FRACTURE MODELLING OF BRITTLE-MATRIX COMPOSITES WITH SPATIALLY DEPENDENT CRACK BRIDGING

Abstract In brittle-matrix composites cracking of the matrix is often accompanied by bridging of the crack surfaces. The bridging will reduce the net stress intensity factor at the crack tip and consequently increase the toughness of the composite material. The bridging mechanism is due to for example unbroken whiskers, fibres, ductile particles or interlocking grains. Analysis of the bridging mechanism in cracked structures is conveniently carried out using the concept of cohesive zone modelling. In this case the action of the bridging elements is replaced by a distribution of forces, so called cohesive forces trying to close the crack. The commonly used approach in such modelling has been to replace the action from individual bridging elements by a continuous spatially independent distribution of closing tractions whose magnitude is a function of the crack opening displacement only. In this paper the influence of the spatial distribution of bridging elements is considered for plane crack problems. The cross section of the bridging elements is assumed to be circular and the distance between the different bridging elements is determined by the volume fraction, the radius and the geometrical distribution of the bridging elements. Damage resistance curves have been calculated for typical whiskers-reinforced ceramic composites, and the results from the present spatially dependent models are compared with results from calculations with spatially independent models. The influence of the radius of the bridging element, the volume fraction of whiskers and the material properties are illustrated and the use of spatially independent models is discussed.     

TiB2-TiN复合陶瓷刀具材料的显微结构和力学性能研究

热压烧结制备了不同TiN含量的复合陶瓷刀具材料TiB2-TiN-(Ni, Mo),对其性能测试表明,随着TiN含量的增加,材料的抗弯强度和断裂韧度逐渐提高,但是材料的硬度在TiN的含量达到40%(体积分数)时却大幅度降低.利用X衍射(XRD)、扫描电镜(SEM)和能谱(EDAX)分析了复合材料的物相和显微组织,结果表明,烧结过程中生成了MoNi相;随TiN含量增加,材料从以沿晶断裂为主转变为同时有沿晶断裂和穿晶断裂的断裂模式;裂纹扩展过程中有金属颗粒桥连现象.分析认为,材料的主要增韧机制是延性相颗粒桥连和裂纹偏转.     

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。     

Effect of microstructure on elevated-temperature fracture behaviour of two-dimensional carbon/carbon composites

The fracture behaviour of two-dimensional carbon/carbon composites has been studied at temperatures upto 1650°C, using both chevron-and straight-notch single-edge notch beam (SENB) specimens. In all cases, the R-curve behaviour and fracture toughness variations with specimen orientation and temperature are characterized and correlated with the specific microstructure and failure micromechanisms. Higher crack growth resistance and fracture toughness of the longer fibre composite are attributed to the enhanced fibre pull-out and fibre bridging in the following wake region. The relative contribution from the frontal and following wake zone is determined experimentally by the use of renotching methods which demonstrate the effectiveness of the traction zone behind the crack tip. The temperature effects on the toughening mechanisms are examined in terms of crystal structure and fibre matrix interfacial characteristics.     

An efficient BEM to calculate weight functions and its application to bridging analysis in an orthotropic medium

An efficient boundary element method to calculate crack weight functions is developed. The weight function method is applied to bridging effect analysis in a single-edge notched composite specimen by using a bridging law which includes both interfacial debonding and sliding properties between fiber and matrix in ceramic matrix composites. A numerical method to solve the distributed spring model treating bridging fibers as stress distribution to close the crack surface is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor.     

