Initial Crack Distribution Research Articles

Modeling the Fracturing Behavior Transition in Fractured Granite under Thermo-Hydro-Mechanical (THM) Condition

An in-depth understanding of the thermo-hydro-mechanical (THM) effects on rock fracturing becomes progressively important in natural energy exploitation projects. However, the failure mechanisms of fractured granite under THM conditions are very complex. To investigate the effect of THM treatment on the meso-macro fracturing behavior transition in fractured granite, a coupled thermo-hydro-mesostructure-based DEM (T-H-MSBM) model was developed to reconstruct rock microstructures and distinguish the THM responses of varying mineral grains, pores and micro-cracks in the fractured granite. Based on the T-H-MSBM, fractured granite was first generated in terms of large damage degree, and the comparisons of numerical compression simulations in the natural and fractured granites were carried out under the coupled conditions of temperature (25-225 °C) and pore pressure (0-12 MPa). The interplay of THM treatment and damage degree on the mechanical properties of fractured granite was revealed, and the main mechanisms affecting the varied macro mechanical properties were further discussed insight from the fracturing behavior transition in fractured granite during the THM-uniaxial loading process. The results indicate that both temperature and pore pressure exert the amplified deteriorating effect on the macro mechanical properties of fractured granite with increasing damage degree, while the temperature dependence becomes significantly more pronounced in the fractured granite with low damage degree. The unique distribution of initial cracks controlled by mineral characteristics can lead to large variability in the initiation of THM-induced tensile cracks, and hence to the emergence of multiple fragments in the fractured rock with large damage degree during the compression loading, especially under high pore pressure. The findings can provide important insights into geotechnical applications to achieve engineering safety and economic objectives. For example, during the process of deep resource extraction, we can adjust the reservoir reformation methods in a more reasonable and dynamic manner by considering the variations in the damage degree of fractured rock resulting from excavation disturbance.

Three-dimensional fatigue crack growth based method for fatigue reliability of metallic materials

Fatigue is one of the greatest threats to structural integrity. It is sensitive to the uncertainties of material quality, manufacturing quality and service load, making fatigue reliability analysis important and challenging. Here, a reliability analysis method considering these uncertainties is proposed. Firstly, the distribution of equivalent initial crack sizes in the material was obtained from the S-N data by back-extrapolation based on three-dimensional (3D) fatigue crack growth prediction. Then, the sample set for reliability analysis was obtained by randomly combining the applied stresses and crack sizes under the assumption that the crack sizes and applied stresses are independent. Further, the fatigue life of every sample is predicted with the 3D crack growth method, and the cumulative distribution of fatigue life was obtained to analyze the reliability. Based on the obtained initial crack distribution with stress ratio R ≥ 0, the predicted P-S-N diagrams of different stress ratios and stress concentrations were in accordance with the experimental data, indicating that the obtained initial crack size distribution has a certain universality. Finally, the influence of sampling numbers on the reliability analysis is analyzed with five types of commonly used metallic alloys. It is shown that the cumulative distribution of fatigue lives could be obtained with a less sampling number. Compared with Monte Carlo and importance sampling methods, this method can reduce the number of samples effectively and achieve the reliable probability of different fatigue life intervals.

Thermal-oxidation coupled analysis method for unidirectional fiber-reinforced C/SiC composites in air oxidizing environments below 1000 °C

The thermal analysis method for unidirectional fiber-reinforced C/SiC composites (C/SiC-UFRC) in air oxidizing environment below 1000 °C is developed, including a mathematical theoretical model and a finite element model. The mathematical model (MM) is established by combining the thermal resistance network method and the oxidation kinetics theory. The influence of oxidation characteristics on C/SiC-UFRC axial thermal conductivity is firstly introduced into MM, which provides a reference for the theoretical calculation method of C/SiC-UFRC axial thermal conductivity under oxidation conditions. The finite element model (FEM) is constructed on the representative volume element (RVE) of C/SiC-UFRC and the numerical heat transfer method. The FEM numerically simulated the microstructure in the oxidation process and firstly be applied to study the effects of oxidation on the micro temperature field and heat transfer of C/SiC-UFRC. Through the mutual confirmation of MM and FEM, the prediction of thermal conductivity of CMC in air oxidation environment is verified. The effects of oxidation time, oxidation temperature and random distribution of initial cracks are investigated to reveal their influences on the heat transfer behavior of C/SiC-UFRC.

