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.     

Slow Crack Growth Behavior in Transformation-Toughened Al2O3-ZrO2(Y2O3) Ceramics

Significant increases in the critical fracture toughness (K _IC ) over that of alumina are obtained by the stress-induced phase transformation in partially stabilized ZrO₂ particles which are dispersed in alumina. More importantly, improved slow crack growth resistance is observed in the alumina ceramics containing partially stabilized ZrO₂ particles when the stress-induced phase transformation occurs. Thus, increasing the contribution of the ZrO₂ phase transformation by tailoring the Y₂O₃ stabilizer content not only increases the critical fracture toughness (K_IC) but also the K _Ia to initiate slow crack growth. For example, crack velocities ( v )≥10^–9 m/s are obtained only at K _Ia≥5 MPa.m^1/2 in transformation-toughened ( K _IC=8.5 MPa.m^1/2) composites vs K _Ia≥2.7 MPa.m^1/2 for comparable velocities in composites where the transformation does not occur ( K _IC=4.5 MPa.m^1/2). This behavior is a result of crack-tip shielding by the dissipation of strain energy in the transformation zone surrounding the crack. The stress corrosion parameter n is lower and A greater in these fine-grained composite materials than in fine-grained aluminas. This is a result of the residual tensile stresses associated with larger (≥1 μm) monoclinic ZrO₂ particles which reside along the intergranular crack path.     

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.     

Toughening Behavior of a Two-Dimensional SiC/SiC Woven Composite at Ambient Temperature: I, Damage Initiation and R-Curve Behavior

The damage initiation and R -curve behavior for a two-dimensional (2-D) SiC/SiC woven composite are characterized at ambient temperature and related to in situ microscopic observations of damage accumulation and crack advance. Matrix cracking and crack deflection/branching are observed and dominate fracture behavior in the early loading stage such that primary crack extension occurs at apparent stress intensity values as high as 12 MPam^1/2. Linear elastic fracture mechanics (LEFM), though questionable, was assumed to be valid in the early stages of damage initiation prior to primary crack advance, but was clearly invalid once primary crack extension had occurred. Such a high primary crack extension toughness value is confirmed by a renotch technique whereby the crack wake is removed and the fracture resistance drops close to the initial value. Based on microstructural observations, multiple matrix cracks are found to be arrested at fiber bundles. The key to toughening appears to be associated with the mechanics of crack arrest at fiber bundles in the woven architecture. Toughening mechanisms include multiple matrix cracking (similar to microcracking), crack branching, and crack deflection in the crack frontal zone. Application of models to evaluate toughening based on these mechanisms results in values comparable to experimental data. In the regime of primary crack extension, a J -integral technique was applied to investigate the R -curve behavior and results showed a rising J_R -curve which started at 1500 J/m² and reached 6150 J/m² after about 13 mm of primary crack extension. There was evidence of substantial crack bridging by fiber tows and fibrous pull-out in this regime of crack advance.     

Indentation Fracture Response and Damage Resistance of Al2O3-ZrO2 Composites Strengthened by Transformation-Induced Residual Stresses

Indentation fracture behavior of three-layer Al₂O₃-ZrO₂ composites with substantial compressive residual stresses was compared with the behaviors of monolithic Al₂O₃ and Al₂O₃-ZrO₂ ceramics without intentionally introduced residual stresses. The indentation cracks were smaller in the three-layer specimens relative to the monolithic specimens in agreement with the predictions of indentation fracture mechanics theory. Indentation and strength testing were used to show that a residual compressive stress of approximately 500 MPa exists in the outer layers of the three-layer composites. The three-layer specimens showed excellent damage resistance in that the strength differential between the three-layer and monolithic indented specimens was maintained at indentation loads up to 1000 N, the maximum indentation load used in the experiments.     

Controlled Surface Flaws in Hot-Pressed Si3N4

Surface flaws of controlled size and shape were produced in high-strength hot-pressed Si₃N₄ with a Knoop microhardness indenter. Fracture was initiated at a single suitably oriented flaw on the tensile surface of a 4-point-bend specimen, with attendant reduction in the measured magnitude and scatter of the fracture strength. The stress required to propagate the controlled flaw was used to calculate the critical stress-intensity factor, K _IC, from standard fracture-mechanics formulas for semielliptical surface flaws in bending. After the bend specimen had been annealed, the room-temperature K _IC values for HS-130 Si₃N₄ increased to a level consistent with values obtained from conventional fracture-mechanics tests. It was postulated that annealing reduces the residual stresses produced by the microhardness indentation. The presence of residual stresses may account for the low K _IC, values. Elevated-temperature K_IC values for HS-130 Si₃N₄ were consistent with double-torsion data. Controlled flaws in HS-130 Si₃N₄ exhibited slow crack growth at high temperatures.     

