Experimental and numerical analysis of delamination growth in double cantilever laminated beams

Delamination crack growth in laminated composites is investigated using experiments and finite element (FE) models. Tests are performed on cross-ply graphite/epoxy specimens under static conditions. The load-displacement response is monitored in the tested coupons along with crack length. The FE models employ a cohesive layer that is used to simulate the debonding and crack propagation. The cohesive parameters are calibrated from the experimental load-displacement curves. Crack growth and strain measurements are compared with those from the FE models. The predicted results from the FE models are in good agreement with the test results. The same modeling approach is also used to simulate crack propagation in the transverse direction of a notched laminate. The proposed FE analysis with cohesive layers can simplify fracture toughness assessment in multilayered specimens.     

Nonlinear constitutive models for FRP composites using artificial neural networks

This paper presents a new approach to generate nonlinear and multi-axial constitutive models for fiber reinforced polymeric (FRP) composites using artificial neural networks (ANNs). The new nonlinear ANN constitutive models are complete and have been integrated with displacement-based FE software for the nonlinear analysis of composite structures. The proposed ANN constitutive models are trained with experimental data obtained from off-axis tension/compression and pure shear (Arcan) tests. The proposed ANN constitutive model is generated for plane–stress states with assumed functional response in some parts of the multi-axial stress space with no experimental data. The ability of the trained ANN models to predict material response is examined directly and through FE analysis of a notched composite plate. The experimental part of this study involved coupon testing of thick-section pultruded FRP E-glass/polyester material. Nonlinear response was pronounced including in the fiber direction due to the relatively low overall fiber volume fraction (FVF). Notched composite plates were also tested to verify the FE, with ANN material models, to predict general non-homogeneous responses at the structural level.     

Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen

Experimental and numerical analyses are performed to determine the translayer mode-I fracture toughness of a thick-section fiber reinforced polymeric composite using the eccentrically loaded, single-edge-notch tension, ESE(T) specimen. Finite element analyses using the virtual crack closure technique were performed to assess the effect of material orthotropy on the mode-I stress intensity factors in the ESE(T) specimen. The stress intensity factors for the proposed ESE(T) geometry, are calculated as a function of the material orthotropic parameters. The formula is validated for a class of thick composite materials. The thick composite tested in this study is a pultruded composite material that consists of roving and continuous filament mat layers with E-glass fiber and polyester matrix materials. Data reduction from the fracture tests was performed using two methods based on existing metallic and composite ASTM [ASTM E 1922, Standard Test Method for Translaminar Fracture Toughness of Laminated Polymer Matrix Composites, Annual Book of ASTM Standards, 1997; ASTM E 399, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, 1997] fracture testing standards. Criteria for assessing test validity and for determining the critical load used in calculating the fracture toughness were examined. Crack growth measurements were performed to determine the amount of stable crack growth before reaching critical load. The load versus notch mouth opening displacement, for different crack length to width ratios is affected by material orthotropy, nonlinearity, and stable crack propagation. The mode-I translayer fracture toughness and response during crack growth is reported for ESE(T) specimen with roving layers oriented both, transverse and parallel to the loading direction.     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.     

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.     

陶瓷基复合材料界面结合强影响断裂过程的有限元研究

提出了纤维增强复合材料断裂有限元模型,该模型既用弹簧单元考虑了基体与纤维之间的分离,又用接触单元考虑了基体与纤维之间的摩擦,较真实地模拟了纤维增强复合材料的断裂过程。通过有限元计算,预测了基体与纤维之间的界面结合强度对整个复合材料断裂模式的影响。还对强弱两种不同基体弹性模量的材料进行进一步的探讨。对比其他文献 , 本文中预测结果与真实情况较为吻合。结果表明,对于纤维增强复合材料,不论是强基体还是弱基体,适中的界面结合强度有助于提高其韧性及整体抗拉强度。       

A micro-to-meso sublaminate model for the viscoelastic analysis of thick-section multi-layered FRP composite structures

