Crack Growth Process Research Articles

Digital Image Correlation parameters optimized for the characterization of fatigue crack growth life

This paper presents a novel methodology to obtain the fatigue crack growth rate versus the stress intensity range, da/dNvsΔK curve, by only using the digital image correlation (DIC) technique. First, an optimization of the DIC and William’s series parameters is performed. The optimal parameters are obtained by comparison with reference calculations performed by the extended finite element method. Finally, the DIC technique considering the previous results is used to characterize the fatigue crack growth process on a standard middle tension (MT) specimen under mode I loading to build up the da/dNvsΔK curve. The differences in the characterization using the DIC and traditional measurements range from the 14% and the 3% for stress intensity factors (SIFs) between 14 and 18 MPa√m, and about 1% for SIFs between 18 and 36 MPa√m. The fatigue crack growth curve obtained is checked by comparison with traditional measurement methods.

Study on Eccentric Uncoupled Blasting Effect of Cutting Seam Pipe

In order to study the blasting effect and the damage to the rock mass when the cutting seam cartridge is eccentrically and uncoupled. The ANSYS/LS-DYNA® nonlinear dynamic platform was used to simulate the blasting effect of five eccentric uncoupled coefficients on the cutting seam cartridge, and the crack growth process under the condition of complete eccentricity was simulated. By comparing and analyzing the stress of measuring points in the direction of cutting seam, vertical cutting seam direction, and circumferential cutting seam pipe under different working conditions. It is concluded that the effect of detonation products is affected by the wrapping property of the cutting seam pipe and the eccentric uncoupled coefficient. With the increase of the eccentric uncoupled coefficient, the load distribution presents obvious non-uniformity. The pressure on the uncoupled side of the blasthole is smaller than that on the coupled side, and the peak time of the uncoupled side also lags behind that on the coupled side. When the eccentric uncoupled coefficient is 1, the peak pressure on the coupled side is 5.78 times that of the uncoupled side, and the explosive stress field is biased toward the coupled side. The existence of the cutting seam pipe causes stress concentration at the opening, which enhances the guiding effect of the initial crack, and the stress in the non-cutting seam direction is buffered. Therefore, the eccentric arrangement of the cutting seam pipe determines the formation of the initial crack and the subsequent blasting effect. When the cutting seam cartridge is arranged eccentrically and uncoupled, it will cause under-excavation at the connection direction of blasthole, which will cause less disturbance to the rock mass on the uncoupled side. If the retaining side rock mass is on the coupled side in actual blasting, the eccentric uncoupled arrangement will cause greater over-excavation and damage. Therefore, it is necessary to avoid this situation as far as possible and provide better guidance for the actual construction.

Analytical and numerical assessments of probabilities of fatigue fracture of pipeline components under internal pressure

The paper presents analytical and numerical approaches to assessing the probability of failure of structural components of technical systems subjected to cyclic loading. The kinetics of the crack is described by the modified Paris equation. The analytical solution is based on the inverse extrapolation of the critical crack depth. In this case, the only probabilistic parameter is considered to be the initial crack depth, which is assumed to be distributed according to an exponential law. The numerical solution uses the Monte-Carlo method. The initial crack depth, fracture toughness of the structural material, and parameters C and m of the Paris equation are taken as probabilistic parameters. For the statistical description of the process of fatigue crack growth in structural components, a computer code was developed in the Matlab environment, which allows using appropriate random number generators to simulate various laws of distribution of random parameters, including the laws of uniform density, exponential law, normal law, Weibull's law, etc. An example of analytical and numerical calculation of the probability of fatigue failure of a pipeline component containing an axial crack on the inner surface and loaded with internal pressure is given. Comparison of the obtained results of analytical and numerical solutions allows us to conclude that an approximate analytical estimate of the fracture probability can be used for preliminary calculations at the design stage of structural components, as well as for obtaining a prior estimates of the fracture probability when implementing Bayesian updating procedures for specifying the fracture probability and determining the frequency of technical inspections of the condition of the components under consideration as part of the implementation of risk-oriented approaches to ensuring their strength and safety.

