Mixed-Mode Fracture from Controlled Surface Flaws in Hot-Pressed Si3N4

The room-temperature mixed-mode fracture of commercial hot-pressed Si₃N₄ was examined using controlled surface flaws in 4-point bending, oriented at various angles 6 with respect to the outer fiber tensile stress direction. Catastrophic fracture paths were non-coplanar with the initial flaw plane, and the stress intensity factor ratio K_I/K_IC was < 1 for fracture in modes II and III. A non-coplanar maximum strain-energy release rate fracture criterion best described mixed-mode fracture.     

Controlled Surface Flaws in Hot-Pressed SiC

Controlled semi-elliptical surface flaws were produced in hot-pressed SiC by Knoop microhardness indentation. Flawed specimens were placed in 4-point bending in order to determine their critical stress intensity factor, K_IC, at both room and high temperatures. Room-temperature fracture and K_IC values after annealing were sensitive to the annealing environment; this behavior correlated with the active/passive nature of the oxidation process. Flaw healing was observed for annealing exposures in air. Room-temperature K_IC values increased with increasing annealing temperature. High-temperature K_ICvalues decreased with increasing temperature as a result of a decrease in the fracture surface energy.     

New Statistical Treatment of Ball Indentation Data to Determine Distribution of Flaws in Glass

Ring fractures generated by a steel ball indenting a flat glass plate occur outside the contact circumference, not at the circumference as theory predicts. It has been proposed by others, and is accepted as a basis for the present work, that the position of ring fracture is not determined by the locus of maximum stress but by the presence of a flaw which is severe enough to initiate fracture under the local condition of stress. The ring fracture radii thus locate flaws of various sizes at various distances from the center of contact. A new statistical method is introduced for calculating the distribution of such flaws with respect to both sizes of flaw and surface density of flaws. Application of this analysis to data taken from indentations of HF-etched surfaces shows that flaw densities range from 15 to 30 per mm² per 5 A depth interval (150 to 300 flaws per mm² over the range detected by the indenter). Since continued removal of the surface did not change this density distribution, it is concluded that these flaws are due to inhomogeneities in the glass structure rather than to surface flaws which are accidental in origin. The limitation of the strength of flat glass to 300,000 psi is due to these inhomogeneities.     

Effect of Surface Flaw Size on Fracture Strength of Alumina Ceramics

Semielliptical surface flaws of different sizes were introduced into Al₂O₃ by Knoop microhardness indentation. The specimens were fractured by four-point bending and the profiles of the indentation flaws were determined by observing the fracture surfaces with a scanning electron microscope. The relation between the indentation flaw size and the fracture strength could be well explained by applying the fracture-mechanics analysis for semielliptical surface flaw in bending. The calculated values of the as-indented critical stress intensity factor, K_IC, were lower than previously reported presumably because of the influence of the residual stresses produced by the indenter.     

Mixed-Mode Fracture of Hot-Pressed Si3N4

The mixed-mode fracture of hot-pressed Si₃N₄ was investigated using inclined indentation surface flaws in bending and large crack geometries in combined tension/torsion. Non-coplanar fracture was observed in all cases. Values of K_Ic, K_IIc, and K_IIIc stress intensity factors were obtained, with ratios K_IIc/K_Ic= 0.79 and K_IIIc/K_Ic= 1.55 observed. For large cracks, mode II conditions had more of an effect on mode I fracture than mode III conditions. The mixed-mode I-II fracture of surface flaws was significantly different from that for large cracks, suggesting surface flaw shear resistance effects. A model describing these effects was derived, based on the ratio of the crack-opening displacement to the crack surface asperity height.     

焦炭塔裙座环缝裂因及安全分析

文章对焦炭塔的检验及存在的缺陷进行了分析和探讨,通过全面的应力分析、总应力超过材料屈服应力时的安全性分析、无缺陷部位焊缝的热机械疲劳分析、缺陷部位的断裂评定及疲劳分析,提出了裂纹防治及处理的建议。     

Photoelastic Determination of Flaw Size and Distribution Effects on Adhesively Bonded Lap Joints

It is well known that the load carrying capacity of adhesively bonded lap joints can be influenced by the presence of flaw-like defects which are often created during its bonding process. To design an effective adhesive joint containing possible bonding defects, adequate knowledge and understanding of the shear stress distribution along the entire lap joint are necessary.

