Subcritical Crack Growth Rate Research Articles

Application of Asymmetric Notched Semi-Circular Bending Specimen to Evaluate Mixed-Mode I-II Fracture Behaviors of Sandstone

In this paper, to investigate mixed-mode I-II fracture behaviors, three different asymmetric notched semi-circular bending specimens (ANSCB) were designed by adjusting the angle and the distance between supporting rollers to conduct asymmetric three-point bending tests. Several aid technologies, including acoustic emission (AE), digital image correlation (DIC), crack propagation gauge (CPG), and scanning electron microscopy (SEM), was utilized to monitor and assess the fracture characteristic. Meanwhile, the fractal dimension of the fracture surface was assessed based on the reconstructed digital fracture surface. The results show that mixed-mode I-II ANSCB three-point bending fracture is a brittle failure with the characteristics of the main crack being rapidly transfixed and the bearing capacity decreasing sharply. Based on the DIC method, the whole fracture process consists of a nonlinear elastic stage, fracture process zone, crack initiation stage and crack propagation stage. The crack initiation is mainly caused by the tension-shear strain concentration at the pre-existing crack tip. At the microscale, the crack propagation path is always along the grain boundary where the resultant stress is weakest. According to the monitoring of the AE, it can be found that micro-tensile cracks are mainly responsible for the asymmetric three-point bending fracture. The data obtained by CPG suggest that the subcritical crack growth rate is positively correlated to the ultimate load. In addition, asymmetric loading leads to a coarser fracture surface, and thus a higher fractal dimension of the fracture surface. The current study can provide a better understanding of the mixed-mode I-II fracture behaviors of rock.

On-chip environmentally assisted cracking in thin freestanding SiO2 films

An on-chip fracture mechanics method is extended to characterize subcritical crack growth in submicron freestanding films. The method relies on a self-actuated concept based on MEMS fabrication principles. The configuration consists of a notched specimen attached to actuator beams involving high internal stress. Upon release, a crack initiates at the notch, propagates, and arrests. Several improvements are worked out to limit the mode III component and to avoid crack kinking. The method is applied to subcritical crack growth in 140-nm-thick SiO2 films under different humidity conditions. The data reduction scheme relates crack growth rate to stress intensity factor. The static fracture toughness value is ~ 0.73 MPa sqrt{mathrm{m}}, with standard error of 0.01 MPa sqrt{mathrm{m}} and standard deviation of 0.17 MPa sqrt{mathrm{m}}. Subcritical crack growth rates are much smaller than in bulk specimens. A major advantage is that many test samples can be simultaneously monitored while avoiding any external equipment.Graphic

Compactive Deformation of Sandstone Under Crustal Pressure and Temperature Conditions

AbstractThe transition from macroscopically brittle to macroscopically ductile deformation in porous sandstones is known to be pressure dependent, with compactive, ductile behavior occurring only once significant effective pressures have been reached. Within the crust, such effective pressures are associated with burial depths in the range 0.5–6 km, where the temperature is likely 35°C–200°C. To test the importance of such elevated temperature on the strength and deformability of sandstone, a series of constant strain rate, triaxial deformation experiments were performed on three different water saturated sandstones at either ambient temperature or 150°C. For each sandstone, an effective pressure range was used which spanned both the brittle and ductile deformation regimes, up to a maximum of 120 MPa. In the brittle regime, we observed a temperature‐dependent lowering of the yield stress of between 8% and 17%. Within the ductile regime, we observed an even greater reduction in the yield stress of between 9% and 37%. A further notable observation is that the transition from dilatant, brittle behavior to compactive, ductile behavior tends to occur at a lower effective pressure at elevated temperature. The weakening observed at elevated temperature can be explained by a reduction in fracture toughness, which is shown mathematically to cause greater weakening in the ductile regime than in the brittle regime. The apparent reduction in fracture toughness at elevated temperature is potentially driven by a combination of a reduction in surface energy and, to a minor extent, an increase in subcritical crack growth rate.

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.

