element (RVE) consists of an r × c unit cells in which a quarter of the fiber is surrounded by matrix sub-cells. The constant compliance interface (CCI) model is modified to model interfacial de-bonding and the successive approximation method together with Von-Mises yield criterion is used to obtain elastic–plastic behavior. Dominance mode of damage including fiber fracture, interfacial de-bonding and matrix yielding and ultimate tensile strength of the SiC/Ti MMC are predicted for various loading directions. The effects of thermal residual stress and fiber volume fraction (FVF) on the stress–strain response of the SiC/Ti MMC are studied. Results revealed that for more realistic predictions both interface damage and thermal residual stress effects should be considered in the analysis. The contribution of interfacial de-bonding and thermal residual stress in the overall behavior of the material is also investigated. Comparison between results of the presented model shows very good agreement with finite element micromechanical analysis and experiment for various off-axis angles.     

Prediction of thermal expansion coefficients of plain weave fabric composites

Three plain weave fabric composite analysis models are presented for the prediction of the on-axes thermal expansion coefficients. These are two-dimensional models in the sense that the actual strand cross-sectional geometry, strand undulation and the presence of a gap between the adjacent strands are taken into account. In the first two models, termed refined models, the representative unit cell is discretised into slices and elements and analysed. In the third method, a closed-form solution is presented. In this case, the representative unit cell is idealised as a crossply laminate and analysed. The relative merits and demerits of the models are also discussed. The predicted results are compared with the experimental values. A good correlation is observed.     

Cracking orientation and induced anisotropy of a ceramic matrix composite under off-axis loading

The effect of matrix microcracking on the stiffnesses of a carbon-fibre/SiC-matrix woven composite is studied by means of an ultrasonic method. It provides the whole set of the stiffness tensor coefficients which are inaccessible by classical strain measurements and which are required to identify anisotropic damage. The induced anisotropy depends on the loading direction. If a tensile solicitation in a fibre direction leads to stiffnesses decreases without any rotation of principal axes, a tensile solicitation of 45° from a fibre direction creates microcracks with a predominant orientation that does not coincide with the elastic symmetry axes, and induce a fully anisotropic elastic degradation.     

A micromechanical approach for the fatigue failure prediction of unidirectional polymer matrix composites in off-axis loading including the effect of viscoelasticity

A novel micromechanical approach is used to study the fatigue failure of unidirectional polymer matrix composites subject to off-axis loading. The main advantage of the present micromechanical model lies in its ability to give closed form solutions for the effective nonlinear response of unidirectional composites and to predict the material response to any combination of shear and normal loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S–N diagrams of the composite material in longitudinal, transverse, and shear loadings; thus, eliminating the need for any further experimentation. Unlike previous works, the present study accounts for the viscoelasticity of the matrix material rendering it the capability of modeling creep damage accumulation in high-temperature composite materials. The results are found to be in good agreement with the literature. In particular, for higher off-axis angles, the results are seen to be in better concurrence with the experimental data compared to when the effect of viscoelasticity is overlooked. The present approach is also capable of accounting for the strain evolution due to viscoelasticity of the matrix material.     

Thermo-mechanical behaviour of plain weave fabric composites: Experimental investigations

An experimental investigation has been performed to elucidate the on-axes thermo-mechanical behaviour of two-dimensional orthogonal plain weave fabric laminates. Specifically T-300 carbon/epoxy and E-glass/epoxy systems were investigated for Youngs modulus, inplane shear modulus, Poissons ratio, linear thermal expansion coefficient, tensile strength and inplane shear strength. It is observed that there is a significant effect of weave geometrical parameters on the thermo-mechanical behaviour of woven fabric laminates. Properties of the woven fabric laminates are compared with the properties of the corresponding unidirectional balanced symmetric crossply laminates. A good correlation is observed between the experimental results and analytical predictions.     

Compressive damage mechanism of GFRP composites under off-axis loading: Experimental and numerical investigations

Experimental and computational studies of the microscale mechanisms of damage formation and evolution in unidirectional glass fiber reinforced polymer composites (GFRP) under axial and off-axis compressive loading are carried out. A series of compressive testing of the composites with different angles between the loading vector and fiber direction were carried out under scanning electron microscopy (SEM) in situ observation. The damage mechanisms as well as stress strain curves were obtained in the experiments. It was shown that the compressive strength of composites drastically reduces when the angle between the fiber direction and the loading vector goes from 0° to 45° (by 2.3–2.6 times), and then slightly increases (when the angle approaches 80–90°). At the low angles between the fiber and the loading vector, fiber buckling and kinking are the main mechanisms of fiber failure. With increasing the angle between the fiber and applied loading, failure of glass fibers is mainly controlled by shear cracking. For the computational analysis of the damage mechanisms, 3D multifiber unit cell models of GFRP composites and X-FEM approach to the fracture modeling were used. The computational results correspond well to the experimental observations.     

Progressive damage analysis and strength prediction of 2D plain weave composites

A two-step, multi-scale progressive damage analysis is implemented to study the damage and failure behaviors of 2D plain weave composites under various uniaxial and biaxial loadings. In the progressive damage mode (PDM), a formal-unified 3D Hashin-type criterion is formed to facilitate analysis work and engineering application, with shear nonlinearity considered in the stiffness matrix of yarn. The periodic boundary conditions are developed for the off-axis loading simulations. The simulated stress–strain curves under on-axis uniaxial tension and compression show good agreements with experimental results. The influences of different 3D Hashin-type criteria are subsequently discussed. Moreover, the strength decrease at different off-axis angles and the failure envelopes under on-axis and 45° off-axis biaxial loadings are obtained, with the discussion of different failure characteristics under each loading condition.     

