Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, K_o, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.     

Peak stress intensity dictates fatigue crack propagation in UHMWPE

The majority of total joint replacements employs ultra-high molecular weight polyethylene (UHMWPE) for one of the bearing components. These bearings may fail due to the stresses generated in the joint during use, and fatigue failure of the device may occur due to extended or repeated loading of the implant. One method of analysis for fatigue failure is the application of fracture mechanics to predict the growth of cracks in the component. Traditional analyses use the linear elastic stress intensity factor K to describe the stresses near a loaded crack. For many materials, such as metals, it is the range of stress intensity, ΔK, that determines the rate of crack propagation for fatigue analysis. This work shows that crack propagation in UHMWPE correlates to the maximum stress intensity, K_max, experienced during cyclic loading. This K_max dependence is expected due to the viscoelastic nature of the material and the absence of crazing or other cyclic load dependent crack tip phenomena. Such a dependence on a non-cyclic component of the stress allows cracks to propagate under load with little or no fluctuating stresses. Consequently, traditional fatigue analyses, which depend on the range of the stress to predict failure, are not always accurate for this material. For example, significant static stresses that develop near stress concentrations in the component locking mechanisms of orthopedic implants make such locations likely candidates for premature failure due the inherent underestimate of crack growth obtained from conventional fatigue analyses.     

Measurement of the silica glass fatigue limit

The static fatigue limit, or the threshold stress intensity factor, K_o, for first subcritical crack growth has been measured directly in silica glass for T ≥ 600°C using the double cantilever beam (DCB) crack growth technique. Values measured ranged from 0.48 to 0.61 MPa·m^1/2 for a temperature range of 600°C-850°C, respectively. Cracks growing near the static fatigue limit had a time-dependence, where the crack growth decreased and appeared to stop at K ≈ K_o. Slow crack growth curves (K-v) have been measured from room temperature, 50% RH, up to 850°C with subcritical crack growth not measurable for T > 900°C. Increasing temperature was found to first increase, and then decrease the slope of Region I, and a peak in fatigue resistance was found around 150°C-300°C. At T > 600°C subcritical crack growth was observed for K higher than previously measured K_IC values. This observation and the static fatigue limit in silica are explained by a water-assisted stress relaxation mechanism at the crack tip.     

Measurement of Very Slow Crack Growth in Glass

The rate of very slow crack growth in glass is measured by inducing small, controllable changes in the direction of propagation of Hertzian cone cracks at known times. After completion of a growth sequence, the sample is sectioned to reveal the fracture surface. The stress intensity factor at each stage of crack growth is calculated by using finite-element modeling of the stresses near the crack tip. Data are presented for crack growth velocities as low as 10⁻¹⁴ m/s in soda–lime glass. These data provide strong evidence for the existence of a subcritical limit for crack growth in this material.     

Crack-tip Degradation Processes Observed during in situ Cyclic Fatigue of Partially Stabilized Zirconia

It is proposed that reduced transformation zone widths in Mg-PSZ in cyclically versus critically propagated cracks are due to reductions in the crack-tip toughness, consistent with an intrinsic cyclic fatigue mechanism. Cyclic fatigue crack growth in Mg-PSZ was observed in situ in a SEM. Following cyclic fatigue, the samples were critically broken and the fracture surfaces observed. Extensive crack bridging by the precipitate phase was observed near the crack tip, and it is proposed that this crack bridging significantly affects the material's intrinsic toughness. Frictional degradation of the precipitate bridges occurs during cyclic loading and hence reduces the critical crack-tip stress intensity factor for crack propagation. Reductions in the critical crack-tip stress intensity factor also lead to reductions in the transformation zone widths during cyclic loading and hence the level of crack-tip shielding caused by phase transformation. This appears to be the mechanism of cyclic fatigue. A degree of uncracked ligament bridging was also observed and is linked with the frequency of random large precipitates. However, analysis shows that its effect upon crack growth rates under cyclic load is limited.     

