Crack Coalescence Process Research Articles

Study on Acoustic Emission Evolution Characteristic of Plastic and Brittle Coal Failure Process

Under uniaxial compression loading, the failure experiments of plastic and brittle coal are carried out to study the acoustic emission evolution characteristic. The results show that the evolution of acoustic emission during the coal failure process corresponds with the process of coal crack initiation, propagation and coalescence. The acoustic emission event rate of the typical plastic coal displayed the variation of up-peak-down during the failure process. The event rate of acoustic emission increase sharply and then drop steadily is the precursor that the main crack plane of the plastic coal would coalescence and the coal will lose its stability. During the failure process of typical brittle coal, the event rate increased steadily with the increase of stress, showing the variation of up-peak; the down stage of acoustic emission is not obvious because the brittle coal suddenly fail after stress peak. The study results can provide a theoretical basis for explanations of the variation of acoustic emission and the establishment of instability criteria in coal and rock stability monitoring engineering by AE technology.

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β⩽30°). When the pre-existing flaws are steep (such as β⩾75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L⩽2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L⩽a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L⩾2a).

Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism

The present study evaluates the discrete element method (DEM) as a tool for understanding the step-path failure mechanism in fractured rock masses. Initially, the study simulates crack propagation and coalescence in biaxial and triaxial laboratory tests. The results of this analysis show that the DEM accurately represents these processes in comparison to other studies in the technical literature. The crack propagation and coalescence processes are important in the step-path failure mechanism for slopes. Simple examples of this mechanism were modeled, and their results were compared with those of the analytical model proposed by Jennings (1970). Among the possibilities suggested by Jennings, modeling with DEM did not provide a good approximation for the case of coplanar cracks, for which failures in the intact rock bridges should only be caused by shear forces. In modeling with DEM, tensile failures occur within the sliding block, generating forces that are not considered in the Jennings model. The non-coplanar crack condition provided a better approximation, since the Jennings model formulation for this case includes the tensile failure of the rock. The main advantage of the DEM over other computational tools is its micromechanical representation of discontinuous media, which permits a better understanding of the step-path failure mechanism. However, good calibration of the macroscopic parameters of the rock and its discontinuities is necessary to obtain good results.

An Experimental Study of the Fracture Coalescence Behaviour of Brittle Sandstone Specimens Containing Three Fissures

To analyse the fracture coalescence behaviour of rock, rectangular prismatic sandstone specimens (80 × 160 × 30 mm in size) containing three fissures were tested under uniaxial compression. The strength and deformation behaviours of the specimens are first analysed by investigating the effects of the ligament angle β2 on the peak strength, peak strain and crack initiation stress of the specimens. To confirm the sequence of crack coalescence, a photographic monitoring technique is used throughout the entire period of deformation. Based on the results, the relationship between the real-time crack coalescence process and the axial stress–strain curve of brittle sandstone specimens is also developed, and this relationship can be used to evaluate the macroscopic deformation characteristics of pre-cracked rock. The equivalent strain evolution fields of the specimen, with α = β1 = 45° and β2 = 90°, are obtained using the digital image correlation technique and show good agreement with the experimental results of pre-cracked brittle sandstone. These experimental results are expected to improve the understanding of fracture mechanisms and be used in rock engineering with intermittent structures, such as deep underground excavated tunnels.

Crack Propagation of Jointed Rock and Application

Brittle media, such as rock mass, usually contain a great number of joints or cracks, which lead to varying mechanical properties and failure behaviors of different rock masses. In this paper, the DDARF method is adopted to simulate the crack initiation, propagation, coalescence and failure process in rock masses prefabricated with the different crack number and spacing under loading. The corresponding stress-strain curves and strength envelope are obtained. The parameters are applied in a case study. The differences in the failure behaviors of the intact and jointed rock masses after cavern excavation are analyzed and compared.

A multifractal model of crack coalescence in rocks

Geometric characteristics of fractal sets of cracks are investigated from the standpoint of their coalescence. A 1D computer model, in which a realistic character of forms of crack sets is achieved through the inducing of sets with the use of the multiplicative cascade procedure, is considered. The investigation is aimed at the determination of conditions of coalescence of cracks organized as a superposition of fractal subsets of a unified set of cracks. The process of crack coalescence is investigated for three different values of the coalescence criterion. The geometric characteristics of the sets of cracks that are necessary for the transition of the crack coalescence process into an avalanche-like stage are estimated.

Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression

Uniaxial compression experiments were performed for brittle sandstone samples containing a single fissure by a rock mechanics servo-controlled testing system. Based on the experimental results of axial stress-axial strain curves, the influence of single fissure geometry on the strength and deformation behavior of sandstone samples is analyzed in detail. Compared with the intact sandstone sample, the sandstone samples containing a single fissure show the localization deformation failure. The uniaxial compressive strength, Young’s modulus and peak axial strain of sandstone samples with pre-existing single fissure are all lower than that of intact sandstone sample, which is closely related to the fissure length and fissure angle. The crack coalescence was observed and characterized from tips of pre-existing single fissure in brittle sandstone sample. Nine different crack types are identified based on their geometry and crack propagation mechanism (tensile, shear, lateral crack, far-field crack and surface spalling) for single fissure, which can be used to analyze the failure mode and cracking process of sandstone sample containing a single fissure under uniaxial compression. To confirm the subsequence of crack coalescence in sandstone sample, the photographic monitoring and acoustic emission (AE) technique were adopted for uniaxial compression test. The real-time crack coalescence process of sandstone containing a single fissure was recorded during the whole loading. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle sandstone sample containing a single fissure is analyzed under uniaxial compression. The present research is helpful to understand the failure behavior and fracture mechanism of engineering rock mass (such as slope instability and underground rock burst).

Meso-Level Numerical Study on Different Type of Fiber Reinforced Concrete

To investigate failure mechanism and toughening features of fiber reinforced concrete (FRC) with different reinforced fibers, meso-level numerical simulations have been conducted on FRCs incorporated with steel, glass and polypropylene fibers, respectively (which were named as SFRC, PPRC and GRC). The complete failure process of crack initiation, coalescence and development, interaction and final break have been simulated. By analyzing the failure patterns of specimens, also the spatial and temporal distribution of acoustic emission and loading - step curves, it can be concluded that both peak strength and toughness of SFRC and GRC can be greatly improved. However, for PRC, the improvement of peak strength is little while its toughness can be enhanced significantly.

A LIFE PREDICTION MODEL OF THERMAL BARRIER COATINGS

The durability and reliability of thermal barrier coatings(TBCs) have become a major concern of hot-section components due to lack of a reliable life prediction model. In this paper, it is found that the failure location of TBCs is at the TBC/TGO interface by a sequence of crack propagation and coalescence process. The critical crack length of failure samples is 8.8mm. The crack propagation rate is 3-10µm/cycle at the beginning and increases largely to 40µm/cycle near coating failure. A life prediction model based a simple fracture mechanics approach is proposed.

Experimental study of the cracking behavior of specimens containing inclusions (under uniaxial compression)

This paper presents the results of an experimental investigation on the cracking behavior of brittle heterogeneous materials. Unconfined, uniaxial compression tests were conducted on prismatic gypsum specimens containing either one, or two, inclusions. These inclusions were of different strengths, stiffnesses shapes, and sizes. Emphasis was placed on crack coalescence processes associated with specimens containing an inclusion pair, as this was the primary objective of the research. Some observations reported in this study compare well with those of other researchers as the overall cracking sequences are similar. On the other hand, the amount of debonding observed in this study at the inclusion interface is significantly less than what was previously observed. Moreover, the extent of shear crack growth at an inclusion boundary increased substantially in specimens containing two inclusions, compared to those with single inclusions.

Numerical Approach to Investigating Pre-Existed Cracks in Rocks

Rock failure analysis is an important research in investigating the behavior of rocks, especially its failure process. And a rock sample, which contains pre-existing cracks, is a typical sample to investigate the rock failure behavior which under tension or compression, because almost all the natural materials exist micro-flaws more or less. This mode is closed to the natural material character. By using Rock Failure Process Analysis code, RFPA2D, we present a numerical simulation and similar materials experiment on rock samples with two pre-existing cracks in uniaxial compression were conducted to investigate the initiation, propagation, coalescence of cracks and failure mechanism of rock. Numerical simulations visually reproduce the process of crack initiation, propagation and coalescence in rock, which are well tallied with experiments in laboratory.

3-D Micromechanics Model for Progressive Failure Analysis of Laminated Cylindrical Composite Shell

A newly developed numerical code MFPA3D is applied to simulate the progressive damage and failure process of laminated cylindrical composite shell. Heterogeneities in meso-scale are taken into account by randomly distributing the material properties throughout the model by following a Weibull statistical distribution. The cylindrical composite shell is discretized into 3-D block elements with the fixed size and is subjected to a lateral compressive loading, applied with a constant displacement control manner. The numerical simulation results show that not only the process of crack initiation, propagation and coalescence but also the failure process can be numerically obtained in three dimensional. The MFPA3D modeling demonstrates that the code can simulate non-linear behavior of brittle materials with a simple mesoscopic constitutive law with a strength and elastic modulus reduction of the weaken elements.

