Statistical failure analysis of brittle coatings by spherical indentation: theory and experiment

The mode of failure and failure probability of a brittle coating on a compliant substrate subjected to a static load through a spherical indenter is investigated experimentally and theoretically. We extend our recent study (2003, J Mat Sci 38:1589) of surface crack initiation in a monolithic solid to the layered system, and account for the multi axial stress state of the indentation in the failure probability analysis. Two modes of failure, a Hertzian cone crack initiating from the contacting surface and a half-penny-shaped crack initiating from the interface, are investigated and the probability of failure initiation for both surfaces are theoretically predicted and compared with experimental data.The effect of interface debonding on failure phenomena is investigated. For a given load the failure probability for debonded specimens is significantly higher than that of well-bonded samples. For the debonded case the theoretical failure probability curve falls within the 90% confidence interval of the experimental data, while the experimental values for the completely bonded case show somewhat lower failure probabilities than that predicted. This may be attributed to the possible bridging effect by the adhesive on interfacial surface defects in the ceramic that is not accounted for in our model.     

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.     

Thermal shock cracking in a metal-particle-reinforced ceramic matrix composite

We study thermal crack shielding and thermal shock damage in a double-edge cracked metal-particle-reinforced ceramic matrix composite subjected to sudden cooling at the cracked surfaces. Under severe thermal shocks, the crack will grow but will be bridged by the plastically stretched metal particles. A linear softening bridging law is used to describe the metal particle bridging behavior. An integral equation of the thermal crack problem incorporating the bridging effect is derived and the thermal stress intensity factor at the bridged crack tip is calculated numerically. It is found that the thermal stress intensity factor is significantly reduced by the metal particle bridging. While the crack growth in thermally shocked monolithic ceramics is unstable, the composite can withstand sufficiently severe thermal shocks without failure.     

Notch sensitivity of fiber-reinforced ceramics

Crack bridging from an elliptical hole in fiber-reinforced ceramic composites is studied. For some fiber-reinforced ceramic composites, matrix toughness is much less than the toughness gained in the bridging zone, i.e. the bridging zone runs across the entire width of a specimen at a small load. In such case, load-carrying capacity of the specimen only depends on one parameter which is the measure of notch sensitivity. Solving the crack bridging problem for various aspect ratios of the elliptical hole and various bridging law shapes, the role of crack bridging from the hole is determined. The results presented may be used to guide design in addition to providing an improved understanding of the mechanism of fiber-matrix failure.     

Combination of biological mechanisms for a concept study of a fracture-tolerant bio-inspired ceramic composite material

The biological materials nacre and wood are renowned for their impressive combination of toughness and strength. The key mechanisms of these highly complex structures are crack deflection at weak interfaces, crack bridging, functional gradients and reinforcing elements. These principles were applied to a more fracture-tolerant model material which combined porous stiff ceramic layers, manufactured by freeze casting, infiltrated and bonded by a polymer phase reinforced with fabric layers. In the hybrid composites, crack deflection occurred at the ceramic–fabric interface and the intact fabric layers served as crack-bridging elements. Fabric-reinforced epoxy layers stabilized the fracture behaviour and delayed catastrophic failure of the material. The influence of the different components was analysed by varying the ceramic, fabric and interface properties. More ductile fabrics lead to larger strain to failure and more crack bridging but reduced the composite strength and stiffness after initial cracking. Higher elastic mismatch between the components improved crack deflection and bridging but resulted in deterred load transfer and a lower strength. The stiffness and strength of the ceramic layers influenced the elastic properties of the laminar composite and the initial crack resistance. Flaw tolerance was increased with polymer infiltration. We show with our hybrid ceramic–fabric composite as a bio-inspired concept study how fracture toughness, work of fracture and tolerance for cracking can be tailored when the contributing factors, i.e. the ceramic, the fabric and their interface, are modified.     

