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.     

Fabrication,characterization and mechanical properties of SiC-whisker-reinforced Y-TZP composites

The microstructure and mechanical properties of hot-pressed yttria-stablized tetragonal zirconia polycrystals (Y-TZP) reinforced with up to 30 vol % SiC whiskers were investigated. The homogeneously dispersed and fully dense SiC whisker/Y-TZP composites were fabricated by wet-mixing the constitutents and uniaxially hot-pressing the resulting powder. The grain size of the matrix depended on the whisker volume fraction and the hot-pressing temperature. The significant increase of fracture toughness of about MPa m^1/2 at 10 Vol % SiC and a small increase in strength were achieved by uniformly dispersing the whiskers in the Y-TZP matrix. Fracture surfaces revealed evidence of toughening by the mechanisms of crack deflection, pullout, and crack bridging by the whiskers and also a phase transformation of ZrO₂. The observed increase in the fracture toughness of Y-TZP due to the addition of SiC whiskers was correlated with existing models of toughening mechanisms. Good agreement was achieved between the theoretical predictions and the experimental toughness values, obtained from the Y-TZP/SiC_w composites.     

A cohesive crack model to study the fracture behaviour of fiber-reinforced brittle-matrix composites

A cohesive crack model analysis of the fracture resistance and ductility of fiber-reinforced brittle-matrix composites was performed. The bulk material is assumed to behave as a linear elastic solid. The constitutive equation for the cohesive crack is obtained through micromechanical considerations based on the shear lag model of fiber-matrix interaction and on the statistical nature of fiber failure. A parametrical study of the influence of fiber volume fraction, fiber strength and flaw distribution, interfacial shear stress and specimen geometry on the fracture resistance of these composites was carried out. The results illustrate the role of each of these factors in overall composite toughening, and suggest various strategies to improve the composites' performance.     

Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials

This work investigates elastic-plastic crack growth in ceramic/metal functionally graded materials (FGMs). The study employs a phenomenological, cohesive zone model proposed by the authors and simulates crack growth by the gradual degradation of cohesive surfaces ahead of the crack front. The cohesive zone model uses six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) to describe the constitutive response of the material in the cohesive zone. A volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model) describes the elastic-plastic response of the bulk background material. The numerical analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive zone model and the computational scheme to analyze crack growth in a single-edge notch bend, SE(B), specimen made of a TiB/Ti FGM. Cohesive parameters are calibrated using the experimentally measured load versus average crack extension (across the thickness) responses of both Ti metal and TiB/Ti FGM SE(B) specimens. The numerical results show that with the calibrated cohesive gradation parameters for the TiB/Ti system, the load to cause crack extension in the FGM is much smaller than that for the metal. However, the crack initiation load for the TiB/Ti FGM with reduced cohesive gradation parameters (which may be achieved under different manufacturing conditions) could compare to that for the metal. Crack growth responses vary strongly with values of the exponent describing the volume fraction profile for the metal. The investigation also shows significant crack tunneling in the Ti metal SE(B) specimen. For the TiB/Ti FGM system, however, crack tunneling is pronounced only for a metal-rich specimen with relatively smaller cohesive gradation parameter for the metal.     

Fatigue Propagation of Fibre-Bridged Cracks in Unidirectional Polymer-Matrix Composites

In order to improve the fatigue resistance of polymer-matrix composites by materials design, or to conceive micromechanics based models for life predictions, the underlying micromechanisms must be understood. Experimental investigations have revealed fibre-bridged cracking as a toughening micromechanism that retards further fatigue crack growth in a unidirectional 0° carbon-fibre-reinforced epoxy. The bridging fibres exert a closing traction on the crack surfaces, thereby reducing the driving force for crack growth. In this study, the growth of bridged cracks has been quantified by a surface replication technique. The da/dN–K curve defined in terms of nominal stress-intensity factors shows a crack retarding behaviour. The crack growth curve can be replotted in terms of the effective stress-intensity factor where the contribution of the cohesive crack surface forces from the bridging fibres are taken into account. This curve falls somewhat closer to that of the neat matrix material, but the difference is still considerable, and it shows a decelerating propagation. Therefore, there must be other active toughening mechanisms besides fibre bridging, that slow the crack propagation down, and account for the fatigue resistant behaviour of the tested material. Ways by microstructural design to promote the fatigue resistant mechanisms are discussed.     

