Subcritical Crack Growth of Macrocracks in Alumina with R-Curve Behavior

Subcritical crack growth of macroscopic cracks in two Al₂O₃ ceramics is investigated with single-edge-notched bending specimens under constant load. The resulting v - K _I-curves are in complete contrast to the behavior of natural cracks. In spite of the monotonic increase of the externally applied stress intensity factor due to crack extension, the crack growth rates first decrease. This behavior is caused by crack shielding due to crack border interaction and can be described by a rising crack growth resistance. Two methods are applied to determine the R -curve under subcritical crack growth conditions.     

Statistical Analysis of the Fatigue Life Distribution of Monolithic Silicon Nitride

Cyclic fatigue testing of silicon nitride ceramics was performed at a frequency of f = 150 Hz and a stress ratio of R = 0.1 using a piezoelectric bimorph fatigue device. Based on the method proposed by Fett and Munz, a fatigue crack growth diagram ( K ₁– V diagram) was estimated from fatigue lifetime distribution data. A change in the slope of the K _I– V diagram was observed. A statistical analysis for predicting the lifetime of ceramics exhibiting a transition in a K _I– V diagram was devised on the basis of this observation. Analytical results obtained with this method showed good agreement with experimental data.     

Direct Measurement of Crack Tip Stresses

Raman microprobe spectroscopy was used to measure the crack tip stress distribution in single-crystalline silicon using a wedge-loaded double cantilever beam (dcb) specimen. The wedge was advanced until the crack just propagated. After the crack arrested, the stresses were measured between 3 and 20 μm directly ahead of the crack. An average value of –0.43 was obtained for the slope of log stress vs log distance from the crack tip, rather than the theoretical value of –0.5. The value of K _I was determined from (1) the intercept of this curve and (2) the slope of stress against     . The values were in good agreement. The average experimental value of K _I was determined to be 0.71 MPa · m^1/2, compared to literature values for the K _IC ranging from silicon of 0.8 to 0.94 MPa · m^1/2. The value measured with the Raman is the arrest value of K _I and is expected to be lower from kinetic energy considerations associated with wedge-loaded dcb specimens.     

Cyclic Fatigue Crack Propagation Behavior of 9Ce-TZP Ceramics with Different Grain Size

Cyclic fatigue crack growth behavior has been investigated in 9 mol% Ce-TZP ceramics with grain sizes varying from 1.1 to 3.0 μm. To ascertain the interaction between crack resistance curve behavior and cyclic fatigue crack growth, cyclic fatigue tests were conducted with short double-cantilever-beam specimens in two conditions: (a) with a sharp precrack without preexisting t - m transformation and (b) with a sharp crack after R -curve measurements, i.e., with preformed t - m transformation in the crack region. Fatigue crack propagation occurs at applied stress intensity factor values as low as about 40% of the K _I,∞ values measured in the R -curves. The size and shape of the t - m transformation zones are found to be different for specimens obtained in monotonic loading R -curve measurements and in cyclic fatigue tests. For the specimens without preexisting t - m transformation the overall crack growth behavior can be described by the Paris power law relation: d a /d N = AδK^m _I with m values of 15 for the 1.1-μm grain size and between 8 and 9 for the material with larger grain sizes. For the specimens with the preformed transformation zone, a "V"shape d a /d N versus Δ K _I relation is obtained. Explanations for these different results in the two conditions are discussed in terms of crack tip shielding effects.     

Estimation of Crack Closure Stresses for In Situ Toughened Silicon Nitride with 8 wt% Scandia

An 8-wt%-scandia silicon nitride with an elongated grain structure was fabricated. The material exhibited high fracture toughness (∼ 7 MPa · m^1/2) and a rising R -curve as measured by the indentation strength technique. The "toughening" exponent m was found to be m ∼ 0.1. The high fracture toughness and R -curve behavior was attributed mainly to bridging of the crack faces by the elongated grains. The crack closure (bridging) stress distribution in the wake region of the crack tip was estimated as afunction of crack size from the R -curve data, with an arbitrarily assumed distribution function.     