Use of DC voltage fluctuation method to investigate real-time Mode I and Mode II subcritical crack growth behavior in gypsum rock

Subcritical crack growth strongly influences the mechanical behavior of rock and the precursory phase of geohazards and catastrophic failure. In earlier studies, indirect measuring methods were used to investigate the subcritical crack growth behavior of rock materials. However, these methods cannot fully reflect the whole process of subcritical crack growth of geomaterials. Therefore, in this study, a new method (DC voltage fluctuation method) was developed which can monitor the whole process of crack growth and measure the crack growth rate in real time. This method is based on the monitoring principle of change in voltage caused by the change in resistance. Then, the whole processes of Mode I and Mode II subcritical crack growth of gypsum specimen were monitored in real time by the self-designed fracture strain gauge, which consists of 10 breakable resistance wires, and a DC voltage signal monitor. Furthermore, using the measured crack growth rates and the stress intensity factors of varying crack path lengths, the parameters of the modified Charles model were fitted. The results show that: (1) the subcritical crack growth process mainly includes three stages: cracking latent period (primary stage), steady-state crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period lasts for the largest proportion of the entire fracture process duration. The duration of each stage decreases gradually with increasing applied load. (2) In the steady-state crack growth stage, both Mode I and Mode II crack growth rates increase with increasing applied load. However, the crack growth rates in the accelerated stage are basically the same with increasing applied load. When a specimen is subjected to a given constant applied load, the subcritical crack growth rate of Mode II is higher than that of Mode I in the secondary and tertiary stages. (3) The parameters A and n of the subcritical crack growth model (modified Charles model) (secondary stage) increase with increasing external applied load. The parameters are closely associated with the size of fracture process zone at the crack tip. The results of this study can provide a deeper insight into the macroscopic failure of rock, and also provide the parameters for the time-dependent damage evolutional process of underground constructions.

Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model

Abstract A three-dimensional discrete element grain-based stress corrosion model incorporating the theories of subcritical crack growth and chemical reaction rate was built to explore the time-dependent behavior of damage evolution and fracture patterns of brittle rocks on a mesoscopic scale. The model was first validated and the model accurately captured the evolution of damage (tensile and shear microcracks) on the mesoscopic scale and the macroscopic mechanical behavior (the strength, and failure patterns) observed in laboratory experiments. The subcritical parameters of the model were calibrated to match the time-dependent damage deformation behavior observed in laboratory experiments. The time-dependent numerical results replicated the typical decelerating-accelerating axial strain behavior seen in laboratory brittle creep experiments. The crack propagation pattern in the simulation indicated that tension cracks were dominant. The results of numerical simulation showed that the time-to-failure during brittle creep decreased with the increase of the stress level, while the initial strain value, initial damage value, and minimum creep strain rate increased, as observed previously in the laboratory. We conclude therefore that the presented model supports a rich set of grain-scale discontinuities that can be related to microstructural features and provides a deeper understanding of the evolution of time-dependent damage on the mesoscale.

Hydrogen Embrittlement of Low Alloy Steels Under Cathodic Polarization

Hydrogen embrittlement of low alloys steels at three different strength levels (745 Mega Pascals [MPa], 904 MPa, and 1,166 MPa) were evaluated under cathodic polarization. Crack growth rate measurements were performed under constant stress intensity (K) conditions, as a function of applied K values as well as applied potential to characterize the behavior of the three different steels. At −1,050 mVSCE saturated calomel electrode (SCE), the threshold stress intensity (Kth) value increased from 44 MPa√m to 60 MPa√m as the yield strength decreased from 1,166 MPa to 745 MPa. The crack growth rate at 66 MPa√m and −1,050 mVSCE decreased from 3 × 10−5 mm/s to 4 × 10−8 mm/s as the yield strength decreased from 1,166 MPa to 745 MPa. For the 1,166 MPa steel at low values of K, the crack growth rate decreased by two orders of magnitude as the potential decreased from −1,000 mVSCE to −950 mVSCE. At higher values of K, the effect of potential on the crack growth rate was not as significant. The 745 MPa steel in general exhibited slow crack growth rate values (2 to 4 × 10−8 mm/s) over the range of K values and applied potentials in which it was evaluated. Water adsorption on fresh metal surfaces in the estimated crack tip chemistry was modeled using density functional theory. The variation in crack growth rate with applied potential at low and intermediate values of K correlated with the fractional coverage of water adsorption on the fresh metal surface. It is proposed that the water reduction reaction and the subsequent generation of hydrogen are the rate limiting steps in the slow subcritical crack growth rate processes for low alloy steels under the conditions evaluated. For the higher values of K, where the crack growth rate showed a weak dependence on applied potential, water reduction, and generation of hydrogen are likely not the rate limiting steps.

