Subcritical Crack Growth Research Articles

Mechanical Reliability Prediction of Foldable Displays Using Subcritical Crack Growth in Siloxane-Based Cover Window by Two-Point Bending Test

Mechanical Reliability Prediction of Foldable Displays Using Subcritical Crack Growth in Siloxane-Based Cover Window by Two-Point Bending Test

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part II, Pipes subjected to bending moment

If cracks are detected in power plant pipes and the cracks are allowable, the plants can continue operating without the need for repair/replacement. The allowability of cracks is determined by means of allowable stresses, based on failure stresses. Failure bending stress at crack penetration is estimated by applying the Local Approach of Limit Load Criteria, which is based on the net-section stress approach. Using the stress at crack penetration, the allowable bending stress can be calculated for a pipe with a circumferential part-through crack. The allowable bending stress decreases with increasing crack depth and angle, as expected. However, the allowable bending stress can have one of three characters, depending on crack size: i) leak-before-break (LBB) and crack growth stability, ii) non-LBB and crack growth stability, and iii) non-LBB and crack growth instability. Character iii) represents a severe crack, and special attention needs to be paid to such a crack, even if it is allowable. Frequent non-destructive inspection and precise calculation of subcritical crack growth are recommended in order to prevent unexpected failure, especially for small-diameter thin-walled pipes. The boundaries of leak-before-break and crack growth stability can be successfully expressed by appropriate equations.

The crack shape evolution in unstable, flexural fractures for soda-lime glass beams by phase-field analysis

In this work, phase-field simulations were used to investigate the unstable crack propagation in brittle plates fractured in bending. The evolution of crack front shapes was studied considering over 20 scenarios and accounted for both the effects of the Poisson’s ratio and the plate’s width. The crack front in unstable cracks was found to be nearly elliptical only when the cracks were relatively short, with depths less than half the plate’s thickness. In general, unstable cracks resulted in intersection angles of 88°±6° between the crack front and the free surface. Higher Poisson’s ratios led to more oblong cracks but had no obvious effects on the intersection angles. It was found that the evolution of the crack shape was unaffected by the plate’s finite width up to crack lengths equal to 80% of the plate’s width. A cursory literature review on flexural fatigue cracks in steel and on subcritical crack growth in glasses suggested that the description of the crack front proposed in this work could also accurately describe the crack shapes for these types of fractures. However, differences in the behavior among these cases became more evident for crack depths larger than 60% of the plate’s thickness.

Environmental impact on the strength of subcritical cracking AlON material

Subcritical crack growth is often observed in oxide ceramics. This effect is ascribed to the interaction between the strained chemical bonds at the crack tip and water molecules present in the working environment of the material. Owing to this reaction, combined with stresses at the crack tip, slow cracking of the material and relevant strength reduction may occur. In non-oxide ceramics (i.e., without significant oxide sintering additives), no subcritical crack growth was observed. The present work demonstrates slow crack propagation in an aluminum oxynitride (AlON) material. AlON samples were prepared via sintering in nitrogen at 1800 °C. This resulted in dense translucent samples. Constant stress rate tests were carried out in both air and water to assess the influence of water on material strength. The strength results were used to further evaluate the effects of subcritical cracking. A clear decrease in strength was observed at low stress rates. Measurement points below 10 MPa/s were used to determine the lowest stress rate for inert strength. The slope of the fitting line indicated the value of subcritical cracking parameter n.

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.

Structural integrity assessment for deep-water subsea pipelines

Deep-water subsea pipelines often have to face highly challenging service conditions such as high pressure/high temperature (HP/HT). Structural integrity assessments accounting for corrosion fatigue (CF) and low-cycle fatigue (LCF) therefore are crucial from the perspective of structural safety and cost efficiency. In this paper, engineering critical assessment (ECA) and structural integrity issues of subsea pipelines associated with the HP/HT service conditions are discussed and a new specified ECA scheme is developed. The development includes two parts. In the first part, CF is addressed in 3 levels, i.e., deriving the corrosion-crack correlation model for hydrogen embrittlement (HE) influenced subcritical fatigue crack growth (SFCG), establishing the synthetic SFCG model for CF and finally utilizing the transition stress intensity factor (SIF) for achieving reasonable assessments of CF in seawater. In the second part, 2 levels of work related to LCF is performed, i.e., building up the energy principles based SFCG model for high-cycle fatigue (HCF) and adapting it to LCF. In each subpart, advancement in relevant studies is reviewed with reference to current industrial codes. The work is examined and its effectiveness is demonstrated with applications.