Influence of multiwall carbon nanotube functionality and loading on mechanical properties of PMMA/MWCNT bone cements

Poly (methyl methacrylate) (PMMA) bone cement—multi walled carbon nanotube (MWCNT) nanocomposites with weight loadings ranging from 0.1 to 1.0 wt% were prepared. The MWCNTs investigated were unfunctionalised, carboxyl and amine functionalised MWCNTs. Mechanical properties of the resultant nanocomposite cements were characterised as per international standards for acrylic resin cements. These mechanical properties were influenced by the type and wt% loading of MWCNT used. The morphology and degree of dispersion of the MWCNTs in the PMMA matrix at different length scales were examined using field emission scanning electron microscopy. Improvements in mechanical properties were attributed to the MWCNTs arresting/retarding crack propagation through the cement by providing a bridging effect and hindering crack propagation. MWCNTs agglomerations were evident within the cement microstructure, the degree of these agglomerations was dependent on the weight fraction and functionality of MWCNTs incorporated into the cement.     

Strengthening and toughening mechanisms in microfiber reinforced cementitious composites

Materials with quasi-brittle stress strain curves exhibit desirable properties such as enhanced durability, flaw tolerance and toughness. This study reveals that steel microfiber reinforced cement based composites exhibit such quasi-brittle behavior. Mechanical properties of steel microfiber reinforced cement based composites are obtained through flexure and splitting tension tests. The cracking process and crack fiber interactions that lead to the quasi-brittle behavior in these composites were investigated. The strength and toughness enhancement is associated with crack wake mechanisms. Aggregate bridging and pullout and secondary crack formations associated with microfiber bridging sites are predominant during the strain hardening regime. Multiple secondary microcracks perpendicular to the fiber/matrix interface is the dominant failure mode beyond peak load in the strain softening regime.     

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。     

Mixed-mode quasi-static failure criteria for adhesively-bonded pultruded GFRP joints

The strain energy release rates of adhesively-bonded pultruded GFRP joints were determined experimentally. The crack propagated in the adherend along paths outside the symmetry plane accompanied by fiber bridging. A new method, designated the “extended global method”, was introduced to facilitate mode partitioning in the mixed-mode experiments. Non-linear finite element models were developed in order to quantify the effect of the observed fiber bridging on crack propagation. An exponential traction-separation cohesive law was used to model the fiber bridging zone and calculate the energy release rate due to the fiber bridging, while the virtual crack closure technique was used for calculation of the fracture components at the crack tip. Experimental, analytical and numerical analyses were used to establish quasi-static mixed-mode failure criteria for crack initiation and propagation. The derived mixed-mode failure criteria can be used for simulating progressive crack propagation in other joint configurations comprising the same adhesive and adherends.     

Quantitative Crack Surface Morphology of Bone Cements in Relation to Propagation Rate

Morphology of the crack surface of surgical bone cements has seldom been studied in the past despite the clinical relevance of cement failure. Previous studies on a specific cement type suggest that crack morphology depends on crack propagation rate. The objectives of this work were: (i) to develop a quantitative indicator for describing crack morphology; and (ii) to assess if dependency on crack‐propagation rate is affected by cement formulation. Known crack surfaces were obtained from specimens under controlled loading conditions. Crack surface roughness was measured for different crack‐propagation rates, and compared against the amount of cleaved pre‐cured beads (measured with a semi‐automated procedure based on micrographs). Such indicators were extremely robust, operator‐independent, highly correlated, and sensitive to the type of fracture. Moreover, it was found that crack surface morphology heavily depends upon cement composition. Thus, crack surface roughness is proposed as a method for quantitatively identifying crack morphology, and finally classifying fracture type.     