Research on the Behavior and Mechanism of Three‐Dimensional Crack Growth under Uniaxial Loading

Most of the cracks in the rock masses are in a three‐dimensional (3D) state, and it is always a hot topic to reveal the mechanical mechanism of 3D crack growth. In this paper, the research on the growth behavior of 3D crack is performed through laboratory experiments and numerical simulations. Cement samples with different angles of 3D crack are prepared, and the uniaxial compression experiment is carried out. The results indicate that initiation of preexisting crack with an angle of 45° is easier and shear failure characteristics of corresponding samples are obvious. Through theoretical analysis, the preexisting crack starts to grow at the end of the short axis, along the short axis end to the long axis end of the preexisting crack, the shear effect decreases gradually, and the tearing effect increases gradually. Combined with numerical simulation, the experimental and analysis results are verified, and the preexisting crack growth process is presented. The growth direction of the preexisting crack changes from perpendicular to the crack surface to parallel principal stress direction, and the maximum growth length can reach 1.2 times the minor axis radius of the preexisting crack. The research results can provide an important theoretical basis for revealing the evolution process of the cracks in rock masses.

An Approach to Predicting Fatigue Crack Growth Under Mixed-Mode Loading Based on Improved Gaussian Process

This paper proposes an approach to predicting fatigue crack growth under mixed-mode loading based on improved Gaussian process. In terms of analyzing the theoretical background for fatigue crack growth, a corresponding finite element model is built to generate sufficient simulation data, which is utilized to obtain the key parameters (e.g., stress intensity factor) for the fatigue crack growth process. And then, a Gaussian process model is achieved to meet the condition that the stress intensity factor is a nonlinear continuous change in crack growth, especially for mixed-mode loading. Following, an idea of local sample densification method is implemented to improve Gaussian sample generation process according to the simplified model of the crack growth path. Based on the above investigation, a fatigue crack growth prediction model using the improved Gaussian process is finished, which is subsequently verified through the test data of lower bainite steel (SCM435) material. The results show that the proposed approach has better computational accuracy and efficiency than the traditional finite element method in predicting fatigue crack growth under mixed-mode loading.

Roles of Hydrogen and Plastic Strain Distribution on Delayed Crack Growth in Single-crystalline Fe–Si alloy

Abstract Effects of hydrogen on macroscopic and microscopic features of crack growth in thin specimens were investigated using a thin sheet of single-crystal Fe-3wt%Si alloy. Center-cracked specimens were tested under a sustained load in a hydrogen environment, and under continuous stretching in an air environment. The fracture features were compared to elucidate the role of hydrogen in hydrogen-induced delayed crack growth. In both air and hydrogen environments, the crack growth mode of the thin specimens was the same as that of the thick specimens, despite the significantly reduced thickness. Surprisingly, the crack grew discontinuously, and left striations on the fracture surface, in which shorter striation spacing was observed in hydrogen. In addition, there was a similarity in the deformation microstructures beneath the fracture surface, that is, both microstructures were composed of three distinct layers characterized by different plastic strain gradients and dislocation densities. In the hydrogen environment, the hydrogen-enhanced localized plasticity (HELP) mechanism is believed to be relevant to the crack growth process. Also, HELP was supposed to cause different characteristics (the magnitude of plastic strain, the plastic strain gradient, and dislocation structure) of the three layers in the hydrogen compared to those in the air. Reverse plastic deformation occurred in the regions behind the crack front during crack growth, which is speculated to contribute not only to enlarge the crack tip opening angle (CTOA) but also to blunt the crack tip.