Impact Damage and Strength Degradation in a Silicon Carbide Reinforced Silicon Nitride Composite

Adding SiC particles to Si₃N₄ and subjecting the mixture to a sinter-hot-isostatic-pressing process increases both the strength and elastic modulus. It also decreases the hardness but maintains the fracture toughness, which results in a higher resistance to crack initiation and propagation during spherical particle impact. Sinter-hot-isostatically-pressed composites exhibit elastic response as their dominant behavior. They also display a high resistance to Hertzian cone crack initiation and extension. This is due to the increased degree of inelastic deformation of sinter-hot-isostatically-pressed composites.     

In Situ Measurement of Bridging Stresses in Toughened Silicon Nitride Using Raman Microprobe Spectroscopy

Bridging stresses that result both from elastic tractions and frictional interlocking in the wake of an advancing crack have been evaluated quantitatively via in situ Raman microprobe spectroscopy in a toughened Si₃N₄ polycrystal. Crack opening displacement (COD) profiles of bridged cracks also have been measured quantitatively via scanning electron microscopy to substantiate the piezospectroscopic determination of microscopic stresses via Raman spectroscopy. The highest spatial resolution of the stress measurement in the Raman apparatus was 1 µm, as dictated by the optical lens that was used to focus the laser on the sample. Measurements of the bridging stresses were performed both at fixed sites (as a function of the applied load) and along the profile behind the crack tip (under a constant load). Rather high stress values (i.e., 0.4-1.1 GPa) were measured that corresponded with unbroken ligaments that bridged the crack faces in elastic fashion, whereas frictional sites were typically under a lower tensile stress (0.1-0.5 GPa). Mapping the near-tip COD profile and the bridging stresses at the (normal) critical load for catastrophic fracture enabled us to calculate the crack-tip toughness and to explain the rising R -curve behavior of the material. From a comparison with conventional fracture-mechanics data, a self-consistent view of the mechanics that govern the toughening behavior of the Si₃N₄ polycrystal could be obtained. In particular, crack bridging is proven to be, by far, the most important mechanism that contributes to the toughening of polycrystalline Si₃N₄ materials.     

J-Integral Measurements of the Fracture of 50% Alumina Refractories

The J -integral experimental technique was used to study fracture initiation in burned refractory bricks and refractory casta-bles of the 50% alumina variety. In a comparison of J _Ic and G_Ic, and 2 y_wof it is consistently observed that G _Ic Ic<2ry _Wof. The quantities ( J _Ic -G _Ic) or ( J _IC/ G _IC), as well as ( 2y _wof/ G _Ic), can be applied to estimate the inelastic energy contribution to the crack-tip process zone of these refractories. The latter two parameters distinctly classify the burned bricks and the casta-bles into different fracture characteristics. As such, these parameters are potentially very useful in the microstruetural design of refractories.     

Effect of Micmcracking on the Fracture Toughness and Fracture Surface Fractal Dimension of Lithia-Based Glass-Ceramics

The effect of thermally induced microcracks on the fracture toughness and fractal dimension of fully crystalline lithia disilicate glass-ceramics was studied. The fracture toughness, K _IC, for the nonmicrocracked lithia disilicate, 3.02 ± 0.12 MPa·m^1/2, was significantly greater than the value of 1.31 ± 0.05 MPa·m^1/2 for the microcracked specimens. The fractal dimensional increment, D *, was 0.24 ± 0.01 for nonmicrocracked lithia disilicate specimens compared with a value of 0.18 ± 0.01 for the microcracked specimens. The relationship between K _IC and D * implies that the two materials exhibit dissimilar fracture behavior because of microstructural differences. Estimates of the characteristic length involved in the fracture process, a ₀, indicate that the materials have an identical fracture process at the atomic level. This apparent contradiction may be explained by the scale on which the measurements were taken. It is suggested that fractal analysis at the atomic level would yield equivalent D * values for the two different microstructures.     

