Micromechanical analysis for thermoviscoplastic behavior of unidirectional fibrous composites

A three-dimensional micromechanics formulation for fiber-reinforced composites containing viscoplastic matrix materials is presented. The micromechanics model is based on the relaxation of the coupling effect between the normal and shear stresses. Three variations of Bodner's theory of viscoplasticity are used to predict the thermoviscoplastic behavior of unidirectional metal-matrix composites; first, the original isotropic-hardening model of Bodner and Partom; second, Ramaswamy's extension of the theory through the inclusion of a back stress; and third, Stouffer and Bodner's extension of the theory through a special form of directional hardening. Comparisons with numerical solutions and experimental data of other researchers are made to demonstrate the accuracy of the model. Micromechanical analyses of metal-matrix composites under both in-phase and out-of-phase thermomechanical fatigue-loading conditions are also presented for comparison with experiments and previous models.     

Micromechanical analysis of fuzzy fiber reinforced composites

A novel fuzzy fiber reinforced composite (FFRC) reinforced with zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is proposed. The distinct constructional feature of this composite is that the uniformly aligned CNTs are radially grown on the surface of carbon fibers. Analytical models based on the mechanics of materials approach and the Mori–Tanaka method are derived to estimate the effective elastic constants of this proposed FFRC. The values of the effective elastic properties of this composite are estimated with and without considering an interphase between the CNT and the polymer matrix. It has been found that the transverse effective properties of this composite are significantly improved due to the radial growing of CNTs on the surface of carbon fiber. The effective properties are also found to be sensitive to the CNT diameter.     

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.     

Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: A review

An overview of methods of the mathematical modeling of deformation, damage and fracture in fiber reinforced composites is presented. The models are classified into five main groups: shear lag-based, analytical models, fiber bundle model and its generalizations, fracture mechanics based and continuum damage mechanics based models and numerical continuum mechanical models. Advantages, limitations and perspectives of different approaches to the simulation of deformation, damage and fracture of fiber reinforced composites are analyzed.     

Elastoplastic shear-lag analysis of single-fiber composites and strength prediction of unidirectional multi-fiber composites

A new procedure is proposed to predict the strength of multi-fiber composite based on the single fiber composite test. First, the flaw distribution in an embedded fiber is estimated with the statistical simulation. The stress distribution in the simulation is obtained by the elastoplastic shear-lag analysis considering the linear strain hardening effect of matrix. The simulated results are found to fit well with the experimental data, which shows the validity of the present simulation to estimate the statistical strength parameters for the embedded fiber. Then, the multi-fiber composite strength is predicted based on the obtained statistical fiber strength parameters. The stress profile in the multi-fiber composite is calculated with the elastoplastic three-dimensional (3D) shear-lag-analysis. The predicted strength via the weakest size scaling technique has a good agreement with our previous experimental data.     

Micromechanical analysis of fiber-reinforced composites on account of influence of fiber coatings

The new asymptotic method for the analysis of inhomogeneous composite materials on account of the micromechanical influence of fiber coatings is proposed in the present paper. The problem of longitudinal shear of the fiber-reinforced composites with the square and hexagonal lattices of periodically distributed parallel cylindrical fibers is examined. The asymptotic homogenization method is applied and the relevant unit cell problem is solved with the aid of the method of perturbation of boundary shape. The asymptotic analytical solutions are found for the effective longitudinal shear moduli and for the local stresses occurring in the composites on the microlevel. Local shear stresses along the fiber-coating and the matrix-coating interfaces are calculated. The influence of properties of coatings on the maximum local shear stresses on the interfaces of constituents is analysed. The obtained results are suitable for any values of stiffness and volume fractions of constituents, including the limiting case of absolutely rigid fibers converging to contact.     

The longitudinal tensile strength of unidirectional fibrous composites

When a fibre-plastic composite in which the fibres are brittle, continuous, and unidirectional is subjected to longitudinal tension under essentially static loading conditions, there exists a range of possible composite strengths. This paper presents a model which may be used to predict that range of possible composite strengths. An important feature of the model is that it considers both static and dynamic stress concentration effects on intact fibres which result from a fibre failure. A computer simulation technique is used to generate a set of generalized scatter limits for the average fibre stress at composite failure from the model. The generalized scatter limits may be used to predict the range of strengths for a composite material. The model results are used to predict the ranges of strength for composite materials prepared from three types of carbon fibre and these are compared with experimental results.     