Fatigue properties and fatigue fracture mechanisms of SiC whiskers or SiC particulate-reinforced aluminium composites

Fatigue properties and fracture mechanisms were examined for three commercially fabricated aluminium matrix composites containing SiC whiskers (SiC_w) and SiC particles (SiC_p) using a rotating bending test. The fatigue strengths were over 60% higher for SiC_w/A2024 composites than that for the unreinforced rolled material, while for the SiC_p/A357 composites, fatigue strengths were also higher than that for the unreinforced reference material. For the SiC_p/A356 composites at a volume fraction of 20%, the fatigue strength was slightly higher than that of the unreinforced material. Fractography revealed that the Mode I fatigue crack was initiated by the Stage I mechanism for the SiC_w/A2024 and SiC_p/A357 composites, while for the SiC_p/A356 composite, the fatigue crack initiated at the voids situated beneath the specimen surfaces. On the other hand, the fatigue crack propagated to the whisker/matrix interface following the formation of dimple patterns or the formation of striation patterns for SiC_w/A2024 composites, while for the SiC_p/A356 and SiC_p/A357 composites the fatigue crack propagated in the matrix near the crack origin and striation patterns were found. Near final failure, dimple patterns, initiated at silicon carbide particles, were frequently observed. Mode I fatigue crack initiation and propagation models were proposed for discontinuous fibre-reinforced aluminium composites. It is suggested that the silicon carbide whiskers or particles would have a very significant effect on the fatigue crack initiation and crack propagation near the fatigue limit.     

SiC w/BAS复合材料的显微结构及力学性能的研究

本文采用热压烧结法制备出致密的SiCw增强BAS玻璃陶瓷基复合材料．结果表明,BAS基体晶化后获得以钡长石为主晶相和莫来石为次晶相的复相BAS玻璃陶瓷．晶须的加入对BAS基体有显著的强韧化效果,加入30vol％SiCw可使材料的室温抗弯强度和断裂韧性分别由基体的156MPa和1．40MPa·m1/2提高到356MPa和4．06MPa·m1/2．TEM观察结果表明,晶须／基体界面结合良好,无界面反应物和非晶层的存在．断口形貌和压痕裂纹扩展路径的SEM观察结果表明,复合材料的主要增韧机制为裂纹偏转、晶须的拔出和桥接．     

COHESIVE ZONE MODELLING OF DAMAGE AT THE TIP OF CRACKS IN SLENDER BEAM STRUCTURES

The use of simple beam theory for cohesive zone modelling of the damage response at the crack tip in linear elastic isotropic double cantilever beam (DCB) specimens has been investigated. Damage resistance curves (DR-curves) relating the applied stress intensity factor to the growth of the cohesive zones for beam theory modelling has been compared with two-dimensional elasticity calculations for different material parameters and specimen dimensions. A substantial difference is observed between DR-curves for the two types of models. As expected this difference vanishes for decreasing beam heights. For large beam heights the DR-curves calculated by two-dimensional elasticity are approaching small-scale yielding DR-curves, i.e. DR-curves for an edge crack in an infinite plate. The beam height for which beam theory is applicable could be up to 10^-3 times the height for which small scale bridging DR-curves are applicable.     

Predicting mode-II delamination suppression in z-pinned laminates

A finite element model for predicting delamination resistance of z-pin reinforced laminates under the mode-II load condition is presented. End notched flexure specimen is simulated using a cohesive zone model. The main difference of this approach to previously published cohesive zone models is that the individual bridging force exerted by z-pin is governed by a specific traction-separation law derived from a unit-cell model of single pin failure process, which is independent of the fracture toughness of the unreinforced laminate. Therefore, two separate traction-separation laws are employed; one represents unreinforced laminate properties and the other for the enhanced delamination toughness owing to the pin bridging action. This approach can account for the so-called large scale bridging effect and avoid using concentrated pin forces in numerical models, thus removing the mesh-size dependency and permitting more accurate and reliable computational solutions.     