This paper describes an investigation into the effects of internal adhesive flaw size and distribution on the fracture behaviour of adhesively bonded lap joints. Photoelasticity is used to gain a quantitative understanding of the localized shear stress concentrations due to the presence of the internal flaws along the bonding layer. It is observed that a 20% increase in the maximum shear stress may be induced when an isolated central flaw of S. O mm was extended to 37.5 mm representing a flaw size of 75% of the lap length. For the presence of multiple flaws along the bonding line, there is no significant effect of the flaw separation distance on the maximum shear stresses. There is, however, a marked increase in the maximum shear stress up to about 45% when a flaw size is increased from 2.5 mm to 7.5 mm.     

Detection and Analysis of Crack Propagation in PZT Multilayer Ceramics

The flaw propagation in Lead zirconate titanate (PZT) multilayer ceramics under mechanical load was examined using impedance spectroscopy and three‐point bending studies. Initial flaws were generated by applying a positive sinusoidal electric field to the specimens. The cracks were sequentially propagated and after the release of the external mechanical load, impedance spectroscopy was conducted. The shift in the resonance frequencies and the subresonance height of the impedance spectroscopy were used as a measure of flaw extension. A functional dependence of the resonance frequency and the phase shift on the crack length was found. The crack propagation was studied on flaws starting at the positive and negative electrode, respectively. The maximum fracture strength, as well as the crack path, depends on the electrode potential. The variation in the fracture strength was caused by different observed fracture mode: interface cracking, matrix‐cracking, or a combination of both. The morphology of the fracture surfaces was ascribed to a textured microstructure, which is created by the sample processing, for example, by the poling process. A modified poling procedure with a lower poling temperature was analyzed, which yielded a reduction of the anisotropy of the electrode strength. Impedance spectroscopy was found to be a reliable measurement tool for automated flaw detection in PZT multilayer ceramics.     

Corrosion Behavior of Single-Crystal Alumina in Argon, Air, and Water Vapor Atmospheres at 1700-2000°C

The results for the corrosion of alumina single crystals at 1700-2000°C in argon, argon/water vapor, air, and air/water vapor for 10 h are reported. There were no obvious weight and volume changes after corrosion. White spots were observed on the surfaces of the specimens after corrosion tests. The initial temperature for the appearance of these white spots was 1800°C for argon and air, 1900°C for argon/water vapor, and 2000°C for air/water vapor. These white spots were likely formed by internal impurities, which diffused outward to the surface and coalesced at high temperatures. There was no evidence of corrosion damage inside the specimens. The flexural strength of the specimens was clearly enhanced after the corrosion tests and showed no evident relation to the corrosion conditions. This increase in strength after corrosion was likely due to the healing of surface machining flaws. The surface flaw healing temperature for alumina crystals was higher than 1400°C.     

Assessment of Surface Flaws in Glass via Thermal Downshock Test

The severity of surface flaws in a sodium aluminosilicate glass was assessed by subjecting flat glass plates to successively higher thermal downshock and determining the temperature range that causes failure. The temperature data are then translated to short-lived tensile stresses, which, in turn, provide an estimate of flaw depth using Griffith's fracture criterion. The data show that the failure occurs from the edge zone indicating a more severe flaw population associated with edge finishing than that with manufactured flat surfaces. Etching of the edge region reduces flaw severity and increases the failure temperature nearly twofold. The observed fragmentation density appears to vary with stored elastic energy. The estimated thermal stresses, flaw depth, and elastic energy during thermal downshock are discussed.     