Subcritical growth of a crack interacting with the stress field of mobile solutes in an elastic solid in the presence of image effects: A kinetic Monte Carlo study

It is well known that the presence of foreign solutes could critically affect fracture properties of the solid solutions of critical importance to many technological advances. It has been shown recently that a prevalent continuum theory widely applied to such systems is inconsistent with classical elasticity which predicts that two point defects in an isotropic unbounded solid do not interact, and interact only in a finite solid through image stresses arising due to the presence of the boundaries. Previous studies have shown that the image stresses resulting from an external boundary of a finite solid also generally raise the stress intensity factors (SIFs) induced by the solutes at a crack tip. Here, we examine the possibility that the increase in the SIFs by image stress effects together with variations in the configuration of mobile solutes around a crack tip could from time to time push the crack tip SIFs beyond the critical value required for crack growth, and hence cause subcritical crack growth over time. Incorporating crack growth criterion in kinetic Monte Carlo (KMC) simulations and fully accounting for the image stress effects, we investigate this possibility by examining how temperature, solute concentration, and the difference between the loading-induced SIF and the critical SIF could affect crack growth. In agreement with an analysis based on the central limit theorem presented for the limit of high temperatures, our simulations indicate that the probability of the Griffith-Irwin criterion being met among various solute configurations generally increases with increasing solute concentration. The model shows that, within a certain range of the loading-induced SIF below the critical SIF, the crack growth rate increases with solute concentration, and this effect becomes particularly more evident at larger temperatures.

Pore structure evolution in andesite rocks induced by freeze–thaw cycles examined by non-destructive methods

In this paper, we compare the values of petrophysical properties before and after 100 freeze–thaw (F–T) cycles, as well as recorded length change behaviour and temperature development on a vacuum-saturated fractured andesite rock sample taken from the Babina Quarry in Slovakia using a specially-constructed thermodilatometer, VLAP 04, equipped with two HIRT-LVDT sensors. We also used non-destructive visualization of the rock pore network by µCT imaging in order to study the development of the pore structure and fracture network in pyroxene andesites during the freeze–thaw process. The results show that the andesite rock samples, due to good fabric cohesion, low porosity, and low pore interconnection, showed good resistance against frost-induced damage. However, it must be stated that the main process causing disintegration of this type of rock is fracture opening, which is caused by internal stresses induced by water–ice phase transition. The overall residual strain recorded after 100 F–T cycles was not significant, however, the increase of 31 pp in volume of the fracture showed us that repeated freezing and thawing can lead to long term deterioration in terms of subcritical crack growth in brittle-elastic solids like pyroxene-andesite rocks.

Dynamically Triggered Events in a Low Seismically Active Region of Gujarat, Northwest India, during the 2012 Mw 8.6 Indian Ocean Earthquake

ABSTRACT The mainland region of Gujarat, northwest India, is a less investigated region than other parts of India with a low seismicity rate. An Mw >4.7 earthquake has not occurred in this region for 15 yr, and no Mw >5.5 events since 1971. We analyze the local earthquake catalog and waveforms to examine dynamic triggering in the region by the 2012 Mw 8.6 Indian Ocean earthquake, which triggered widespread seismicity globally. Further detection of possibly missing microearthquakes is conducted by applying the matched filter technique to the waveforms. We identify six microearthquakes (∼ML 1.0–2.1) triggered during the surface and coda wave of the 2012 mainshock. Also, an earthquake of Mw 2.6 was likely triggered five hours after the mainshock near Bhavnagar city, because the record since 2006 would indicate such a magnitude event to have only a 0.8% chance of occurring independently any given day. Indeed, only 35 earthquakes with Mw≥2.5 were recorded since 2006 within a 100 km radius of this city. The β-statistics indicate an increase in seismicity and further confirm the triggering. The seismicity rate increased immediately after the 2012 mainshock and continued for three days, indicating a possible delayed triggering. The delayed triggering may be due to the crustal fluid, and/or subcritical crack growth model may be responsible for triggering. Our study suggests that dynamic triggering tends to occur near active faults that have ruptured in ancient times. Other recent earthquakes, for example, 2011 Tohoku-Oki, did not trigger seismicity despite significant peak dynamic stresses values. Investigation of dynamic triggering in regions experiencing infrequent earthquakes can be crucial in understanding the origin of such earthquakes, which can be achieved by grasping the ambient stresses and geodynamic mechanisms in a particular region. Thus, we evaluate character and behavior of high-amplitude surface waves to grasp better the undergoing processes and stress transfer in the intraplate mainland region.