Size effect and strength variability of unidirectional composites

Statistical theories have been proposed for damage accumulation and tensile failure of unidirectionally reinforced fibrous composites. These theories involve the mechanical properties of the constituent fibers, the geometry of the composite, and some inadequately known functions such as stress distributions in the vicinity of single and multiple fiber breaks. As a result in trying to correlate theory and experiment some quantities have to be treated as unknown parameters.It was found that use of Hedgepeth and Van Dyke's stress concentration factors led to good agreement between theory and Bullock's data on graphite epoxy only when the overloaded length of fiber at crack tips was assumed to have an unrealistically large value. A possible explanation is that the Hedgepeth and Van Dyke stress concentration factors were calculated for composites with a geometrically perfect fiber array. In real composites the fiber spacing is quite irregular. A theory is developed for strength of irregularly constructed composites and compared with experiment. Taking the effect into account improves agreement in the case of one experiment and impairs agreement in the case of another.

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Résumé On a proposé des théories statistiques pour évaluer l'accumulation du dommage et la rupture par traction dans des composites fibreux à renforcement unidirectionnel. Ces théories incluent les propriétés mécaniques des fibres constituantes, la géométrie du produit composite ainsi que certaines fonctions indéterminées, telles que la distribution des contraintes au voisinage de rupture de fibres simple ou multiple. En conséquence, et afin de tenter une correlation entre la théorie et l'expérience, certaines quantités ont été considérées comme des paramètres inconnus.On a trouvé que l'utilisation des facteurs de concentration de tensions de contraintes de Hegepeth et de Van Dyke conduisent à un bon accord entre la théorie et les données obtenues par Bullock sur des epoxys au graphite, pour autant que la longueur de fibre surchargée aux extrémités d'une fissure soit supposée avoir une taille exagérément grande. Une explication possible est que les facteurs de concentration de Hedgepeth et Van Dyke ont été calculés pour des composites présentant une distribution géométrique parfaite de fibres. Dans des composites réels, l'espacement entre les fibres est assez irrégulier. On développe une théorie sur la résistance de composites élaborés de manière irrégulière et on compare la théorie avec l'expérience. En prenant en compte cet effet, on observe une amélioration de la correlation dans le cas d'une expérience et une détérioration de la correlation dans le cas d'une autre expérience.

     

孔隙微观特征对碳纤维/环氧树脂复合材料横向拉伸强度的影响

通过有限元方法研究了相同孔隙率下孔隙的分布、尺寸和形状等微观特征对碳纤维增强环氧树脂复合材料单向板横向拉伸强度的影响。首先使用Matlab对复合材料微观图像进行处理,提取孔隙的半径分布。然后通过C++编写多种孔隙随机分布算法,包括可以生成不同分布孔隙、不同尺寸孔隙以及不同形状孔隙的随机分布算法。最后通过Python参数化生成代表性体积单元（RVE）,用有限元方法研究相同孔隙率下孔隙的分布、尺寸和形状对碳纤维/环氧树脂复合材料单向板横向拉伸强度的影响。研究结果显示,孔隙率相同时,碳纤维/环氧树脂复合材料的孔隙形状对横向弹性模量的影响较大,孔隙尺寸和形状对横向拉伸强度有较大的影响。     

Micromechanisms of damage in unidirectional fiber reinforced composites: 3D computational analysis

Numerical micromechanical investigations of the mechanical behavior and damage evolution of glass fiber reinforced composites are presented. A program code for the automatic generation of 3D micromechanical unit cell models of composites with damageable elements is developed, and used in the numerical experiments. The effect of the statistical variability of fiber strengths, viscosity of the polymer matrix as well as the interaction between the damage processes in matrix, fibers and interface are investigated numerically. It is demonstrated that fibers with constant strength ensure higher strength of a composite at the pre-critical load, while the fibers with randomly distributed strengths lead to the higher strength of the composite at post-critical loads. In the case of randomly distributed fiber strengths, the damage growth in fibers seems to be almost independent from the crack length in matrix, while the influence of matrix cracks on the beginning of fiber cracking is clearly seen for the case of the constant fiber strength. Competition between the matrix cracking and interface debonding was observed in the simulations: in the areas with intensive interface cracking, both fiber fracture and the matrix cracking are delayed. Reversely, in the area, where a long matrix crack is formed, the fiber cracking does not lead to the interface damage.     

