Fracture and Subcritical Crack-Growth Behavior of Y-Si-Al-O-N Glasses and Si3N4 Ceramics

Fracture and environmentally assisted subcritical crack-growth processes are examined in bulk Y-Si-Al-O-N oxynitride glasses with compositions typical of the grain boundary phase of silicon nitride ceramics. Both long-crack (in compact tension specimens) as well as short-crack behavior (using indentation techniques) were investigated to establish a reliable fracture toughness and to elucidate the anomalous densification behavior of the oxynitride glass. Environmentally assisted subcritical crack-growth processes were studied in inert, moist, and wet environments under both cyclic and static loading conditions. Behavior is discussed in terms of the interaction of the environment with the crack tip. Likely mechanisms for environmentally assisted crack growth are discussed and related to the subcritical crack-growth behavior of silicon nitride ceramics.     

Evaluation of Crack Growth in Glass by Using Stress-Wave Fractography

Subcritical crack growth in glass shows three characteristic regions, depending on crack velocity. Among three regions, in region III, where water does not affect crack-growth behavior, the slope of the crack-growth curve can be correlated with the intrinsic nature of glass fracture. In this study, to measure the crack velocity in region III, a periodic stress wave was applied to produce fracture-surface markings in the double-cleavage-drilled compression specimen. The crack-growth data obtained were compared with results obtained via direct observation of the crack front. As a result, this method, by using stress-wave fractography, was found to be effective to obtain the crack-growth curve in region III.     

Fracture Resistance and Stable Crack-Growth Behavior of 8-mol%-Yttria-Stabilized Zirconia

The crack-growth behavior of a yttria-stabilized zirconia ceramic (8 mol% of cubic-phase yttria) was studied at room temperature. Double-cantilever-beam specimens were loaded with pure bending moments in a specially designed loading fixture inside an environmental scanning electron microscope. Crack-growth data were obtained from truly sharp (arrested) cracks, bypassing interpretation problems that involve crack initiation from a machined notch. The crack-growth study was conducted over a range of applied energy-release rates that allowed crack arrest on one hand and fast fracture on the other. Three energy-release-rate values were relevant: initiation of crack growth (3.5 J/m²), crack arrest (2.8 J/m²), and fast fracture (8.0 J/m²). At the macroscopic scale, subcritical crack growth occurred as a continuous process. In situ observations revealed that, at the microscopic scale, crack growth occurred in small jumps. The fracture mode for stable crack growth was identified to be transgranular.     

Cyclic Fatigue-Crack Propagation in Magnesia-Partially-Stabilized Zirconia Ceramics

The subcritical growth of fatigue cracks under (tension-tension) cyclic loading is demonstrated for ceramic materials, based on experiments using compact C(T) specimens of a MgO-partially-stabilized zirconia (PSZ), heat-treated to vary the fracture toughness K _c from ∼3 to 16 MPa·m^1/2 and tested in inert and moist environments. Analogous to behavior in metals, cyclic fatigue-crack rates (over the range 10⁻¹¹ to 10⁻⁵ m/cycle) are found to be a function of the stress-intensity range, environment, fracture toughness, and load ratio, and to show evidence of fatigue crack closure. Unlike toughness behavior, growth rates are not dependent on through0-thickness constraint. Under variable-amplitude cyclic loading, crack-growth rates show transient accelerations following low-high block overloads and transient retardations following high-low block overloads or single tensile overloads, again analogous to behavior commonly observed in ductile metals. Cyclic crack-growth rates are observed at stress intensities as low as 50% of K _c , and are typically some 7 orders of magnitude faster than corresponding stress-corrosion crack-growth rates under sustained-loading conditions. Possible mechanisms for cyclic crack advance in ceramic materials are examined, and the practical implications of such "ceramic fatigue" are briefly discussed.     

Fracture Behavior of Low-Density Fibrous Ceramics

It was established that subcritical crack growth occurs in the silica fiber-based tiles that are currently in use as part of the thermal protection system (TPS) of the Space Shuttle. By measuring the tensile strength distribution and the subcritical crack-growth parameters, it was possible to predict the material's behavior during proof-testing. A similar time dependence of dynamic strength was also found for structural systems using this ceramic tile, suggesting that the ceramic is controlling their strength behavior. It was possible, therefore, to predict the influence of the proof testing currently in use for the Shuttle. These predictions were found to be in reasonable agreement with the experimentally determined strength distributions after proof-testing. This study confirmed that proof-testing and tile densification should lead to improved reliability of the TPS. The research further suggests that the subcritical crack-growth behavior in these fibrous tiles is simiilar to that observed in bulk glass of similar composition and that failure occurs by the tensile fracture and fragmentation of individual fibers.     