基于扩展有限元的陶瓷复合材料多重增韧机制

为了提高陶瓷材料的断裂韧性和可靠度,改善材料抵御破坏的能力,将优化的多重增韧机制应用到氧化铝基陶瓷材料的开发中。相变增韧机制可以耗散部分能量,降低裂纹尖端处的应力集中程度,阻止或延缓裂纹扩展速率。当增强相分布较为合理、材料的致密度较高时,裂纹偏转与桥接增韧机制可以有效地削弱裂纹扩展动力,提高材料的断裂韧性。利用扩展有限元（X-FEM）手段讨论了裂纹扩展问题,为分析陶瓷复合材料的多重增韧机制提供了新思路。     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Characterization of the Reaction Products That Develop in the Processing of Al2O3/BaZrO3 Laminated Composites

The absence of a chemical reaction at an interface is conventionally thought to be an important criterion in producing a tough ceramic matrix composite (CMC). As a result of this criterion, interphases in CMCs were chosen on the basis of their chemical reactivity. A weak interface results in crack deflection, crack bridging, and, in fiber-reinforced ceramics, fiber pullout, resulting in an increased fracture toughness. In this paper, we present microstructural observations on alumina (Al₂O₃)–barium zirconate (BaZrO₃) laminated composites wherein the reaction products that develop during processing resulted in sharp interfaces and appear to be weak enough to deflect cracks. These in situ reaction products in Al₂O₃–BaZrO₃ laminated composites were characterized with the use of a scanning electron microscope, an electron microprobe, and a transmission electron microscope. The phases that develop, ZrO₂, BaO·Al₂O₃, and BaO·6 Al₂O₃, produced sharp interfaces and are arranged in a sequence that could be predicted by using information from the phase diagram.     

A combined experimental-numerical investigation of crack growth in a carbon–carbon composite

A combined experimental–numerical investigation of crack growth in a carbon–carbon composite is reported. In this material, both matrix fracture and fibre bridging contribute significantly to toughness. Crack growth experiments were performed using side‐notched DCB specimens with doublers. A digital image correlation method was used to measure displacements fields on the specimen surfaces, crack extension and crack opening profiles. An effective cohesive zone law was determined from the experimental data. The effective cohesive zone law is subsequently separated into the individual contributions from matrix cracking and fibre bridging. Numerical simulation of crack growth based on this cohesive zone law and experimental data are in good agreement. Special focus of the numerical study is on the investigation of the discontinuous nature of crack growth.     

增强体含量对SiC_W/SiC层状陶瓷复合材料强韧性的影响

采用流延-化学气相渗透(TC-CVI)工艺制备SiC晶须(SiC_W)/SiC层状陶瓷复合材料,研究了SiC_W含量对层状陶瓷复合材料力学性能和微观结构的影响,探讨了SiC_W/SiC层状陶瓷复合材料的强韧化机制。结果表明:TC-CVI工艺能够有效提高复合材料中晶须含量(40vol%),减少制备过程对晶须损伤,所制备的SiC_W/SiC层状陶瓷复合材料具有合适的层内及层间界面结合强度。随着SiC_W含量增加,层状陶瓷复合材料的密度和力学性能均有明显提高。含40vol%晶须的SiC_W/SiC层状陶瓷复合材料的密度、弯曲强度和断裂韧性均比含25vol%晶须的分别提高了8.4%、30.8%和26.7%。断口形貌中能够观察到层间及层内的裂纹偏转,层内的裂纹桥接和晶须拔出等,这些为主要的增韧机制。高含量SiC_W及合适的层间和层内界面结合强度,对提高SiC_W/SiC层状陶瓷复合材料强韧性有明显作用。     

SiC／Al合金层状复合材料的机械性能及损伤行为

在室温条件下测定了Ａｌ合金以连续层状形式存在于ＳｉＣ陶瓷层间并渗透入ＳｉＣ陶瓷层内、Ａｌ合金浓度呈层状变化高低相间，以及Ａｌ合金和ＳｉＣ陶瓷均匀分布相互渗透三种ＳｉＣ含量相同而结构形式不同的ＳｉＣ／Ａｌ合金复合材料的机械性能；用ＳＥＭ和光学显微镜观察分析了复合材料的断口形貌及裂纹扩展过程。结果表明，在ＳｉＣ陶瓷层间以连续层状形式存在的Ａｌ合金在应力作用下发生较大程度的塑性变形，在裂纹尾部被拉伸和形成桥接，引起能量耗散，减缓裂纹扩展速度，防止裂纹张开，使复合材料的韧性得到明显改善；ＳｉＣ／Ａｌ合金陶瓷─金属层状复合材料的损伤形式主要是ＳｉＣ陶瓷层开裂、金属层桥接和裂纹偏转。     