Effect of interfacial adhesion and statistical fiber strength on tensile strength of unidirectional glass fiber/epoxy composites. Part I: experiment results

The effects of fiber surface treatment on ultimate tensile strength (UTS) of unidirectional (UD) epoxy resin matrix composites are examined experimentally. The interfacial shear strength (IFSS) and statistical fiber strength are significantly altered by five different kinds of surface treatments, which are: (a) unsized and untreated; (b) γ-glycidoxypropyltrimethoxysilane (γ-GPS); (c) γ-methacryloxypropyltrimethoxysilane (γ-MPS); (d) mixture of γ-aminoxypropyltrimethoxysilane (γ-APS), film former (urethane) and lubricant (paraffin); and (e) urethane-sized. The maximum UTS is obtained for the relatively strong interfacial adhesion (glass/γ-MPS/epoxy) but not for the strongest interfacial adhesion (glass/γ-GPS/epoxy). The governing micro-damage mode around a broken fiber and the interface region is matrix cracking for γ-GPS treated fibers, and a combination of interfacial debonding and matrix cracking for γ-MPS treated fibers. The micro-damage mode related to the interfacial adhesion strongly affects the fracture process, and thus the UTS of UD composites. The results also indicate that the interfacial adhesion can be optimized for effective utilization of fiber strength for fiber composites. A parameter called “efficiency ratio” of fiber strength in UD composites is proposed to examine and distinguish different effects of IFSS and fiber strength on the UTS of UD composites. The experimental results show that improved UTS of UD composites due to surface treatments mainly result from the increase in fiber strength but not from the modified interface.     

Enhancing compressive strength of unidirectional polymeric composites using nanoclay

Morphology of nanoclay dispersed in resin and suspended in acetone was studied using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). SEM and TEM images show intercalation of resin in the gallery spaces of nanoclay and regions of exfoliated clay with random orientation. A vacuum assisted wet lay-up (VAWL) process was used for the inclusion of nanoclay in conventional fiber reinforced composites. The VAWL specimen displayed improvement in off-axis compressive strength for nanoclay enhanced fiber composites. Addition of nanoclay produced a substantial increase in longitudinal compressive strengths (extracted from off-axis tests) of glass fiber reinforced composites. An elastic–plastic model was used to predict the compressive strength of fiber reinforced composites based on the matrix properties. The model predictions matched well with the experimental results.     

Compressive response and failure of fiber reinforced unidirectional composites

The compressive response of polymer matrix fiber reinforced unidirectional composites (PMC's) is investigated via a combination of experiment and analysis. The study accounts for the nonlinear constitutive response of the polymer matrix material and examines the effect of fiber geometric imperfections, fiber mechanical properties and fiber volume fraction on the measured compressive strength and compressive failure mechanism.Glass and carbon fiber reinforced unidirectional composite specimens are manufactured in-house with fiber volume fractions ranging over 1060 percent. Compression test results with these specimens show that carbon fiber composites have lower compressive strengths than glass fiber composites. Glass fiber composites demonstrate a splitting failure mode for a range of low fiber volume fractions and a simultaneous splitting/kink banding failure mode for high fiber volume fractions. Carbon fiber composites show kink banding throughout the range of fiber volume fractions examined. Nonlinear material properties of the matrix, orthotropic material properties of the carbon fiber, initial geometric fiber imperfections and nonuniform fiber volume fraction are all included in an appropriate finite element analysis to explain some of the observed experimental results. A new analytical model predictionof the splitting failure mode shows that this failure mode is favorable for glass fiber composites, which is in agreement with test results. Furthermore, this modelis able to show the influence of fiber mechanical properties, fiber volume fraction and fiber geometry on the splitting failure mode.     