Crack-Growth Resistance-Curve Behavior in Silicon Carbide: Small versus Long Cracks

Crack-growth resistance-curve (R-curve) behavior for small (<400 μm) surface cracks and long (>3 mm) through-thickness cracks is examined in two silicon carbide (SiC) ceramics that have sharply contrasting fracture properties. The first, an in-situ toughened material designated ABC-SiC, fails by intergranular fracture, whereas the second, a commercial SiC (Hexoloy SA), fails by transgranular cleavage. In the former microstructure, hot pressing with aluminum, boron, and carbon additives yields a network of plate-shaped grains, and the presence of an amorphous grain-boundary film that is ∼1 nm thick promotes debonding and crack deflection. The resultant grain bridging generates R-curve toughening; in contrast, no evidence of crack-tip shielding is observed in Hexoloy SA. R-curve behavior has been evaluated using two techniques for the different crack-length regimes: a small-crack R-curve has been deconvoluted from indentation-strength data and a long-crack R-curve has been directly measured using fatigue-precracked, disk-shaped compact-tension specimens. Although Hexoloy SA fails catastrophically at <3 MPa.m1/2, ABC-SiC exhibits much-improved flaw tolerance with significant rising R-curve behavior and a steady-state fracture toughness of ∼9 MPa.m1/2 after crack extension of ∼600 μm. In ABC-SiC, however, differences in the behavior of long and small cracks exist for crack sizes of less than ∼120 μm, with the small-crack measurements demonstrating much-reduced crack-growth resistance; this effect is not observed in Hexoloy SA. Microstructural sources of this behavior are discussed.     

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.     

Method of Studying Subcritical Cracking of Opaque Materials

Since subcritical cracking often precedes catastrophic failure, it is an important engineering consideration, especially if a structure is to be under stress for a long time. A specimen has been developed for laboratory study of subcritical cracking, but it is assumed that crack growth can be observed visually through the specimen. With opaque materials, such observation is generally impractical or impossible. A compliance method of obtaining crack-growth data is proposed. Experimental examples using polymethyl methacrylate, soda-lime glass, and an opaque glass-ceramic show that the method works very well. The usefulness of the method is illustrated for 3 commercial ceramics. It is shown that subcritical cracking occurs over a range of fracture energies for each of these materials.     

Fracture Resistance Measurement Method for in situ Observation of Crack Mechanisms

A special test fixture has been developed for fracture mechanical testing of brittle materials inside an environmental scanning electron microscope. The fixture loads a double cantilever beam specimen with pure bending moments and provides stable crack growth. Crack growth is detected by in situ observation and acoustic emission. As an example, crack growth in a cubic-phase yttria-stabilized zirconia is detected easily by in situ observation of the crack-tip region. Many fracture toughness measurements are obtained for each specimen, giving high confidence in the measured fracture toughness value. In situ observation is useful for the study of toughening mechanisms and subcritical crack-growth behavior and to sort out erroneous measurements (e.g., due to crack branching).     

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.     

Cyclic Fatigue Crack Propagation in Alumina under Direct Tension—Compression Loading

Cyclically induced crack propagation occurs in alumina subjected to direct tension—compression loading. The crack increment per cycle (da/dN) has a power-law dependence on the peak stress intensity factor (K_max). Cyclic crack growth can occur at lower values of K_max than are required to produce static fatigue effects. Subcritical crack-growth behavior was found to be dependent on specimen geometry: it is suggested that direct compressive loads and crack length are both factors that affect cyclic fatigue behavior, and that the use of K alone to characterize fatigue crack growth in ceramics may be questionable.     

R-Curve Behavior of a Polycrystalline Graphite: Microcracking and Grain Bridging in the Wake Region

The contributions of nonlinear fracture processes both in the microcracking frontal process zone and in the following wake region and of grain bridging to crack-growth resistance parameters are discussed in terms of the R-curve behavior of an isotropic polycrystalline graphite. The R-curve behavior of the graphite is characterized by rapidly increasing values at the initial stage of crack extension (Δa≤1 to 2 mm) followed by a steady-state plateaulike region and then a distinct decrease when the primary crack tip approaches the end surface of the test specimen. Scanning electron microscopy of fracture mechanics specimens revealed a dominant role of grain bridging in the following wake regions on the rising R-curve behavior and confirmed the significant size effect of the large-scale microcracking process zone on the falling R-curve behavior. The stress-derived fracture toughness (K_R) and the energy fracture toughness (R_c) are discussed in relation to the micro-cracking residual strain.     

Crack-growth behavior of epoxy adhesives modified with liquid rubber and cross-linked rubber particles under mode I loading

The crack-growth resistance (R-curve) of bulk single-edge notch bend (SENB) and adhesively bonded double cantilever beam (DCB) specimens was investigated under mode I loading conditions using two types of rubber-modified epoxy adhesive: one was a liquid rubber (CTBN)-modified adhesive and the other was a cross-linked rubber particle (DCS)-modified adhesive. As a result, for both the SENB and DCB specimens, the gradient of the R-curve for the DCS-modified adhesive was steeper than that for the CTBN-modified one, however, the difference in fracture toughness between DCS- and CTBN-modified adhesives is smaller for DCB than for SENB specimens. To elucidate such behavior, crack-growth simulation based on Gurson's model was conducted, where the DCS- and CTBN-modified adhesives were characterized by both the initial void fraction and nucleation. The difference in the behavior of R-curves was also observed in simulations. Moreover, it was found that the difference in fracture surface roughness observed by SEM for both adhesives correspond to the variation in R-curves.     