Stress Ahead of the Tip of a Finite-Width Center-Crack in Fiber-Reinforced Composite Specimen: Subjected to Non-Linearly Distributed Bridging Stresses

The force balance method (FBM) is a simple and effective way to calculate geometric correction factors for the stress distribution ahead of the tip of finite-width center crack specimen. In this paper, the accuracy and effectiveness of the FBM is shown by means of a numerical evaluation of the stress distribution ahead of the tip of finite-width center-cracked specimens subjected to nonlinearly distributed bridging stresses in fiber-reinforced composites. The finite element method is used for this purpose.     

Geometric correction factors for center cracked specimens subjected to nonlinear bridging stresses in the shear lag model

Fiber bridging plays an important role in the fracture mechanism of fiber-reinforced composites. The determination of the geometric correction factors for finite-width specimens subjected to complex bridging stresses is vital for the practical application of various bridging models. An approximate approach named the force balance method (FBM) was recently reported in the literature to evaluate such geometric factors. The main purpose of this study is to assess the effectiveness of the FBM by using the well-established boundary element method. The case of a center cracked specimen subjected to a nonlinear fiber bridging stress in the shear lag model in fiber-reinforced composites is considered. The geometric correction factors computed by the boundary element method are compared with those deduced by the FBM.     

Fracture toughness and reliability in high-temperature structural ceramics and composites: Prospects and challenges for the 21st century

The importance of high fracture toughness and reliability in Si₃N₄, and SiC-based structural ceramics and ceramic matrix composites is reviewed. The potential of these ceramics and ceramic matrix composites for high temperature applications in defence and aerospace applications such as gas turbine engines, radomes, and other energy conversion hardware have been well recognized. Numerous investigations were pursued to improve fracture toughness and reliability by incorporating various reinforcements such as particulate-, whisker-, and continuous fibre into Si₃N₄ and SiC matrices. All toughening mechanisms, e.g. crack deflection, crack branching, crack bridging, etc essentially redistribute stresses at the crack tip and increase the energy needed to propagate a crack through the composite material, thereby resulting in improved fracture toughness and reliability. Because of flaw insensitivity, continuous fibre reinforced ceramic composite (CFCC) was found to have the highest potential for higher operating temperature and longer service conditions. However, the ceramic fibres should display sufficient high temperature strength and creep resistance at service temperatures above 1000°C. The greatest challenge to date is the development of high quality ceramic fibres with associate coatings able to maintain their high strength in oxidizing environment at high temperature. In the area of processing, critical issues are preparation of optimum matrix precursors, precursor infiltration into fibre array, and matrix densification at a temperature, where grain crystallization and fibre degradation do not occur. A broad scope of effort is required for improved processing and properties with a better understanding of all candidate composite systems.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF DYNAMIC DELAMINATION IN COMPOSITES

Abstract A fundamental understanding of dynamic delamination in composites is sought through the application of theoretical and experimental approaches familiar to dynamic fracture mechanics. Analysis of steady-state fracture in an infinite orthotropic strip yields a simple solution which can be used to evaluate numerical procedures and experimental results. The analogous specimen consists of a single edge notched composite strip bonded to stiff steel substrates to enforce the desired displacement boundary conditions. Delamination velocities of the order of 10 to 1000 m/s were measured using a graphite gauge technique. Quasi-static and dynamic finite element methods are applied to investigate the behavior of the specimen and to determine static initiation and dynamic delamination toughness. The experimental observations cannot be explained by linear elastic fracture theory. The absence of a unique G(?) relationship might be rationalized by a simple model relating matrix crack zone size to fiber bridging mechanisms.     