Reliability Analysis of Structural Ceramics Subjected to Biaxial Flexure

Sintered alumina and silicon nitride were tested in uniaxial (four-point and three-point bend) and biaxial (uniformpressure-on-disk) flexure tests in inert conditions. Fracture origins were identified to be surface flaws in alumina and subsurface pores in silicon nitride. Batdorf's statistical fracture theory and two different fracture criteria, the critical normal stress criterion and a noncoplanar strain energy release rate criterion, were used to examine size and stress-state effects on fracture strengths of the two ceramics. Size effects assessed in four-point and three-point bend tests were in good agreement with the theoretical predictions for both ceramics. Measured biaxial strengths of alumina were in good agreement with the prediction when a noncoplanar strain energy release rate criterion and random surface flaw orientations were assumed. On the other hand, biaxial fracture strength of the silicon nitride was consistent with a prediction based on preferred flaw orientation (i.e., normal to the principal stress in the disks) and the normal stress fracture criterion. Orientation distributions of the fracture planes assessed from the fracture patterns of the disks supported the assumptions of random flaw orientations (alumina) and the preferred flaw orientations (silicon nitride), respectively, for the two ceramics. The preferred flaw orientation in silicon nitride is suggested to originate at subsurface pores as a result of crack nucleation in the plane of maximum tensile stress concentration, i.e., a diametral plane normal to the maximum principal stress.     

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.     

Mechanical Properties of Polycrystalline β-Sic

The mechanical properties of chemically vapor-deposited β-Sic were measured in bending between room temperature and 1400°C. Material with grain diameters from less than 1 to 15 μm was tested. No grain-size dependence of the bend strength of dense (<99% of theoretical) Sic was observed at any test temperature. The fracture strength of dense Sic remained approximately constant between room temperature and about 900°C and then increased sharply up to the maximum test temperature of 1215° to 1400°C. This increase in fracture stress coincided with the onset of plastic yielding detectable in the stress-strain curves. The fracture mode of this material was transgranular cleavage at all test temperatures. The fracture stress of Sic of lower density, which was characterized by the presence of grain boundary flaws, decreased slightly at high temperature. The fracture mode of the low-density (3.17 g/cm³) β-Sic underwent a transition from predominantly transgranular at room temperature to predominantly intergranular at high temperature.     

DEM modeling of crack coalescence between two parallel flaws in SiC ceramics

A discrete element model (DEM) of SiC ceramics containing two parallel flaws was used to study crack coalescence under uniaxial compression with different flaw inclination angles, ligament lengths, and ligament angles. A relationship is proposed between coalescence stress state, flaw inclination angle, and horizontal component of the ligament length during the failure process. The effects of coplanar flaws on various characteristics of the specimen, viz. compressive strength, Young's modulus, crack initiation stress, and Poisson's ratio, were studied. Coalescence modes between two parallel flaws observed in the DEM model were in good agreement with nine crack coalescence categories summarized in experimental studies. Meanwhile, the corresponding stress state at the moment of coalescence can be classified into three types – pre-peak, mid-peak, and post-peak. The results also showed that the horizontal component d of the ligament length of parallel flaws significantly influences the coalescence stress state. When parallel flaws overlap in the loading direction (d < 0), with an increase in the inclination angle, the occurrence of crack coalescence changes from pre-peak period to mid-peak period and post-peak period and eventually to non-coalescence. When d = 0, coalescence between the flaw pair mainly occurs before the peak stress and the corresponding flaw geometries are the most dangerous. As distance d increases, the possibility of crack coalescence decreases.     

Effect of Grinding on Flaw Geometry and Fracture of Glass

Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth ( a ) to the half-width ( b ) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a / b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress-intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r , occurs at a constant stress-intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress-intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw-to-mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a / b values.     