Flaw-Tolerance and R-Curve Behavior of Liquid-Phase-Sintered Silicon Carbides with Different Microstructures

β-SiC powder containing 6 wt% A1₂O₃ and 4 wt% Y₂O₃ as sintering additives was pressureless sintered at 2000°C for 1 h (AYE-SiC) and 3 h (AYP-SiC). AYE-SiC consisted of an equiaxed grain structure and AYP-SiC exhibited a micro-structure with platelike grains as a result of grain growth related to β→α phase transformation during sintering, R -curve behavior and flaw tolerance for these silicon carbides were evaluated by the indentation-strength technique. For comparison, the R -curve behavior of conventional sintered, boron- and carbon-doped SiC (SS-SiC) was evaluated. AYE-SiC and AYP-SiC exhibited rising R -curve behavior with toughening exponents of m = 0.042 and m = 0.135, respectively. AYP-SiC exhibited better flaw tolerance and more sharply rising R -curve behavior than AYE-SiC. The more sharply rising R -curve behavior and the better flaw tolerance of AYP-SiC were attributed mainly to grain bridging of crack faces by platelike grains. Because of the high degree of transgranular fracture, SS-SiC exhibited a flat R -curve despite a microstructural feature with platelike grains.     

Determination of Fracture Toughness at High Temperatures after Subcritical Crack Extension

As a consequence of R -curve behavior, ceramic materials may exhibit increased fracture toughness ( K _Ic) following slow crack extention. In this investigation, the effect of crack propagation on fracture toughness is studied in static bending tests. For the calculation of stress intensity factors ( K _I) the stress distribution must be known at the moment of fracture. As a consequence of creep, this stress distribution must deviate from the linear distribution. The corresponding stress intensity factors are computed using the fracture mechanical weight function. Experimental results for fracture toughness are communicated for a 2.5%-MgO-doped hot-pressed Si₃N₄ at 1300°.     

Microstructural Design of Silicon Nitride with Improved Fracture Toughness: I, Effects of Grain Shape and Size

The use of self-reinforcement by larger elongated grains in silicon nitride ceramics requires judicious control of the microstructure to achieve high steady-state toughness and high fracture strength. With a distinct bimodal distribution of grain diameters, such as that achieved by the addition of 2% rodlike seeds, the fracture resistance rapidly rises with crack extension to steady-state values of up to 10 MPam^1/2 and is accompanied by fracture strengths in excess of 1 GPa. When the generation of elongated reinforcing grains is not regulated, a broad grain diameter distribution is typically generated. While some toughening is achieved, both the plateau (steady-state) toughness and the R -curve response suffer, and the fracture strength undergoes a substantial reduction. Unreinforced equiaxed silicon nitride exhibits the least R -curve response with a steady-state toughness of only 3.5 MPam^1/2 coupled with a reduced fracture strength.     

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.     

Subcritical Crack Growth in Soda-Lime Glass under Combined Modes I and III Loading

Fracture and subcritical crack-growth characteristics under combined Modes I and III loading were studied using the modified compact tension (CT) specimens of soda-lime glass. The combined mode load was applied to the specimen in the direction β with respect to the initial crack. By superposition of Mode III, the advancing crack begins to rotate at an angle Ψ to the initial crack plane, which nearly maximizes the Mode I stress intensity factor K _I(Ψ), and the crack continues to propagate in the same direction. In this case, unlike combined Modes I and II, the crack breaks into multiple partial fronts, and ligamentary bridging forms fracture lances when these segmented cracks are held together. The crack velocity d a /d t was plotted versus the maximum Mode I stress intensity factor K _I(Ψ) for combined Modes I and III loading. The d a /d t values are initially high, and the crack growth tends to be discontinuous compared with the result for pure Mode I. The subcritical crack growth seems to occur when the K _I value for the initial crack reaches a certain value. The d a /d t - K _I(Ψ) curves for combined Modes I and III lie roughly on the same curve as that for pure Mode I as the crack growth increases.     