Identification of Initial Crack and Fracture Development Monitoring under Uniaxial Compression of Coal with High Bump Proneness

The rock burst proneness of coal is closely related to the coal mass structure. Therefore, the initial crack distribution of high burst proneness coal, its fracture development, and failure process under loading conditions are of great significance for the prediction of rock burst. In this study, high burst proneness coal is used to prepare experiment samples. The surface cracks of the samples are identified and recorded. The internal crack of the sample is detected by nuclear magnetic resonance (NMR) technology to determine the crack ratio of each sample. Then, 3D-CAD technology is used to restore the initial crack of the samples. Uniaxial compression test is carried out, and AE properties are recorded in the test. The stress-strain curve, the distribution of the fractural points within the sample at different stress states, and the relationship between ring count and stress are obtained. Results show that the stress-strain curves of high burst proneness coal are almost linear, to which the stress-ring count curves are similar. The distributions of fractural points in different bearing states show that the fracture points emerge in the later load stage and finally penetrate to form macrofracture, resulting in sample failure. This study reveals the initial crack distribution of coal with high burst proneness and the fracture development under bearing conditions, which provides a theoretical basis for the prediction technology of rock burst and technical support for the research of coal structure.

Crack propagation prediction of asphalt pavement after maintenance as a function of initial cracks distribution

The fatigue life obtained in the Lab is far from the service life of the field roads because of the influence of pavement maintenance. To evaluate the remaining service life of existing roads, the fracture mechanics principles were conducted to characterize the fatigue cracking of asphalt pavement in Jiangsu province of China. The statistics theory was applied to build a new model as a function of the distribution of initial cracks in order to predict the crack propagation. The annual number of cracks detected on the road and equivalent single axle loads (ESALs) per annum was seen as variables to calculate the initial cracks distribution. This aims to predict the crack growth tendency of asphalt pavement before and after maintenance. It was found that exponential function can be used to characterize the relationship between the number and the length of initial cracks. The results of the model correspond with the downward trend of pavement performance. The model is suitable for predicting the service life of pavements of different service time. Especially those were used over 10 years and data of initial pavement condition were difficult to find. After calibration and validation, a comprehensive model considering local materials, traffic information and environmental conditions were established to predict pavement performance after maintenance and propose preventative maintenance schemes for pavement.

ROLE OF ACTIVE STRUCTURAL ELEMENTS IN LIFE CYCLE OF BUILDING CONSTRUCTIONS

During the life cycle of building constructions, a complex of interconnected and interdependent processes and stages of structural changes are implemented that ensure the safety of their functioning. The structural elements that determines through their existence in the structure of any composite, the conditions of the life history of the construction-system are cracks, inner surfaces of partition and residual deformations. The selected elements belong to the conditionally invisible parts of the material structure. Cracks, internal interfaces and residual deformations can be distinguished as active structural elements, as they are able to react to any influences in the same tempo-rhythm, predeterminations the timely manifestation of structural adaptation (self-organization). This ensures external and internal safety of constructions during operation. However, cracks, inner surfaces of partition and deformities can shorten the life history of the construction, taking it to the path of degradation and death. Thus, cracks, inner surfaces of partition and deformations perform both a structural and destructive role in the life cycle of a construction. Therefore, an important task should be considered an analysis of the role of active elements in the life cycle of building constructions. The carried out analysis contributes to solving the problems related to improvement of safety of structures and products functioning due to directed guidance of active elements in the form of cracks and internal interfaces with mandatory consideration of the influence of residual deformations. To quantify the change of total length of cracks and inner surfaces of partition can be through the coefficients of damage Kd and Kd1. Increasing structural diversity of concrete and expanded clay concrete contributes to the organization of structures in which the distribution of initial cracks prevents them from growing to dimensions dangerous to the structure.

Effect of initial damage variability on hot-spot nucleation in energetic materials

Mechanical insult may be able to produce chemical transformations in solids when the energy is released in highly localized regions. This phenomenon is responsible for the nucleation of hot-spots that are responsible for ignition of energetic materials. The concentration of energy at microstructural defects leads to the probabilistic nature of ignition. The effect of the microstructure of the energetic particles, specifically the influence of the initial crack distribution on the sensitivity to ignition, is studied for a particle embedded in a polymeric matrix at impact velocities 100 m/s and 400 m/s with finite element simulations that couple fracture dynamics and heat transport. A phase field damage model that includes heat sources due to frictional heating at the crack surfaces and heat dissipation during crack propagation is developed and verified. These heat sources are compared and, in the range of impact velocities studied, heat generation due to friction is more important than dissipation due to crack propagation. Hot-spots nucleated at 100 m/s do not reach the critical temperature while conditions consistent with the Lee-Tarver criterion for ignition are observed at 400 m/s impact velocity. The variability observed due to the stochasticity of the initial crack distribution is studied and it increases with a higher impact velocity. In particular, regions of high temperature develop close to cracks intersecting the particle polymer interface. Therefore, controlling the surface quality of the energetic particles may lead to a reduction on the sensitivity uncertainty in polymer-bonded explosives.