Fatigue damage diagnosis and prognosis of an aeronautical structure based on surrogate modelling and particle filter

A key issue affecting the performances of every human-conceived engineering system is its degradation, fatigue crack growth being one of the major structural deterioration phenomena. Fatigue crack growth is usually modelled as a stochastic process: uncertainty sources lie both in the item and in the physical degradation process variability. Fatigue crack growth deserves close attention, especially considering that condition-based maintenance methodologies are recently experiencing a major drive to increase their technology readiness level, requiring validated diagnostic and prognostic methodologies which should be capable of operating online and in real-time. In this regard, particle filters provide a consistent Bayesian framework, where the posterior distribution of the system degradation state is recursively approximated based on a time-growing stream of observations measuring the system response, enabling, in general, increasingly informed lifetime estimates. However, the real-time operation capability of such methods is hindered by their requirements in terms of computational power, which is mainly due to the complexity of the structural models they rely upon. Within this work, a comprehensive particle filter framework, able to deal with fatigue crack growth uncertainty sources while simultaneously addressing the computational burden issue, is proposed. The algorithm structure enables to simultaneously perform the diagnosis and prognosis of fatigue crack growth, while the adoption of the augmented state formulation allows to address scenarios where the degradation process of fatigue crack growth fails to meet the degradation model ruling the particle filter. Artificial neural networks–based surrogate modelling is adopted at different stages and embedded within the particle filter algorithm, relieving the computational burden associated with the evaluation of the trajectory likelihoods as well as enabling a fast estimation of the remaining useful life. Both simulated and experimental data sets regarding fatigue crack growth in an aluminium aeronautical panel are used for the algorithm testing, additionally proving the validity and effectiveness thereof by means of common prognostic performance metrics.

Hydraulic and Mechanical Relationship of Individual Fracture in Rock under Compression and Shearing: Theoretical Study

In this paper, a new approach has been developed for predicting the hydraulic and mechanical relationship of individual fractures subjected to normal stress and compression-shear stress. Considering that the closure process of rough fracture subjected to normal stress can be divided into two phases (linear behavior and nonlinear behavior), a relationship between normal stress and fracture aperture is derived through the minimum potential energy principle. Then, a formulation for calculating fracture permeability during shearing and compression processes is developed. Furthermore, a formulation for determining fracture aperture during the crack growth process is obtained, which is further implanted into the permeability model to predict the hydraulic behavior of fractured rock during fracture propagation. This new model not only considers the normal deformation of the fracture but also, and more importantly, integrates the effect of fracture propagation and shear dilation. Theoretical studies demonstrate that fracture permeability increases nonlinearly during fracture propagation. At last, experimental results and analytic results are compared to demonstrate the usefulness of the proposed models, and satisfactory agreements are obtained.

Study on the shape change of crack growth rate curve under different forms of additional stress field

In this paper, FRANC3D is used to simulate the fatigue crack growth process under different additional stress fields to explore the key mechanical parameters influencing the fatigue crack growth curve. For finite large plate model with penetrating crack, the crack growth rate is calculated under different forms and different values of applied load and additional stress coupling, the fatigue life curves, as well as crack growth rate curves and Pairs formulas under different applied loads are obtained. Through the analysis, the relationship between the additional stress field and the parameters in Pairs formula of crack growth rate is obtained. Because of the existence of the additional stress field, the stress intensity factor amplitude of crack tip changes, which is the root cause of the change of crack growth rate curve shape.

Fatigue crack growth in micro specimens as a tool to measure crack–microstructure interactions

AbstractThe process of short fatigue crack growth plays a significant role for the lifetime of materials in the high and very high cycle regimes. Fatigue crack growth is strongly influenced by interactions with microstructural obstacles, such as grain boundaries or phase boundaries, requiring a better understanding of these interactions to enhance the lifetime in these load regimes and improve lifetime calculations. Although it is possible to obtain crack growth rates from fatigue cracks in the lower micrometre range, further information like the exact position and type of the obstacle are mostly unavailable during the experiment. To overcome this issue, we propose a testing methodology of fatigue crack growth in micro specimens, which allows for an exact positioning of the crack relative to the obstacles and for monitoring the crack behaviour in a scanning electron microscope. The capabilities of this method are demonstrated for the interaction of fatigue cracks with grain boundaries.