单向纤维增强聚合物复合材料压缩渐进破坏单向纤维增强聚合物复合材料压缩渐进破坏

复合材料结构在承压时破坏如何演化,是其强度破坏分析的基础和核心任务。本文提出了基于连续介质损伤力学（CDM）的单向纤维增强聚合物复合材料压缩破坏渐进损伤分析（PDA）模型。建模中考虑了材料非线性行为、失效判断及损伤演化中材料性能退化等基本问题,分别对应于拉压不对称弹塑性本构关系、Puck准则、LaRC05准则及考虑破坏面方向的刚度退化方法。该模型通过用户材料子程序接口VUMAT引入到有限元软件ABAQUS中实现了有限元求解。对文献中提供的纵向、横向及偏轴压缩案例进行了数值计算并与试验数据对比。数值分析结果与试验数据吻合较好,证明了该方法的合理性和有效性,对开展多向层合板压缩破坏分析富有参考价值。      

Characteristics of continuous unidirectional kenaf fiber reinforced epoxy composites

Kenaf fibers generally has some advantages such as eco-friendly, biodegradability, renewable nature and lighter than synthetic fibers. The aims of the study are to characterize and evaluate the physical and mechanical properties of continuous unidirectional kenaf fiber epoxy composites with various fiber volume fractions. The composites materials and sampling were prepared in the laboratory by using the hand lay-up method with a proper fabricating procedure and quality control. Samples were prepared based on ASTM: D3039-08 for tensile test and the scanning electron microscopy (SEM) was employed for microstructure analysis to observe the failure mechanisms in the fracture planes. A total of 40 samples were tested for the study. Results from the study showed that the rule of mixture (ROM) analytical model has a close agreement to predict the physical and tensile properties of unidirectional kenaf fiber reinforced epoxy composites. It was also observed that the tensile strength, tensile modulus, ultimate strain and Poisson’s ratio of 40% fiber volume content of unidirectional kenaf fiber epoxy composite were 164 MPa, 18150 MPa, 0.9% and 0.32, respectively. Due to the test results, increasing the fiber volume fraction in the composite caused the increment in the tensile modulus and reduction in the ultimate tensile strain of composite.     

Single fibre and multifibre unit cell analysis of strength and cracking of unidirectional composites

Numerical simulations of damage evolution in composites reinforced with single and multifibre are presented. Several types of unit cell models are considered: single fibre unit cell, multiple fibre unit cell with one and several damageable sections per fibres, unit cells with homogeneous and inhomogeneous interfaces, etc. Two numerical damage models, cohesive elements, and damageable layers are employed for the simulation of the damage evolution in single fibre and multifibre unit cells. The two modelling approaches were compared and lead to the very close results. Competition among the different damageable parts in composites (matrix cracks, fibre/matrix interface damage and fibre fracture) was observed in the simulations. The strength of interface begins to influence the deformation behaviour of the cell only after the fibre is broken. In this case, the higher interface layer strength leads to the higher stiffness of the damaged material. The damage in the composites begins by fibre breakage, which causes the interface damage, followed by matrix cracking.     

基于纤维束增强树脂基复合材料测试的单向层合板层间剪切性能的预估方法

纤维束增强树脂基复合材料（FBC）及其单向层合板在标准Iosipescu剪切实验中表现出非常相似的破坏特征,然而测量得到的剪切强度却有明显差异。本文使用两种碳纤维和两种环氧树脂制备了3种FBC和单向层合板,对FBC剪切强度和单向层合板层间剪切强度进行了测量与分析。应用界面单元方法分析了纤维束与基体之间的界面应力场,发现FBC剪切试件中纤维束/基体界面附近的应力状态为拉剪耦合,而单向层合板中界面处于纯剪切应力状态,这一差异导致FBC剪切实验测量的强度低于单向层合板的剪切强度。本文基于Yamada-Sun强度理论建立了FBC剪切强度与单向层合板剪切强度之间的关系模型,应用该模型预测的单向层合板剪切强度与实测强度之间达到良好的一致性,相对偏差为10%左右。根据本文提出的方法,通过制样较简单的FBC试验能够预测和评估相应单向层合板的层间剪切性能。