Dynamic Fatigue Analysis of Indentation Flaws Using an Exponential-Law Crack Velocity Function

The effect of residual contact stresses on the dynamic fatigue behavior of indentation flaws was analyzed using an exponential-law crack velocity function based on stress corrosion theory. Analysis of strength data from Vickers-indented soda-lime glass specimens in water showed that the contact residual stress can be properly accounted for and that the exponential-law fatigue parameters can be straightforwardly obtained.     

Micromechanics of Flaw Growth in Static Fatigue: Influence of Residual Contact Stresses

Residual contact stresses about indentation flaws are demonstrated to have a strong deleterious effect on specimen lifetime in static fatigue. The underlying basis of conventional fatigue analysis is first examined critically and is argued to be deficient in the way the stress intensity factor for the flaws is related to the characteristic parameters of crack geometry and applied loading. In general, it is necessary to incorporate a residual term into the stress intensity formulation. A modified theory of static fatigue is accordingly developed, in which the residual contact stresses play a far from secondary role in the micromechanics of flaw evolution to failure. Strength tests on Vickers-indented soda-lime glass disks in water environment provide clear experimental confirmation of the major theoretical predictions. Implications of the residual stress effect concerning fracture mechanics predictions of lifetimes for "real" ceramic components under service conditions are discussed.     

Failure of Glass with Subthreshold Flaws

Conventional postthreshold crack analysis cannot be used to predict the strength and fatigue behavior of glass with subthreshold flaws. Therefore, a fracture mechanics model for failure of glass with subthreshold indentation flaws was developed. This model accounts for both the near- and farfield residual stresses associated with the indentation impression. It is shown that these stresses play a major role in the initiation and subsequent propagation of cracks that eventually cause failure. The model predicts "pop-in" of a well-developed crack and failure under continuous and discontinuous crack growth in both inert and fatigue conditions. The results of experiments with bare fused silica fibers with indentation subthreshold flaws in inert and fatigue (water) environments were in good agreement with the predictions by the model.     

Residual Stresses in Dynamic Fatigue of Abraded Glass

The effect of residual contact stresses on the dynamic fatigue response of glass surfaces containing abrasion flaws is described. Indentation fracture theory is used as a theoretical basis for analyzing the experimental data. The results highlight a general need to incorporate a residual-stress term in the fatigue equations for failure from natural flaws.     

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.     

Strengthening of Zirconia–Alumina During Cyclic Fatigue Testing

Recent fatigue results of advanced ceramics are reviewed. It is pointed out that current statements of fatigue properties often relate to specimens with long artificial cracks; in this study, a Y-ZrO₂+Al₂O₃ ceramic is tested under cyclic stresses using specimens with natural flaws. Cyclic fatigue is restricted to a narrow range of stresses near the ultimate strength. Survivor specimens reveal increased residual strength, possibly resulting from a higher ZrO₂ phase transformation encouraged by long-term cyclic stresses.     

Strength and Fatigue Properties of Optical Glass Fibers Containing Microindentation Flaws

The inert strength and dynamic fatigue properties of fused-silica optical fibers are studied using subthreshold indentation flaws, i.e., flaws without radial cracks. These subthreshold properties differ from those obtained in comparative tests on silica rods containing postthreshold indentation flaws in three major respects: (1) the inert strengths are significantly higher than predicted by extrapolation of the postthreshold data; (2) the slopes of the dynamic fatigue plots are likewise greater, indicating a greater susceptibility of the subthreshold flaws to chemical kinetic effects; and (3) the scatter in strengths is wider. These trends reflect the change in mechanical response reported for optical fibers with "natural" flaw populations in going from ordinary to ultra-high-strength regions. Direct observations of the indentation sites up to the point of failure indicate that the property differences can be interpreted in terms of a transition from propagation-controlled to initiation-controlled fracture instabilities at reduced contact loads. The subthreshold instability condition is modeled qualitatively as a two-step, deformation-fracture process, with strong emphasis on the importance of residual stress fields in parametric evaluations. The relevance of the results to the practical issue of fiber reliability, most notably in connection with the potential dangers of using macroscopic crack velocity data to predict long-lifetime characteristics, is addressed.     

Mixed-Mode Fracture in Soda-Lime Glass Using Indentation Flaws

Mixed-mode failure of soda-lime glass under inert and fatigue test conditions was studied using Knoop indentation flaws. For annealed cracks (residual stress-free) crack extension (catastrophic or subcritical) is by an abrupt transition from the initial crack plane to a noncoplanar crack plane followed by a reorientation of the crack normal to the applied stress. Although fatigue strength of these inclined flaws increased linearly with respect to orientation of the flaws to the applied stress up to an angle of 60°, this increase was considerably less than what was predicted by existing theories. It is believed that subcritical crack growth causes the crack to be realigned perpendicular to the applied stress before failure for all orientations; hence, fatigue strength does not show the dramatic increase at orientation angles as predicted by theory. For as-indented cracks the contact residual stress causes the crack extension to be less inclined to the initial crack plane than for annealed cracks, but in this case also, the crack realigns itself perpendicular to the applied stress. Again, fatigue strength is relatively insensitive to the orientation angle as predicted by theory and subcritical crack growth is believed to play a primary role in determining this strength dependency.     