Comparative Research on Fatigue Performance of High-Strength Bainitic Steel with or without Corrosion

High-strength bainitic steels have acquired a promising place among steels due to their wide applications in engineering structures. It is, therefore, worthwhile to investigate their fatigue performance in different environments. When fatigue is atmospheric, lattice strength of weaker zones including granular bainite, phase boundary and MA constituents determines the nucleation life of fatigue. The deflected microstructural short cracks enhance the early propagation life of fatigue. In lath bainite, fine ferrite laths, high-density dislocations within the grains, small grain size and high proportion of HAGBs inhibit the crack growth process to improve propagation life of fatigue. The fracture reveals transgranular mode for propagation of fatigue. The pre-corrosion strategy is adopted before investigating corrosion fatigue process, so that there is an adequate corrosion effect on samples. The pre-corrosion time is determined to be 3 days through the analysis of electrochemical parameters, viz. corrosion potential and current. For overall fatigue life, corrosion grooves have significant deterioration effect. The transgranular and intergranular features are observed in fracture at initial stage of crack growth. Only transgranular features are found at middle and final stages.

Effect of cold working on crack growth rate of environmentally assisted cracking of 316L SS

Environmentally assisted cracking (EAC) is a main failure mode of key structural materials of nuclear power pressure vessels and pipelines in service. The key structural materials of nuclear power will undergo plastic deformation due to cold working during manufacturing, assembly and welding, and cold working will affect the EAC crack growth rate. In order to understand effect of cold working on crack growth rate of EAC, a combination of theory, experiment and finite element simulation is used. There are experiments to obtain the mechanical properties of 316L stainless steel at different degrees of cold working, and the creep characteristics of 316L stainless steel at low temperature and high stress were obtained by experiment. Based on experiment and theoretical analysis, creep rate of crack tip is used to replace strain rate of crack tip in Ford-Andresen model, and effect of cold working on crack growth rate of EAC is analyzed with hardening at crack tip and without hardening at crack tip. The results show that cold working accelerates crack growth rate of EAC, and the hardening of crack tip micro zone restrains crack growth rate of EAC, causing the “hysteresis” phenomenon in the EAC crack growth process. It is more reasonable to use creep rate of crack tip instead of strain rate of crack tip to calculate crack growth rate of EAC.

A Time Dependent Process Zone Model for Slow Crack Growth of Polyethylene Pipe Material

Polyethylene (PE) pipe is widely used in water supply and gas transportation engineering. Its fracture behavior is very important for the safe operation of the pipeline. The objective of this work is to simulate the slow crack growth (SCG) process of PE pipe material via a time dependent crack-tip process zone model. To achieve this end, the crazing damage caused by stress concentration at crack tip of PE material is taken into account, the stress on the bulk/craze interface layer is supposed to be uniformly distributed due to the micro necking mechanism of the layer, and a linear crack growth kinetics is used. In order to describe the delay characteristics of the fracture process of PE materials, the fracture surface energy is considered as an exponential decay function of time, which is attributed to the creep damage of the craze fibrils. A simulation algorithm of the proposed process zone model is suggested using iterative method. The model is verified by comparing the simulation with the discontinuous SCG behavior reported in the literature.