The effects of frequency on fatigue threshold and crack propagation rate in modified and unmodified polyvinyl chloride

The cyclic fatigue crack behavior of polyvinyl chloride (PVC), with (PVC‐M) and without (PVC‐U) chlorinated polyethylene (CPE) impact modifier, was studied. The effect of impact modifier upon fatigue crack growth rate and threshold was evaluated at frequencies of 1, 7, and 20 Hz. It was shown that the addition of CPE lowered the threshold stress intensity factor amplitude for crack growth (ΔK_th) of PVC‐M compared to that of PVC‐U at lower frequencies, and that the effect became more pronounced at lower frequency. At lower stress intensity factor amplitudes (below ΔK = 1 MPa·m^1/2), there was a slight difference between the crack growth rates of U‐ and M‐PVC. The crack advance mechanism is investigated by microscopic observation of the crack tip process zone. Although the zone is relatively large in PVC‐M, associated with higher toughness, it did not improve the fatigue crack growth resistance significantly. Fracture surface observations reveal a higher density of fibrils on the fatigued surface of PVC‐M with the density, relative to that observed in PVC‐U, reducing with frequency. It is therefore hypothesized that accelerated fibril failure is a mechanism of fatigue. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Damage Development and Moduli Reductions in Nicalon—Calcium Aluminosilicate Composites under Static Fatigue and Cyclic Fatigue

Unidirectional and cross-ply Nicalon fiber-reinforced calcium aluminosilicate (CAS) glass-ceramic composite specimens were subjected to tension–tension cyclic fatigue and static fatigue loadings. Microcrack densities, longitudinal Young's modulus, and major Poisson's ratio were measured at regular intervals of load cycles and load time. The matrix crack (0° plies) density and transverse crack (90° plies) density increased gradually with fatigue cycles and load time. The crack growth is environmentally driven and depends on the maximum load and time. Young's modulus and Poisson's ratio decreased gradually with fatigue cycles and load time. The saturation crack densities under fatigue loadings were found to be comparable to those under monotonic loading. A matrix crack growth limit strain exists, below which matrix cracks do not grow significantly under fatigue loading. This limit coincides with the matrix crack initiation strain. Linear correlations between crack density and moduli reductions obtained from quasi-static data can predict the moduli reductions under cyclic loading, using experimentally measured crack densities. A logarithmic correlation can predict the Young's modulus reduction in a limited stress range. A fatigue crack growth model is proposed to explain the presence of two distinct regimes of crack growth and Young's modulus reduction.     

Fatigue Crack Growth from Small Surface Cracks in Transformation-Toughened Ceramics

A theoretical model based on the theory of complex potentials and dislocation formalism is used to simulate the fatigue crack growth of small cracks in a transformation-toughened ceramic. Assuming power-law crack growth in which the growth rate depends on the effective stress intensity at the crack tip instead of the applied stress intensity, it is shown that the crack growth rate decreases with the applied stress intensity in the initial stage of fatigue crack growth. This is in agreement with existing experimental evidence for the growth of small cracks in Mg-PSZ. New experimental results obtained by in situ observation in a scanning electron microscope of a similar material confirm this behavior. The numerical results also confirm the plausibility of using the steady-state toughness value obtained from quasi-static crack growth as a normalizing parameter in the power-law for fatigue crack growth.     

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.     

Inelastic relaxation in silica via reactive molecular dynamics

Silica glass exhibits rate-dependent and irreversible processes during deformation and failure, resulting in inelastic effects. To explore this phenomena, molecular dynamics simulations of structural relaxation surrounding a crack tip in silica glass were performed at four different temperatures (100, 300, 600, 900 K) using a reactive force field. Per-atom stresses were found to relax during the simulation, with the highest stress relaxation occurring at 900 K. Stress relaxation was radially dependent relative to the crack tip, with stress dissipation occurring primarily within a 25–30 Å inelastic region. Within 10 Å of the crack tip, the defect concentration decreased from 0.18 to 0.09 #/nm² during inelastic relaxation at 900 K. Conversely, the defect concentration 20 Å from the crack tip increased from 0.105 to 0.118 #/nm² at 300 K, and from 0.113 to 0.126 #/nm² at 600 K, which formed a defect-enriched region ahead of the crack tip. The difference in defect concentrations suggests the possibility of a stress mediated defect migration mechanism, where defects move away from the crack tip during inelastic relaxation. Additionally, defect speciation indicated that undercoordinated silica defects, such as non-bridging oxygen, were removed through the formation of higher coordination defects during relaxation. Overall, stress relaxation causes changes in the defect concentration profile near the crack tip, which has the potential to alter the properties of silica glass in the inelastic region during relaxation.     