Effect of whisker surface treatment on the mechanical properties of 20vol%SiCw/BAS glass-ceramic composites

20vol%SiCw/BAS (barium aluminosilicate) composites with as-received, acid-leached and heat-treated whiskers were fabricated by a hot-pressing technique and their mechanical properties were evaluated. The whiskers used in these composites were characterized using Auger electron spectrometry (AES) and scanning electron microscopy (SEM), and the observations were correlated with the mechanical properties. The results show that the oxygen content of the whisker surfaces was reduced by the hydrogen fluoride (HF) acid-leaching treatment and the surface geometry of whiskers was smoothed by the heat-treatment in an inert gas atmosphere. The corresponding composites show an obvious increase (18% and 31%, respectively) in toughness compared with the composites reinforced with as-received whiskers. Fracture surfaces revealed evidence of toughening by the mechanisms of crack deflection, crack bridging and whisker pullout for the composites with surface treated whiskers.     

SiCw/BAS复合材料的显微结构及力学性能的研究

本文采用热压烧结法制备出致密的SiC_w增强BAS玻璃陶瓷基复合材料．结果表明,BAS基体晶化后获得以钡长石为主晶相和莫来石为次晶相的复相BAS玻璃陶瓷．晶须的加入对BAS基体有显著的强韧化效果,加入30vol％SiC_w可使材料的室温抗弯强度和断裂韧性分别由基体的156MPa和1．40MPa·m^1/2提高到356MPa和4．06MPa·m^1/2．TEM观察结果表明,晶须／基体界面结合良好,无界面反应物和非晶层的存在．断口形貌和压痕裂纹扩展路径的SEM观察结果表明,复合材料的主要增韧机制为裂纹偏转、晶须的拔出和桥接．     

晶须增韧陶瓷基复合材料裂纹扩展行为模型

在考虑晶须桥联和裂纹转两种增韧机理的基础上，建立了晶须增韧陶瓷复合材料裂纹扩展行为的理论模型，利用该型计算了单边切口梁三点弯曲的Ｒ－阻力曲线和载荷－位移曲线。     

Al_6Si_2O_(13)晶须和TiC颗粒复合强化多孔Al_2TiO_5基复合材料

以γ-AlOOH和TiO_2为原料,添加不同质量分数SiC晶须(SiCw),采用无压反应烧结法制备多孔(Al_6Si_2O_(13)+TiC)/Al_2TiO_5复合材料,分析了SiCw质量分数对(Al_6Si_2O_(13)+TiC)/Al_2TiO_5复合材料孔隙率和抗压强度的影响,讨论了SiCw的强化机制。结果表明:不添加SiCw时,产物主要为Al_2TiO_5和少量Al_2O_3,还有少量未反应的TiO_2;加入SiCw之后,还形成了Al_6Si_2O_(13)和TiC相,TiC和Al_6Si_2O_(13)分别以规则颗粒状和晶须形态存在于Al_2TiO_5基体中。TiC颗粒与Al_6Si_2O_(13)晶须通过细化显微组织、裂纹偏转和晶须桥连机制,起到协同强化作用。SiCw的添加使孔隙率和抗压强度同时大幅度提高,随着SiCw质量分数的增加,(Al_6Si_2O_(13)+TiC)/Al_2TiO_5复合材料孔隙率降低,抗压强度提高的速率减小,当SiCw的质量分数为7.2%时,抗压强度最高,达到301.81 MPa。     

纳米粒子在SiC/PTFE复合材料中分散三维仿真与分形表征

为了从理论上探讨纳米粒子在基体材料中的分布规律, 以纳米SiC质量分数为3%、 5%、 7%、 9%的SiC/PTFE(聚四氟乙烯)复合材料为例, 根据纳米SiC的半径(25 nm)、 密度(3.2 g/cm³)、 质量分数和基体材料的密度(2.2 g/cm³), 以10^-12 g为质量单位、 25 nm:1像素为比例尺, 建立了纳米粒子在基体中均匀／偏聚分布的三维仿真模型, 基于其盒维数定量表征了不同团聚／偏聚程度的纳米粒子的分散度, 并进行了力学实验验证。结果表明: 均匀分布下随着纳米SiC粒子半径的不断增加, 或体积分数的不断减小, 其盒维数也逐渐减小; 当SiC粒子半径超过100 nm时, 不再具有分形特性。偏聚分布下随着纳米SiC粒子(半径为50 nm)间距的不断加大, 或体积分数的不断减小, 或层状、 线状、 团状分布的依次改变, 其盒维数也逐渐减小; 相同体积分数下偏聚分布的盒维数低于均匀分布; 当粒子间距超过450 nm时, 不再具有分形特性。均匀分布下纳米SiC/PTFE复合材料的力学性能测试结果与其三维仿真模型的盒维数线性相关(|R|>0.9)。盒维数可定量表征纳米粒子的分散度, 并可用于预测纳米复合材料的宏观性能。     