Influence of a Partial Substitution of Co by Fe on the Phase Stability and Fatigue Behavior of a CoCrWC Hard Alloy at Room Temperature

The deformation-induced phase transition from fcc to hcp causes local embrittlement of the metal matrix in Cobalt-base alloys, facilitating subcritical crack growth under cyclic loading and reducing fatigue resistance. Our approach to increasing the fatigue life of Co-based hard alloys is to suppress the phase transition from fcc to hcp by an alloy modification that increases the stacking fault energy (SFE) of the metal matrix. Therefore, we substitute various contents (15, 25, and 35 mass pct) of Co by Fe and analyze the effect on the fatigue life and resistance against subcritical crack growth. Subcritical crack growth in the specimens takes place in a cyclic load test. The proceeding crack growth and the occurrence of phase transformations are monitored by scanning electron microscope (SEM) investigations and electron backscatter diffraction (EBSD). We determined an SFE of 35 mJ/m2 at an iron content of 35 mass pct, which leads to a change of the main deformation mechanism from deformation-induced martensitic transformation to deformation twinning. Analysis of cyclically loaded specimens revealed that the resistance against subcritical crack growth in the metal matrix is facilitated with increasing Fe content, leading to a significant increase in fatigue life.

The Effect of Unloading Path on the Time-Dependent Behavior of Beishan Granite

Abstract Understanding the time-dependent characteristics of Beishan granite after excavation is critically important for the long-term stability and disaster control of the high-level radioactive waste repository. In this context, a series of creep tests under different unloading paths are designed to simulate the time-dependent behavior of rock mass after excavation. Results show that the instantaneous volume deformation under each loading step is greatly influenced by the unloading path. Moreover, the unloading path has minor effects on the creep strain. The axial and lateral creep strain is dominated by creep fracture potential, which can be characterized by a unified time-dependent fracture potential index (ξTFPI) for different stress states. It is observed that the creep strain generally increases with increasing ξTFPI. In order to describe the fracture mechanism during the creep process, a damage mechanical model based on time-dependent subcritical crack growth theory is adopted. It reveals that the strain hardening behavior dominates the granite creep process, and the strain softening effect is gradually strengthened with increasing ξTFPI.

Simulation of crack propagation through voxel-based, heterogeneous structures based on eigenerosion and finite cells

This paper presents an algorithm for the efficient simulation of ductile crack propagation through heterogeneous structures, as e.g. metallic microstructures, which are given as voxel data. These kinds of simulations are required for e.g., the numerical investigation of wear mechanisms at small length scales, which is still a challenging task in engineering. The basic idea of the proposed algorithm is to combine the advantages of the Finite Cell Method allowing for a convenient integration of heterogeneous finite element problems with the eigenerosion approach to still enable the mesh-independent simulation of crack propagation. The major component is to switch from finite subcells to finite elements wherever the crack progresses, thereby automatically adaptively refining at the crack tip by managing the newly appearing nodes as hanging nodes. Technically relevant problems of crack propagation at the microscale are mostly linked with sub-critical crack growth where the crack moves fast and stepwise with subsequent load cycles. Therefore, inertia may become important which is why dynamics are taken into account by spreading the mass of the eroded elements to the nodes to avoid a loss in mass resulting from the erosion procedure. Furthermore, a certain treatment for the finite cell decomposition is considered in order to ensure efficiency and accuracy. The numerical framework as well as the voxel decomposition techniques are analyzed in detail in different three-dimensional numerical examples to show the performance of the proposed approach.