Rising Crack-Growth-Resistance (R-Curve) Behavior of Toughened Alumina and Silicon Nitride

R -curves for a sinter/HIPed SiC(whisker)-reinforced alumina and a sintered silicon nitride were assessed by direct measurements of lengths of cracks associated with Vickers indentation flaws. The fracture toughness measurements based on (a) initial (as-indented) crack lengths, (b) equilibrium growth of cracks during increasing far-field loading, and (c) crack lengths corresponding to unstable fracture showed definitive trends of R -curves for both materials. The fracture mechanics analyses employed an indenter-material constant that was independently estimated using a physical model for the residual driving force and a free surface correction factor that accounted for the effects of size and shape of the cracks on stress intensity. It is shown that R -curve estimations based on crack length measurements have the intrinsic advantage that crack length dependence of fracture toughness is not assumed a priori as is done in conventional analysis based on strength. The measured fracture toughness of SiC(whisker)-reinforced alumina was in agreement with the prediction of a toughening model based on crack bridging by partially debonded whiskers.     

Crack-Growth Resistance of in Situ-Toughened Silicon Nitride

The fracture toughness of a commercial, hot-pressed, in situ -toughened silicon nitride with an elongated grain structure is determined by four different testing methods. The fracture toughness is found to be 5.76 ± 0.27, 8.48 ± 0.50, 10.16 ± 0.66, and 10.68 ± 0.39 Mpa.m^1/2, respectively, by indentation crack size measurement, indentation strength, single-edge-precracked-beam, and chevron-notched-beam methods. The discrepancy in fracture toughness between the testing methods is related to R -curve behavior, as measured using the indentation strength technique. These results indicate that there is no unique fracture toughness value and that a fracture toughness testing method with appropriate qualifiers is needed for rising R -curve materials. Therefore, care should be taken in interpreting and utilizing fracture toughness values evaluated from different testing methods if a material exhibits a rising R -curve. Complete characterization of the R -curve may be a prerequisite.     

Anisotropic Fracture Behavior in Ferroelectric Relaxor PZN–4.5%PT Single Crystals

The anisotropic fracture behavior in unpoled and poled (1− x )Pb(Zn_2/3Nb_1/3)− x PbTiO₃ ( x =0.045) (PZN–4.5%PT) single-crystal relaxor ferroelectrics cut along the crystal planes, [010] and [001], was characterized. The crack tip toughness ( K _tip) determined from Vickers indentations was compared with the R -curve behavior measured using the single-edge V-notch beam (SEVNB) method. Several of the SEVNB fracture experiments resulted in cracks forming and propagating under mixed mode loading ( K _I and K _II) along the [110] crystal plane. Other specimens formed cracks at 0° along the [010] plane. To assess the anisotropic fracture behavior, the local and global critical energy release rates were determined using Stroh's formalism.     

R-Curve Behavior and Strength for In-Situ Reinforced Silicon Nitrides with Different Microstructures

R -curves for two in-situ reinforced silicon nitrides A and B of nominally the same composition are characterized using the Griffith equation and indentation fracture mechanics. These R -curves are calibrated against fine-grained silicon nitrides which have a known chevron-notch (long-crack) toughness and with a nearly flat R -curve behavior. Silicon nitride A, with its coarser microstructure and higher chevron-notch toughness, shows lower resitance to crack growth than silicon nitride B if the crack size is less than ∼200 μm. These results are consistent with the indentation–Strength measurements which show a crossover of strength between the two materials at an indentation load between 49 and 98 N, and below the crossover A has a lower strength. The toughening behavior is explained using an elastic-bridging model for the short crack, and a pullout model for the long crack. The effects of R -curve properties on design are discussed.     