Micromechanics models for the elastic constants and failure strengths of plain weave composites

In this paper, two models are presented for plain weave composites. One is finite element analysis (FEA) model for elastic constants, namely, sinusoidal yarn model. Another is analytical model for failure strengths, namely, sinusoidal beam model. The FEA model is generated by interfacing an in-house computer code with FEA software strand6, and the analytical model is developed using the theory of elasticity. Numerical studies are carried out using the present models to investigate the effects of some major geometrical parameters on the properties of plain weave composites. It is concluded that the failure strengths are closely related to the fiber volume fraction of a yarn, and the mechanical properties are closely related to the overall fiber volume fraction of the composites. An experimental testing program is conducted for T300/934 plain weave composites to validate the developed models. A good agreement exists between the predicted and measured results.     

Durability of polymer matrix composites: Viscoelastic effect on static and fatigue loading

The structural applications of polymer matrix composites (PMC) demand lifetimes of 15, 25 and 50 years. However, the mechanical properties of these composites have a time dependent nature, i.e. strength and stiffness are time-dependent due to the hereditary nature (viscoelasticity) of polymers. In this context lifetime models for viscoelastic materials, i.e. energy-based criteria and fracture mechanics extended to viscoelastic media, are revised. These models are applied to predict the lifetime of composite materials under special cases of constant load (creep rupture) and constant stress rate to failure. It is verified that these lifetime theories predict similar relationship between creep failure and constant stress rate failure strength. Alternative approaches based on Strength Evolution Integral [Reifsnider KL, Stinchcomb WW. A critical element model of the residual strength and life of fatigue–loaded composite coupons. In: Hahn HT, editor. Composite materials: fatigue and fracture (ASTM STP 907). Philadelphia (PA): American Society for Testing and Materials; 1986. p. 298–313; Reifsnider KK, Case SC, Duthoi J. The mechanics of composite strength evolution. Compos Sci Technol 2000; 60:2539–46; Reifsnider KK, Case SC. Damage tolerance and durability in material systems. Wiley-Interscience; 2002] and on Linear Damage Accumulation (LCD) law confirm these results. In addition the LCD law was found to be generally unsatisfactory except for the special case of constant stress rate to failure. Accordingly this result validates the accelerated methodology proposed by [Miyano Y, McMurray M, Enyama J, Nakada M. Loading rate and temperature dependence on flexural fatigue behavior of a satin woven CFRP laminate. J Compos Mater 1994;28(13):1250–60; Miyano Y, Nakada M, McMurray MK, Muki R. Prediction of flexural fatigue strength of CRFP composites under arbitrary frequency, stress ratio and temperature. J Compos Mater 1997;31(6):619–38; Miyano Y, Nakada M, Kudoh H, Muki R. Prediction of tensile fatigue life for unidirectional CFRP. J Compos Mater 2000;34(7):538–50; Miyano Y, Nakada M, Sekine N. Accelerated testing for long-term durability of GFRP laminates for marine use. Compos: Part B 2004;35:497–502; Miyano Y, Nakada M, Sekine N. Accelerated testing for long-term durability of FRP laminates for marine use. J Compos Mater 2005;39(1):5–20], which is based on LCD law, to characterize long-term creep failure of polymer composites based on the constant stress rate failure strength curves.Finally a new formulation is proposed, based on Strength Evolution Integral, to predict of fatigue failure load for an arbitrary load ratio.     

Thermal–mechanical cell model for unbalanced plain weave woven fabric composites

A high fidelity assessment of accumulative damage of woven fabric composite structures subjected to aggressive loadings is strongly reliant on the accurate characterization of the inherent multiscale microstructures and the underlying deformation phenomena. The stress and strain fields predicted at a global structural level are unable to determine the damage and failure mechanisms at the constituent level and the resulting stiffness degradation. To establish a mapping relation between the global and constituent response parameters, a new four-cell micromechanics model is developed for an unbalanced weave subjected to a thermal–mechanical loading. The developed four-cell micromechanics model not only bridges the material response from one length scale to another but also quantifies the composite thermal–mechanical properties at a given state of constituent damage. The thermal–mechanical mapping relations at different microstructural levels are derived based on the multicell homogenization, intercell compatibility conditions, and energy methods. Because of the high computational efficiency of the developed thermal–mechanical micromechanics model, it can be linked with a finite-element-based dynamic progressive failure model, where the response parameters at different microstructural levels can be extracted for each Gaussian point and at each time step. The accuracy and the dual function of the developed micromechanics model are demonstrated with its application to a balanced plain weave, an unbalanced plain weave, and failure mode simulation of a tensile coupon test.     

Modeling behavior of cross-ply ceramic matrix composites under quasi-static loading

This paper presents a simplified analysis (model and failure criteria) for predicting the stress-strain responce of cross-ply fiber-reinforced ceramic composite laminates under quasi-static loading and unloading conditions. The model formulation is an extension of the modified shear-lag theory previously introduced by the authors for analyzing unidirectional laminates for the same loading conditions. The present formulation considers a general damage state consisting of matrix cracking in both the transverse and longitudinal plies, as well as fiber failure. These damage modes are modeled by a set of failure criteria with the minimum reliance on empirical data, and can be easily employed in a variety of numerical or analytical methods. The criteria used to estimate the extent of matrix cracking and interfacial debonding are closed-form and require the basic material properties. The failure criterion for fiber failure requires a priori knowledge of a single empirical constant. This parameter, however, may be determined without microscopic investigation of the laminate microstructure. The results from the present simplified analysis match well with the experimental data.The U.S. Government right to retain a non-exclusive royalty-free license in and to any copyright is acknowledged.