Subcritical Crack Growth Mechanisms Research Articles

Subcritical crack growth models for SiC fiber in air and steam: Low temperature data and possible effects of residual stress

Failure times (tf) and brittle creep strain rates (ἑ) for static fatigue of Hi-Nicalon™-S fiber tows were measured at 500 and 600 °C. These measurements added to those done previously at 700–1100 °C. Subcritical crack growth (SCG) based models developed to predict tf and ἑ from the 700–1100 °C data were modified to include the additional data. Parameters for two SCG laws were determined for air and Si(OH)4 saturated steam environments, and an additional parameter for effective room-temperature residual stress (σRo) along the crack path was introduced. Tow failure was modelled as sequential filament failure by SCG from weakest to strongest in a Weibull distribution. The increase in stress on intact filaments as they oxidized and as other filaments failed caused brittle creep strain. SCG-based models for both surface and interior cracks were considered. Orthogonal direction regression (ODR) was used to find the best parameter fits to data. Faster numerical methods to find the global parameter-space minima and avoid local minima were developed. New model parameters were determined using the entire 500–1100 °C tf and ἑ data set, done at initial applied stresses from 260 to 1526 MPa. In air, measured tf and ἑ at 500 and 600 °C follow the trends previously observed for higher temperatures. However, beneath 700 °C in steam, tf are longer and ἑ are much slower than expected. They are similar to values measured for air, suggesting an SCG mechanism change between 700° and 600 °C in steam. An atomistic SCG law-based model with activation energy (Q) of 310 kJ/mol and σRo of ∼200 MPa compression is suggested to be appropriate for static fatigue in air. An atomistic SCG law-based model with Q of 360 kJ/mol and σRo of ∼0 MPa best fit data measured in steam. However, differences in data fit quality between models were small, so firm conclusions about the correct model, residual stress effects, and associated crack paths could not be made. As stress approaches zero, the model converges to tow failure times that are the times for complete fiber oxidation. As failure times approach zero and temperatures decrease, the model converges to tow strengths predicted by fiber bundle theory at room temperature. The sources of error in data fit, the merit of different SCG models, and the possible roles of residual stress in SCG for Hi-Nicalon™-S fibers are discussed.

Subcritical crack growth models for static fatigue of Hi‐NicalonTM‐S SiC fiber in air and steam

AbstractThree subcritical crack growth (SCG) laws were used to model strain‐rates and failure times for static fatigue of Hi‐NicalonTM‐S SiC fiber tows in air and Si(OH)4(g)‐saturated steam. Models were fit to tow failure times (tf) and steady‐state strain rates (ἑ) for brittle creep measured at 700 to 1100°C under initial applied stresses (σA) of 260 to 1260 MPa. A power law, a reaction‐rate law, and a bond‐energy law were used to describe SCG that caused sequential filament failure, and ultimately tow failure. Two versions of each model were developed. One allowed access of chemisorbed species to flaws throughout the fiber (mode 1) and another only allowed access to flaws at the SiC‐SiO2 interface (mode 2). The stress increase on intact filaments as others fractured and as filaments oxidized, and the increase in stress intensity geometric factors (Y) as crack size increased were incorporated in the models. The fits to data were compared for the different models by using both simple regression analysis and orthogonal distance regression (ODR) analysis. Faster convergence and more consistent results were achieved using ODR analysis. Regression analyses found parameters for all models with similar error in data fits, so validity of a model could not be distinguished by regression analysis alone. For all models, the stress dependence of SCG rates was much stronger in steam than in air, and for most models activation energies were between 300 and 420 kJ/mol, regardless of environment. For the steam environment, the bond‐length parameter (δ) for the bond‐energy model was very close to the lattice parameter of β‐SiC (.436 nm), but in air it was significantly lower at 0.25‐0.26 nm, but still larger than the Si‐C bond length of 0.189 nm. Other factors suggest that either a bond‐energy based law or a modified version of a reaction‐rate law are the best choices for a SCG law. Filament strength distributions initially described by Weibull distributions could not be described by such distributions after application of the models. SCG mechanisms are discussed.

Effect of microstructure and chemical composition on subcritical crack growth in SiC-based fiber tows

SiC-based fibers, a key component for the reinforcement of thermostructural ceramic matrix composites, are subjected to subcritical crack growth (SCG) causing their delayed failure. Stress exponents <10 were reported for various fiber types, standing out from other types of ceramic or glass. The continuum of silicon oxycarbide (SiCO) and carbon free phases is suspected to govern the environmentally assisted crack growth phenomenon, highlighted by relationships between SCG parameters and oxygen or carbon free contents. Metallic heteroelements (Ti or Zr, found in Tyranno® fibers) play a critical role on this sensitivity as well. The existence of 2 distinct groups of fiber types, possibly associated to different SCG mechanisms, is discussed.

