Propagation Of Single Crack Research Articles

From fracture to fragmentation: Discrete element modeling

Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack ensembles to the rapid fragmentation of materials DEM had a substantial contribution to our understanding over the past decades. Recently, the combination of DEM with other simulation techniques like Finite Element Modelling further extended the field of applicability. In this paper we briefly review the motivations and basic idea behind the DEM approach to cohesive particulate matter and then we give an overview of on-going developments and applications of the method focusing on two fields where recent success has been achieved. We discuss current challenges of this rapidly evolving field and outline possible future perspectives and debates.

Analyzing the mechanisms of fatigue crack initiation and propagation in CRH EMU brake discs

A significant number of high-speed electric multiple units’ (EMU) brake discs, manufactured from forged steel, showed thermal cracks during work and NDT. There exist three kinds of cracks on the friction surface; namely, the crackle, radial crack and circumferential crack. Macro-morphologies of the friction surface indicate that the cracks appeared in the interior and edges of the hotspots. Crack growth methods include the single crack propagation and multiple crack connectivity. A finite element analysis (FEA) was performed to determine temperature and stress distribution in the brake disc as well as to estimate stress distribution during braking. Simulation results indicate more significant residual, circumferential tensile stress on the external friction surface after emergency braking. The maximum residual circumferential tensile stress is 200MPa after 300km/h emergency braking. In addition, there is only the circumferential compressive stress on a section which is a certain distance from the exterior of the friction surface, and the distance depends on braking conditions. Therefore, not taking into account thickness reduction of the friction surface due to wear, it can be concluded that when the cracks run along the thickness direction to the specified distance, they will cease to run along this direction and begin propagating mainly in the direction of the radius. In addition, based on the simulation results, a measure was presented to prevent and inhibit the crack propagation.

Prediction of the crack bifurcation in layered ceramics with high residual stresses

A computational tool, aiming to predict the crack propagation (i.e. straight propagation, single deflection or bifurcation) in layered ceramics designed with internal residual stresses, is here developed. The laminate consists of ceramic layers of two different materials, alternated in a multilayer structure. The internal stresses developed during sintering are associated with the thermal expansion mismatch between adjacent layers and volume ratio between both materials. The computational model is based on Finite Fracture Mechanics theory, especially focused on cracks terminating at the interface between two different material layers. The method utilises a matched asymptotic procedure to derive the change of potential energy associated with the fracture process. Crack follows the path which maximises the energy released during crack propagation. A combined loading (thermal and mechanical) is taken into consideration to clarify the influence of the residual stresses on the crack path during fracture. The competition between single crack propagation and crack bifurcation (simultaneous propagation in two directions) can be described using the model. The results predicted by the proposed fracture criterion are in a good agreement with the experimental observations on laminate samples.

Application of electrochemical noise to monitor stress corrosion cracking of stainless steel in tetrathionate solution under constant load

Electrochemical noise measurements were applied to study the initiation and propagation of intergranular stress corrosion cracking in sensitised stainless steel under constant load. Characteristic current transients were identified and assigned to different corrosion processes. One type of transient was very similar to signals related to initiation and propagation of single micro cracks, which were found in an earlier study using the electrochemical microcapillary technique. Other signal types were assigned to metastable pitting events, crack coalescence events or crack growth. Crack propagation could be explained by localised metal dissolution along Cr-depleted grain boundaries.

Modeling the cracking process of rocks from continuity to discontinuity using a cellular automaton

A rock discontinuous cellular automaton (RDCA) was developed for modeling rock fracturing processes from continuous to discontinuous deformation under mechanical loading. RDCA is an integration of the following basic concepts: (1) representation of heterogeneity and strong discontinuity of rock material; (2) moving crack tracking with level set method; (3) the cellular automaton updating rule; (4) rock yield criteria and crack growth laws, etc. This model uses a local, “bottom–up” cellular automaton rule set and state input from neighboring cells to update the state of each cell in a stepped manner, avoiding the need to develop and solve large scale linear equations and the complexity therein. RDCA has the ability to simulate the non-linear and discontinuous deformation behaviors such as plastic yielding, crack initiation, propagation and coalescence etc., in the fracturing process of rocks. The theoretical background and numerical implementation of RDCA are introduced, and the associated numerical code is compiled in the C++ environment. Problems involving a central single crack, edge single crack propagation and three-point bending tests were numerically studied, and the results were compared with the analytical and experimental results to demonstrate the robustness of the method.

