Model for Fatigue Crack Growth in Grain-Bridging Ceramics

A model for fatigue crack propagation based on sliding wear of bridging grains is analyzed for polycrystalline ceramics. Taking into account damage development and crack tip energy balance, we have obtained rigorous solutions for equilibrium and compatibility equations in the crack wake under monotonic and cyclic loading/unloading conditions. Fatigue mechanics in ceramics is found to be formally similar to elastic-plastic mechanics of a path-dependent hardening material, due to the frictional resistance to reverse sliding. It features a load-displacement hysteresis causing energy dissipation and wear, and a longer cohesive zone required for supporting the same peak load with the wear-reduced bridging stresses. The unloading crack opening displacement is more strongly dependent on K _max than on Delta K ; such displacement causes wear on the bridging grains. Meanwhile, incremental crack growth brings in new bridging grains that has a shielding effect on the crack tip stress field; such an effect is strongly dependent on K _max but independent of Delta K . At steady state, when shielding accumulation and shielding degradation are balanced, the fatigue crack growth rate has a form d a /d N = A ( K _max) ^b (Delta K ) ^c , where A, b , and c are material-dependent parameters. Fatigue is predicted to have a very high b , a modest c , a higher fatigue resistance for tougher ceramics, and a stronger K _max dependence for less tough ceramics. These predictions are in agreement with experimental observations.     

Fatigue and Durability of Silane-Bonded Epoxy/Glass Interfaces

Fatigue (slow) crack growth in epoxy/glass interfaces bonded with the silane coupling agent 3-aminopropyltriethoxysilane was studied under static and cyclic loading at 23°C, 95% RH using the double cleavage drilled compression test. Crack growth rates under cyclic loading were significantly greater than under static loading, in contrast to crack growth rate results in monolithic glass. After aging up to 34 h at 94°C in distilled water, the silane-bonded epoxy/glass specimens exhibited somewhat greater resistance to fatigue crack growth than the unaged samples; however, after aging at 98°C in distilled water and at 70°C in an aqueous KOH solution at pH 10, crack growth became cohesive and exhibited fractal behavior. Mechanisms for fatigue crack growth at silane-bonded epoxy/glass interfaces are proposed.     

Fatigue and Durability of Silane-Bonded Epoxy/Glass Interfaces

Fatigue (slow) crack growth in epoxy/glass interfaces bonded with the silane coupling agent 3-aminopropyltriethoxysilane was studied under static and cyclic loading at 23°C, 95% RH using the double cleavage drilled compression test. Crack growth rates under cyclic loading were significantly greater than under static loading, in contrast to crack growth rate results in monolithic glass. After aging up to 34 h at 94°C in distilled water, the silane-bonded epoxy/glass specimens exhibited somewhat greater resistance to fatigue crack growth than the unaged samples; however, after aging at 98°C in distilled water and at 70°C in an aqueous KOH solution at pH 10, crack growth became cohesive and exhibited fractal behavior. Mechanisms for fatigue crack growth at silane-bonded epoxy/glass interfaces are proposed.     

Cyclic Fatigue in Ceramics: A Balance between Crack Shielding Accumulation and Degradation

Cyclic fatigue growth rates in R-curve ceramics have been observed to depend very strongly on the maximum applied stress intensity, K _max, and only weakly on the stress intensity range, Δ This behavior is rationalized through measurement of crack wake shielding characteristics as a function of these fatigue parameters in a gas-pressure-sintered silicon nitride. In particular, evidence for a mechanical equilibrium between shielding accumulation by crack growth and shielding degradation by frictional wear of sliding interfaces is found for steady-state cyclic fatigue. This equilibrium gives rise to a rate law for cyclic fatigue. The data suggest that the accumulation process is the origin of the strong K _max dependence, and that the degradation process is the origin of the weak Δ dependence. These features are shown to be related to the "cyclic" R -curve and to the cyclic crack opening displacement, respectively.     