Toughness characterization of damageable ceramic matrix composites

As for concrete and many other heterogeneous materials, the damageable behavior of numerous ceramic matrix composites (CMCs) renders their toughness characterization particularly difficult. However, the need to compare CMCs' resistance to crack propagation has given rise to a new type of toughness test based on the use of a mixed CT–DCB specimen associated with steel frames and named Steel Framed Assisted Tension (SFAT). This type of specimen, whose shape and dimensions were adjusted by numerical simulation, allows the development and the steady state propagation of the process zone, while preventing the occurrence of damage outside the vicinity of notch or macrocrack tips. A study of the use of steel frames glued on each side of the specimens allowed the choice of a sufficiently rigid and resistant glue offering a good repeatability of the tests at a wide range of loading speeds. A compliance calibration procedure has been defined for SFAT specimens in view of the need to apply the method to anisotropic composites. Testing glass/epoxy composites with this procedure has shown its validity and pointed out the influence of the notch length on the R curves which can be derived in terms of crack growth release rate G from the related load–displacement curves. In addition, examination of the resulting G_R curves shows the possible use of various parameters to represent the tested material toughness. Finally, the whole testing procedure has been evaluated on the 2D–SiC/SiC and 2D–C/SiC composites.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Work-of-fracture of brittle materials with microcracking and crack bridging

The fracture mechanics basis of fracture energies is considered through micromechanical phenomena in the crack tip frontal process zone, the following crack wake and crack bridging regions of brittle materials, such as cement-based materials, rocks, ceramics, and ceramic composites. The discussion is mainly focused on the work-of-fracture parameter ({ie65-1}) as a material characteristic for representing the resistance to crack extension. Theoretical considerations of the dependence of {ie65-2} on the unnotched remaining ligament length of the fracture test specimen lead to the concept of the essential work-of-fracture, {ie65-3}. The experimental results obtained for three different types of ceramic materials support the theoretical predictions.     

连续纤维增强陶瓷基复合材料微观力学研究进展

微观力学参数是构建连续纤维增强陶瓷基复合材料(CFRCMCs)组分、微观结构和宏观力学性能的桥梁, 但受限于CFRCMCs的脆性和微观力学参数测试水平, 微观力学研究工作进展缓慢。随着基于纳米压痕的微观力学测试技术和基于聚焦离子束微观测试样品制备技术的飞速发展, 近年来CFRCMCs的微观力学研究工作取得显著进步。本文结合国防科技大学刘海韬课题组的研究工作, 重点对CFRCMCs组分的原位模量、断裂韧性以及界面结合强度的测试方法和典型应用进行了讨论, 最后举例说明了基于微观力学参数的CFRCMCs宏观力学行为的预判方法。     

Development of a process zone in rubber-modified epoxy polymers

The effects of a process zone on toughness and on R-curve behavior were investigated for a model, rubber-modified epoxy polymer. The system studied was one in which the bridging mechanism of toughening does not operate. The characteristic features of R-curve behavior, a rise in toughness with crack extension until an approximate steady-state is reached, were observed using double-cantilever-beam tests. The evolution of the process zone was studied using transmission-optical microscopy. As the crack grew, the process zone appeared to fan out until it reached a steady-state thickness; it then remained a uniform size upon further crack advance. The features of the experimental R-curves were shown to be directly correlated to the evolution of the process zone. Furthermore, the effect of the portion of the process zone in the crack wake was examined by a series of experiments in which the wake was partially removed, and the R-curve re-established by subsequent loading. These experiments demonstrated that removal of the crack wake caused the crack-growth resistance to drop. The toughness then built back up to the steady-state value as the crack wake re-developed. This unambiguously demonstrated a contribution to toughening from the crack wake despite the absence of any observable bridging mechanism. These results support the accepted notion that an extrinsic toughening mechanism is responsible for the increased toughness observed upon adding rubber particles to an epoxy matrix This revised version was published online in August 2006 with corrections to the Cover Date.