Experimental Investigation and Micromechanical Modeling of Elastoplastic Damage Behavior of Sandstone

The mechanical behavior of the sandstone at the dam site is important to the stability of the hydropower station to be built in Southwest China. A series of triaxial compression tests under different confining pressures were conducted in the laboratory. The critical stresses were determined and the relationship between the critical stress and confining pressure were analyzed. The Young’s modulus increases non-linearly with the confining pressure while the plastic strain increment and the dilation angle ϕ showed a negative response. Scanning electron microscope (SEM) tests showed that the failure of the sandstone under compression is a coupled process of crack growth and frictional sliding. Based on the experimental results, a coupled elastoplastic damage model was proposed within the irreversible thermodynamic framework. The plastic deformation and damage evolution were described by using the micromechanical homogenization method. The plastic flow is inherently driven by the damage evolution. Furthermore, a numerical integration algorithm was developed to simulate the coupled elastoplastic damage behavior of sandstone. The main inelastic properties of the sandstone were well captured. The model will be implemented into the finite element method (FEM) to estimate the excavation damaged zones (EDZs) which can provide a reference for the design and construction of such a huge hydropower project.

Measuring Crack Growth and Rise in Temperature around a Cylindrical Defect in Explosive Simulants under Low‐Pressure and Long‐Pulse Loadings

AbstractLow‐pressure and long‐pulse loadings are critical loading modes in research on non‐shock ignition. Under such loadings, viscoplastic deformation, fracture, and a local rise in temperature may occur around inherent defects in condensed explosives to cause non‐shock ignition. In this study, transparent poly(methyl methacrylate) was chosen as an explosive simulant to elucidate the processes of crack growth, pore collapse, and rise in temperature at a cylindrical defect by using a set of modified split Hopkinson pressure bars. A recently developed optical temperature‐sensing technique that uses the multiphonon‐assisted anti‐Stokes‐to‐Stokes fluorescence intensity ratio was used to monitor the rise in temperature in the cracks. By combining the work here with our previous research, two significant conclusions are arrived at: 1) Around the cylindrical defect, the opening‐mode crack initiated earlier than the shearing‐mode crack did but its rate of propagation was considerably lower. Moreover, the smaller the cylindrical defect was, the lower was the rate of propagation of the cracks. 2) The rise in temperature in shearing‐mode cracks was higher than that of the opening‐mode cracks. It can be inferred that the local rise in temperature caused by shearing was the major factor leading to the non‐shock ignition of condensed explosives

On an alternative approach for simulating chemically induced crack pattern evolutions in a single crystal

The evolution of essentially periodic crack patterns appears in many natural and technical processes. For example, typical cases of periodic crack patterns are known from drying soils, from the formation of basalt columns, from high temperature loaded ceramics, from fissure formation in coke, and from drying protein solution drops.The appearance of more or less periodic crack patterns is the result of cascades of bifurcation-instabilities of the propagation process. There exist established, mathematically rigorous criteria for the bifurcation of the crack growth process of two initially equally long parallel cracks (Nemat-Nasser et al., 1978; Bazant et al., 1979). These criteria require the determination of the mutual influence of the neighboring cracks on their growth by calculation of partial derivatives. If discretization methods are used for simulating such a growth process, the calculation of these partial derivatives may become very sensitive with respect to the density of the spatial discretization. This is especially true if strong gradients of a crack driving eigenstress field appear as, for instance, in chemical diffusion processes.In the present paper, an alternative approach is introduced, which circumvents estimations of partial derivatives and, in addition, provides a more realistic picture of the generation of crack patterns. This approach is inspired by a computationally efficient method for investigating the buckling and post-buckling behavior in structural mechanics by introducing small imperfections.As a typical example, in which the approach introduced here is especially beneficial, the simulation of self-organized crack pattern evolution in alkali feldspar, a very common brittle crystal, is presented. There, the cracks are driven by eigenstrains caused by cation exchange between the crystal and a salt melt. Comparisons between the character of the pattern formation in the simulation and in experiments show excellent agreement. Furthermore, by combining simulations and experiments the Jc-value can be determined at considerably high accuracy.