水灰比对PVA纤维增强水泥基复合材料性能和显微结构的影响

对3种不同水灰比(0.2,0.4,0.65)形成的聚乙烯醇(PVA)纤维增强水泥基材料,通过三点弯曲试验,结合表观裂缝形状和裂缝处PVA纤维形态,研究了水灰比对材料弯曲性能的影响;通过对断裂面处纤维表面、纤维嵌入端和纤维拉断或拔出端的SEM影像分析,从微观层面研究了水灰比对PVA纤维-基体界面显微结构的影响。弯曲试验结果表明:随着水灰比增加,跨中部位裂缝数量明显增加,裂缝处拔出的纤维数量增多而拉断的数量减少,材料的弯曲韧度和开裂强度到弯曲强度的增强幅度提高。界面显微结构表明:随着水灰比增加,基体结构由致密变疏松,界面粘结力减弱,桥接裂缝的PVA纤维状态由瞬间猝断转变为滑动拔出且表面有轻微刮削,纤维对材料增强增韧的效率显著提高。     

可加工Ce-ZrO2/CePO4陶瓷材料的裂纹扩展及加工损伤

对可加工Ce—ZrO2／CePO4陶瓷材料中裂纹扩展及加工损伤进行了研究。发现其与一般脆性陶瓷中裂纹扩展有所不同，由于CePO4的加入在基体中形成了弱界面，在荷载作用下弱界面处易形成微裂纹，并发生裂纹的偏转、分支和桥联等形式，使得材料中裂纹的扩展呈现不连续性。而且CePO4加入量对裂纹扩展和加工损伤具有较大的影响，加入量较小时裂纹扩展不连续性并不明显，加工损伤大，加工困难；加入量较大时裂纹呈发散状态，加工损伤小，但材料性能降低。     

Micro-mechanical theory of macroscopic stress-corrosion cracking in unidirectional GFRP

A micro-mechanical theory of macroscopic stress-corrosion cracking in a unidirectional glass fibre-reinforced polymer composite is proposed. It is based on the premise that under tensile loading, the time-dependent failure of the composite is controlled by the initiation and growth of a crack from a pre-existing inherent surface flaw in a glass fibre. A physical model is constructed and an equation is derived for the macroscopic crack growth rate as a function of the apparent crack tip stress intensity factor for mode I. Emphasis is placed on the significance of the size of inherent surface flaw and the existence of matrix crack bridging in the crack wake. There exists a threshold value of the stress intensity factor below which matrix cracking does not occur. For the limiting case, where the glass fibre is free of inherent surface flaws and matrix crack bridging is negligible, the relationship between the macroscopic crack growth rate and the apparent crack tip stress intensity factor is given by a simple power law to the power of two.     

Uncertainty analysis of reliability predictions for brittle fracture

Reliability analysis of ceramic components under stationary or transient loading is generally performed on the basis of a Finite Element stress analysis from which the failure probability according to the multi-axial Weakest Link theory is calculated with the help of a suitable post-processing routine. We use the STAU post-processing routine and the general purpose Finite Element code ABAQUS. Due to scatter in the material parameters, the resulting failure probability is also prone to statistical uncertainties. We present a method of assessing this scatter using so-called resampling simulation methods. The analysis leads to confidence intervals for the failure probability which is a novel and important result especially for the purpose of design sensitivity considerations and the assessment of pooling procedures. In a simple example using a four-point bend specimen, the effect of pooling (i.e. grouping of results from different experiments by suitable scaling procedures) on the numerical result and on the scatter of failure probability is demonstrated. Here, pooling is done using results of inert strength measurements at various temperatures and scaling to room temperature values. A technologically more relevant example deals with a ceramic component in a model clutch under thermo-mechanical frictional loading. As a first step, the local risk of rupture is calculated which leads to the identification of the most critical regions of the component. As a second step, resampling confidence intervals for the failure probability are determined. As resampling data base, we use inert strength values at different temperatures as well as material data for sub-critical crack propagation.     