Crack-Tip Toughness Measurements on a Sintered Reaction-Bonded Si3N4

An evaluation of measurements of crack opening displacements (CODs) on a commercial sintered reaction-bonded silicon nitride (SRBSN) was performed. To determine the intrinsic fracture toughness of this material, a new evaluation method is presented, which takes into account not only the near tip CODs, but the CODs of the complete crack profile. The method is applied on through-thickness cracks in bend bars and contrasted to CODs of Vickers radial cracks. A crack-tip toughness of ∼1.7 MPa·m^1/2 is obtained.     

R-Curve Behavior and Flaw Insensitivity of Ce-TZP/Al2O3 Composite

A ceria-partially-stabilized zirconia-aiumina (Ce-TZP/Al₂O₃) composite optimized for transformation toughening was used to demonstrate its flaw insensitivity due to R -curve behavior. Four-point bend specimens fabricated with a controlled distribution of spherical pores showed nearly the same characteristic strength and strength variability (Weibull modulus) as specimens fabricated without the artificial pores. In situ observations confirmed stable growth of cracks initiated at pores and the crack lengths at fracture instability were much greater than the pore sizes, thus resulting in fracture strengths insensitive to the pores. The small variability in the fracture strength was found to be associated with variability in the R -curve and the instability crack lengths. An analysis based on the fracture instability criterion for rising crack growth resistance accounted for the strength variability due to variability in the R -curve. Comparable four-point bend experiments were also conducted on a sintered yttria-partially-stabilized zirconia (2Y-TZP) ceramic. This ceramic showed significant degradation of strength due to the presence of the pores. This flaw sensitivity is attributed to its steep rising R -curve over short crack lengths.     

R-Curve for a Lead Zirconate Titanate Ceramic Obtained from Tensile Strength Tests with Knoop-Damaged Specimens

A procedure was used that made it possible to determine the R -curve for piezoelectric ceramics from tensile strength tests conducted with Knoop-damaged specimens. The resulting crack-tip toughness K _I0 was 0.6 MPa·m^1/2, and the R -curve starting from this value increased to 1.4 MPa·m^1/2 within a 0.7 mm crack extension.     

VAMAS Round Robin on Fracture Toughness of Silicon Nitride

Eight laboratories in Germany, Japan, U.K., and U.S. participated in the VAMAS round robin. The fracture toughness of silicon nitride at room temperature and at 1200^deg;C was measured by three methods: the single-edge V-notched beam (SEVNB), single-edge precracked beam (SEPB), and chevron notched beam (CNB). The obtained values show hardly any crosshead speed dependence, irrespective of test temperature and atmosphere. Results may have been influenced by a small amount of slow crack growth, but distinct R -curve behavior could not be detected within the scope of the tests. The values at 1200^deg;C in N₂ can be measured by the SEVNB and SEPB methods with small scatters. The oxidation of silicon nitride, caused by heating in air, increases the SEVNB and SEPB values. The CNB values are free from the effects of test temperature and atmosphere, but they show a large scatter between laboratories. However, the chevron V-notched beam (CVNB) method, which is an improved CNB method, shows values with a small scatter, irrespective of the measurement conditions. The SEVNB and SEPB measurements in N₂ and the CVNB measurement under any conditions are recommended for the measurement of high-temperature fracture toughness.     

A Compression-Loaded Double Cantilever Beam Specimen

In crack propagation studies, double cantilever beam specimens are typically loaded in tension or by an applied moment. A method of compression loading is described in which the stress intensity K _I decreases with crack length. This new arrangement offers added crack stability over other techniques, as well as a convenient method of loading.     

Double Cantilever Beam Measurements of Crack Growth in Indium(III) Phosphide

Crack growth measurements in InP crystals were conducted using an applied-moment, double cantilever beam (DCB) geometry. Controlled, smooth crack growth was observed in water; however, the crack growth velocities were not constant for constant applied stress intensity ( K _I). More importantly, there was no clear functional dependence of the crack growth rate (ν) on K _I.