Crack Growth Parameters Research Articles

Prognosis of reflective pavement cracking development with Bayesian updating and surrogate models

ABSTRACT The main objective of this study is to establish an integrated prognostic method for predicting the development of thermal-induced reflective cracking in asphalt overlay on concrete pavement. The integrated prognosis process for crack growth is developed on the modified Paris’ law and includes three steps: (1) calculation of J-integral; (2) Bayesian updating of crack growth parameters and (3) prediction of remaining life. Finite element modelling (FEM) was conducted to calculate J-integrals at different crack depths and cold weather conditions. A surrogate model was built based on the original Kriging method and it shows high accuracy in predicting J-integrals from maximum air temperature, temperature drop and crack depth. The Bayesian updating process starts from the laboratory-measured distribution of fracture model parameters (A and n) in Paris’ Law and converges to the true values to match the measured crack depths at different loading cycles from field inspection. On the other hand, the consideration of material damage in asphalt overlay avoids over-estimation of remaining loading cycles for reflective cracking to reach the pavement surface. Further study is recommended to accurately assess in-situ pavement modulus and detect crack depth over concrete joints for implementation of the proposed prognostics method.

Investigating the impact of thermal treatment on fracture toughness and sub-critical crack growth parameters under mode II loading

Studying subcritical crack growth is crucial to investigating the long-term behavior of rocks under applied loads and evaluating the long-term stability of underground and surface structures in rock masses. While considerable research has been done to determine subcritical crack growth parameters in mode I, Studies on subcritical crack growth under mode II loading are limited despite its important applications in rock engineering problems. The purpose of the study is to understand the thermal effect on the fracture behavior of hornfels rock, which were heated at 25 °C (without thermal treatment), 250 °C, 500 °C, and 750 °C, respectively. The subcritical crack growth parameters were determined using the constant stress rate test and one of the available fracture mechanics tests for mode II loading, namely, the four-point bending test. Experiments were conducted at three fixed displacement rates of 0.06 mm/min, 0.6 mm/min, and 6 mm/min, and three experiments were performed in each case to ensure repeatability. The results showed that the fracture toughness of hornfels samples increased with increasing temperature up to 250 °C and then decreased with increasing heat treatment temperature. The fracture toughness decreased drastically due to the thermal breakdown of the quartz crystal structure and the creation of wider intergranular fractures. The study indicated that for the hornfels samples, the subcritical parameter A decreased and beyond this temperature, parameter A began to increase while parameter n remained relatively constant as the temperature rose to 750 °C. The subcritical crack growth rate was calculated using the subcritical crack growth parameters and the stress intensity factor under mode II loading. For a certain value of the stress intensity factor KII, the highest subcritical crack velocity occurred at the temperature of 750 °C (5.76×10−7–2.47×10−1 m/s), and the lowest velocity of the subcritical crack occurred at the temperature of 250 °C (3.30×10−11–6.84×10−5 m/s). The impact of inert strength, calculated at the highest loading rate, on subcritical parameters across various temperatures was examined. The findings indicate that the subcritical crack growth parameter A is reliant on inert strength.

An innovative approach to planar mixed-mode fatigue crack growth study

Determining fatigue crack growth parameters under mixed-mode loading is crucial for damage tolerance design, particularly in assessing a component's residual life with defects to prevent disasters. This study introduces a novel methodology for determining fatigue crack growth rate. A digital microscope is utilized to track the fatigue crack tip with respect to local coordinate systems established on the specimen surface. A grid is drawn and subdivided into units with proposed nomenclature. Compact Tension and Shear (CTS) specimens, extracted from AA-7085 plates, undergo fatigue loading in a servo-hydraulic universal testing machine. A fixture proposed by Richard et al. induces planar mixed-mode loading cases in the specimen. During experiments, the digital microscope tracks the crack tip using grid unit corners as local origins. The local coordinates of the crack tip are transformed into the crack tip coordinates with respect to the pre-crack tip. Crack evolution data are used to determine the fatigue crack growth rate by analyzing tangents of a three-parameter fitted curve. The equivalent SIF ranges are computed at different crack lengths in an XFEM script written in Ansys. The modified Paris parameters are found and experimentally observed crack deflection angles are compared with the Maximum Tangential stress, Strain energy density, and Richard’s criterion.