Cohesive Zone Model Characterization of the Adhesive Hysol EA-9394

Abstract

The cohesive zone model approach is attractive for the analysis of failure of adhesively bonded structures. While the numerical implementation of cohesive elements has been well established, there remains a lack of cohesive material data. The present paper contributes to efforts to fill this void. An investigation of crack growth in the widely used structural adhesive Hysol EA-9394 is presented, and the adhesive is characterized by a cohesive zone law. Crack growth experiments were performed on specimens consisting of aluminum adherends bonded by use of the adhesive. Measurements of the surface topography leading reconstruction of fracture processes indicate that plastic deformation is absent during fracture. Thus, the cohesive zone law can directly be determined from the energy release rate and the material separation measured at the initial crack tip. The cohesive zone law is then applied in finite element model to predict crack growth. The predicted strain fields during crack growth are well matched to those obtained by digital image correlation measurements. An independent set of crack growth experiments was performed, and finite element models based on the cohesive law were used to predict the outcome of these experiments. Again good agreement between simulation and experiment was obtained. The results give confidence that the cohesive zone model parameters are transferable to the analysis of structures bonded with the adhesive Hysol EA-9394 in general. A comparison of the cohesive zone law for Hysol EA-9394 demonstrates that this adhesive possesses high strength and moderate toughness. Limits to the transferability regime are discussed.     

Crack-Bridging Analysis for Alumina Ceramics under Monotonic and Cyclic Loading

Frictional degradation of grain-localized bridges behind a crack tip has been recognized as the major cyclic fatigue mechanism in alumina ceramics. Such a fatigue mechanism implies that the crack growth resistance ( R ) curve behavior during cyclic fatigue is different from that of monotonic loading due to the reduction in crack-tip shielding. A recent crack-bridging theory based on crack compliances is used to study the bridging stresses under monotonic loading and during cyclic fatigue. The bridging-stress distributions of two coarse-grained aluminas under monotonic loading are determined using compliance measurements. Because the interlocking grain bridges at the crack wake are subject to frictional damage from cyclic loading, the bridging-stress distribution evaluated during cyclic fatigue is distinct from that for monotonic loading. These results indicate that it is incorrect to incorporate the R -curve behavior from monotonic loading to the analysis of cyclic fatigue of alumina ceramics.     

Numerical and experimental analyses of composite bonded double-strap repairs under high-cycle fatigue

This work addresses the behaviour of double-strap repairs of carbon-epoxy laminates under high-cycle fatigue loading. Experimental static and fatigue three-point bending tests were performed considering simpler double-strap bonded joints. Numerical analyses involving a cohesive mixed-mode I+II zone model appropriate for high-cycle fatigue loading considering quasi-static and fatigue degradation in a sole damage parameter were accomplished. The numerical fatigue life prediction and normalised compliance versus number of cycles curve are in close agreement with the experimental results. The numerical model was subsequently used to assess the influence of ±5% variation of several parameters intrinsic to fatigue behaviour on the numerically obtained fatigue lives. It was concluded that the exponent parameter of the modified Paris law is the most influent one. In addition, it was concluded that a concurrent variation of ±5% of all analysed parameters can explain the experimental scatter obtained.     

Origin of moisture effects on crack propagation in composites

A study has been made of the origin of unexpected moisture effects on crack extension in fiberglass laminates. Water immersion has been found to greatly reduce the rate of crack growth under constant loading while increasing the rate under cyclic loading, the latter effect being the expected one. Observations were made of the extension of the stable damage zone at the tip of precut notches in wet and dry environments. The damage zone size is postulated as a critical element in the relaxation of high stress concentrations in composites, such as those at notch or crack tips. Under constant load, moisture is shown to greatly expand the interply delamination region in the damage zone, thus reducing the local fiber stresses and increasing crack resistance. Under cyclic loading moisture has little effect on the delamination region, which is large even for dry environments, and the only effect is weakening of the material and acceleration of cracks. Severe hygrothermal conditions can so weaken the material that the crack resistance is reduced under constant loading as well.     