Mode I Fracture Toughness of a Small-Grained Silicon Nitride: Orientation, Temperature, and Crack Length Effects

The Mode I fracture toughness ( K _{I C} ) of a small-grained Si₃N₄ was determined as a function of hot-pressing orientation, temperature, testing atmosphere, and crack length using the single-edge precracked beam method. The diameter of the Si₃N₄ grains was <0.4 µm, with aspect ratios of 2–8. K _{I C} at 25°C was 6.6 ± 0.2 and 5.9 ± 0.1 MPa·m^1/2 for the T–S and T–L orientations, respectively. This difference was attributed to the amount of elongated grains in the plane of crack growth. For both orientations, a continual decrease in K _IC was observed through 1200°C, to ∼4.1 MPa·m^1/2, before increasing rapidly to 7.5–8 MPa·m^1/2 at 1300°C. The decrease in K _IC through 1200°C was a result of grain-boundary glassy phase softening. At 1300°C, reorientation of elongated grains in the direction of the applied load was suggested to explain the large increase in K _IC. Crack healing was observed in specimens annealed in air. No R -curve behavior was observed for crack lengths as short as 300 µm at either 25° or 1000°C.     

Elevated-Temperature R-Curve Behavior of a Polycrystalline Alumina

The fracture behavior of a polycrystalline alumina was examined at temperatures ranging from ambient through 1400°C, using three-point bend bar test specimens. R -curves were determined at all temperatures studied, and when accompanied by renotching procedures, a wake removal technique, conclusive evidence was provided to support the existence of a following wake region in this monolithic ceramic material. The crack closure stresses identified in this region are responsible for all toughening with crack extension observed in this study. Room-temperature " K _IC" fracture toughness values of 4.5 MPa · m^1/2 for the chevron-notch specimen and 3.9 MPa · m^1/2 for the straight-notch configuration were obtained. The critical stress intensity factor of the renotched chevron-notch specimen compared very closely with that of the straight-notch specimen. These findings further confirm the toughening role of the microstructural features found in the following wake region. This paper considers, in detail, these observations in terms of the microstructure and its role in the toughening mechanism.     

Crack Resistance and Fatigue of Transforming Ceramics: I, Materials in the ZrO2–Y2O3–Al2O3 System

Crack resistance characteristics and fatigue properties have been studied in four types of Y₂O₃–TZP ceramics including one containing Al₂O₃. The largely linear-elastic behavior connected with the very small transformation zone (<5 μm) explains the absence of any resistance-curve behavior and the flaw-controlled strength. The crack resistance shows high sensitivity to environment-induced subcritical crack growth. This influence is also operative in both types of fatigue experiments, i.e., under static and cyclic stresses, leading to reduced fatigue thresholds compared with K _IC. While for static conditions a benefit is observed from enhanced t-m ZrO₂ transformation, cyclic stresses provoke an additional fatigue effect. However, if the cyclic stresses are restricted to subthreshold values, cyclic stress-induced effects in the process zone provide an improvement of the materials being visible as a strengthening effect.     

Application of the J-integral concept for the description of toughness properties of fiber reinforced polyethylene composites

For the determination of toughness properties of HDPE/glass fiber and HDPE/cotton fiber composites, an instrumented Charpy impact test has been used. The interpretation of impact load-deflection curves has been carried out with several concepts of fracture mechanics. Here the limits of linear elastic fracture mechanic (LEFM) have been shown. The change of toughness properties with increasing fiber volume can be described for short fiber reinforced composites with the help of the J-integral concept in a suitable mode. An application of the conventional Charpy impact test will result in an overestimation of material behavior because of the energy of crack propagation. With the help of a micromechanical model to describe failure processes, taking account of energy dissipative processes, it is possible to calculate fracture mechanical material parameters. Because of the peculiarities of deformation and fracture behavior, the application of elastic-plastic fracture mechanic (EPFM)-concepts for fiber reinforced polymers is required.     

Mixed-Mode Fracture of Ceramics in Diametral Compression

Mixed-mode fracture of a glass-ceramic and an alumina ceramic from inclined Knoop indenter flaws was studied in diametral compression and four-point-bend tests. In annealed specimens the directions of extension of the cracks and mode I and mode II stress-intensity factors at fracture were analyzed and compared to the predictions of a maximum crack-tip hoop stress theory. Knoop flaws in all cases extended in directions normal to the principal maximum tension rather than in the direction of maximum hoop stress near the crack tip. Mixed-mode fracture envelopes assessed in experiments, particularly with the diametral-compression test, showed significant deviation to higher K_II values relative to the fracture-mechanics predictions. As a consequence, an apparent K _IIc value assessed in the diametral-compression test was approximately twice the value of K _Ic.     