A MODEL TO PREDICT THE FATIGUE LIFE OF FIBRE-REINFORCED TITANIUM MATRIX COMPOSITES UNDER CONSTANT AMPLITUDE LOADING

A model based on micro-mechanical concepts has been developed for predicting fatigue crack growth in titanium alloy matrix composites. In terms of the model, the crack system is composed of three zones: the crack, the plastic zone and the fibre. Crack tip plasticity is constrained by the fibres and remains so until certain conditions are met. The condition for crack propagation is that fibre constraint is overcome when the stress at the location of the fibre ahead of the crack tip attains a critical level required for debonding. Crack tip plasticity then increases and the crack is able to propagate round the fibre. The debonding stress is calculated using the shear lag model from values of interfacial shear strength and embedded fibre length published in the literature. If the fibres in the crack wake remain unbroken, friction stresses on the crack flanks are generated, as a result of the matrix sliding along the fibres. The friction stresses (known as the bridging effect) shield the crack tip from the remote stress, reducing the crack growth relative to that of the matrix alone. The bridging stress is calculated by adding together the friction stresses, at each fibre row bridging the crack, which are assumed to be a function of crack opening displacement and sliding distance at each row. The friction stresses at each fibre row will increase as the crack propagates further until a critical level for fibre failure is reached. Fibre failure is modelled through Weibull statistics and published experimental results. Fibre failure will reduce the bridging effect and increase the crack propagation rate. Calculated fatigue lives and crack propagation rates are compared with experimental results for three different materials (32% SCS6/Ti-15-3, 32% and 38% SCS6/Ti-6-4) subjected to mode I fatigue loading. The good agreement shown by these comparisons demonstrates the applicability of the model to predict the fatigue damage in Ti-based MMCs.     

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.     

Influential Factors of Z-pin Bridging Force

The nine-pin bridging force experiments are conducted at room temperature (20 °C) and at 75 °C. A three-dimensional z-pin unit cell for finite element analysis is established to study the influential factors of the z-pin bridging force. The experimental results show that the z-pin bridging force at 75 °C is smaller than at 20 °C. The z-pin bridging force is highly dependent on the surface area of z-pin. Therefore, it is feasible that the bridging force can be enhanced by changing the surface area of z-pin. The study also shows that the lay-up sequences of laminates have an impact on the z-pin bridging force, and the maximum bridging force of z-pin rises with the increase elastic modules of the resin. The z-pin bridging force reduces with rise of temperature for two reasons: The elastic modulus and shear strength of the resin decrease with rise of temperature, forcing the bridging force to reduce and the resin makes some clamping effect on z-pin, pushing the bridging force to increase.     

Numerical analysis of fibre bridging and fatigue crack growth in metal matrix composite materials

The analysis of bridged crack configurations in unidirectional fibre-reinforced composites is relevant to a variety of crack growth problems, including the fatigue of metal matrix composites and the study of fibre failure in the wake of a bridged matrix crack. Details of numerical procedures for predicting fibre stresses and their effect on crack tip stress intensity factors are presented here to provide a useful overview of how standard bridging calculations are done. Results are presented and discussed in the context of predicting fatigue crack growth with fibre failure in metal matrix composites.     

Toughening polymeric composites using nanoclay: Crack tip scale effects on fracture toughness

Fracture behavior of vinyl ester resin and the methods that can be used to toughen vinyl ester resin were studied. Neat resin, 5% by weight nanoclay, 5% by weight core shell rubber (CSR) and hybrid system (3% nanoclay and 2% CSR by weight) were the material systems considered for comparing fracture toughness. Three types of cracks were used to determine the stress intensity factors at failure, viz., sharp crack, blunt crack and notch. The critical stress intensity factor in the case of sharp cracks improved significantly when compared to neat resin. In the case of notched and blunt cracked specimens, a reduction in stress intensity factors (at failure) was observed for reinforced systems. However, for notched and blunt cracked specimens, it was shown from the morphology of the fracture surface that the stress intensity factor calculated by assuming a notch or a blunt crack as an ideal crack was not the controlling parameter for fracture. A method for quantifying the crack tip sharpness using fracture surface roughness has been proposed.     

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。