Crack-tip Degradation Processes Observed during in situ Cyclic Fatigue of Partially Stabilized Zirconia

It is proposed that reduced transformation zone widths in Mg-PSZ in cyclically versus critically propagated cracks are due to reductions in the crack-tip toughness, consistent with an intrinsic cyclic fatigue mechanism. Cyclic fatigue crack growth in Mg-PSZ was observed in situ in a SEM. Following cyclic fatigue, the samples were critically broken and the fracture surfaces observed. Extensive crack bridging by the precipitate phase was observed near the crack tip, and it is proposed that this crack bridging significantly affects the material's intrinsic toughness. Frictional degradation of the precipitate bridges occurs during cyclic loading and hence reduces the critical crack-tip stress intensity factor for crack propagation. Reductions in the critical crack-tip stress intensity factor also lead to reductions in the transformation zone widths during cyclic loading and hence the level of crack-tip shielding caused by phase transformation. This appears to be the mechanism of cyclic fatigue. A degree of uncracked ligament bridging was also observed and is linked with the frequency of random large precipitates. However, analysis shows that its effect upon crack growth rates under cyclic load is limited.     

Cohesive zone modelling of crack growth in polymers Part 2 –Numerical simulation of crack growth

Abstract

Cohesive zone models, which incorporate some form of cohesive law as the fracture criterion within the localised damage zone, are increasingly being used in the fracture assessment of tough engineering materials. However, the exact characterisation of the material within the damage zone is crucial as it has a fundamental bearing on the computed crack growth rates. A procedure is presented for implementing a cohesive zone model using the finite volume method by incorporating experimentally measured traction curves as the local fracture criterion. Experimental load–time and crack growth data in tough polyethylene for a three point bend geometry are compared with numerical predictions. Reasonable agreement is achieved between experiment and model predictions when a single fixed rate traction–separation curve is used for all cells along the prescribed crack path. Predictions are improved by incorporating a scheme for switching between a family of rate dependent curves in place of a single fixed rate curve. Results also indicate the necessity of incorporating the effect of difference in constraint along the crack path into the choice of the local traction–separation law.     

Contact Fatigue of a Silicon Carbide with a Heterogeneous Grain Structure

A comparative study of cyclic fatigue damage from Hertzian contacts in silicon carbide ceramics with homogeneous microstructure (fine, equiaxed grains, strong grain boundaries) and heterogeneous microstructure (coarse, contiguous elongate grains, weak interphase boundaries) is presented. Observations of the surface and subsurface damage patterns using optical microscopy reveal fundamentally different cyclic fatigue mechanisns: in the homogeneous material, by slow growth of a well-developed cone crack outside the contact area; in the heterogeneous material, by progressive mechanical degradation within a distributed damage zone below the contact area. Scanning electron micrographs of the latter material show copious fine debris in the damage zone, consistent with a degradation mechanism by frictional attrition by forward-reverse sliding at the weak interphase boundaries. Acoustic emission is recorded during both load and unload half-cycles, confirming hysteresis in the sliding process. Flexure tests indicate initially slight strength losses from the cyclic contact damage in both microstructures, followed by accelerated losses at higher numbers of cycles. The underlying basis for establishing an analytical model of damage accumulation in the heterogeneous microstructure in terms of shear-fault sliding, and for designing micro-structures for optimal properties in fatigue and wear applications, is foreshadowed.     

Behavior and failure of adhesive bonds in pin fin heat sinks using cohesive zone model

Adhesive bonding is a versatile material joining method that tends to distribute the load over the bonded area and provide more flexibility in selecting the base material without worrying about the joining process and its effects. To improve the performance of heat sinks, polymer composite pin fin are used to improve the thermal conductivity. Adhesives are usually used in bonding composite fins to their metal base plate. In this work we provide a methodology for estimating the fatigue life of the adhesive joint. A thermo-mechanical cohesive zone model (CZM) is used at the interfaces to measure the softening of the bond under thermal cyclic loading which in turn decreases the critical stress for failure. A summary of the fatigue crack initiation (FCI) life prediction model is presented before a qualitative study is performed to estimate the effect of convection environment on the life and behavior of the adhesive bond.     