Comparison of subcritical growth parameters of a Y-TZP obtained via cyclic or dynamic fatigue tests

ObjectiveThe objective of this study was to 1) compare the stress corrosion coefficient (n) of a Y-TZP obtained by two fatigue tests: cyclic and dynamic and 2) evaluate the effect of frequency in the characteristic lifetime and the existence of interaction between the cyclic fatigue and slow crack growth. MethodsA total of 145 Y-TZP specimens were produced in accordance with the manufacturer's instructions. These specimens, measuring 4.0 × 3.0 × 25.0 mm, were used for dynamic (n = 70) and cyclic fatigue tests (n = 75). The specimens were obtained from CAD/CAM blocks, sectioned, and sintered in a furnace at 1530 °C with a heating rate of 25 °C/min. They were tested in their "as-sintered" form without any additional surface treatment. The fatigue tests were conducted using a four-point bending to obtain the slow crack growth parameters (n). The cyclic fatigue test was also conducted in two frequencies (2 and 10 Hz), using stress levels between 350 and 600 MPa. Data from these tests were analyzed using ASTM C 1368–00 formulas and Weibull statistics. Scanning electron microscope (SEM) was used for fracture surface analysis to identify the origin of the fracture. Critical defect size was measured and used, along with flexural strength values, to estimate fracture toughness. Dynamic fatigue test data were used to obtain subcritical crack growth (SCG) parameters and perform Weibull statistical analysis. The cyclic fatigue data were used in the General Log-linear Model equation using the ALTA PRO software. Data were analyzed using one-way ANOVA followed by Tukey post-hoc tests and Student's t-test at a significance level of p ≤ 0.05. ResultsIn the dynamic fatigue test, the values obtained for σfo and n were 667 and 54, respectively. This parameter indicates how the strength of the material diminishes over time due to internal cracks. The Weibull parameters obtained from the same test results were m = 7.9, σ0 = 968, 9 and σ5% = 767, which indicates the reliability of the material. The Weibull parameters obtained by cyclic fatigue were statistically similar for the two frequencies used, the m* was 0.17 (2 Hz) and 0.21 (10 Hz); characteristic lifetimes (η) were 1.93 × 106 and 40,768, respectively. The n values obtained by cyclic fatigue were 48 and 40 at frequencies of 2 and 10 Hz, respectively. There was no effect of the frequency, the stress level or the interaction of the two in the Y-TZP lifetime, when analysed by General Log Linear Model. Significancethe n values obtained by cyclic and dynamic fatigue tests showed no statistically significant difference and the effect of frequency in the characteristic lifetime and the existence of interaction between the cyclic fatigue and subcritical growth were not observed in the tested specimens.

The Behavior of Ceramic Fiber Geopolymer Concrete under the Effect of High Temperature

Geopolymer concrete (GC), also known as green concrete, contains slag, silica fume, and fly ash as binders. The absence of cement in concrete is critical to protect the world from the environmental impacts of cement production. In addition, exposure to high temperatures is a critical parameter that causes loss of strength in concrete. In this study, Geopolymer concrete samples were prepared with 10 different samples containing different proportions of slag, silica fume, and porous ash and subjected to various physical, mechanical, and optical tests. The sample (GS90) with optimum workability and compressive strength, which also showed high performance in water absorption, freeze-thaw, and UPV tests, was used in high-temperature tests. Portland cement concrete (PCC) was used as a control sample. This study investigated the effect of high temperatures on the physical and mechanical properties of fiber-free GCs containing 2%, 5%, and 10% by volume of ceramic fibers. Therefore, fiber-reinforced, fiber-free, and PCC specimens were subjected to high-temperature tests at 100, 300, 600, and 900 °C. As a result of the observation of crack growth, color changes, and compressive strength parameters in the samples subjected to high-temperature tests, the thermal resistance of the 10% ceramic fiber geopolymer concrete sample was 2.5% higher than other samples. There is no study in the literature that examines the behavior of ceramic fiber-reinforced geopolymer concrete at high temperatures. This research revealed an important finding by proving that ceramic fiber reinforcement increases the compressive strength of geopolymer concretes at a remarkable rate after high-temperature impact.

Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures

In the shipbuilding, construction, automotive, and aerospace industries, welding is still a crucial manufacturing process because it can be utilized to create massive, intricate structures with exact dimensional specifications. These kinds of structures are essential for urbanization considering they are used in applications such as tanks, ships, and bridges. However, one of the most important types of structural damage in welding continues to be fatigue. Therefore, it is necessary to take this phenomenon into account when designing and to assess it while a structure is in use. Although traditional methodologies including strain life, linear elastic fracture mechanics, and stress-based procedures are useful for diagnosing fatigue failures, these techniques are typically geometry restricted, require a lot of computing time, are not self-improving, and have limited automation capabilities. Meanwhile, following the conception of machine learning, which can swiftly discover failure trends, cut costs, and time while also paving the way for automation, many damage problems have shown promise in receiving exceptional solutions. This study seeks to provide a thorough overview of how algorithms of machine learning are utilized to forecast the life span of structures joined with welding. It will also go through their drawbacks and advantages. Specifically, the perspectives examined are from the views of the material type, application, welding method, input parameters, and output parameters. It is seen that input parameters such as arc voltage, welding speed, stress intensity factor range, crack growth parameters, stress histories, thickness, and nugget size influence output parameters in the manner of residual stress, number of cycles to failure, impact strength, and stress concentration factors, amongst others. Steel (including high strength steel and stainless steel) accounted for the highest frequency of material usage, while bridges were the most desired area of application. Meanwhile, the predominant taxonomy of machine learning was the random/hybrid-based type. Thus, the selection of the most appropriate and reliable algorithm for any requisite matter in this area could ultimately be determined, opening new research and development opportunities for automation, testing, structural integrity, structural health monitoring, and damage-tolerant design of welded structures.

Failure location effects on slow crack growth parameter estimates

AbstractAs part of Roman Space Telescope component development, the slow crack growth (SCG) parameters of a glass were measured using constant stress rate testing of ASTM C1161 beams. Failures occurred on the faces, bevels and sides of the test specimens thereby providing an opportunity to examine the effects of failure location on SCG parameter estimates. Censoring of the data by location did not have a statistically significant effect on the slow crack growth parameter estimates. Linear and nonlinear fits were also made to various strength estimators. Nonlinear fits gave slightly lower estimates of the parameters. The main influence on parameter estimates was a low strength, infrequent flaw population. Exponential model parameters were estimated via swarm optimization.

Graphene oxide increases PMMA's resistance to fatigue and strength degradation.

to characterize the effects of graphene oxide (GO) on polymethyl methacrylate's (PMMA) reliability and lifetime. The hypothesis tested was that GO would increase both Weibull parameters and decreased strength degradation over time. PMMA disks containing GO (0.01, 0.05, 0.1, or 0.5wt%) were subjected to a biaxial flexural test to determine the Weibull parameters (m: modulus of Weibull; σ0: characteristic strength; n=30 at 1MPa/s) and slow crack growth (SCG) parameters (n: subcritical crack growth susceptibility coefficient, σf0: scaling parameter; n=10 at 10-2, 10-1, 101, 100 and 102MPa/s). Strength-probability-time (SPT) diagrams were plotted by merging SCG and Weibull parameters. There was no significant difference in the m value of all materials. However, 0.5 GO presented the lowest σ0, whereas all other groups were similar. The lowest n value obtained for all GO-modified PMMA groups (27.4 for 0.05 GO) was higher than the Control (15.6). The strength degradation predicted after 15 years for Control was 12%, followed by 0.01 GO (7%), 0.05 GO (9%), 0.1 GO (5%), and 0.5 GO (1%). The hypothesis was partially accepted as GO increased PMMA's fatigue resistance and lifetime but did not significantly improve its Weibull parameters. GO added to PMMA did not significantly affect the initial strength and reliability but significantly increased PMMA's predicted lifetime. All the GO-containing groups presented higher resistance to fracture at all times analyzed compared with the Control, with the best overall results observed for 0.1 GO.