Classical ply-by-ply analysis of multi-layered thick-section composite structures with tens of layers through the cross-section is often impractical, especially when material nonlinearity and time-dependent effects are included. This study introduces an integrated micromechanical-sublaminate modeling approach for the nonlinear viscoelastic analysis of thick-section and multi-layered composite structures. The sublaminate model is used to generate three-dimensional (3D) effective nonlinear responses at through-thickness material integration points with given spatial variations of strains determined from the trial strain increments of the standard displacement-based finite-element (FE). The number of material integration points is determined by the resolution of the FE discretization of the composite structure. The sublaminate model at a selected material point represents the effective nonlinear continuum behavior in its neighborhood using the 3D lamination theory with uniform in-plane strain and out-of-plane stress patterns through the representative layers. Therefore, the sublaminate has first-order stress and strain paths and cannot recognize the local sequence of the layers. While this approach is very effective approximation especially in the case of a very large number of repeating layers using relatively few elements (integration points) through the thickness, it cannot be used to represent the interlaminar stresses or bending/extension/twisting coupling effects within a sublaminate. A previously developed micromechanical model by the authors for a nonlinear viscoelastic unidirectional lamina is used for each layer in the sublaminate. The proposed modeling approach is first calibrated and verified against creep tests on off-axis glass/epoxy performed by Lou and Schapery (J. Compos. Mater. 5:208–271, 1971). Analyses for different thick-section laminated structures are presented using the integrated sublaminate with both shell and 3D continuum elements. The proposed 3D nonlinear time-dependent sublaminate model is computationally efficient and robust in analyzing multi-layered composite structures having large number of plies.     

A Numerical Method for Simulating the Microscopic Damage Evolution in Composites Under Uniaxial Transverse Tension

In this paper, a new numerical method that combines a surface-based cohesive model and extended finite element method (XFEM) without predefining the crack paths is presented to simulate the microscopic damage evolution in composites under uniaxial transverse tension. The proposed method is verified to accurately capture the crack kinking into the matrix after fiber/matrix debonding. A statistical representative volume element (SRVE) under periodic boundary conditions is used to approximate the microstructure of the composites. The interface parameters of the cohesive models are investigated, in which the initial interface stiffness has a great effect on the predictions of the fiber/matrix debonding. The detailed debonding states of SRVE with strong and weak interfaces are compared based on the surface-based and element-based cohesive models. The mechanism of damage in composites under transverse tension is described as the appearance of the interface cracks and their induced matrix micro-cracking, both of which coalesce into transversal macro-cracks. Good agreement is found between the predictions of the model and the in situ experimental observations, demonstrating the efficiency of the presented model for simulating the microscopic damage evolution in composites.     

A numerical study on carbon nanotube pullout to understand its bridging effect in carbon nanotube reinforced composites

Carbon nanotube (CNT) reinforced polymeric composites provide a promising future in structural engineering. To understand the bridging effect of CNT in the events of the fracture of CNT reinforced composites, the finite element method was applied to simulate a single CNT pullout from a polymeric matrix using cohesive zone modelling. The numerical results indicate that the debonding force during the CNT pullout increases almost linearly with the interfacial crack initiation shear stress. Specific pullout energy increases with the CNT embedded length, while it is independent of the CNT radius. In addition, a saturated debonding force exists corresponding to a critical CNT embedded length. A parametric study shows that a higher saturated debonding force can be achieved if the CNT has a larger radius or if the CNT/matrix has a stronger interfacial bonding. The critical CNT embedded length decreases with the increase of the interfacial crack initiation shear stress.     

Tensile fracture process of Strain Hardening Cementitious Composites by means of three-dimensional meso-scale analysis

There are a wide variety of short fiber reinforced cement composites. Among these materials are Strain Hardening Cementitious Composites (SHCC) that exhibit strain hardening and multiple cracking in tension. Quantitative material design methods considering the properties of matrix, fiber and their interface should be established. In addition, numerical models to simulate the fracture process including crack width and crack distribution for the material are needed.This paper introduces a numerical model for three-dimensional analysis of SHCC fracture, in which the salient features of the material meso-scale (i.e. matrix, fibers and their interface) are discretized. The fibers are randomly arranged within the specimen models. Load test simulations are conducted and compared with experimental results. It is seen that the proposed model can well simulate the tensile failure of Ultra High Performance-Strain Hardening Cementitious Composites (UHP-SHCC) including strain-hardening behavior and crack patterns. The effects of matrix strength, its probability distribution inside the specimen and fiber distribution on the tensile fracture are numerically investigated. Consideration of the probability distributions of material properties, such as matrix strength, appears to be essential for predicting the fracture process of SHCC.     

Responses of viscoelastic polymer composites with temperature and time dependent constituents

This study formulates a concurrent micromechanical model for predicting effective responses of fiber reinforced polymer (FRP) composites, whose constituents exhibit thermo-viscoelastic behaviors. The studied FRP composite consists of orthotropic unidirectional fiber and isotropic matrix. The viscoelastic material properties for the fiber and matrix constituents are allowed to change with the temperature field. The composite microstructures are idealized with periodically distributed square fibers in a matrix medium. A unit-cell model, consisting of four fiber and matrix subcells, is generated to obtain effective nonlinear thermo-viscoelastic responses of the composites. A time-integration algorithm is formulated to link two different thermo-viscoelastic constitutive material models at the lowest level (homogeneous fiber and matrix constituents) to the effective material responses at the macro level, and to transfer external mechanical and thermal stimuli to the constituents. This forms a concurrent micromechanical model, which is needed as the material properties of the constituents depend on the temperature field. Consistent tangent stiffness matrices are formulated at the fiber and matrix constituents and also at the effective composite level to improve prediction accuracy. The thermo-viscoelastic responses obtained from the concurrent micromodel are verified with available experimental data. Detailed finite element (FE) models of the FRP microstructures are also generated using 3D continuum elements for several fiber volume fractions. Thermo-viscoelastic responses of the concurrent micromodel are also compared to the ones of the detailed FRP microstructures.     