Strength and Static Fatigue of Abraded Glass Under Controlled Ambient Conditions: II, Effect of Various Abrasions and the Universal Fatigue Curve

A controlled grit blast was found to be a reproducible method of producing standardized damage to a glass surface. The effects of grit size, blast pressure, and amount of grit on the strength of the resulting specimens are reported. Static fatigue curves (strength vs. load duration) were obtained for specimens immersed in room-temperature distilled water and in liquid nitrogen (77°K.) after the specimens had been subjected to various abrasion treatments. The low-temperature strength was independent of load duration, and for surface damage of simple geometry it was inversely proportional to the square root of the initial crack depth, consistent with the Griffith theory. Abrasions of different geometry produced differing static fatigue curves at room temperature, and in one case curves actually crossed. If, however, the strength values for each abrasion were divided by the low-temperature strength for that abrasion and plotted vs. a reduced time coordinate, all the data could be fitted to a single "universal fatigue curve." This analysis led to a clear distinction between "linear" and "point" flaws, the former being flaws (such as emery scratches) which have an extension in a direction perpendicular to the applied stress and the latter being of a more localized character. Linear flaws fatigue more rapidly than point flaws by a factor of fifty and for each type of damage the fatigue rate is inversely proportional to the exponential of the initial flaw depth. A detailed analysis of the data in terms of several static fatigue theories from the literature shows that none of them provides a complete and adequate explanation of these results.     

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.     

Rate Effects in Critical Loads for Radial Cracking in Ceramic Coatings

Rate effects in the Hertzian contact loading of model glass/polycarbonate and silicon/polycarbonate bilayers bonded by epoxy adhesive are examined. Glass is used because of its high susceptibility to slow crack growth, making this conventional contribution to the rate dependencies easy to distinguish. Silicon is used as a control material with effectively no slow crack growth. Abrasion damage is introduced into the undersurfaces of the brittle coating layers to provide controlled flaws for the initiation of radial cracks from flexural stresses introduced by the contact loading. Critical loads are measured as a function of loading rate. Comparative flexural strength tests on free-standing abraded specimens show a pronounced rate dependence in the glass but none in the silicon, entirely consistent with slow crack growth effects. The glass/polycarbonate bilayer critical load data show a similar trend, but with stronger loading-rate dependence, suggesting an extraneous contribution to the kinetics from the adhesive/substrate. The silicon/polycarbonate bilayer data also show a loading-rate dependence, albeit much smaller, confirming this last conclusion. Data from cyclic contact tests on the glass/polycarbonate bilayers coincide with the loading-rate data on lifetime plots, eliminating the likelihood of a mechanical component in the fatigue response. It is concluded that the adhesive/substrate contribution is viscoelastic in nature, from energy-dissipating (but noncumulative) anelastic deformation during the cyclic loading. Critical load tests on bilayers with different exposures to external water show no influence of external environment, suggesting that internal moisture is responsible for the slow crack growth in the glass-coating bilayers.     

Effect of Indenter Geometry on Controlled-Surface-Flaw Fracture Toughness

Fracture toughness values obtained using both Knoop and Vickers-indentation-produced controlled surface flaws were compared as a function of indentation load for a well-characterized glass-ceramic material. At the same indentation load, Knoop cracks were larger than Vickers. As-indented K_c values calculated from fracture mechanics expressions for surface flaws were higher for Knoop flaws than Vickers, but both types gave low K_c values due to indentation residual stress effects. Analysis suggested that theoretical formalisms for indentation residual stress effects based on fracture mechanics solutions for a center-loaded penny crack in an infinite medium should apply to both indentation types. K_c values calculated using the residual stress approach were identical for Knoop and Vickers controlled surface flaws when a "calibration" value for a constant term in the expression for K_c was used for both indentation types.     

Effect of water absorption and temperature gradients on polycarbonate injection moldings

Polycarbonate injection moldings have been conditioned for various times in (i) hot water (40, 60, 80, and 100°C) or (ii) in a temperature gradient (with hot surface/cold surface temperatures 80/25, 100/25, 120/35, and 140/60°C). Water absorption occurred in hot water and caused the formation of disc-shaped flaws, which were located at all depths within the bars and at all orientations. The presence of the flaws caused severe embrittlement and cracks were nucleated by them during uniaxial tensile testing. Residual stress levels were found to be diminished by hot water conditioning more than those in bars conditioned at the same temperatures in air. The sense of the residual stresses reversed in a bar that was allowed to cool slowly in the water bath, an observation attributed to desorption. It was generally found that the flaws near the surface healed on allowing the bars to stand in air at room temperature. Temperature gradient conditioning caused reversal of the sense of the residual stresses near to the hot surface at the two higher temperatures used and significant reduction in magnitude at the lower temperatures. Fracture nucleated at this surface during uniaxial tensile testing.     

