Fatigue Crack Propagation in Ceria-Partially-Stabilized Zirconia (Ce-TZP)-Alumina Composites

Fatigue crack propagation rates in tension-tension load cycling were measured in ZrO₂-12 mol% CeO₂-10 wt% Al₂O₃ ceramics using precracked and annealed compact tension specimens. The fatigue crack growth behavior was examined for Ce-TZPs of different transformation yield stresses obtained by sintering for 2 h at temperatures of 1500°C (type A), 1475°C (type B), 1450°C (type C), and 1425°C (type D). The threshold stress-intensity range, ΔK_th, for initiation of fatigue crack propagation increased systematically with decreasing transformation yield stress obtained with increasing sintering temperature. However, the critical stress-intensity range for fast fracture, ΔK_c, as well as the stress-intensity exponent in a power-law correlation (log (da/d N ) vs log ΔK) were relatively insensitive to the transformation yield stress. The fatigue crack growth behavior was also strongly influenced by the history of crack shielding via the development of the crack-tip transformation zones. In particular, the threshold stess-intensity range, Δ K _th, increased with increasing size of the transformation zone formed in prior quasi-static loading. Crack growth rates under sustained peak loads were also measured and found to be significantly lower and occurred at higher peak stress intensities as compared to the fatigue crack growth rates. Calculations of crack shielding from the transformation zones indicated that the enhanced crack growth susceptibility of Ce-TZP ceramics in fatigue is not due to reduced zone shielding. Alternate mechanisms that can lead to reduced crack shielding in tension-tension cyclic loading and result in higher crack-growth rates are explored.     

Improved Endurance Limit of Zirconia Ceramics by Overloading

The influence of initial overloads upon the subsequent fatigue crack growth in transformation-toughened ceramics (TTCs) is investigated. It is revealed that initial overloading can be beneficial to these ceramics. In particular, it is shown that an overload will facilitate crack arrest in a low transformation strength material which would otherwise be prone to cyclic fatigue degradation and eventual failure. Based on the results of this investigation, a proof test may be designed to screen out TTC components which do not attain a prescribed endurance limit.     

Fatigue Crack Growth from Small Surface Cracks in Transformation-Toughened Ceramics

A theoretical model based on the theory of complex potentials and dislocation formalism is used to simulate the fatigue crack growth of small cracks in a transformation-toughened ceramic. Assuming power-law crack growth in which the growth rate depends on the effective stress intensity at the crack tip instead of the applied stress intensity, it is shown that the crack growth rate decreases with the applied stress intensity in the initial stage of fatigue crack growth. This is in agreement with existing experimental evidence for the growth of small cracks in Mg-PSZ. New experimental results obtained by in situ observation in a scanning electron microscope of a similar material confirm this behavior. The numerical results also confirm the plausibility of using the steady-state toughness value obtained from quasi-static crack growth as a normalizing parameter in the power-law for fatigue crack growth.     

Fatigue Crack Propagation in Transformation-Toughened Zirconia Ceramic

Fatigue crack propagation under tension-tension loading is observed in a transformation-toughened partially stabilized zirconia (PSZ) ceramic containing 9 mol% MgO. Such subcritical crack growth behavior is demonstrated to be cyclically induced, based on a comparison with behavior under sustained loading (at the maximum load in the fatigue cycle) and at varying cyclic frequencies. Crack extension rates, which are measured as a function of the cyclic stress intensity range ΔK over the range 10^-10 to 10^-6 m/cycle, are found to be load ratio dependent and to show evidence of fatigue crack closure, similar to behavior in metals. Cyclic crack growth rates are observed at ΔK levels as low as 3 MPa m^1/2 and are typically many orders of magnitude faster than reported data on environmentally assisted, subcritical crack growth in PSZ under sustained-load conditions.     