Elastic response of a carbon nanotube fiber reinforced polymeric composite: A numerical and experimental study

Premature failure due to low mechanical properties in the transverse direction to the fiber constitutes a fundamental weakness of fiber reinforced polymeric composites. A solution to this problem is being addressed through the creation of nanoreinforced laminated composites where carbon nanotubes are grown on the surface of fiber filaments to improve the matrix-dominated composite properties. The carbon nanotubes increase the effective diameter of the fiber and provide a larger interface area for the polymeric matrix to wet the fiber. A study was conducted to numerically predict the elastic properties of the nanoreinforced composites. A multiscale modeling approach and the Finite Element Method were used to evaluate the effective mechanical properties of the nanoreinforced laminated composite. The cohesive zone approach was used to model the interface between the nanotubes and the polymer matrix. The elastic properties of the nanoreinforced laminated composites including the elastic moduli, the shear modulus, and the Poisson’s ratios were predicted and correlated with iso-strain and iso-stress models. An experimental program was also conducted to determine the elastic moduli of the nanoreinforced laminated composite and correlate them with the numerical values.     

Micromechanics models for the effective nonlinear electro-mechanical responses of piezoelectric composites

The nonlinear behavior of piezoelectric composites becomes prominent when the composites are subjected to high electric fields, which is often the case in actuator applications. Understanding the nonlinear behavior of piezoelectric composites is crucial in designing structures comprising of these materials. This study presents micromechanics models for predicting nonlinear electro-mechanical responses of polarized piezoelectric composites, comprising of a linear non-piezoelectric homogeneous medium (matrix) reinforced by either nonlinear piezoelectric fibers or particles, subjected to high electric fields. The maximum electric field applied is within the coercive electric field limit. The constitutive relations for the polarized piezoelectric inclusions consist of the third- and fourth-order electro-mechanical coupling tensors and the second- and third-order electric permeability tensors. The Mori–Tanaka micromechanics and simplified unit-cell micromechanics models are formulated to predict the effective nonlinear electro-mechanical responses of piezoelectric fiber reinforced and particle reinforced composites, respectively. Linearized micromechanical relations are first used to provide trial solutions followed by iterative schemes in order to correct errors from linearizing the nonlinear responses. Numerical results are presented to illustrate the performance of each micromechanics model.     

短纤维复合材料宏微观内聚力模型参数测量的实验与数值混合法

提出了一种改进的实验与数值混合法。该方法采用随机短纤维增强复合材料的紧凑拉伸实验,首先得到材料的宏观内聚力模型,进而确定该材料纤维基体界面微观内聚力模型参数。通过有限元法和基于场投影的反解法得到了宏观内聚力模型结果,对比分析这两个方法的结果,得出该反解法对误差的容忍度较低。随后采用改进的反解法,用数字图像相关法(DIC)直接获取宏观内聚力模型分离量,减少了该反解法未知数的数量,提高了容错率。再将DIC和改进的反解法结合,对该材料裂纹尖端宏观内聚力区的牵引力进行了反解。采用双线性内聚力模型,根据Mori-Tanaka方法,将求得的宏观内聚力定律与纤维基体界面微观内聚力定律关联起来,从而求得了纤维基体界面微观内聚力模型参数。该方法和结果可为短纤维增强复合材料纤维基体界面的微观力学分析提供实验基础。     

Modelling post-crack tension-softening behavior of fiber-reinforced materials

We present a general method for the traction-separation law for the cohesive model of fiber reinforced materials with brittle matrix. The proposed approach is based on results from the theories of marked point and fiber processes. The application of stochastic notions in the field of traction-separation laws and tension-softening curves for fiber reinforced composites allows the thorough investigation of the random effect of the fiber reinforcement on cohesive behavior. The presented method accounts for correlations between length and orientation as may be the case in real fiber reinforced composites. We study the influence of randomness of fiber length and degree of anisotropy on the post-crack tension softening curves. It turns out that fiber length and orientation distributions have a tremendous effect on the crack-opening behavior.     