Crack growth under three-point beam bending and fracture energy estimation for snow in relation to acoustic emission responses

The non-invasive monitoring of crack initiation and growth processes within snow, a poro-composite matrix, could be useful to predict the structural failure of a composite material. Present work is a new approach utilizing the non-invasive technique of acoustic emission (AE) to study the ongoing cracking and failures processes within snow beams which is difficult to visualize in real time. The progressive crack growth within the beams of snow followed by their failures is studied under three point beam bending in relation to AE. In this work, AE detection platform is developed and implemented for non-contact detection of acoustic emissions generated within a beam with the help of specialized needle-type AE waveguides in conjunction to wideband AE acquisition system. The AEs are detected for entire course of bending, crack nucleation, crack growth and rupture of the beams, both under static and dynamic load conditions. The crack initiation and growth in snow beams were generated without any predefined notch on its surface in a controlled and perceptible manner, particularly at low deformation rates (<0.2 mm/min). The ongoing crack growth, in terms of crack lengths and openings, were also studied from high resolution images, regularly collected during the experimental course. The prominent AE characteristics such as counts, amplitude, absolute energy, etc. were analyzed in context of bending, cracking and rupture of the snow beams for static as well as dynamic load conditions. The total strain energy, estimated in terms of the strain energy density, was imparted to the snow beam which contributed in the crack initiation and growth processes. Further, a fraction of the crack surface energy was manifested in the form of AE energy; therefore, a correlation was established between the crack surface energy and the liberated AE energy for static as well as dynamic loading of snow. The Griffiths model for global energy balance was applied to estimate the crack surface energy. The relation between crack surface energy and corresponding AE energy (released) could be very useful to estimate the fracture energy of the materials directly in terms of AE, non-invasively.

Joint optimization of safety barriers for enhancing business continuity of nuclear power plants against steam generator tube ruptures accidents

In nuclear power plants (NPPs), different types of safety barriers are designed to ensure the safe and continuous operation of the NPP against disruptive events. These safety barriers, although designed to operate in different phases of the accidents evolution, are often optimized separately, without considering their collective effects on preventing disruptions and quickly recovering from the disruptions. This paper develops a joint optimization model for synthetically optimizing safety barriers of different natures, including prevention, mitigation, emergency and recovery barriers to enhance the business continuity of the NPP, considering the threat of steam generator tube rupture (SGTR) accidents. The joint optimization is guided by a business continuity metric called expected business continuity value (EBCV). A physics-of-failure model is developed to describe the crack growth process of the steam generator tube and to model the effect of the prevention barriers, i.e., periodical inspection of the crack length. An event tree model is developed to describe the evolution of the SGTR-initiated accident and to model the effect of the mitigation and emergency barriers. Recovery measures are also considered via a widely-used logarithmic function model. A mixed-integer genetic algorithm (MIGA) is used to obtain optimal solutions of the joint optimization model. The results show that the developed joint optimization model can achieve better performance in terms of business continuity, compared to the conventional methods that optimize the safety barriers separately.

Investigation of creep-fatigue crack growth of G115 steel using a novel damage model

The flexible operation of power-plant structures could cause creep-fatigue crack propagation, which is a major concern for design and maintenance. Therefore, this study investigated the crack propagation in G115 steel under isothermal creep-fatigue loading by using a novel damage model. Creep and fatigue damage were determined by the exhaustion of the creep ductility and the total plastic strain energy during the crack growth process, respectively. The crack propagation behavior was simulated by the finite element method, and the calculated data were compared with experimental results, which demonstrated the high precision of this model. The calculated damage values at the crack tip were analyzed, and the creep damage (cavities) around the main crack under 60 and 600 s hold times were observed based on X-ray micro-computed tomography. The cavity density for the test with 600 s of holding was obviously larger than that for the 60 s dwell test, with the former showing more significant creep damage. Calculations of compact tension specimens with different hold times, specimen thicknesses, and crack lengths were further conducted and analyzed. The results revealed that increasing the hold times, specimen thicknesses, and crack lengths increased the cyclic crack growth rate.

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.