Subcritical Crack Growth and Progressive Failure in Carrara Marble Under Wet and Dry Conditions

AbstractOur concept of progressive rock slope failures is on the one hand embedded in aggregated subcritical crack growth mechanisms and on the other sensitive to environmental conditions, especially water. To anticipate failure dynamics in rock slopes, it is a key requirement to reveal the influence of water on subcritical crack growth mechanisms and material properties. We present experimental data on the time‐dependent deformation of an exemplary rock, Carrara marble. We employed inverted single‐edge notch bending creep tests on large Carrara marble samples to mimic an open joint system with controlled water supply. Constant stress was applied in two steps approaching 22–85% of a previously determined critical baseline stress. Introducing calcite‐saturated water to subcritical stressed samples caused an immediate increase in strain by up to an order of magnitude. Time‐dependent accumulation of inelastic damage at the notch tip occurred in wet and dry samples at all load levels. Subcritical crack growth and the evolution of localized intergranular fractures are enhanced if water is present and readily approach tertiary creep when loaded above 80%. The immediate strain response is attributed to the reduction of surface energy and diffusion of the water into the rock. The resultant more compliant and weaker rheology can even turn the subcritical stress into a critical state. Over time, subcritical and chemically enhanced mechanisms progressively alter especially grain boundaries, which become the key controls of progressive failure in Carrara marble.

Testing Study of Subcritical Crack Growth Mechanism During Water Rock Interaction

Subcritical crack growth plays an important role in evaluating the long-term stability of structures in rocks. By applying the constant-displacement-relax method, two groups of test specimens that one immersed in groundwater and the other in air were tested to get the parameters of subcritical crack growth in double torsion test. The relations of the stress intensity factor K I versus the subcritical crack growth velocity V were obtained under the two different environments, and the behavior of subcritical crack growth was also analyzed. The results showed: the relations of lg K I − lg V accorded with linear rules, which is in good agreement with Charles theory; Compared with specimens in nature state, the lg K I − lg V curves of saturated water specimens locate top left comer of those of air specimens. The slope of curve is smaller, and the intercept is bigger, which shows that the water–rock interaction speeds up the subcritical crack growth. And A increases 2.9 × 1018 folds but n decreases from 85.12 to 40.83 because of the water–rock interaction. Meanwhile, the fracture toughness K IC also decreases obviously from 2.55 in air to 2.26 in water due to water rock interaction. The testing results provide a basis for time-dependence of rock engineering stability.

Numerical simulation of time-independent and -dependent fracturing in sandstone

A grain-based model has been developed to simulate both the time-independent and -dependent damage evolution leading to ultimate failure. The mechanical behaviors of the Coconino sandstone during uniaxial compression, Brazilian splitting and fracture toughness tests were simulated. Simulation results are in satisfying agreement with the lab results. Mode-I, Mode-II and mixed mode subcritical crack growth mechanisms considering randomly distributed initial microcracks have been used in the calibrated time-independent model. One-edged time-dependent crack growth in the sandstone specimen due to stress corrosion has been analyzed both theoretically and numerically. It reveals that the lifetime of the specimen decreases nonlinearly with increasing length of the initial microcracks and the applied tensile load. In order to validate the developed numerical simulation scheme, a series of simulations only considering the influence of stress were conducted for a landscape arch which was assumed to be composed by the intact sandstone. The safety factor and the final failure pattern of the arch (time-independent) were determined using the strength reduction method. In parallel, the failure process of the arch due to stress corrosion (time-dependent) was studied in detail. Both approaches revealed similar final failure patterns. The proposed modeling scheme not only exhibits macroscopic mechanical response of the sandstone, but also provides deeper insight into the microscopic damage process, and allows time-related prediction of damage evolution.

Influence of temperature and humidity on the strength of low temperature co-fired ceramics

Strength degradation in glass and ceramic materials is related to subcritical crack growth mechanisms acting at the crack tip during mechanical loading. In this work the effect of humidity and temperature on the strength of a commercial low temperature co-fired ceramic was investigated using a biaxial testing procedure. Experiments were performed in argon and in air at different stress rates between 25 and 125°C. The effect of humidity on strength was assessed at room temperature varying only the relative humidity. The sole effect of temperature was evaluated in argon at high stress rates. The combined effect of humidity and temperature was determined in air, testing at different temperatures. Results showed the existence of an inert strength of the material at room temperature. Measurements in ambient air showed a counterbalance effect of temperature and humidity yielding an almost constant strength for this material between 25 and 125°C.