Mechanical and crack evolution characteristics of coal–rock under different fracture-hole conditions: a numerical study based on particle flow code

Coal–rock material contains many fractures and holes and it is of great significance to study their mechanical characteristics for understanding the instability mechanism of coal body. In this manuscript, considering fracture with different inclinations and hole with different positions, a variety of defective coal–rock specimens were established by PFC2D software, then characteristics of stress–strain and crack evolution law of coal–rock with different fracture-holes were discussed. The results show that mechanical properties, crack evolution characteristics, propagation forms of initial crack and final crack distribution form of coal–rock specimens with different fracture holes are different; the fracture angle has a larger influence than the hole position. Peak strength, peak strain, peak step and the total crack number show an increasing trend with the increase of fracture angle, while the crack initial propagation length becomes shorter and shorter.

A parametric study of the dynamic failure of energetic composites

Heating by frictional sliding of cracks is often considered to be one of the most important causes of localized melting and ignition in solid explosives. Furthermore, recent high speed X-ray phase contrast experiments on energetic composites under dynamic compression [Parab et al., Appl. Phys. Lett. 109(13) (2016)] show that most fracture events appear inside the particles. Initial cracks develop in regions where particles are close, and widespread fragmentation is observed in the interior of the particles as the stress waves propagate through the sample. However, most simulations have focused on interface debonding of energetic composites and, in general, do not include fracture of the particles explicitly. A phase field damage approach is used to model the dynamic response of a system of cyclotetramethylene-tetranitramine particles embedded in a Sylgard matrix. The simulations show several damage mechanisms observed in the experiments. The effects of the energy release rate and the initial crack distribution on the energy dissipation due to fracture are studied. The numerical results confirm that initial cracks play an important role in the evolution of damage, energy dissipation and consequently, the formation of hot-spots.

Dynamic damage localization in crack-weakened rock mass: Strain energy density factor approach

The key failure mechanism of rock mass subjected to compressive loads is due to the damage localization. Conventional methods can not be applied to study the dynamic damage localization physical behavior of crack-weakened rock mass. The strain energy method has the capability to investigate the dynamic damage localization feature in crack-weakened rock mass. Therefore, in order to analyze the dynamic damage localization behavior, strain energy density factor approach is adopted in this paper. A two-dimensional model with periodic rectangular noncollinear array of cracks is established. Then, the onset condition of periodic distribution cracks in rock mass is obtained using strain energy density factor approach. By analyzing the bifurcation of crack growth pattern, the critical length and stress of damage localization of crack-weakened rock mass is determined as well as the location of damage localization. In addition, parameters sensitivity analysis is carried out, the effects of the length of crack, friction coefficient, fracture toughness, confining stress, velocity of crack growth, inclination and spacing between lines and rows on the onset condition for damage localization and bifurcation pattern of rocks are discussed. It can be concluded that onset condition of damage localization is mainly affected by its distribution of initial cracks.

Influence of corrosion-induced cracking on structural behavior of reinforced concrete arch ribs

This paper experimentally investigates the effects of corrosion-induced cracking damage on the static behavior of corroded reinforced concrete arch ribs. Four circular reinforced concrete arches including an uncorroded arch rib and three corroded arch ribs are designed and made in laboratory conditions. The initial crack distribution and crack width are discussed by accelerated corrosion test observations. Based on a five-loading static test, the crack propagation, the load–displacement response, the ultimate load bearing capacity and the failure modes of arch ribs are also discussed. Following this, a developed calculation model considering the effect of corrosion damage is used to assess the capacity of the arch ribs. Experimental data are used to validate the proposed method and reasonable agreement is observed between theoretical predictions and experimental results.

A Probabilistic Environmentally Assisted Cracking Model for Steam Generator Tubes