Fatigue and fracture characteristics of a fine-grained (Mg,Y)–PSZ zirconia ceramic

The fatigue and fracture characteristics of a partially-stabilized fine-grained zirconia with spinel additions, (Mg,Y)–PSZ, were studied. Fracture toughness, crack growth resistance curves and fatigue crack growth (FCG) behavior, under both sustained and cyclic loading, were evaluated. Mechanical fatigue effects were clearly evidenced by (1) remarkable crack growth rate differences under cyclic and static loading and (2) significant loading ratio effects. Comparing the cyclic and the static FCG behavior allows to deduce a higher cyclic fatigue sensitivity of the fine-grained (Mg,Y)–PSZ with respect to a commercial peak-aged Mg–PSZ used as a reference material. By in situ observation of crack extension under cyclic loading, the fatigue mechanisms could be resolved. Mechanical degradation of bridging ligaments, as already known for coarse-grained Mg–PSZ, is one source of cyclic fatigue. An additional source attributed to the particle dispersed microstructure of the (Mg,Y)–PSZ is the interaction between crack faces and hard spinel particles. The sensitivity of (Mg,Y)–PSZ and Mg–PSZ to cyclic fatigue is discussed in terms of the respective microstructures, prevalence and operativity of distinct mechanical fatigue mechanisms.     

Cyclic Fatigue Crack Growth in Three-Point Bending PZT Ceramics under Electromechanical Loading

This paper investigates experimentally and analytically the cyclic fatigue crack growth in piezoelectric ceramics under electromechanical loading. Cyclic crack growth tests were conducted on lead zirconate titanate (PZT) ceramics subjected to dc electric fields, and a finite element analysis was used to calculate the maximum energy release rate for the permeable crack model. Based on bending experiments using single-edge precracked-beam specimens, cyclic fatigue crack growth rates are found to be sensitive to the maximum energy release rate and applied dc electric fields. Possible mechanisms for crack growth were discussed by scanning electron microscope examination of the fracture surface of the PZT ceramics.     

A stochastic approach for continuous and discontinuous crack growth in polycarbonate under cyclic loading

This article presents a stochastic approach to predict fatigue crack propagation (FCP) diagrams of continuous crack growth (CCG) and discontinuous crack growth (DCG) in polycarbonate (PC) under cyclic loading. First, it is assumed that the macroscopic fatigue crack propagates stochastically. The transition probability is then expressed in conjunction with the craze fibril breakdown model for CCG. Second, the stochastic process is applied to DCG assuming that DCG occurs because of an unstable crack growth in the craze zone. A fracture criterion using a stress intensity factor is introduced for the unstable crack growth. As a result, we obtain an FCP diagram where the rate in CCG is lower than that in DCG. The stress intensity factor range for the DCG–CCG transition can be theoretically determined. Finally, to verify the present approach, the experimental data of DCG and CCG of PC are fitted to the Paris equation. In addition, the relationship between the DCG band size and the number of cycles required for DCG is predicted in order to compare it with the experiment data. POLYM. ENG. SCI., 2013. © 2013 Society of Plastics Engineers     

Role of fatigue in damage development of refractories under thermal shock loads of different intensity

Refractories insulation of industrial furnaces often fail under repetitive thermal shock. Degradation of silica refractories under thermal shock loads of different intensity was studied. The load variation was achieved by utilisation of geometrically similar samples of different dimensions. Finite element method modelling predicted loads developing during the test. Resulting damage was determined by the ultrasound velocity and crack patterns. Tests involving up to 150 cycles demonstrated the role of fatigue in enabling sub-critical crack formation and countering the crack arrest. Repetitive cycles reduce crack wake friction and intensify loading due to crack debris re-location. Damage saturation, sigmoidal and near-exponential damage growth was typical for low, intermediate and high loads, respectively. Similar trends of damage accumulation were observed in mechanical displacement controlled cyclic fatigue tests performed in wedge splitting set-up. Strain and strain energy based criteria of thermal shock intensity seem to have complimentary value in predicting the crack formation and growth. Thermal shock damage after the first cycle seems to be an effective parameter to predict overall resistance to the degradation in the sample. Load reduction due to previous crack formation related to the fatigue potential for subsequent crack development can explain the crack size variation typically observed in refractories after multiple thermal shocks. For thermal shock tests, the variation of sample size, instead of the temperature interval, is a suitable alternative for refractories with strongly temperature dependant material properties.     

