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.     

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.     

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.     

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.     

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.     

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.     

Measurement of Indentation Residual Stresses in Materials Susceptible to Slow Crack Growth

Knowledge of the size and distribution of the indentation residual stress field is important when interpreting slow crack growth data for indented ceramic materials. A technique based on compressively loading indentation cracks has been used to measure the wedging residual stresses at radial indentation cracks. The method also gives information on the fatigue limit and can be applied on any ceramic material susceptible to slow crack growth. Soda–lime glass specimens were indented and the resulting residual stresses, wedging the radial cracks, were measured as a function of indentation load. Calculations of K ₀, the fatigue limit, were made for both virgin indentation cracks and cracks aged until saturation. The magnitude of closing stress needed to prevent slow crack growth was found to depend linearly on the indentation load. For example, for indentation loads of 20 and 60 N, the corresponding closing stresses were 14 and 26 MPa, respectively.     

Relation Between Multiregion Crack Growth and Dynamic Fatigue of Glass Using Indentation Flaws

The influence of transport-limited kinetic crack growth on the fatigue properties of soda-lime glass was examined. Dynamic fatigue data were taken on specimens with controlled indentation flaws and were compared with the predicted response from measured crack velocity characteristics. Heptane was used as the operational test environment because of its pronounced crack velocity plateau; control tests in water served to establish a baseline reference for comparing the results. Frac-tographic observations using a stress wave marker technique showed a complex growth history for flaws broken in heptane compared to that for flaws broken in water. The magnitude of the predicted region II influence is too small to be detected in the dynamic fatigue results, even allowing for the relatively high degree of data reproducibility. The implications of this conclusion for lifetime predictions are discussed.     

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.     

Cyclic Fatigue from Frictional Degradation at Bridging Grains in Alumina

Tension—tension cyclic loading tests have been conducted on a coarse-grained alumina ceramic that exhibits toughnesscurve behavior by grain-interlock bridging. Fatigue effects are observed in the regions of both short cracks, using indentation flaws, and long cracks, using compact-tension specimens. A true mechanical fatigue effect is demonstrated by running the tests below the static fatigue limit. A custom-made device for in situ observation of crack propagation in the scanning electron microscope enables us to identify bridge degradation as a cause of the fatigue process. "Wear" debris cumulates at the sliding intergranular frictional contact points, indicating a loss of traction at the junction. The basis of a fracture mechanics model describing the effect of this frictional degradation in reducing crack-tip shielding is outlined and fitted to the data. It is suggested that the bridge degradation fatigue mechanism may be widespread in polycrystalline ceramics with pronounced toughness curves.     

Objective Evaluation of Short-Crack Toughness Curves Using Indentation Flaws: Case Study on Alumina-Based Ceramics

An objective methodology is developed for evaluating toughness curves ( T -curves) of ceramics using indentation flaws. Two experimental routes are considered: (i) conventional measurement of inert strength as a function of indentation load; (ii) in situ measurement of crack size as a function of applied stress. Central to the procedure is a proper calibration of the indentation coefficients that determine the K -field of indentation cracks in combined residual-contact and applied-stress loading, using data on an appropriate base material with single-valued toughness. Tests on a fine-grain alumina serve to demonstrate the approach. A key constraint in the coefficient evaluation is an observed satisfaction of the classical indentation strength–(load)^−1/3 relation for such materials, implying an essential geometrical similarity in the crack configurations at failure. T -curves for any alumina-based ceramic without single-valued toughness can then be generated objectively from inert-strength or in situ crack-size data. The methodology thereby circumvents the need for any preconceived model of toughening, or for any prescribed analytical representation of the T -curve function. Data on coarse-grained aluminas and alumina-matrix material with aluminum titanate second-phase particles are used in an illustrative case study.     

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.     

Subcritical Growth of Indentation Median Cracks in Soda-Lime-Silica Glass

The influence of load and dwell time on the subcritical growth of indentation cracks was investigated. The behavior of soda-lime-silica glass in both active and inert environments was considered. Vickers indentations were obtained.using loads ranging from 1.96 to 39.2 N and the dwell time.at maximum load was varied between 5 s and 30 min. Indented samples were broken and the fracture surfaces.observed using optical microscopy. Anomalous crack shapes were obtained in air and water for long dwell times, particularly at higher indentation loads. The cracks were markedly circular in shape and substantially deeper than conventional median/radial indentation cracks, evidencing a time-dependent growth. Comparison of the measured crack depth with a theoretical analysis demonstrated that the appearance of the "circular" cracks was related to the subcritical growth of median cracks.     