Multi-field modelling of hydride forming metals Part II: Application to fracture

In Part I of the present article, we formulated a continuum-based computational model for stress- and temperature-directed diffusion of hydrogen in metals that form brittle binary hydrides, such as Zr and Ti alloys. Among the space–time dependent parameters calculated by the model are the volume fraction and the mean orientation of hydride precipitates. These parameters are of importance for quantifying the embrittlement of hydrided materials. In this second part of the work, we use measured data for the strength and toughness of hydrided Zr alloys to correlate the local fracture properties of the two-phase (metal+hydride) material to the aforementioned parameters. The local fracture properties are used as space–time dependent input to a cohesive zone type submodel for fracture, which is fully integrated with the hydrogen transport model from Part I. The complete model is validated against fracture tests on hydrogen-charged Zr–2.5%Nb, a material used in nuclear reactor pressure tubes. More precisely, we study local embrittlement and crack initiation at a blunt and moderately stressed notch, resulting from gradual accumulation of hydrides at the notch during temperature cycling. We also simulate tests on crack initiation and growth by delayed hydride cracking, a subcritical crack growth mechanism with a complex temperature dependence. From the results of the simulations, we conclude that the model reproduces many observed features related to initiation and propagation of hydride induced cracks in the Zr–2.5%Nb material. In particular, it has the capacity to reproduce effects of the material’s temperature history on the fracture behaviour, which is important for many practical applications.

Crack path support for deformation mechanisms in fatigue of polycarbonate

A significant amount of research has been directed towards characterising and predicting sub-critical crack growth mechanisms in polycarbonate (PC) materials. In particular the initiation of crazes, damage evolution and growth of fatigue cracks has attracted significant attention. It is only relatively recently that there has been clarification of the underlying physics of craze initiation and growth, and of the craze influence on crack paths. In the interpretation of mechanisms of deformation, the polymer community has perhaps not embraced the use of fractographic crack path information as fully as the metals community. This paper considers the ability of advanced imaging techniques including confocal laser scanning microscopy (CLSM), and field emission scanning electron microscopy (FESEM) to provide evidence of crack path morphology for existing models of plastic deformation and crazing in amorphous polycarbonate. It also presents the outline of a new model of crack tip stresses which takes account of craze-induced shielding mechanisms and appears able to characterise fatigue crack growth in PC.

岩石のサブクリティカル亀裂進展に関する既往の研究と新たな展開

A review of studies of subcritical crack growth in rock is presented. First, theoretical background of subcritical crack growth is presented. It has been considered that the main mechanism of subcritical crack growth in silicate materials is stress corrosion under low homologous temperature and pressure. Next, theoretical background of stress corrosion is presented. Especially, the theoretical relation between the crack velocity and the stress intensity factor is described. Then, progress of the study of subcritical crack growth in silicate materials is presented by reviewing previous studies for glass, quartz, and silicate rocks. It has been clarified that the reactive species of stress corrosion is water and hydroxyl ion. For anisotropic rock, the crack velocity was dependent on the propagation direction and opening direction even at the same stress intensity factor.Finally, recent results of subcritical crack growth in rock are presented. It was clarified that the relation between the crack velocity and the stress intensity factor was decided by the crack opening direction. The crack velocity was higher when the temperature and the humidity were higher. It was shown that the activation energy became smaller when the crack path was smooth from the observation of the crack path.

Deaerator feedwater vessel weld cracking monitored over a service time of around 80,000 hours

This paper describes the fatigue crack growth data which were recorded during a 12-year study on weld cracking in a small deaerator feedwater storage vessel. The sub-critical crack growth mechanism was corrosion fatigue in nature and varied from 5×10 −9 to 5×10 −8 mm/s. Also, crack extension was tunnelled in nature and resulted in a thumbnail shape with the crack depth growth outstripping the surface crack growth rate. A detailed fractographic study indicated that flat fan-shaped facets were common and typified corrosion fatigue in high temperature aqueous conditions. The reported fatigue crack growth data were compared with published results for low alloy steels in high temperature waters in terms of frequency, average crack tip strain rate and stress intensity factor range and favourable agreement was observed in all instances.