A probabilistic environmentally assisted cracking (PEAC) model was developed to describe the propagation of primary water stress corrosion cracking for Alloy 600 in roll-transition region of steam generator (SG), a severe environmentally assisted cracking problem in pressurized water reactors (PWRs). In the PEAC model, crack growth rate (CGR) and probability of failure (POF) were obtained by adopting a Bayesian inference that decreases the uncertainties of unknown parameters and their distributions in theoretical equations. The CGR is mainly dependent on three factors: probability of detection (POD), initial crack size distribution, and stress distribution. The POD, which is a logistic link was updated with Bayesian inference based on SG inspection data. The crack size distribution, which is relative to initiation time expressed by a Weibull function, was also updated with Bayesian inference using POD. The stress distribution caused by mechanical rolling is considered to be a major contributing factor along the SG tube. It based on finite element analysis is deterministic model unlike POD and initial crack distribution. According to this model, the uncertainty of hyperparameters in the CGR which are parameters of a prior distribution was reduced, and the appropriate level of confidence was achieved by utilizing the available data. Moreover, a benchmark study for the SG tube was performed to evaluate reliability of Alloy 600 SG components in nuclear power plants. The POF was estimated from the developed PEAC model and failure criteria by taking into account the effects of inspection and repair of defective tubes. The results from this study are applied to demonstrate risk reduction in PWRs by adopting risk-informed in-service inspection.

The Elastic Strain Energy of Damaged Solids with Applications to Non-Linear Deformation of Crystalline Rocks

Laboratory and field data indicate that rocks subjected to sufficiently high loads clearly deviate from linear behavior. Non-linear stress–strain relations can be approximated by including third and higher-order terms of the strain tensor in the elastic energy expression (e.g., the Murnaghan model). Such classical non-linear models are successful for calculating deformation of soft materials, for example graphite, but cannot explain with the same elastic moduli small and large non-linear deformation of stiff rocks, such as granite. The values of the third (higher-order) Murnaghan moduli estimated from acoustic experiments are one to two orders of magnitude above the values estimated from stress–strain relations in quasi-static rock-mechanics experiments. The Murnaghan model also fails to reproduce an abrupt change in the elastic moduli upon stress reversal from compression to tension, observed in laboratory experiments with rocks, concrete, and composite brittle material samples, and it predicts macroscopic failure at stress levels lower than observations associated with granite. An alternative energy function based on second-order dependency on the strain tensor, as in the Hookean framework, but with an additional non-analytical term, can account for the abrupt change in the effective elastic moduli upon stress reversal, and extended pre-yielding deformation regime with one set of elastic moduli. We show that the non-analytical second-order model is a generalization of other non-classical non-linear models, for example “bi-linear”, “clapping non-linearity”, and “unilateral damage” models. These models were designed to explain the abrupt changes of elastic moduli and non-linearity of stiff rocks under small strains. The present model produces dilation under shear loading and other non-linear deformation features of the stiff rocks mentioned above, and extends the results to account for gradual closure of an arbitrary distribution of initial cracks. The results provide a quantitative framework that can be used to model simultaneously, with a small number of coefficients, multiple observed aspects of non-linear deformation of stiff rocks. These include, in addition to the features mentioned above, stress-induced anisotropy and non-linear effects in resonance experiments with damaged materials.

Interaction of microfractures: The mechanism of network building

Microscopic study of fractures in polished sections of Precambrian metamorphic sulphide ore reveals that distinct crack morphologies such as dimensions, orientation, shape and distribution are controlled by mineral associations and temperature conditions during failure. Microfractures developed in a regime of low differential stress where hydraulic pressure triggered the episodic crack opening by pressurized fluids. Fracture arrays consist of segments of varied orientation and width resulting from initially isolated cracks. Linear geometry of fracture systems is complicated by interaction of their segments. Three distinguished types of interaction include in-line propagation of two cracks tip-to-tip (type 1), propagation of two cracks along curved paths towards each other (type 2) and propagation of single crack obliquely towards the other crack (type 3). Different interaction types result from variation in fracture spacing and relative position of their tips and distinguished by the angle of propagation. The ratio of overlap/spacing for interacting fractures is negative (− 0.25 to 0) for type 1 interaction and positive for type 2 (0 to 45), and type 3 (0 to 15) interactions. The mean value of the angle of fracture propagation in the onset of the interaction is obtained as 12° for type 1, 25° for type 2 and 38° for type 3 interactions. The mean value of the angle of fracture propagation accommodating linkage is 4° for type 1, 36° for type 2 and 12° for type 3 interactions. The initial crack distribution is crucial in determining whether their coalescence occurs resulting in mature fracture networks.

Griffith cracks in the mesoscopic microcrack theory

The mesoscopic concept is applied to the description of microcracked brittle materials. The mesoscopic equations are solved in a special case when the microcracks are developing according to the Rice-Griffith evolution law. The evolution of the crack distribution function is investigated in case of simple loading conditions and for two different initial crack distribution functions. The time dependence of the average crack length is calculated, too.