Crack Shielding in Ce-TZP/Al2O3 Composites: Comparison of Fatigue and Sustained Load Crack Growth Specimens

Crack shielding stress intensities in in situ loaded compact tension specimens of two types of ceria-partially-stabilized zirconia/alumina (Ce-TZP/Al₂O₃) composites with prior histories of subcritical crack growth in sustained and tension-tension fatigue loading were directly assessed using laser Raman spectroscopy. Crack-tip stress fields within the transformation zones were measured by measuring a stress-induced frequency shift of a peak corresponding to the tetragonal phase. The peak shift as a function of the applied stress was separately calibrated using a ball-on-ring flexure test. Total crack shielding stress intensity was estimated from the far-field applied stress intensity and the local crack-tip stress intensity assessed from the measured near-crack-tip stresses. The shielding stress intensities were consistently lower in the fatigue specimens than in the sustained load crack growth specimens. The reduced crack shielding developed in the fatigue specimens was independently confirmed by measurements of larger crack-opening displacement under far-field applied load as compared to the sustained load crack growth specimens. Thus, diminished crack shielding was a major factor contributing to the higher subcritical crack growth rates exhibited by the Ce-TZP/Al₂O₃ composites in tension–tension cyclic fatigue. Calculations of zone shielding considering only the dilatational strains in the transformation zones accounted for 81% and 86% of the measured values in the sustained load crack growth specimens, but significantly overestimated the shielding in the fatigue specimens. Possible reasons for the diminished crack shielding in the fatigue specimens are discussed.     

Use of Cube-Corner Nano-Indentation Crack Length Measurements to Estimate Residual Stresses Over Small Spatial Dimensions

Cube-corner indenters, by virtue of their acuity, possess a lowered threshold load for cracking. Shorter crack lengths allow the sampling of residual stresses in small spatial dimensions. We conducted cube-corner indentation on tempered and annealed glasses. Indentation crack geometry was found to be "quarter-penny." A stress-intensity factor for this geometry, and crack length decrements on tempered materials were used in a stress-intensity superposition to provide reasonable estimates of residual stress. Stresses ∼100 MPa over a length scale of 10 μm, and 30 MPa over 20 μm were measured accurately, indicating that cube-corner indentation is a promising tool for materials characterization.     

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.     

Fatigue and Static Crack Propagation in Yttria-Stabilized Tetragonal Zirconia Polycrystals: Crack Growth Micromechanisms and Precracking Effects

The influence of precracking techniques in the crack growth behavior of yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) is investigated. Load-bridge and cyclic-compression precracking enhance subsequent tensile crack growth rates, in comparison to results that are found with precracks that are extended under four-point bending prior to testing. The actual influence of these precracking techniques in the near-threshold crack growth regime is remarkably different. Although load-bridge precracking produces a pattern of crack growth fluctuations for stress intensity factors, K , lower than the effective crack-growth threshold of the material, compression-fatigue precracks start to propagate under far-field tensile loads at very fast growth rates and for K values that are slightly higher than the effective threshold. Crack-tip shielding by tetragonal-to-monoclinic transformation develops gradually, influencing the crack growth behavior in Y-TZP. Proposed fatigue crack growth micromechanisms involve damage accumulation at the crack-tip region. For K _max > 3 MPa·m^1/2, fatigue crack growth rates are strongly affected by environmental interactions at the crack tip, and postulated fatigue micromechanisms include the cyclic degradation of crack-tip shielding.     

拉弯复合应力下焊接头表面裂纹疲劳扩展规律的研究

通过对16MnR钢对焊的弓形试极疲劳裂纹扩展试验，研究了在拉弯复合应力下对焊接头表面裂纹疲劳扩展规律。采用Newman－Raju公式分析了有限宽板在拉弯复合应力下表面裂纹的应力强度因子的计算。试验研究表明在拉弯复合应力下当a／t≤0．8时表面裂纹疲劳扩展规律仍可用Paris公式来描述，并且c向和a向的Paris系数之间仍存在着C_c＝0．9~nC_a的关系。     

A technique for measuring stresses in small spatial regions using cube-corner indentation: Application to tempered glass plates

Vickers indentation cracks have been used to estimate residual stress in materials; however, a high threshold load for cracking limits the smallest spatial region for stress measurement. Cube-corner indenters have a lower included angle, and their sharpness leads to lowered cracking thresholds enabling stress measurement in small spatial regions. Cube-corner indentations on tempered glass plate and on annealed soda-lime-silica glass revealed that crack surface traces on the tempered material were significantly smaller. Cracks were found to be quarter-penny shaped as opposed to half-penny/radial for Vickers indentation. Using an appropriate stress-intensity factor and a stress-intensity factor superposition approach, surface stresses in the tempered plate were calculated. The stresses were in good agreement with those determined using well-established Vickers indentation approach; however, the spatial region sampled is 6–10 times smaller. An estimate of the smallest spatial region at which a particular stress may be measured using this technique is presented.     