Creep-Crack Growth by Damage Accumulation in a Glass-Ceramic

The growth rate, near-tip creep response, and damage processes of creep cracks in a pyroceram glass-ceramic were studied under tensile loading at elevated temperatures. The rates of crack extension were characterized as a function of the applied stress intensity factor. The damage processes which occurred near the crack tip and led to creep crack extension were identified using a replica technique and by direct observations in a scanning electron microscope equipped with a high-temperature loading stage. The accumulated creep strains near the crack tip were measured via the stereoimaging technique. The results indicate that creep-crack growth in the pyroceram glass-ceramic occurs in both continuous and discontinuous manners, with the damage processes manifested as the nucleation, growth, and coalescence of inhomogeneously distributed cavities and microcracks. Measurements of the total accumulated creep strain near the crack tip suggest that crack extension follows a critical strain criterion. Both the microcrack density and the total accumulated creep strain show similar dependence with distance from the crack tip. These observations suggest that damage accumulation and crack extension in the glass-ceramic are controlled by the near-tip creep rates.     

Nonlocal criterion of bridged cracks growth: Weak interface

A nonlocal fracture criterion with accounting of the work during bonds deformation at a fracture process zone has been implemented analytically for analysis of quasistatic cracks growth along a weak interface. The criterion consists of two clauses: (1) the necessary energy condition of the crack tip limit equilibrium which takes into account the energy release rate to the crack tip and the rate of the deformation energy consumed by bonds in the crack process zone; (2) the sufficient condition is the equality of the crack opening at the process zone trailing edge to the bond limit stretching. Subcritical and quasi-statical regimes of cracks growth are analyzed for the case of a homogeneous plate with internal straight bridged crack and bonds traction which is constant and independent of the external loading. The critical fracture stress and the crack bridged zone size in the limit equilibrium state have been determined and analyzed. The limit case of a crack which is filled with bonds is considered as a weak interface model.     

Distribution of Matrix Cracks in a Uniaxial Ceramic Composite

Conventional shear-lag analyses of matrix cracking and debonding in uniaxial composites loaded in tension predict that the matrix stress varies only very slowly with position except near existing cracks. It therefore follows that the location of subsequent cracks is very sensitive to minor local variations in matrix strength, leading to significant statistical variation in crack spacing. This question is investigated using a discrete random process model of a composite and by direct experimental measurements of crack spacing. In the limit of a completely homogeneous composite, it is shown that the crack spacing distribution tends to an inverse square distribution between the theoretical maximum spacing and half that value. The random process model recovers this behavior in the limit and exhibits an approximately Weibull distribution of crack spacings when the matrix strength has significant variance. The theoretical predictions are compared with experimental results obtained for a unidirectional ceramic-matrix composite (SiC fibers in a calcium aluminosilicate matrix). The experimental results exhibit features similar to those predicted by the model and are compatible with a matrix strength whose standard deviation is of the order of 40% of the mean strength. An important point is that, with this magnitude of strength variation, the material exhibits a significant size effect and it is essential to take this into account in estimating the mean crack spacing from the corresponding mean matrix properties.     

Creep Cavitation in a Siliconized Silicon Carbide Tested in Tension and Flexure

Cavity formation was quantified in a grade of siliconized silicon carbide containing 33 vol% silicon. The type, size, and density of cavities were determined for smooth-bar specimens tested in both tension and bending, and for indented specimens tested in tension. In both tension and bending, the volume fraction of cavities was found to be proportional to the tensile creep strain. Cavities nucleated at random locations throughout the test specimen, eventually coalescing into cracks that were the source of failure at high temperatures. In tension, the strain to failure was about 1%. In flexure, stress relaxation at the tensile surface of test specimens helped stabilize cracks that formed during creep. As a consequence, strains to failure were about twice as large in bending as in tension. In tensile specimens containing large, >300 μm, indentation cracks, cavitation was profuse near the crack tips. At a volume fraction of about 3%, cavities coalesced to form secondary cracks near the tip of the indentation crack. Cracks advanced by linkage of cavitation cracks with the indentation crack. Crack growth was intermittent, requiring the buildup of cavities in front of the crack tip before crack advance could occur. If the indentation crack length was less than about 200 μm, cavity formation at the tip of the crack was not sufficient for crack advance. In such case, failure would have to occur by cavity coalescence and crack formation at some other location in the test specimen.     