Experimental investigation on Mode I crack growth and damage mechanism of sandstone subjected to cyclic loading

To further investigate the Mode I crack growth and damage mechanism, compression tests were performed on notched semi-circular bending (NSCB) specimens at different cycle amplitudes. The crack propagation gauge and digital image correlation (DIC) recorded the entire process of crack growth. The real-time crack growth rate and evolution of the horizontal strain field during crack growth were obtained. Based on the crack growth rate, the crack growth process can be divided into three stages: the cracking latent period (primary stage), stable crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period accounts for a large proportion of the entire crack growth. The stable crack (i.e., steady subcritical crack growth) expanded slowly to a certain extent after initiation, and then the accelerated crack growth led to failure. With the increase in the cyclic amplitude, the cracking latent period is shortened and the crack growth rate is accelerated. The crack growth rate is positively correlated with the stress intensity factor. Moreover, scanning electron microscopy (SEM) was used to analyse the development of the fracture process zone (FPZ) and the subcritical crack damage mechanism. The SEM images showed two damage phenomena: (1) intergranular cracks caused by grain debonding (primary mechanism) and (2) transgranular cracks (secondary mechanism).

A NEW CONSTITUTIVE MODEL FOR THE TIME-DEPENDENT BEHAVIOR OF ROCKS WITH CONSIDERATION OF DAMAGE PARAMETER

Deformation and time-dependent behavior of rocks are closely related to the stability and safety of underground structures and mines. In this paper, a numerical-analytical model is presented to investigate time-dependent damage and deformation of rocks under creep. The proposed model is obtained by combining the elastic-visco-plastic model based on the theory of over-stress and stress hardening law with the sub-critical crack growth model. The advantage of this model is that it is in incremental form and therefore can be implemented numerically. First, the governing equations of the model and its numerical computational algorithm are described. The proposed constitutive model is then implemented in the FLAC code using the FISH function. Determination of model parameters and calibration is done by various laboratory tests performed on a type of gypsum. The creep test was performed on gypsum under a stress of 13 MPa, which is equal to 70% of its compressive strength. After determining the parameters, by fitting the creep curve of the presented analyticalnumerical model, a good agreement is observed with the creep curve obtained from the laboratory data. It is also observed that during creep, the damage parameter and wing crack length increase.

Double cantilever beam fracture toughness measurement method for glass

AbstractA simple method of measuring Mode I fracture toughness, KIC, of glass using the double cantilever beam (DCB) geometry is presented. An inert atmosphere is created at the crack tip to prevent subcritical crack growth and enable “pinning” the crack while the specimen is loaded to failure. This was achieved experimentally using liquid toluene or a glovebox with dry argon. KIC values measured by this method showed good agreement with published literature values for selected glasses. Applicability of the analytical stress intensity factor solution based on crack length, crack front curvature, and the height of the crack guiding groove are confirmed through experimental data and finite element analysis. The experimentally observed crack front curvature, which leads near the edges for small groove heights and leads in the center for larger groove heights, is predicted from the geometry of the DCB specimen for a linear elastic solid through finite element modeling.

A Polynomial Equation Model for Fatigue Crack Propagation in an Aeronautical Steel Material

The model widely used in the fatigue crack growth study in materials science and fracture mechanics is the Paris-Erdogan, which relates the stress intensity factor with the subcritical crack growth, under a fatigue regime. In this work, a seven degree polynomial is used as an alternative to model the crack propagation behavior and to be able to analyze the three regions charts of the cycles by load, in contrast to the common model that it performs at a slight approximation of the propagation phase of the trinca (region II). Finally, a comparison has been made between the proposed model and the secant method by the ASTM 647,2000 standard that adjusts the points obtained experimentally. This proposed equation is new as another alternative analytical model for which the adjustment parameter “R” are compared in relation to the classical approach in a aeronautical ABNT 4130 steel.

Failure diagrams for subcritical crack growth

Failure diagrams help evaluate safe use, require monitoring or replacement of structural components subjected to service loads based on the material properties. They are commonly used in the pipeline industry as failure assessment diagrams based on the fracture toughness data and Yield Stress. Failure diagrams could help evaluate the fatigue life or crack growth leading to failure of a component subject to fluctuating loads experienced during the service environment. Understanding the subcritical crack growth behavior, its quantification, and application to components in service are essential. In the following, basic understanding and the development of these failure diagrams using Kitagawa-Takahashi plots and the two-parametric approach that we have developed in the past are discussed, taking several examples from the literature.