Probability estimation method for fatigue crack growth rate based on a ∼ t data from service

PurposeThe study aims to provide a basis for the effective use of safety-related information data and a quantitative assessment way for the occurrence probability of the safety risk such as the fatigue fracture of the key components.Design/methodology/approachThe fatigue crack growth rate is of dispersion, which is often used to accurately describe with probability density. In view of the external dispersion caused by the load, a simple and applicable probability expression of fatigue crack growth rate is adopted based on the fatigue growth theory. Considering the isolation among the pairs of crack length a and crack formation time t (a∼t data) obtained from same kind of structural parts, a statistical analysis approach of t distribution is proposed, which divides the crack length in several segments. Furthermore, according to the compatibility criterion of crack growth, that is, there is statistical development correspondence among a∼t data, the probability model of crack growth rate is established.FindingsThe results show that the crack growth rate in the stable growth stage can be approximately expressed by the crack growth control curve da/dt = Q•a, and the probability density of the crack growth parameter Q represents the external dispersion; t follows two-parameter Weibull distribution in certain a values.Originality/valueThe probability density f(Q) can be estimated by using the probability model of crack growth rate, and a calculation example shows that the estimation method is effective and practical.

Fatigue crack growth in wheel-rail rolling-sliding contact: A perspective of elastic-plastic fracture mechanics criterion

The presence of fatigue crack is a common damage pattern in railway wheel-rail system, which will reduce service life and increase the maintenance costs of railway transportation. In this study, a two-stage simulation strategy was proposed to investigate the elastic-plastic fatigue crack growth behaviour of the wheel and rail, where a three-dimensional wheel-rail rolling contact finite element model was first built to solve the elastic-plastic wheel-rail contact pressure and tangential traction modification, and then a simplified three-dimensional finite element model of the wheel and rail inserted with vertical cracks under the equivalent moving load was built to explore the fatigue crack growth. Taking the J-integral at the crack tip as an elastic-plastic crack growth parameter, the influences of crack face friction, crack depth and traction coefficient on the crack growth were elucidated. Meanwhile, the competing mechanisms of wheel/rail wear and fatigue crack growth under rolling-sliding contact condition was illuminated based on the Archard wear model. The simulation results indicate that two critical locations for crack growth appear during the contact load approaching and departing from the crack. The Mises stress near the deepest crack tip exceeds the yield stress, causing a small plastic zone with the greatest crack growth rate. The reduction in the crack face friction, and/or the increase in crack depth and traction coefficient will accelerate the propagation of fatigue crack. In the case of only normal contact load or rolling-sliding contact (μ ≤ 0.375), the crack growth on the wheel and rail is dominant compared to wear and crack will continue to grow.

A material characterisation framework for assessing brickwork masonry arch bridges: From material level to component level testing

This paper aims to present a systematic framework for material characterisation to assess brickwork masonry arch bridges. An extensive laboratory campaign was carried out to characterise brickwork and backfill material in masonry arch bridges. Initially, the strength and Young’s modulus of bricks and mortar, as well as the internal friction angle and cohesion of the backfill materials (e.g., crushed limestone and puddling clay), were characterised by undertaking small-scale material level tests. Then, the compressive strength and Young’s modulus of masonry prisms, as well as unit-to-mortar bond properties (e.g., tensile strength, angle of friction and cohesion) were assessed at the component level. Further, large-scale shear box tests were carried out to identify the frictional properties, including the interface friction angle and cohesion, between the brickwork and backfill material. Moreover, both static and high-cycle fatigue three-point bending tests were performed on masonry flat arches to obtain fatigue crack growth and stiffness degradation parameters. Outputs from this experimental campaign can be used for parameter identification and model calibration of complex/high-fidelity numerical models developed to assess masonry arch bridges.

Investigation of force modeling in ultrasonic vibration-assisted drilling SiCf/SiC ceramic matrix composites

Due to their exceptional high-temperature and rust resilience, SiCf/SiC ceramic matrix composites have been regarded as potential high-temperature components. For application, to overcome issues resulting from the high hardness and brittleness, the ultrasonic vibration-assisted machining technique is primarily adopted in the machining of SiCf/SiC ceramic matrix composites. It is essential to develop a force model for a better understanding of the material removal and cutting processes by applying ultrasonic vibration. As a result, studies on force modeling during ultrasonic vibration-assisted drilling of SiCf/SiC ceramic matrix composites have been conducted in this study, taking into account the trajectory of the drilling tool, the tool-workpiece contact state, and the material removal mode. Based on the coefficient calibration experiment and least square method, the irregular coefficient of abrasive grains, the crack growth parameters of materials, and the mechanical parameters that are difficult to be measured were determined. After that, the drilling parameters and vibration parameters were merged to build the analytical force model, and the parameter influence rules on the force was also studied. The suggested drilling force model concurred well with tests under the highest relative error of 17.34 %, according to the findings of the confirmation experiments.