Crack Growth in Soda–Lime–Silicate Glass near the Static Fatigue Limit

The atomic force microscope (AFM) was used to explore the nature of features formed on the surfaces of cracks in soda–lime–silicate glass that were held at stress intensity factors below the crack growth threshold. All studies were conducted in water. Cracks were first propagated at a stress intensity factor above the crack growth threshold and then arrested for 16 h at a stress intensity factor below the threshold. The stress intensity factor was then raised to reinitiate crack growth. The cycle was repeated multiple times, varying the hold stress intensity factor, the hold time, and the propagation stress intensity factor. Examination of the fracture surface by optical microscopy showed surface features that marked the points of crack arrest during the hold time. These features were identical to those reported earlier by Michalske in a similar study of crack arrest. A study with the AFM showed these features to be a consequence of a bifurcation of the crack surface. During the hold period, waviness developed along the crack front so that parts of the front propagated out of the original fracture plane, while other parts propagated into the plane. Crack growth changed from the original flat plane to a bifurcated surface with directions of as much as 3° to 5° to the original plane. This modification of crack growth behavior cannot be explained by a variation in the far-field stresses applied to the crack. Nor can the crack growth features be explained by chemical fluctuations within the glass. We speculate that changes in crack growth direction are a consequence of an enhancement in the corrosion rate on the flank of the crack at stresses below the apparent crack growth threshold in a manner described recently by Chuang and Fuller.     

Cyclic Fatigue Life and Crack-Growth Behavior of Microstructurally Small Cracks in Magnesia-Partially-Stabilized Zirconia Ceramics

Cyclic fatigue stress/life ( S / N ) and crack-growth properties are investigated in magnesia-partially-stabilized zirconia (Mg-PSZ), with particular reference to the role of crack size. The material studied is subeutectoid aged to vary the steady-state fracture toughness, K_c , from ∼3 to 16 MPa · m^1/2· S / N data from unnotched specimens show markedly lower lives under tension—compression compared with tension—tension loading; "fatigue limits"(at 10⁸ cycles) for the former case approach 50% of the tensile strength. Under tension—tension loading, cyclic crack-growth rates of "long"(> 3 mm) cracks are found to be power-law dependent on the stress-intensity range, Δ K , with a fatigue threshold, Δ K _TH, of order 50% of K_c . Conversely, naturally occurring "small"(1 to 100 μm) surface cracks are observed to grow at Δ K levels 2 to 3 times smaller than Δ K _TH, similar to behavior widely reported for metallic materials. The observed small-crack behavior is rationalized in terms of the restricted role of crack-tip shielding (in PSZ from transformation toughening) with cracks of limited wake, analogous to the reduced role of crack closure with small fatigue cracks in metals. The implications of such data for structural design with ceramics are briefly discussed.     

Static and cyclic crack propagation in Ce-TZP ceramics with different amounts of transformation toughening

Ceria partially stabilized zirconia ceramics (Ce-TZP) with identical grain size and different amounts of transformation toughening were processed to investigate the influence of phase transformation on static and cyclic fatigue crack growth.Static crack growth is governed by environmentally stress induced corrosion at the crack tip and it is highly influenced by the crack shielding due to the phase transformation. Three fatigue mechanisms are expected to be operative at different proportions depending on the amount of transformation: wedge effect due to debris, degradation of bridging and modification of the shielding effect of the transformation zone. However, it is difficult to separate the contribution of the different mechanisms as grain bridging is induced by crack arrest due to phase transformation.     

Crack Initiation and Arrest in a SiC Whisker/A12O3 Matrix Composite

The fracture initiation and arrest stress intensity factors were determined for a SiC-whisker-reinforced AI₂O₃ matrix composite. A chevron-notched, three-point-bend specimen was used to genera e the load/displacement curve, which exhibited repeated crack initiation, followed by crack arrest behavior. Corresponding stress intensity factors were determined for both situations using the compliance technique. Calculated crack arrest positions were in agreement with fractographic observations. Both the crack arrest and the crack initiation stress intensity factors exhibited a rising R -curve with increasing crack length, suggesting the presence of wake toughening effects on the crack growth resistance.     