Evaluation of electrical fatigue limits in REBCO coated conductor tapes through static fatigue testing at 77 K

Significant development has been made toward guaranteeing the performance of high-temperature superconducting (RE)Ba2Cu3O7−x coated conductor (CC) tapes in superconducting devices such as high-field magnets and coils. To understand the superconducting behaviors of CC tapes used in such devices under various mechanical- and thermal-induced loads, their mechanical and electromechanical properties should be evaluated in consideration of their application environments. Under static or cyclic fatigue loads, critical current (I c) can degrade as a result of damage to the superconducting layer, even under loads that do not exceed the irreversible stress limits for I c degradation (σ irr). Therefore, prediction of the stress level that can degrade I c under various conditions, such as the endurance limit (stress), is significant for actual coil or magnet applications of CC tapes. A static fatigue tester for CC tapes at 77 K was used in this study to apply a static fatigue load to a 12 mm wide GdBa2Cu3O7−x CC tape specimen under simultaneous axial tension and bending stresses in a U-shaped configuration. Bending mandrels were used to superimpose various bending strains onto the applied static axial tensile strain, and I c across various voltage tap separations was measured over time, up to 100 h. The electrical static fatigue strength and endurance limit for I c degradation were determined based on the 95% I c retention criterion and 100 h of elapsed time, respectively. Results show that bending strain, dependent on mandrel diameter, can greatly influence I c degradation behaviors and that I c can drop considerably in the bent sections compared to the straight sections over time. Analyses of the combined strains in the bent sections allowed the prediction of diameter-dependent electrical static endurance limits under subcritical crack growth. The CC tape’s electrical static endurance limit was greatly affected at smaller bending diameters. When CC coils with diameters smaller than or equal to 50 mm are made using 12 mm wide CC tapes, the electrical static endurance limit is low, roughly ⩽0.63σ irr.

Breaking down chipping and fragmentation in sediment transport: the control of material strength

Abstract. As rocks are transported, they primarily undergo two breakdown mechanisms: fragmentation and chipping. Fragmentation is catastrophic breakup by fracture in the bulk – either by subcritical crack growth under repeated collisions, or from a single high-energy (supercritical) collision – and produces angular shards. Chipping is a distinct low-energy mechanism of impact attrition that involves shallow cracking; this process rounds river pebbles in a universal manner under bed-load transport. Despite its geophysical significance, the transition from chipping to fragmentation is not well studied. Here, we examine this transition experimentally by measuring the shape and mass evolution of concrete particles of varying strength, subject to repeated collisions in a rotating drum. For sufficiently strong particles, chipping occurred and was characterized by the following: attrition products were orders of magnitude smaller than the parent; attrition rate was insensitive to material strength; and particles experienced monotonic rounding toward a spherical shape. As strength decreased, we observed the onset of a subcritical cracking regime associated with fragmentation: mass of attrition products became larger and more varied; attrition rate was inversely proportional to material strength; and shape evolution fluctuated and became non-monotonic. Our results validate conceptual and numerical models for impact attrition: chipping follows “Sternberg's law” of exponential mass loss through time; for fragmentation, the lifetime of particles increases nonlinearly with material strength, consistent with “Basquin's law” of fatigue failure. We suggest that bedrock erosion models must be clarified to incorporate distinct attrition mechanisms, and that pebble or bedrock-channel shape may be utilized to deduce the operative mechanism in a given environment.

Subcritical Crack Growth Parameters for Glass under Different Environmental Conditions

In the present work, subcritical crack growth in soda‐lime silicate glass is investigated under different environmental conditions. Crack growth parameters as a function of temperature and humidity were determined by dynamic fatigue tests. The specimens were pre‐damaged for constant initial crack lengths in all specimens using the Vickers indenter. The initial flaw size induced by the Vickers indenter was obtained by a scanning electron microscope picture of the fracture surface, which could also show the initial flaw geometry. Furthermore, the influence of humidity and temperature on the failure stress of specimens with a constant initial crack length was simulated and the deviations are shown. A comprehensive version of this investigation is currently (16.03.2021) under review in the Journal for Glass Structures and Engineering.