The Role of Microstructure on Damage Tolerance in Nano-Bainitic Steels

Three nanostructured bainitic steels have been produced by austempering at 250, 300 and 350°C respectively after a similar austenitization treatment at 950°C. It has been found that a decrease in austempering temperature causes increase in content of bainitic ferrite (BF) as well as refinement of BF and retained austenite (RA) resulting in strengthening of the steel. However, results of sub-critical fatigue crack growth rate tests on these steels revealed that the steel transformed at higher austempering temperature which showed coarser morphology of BF and RA and also higher content of RA are more damage tolerant. It appeared that the thickness of BF plates and its volume fraction in the microstructure plays a major role in enhancing the strength whereas improved damage tolerance has been attributed to higher content of ductile phase RA. Scanning electron microscopy, nano-indentation and surface profilometry techniques revealed that the larger plastic zone size, higher amount of strain energy consumed during austenite to martensite transformation (TRIP effect) and tortuous crack path are the main factors for slower fatigue crack propagation rates in steel with the coarser morphology and higher retained austenite content.

An experimental setup for characterizing subcritical debonding of materials interface under mixed mode fatigue loading

A mixed mode bending experimental setup was developed for quantifying the subcritical debonding growth behavior for materials interfaces under a full spectrum of loading mode mixity. In the experimental system, the control program calculates and adjusts the cyclic bending forces to maintain a constant phase angle at the prescribed value. The relationship between the subcritical crack growth rate and the applied strain energy release rate range is obtained by post-processing the experimental results with analytical formulas. As a preliminary application example, a phase-angle dependent power-law model was constructed for the subcritical debonding growth rate of the Al-epoxy interface. It was observed that both the logarithm of the scaling constant and the power-law exponents of the subcritical debonding growth model exhibit linear relationships with the phase angle.

Influence of Polymer Substrate Damage on the Time Dependent Cracking of SiNx Barrier Films

This work is concerned with the long-term behavior of environmentally-assisted subcritical cracking of PECVD SiNx barrier films on polyethylene terephthalate (PET) and polyimide (PI) substrates. While environmentally-assisted channel cracking in SiNx has been previously demonstrated, with constant crack growth rates over short periods of time (<1 hour) during which no substrate damage was observed, the present experiments over longer periods reveal a regime where cracking also develops in the polymer substrate. This time-dependent local cracking of the polymer underneath the channel crack is expected based on creep rupture or static fatigue. Our combined in-situ microscopy and finite-element modeling results highlight the combined effects of neighboring cracks and substrate cracking on the crack growth rate evolution in the film. In most cases, the subcritical crack growth rates decrease over time by up to two orders of magnitude until steady-state rates are reached. For SiNx on PI, crack growth rates were found to be more stable over time due to the lack of crack growth in the substrate as compared to SiNx on PET. These results provide a guideline to effectively improving the long-term reliability of flexible barriers by a substrate possessing high strength which limits substrate damage.

Effect of sandblasting on bending strength and subcritical crack growth of the dental zirconia ceramics

Objective: To evaluate the effect of sandblasting on bending strength and subcritical crack growth (SCG) under cyclic loading of yttria-stabilized tetragonal zirconia polycrystal (Y-TZP) ceramics. Methods: After being polished, sixty bar-shaped specimens of Y-TZP (Wieland zirconia ceramics) were assigned to two groups (n=30) according to the random number table, the sandblasting group (SG) which was treated with sandblasting and the control group (CG) which remained untouched. In each group, half of the specimens (n=15) were subjected to bending strength test, and the results were examined by Weibull statistics and analyzed with ANOVA. The other 15 specimens in each group were subjected to fatigue tests. The results were examined by Weibull statistics and subcritical crack propagation rates were calculated. Results: The bending strengths of SG and CG were (1 291±133) and (1 140±124) MPa (F=10.117, P=0.004), and the Weibull modules of the two groups were 11.06 and 10.64 respectively. The crack growth rate of SCG of SG was lower than that of CG under the same cyclic loading. Conclusions: Proper sandblasting on Y-TZP ceramic can increase its bending strength and resistance to SCG.