Debonding detection in FRP-strengthened concrete structures utilising nonlinear Rayleigh wave mixing

This paper reports an investigation on the use of Rayleigh wave mixing method for the debonding detection in concrete structures strengthened with externally bonded fibre-reinforced polymer (FRP) composite plates. A three-dimensional (3D) finite element model is developed to simulate the propagation of Rayleigh waves in FRP-strengthened concrete structures. In this model, the frequency domain of the transmitted waves shows the generation of second harmonics and combinational harmonics on account of debonding. The numerically simulated results are then experimentally validated with carbon fibre-reinforced polymer (CFRP)-plated concrete blocks containing two different sizes of debonding. Based on the experimentally verified numerical model, parametric studies are then conducted, where a nonlinear debonding crack growth parameter is proposed. The nonlinear Rayleigh wave mixing method is proven to be practical, reliable, and sensitive for detecting debonding at bonded concrete-FRP interfaces in FRP-strengthened reinforced concrete (RC) structures.

Effect of surface treatment on flexural strength and subcritical crack growth of lithium disilicate: an in vitro study

Alternative surface treatments have been proposed for the cementation of lithium disilicate ceramics aiming to improve adhesive and flexural strength under fatigue. This study aimed to evaluate the slow crack growth (SCG) parameters of the lithium disilicate ceramic after hydrofluoric acid (HF) etching or air abrasion (AB) as surface treatments. Ceramic discs were treated with HF (5%, 20 s) or AB (30 µm silica-modified alumina particles, 2.8 bar, 10 mm distance, 15 s), and received a layer of resin cement. The surface roughness after surface treatment was evaluated (n = 5). Samples were tested in a piston-on-three-ball assembly to evaluate the flexural strength (n = 20), inert strength (n = 25), and to determine SCG parameters n and D (n = 35). The highest roughness (p < 0.01) was observed in the AB group, with the highest reliability according to the Weibull analysis, but the lowest SCG susceptibility. Flexural (p = 0.03) and inert strength (p < 0.01) were the greatest in the HF group. Despite exhibiting lower strength than 5% HF, air abrasion may be an alternative for the surface treatment of lithium disilicate surfaces, indicating the best prognosis over time.

Setting Adaptive Inspection Intervals in Helicopter Components, Based on a Digital Twin

Setting inspection intervals based on an accurate prediction of fatigue crack sizes is essential for sustaining the integrity of aeronautical structures. However, the fatigue crack growth and its prognosis are affected by various uncertainties, which makes the current inspection strategy with fixed intervals challenging in managing the aircraft with diverse damage states in a fleet. In this study, an intelligent crack inspection strategy is proposed based on a digital twin, in which a reduced-order fracture mechanics simulation methodology, a validated fatigue crack growth model, and the historical crack length inspection results are integrated into a dynamic Bayesian network. The proposed strategy uses two connected probabilistic processes, which conduct the diagnosis/prognosis and calculate the inspection intervals, respectively, to adaptively set the inspection intervals according to the updating of the digital twin model. The proposed inspection strategy is demonstrated by the various crack growth histories of a helicopter component and benchmarked against several baselines. The results show that the probability of failure can be kept below the threshold, even though the initial crack size and the crack growth parameters are underestimated in the prior distribution. Further applications on more realistic aircraft structures will be carried out in the future.