Fatigue Crack Propagation at Polymer Adhesive Interfaces

Fatigue (slow) crack growth in epoxy/glass, epoxy acrylate/glass and epoxy/PMMA interfaces was studied under constant and cyclic loading at both high and low humidities using the interfacial, four-point flexure test. Finite element analysis was used to determine the energy release rate and phase angle appropriate for the different crack geometries observed. The experimental results show that for the polymer/glass interfaces, the primary driving force for fatigue crack growth is the applied energy release rate at the crack tip and that increasing test humidity enhances crack growth under constant loading but has an insignificant effect under cyclic loading. At low humidity the crack growth rates under cyclic loading are significantly greater than under constant loading. For epoxy/PMMA interfaces the crack growth results were independent of the applied energy release rate, relative humidity, and cyclic vs. constant loading, within experimental scatter. In addition, for polymer/glass interfaces the effect of phase angle (13 to 54°) on crack growth rates is not significant. However, for epoxy/PMMA interfaces the applied energy release rate for the initiation of crack growth is considerably greater for a phase angle of 66° than for 5°, indicating that increasing shear at the crack tip makes the initiation of crack growth more difficult. These results are discussed in terms of possible mechanisms of fatigue crack growth at polymer adhesive interfaces.     

Fatigue crack growth in fiber reinforced plastics

Crack extension during fatigue loading is one of the primary causes of failure in engineering materials. While the fatigue crack resistance of homogeneous and even adhesive systems has received detailed study and characterization, relatively few and scattered results are available for fiber composites. One difficulty with obtaining such data for composites is their tendency to develop complex patterns of intra- and interlaminar damage which expand in a stable manner during fatigue. Such damage usually does not severely reduce the load carrying capacity of a structure but the complexity of the damage geometry has so far frustrated efforts to apply any unifying theories of growth. Measurement of the rate of macroscopic crack growth, through thickness crack extension, has been possible for certain composites and crack direction where the stable damage is constrained. These include cracks in 0°/90° laminates, woven fabric laminates, chopped strand mat laminates, sheet molding (SMC) materials, and short fiber reinforced thermoplastics. Macroscopic interlaminar cracks in continuous fiber systems have also received some recent attention. Fatigue crack growth in glass fiber composites for which most data are available, involves significant contributions from both static and cyclic load effects. A simple model for predicting fatigue crack growth rates from traditional S-N curve and fracture toughness data has proven useful for certain well behaved systems. Limited study has also been made of the effects of moisture and salt water on the fatigue crack growth rate.     

Fatigue Analysis of Adhesive Joints Under Vibration Loading

Adhesively bonded joints have been used extensively for many structural applications. However, one disadvantage usually limiting the service life of adhesive joints is the relatively low strength for peel loading, especially under dynamic cyclic loading such as impulsive or vibrational forces. Moreover, accurately predicting the fatigue life of bonded joints is still quite challenging. In this study, a combined experimental–numerical approach was developed to characterize the effect of the cyclic-vibration-peel (CVP) loading on adhesively bonded joints. A damage factor is introduced into the traction-separation response of the cohesive zone model (CZM) and a finite element damage model is developed to evaluate the degradation process in the adhesive layer. With this model, the adhesive layer stress states before and after being exposed to various CVP loading cycles are investigated, which reveals that the fatigue effect of the CVP loading starts first in the regions close to the edges of the adhesive layer. A good correlation is achieved when comparing the simulation results to the experimental data, which verifies the feasibility of using the proposed model to predict the fatigue life of adhesively bonded joints under the CVP type of loading.     

Push-Pull Fatigue of Sintered Silicon Nitride Ceramics at Elevated Temperatures

The fatigue tests under push-pull completely reversed loading and pulsating loading were performed for silicon nitride ceramics at elevated temperatures. Then the effects of stress wave form, stress rate, and cyclic understressing on fatigue strength, and cyclic straining behavior, were examined. The cycle-number-based fatigue life is found to be shorter under trapezoidal stress wave loading than under triangular stress wave loading, and to become shorter with increasing hold time under the trapezoidal stress wave loading. Meanwhile, the equivalent time-based life curve, which is estimated from the concept of slow crack growth, almost agrees with the static fatigue life curve in the short and intermediate life regions, showing the small cyclic stress effect and the dominant stress-imposing period effect on cyclic fatigue life. The fatigue strength increased in stepwise stress amplitude increasing test, where stress amplitude is increased stepwise every given number of stress cycles, at 1100° and 1200°C. Occurrence of cyclic strengthening was proved through a gradual decrease in strain amplitude during a pulsating loading test at 1200°C in this material, corresponding to the above cyclic understressing effect on fatigue strength.