Adhesion improvement of silicon/underfill/polyimide interfaces by UV/ozone treatment and sol–gel derived hybrid layers

Adhesion and mechanical reliability improvement is an important issue for flexible electronics due to weak bonds between silicon/underfill/polyimide interfaces. These interfaces are bonded with weak hydrogen and ester bonds which are vulnerable to humidity. Therefore, in this study, adhesion and reliability of silicon/underfill/polyimide interfaces are enhanced by using UV/Ozone treatment and sol–gel derived hybrid layers. In order to examine the effectiveness of those surface treatment methods, double cantilever beam (DCB) test and subcritical crack growth test were applied to accurately measure the adhesion energy and subcritical crack growth rate. The results showed that the adhesion and reliability against humidity were enhanced by more than 300% and 1000% when both surface treatment methods were applied. Also, the adhesive failure path was altered to mixed mode failure of both cohesive and adhesive failure paths.

OS2112 部分安定化ジルコニアのR曲線及び皮労き裂進展挙動

R-curve and fatigue crack growth behavior of partially stabilized zirconia were studied using indentation-strength-in-bending (ISB) method and static and cyclic fatigue tests. The indentation-strength measurements in ISB method indicated that there is no increasing crack extension resistance, that is, a flat R-curve behavior. On the other hand, the relation between crack growth rate and stress intensity factor in subcritical crack growth obtained from lifetime measurements in the static and cyclic fatigue tests indicated that the cyclic loading accelerated the subcritical crack growth rate. X-ray diffraction patterns of fracture surfaces showed that stress induced phase transformation from tetragonal to monoclinic occurred by the loading. As the results, it is considered that the R-curve appeared to be rising fast but saturated at high toughness value, and the micro cracks induced by cyclic loading facilitated the subcritical crack growth.

The Acoustic Emission Method Application for Producing a Growing Sharp Crack and Evaluation of the Fracture Toughness of Ceramic Materials

A method has been developed for producing a sharp crack and evaluating the fracture toughness characteristics of ceramic materials from the acoustic emission parameters. The method involves the use of a computer-aided measuring and control system and the appropriate FAE 1.0 software. With this method, it is possible to determine the important characteristics of the fracture toughness of ceramics, such as the R-curve for a fixed crack growth rate and V − K 1-diagram in a wide range of subcritical crack growth rates.

An Environmentally Assisted Cracking Evaluation of UNS C64200 (Al–Si–Bronze) and UNS C63200 (Ni–Al–Bronze)

A recent failure of a union nut, UNS C64200, made of Al–Si–Bronze (ASB) in a breathing air system of a marine platform has highlighted the need for environmentally assisted cracking (EAC) data for both ASB and Ni–Al–Bronze UNS C63200 (NAB) components in environments relevant to marine use. In addition, the possibility of exposure to ammonia environments via cleaning agents or biological processes warrants consideration because of the known susceptibility of bronze to EAC in ammonia environments. A displacement-controlled, rising step load (RSL) technique was employed on precracked compact tension specimens to quantify and compare the threshold stress intensities for EAC in air, seawater (SW), and SW + ammonia environments for wrought ASB and NAB materials. These results are compared to calculations of the stress intensity in service to determine the probability of EAC initiation. ASB was found to be susceptible to subcritical intergranular EAC initiation in laboratory air, SW, and SW + ammonia environments. NAB was immune to EAC under the conditions tested in laboratory air and SW, but was susceptible to intergranular EAC in SW + ammonia solution. The threshold stress intensity in SW + ammonia was found to be similar for both ASB and NAB; however, the subcritical crack growth rate for NAB was found to be 2–3 times faster than ASB. Calculations of stress intensity indicate that, in the air system applications where the installation torques are higher, the likelihood of subcritical cracking in ammonia environments is high. Stress intensities approach the ASB threshold values for subcritical intergranular cracking in air when the defect depth approaches half the wall thickness of the nut.

Effect of frequency on high-temperature fatigue crack growth in a silicon carbide reinforced silicon nitride composite

A detailed study on a silicon nitride reinforced with silicon carbide whiskers, Si3N4SiCW, has been undertaken at elevated temperature during static and dynamic loading at increasing K and ΔK respectively. It is shown that cyclic sub-critical crack growth rates are lower than static crack growth rates. The increased crack growth rate during static far field loading is attributed to the stress relaxation of the inter-granular glass phase which allows time-dependent processes to occur ahead of the crack tip which lead to enhanced sub-critical crack growth rates. During cyclic fatigue the glass phase has insufficient time to relax and glassy ligaments are able to bridge the crack wake thereby shielding the crack tip from the full force of the applied load. Also, at particular temperatures, bridging between the surfaces of the crack wake by the inter-granular glass phase results in increased strength and fatigue retardation. The extent of ‘crack wake healing’ is shown to be time and temperature dependent. The viscosity of the glass phase is directly related to the temperature and the bonding force associated with glass phase bridging is observed to reduce with increasing temperature. The results from a previous study at room temperature are compared to those found during this investigation.