R Curves and Crack-Stability Map: Application to Ce-TZP/Al2O3

The concept of a crack-stability map is developed by considering the interaction between the crack-driving force and the rising crack-growth resistance of a toughened ceramic. The map plots normalized transition crack length as function of the ratio of the crack-initiation fracture toughness and the plateau toughness to delineate regimes of stable and unstable crack growth. The plot is used to analyze R curves and fracture stresses of a transformation-toughened Ce-TZP/Al₂O₃. It is shown that the fracture stress and the small scatter measured for this ceramic are consistent with its R- curve behavior, which enables stable growth of surface cracks from flaws (pores and second-phase particles), leading to a flaw-insensitive ceramic.     

Combined Mode I and Mode II Fracture of Monolithic Ceramics

The mode I, mode II, and combined mode I–mode II fracture behaviors of a coarse-grained silicon nitride, a fine-grained silicon nitride, and an alumina were investigated. These ceramics were fractured from two types of fracture initiating flaws: small surface flaws and large single edge precracks. The small surface flaws were introduced by Knoop indentation in flexural samples at various angles to the tensile stress direction and fractured in four-point bending. The samples with large precracks were fractured in the asymmetric four-point-bend geometry. The mixed-mode fracture toughness values obtained from the two flaw configurations were in good agreement with each other. All three ceramics displayed very similar mixed-mode fracture behavior, although their microstructures were not similar. Comparison of experimental data to mixed-mode fracture theories revealed that the minimum strain energy density theory best described the mixed-mode fracture behavior of all three ceramics.     

Effects of Damage on Thermal Shock Strength Behavior of Ceramics

When subjected to severe thermal shock, ceramics suffer strength degradation due to the damage caused by the shock. A fracture-damage analysis is presented to study the effects of damage on the thermal shock behavior of ceramics. It is assumed that a narrow strip damage zone is developed at the tip of a preexisting crack after a critical thermal shock and the damage behavior can be described by a linear strain-softening constitutive relation. Damage growth and strength degradation are determined based on fracture and damage mechanics. Numerical calculations are carried out for two ceramic materials, and the strength degradation agrees quite well with experimental results. The effects of bridging/damage stress, the fracture energy of the bridging/damage zone, and specimen size on thermal shock strength behavior are studied. A higher fracture energy can enhance the residual strength of thermally shocked ceramics and, for a given fracture energy, a higher bridging stress is needed to reduce the strength degradation. It is also shown that the thermal shock strength behavior is size-dependent, and a high value of ( K _IC/O_b)², where K _IC is the intrinsic fracture toughness and O_b is the bending strength, can improve significantly the residual strength.     

Effect of Step Size in Incremental Loading Tests

Using the crack-growth model, the deviation of real fracture stress from the stressing level measured by stepwise incremental loading with three starting modes is calculated. For both static and dynamic fatigue, the relative error depends only on the relative increment size and the crack-growth parameter, n. The usefulness of stepwise incremental loading for strength testing can be confirmed.     

Effect of Grain Size and Poling on the Fracture Mode of Lead Zirconate Titanate Ceramics

The fracture mode of lead zirconate titanate (PZT) ceramics at room temperature is investigated as a function of grain size. The fracture mode is almost intergranular at small grain size and changes to predominantly transgranular at large grain size. Application of an electric field (poling) causes a change in the fracture mode from transgranular to intergranular. The observed fracture behavior of PZT ceramics is explained in relation to a possible domain structure.     

分形理论在陶瓷材料研究中的应用

介绍了分形理论的产生、分形维数的定义和几种常见的计算方法,主要包括：盒维数法、Hausdorff维数法和长度—面积关系公式法。并概述了分形理论在陶瓷材料研究中微观结构、晶体生长动力学和断裂行为等方面的应用情况。其中重点介绍了分形在陶瓷材料断裂行为研究中的国内外现状。     

Classification of ceramics and glass (edge chipping and fracture toughness)

The standard classification of advanced ceramics is based on their strength, although in many cases the performance of products made of such materials is controlled by their deformation behavior and fracture resistance. In this article, ceramics and glass are classified according to their edge chipping resistance (EF-method). Such a classification is based on the idea of a baseline (direct proportionality between edge chipping resistance and fracture toughness of ceramics that are similar to the model material of linear elastic fracture mechanics). Use was made of various elastic and inelastic, oxide and non-oxide ordinary ceramics, composite ceramics capable and incapable of retarding cracks and intended for engineering and biomedical applications. Attention is also given to silicate glass.