Theory of Fatigue for Brittle Flaws Originating from Residual Stress Concentrations

A theory is formulated for the general fatigue response of brittle flaws which experience residual stress concentrations. The indentation crack is taken as a model flaw system for the purpose of setting up the basic fracture mechanics equations, but the essential results are expected to have a wider range of applicability in the strength characterization of ceramics. A starting fatigue differential equation is first set up by combining an appropriate stress intensity factor for point- or line-contact flaws with a power-law crack velocity function. Analytical solutions are then obtained for the case of static fatigue. The resulting relation between lifetime and failure stress is shown to have exactly the same power-law form as the conventional solution for Griffith (residual-stress-free) flaws. This "equivalence" is used as a basis for extending the results to dynamic fatigue. A comparison of these analytical solutions with numerical counterparts defines the limits of accuracy of the theoretical procedure. However, while the form of the lifetime relation remains invariant, the values of the exponent and coefficient differ significantly for flaws with and without residual stress. Accordingly, the application of conventional fatigue theory to evaluate crack velocity parameters, without due regard for the nature of the critical flaw, can lead to serious errors. Explicit conversion formulas are given for transforming "apparent" velocity parameters for indentation flaws directly into "true" parameters. The implications of these results concerning the use of the indentation method for materials evaluation are discussed.     

The Fracture Mechanics of the Pin and Collar Test for High Temperature Anaerobic Adhesives

A mechanical test method for the studies of high-temperature anaerobic adhesives has been established, based on fracture mechanics, by modifying the standard test method of collar and pin test. Linear Elastic Fracture Mechanics approach was applied to the establishment of the relationship between adhesive fracture surface energy “R”, fracture load and crack length. Hence, from the joints containing a given artificial flaw the adhesive fracture surface energy can be determined; alternatively, from the strength of the joints without artificial flaws the inherent flaw size “a_i” can be calculated to account for the decrease of joint strength.

The experimental techniques were applied to examine the mechanical behaviour of the joint system based on high temperature anaerobic adhesives. It was found that the joints cured at room-temperature had higher adhesive fracture surface energy but lower joint strength than the joints postcured at high temperatures. The “a_i” data explained this interesting phenomenon. The joints cured at room-temperature had extraordinarily large “a_i”, which was found to be formed by the uncured adhesive near the edges of the joints and the adhesive further cured in the postcure processes to reduce the “a_i”. Also, the growth of intrinsic flaw was found to be responsible for the deterioration of the joints in a short-term, high-temperature ageing process.     

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.     

Effects of Postdeposition Treatments on the Mechanical Properties of a Chemical-Vapor-Deposited Silicon Carbide

The influence of different postdeposition treatments such as water quench and thermal heating in air, nitrogen, and vacuum on mechanical properties of chemical-vapor-deposited (CVD) silicon carbide was investigated. The results showed that these postdeposition treatments increased the flexural strength by as much as 60% but did not significantly change other properties such as hardness and fracture toughness. The strength increase was achieved by treatments performed in both the oxidizing and nonoxidizing environments. Compressive residual stresses in CVD SiC increased because of these treatments, but this increase was not large enough to explain fully the observed increase in the flexural strength. It is proposed that these thermal treatments led to strength increase via healing of surface machining flaws. Thermal treatments in nonoxodizing environments reduced or blunted the flaws through the rearrangement of atoms and restoration of damaged crystal structure in SiC, while in oxidizing environments, passive oxidation may have served as an additional flaw healing mechanism.     

Strength and Its Variability in Ceramics with Particular Reference to Alumina

Research was conducted to measure the strength and its variability in polycrystalline alumina with a wide variety of high-density arrays of flaws. The flaw arrays were produced by grit-blasting the surface, processing samples with small (10 μm diameter) and large (100 μm diameter) closed pores, underfiring samples to give interconnected grain-boundary pores, and fabricating microcracked Al₂O₃-ZrO₂ composites. Although details of the failure process can be complicated, strength was controlled in all cases by either the stress to propagate a large flaw or the stress to cause linking of smaller flaws. Strength variability was correspondingly due to either the distribution of critical flaws or the variability in the spatial array of flaws. Fracture mechanics principles can be applied in understanding these results although in many cases a unique solution is not possible because of the nonidealized flaw structure in ceramics. Because of the difficulty in controlling the detailed microstructure of ceramics during fabrication, the attainment of uniform ceramic strengths is an extremely difficult goal.