Subcritical crack growth in Al2O3 with submicron grain size

Abstract Gelcast sintered α-Al 2 O 3 (corundum) ceramics were developed with a sub-μm grain size at densities >99%. Highly perfect samples with a minimum of flaws were prepared by an approach that maintains the high purity of the raw powder >99.99% Al 2 O 3 throughout processing. As a consequence, all grain boundaries are free of even thinnest amorphous interface films, amorphous triple junctions are ⩽150 nm, and their frequency is low. Subcritical crack growth was investigated by an approach recording growth rates as low as 10 −13 m/s. The outstanding purity of grain boundaries gives rise to a resistance against subcritical crack growth which is similar or even below that of coarser conventional alumina ceramics. No significant promotion of subcritical crack growth by water was observed for the new gelcast high-purity ceramics with grain sizes K I0 below which no crack growth would occur. The results suggest that in sintered alumina ceramics with a given purity of grain boundaries the subcritical crack-growth mechanism of stress corrosion is independent of the grain size. With their high mechanical reliability, these corundum grades are promising candidates for the use in new prostheses for joints with a high load bearing capability and with small calliper sizes.

Subcritical crack growth mechanisms in ceramic matrix composites: experimental observations and modelling

Various experimental techniques were used to identify failure mechanisms that occur under occur in continuous fibre-reinforced ceramic matrix composites containing interphases that are susceptible to oxidation. The conditions under which these mechanisms occur were dictated by environmental conditions and microstructural parameters, such as temperature, oxygen concentration, and interphase thickness. Details of the mechanical state of fibres that bridge matrix cracks, during the operation of each mechanism, were developed to allow the application of models that can predict time-dependent, subcritical crack growth. This paper will present evidence of environmentally induced crack growth and discuss a model for predicting the rate of time-dependent, subcritical crack growth.

Role of the adsorption factor in reduction of the long-term static crack resistance of high-strength steel in gaseous media

The purpose of this work was to establish the role of the adsorption layer in subcritical crack growth in high-strength steel subject to long-term static loading in controlled-composition gaseous media. Investigations of long-term crack resistance were made in a sealed chamber on 45KhN2MFA steel with an edge crack loaded by four-point bending. The gaseous media were commercially pure hydrogen and helium. The most aggressive medium was deoxygenated and dried hydrogen and the least aggressive helium. The effect of helium moisture content on crack growth kinetics was evaluated. Subcritical crack growth mechanisms were determined, by fractography with a scanning electron microscope, to be typically intergranular. Hydrogen embrittlement occurred in three stages: establishment of adsorption equilibrium, adsorbed molecule dissociation into atomic hydrogen, and transport of hydrogen atoms into the prefailure zone. Local fracture occurred as a result of a reduction in critical stress in connection with hydrogen impregnation of the prefailure zone.

The Effect of the Rate of Loading on the Strength of Glass/Epoxy and Graphite/Epoxy Composites

Abstract The strength of [0/90] crossply composites was measured at a wide range of loading rates. The specimens were loaded as beams in 3-point bending in air or water environments.The glass/epoxy composite specimens were measurably stronger at very high loading rates both in air and in water. The specimens tested in water were slightly stronger than those tested in air. The graphite/epoxy specimens were insensitive to both loading rate and environment.The results appear to show that glass/epoxy composites undergo subcritical crack growth while graphite/epoxy composites do not. However the mechanism of subcritical crack growth in glass/epoxy is not revealed by these experiments nor by other studies that have been reported in the literature. Resume Nous avons mesure la resistance des composites [0.90] a des vitesses de chargement a large gamme. Les echantillons etaient charges en flexion trois points dans un environnement d'air ou d'eau. Les echantillons de verre/epoxy etaient assez plus forts a des vites...

Investigation of the Kinetics and Mechanism of Subcritical Crack Growth by Delayed Failure of Titanium Alloys In and Out of Corrosive Environments

Abstract The kinetics of crack growth by SCC of titanium alloys in some solutions have been studied by the electrical resistivity method. The effect of cathodic polarization on crack growth rate was used for investigation of the mechanism of SCC of titanium alloys in different conditions. The hydrogen diffusion model is proposed to describe the kinetics of delayed failure of titanium alloys in the absence of a corrosive environment. According to this model, it is possible to determine DH from kinetic data. The subcritical crack growth mechanism in the absence of a corrosive environment is shown to be internal hydrogen embrittlement.

Crystallization of grain boundary phases in hot-pressed silicon nitride materials

The mechanical properties of hot-pressed silicon nitrides containing crystalline magnesium silicate phases were investigated at room temperature and at elevated temperatures. Scanning electron microscopy of fracture surfaces was used to identify the fracture-initiating flaws at room temperature and the modes of fracture at higher temperatures. The mechanical properties of these materials at elevated temperatures were interpreted in terms of a subcritical crack growth mechanism involving grain boundary sliding, which implied the presence of residual glass phases at the grain boundaries.