陶瓷纤维增强SiO2气凝胶复合材料面内拉伸非均匀全场应变测量与分析

通过设计圆弧边缘夹持方案和狗骨形拉伸试样,开展了陶瓷纤维增强SiO₂气凝胶复合材料室温环境中的面内拉伸性能试验,采用数字图像相关方法对陶瓷纤维增强SiO₂气凝胶复合材料表面的全场变形进行测量和分析,并结合获得的非均匀应变分布情况进一步讨论其力学行为特征和变形断裂机制。结果表明:纤维增强增韧机制使陶瓷纤维增强SiO₂气凝胶复合材料的面内拉伸行为表现出一定的非线性及韧性特征;在一定载荷水平下,陶瓷纤维增强SiO₂气凝胶复合材料表面应变分布呈显著的非均匀特征,与内部随机的纤维排布及各处传力情况不同相关,可选择较大计算区域进行平均化处理来减弱对测试中应变度量的影响;在加载和断裂过程中陶瓷纤维增强SiO₂气凝胶复合材料表面存在局部应变集中现象,并随着裂纹扩展而发生演变,面内拉伸载荷下的宏观断口呈锯齿状特征,主要由剪应力主导的基体断裂、法向针刺对纤维铺层的约束等原因所致。本文研究结果为隔热复合材料的强韧化性能提高指明了方向。      

Fracture mechanic modeling of fiber reinforced polymer shear-strengthened reinforced concrete beam

A numerical method is developed to model shear-strengthening of reinforced concrete beam by using fiber reinforced polymer (FRP) composites. Tensile crack is simulated by a non-linear spring element with softening behavior ahead of the crack tip to model the cohesive zone in concrete. A truss element is used, parallel to the spring element, to simulate the energy dissipation rate by the FRP. The strain energy release rate is calculated directly by using a virtual crack closure technique. It is observed that the length of the fracture process zone (FPZ) increases with the application of FRP shear-strengthening. The present model shows that the main diagonal crack is formed at the support in the control beam while it appears through the shear span in the shear-strengthened beam. Another important observation is that the load capacity increases with the number of CFRP sheets in the shear span.     

双斜接修补复合材料层合板的拉伸行为及影响因素双斜接修补复合材料层合板的拉伸行为及影响因素

基于试验和有限元数值方法对双斜接修补碳纤维增强聚合物（CFRP）复合材料层合板在拉伸载荷作用下的力学行为开展研究。通过试验分析了两种不同厚度的双斜接修补复合材料结构的承载能力和失效形式。结果表明,对于不同厚度的双斜接修补复合材料结构,失效强度接近,主要破坏形式均以胶层内聚破坏为主,伴随局部的90°基体开裂。利用连续介质损伤力学模型和内聚力模型分别对复合材料和胶层失效进行描述,通过数值方法开展双斜接修补结构的强度预测和损伤演化分析。数值结果与试验吻合较好,并且指出复合材料基体开裂起始早于胶层失效。通过有限元模型讨论了附加层、双斜接内部尖端所处位置和修补胶层参数对修补性能的影响。      

Z-pin增强CMC层间Ⅰ+Ⅱ混合型断裂韧性

提出手工预缝纫方法将3K丝束的T300碳纤维引入预成型体,采用CVI工艺在预成型体和缝线处同时渗透SiC基体,制备了Z-pin增强平纹编织C/SiC陶瓷基复合材料。通过三点弯曲试验测定了Ⅰ+Ⅱ混合型应变能释放率,分析了材料的裂纹扩展行为和Z-pin增强机理。结果表明:随着裂纹扩展长度的增大,Ⅰ+Ⅱ型裂纹扩展阻力不断增大,相同裂纹扩展长度,增加Z-pin植入密度可以提高粘结强度,增大止裂作用。Z-pin增强平纹编织C/SiC陶瓷基复合材料裂纹扩展的耗能途径主要是层间界面剥离、Z-pin弹性剪切和拉伸变形。     

Crack/fiber interaction and crack growth resistance behavior in microfiber reinforced mortar specimens

Performance enhancement due to microfibers is well known. However, fracture processes that lead to strain hardening behavior in microfiber reinforced composites are not well understood. Crack growth resistance behavior of mortar reinforced with steel microfibers and polypropylene microfibers was investigated in-situ during load application. The polypropylene fibers were inter-ground in the cement mill to enhance the fiber/matrix interfacial frictional stress. A more homogeneous fiber distribution was observed in the inter-ground polypropylene composites compared to the steel microfiber reinforced composites. In steel microfiber reinforced composites the dominant toughening mechanisms were multiple microcracking and successive debonding along the fiber/matrix interface. Fiber pullout, the dominant mechanism in conventional macrofiber reinforced composites was rarely observed. In-situ observation of crack/fiber interaction in the inter-ground polymer fibers also revealed multiple microcracking along the length of the fibers followed by fiber pullout.