Preloading Technique in Dynamic Fatigue Testing of Glass and Ceramics with an Indentation Flaw System

The solution of fatigue strength as a function of preloading in dynamic fatigue testing was obtained numerically for an indentation flaw system. The dynamic fatigue strength is dependent on preloading and fatigue parameter (K). The effect of preloading on dynamic fatigue strength decreases with increasing fatigue parameter: for n 20 the effect is negligible up to a preloading of 90%. The solution was verified by dynamic fatigue experiments conducted with soda-lime glass and alumina specimens with as-indented flaws in room-temperature distilled water. The result indicates that one can apply a preloading corresponding up to 90% of fatigue strength for most glass and ceramic materials with no change in fatigue strength, resulting in a dramatic saving of testing time.     

Fatigue of Yttria-Stabilized Zirconia: II, Crack Propagation, Fatigue Striations, and Short-Crack Behavior

Fatigue crack propagation in 3Y-TZP was investigated using controlled surface flaws. A unique growth law strongly dependent on the maximum stress intensity factor and quadratically dependent on the amplitude of the range of stress intensity factor was established. This growth law was found to apply for both surface flaws and internal flaws and could be used to predict fatigue lifetime. The presence of residual stress altered the growth mechanics so that an inverse growth rate dependence on the applied stress, reminiscent of the so-called "short-crack behavior," was manifested. Fatigue striations resulting from alternate overload fracture and fatigue fracture during stress cycling were observed. The appearance of striations varied with the R ratio and was very sensitive to the loading condition and crack geometry.     

Crack-Resistance Curves of Surface Cracks in Alumina

The resistance of coarse-grained alumina to stable crack growth, initiated from "naturally'occurring surface flaws, was studied in strength tests with a bend-bar technique. The surface cracks experienced R-curve behavior over the first few hundred micrometers; i.e., the applied crack driving force had to be increased with crack extension. Compared to R curves generated from long cracks in standard single-edge-notched-bend specimens, the surface-crack curves have lower initial values. The possible influence of localized residual stresses, counteracting the applied crack driving force, is discussed.     

On the Fracture of Glass Which Is Subjected to Slowly Increasing Stress

A single number called the "strength" does not serve to describe adequately the fracture properties of glass subjected to a slowly increasing tensile stress. Instead, it is found that the surface where fracture originates may be represented as a continuum over which flaws of differing "critical breaking stresses" are distributed. The distribution function for the flaws is given by S σ where σ is the tensile stress initiating fracture and S and b are constants which are properties of the surface for slowly increasing stresses. The testing procedure and nature of the flaws are discussed.     

Mechanisms of Failure from Surface Flaws in Mixed-Mode Loading

Mechanisms of failure from surface cracks in combined tension and shear are identified by directly observing the cracks during failure testing. Under the combined influences of residual contact stresses and applied loading, indentation cracks propagate stably and realign normal to the principal applied tension prior to failure. Annealing of indentation flaws causes relaxation of the residual stresses and thereby leads to a change in the mechanics of fracture; unstable propagation occurs from the initial crack at a critical applied loading, with an abrupt change in fracture plane. Strengths of indentation flaws and machining damage in both the as-formed and annealed states are measured as a function of flaw orientation relative to an applied uniaxial tension. Strength variations of indentations and machining flaws are similar. The results are assessed in terms of various proposed mixed-mode fracture criteria, and the implications of the results for nondestructive testing using scattering of surface acoustic waves are discussed.     

Effect of thermo-mechanical and low-cycle preloading on the strength of carbon fiber-reinforced ceramic matrix composites

Fiber-reinforced ceramic matrix composites (CMCs) exhibit excellent thermo-mechanical properties including outstanding resistance against damage and fatigue. Some CMCs show occasionally even a strength enhancement after fatigue, often interpreted with relieve of internal stresses and interfacial degradation. This study reports the influence of low-cycle thermo-mechanical preloading on the bending and tensile strength of carbon fiber-reinforced silicon carbon (C/C-SiC). For this purpose two C/C-SiC materials with the same fiber architecture but different assumed internal stress states were subjected to single and cyclic mechanical preloads up to 90% of their ultimate strength level at room temperature and at 350 °C. Statistical evaluations of the experiments show that the ultimate strength values were surprisingly unchanged after preloading. The results are discussed regarding the thermal residual stresses (TRS).