Calculation of Residual Stresses in Glass

Lee, Rogers, and Woo presented a theory for calculating the stresses produced in glass by tempering. Unlike earlier treatments, theirs takes account of the viscoelastic properties of glass. The purpose of this paper is to evaluate this theory by comparison with experimental data. Discrepancies were found to exist between calculated and observed stress distributions. For cases in which glass is quenched from initial temperatures well above the strain point, these discrepancies result from the numerical formulation of the theory, not from any shortcomings of the theory itself. A modification of this formulation brought calculated and observed stresses into good agreement. For quenching from lower initial temperatures , the present theory could not be brought into agreement with experimental data. The reasons for this are briefly considered in the context of the structural heterogeneity of tempered glass and its possible effects on residual stresses.     

Flaw Characteristics in Dynamic Fatigue: The Influence of Residual Contact Stresses

The effect of residual contact stresses on the dynamic fatigue response of surfaces containing indentation-induced flaws is studied. Indentation fracture mechanics is used to analyze the growth of well-defined "median/radial" cracks in combined residual (elastic/plastic) contact and applied (uniform) tensile fields, and thence to determine strength characteristics. In this way a general formulation is obtained for the fatigue strength at constant stress rate. Experimental confirmation of the essential predictions of the theory is obtained from strength tests on Vickers-indented soda-lime glass disks in water environment. It is thereby implied that residual stresses can have a significant deleterious influence on the fatigue behavior of any brittle solid whose controlling flaws have a contact history. Such effects need to be considered in the design of structural ceramics, most notably where fracture-mechanics calibrations of crack-velocity parameters are used for lifetime predictions.     

Dynamic Fatigue of Float Glass

The dynamic fatigue Of bulk float glass was measured Over a wide range of stressing rates. The results are compared with theoretical predictions based on integration of ( K₁, V ) diagrams. It is thought that there are distinct differences in the growth of microcracks and macrocracks in glass, particularly with regard to the region of transport control.     

Residual Stresses in a Glass Plate Cooled Symmetrically from Both Surfaces

Residual stresses in tempered glass are generated by interactions between thermal contraction, elasticity at low temperatures, viscoelastic flow at higher temperatures, and temperature gradients caused by cooling. To date, analyses have assumed highly idealized material behavior, such as elasticity below, and inviscid fluid flow above, a critical temperature. The theory presented in this paper is based on measured relaxation characteristics of glass and temperature influence through thermorheologically simple response, which prescribes an acceleration of all relaxation phenomena with rising temperature by a factor determined by experiment. The analysis of the varying stress history for a glass plate cooled symmetrically on both sides is developed and solved for several furnace and coolant temperature combinations by numerical solution of the integral equations which arise. The determination of the residual stress distribution follows naturally in terms of a reduced time used in the analysis. Maximum compressive residual stresses under the surface increase extremely rapidly with increasing furnace temperature above 60O°C. The method is compared with previous work on the same problem.     

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.     

Use of Crack Branching Data for Measuring Near-Surface Residual Stresses in Tempered Glass

An analytical procedure based on fracture mechanics is used to obtain the amount of residual stress in glass from measurements on the fracture surface. The technique utilizes the measurement of microcrack branching distances, known as the mirror — mist boundary, which occur at a critical crack branching stress intensity (K _m ) value. This procedurre shows that σ _A r _m ^1/2 Y _F (θ) =σ _R r ^1/2 _m +Ψ₀, where σ _A is the applied stress, r _m is the microcrack branching radius, σ _R is the residual stress, Y _F ( θ ) is the crack-border correction factor, and Ψ₀ is a material constant based on K _m . Thus, the equation is that of a straight line with the slope equal to the magnitude of the residual stress. Data for tempered glass from the literature are used to demonstrate the applicability of the technique.     