Microstructure and Fracture Toughness of Hot-Pressed Silicon Carbide Reinforced with Silicon Carbide Whisker

The effects of β-SiC whisker addition on the microstructural evolution and fracture toughness ( K _IC) of hot-pressed SiC were investigated. Most of the whiskers added disappeared during the densifcation process by transformation into the α-phase. The remaining whiskers acted as nuclei for grain growth, resulting in the formation of large tabular grains around the whiskers. The tabular grains around the whiskers were believed to be formed because of the extreme anisotropy of the interfacial energy between α- and β-SiC. The K _IC of the material was improved significantly by the whisker addition. The increase in the K _IC was attributed to crack bridging followed by grain pullout as a result of the formation of tabular grains in a fine matrix.     

Fracture Energy and Strength Behavior of a Sodium Borosilicate Glass-Al2O3 Composite System

Fracture energy and strength were determined for three series within a sodium borosilicate glass-Al₂O₃ dispersed composite system. The average particle sizes of the Al₂O₃ dispersions were
, and
μm. Within each series, composites containing 0.10, 0.25, and 0.40 vol fractions of the Al₂O₃ dispersed phase were vacuum hot-pressed. The fracture energy was determined at 77°K with the double cantilever specimen configuration. Strength was measured by a 4-point flexural test. A significant increase in fracture energy was observed (up to 5 times the fracture energy of the glass without second-phase dispersion). The fracture energy depended on the interparticle spacing and average particle size of the Al₂O₃ dispersion. These results could best be explained by a previously proposed model for the interaction of a crack front with a second-phase dispersion. Surface roughness also contributed to the increased fracture energy. Some composites were strengthened significantly relative to the glass without a dispersion. Calculation of the crack size showed that the Al₂O₃ dispersion increased the crack size of the glass by ∼1 to 3 times the average particle size of the Al₂O₃ dispersion. Thus, the dispersion increased both the fracture energy and the crack size. These opposing parameters ultimately determined the strength behavior of these composites.     

聚乙烯醇纤维混凝土动态断裂过程试验研究

为探究纤维体积掺量对聚乙烯醇纤维增强水泥基复合材料(PVA-ECC)断裂过程的影响,基于50 mm的分离式霍普金森压杆(SHPB)装置对不同纤维体积掺量(0%、0.75%、1.50%、2.25%、3.00%)的PVA-ECC中心切槽半圆盘弯曲(NSCB)试件进行冲击试验,同时结合超高速数字图像(DIC)相关试验系统对PVA-ECC材料的动态断裂过程进行试验研究,得到了预制裂纹尖端张开位移的变化规律以及各组试件的临界裂缝尖端张开位移(CTOD_C)。结果表明,当不添加PVA纤维或添加较少(小于1.50%)时,裂尖宏观裂纹基本出现在裂尖荷载的峰值时刻处,而随着PVA纤维掺量的增加,裂尖宏观裂纹的出现显著早于裂尖荷载的峰值时刻,并且纤维体积掺量越大,裂尖宏观裂纹出现得越早,裂纹扩展至完全断裂的时间也显著增加。添加聚乙烯醇纤维可以显著提高混凝土试件的CTOD_C值,提高试件的阻裂能力,相同冲击荷载下,体积掺量为2.25%的聚乙烯醇纤维试件具有较大的CTOD_C值。     

Analysis of thermoelastic interaction of manufacturing stresses along the interface on interlaminar delamination progression in multi-ply composite laminates

This paper deals with the study of interaction of manufacturing thermal residual stresses and mechanical loading in penny-shaped delaminations embedded between dissimilar, anisotropic fiber composite layers by conducting two sets of three-dimensional thermoelastic finite element analyses with and without residual stress effects. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of strain energy release rates obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply sequence and orientation, thermoelastic anisotropy and material heterogeneity, and ply properties of the delaminated interface dictate the interlaminar fracture behavior of multi-ply laminated FRP composites.     

Effect of Fiber Volume Fraction on the Off-Crack-Plane Fracture Energy in Strain -Hardening Engineered Cementitious Composites

In this paper, the results of an experimental study on the effect of fiber volume fraction on the off-crack-plane fracture energy in a strain-hardening engineered cementitious composite (ECC) are presented. Unlike the well-known quasi-brittle behavior of fiber reinforced concrete, ECC exhibits quasi-ductile response by developing a large damage zone prior to fracture localization. In the damage zone, the material is microcracked but continues to strain-harden locally. The areal dimension of the damage zone has been observed to be on the order of 1000 cm² in double cantilever beam specimens. The energy absorption of the off-crack-plane inelastic deformation process has been measured to be more than 50% of the total fracture energy of up to 34 kJ/m². This magnitude of fracture energy is the highest ever reported for a fiber cementitious composite.