An investigation of crack growth behaviour under creep-fatigue condition

An investigation has been carried out on short crack growth behaviour of AISI type 316 stainless steel under creep-fatigue conditions at 550 °C for high strain ranges of 0.9–2.5% and 60 min hold-time using a high temperature reverse bending rig. The analysis revealed the dominant failure characteristics to be the individual initiation and growth behaviour of many minor cracks in Stage I, and their subsequent coalescence in Stage II. Increasing the strain range increases the number of minor cracks and promotes the process of minor crack coalescence. Predominantly intergranular long cracks are found to form under tensile stresses and transgranular short cracks under compressive stresses.

A theoretical approach to the propagation of interacting cracks

SUMMARY We propose a scheme to compute interaction effects between two randomly oriented cracks under compressive stresses and we discuss the role crack interactions play in the crack coalescence process. Stress intensity factors are computed by using an iterative technique based on the method of successive approximations. Once crack propagation occurs, curved wing cracks grow from the initial crack tips. The stress intensity factors at the wing crack tips are calculated as the sum of two terms: a component for a single wing crack subjected to both the applied stresses and the interaction effect, and a component due to the sliding of the initial crack. We have applied our procedure to various crack geometries. Our results show that interaction effects act on the crack propagation path. For cracks under tension, our approach correctly predicts the curving, hook-shaped paths of interacting cracks that have been observed in various materials. For en echelon compressive cracks, interaction effects depend on the geometry of stepping. For right-stepping cracks, no mode I crack coalescence occurs. A mixedmode propagation criterion may be introduced to check whether coalescing secondary shear fractures initiate. For left-stepping cracks, depending on whether or not there is overlapping, crack coalescence is achieved by tension wing cracks at the inner crack tips. Without overlapping, the growing wing cracks delimit a region where a tensile secondary fracture may develop and lead to coalescence. These results are consistent with previous work and show that our procedure may be now extended to a population of cracks.

Effects of Multiple Cracking on Crack Growth and Coalescence in Contact Fatigue

A three-dimensional fracture analysis is applied to investigate the interaction effects of multiple cracking on the crack growth in contact fatigue and to simulate the process of crack coalescence that leads to pitting failure. The rolling contact fatigue is simulated by a cyclic Hertzian contact loading moving across the surface of an elastic half-space containing several planar cracks. The body force method is applied to determine the three modes of stress intensity factors around the three-dimensional crack fronts. The fatigue crack propagation under contact loading is estimated based on the modified Paris law for mixed mode crack growth. For coplanar cracks, the growth rate increases significantly as the adjacent cracks are very close while parallel cracks appear to constrain the cracks from coalescing. A numerical simulation for the propagation of crack fronts versus contact cycles is shown to agree with the pitting cracks observed in gears.

SHORT CRACK COALESCENCE AND GROWTH IN 316 STAINLESS STEEL SUBJECTED TO CYCLIC AND TIME DEPENDENT DEFORMATION

Abstract— A study has been undertaken into short crack growth behaviour of AISI type 316 stainless steel under creep‐fatigue conditions at 550°C within the high strain range of 0.9 to 2.5% and including a 60 min hold‐time. During the high‐temperature, reverse‐bending tests, surface crack initiation and growth on both the tensile‐hold and the compressive‐hold sides of circular‐section specimens were monitored by means of a plastic replication technique. Detailed analysis revealed that under creep‐fatigue conditions, the initiation and growth behaviour of many individual cracks and their subsequent coalescence to form a major Stage II (tensile) crack was the dominant feature in the failure process. A life prediction model is proposed which incorporates the process of short crack coalescence. Satisfactory predictions of creep‐fatigue lifetimes are derived from the model.

Fatigue crack growth and coalescence at notches

An experimental study of the process of fatigue crack growth and coalescence in the region of a notch has been performed. The testing programme consisted of constant amplitude fatigue tests of 24 notched steel bar specimens, 11 of which modelled the crack coalescence process. The results of the experimental programme are examined and compared to exosting design codes that prescribe a method for dealing with adjacent cracks. The crack growth and shape development data presented in the present study indicate that pre-coalescence interaction between adjacent cracks is not an important process and, in fact, that coalescence itself is not instantaneous as the design codes suggest.

Modelling fatigue crack growth and coalescence in notches

An experimental and analytical study of the process of fatigue crack growth and coalescence in the region of a notch has been performed. The experimental program consisted of constant amplitude fatigue tests of 24 V-notched steel bar specimens, 11 of which had two starter cracks designed to simulate crack coalescence. The results of the experimental program are presented and compared to computer predictions of fatigue crack growth. These were produced by software that performs an integration of the Paris crack growth law and incorporates a new crack shape development and crack coalescence model. It has been found in the present study that pre-coalescence interaction between adjacent cracks is not evident and, in fact, that coalescence itself is not an instantaneous process. This result is of interest because it is at variance with the existing design codes that deal with the case of adjacent collinear fatigue cracks.

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.