Strength and Static Fatigue of Abraded Glass Under Controlled Ambient Conditions: IV, Effect of Surrounding Medium

The strength and static fatigue behavior of abraded glass specimens tested in various surrounding media have been studied. The test media included distilled water, nitrogen atmospheres of varying humidity, methyl and isopropyl alcohol and mixtures of these with distilled water, and various acidic and basic solutions. For intermediate durations of load the strength values in atmospheres of 0.5 and 43% relative humidity were 45 and 20% greater, respectively, than in distilled water. The value of t_0.5, the characteristic duration for static fatigue, under these three test conditions was 3500, 200, and 8 seconds, respectively, for the particular grit-blast abrasion studied, indicating that liquid water is the most effective agent for promoting a high rate of static fatigue and very dry air with a small concentration of water vapor is least effective. In reagent-grade methyl or isopropyl alcohol (0.01 to 0.05% H₂O) the strength at an intermediate load duration of 10 seconds was about 40% greater than in distilled water and the slope of the static fatigue curve differed somewhat from that obtained for tests in water. With the addition of water to the alcohol solutions the fatigue curve became parallel to that for water, and as the water content was increased, the curves shifted toward the water curve. For tests in acidic and basic solutions the strength at an intermediate load duration was independent of pH over the range pH 1 to 13. For more acidic solutions the strength was slightly less and for more basic solutions slightly greater than in this range. The results are discussed in terms of possible mechanisms for static fatigue. It is concluded that the static fatigue of abraded glass results from changes in the shape or size of surface abrasion cracks under the combined action of stress and the surrounding medium. In general, water or water vapor is the primary agent in promoting fatigue, and, unlike the usual chemical attack, the interaction appears to involve primarily the neutral water molecule and the SiO₂ network of the glass. The presence of other ions or molecules is relatively unimportant except as it may serve to reduce the concentration of water and its availability to the tip of the abrasion crack.     

Strength and Static Fatigue of Abraded Glass Under Controlled Ambient Conditions: III, Aging of Fresh Abrasions

The effect of aging under various conditions on the strength and static fatigue of freshly abraded specimens has been studied. For both grit-blast and emery cloth abrasions the liquid nitrogen (fatigueless) strength increased with storage time after formation of the abrasions for specimens stored in liquid water or in an atmosphere containing water vapor. After 1 day of storage in water the strength increase was about 60% of the freshly abraded value for emery cloth abrasions and about 30% for grit-blast abrasions. The aging depended strongly on the medium in which the specimens were stored and on the relative humidity when they were stored in air. In very dry air or vacuum the aging effect appeared to be eliminated. Static fatigue curves (strength vs. load duration) in water were measured for specimens containing fresh abrasions and aged abrasions. Ordinary aging did not change the static fatigue behavior of fresh abrasions. The liquid nitrogen strength and static fatigue also were studied for specimens which had been baked at 470°C. in high vacuum after being abraded. This treatment increased the fatigueless strength by approximately the same amount as aging in water. The rate of static fatigue, however, which was unaffected by ordinary aging, was reduced by a factor of approximately 25 for vacuum-baked as compared with fresh abrasions. Possible mechanisms for aging are discussed in some detail. It is proposed that the observed aging effects on the fatigueless strength can be accounted for by an increase of the radii of the tips of the abrasion cracks in the surfaces of the specimens. The suppression of fatigue for the vacuum-baked specimens is believed to be related to the non-wettability of their surfaces which was observed in the course of the experiments.     

Origin of Strength Increase of Abraded or Indented Glass upon Annealing

The mechanical strength of soda-lime and boresilicate glass rods with an extended crack was found to increase upon annealing. Since the residual stress near the extended crack tip is small, this strength increase indicates that crack tip blunting is taking place.     

Strength and Static Fatigue of Abraded Glass Under Controlled Ambient Conditions: I, General Concepts and Apparatus

An extensive experimental study of the factors affecting the tensile strength and static fatigue of bulk glass has been conducted. To minimize the effects of past history of the specimens, all specimens were subjected to a controlled, reproducible surface abrasion. Time, temperature, and chemical environment were subject to control and systematic variation during the period from abrasion to test and during the strength test itself. Specimens consisted of flat laths tested in cross bending with the abraded spot in the center of the tension face. An electronically controlled electromagnetic tester permitted applications of pulse loads or constantly increasing loads with controllable durations from about 0.0025 second up to any desired value. The apparatus and methods for producing the abrasions, controlling the environment, and performing the tests are described in this paper. A brief review of the experimental background on the strength of glass is also presented as an introduction to the aims and concepts of this study.     