Adhesion Reliability Enhancement of Silicon/Epoxy/Polyimide Interfaces for Flexible Electronics

Adhesion and mechanical reliability of silicon/epoxy/polyimide interfaces are critical issues for flexible electronics. Bonds between these interfaces are mainly hydrogen bonds, so their adhesion is weaker than cohesive fracture toughness and vulnerable to moisture. In order to enhance adhesion and suppress moisture-assisted debonding, UV/Ozone treatment and innovative sol-gel derived hybrid layers were applied to silicon/epoxy/polyimide interfaces. The fracture energy and subcritical crack growth rate were measured by using a double cantilever beam (DCB) fracture mechanics test. Results showed that UV/Ozone treatment increased the adhesion, but was not effective for improving reliability against humidity. However, by applying sol-gel derived hybrid layers, adhesion increase as well as suppresion of moisture-assisted cracking were achieved.

The effect of water penetration on crack growth in silica glass

Due to the high stresses at crack tips, stress-enhanced water diffusion into silica occurs and gives rise to a volume expansion zone around the tip. This zone leads to a fracture mechanics shielding effect. In the present paper, the diffusion equation for water into glass is solved in cylindrical coordinates including the effect of the mechanical swelling stresses on the diffusivity. As an application of the volume swelling in the crack-tip region, the shielding stress intensity factor is calculated and the relation between subcritical crack growth rate and the crack tip stress intensity factor is derived from an existing crack growth rate versus applied stress intensity factor curve. The general mathematical procedure is outlined in detail and experimental results are discussed, giving evidence for crack-tip diffusion of water and a consequent zone of swelling around the crack tip.

Experimental investigation of surface energy and subcritical crack growth in calcite

[1] Subcritical cracking behavior and surface energies are important factors in geological processes, as they control time-dependent brittle processes and the long-term stability of rocks. In this paper, we present experimental data on subcritical cracking in single calcite crystals exposed to glycol-water mixtures with varying water content. We find upper bounds for the surface energy of calcite that decrease with increasing water concentration and that are systematically lower than values obtained from molecular dynamics simulations. The relation of surface energy to water concentration can explain water weakening in chalks. The rate of subcritical crack growth in calcite is well described by a reaction rate model. The effect of increasing water on crack velocity is to lower the threshold energy release rate required for crack propagation. The slope of the crack velocity curve remains unaffected, something which strongly suggests that the mechanism for subcritical cracking in calcite does not depend on the water concentration.

Nano-mechanics based modeling of lifetime distribution of quasibrittle structures

The statistics of structural lifetime under constant load are related to the statistics of structural strength. The safety factors applied to structural strength must ensure failure probability no larger than 10 - 6 , which is beyond the means of direct verification by histogram testing. For perfectly brittle materials, extrapolation from the mean and variance to such a small tail probability is no problem because it is known that the Weibull distribution applies. Unfortunately, this is not possible for quasibrittle materials because the type of cumulative distribution function (cdf) has been shown to vary with structure size and shape. These are materials with inhomogeneities and fracture process zones (FPZ) that are not negligible compared to structural dimensions. A probabilistic theory of strength of quasibrittle structures failing at macro-crack initiation, which can be experimentally verified and calibrated indirectly, has recently been deduced from the rate of jumps of atomic lattice cracks governed by activation energy barriers. This paper extends this nano-mechanics based theory to the distribution of structural lifetime. Based on the cdf of strength and a power law for subcritical crack growth rate, the lifetime cdf of quasibrittle structures under constant loads is derived. The lifetime cdf is shown to depend strongly on the structure size as well as geometry. It is found that, for the creep rupture case, the mean structural lifetime exhibits a very strong size effect, much stronger than the size effect on the mean structure strength. The theory also implies temperature dependence of the lifetime cdf. For various quasibrittle materials, such as industrial ceramics and fiber composites, it is demonstrated that the proposed theory correctly predicts the experimentally observed deviations of lifetime histograms from the Weibull distribution.