Subcritical Crack Growth in Y-TZP and Al2O3-Toughened Y-TZP

Crack velocity curves for Y-TZP and Al₂O₃-toughened Y-TZP were determined for long cracks in compact tension specimens with an in situ fracture device on the stage of an optical microscope. Indications for a crack velocity threshold were found for both materials. Above this threshold, at 2.6 MPa·m^1/2 for Y-TZP and 3.6 MPa·m^1/2 for Al₂O₃-toughened Y-TZP, chemically assisted subcritical crack growth occurs over an extended regime of applied stress intensity factors of width 2.1–2.8 MPa·m^1/2. It is recognized that the dependence of the shielding term on the crack-tip stress field renders transformation-toughened materials particularly susceptible to stress-corrosion cracking. This interrelation leads to the definition of a steady-state velocity at constant applied stress intensity factor. This velocity is obtained in the situation where the shielding term is fully defined by the present crack-tip stress field, not depending on prior loading history.     

弯曲载荷作用下孔边角裂纹的应力强度因子与疲劳扩展规律

本文运用边界元方法提出了弯曲载荷作用下,平板中孔单边角裂纹裂尖的应力强度因子(SIF)的计算式。并通过实验研究了孔单边角裂纹在交变的弯矩作用下,裂纹的形貌变化规律及裂纹扩展速率,指出角裂纹沿长度方向的扩展可以用Paris公式来描述,而沿深度方向则不然,但两者之间具有幂函数的关系。     

Fatigue crack growth model and mechanism of a random fiber SMC composite

The primary purpose of this study is to investigate the fatigue crack growth rate and mechanism in a random fiber sheet molding compound (SMC) composite. The fatigue crack growth rate in this study was measured using a compliance approach. The fatigue crack growth rate in the SMC studied here shows a good agreement with a new power law model proposed earlier. This new model takes into account not only the effect of the stress intensity factor range, but also the effect of crack growth at various stages of loading using a weight average stress intensity factor. It was observed that this new model can represent the fatigue crack growth rate of the SMC at three different load ratios in a single unifying curve.     

Characterisation of subcritical crack growth in ceramics using indentation cracks

Abstract

The introduction of indentation cracks into brittle materials has proved to be a useful tool in characterising subcritical crack growth, notably in efficiently measuring the kinetic growth parameters and in defining whether the material exhibits a fatigue threshold. The accuracy of the subcritical crack growth parameters obtained using indentation mechanics can be excellent, provided the stress intensity factor associated with the indentation cracks is well characterised. Indentation cracks can also be used to measure crack velocity as a function of the applied stress intensity factor by direct observation. In such testing, it is critical that the changes in crack shape as the crack extends are known or accurately predicted. Numerical simulations suggest that the shape changes can be influenced not only by the testing geometry but also the growth kinetics. Finally, it is shown that the fatigue threshold can be determined by allowing median cracks to extend subcritically during indentation.     

Factors Affecting Threshold Strength in Laminar Ceramics Containing Thin Compressive Layers

Compressive layers placed within a laminate can arrest cracks. With increasing applied stress, the arrested crack can propagate through the compressive layer. These phenomena produce a material with threshold strength, i.e., failure cannot occur below a critical applied stress. A previously reported stress intensity function describes different variables, e.g., magnitude of compressive stress, thickness of compressive layer, and distance between compressive layers, which govern threshold strength. Laminar composites composed of thicker Al₂O₃ layers separated by thinner Al₂O₃/mullite layers were fabricated to test the different variables that are predicted to govern threshold strength. The data agreed well with the predicted values only when the magnitude of compressive stress and/or the thickness of the compressive layer were low. For these conditions, the crack extended straight through the compressive layers, as assumed by the model used to predict threshold strength. On the other hand, when the compressive stress and/or layer thickness were large, threshold strength was larger than the predicted value. In addition, for these conditions, the crack bifurcated through the compressive layer. The angle between the bifurcated cracks increased with increasing compressive stress.     

Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, K_o, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.