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.     

Residual Stresses in Dried Bodies

The problem of residual stresses in porous materials as a result of drying and the presumable influence of these stresses on the swelling effect by rehydration are discussed. The drying model comprising the specific mechanisms suitable for the first and second periods of drying is applied, and the numerical algorithm enabling calculation of the drying-induced stresses is constructed. The numerical calculations exemplifying the history of stresses leading finally to the residual stresses are carried out. The outcome of these stresses on the swelling strains during rehydration is illustrated using an example of a finite dimensions kaolin cylinder dried convectively.     

Residual Stresses in Dried Bodies

The problem of residual stresses in porous materials as a result of drying and the presumable influence of these stresses on the swelling effect by rehydration are discussed. The drying model comprising the specific mechanisms suitable for the first and second periods of drying is applied, and the numerical algorithm enabling calculation of the drying-induced stresses is constructed. The numerical calculations exemplifying the history of stresses leading finally to the residual stresses are carried out. The outcome of these stresses on the swelling strains during rehydration is illustrated using an example of a finite dimensions kaolin cylinder dried convectively.     

Residual Stresses in Machined Ceramic Surfaces

Residual surface stresses generated in ceramic materials by diamond grinding were studied. The stresses are characterized both by X-ray measurements of stress magnitudes and by line forces (product of stress and layer thickness) obtained from the bending of plates that were machined on one side. The line forces tend to increase with the hardness of the material but are insensitive to the rate of material removal during grinding (over a limited range of variation). Residual stress measurements are compared with measurements of strengths of the ground surfaces.     

Residual Stresses in Microcomposites and Macrocomposites

Existing models for built-in residual stresses in composite materials are reviewed and discussed. In particular, the thermal longitudinal stress present in the fiber prior to a single-fiber fragmentation experiment is studied using various model composite data. It is found that this stress is typically compressive in nature and that, quantitatively, it depends on the fiber content, the degree of undercooling, and the thermoelastic constants of the fiber and the matrix. In the case of single-fiber composites (or microcomposites), the thermal longitudinal stress present in the fiber is high enough to either induce fiber sinewave buckling (such as in E-glass/epoxy), or extensive fiber fragmentation (such as in graphite HM/polypropylene) that may then be used to measure the dependence of compressive fiber strength upon length. This has to be accounted for in quantitative models that calculate interfacial adhesion parameters using single-fiber tests, such as the fragmentation test or the microbond test. Implications for high fiber content composites (or macrocomposites) are discussed.     

Residual Stresses in Machined MgO Crystals

The residual stresses introduced in MgO crystals by grinding on {100} surfaces in 〈100〉 directions were measured using photoelastic techniques. Grinding was conducted with two wheels; a 100-grit diamond wheel removed material by brittle fracture, and a 46-grit alumina wheel caused plastic flow and burnishing. Both wheels introduced a discrete, highly deformed layer adjacent the machined surface. In all cases the machined surfaces were under a residual tensile stress which became compressive within the deformed region. Beneath the deformed layer the residual stress patterns were distinctly different. In crystals ground with the alumina wheel the stresses became tensile again within 0.5 mm of the ground surface, whereas the subsurface stresses in crystals ground with the diamond wheel remained compressive to distances ≥1 mm. These residual stress distributions are discussed in terms of a simple model based on the superposition of mechanically and thermally induced stresses.     

Residual Stresses in Titanium Carbide-Nickel Cermets

A critical examination reveals certain weaknesses in the paper under discussion. New experimental evidence is presented which qualitatively confirms the conclusion of Newkirk and Sisler that large residual stresses may be present in cermets, but the magnitude of the stresses found is less than that previously reported.