Mode I intra-laminar crack growth in composites — modelling of R-curves from measured bridging laws

In this paper R-curves for mode I crack growth in composites are modelled based on measured bridging laws. It is shown that simulated and measured R-curves are in good agreement. Simulations show that variations in the measured bridging law parameters can explain the scatter in overall R-curves. Finite element procedures for treating a generalised nonlinear law for intra-laminar fibre bridging (longitudinal splitting) in combination with R-curve modelling are demonstrated for mode I loading. The difference between calculating the crack growth resistance by linear elastic fracture mechanics and by the J integral for the double cantilever beam specimen loaded by wedge forces is elucidated. It is shown that calculating the crack growth resistance by linear elastic fracture mechanics results in overestimation of the steady-state crack growth resistance.     

Fiber volume fraction effects on fatigue crack growth in SiC/Ti-15-3 composite

The effects of fiber volume fraction (15, 37, and 41%) on fatigue crack growth in unidirectional SiC/Ti-15-3 composite were investigated at room temperature. The effect of fiber volume fraction on the fiber bridging mechanism was studied to support development of physically-based crack growth models. While each fiber volume fraction exhibits similar decreasing crack growth rates prior to fiber bridging induced crack arrest, post-arrest behavior (observed after incrementally increasing the applied stress level) is quite different. After crack arrest, the 15% (37 and 41%) material exhibited higher (lower) crack growth rates and lower (higher) toughness values than the unreinforced matrix. These different behaviors occur because of differences in the amount of fiber bridging during the post-arrest regime. Metallography of interrupted tests revealed the extent of fiber bridging in the crack wake and matrix plasticity ahead of the crack tip. Models for predicting the effective matrix stress intensities were evaluated and compared to experimental data. A fiber pressure model and finite element studies were used to estimate the condition of the bridged fiber zone and associated fiber stresses. Since the vast majority of useful life for these materials experiences fatigue crack growth, these results assist in discerning an optimum fiber volume fraction for structural applications.     

The effects of inter-surface cohesive tractions on linear and penny-shaped cracks

A mesoscopic fracture model of equilibrium slit cracks in brittle solids, including inter-surface cohesive tractions acting near the crack tip, is analyzed and the effects of the cohesive tractions on the in-plane stress fields, crack-opening displacement profiles, and crack driving forces examined quantitatively for linear and penny-shaped cracks. The (numerical) analysis method is described in detail, along with results for four different cohesive forces. The assumed distribution of cohesive tractions were found to suppress the in-plane stress field adjacent to cracks in a homogeneous, isotropic medium when uniformly loaded in mode-I, and the suppression was a function of crack length. The crack-opening displacement profile was also perturbed and a new regime identified between the near-field Barenblatt zone and the far-field continuum zone. The extent of this `cohesive zone' was quantified by use of an interpolating function fit to the calculated profiles and found to be independent of crack size for a given cohesive tractions distribution. Furthermore, the crack-opening displacement at the edge of the cohesive zone was found to be independent of crack size, implying that despite significant perturbations to the stress field, the crack driving force at unstable equilibrium remains unchanged with crack size.     

Fracture behaviour at elevated temperatures of alumina matrix composites reinforced with silicon carbide whiskers

Creep tests were performed on alumina matrix composites containing 9.3,18 and 30 vol % of SiC whiskers. Careful examination after failure showed that the fracture characteristics were dependent upon the microstructure of the material. Whisker pullouts were visible at the fracture surfaces of the composites with 30 and 18 vol % of SiC whiskers due to preferential debonding at the whisker-matrix interfaces, and these composites also developed crack networks due to the propagation of cracks along whisker-free channels between whisker agglomerates. No whisker pullouts or crack networks were visible in the composite with 9.3 vol % of SiC whiskers where the whisker distribution was reasonably uniform.     

Micromechanical modelling of strain hardening and tension softening in cementitious composites

This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids under unidirectional tensile loading. The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite. Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension softening response of two cementitious composites.