Strength Variability of Indented Soda-Lime Glass

Studies of annealed indentation flaws show that specimen strength is inversely proportional to the square root of the surface trace dimension of the strength-controlling radial crack over a range of indentation loads. Using the surface trace as the characteristic dimension in the appropriate fracture mechanics equations, however, underestimates the measured strengths by about 30%. There is also a lack of correlation between the individual strengths and the surface traces at a given indentation load. Despite the complex nature of indentation flaws, strength predictions of individual indentation cracks based on the radial crack depth (not the surface trace) are in agreement with measured strengths. Strength variability of indented glass specimens at a given indentation load is due mainly to the spectrum of crack depths.     

Contact-Induced Failure of Prestressed Glass Plates

An indentation fracture technique was used to determine critical contact conditions under which prestressed brittle surfaces are subject to catastrophic failure. A theoretical model based on the growth of a well-developed, contact-induced half-penny crack leads to a simple inverse-cube power relation between indentation load and tensile prestress. The analysis is developed in terms of fracture parameters which are readily calibrated in routine indentation/strength tests. Experiments on glass disks loaded simultaneously in biaxial flexure and Vickers indentation confirm the essential failure predictions of the theory; toughness is the key material parameter controlling resistance to failure. The results emphasize the danger of spurious tensile stresses in ceramic systems exposed to severe contact events.     

Ion‐Exchanged Lithium Aluminosilicate Glass: Strength and Dynamic Fatigue

Sodium for lithium and potassium for lithium ion‐exchanges of a lithium aluminosilicate glass were conducted and the resulting strength and dynamic fatigue characteristics were studied. Four‐point bend mechanical tests revealed that greater strengthening can be achieved by the potassium for lithium ion‐exchange, compared to the sodium for lithium ion‐exchange, and that the dynamic fatigue tendency is strongly suppressed by both exchanges. This suppression of dynamic fatigue characteristics of ion‐exchange strengthened glass was explained by the ability of the surface compressive layer to delay the onset of slow crack growth. Bulk stresses continue to increase in magnitude while the crack is arrested in the surface compressive stress region. Upon offsetting the surface compressive stress, the crack rapidly propagates into a high‐magnitude tensile stress field until the fracture toughness is reached, resulting in minimal crack growth prior to material failure. A slow crack growth model utilizing a fracture mechanics weight function was developed to simulate the experiments. Dynamic fatigue characteristics of the as‐received glass, without ion‐exchange treatment, were also measured and simulated for comparison.     

Microstructure-Strength Properties in Ceramics: II, Fatigue Relations

The study of crack-size effects in aluminas and other selected ceramics in Part I is here extended to dynamic fatigue properties. Controlled flaws are used to measure the fatigue response in the large-crack (indentation-controlled) and small-crack (microstructure-controlled) regions. It is demonstrated that the "microstructural driving forces" responsible for the R-curve behavior are readily accommodated into existing indentation fracture theories of fatigue strengths. The modified theory provides well-defined solutions for the strengths in terms of stressing rate and indentation load. Two load-invariant quantities, relating to the exponent and coefficient in an assumed power-law crack velocity function, are sufficient to define the entire data set for a given material, at all stressing rates and loads. This is demonstrated graphically by reducing such data sets onto universal fatigue diagrams. The data for sapphire do not coincide with those for the poly crystalline aluminas, suggesting again that it is the grain-boundary structure which holds the key to the fracture properties in the latter. From the standpoint of reliability, the study emphasizes the need to account for microstructural effects when extrapolating to the domain of naturally occurring flaws. In this context, the adjustable quantities obtained from the dynamic fatigue data fits emerge as appropriate design parameters.     

Strength of brittle materials in moderately corrosive environments

The strengths of four brittle materials―cordierite glass ceramic, fused silica, silicon, and polycrystalline alumina were measured after exposure to weakly corrosive water and moderately corrosive buffered HF (BHF) solution. Exposure to water did not alter the strengths in subsequent inert strength tests and decreased the strengths in reactive strength tests. Exposure to BHF increased the strengths in both tests, but only after an incubation exposure time. Prior to the incubation time, the BHF had the same effect as water, suggesting that the bond rupture kinetics were unaffected. Examination of strength‐controlling indentation flaws after the incubation time showed clear corrosive effects on the flaw geometry indicative of reductions in the indentation residual stress fields. The implication is that moderately corrosive environments increase the strength or lifetime of a brittle component by reducing the crack driving force via flaw alteration and do not, as perhaps expected, decrease the strength or lifetime through enhanced chemical reactivity.     

Effect of Contact Residual Stress Relaxation on Fracture Strength of Indented Soda-Lime Glass

The strength of Vickers-indented soda-lime glass measured in air at room temperature steadily increases with time after indentation, whereas optical retardation steadily decreases in the same interval. Annealing after indentation causes further strength increase and retardation decrease. The results are consistent with Marshall and Lawn's treatment of the slow crack growth of indentation flaws driven by the combined influence of residual contact stress and applied stress. Post-indentation strengthening of indentation flaws can be explained without recourse to flaw blunting.     

Experimental Measurement of Residual Stress Field around Sharp Indentation in Glass

A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.