Fatigue crack retardation in polycarbonate

Results are presented from a recent study of the influence of tensile overloads on fatigue crack growth in polycarbonate. Fatigue cracks were grown under conditions of constant range in stress intensity factor in four-point bend specimens. The data presented here indicate that tensile overloads may significantly retard subsequent fatigue crack growth in polycarbonate. The period of delay in crack growth was shown to increase with the magnitude of the overload. Recovery of stable crack extension following the overload appeared to involve reinitiation of separate crack growth sites at the tip of the blunted crack tip, similar to the original crack initiation at sharp V-notches.     

氧化锆增韧陶瓷的室温动态疲劳

用动态疲劳试验法研究了３Ｙ－ＴＺＰ和３Ｙ－ＴＺＰ／Ａｌ_２Ｏ_３（２０ｗｔ％）陶瓷在空气中的室温动态疲劳，并讨论了疲劳慢裂纹扩展特性。另外利用动态疲劳数据对两种陶瓷的平均寿命进行了预测。两种陶瓷材料在室温下均存在着慢裂纹扩展，主要是由空气中水蒸汽的应力腐蚀所造成的，且裂纹是沿晶界玻璃相扩展的。相变诱发的表面压应力和裂纹尖端的正应变可提高疲劳抗力。在８００ＭＰａ应力作用下，３Ｙ－ＴＺＰ和３Ｙ－ＴＺＰ／Ａｌ_２Ｏ_３（２０ｗｔ％）的平均寿命分别为２４ｍｉｎ和７２ｈ，平均寿命随应力的增大而缩短．     

Torsion fatigue response of self-healing poly(dimethylsiloxane) elastomers

Incorporating self-healing functionality in a polysiloxane elastomer successfully retards the growth of fatigue cracks under torsional fatigue loading. The fully in situ self-healing material consists of a microencapsulated vinyl-terminated poly(dimethylsiloxane) resin containing platinum catalyst compounds and a microencapsulated initiator (methylhydrosiloxane), embedded in a poly(dimethylsiloxane) elastomer matrix. A torsion fatigue test protocol is adopted to assess the self-healing performance of two different elastomeric matrices. Significant recovery of torsional stiffness occurs after approximately 5 h, the time required to achieve a measurable degree of cure of the healing agents. Total fatigue crack growth in a self-healing specimen is reduced by 24% in comparison to relevant controls. The retardation of growing fatigue cracks is attributed, in part, to a sliding-crack-closure mechanism, where polymerized healing agent shields the crack tip from the applied far-field stress.     

Modeling Slow Crack Growth Behavior of Glass Strengthened by a Subcritical Tensile Stress Using Surface Stress Relaxation

Glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. It has been observed by several authors that when an oxide glass with a large crack is held under a subcritical stress intensity (where no slow crack growth occurs) in room‐temperature water vapor or liquid water, upon reloading to a higher stress intensity, a finite restart time is observed prior to measurable crack extension. This phenomenon of apparent strengthening, or crack arrest, has been attributed to concepts such as corrosive dissolution of the crack tip, crack tip blunting, or water diffusion, and subsequent swelling of the material around the crack tip. Recently, a newly observed surface stress relaxation process that is aided by molecular water diffusion was used to improve the mechanical strength of glass fibers and to explain the subsurface compressive stress peak observed in ion‐exchange strengthened glasses. The same process is employed here to explain these delayed slow crack growth data. A simple mathematical model has been developed utilizing water‐assisted surface stress relaxation and fracture mechanics. Predictions of restart times using the model agreed well with published experimental data, indicating that surface stress relaxation is responsible for the anomalous delayed slow crack growth behavior.     

Fatigue Mechanisms in Graphite/SiC Composites at Room and High Temperature

Some deductions have been made from fractographic evidence about mechanisms of low-cycle mechanical fatigue in plain woven graphite/SiC composites at room and high temperature in vacuum. At both room temperature and 830°C, fatigue appears to be confined to the crack wake, where attrition reduces the efficacy of bridging fibers. It is inferred that the crack tip advances at some critical value of the crack tip stress intensity factor, as in monotonic growth, rather than by any intrinsic fatigue mechanism in the matrix. However, the manifestations of attrition are very different at room and high temperatures. At high temperature, wear is greatly accelerated by the action of SiC debris within the crack. This distinction is rationalized in terms of the temperature dependence expected in the opening displacement of a bridged crack. This argument leads in turn to plausible explanations of trends in loadlife curves and the morphology of cracks as the temperature rises.