Fracture mechanics properties of fused silicas used for international space station windowpanes

AbstractThe fracture toughness and slow crack growth (SCG) parameters of a quartz‐based silica and a high‐purity fused silica were measured as part of a program to review the reliability of the International Space Station windows. The materials exhibit the same fracture toughness (.75 MPa m1/2 in N2) and very similar SCG parameters. The literature on fused silica indicates excellent agreement of fracture toughness, but a very wide range of SCG parameters, even from the same institution, with strength‐based methods usually yielding a lower power law exponent than direct crack velocity measurements. Use of the exponential function is shown to provide better agreement between test methods, with velocity curves derived from strength tests of bare fiber and polished or ground test specimens paralleling those from wide‐range, direct crack velocity observations, implying that constant stress rate tests can predict long lifetime via the exponential function. However, much variation still exists. SCG parameters for soda–lime silicate are much less sensitive to the test method than fused silica. Static load tests and stress intensity measurements resulted in a fatigue threshold of .3 MPa m1/2 for fused silica.

A unified prediction model for physically small crack and long crack growth based on modified CTOD

A unified model based on CTOD is proposed to calculate the growth rate of physically small crack (PSC) and long crack (LC). Firstly, an in-situ SEM testing under the single overload condition is performed to reveal that CTOD could be the unique driving parameter for fatigue crack growth (FCG). Then, a unified FCG model is established based on the modified CTOD formula which considers the main physical mechanisms of small crack effect. Additionally, a theoretical equation of the transition crack length from PSC to LC is given. Finally, several datasets of different materials are used to validate the model.

Effect of material heterogeneity and testing temperature on fatigue behaviour of Cr-Mo steel welded joints

Successful application of Cr-Mo steel depends crucially on behaviour of all zones in welded joints, i.e. base metal (BM), heat-affected-zone (HAZ) and weld metal (WM), both at room and working temperature. Different amplitude loadings were applied for testing of specimens without a crack, made of welded joint as a whole and of BM, in order to obtain Woehler’s curves and compare their dynamic strength. Amplitude loading was also applied for testing of specimens cracked in BM, HAZ and WM, in order to get fatigue crack growth curves and parameters C and m in Paris law. Results are analysed to get deeper insight into behaviour of welded joints, made of steel SA 387 Gr. 91, under amplitude loading both for room and working temperature.

Deriving exponential and power law slow crack growth parameters from dynamic fatigue of indented or as-polished window material coupons

Knowledge of slow crack growth rate in a window material is required to determine the design life of a window in which cracks grow under the influence of applied service stress. Parameters that characterize crack growth rate can be measured by dynamic fatigue in which coupons are taken to failure at several constant stress rates. The slower the stress rate, the more time is available for cracks to grow during the strength measurement, and the lower the stress at which the coupon fails. That is, coupons tested at a slower stress rate are weaker than coupons tested at a faster stress rate. The rate of slow crack growth is commonly fit to either a power law or an exponential law. The exponential law provides the more conservative estimate of design life and is prescribed for use by the U.S. National Aeronautics and Space Administration to design windows for manned vehicles. Well-established analytical equations are used to derive the power law crack growth parameters from dynamic fatigue measurements of as-polished (unindented) coupons. There are no exact analytical equations to derive power law parameters from indented coupons or to derive exponential law parameters from unindented or indented coupons. Approximate procedures have been used to derive crack growth parameters when there are no exact equations. We now describe a numerical method that gives the power and exponential laws for both unindented and indented coupons by least-squares fitting of dynamic fatigue measurements. A MATLAB code is provided to carry out the calculations.

The study on the overloading effect on fatigue crack growth considering residual stress relaxation in Al 5456-H38

A numerical and experimental study was conducted on fatigue crack growth (FCG) of metallic components to investigate the effect of redistribution of mechanical residual stresses induced by overloading in notched specimens. The compact tension (CT) specimens of an aluminum alloy were used, and mechanical residual stresses were introduced in them by applying tensile overload (OL). Then, the specimens were subjected to fatigue loading. In the calculations of finite element method (FEM), the modified cyclic J-integral was used as the crack growth parameter. Good agreement was observed between the numerical and experimental results. The FEM results demonstrated a clear redistribution of residual stresses during FCG process. It was observed that after a few cycles, the residual stress field reached a lower magnitude value confining in a small zone around the around the crack tip. Furthermore, the effects of stress ratio, load amplitude, and OL ratio (OLR) on the redistribution of residual stresses are studied in this research. It was observed that the residual stresses are considerably released during the initial cycles of fatigue loading.