The feasibility of using large impact to destroy a dangerous asteroid

Some physical aspects of high velocity ( >30 km/ s ) collisions involving an asteroid or comet nucleus are discussed. Impacts by both meteoroids and massive artificial objects are considered; these may result in effects such as gas expansion reaction forces, shock wave propagation, and fragmentation. The approach is based on conservation laws and observed phenomena associated with high energy impacts, combining data on the attenuation of strong and weak shock waves in rocks and data on the strength of meteorites as determined by their observed breakups in the atmosphere. The calculations accept the prevailing view that asteroids are structurally inhomogeneous and contain some initial crack distribution, possibly of the type that has been observed in meteorites. Analytical estimates for the mean fragment size distribution and the volume of a fragmentation zone are derived from a step-by-step analysis of the wave evolution. This leads to the surprising conclusion that a powerful impact can cause the complete disruption into small pieces of a much larger monolithic asteroid (1– 2 km in diameter—by an impact with a kinetic energy of less than 1 Mt) than previously thought. In particular, an artificial very massive projectile might be assembled from low-orbit space debris (dead satellites, abandoned space stations, etc.). This suggests that kinetic energy impacts are a viable alternative to nuclear explosions, which other authors have concluded as that required to protect the Earth from an asteroid on a collision course. Recent experimental and theoretical results are also used to compare the total change of asteroid momentum due to a high energy impact to the momentum produced by gas expansion, and also to that resulting from a nuclear explosion.

Study on Setting the Conditions of Initial Cracks for Fatigue Strength Evaluation of Welded Structures

When the fatigue strength of welded structures is evaluated based on fatigue crack growth analysis, it is needed to set up the initial conditions of surface crack occurrence along weld toe.Based on the investigation of interaction effect and coalescence behavior between adjacent surface cracks during their propagation, numerical simulation of fatigue growth life are performed for various situations of initial surface crack shape, size, number, occurrence region and distribution of initial cracks. The results agree well with experimental ones. Referring to above results, authors propose a procedure to set up the condition of multiple surface crack occurrence along weld toe, other than single initial crack for fatigue crack growth analysis.

Size‐scale and slenderness influence on the compressive strain‐softening behaviour of concrete

In this article the compressive mechanical behaviour of quasi‐brittle materials is analysed by means of experimental tests and by using an ad hoc algorithm for numerical simulations based on the Pseudo‐traction and the Boundary‐element methods. The experimental analysis is carried out on specimens with three different size‐scales, three different values of slenderness and two boundary conditions. The numerical analysis was carried out by taking into account the initial random crack distribution, considering the mutual crack interaction, the crack–boundary interaction and the internal friction between the faces of the cracks. The numerical results, in good agreement with the experimental data, highlight the characteristic strain‐softening behaviour of quasi‐brittle materials, and the influence of size‐scale and slenderness on the structural response. By observing the evolution of the crack patterns, it is possible to emphasize, both experimentally and numerically, the transition from crushing to splitting collapse by increasing the specimen slenderness, as well as the transition from ductile to brittle behaviour by increasing the specimen size‐scale.

Boundary element method for the strain-softening response of quasi-brittle materials in compression

In the present paper, the mechanical compressive behavior of quasi-brittle materials is analyzed by means of an ad hoc boundary element algorithm. The analysis is carried out by taking into account the initial crack distribution, which cannot be neglected if the experimental reality (developing over three scales of observation, micro-, meso- and macro-scale) is to be modeled. The algorithm permits us to follow the evolution of the crack geometry during the loading process, which is characterized, at each step, by the propagation of the most critical meso- or macro-crack. Moreover, in order to take into account the micro-crack effect causing the progressive decay of the material, a decreasing variation of the elastic modulus is assumed, depending on the strain energy density absorbed during the loading process. Different geometries, with different slenderness and size scale, are analyzed by the proposed model, with and without friction between specimen and loading platens. The numerical simulations represent the experimental results consistently.

The effect of characteristic crack sizes on the leak-before-break case of pressure vessels and piping with multiple cracks

The Leak-Before-Break (LBB) case of pressure vessels and piping is achieved with the sufficient margin between detectable leak and catastrophic break. Therefore, the respective characteristic crack sizes, i.e. leak size (the crack size at which leakage amount is great enough to be detected) and the break size (the crack size at which crack propagation becomes unstable) are two important governing parameters for the LBB case. In multiple crack situations, the initial crack distribution and crack coalescence behavior are also LBB governing factors. The multiple crack condition related parameters would affect the LBB margin with the characteristic crack sizes together. The effects of multiple cracks on the LBB case, with respect to the different characteristic crack sizes are investigated in the present article by means of computer simulation. The simulation results show that, in multiple crack situation, the LBB margin is not so sensitive to characteristic crack sizes as in single crack situation.