Nonlinear ultrasound monitoring of single crack propagation in cortical bone

Nonlinear ultrasound monitoring of single crack propagation in cortical bone

Applications of rock failure process analysis (RFPA) method

Brittle failure of rocks is a classical rock mechanical problem. Rock failure not only involves initiation and propagation of single crack, but also is associated with initiation, propagation and coalescence of many cracks. The rock failure process analysis (RFPA) tool has been proposed since 1995. The heterogeneity of rocks at a mesoscopic level is considered by assuming that the material properties follow the Weibull distribution. Elastic damage mechanics is used for describing the constitutive law of the meso-level element. The finite element method (FEM) is employed as the basic stress analysis tool. The maximum tensile strain criterion and the Mohr-Coulomb criterion are utilized as the damage threshold. In order to solve the stability problem related to rock engineering structures, fundamental principles of strength reduction method (SRM) and gravity increase method (GIM) are integrated into the RFPA. And the acoustic emission (AE) event rate is employed as the criterion for rock engineering failure. The prominent feature of the RFPA-SRM and RFPA-GIM for stability analysis of rock engineering is that the factor of safety can be obtained without any presumption for the shape and location of the failure surface. In this paper, several geotechnical engineering applications that use the RFPA method to analyze their stability are presented to provide some references for relevant researches. The principles of the RFPA method in engineering are introduced firstly, and then the stability analysis of tunnel, slope and dam is focused on. The results indicate that the RFPA method is capable of capturing the mechanism of rock engineering stability and has the potential for application in a larger range of geo-engineering.

Cellular Automata to Simulate Crack Propagation of Quasi-Brittle Materials

Crack propagation in quasi-brittle material such as rock and concrete is studied by a new numerical method, lattice cellular automata. Cellular automaton method is an efficient method that simulates the process of self-organization of the complex system by constructing some simple local rules. It is of the advantage of localization and parallelization. Lattice model can transform a complex triaxial problem into a simpler uniaxial problem as well as consider the heterogeneity of the materials. Lattice cellular automata integrate advantages of both cellular automata and lattice model. In this paper the importance of the study of crack propagation, fundamentals and applications of cellular automata are briefly introduced firstly. Then the cellular automata model is presented, and in order to verify lattice cellular automata, the propagation of mode-I crack in homogeneous material is studied. Results of the numerical simulation are in good accordance with the experimental results and theoretical results of classical fracture mechanics. Furthermore, based on lattice cellular automata, the crack propagation of single crack under uniaxial compression was simulated. During the crack growth the wing crack and secondary cracks were found. The simulation results were consistent with the experimental results.

Crackling noise in three-point bending of heterogeneous materials

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting-time distributions have a power-law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasibrittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.

The assessment of creep damage in certain aged alloys based on Al-Cu-Mg system

The mechanism of creep failure was investigated for three different test alloys namely Al-4.0%Cu-0.3%Mg, Al-4.0%Cu-0.3%Mg-0.4%Cd and Al-4.0%Cu-0.3%Mg-0.4%Ag at 125 and 150°C in the fully hardened condition. The room temperature tensile properties of these alloys increased in the order of ternary alloy, Cd-containing alloy and Ag-containing alloy. The creep performance of these alloys also improved in the similar order. The present studies revealed the dominance of intercrystalline creep failures in all the alloys at both the test temperatures. The grain boundary microstructures contained precipitates with narrow Precipitate Free Zones (PFZ’s) with large difference in particle spacings. Ag-containing alloy recorded minimum grain boundary particle spacing as compared to that of ternary and Cd-containing alloys. The creep damage assessment in terms of damage distribution in the gauge portion showed maximum damage in the Ag-containing alloy as compared to other two alloys. In all these alloys, failures occurred by the coalescence of several cracks and the negotiations of few boundary junctions rather than the propagation of single major crack.

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.

Subcritical propagation and coalescence of oil‐filled cracks: Getting the oil out of low‐permeability source rocks

We use a fracture mechanics model to study subcritical propagation and coalescence of single and collinear oil‐filled cracks during conversion of kerogen to oil. The subcritical propagation distance, propagation duration, crack coalescence and excess oil pressure in the crack are determined using the fracture mechanics model together with the kinetics of kerogen‐oil transformation. The propagation duration for the single crack is governed by the transformation kinetics whereas the propagation duration for the multiple collinear cracks may vary by two orders of magnitude depending on initial crack spacing. A large amount of kerogen (>90%) remains unconverted when the collinear cracks coalesce and the new, larger cracks resulting from coalescence will continue to propagate with continued kerogen‐oil conversion. The excess oil pressure on the crack surfaces drops precipitously when the collinear cracks are about to coalesce, and crack propagation duration and oil pressure on the crack surfaces are strongly dependent on temperature.

Studies on Crack Propagation of Carbon Fiber Reinforced Epoxy Resin Composite

Unidirectional carbon fibre reinforced resin matrix composite (CFRP) with different fibre volume fraction are stretched dynamically under static load in SEM, initiation and propagation mechanism of crack is in-situ observed, and tensile fracture of specimens is also observed. The results show that: Microscopic cracks are mainly originated from fracture of fibre, numerous fibre cracks transfixion each other in form of matrix or interface cracking, and cause failure of CFRP. Microscopic crack propagation path is related to the thickness of matrix layer between fibres. Propagation of single fibre crack at interface accord with description of microscopic crack deflection criterion for fibre reinforced composite, but the crack deflection criterion cannot descript microscopic crack propagation mechanism of unidirectional CFRP effectively, because distribution discreteness of fibre and its strength are not considered.

Modelling multiple cohesive crack propagation using a finite element–scaled boundary finite element coupled method

This paper presents an extension of the recently-developed finite element–scaled boundary finite element (FEM–SBFEM) coupled method to model multiple crack propagation in concrete. The concrete bulk and fracture process zones are modelled using SBFEM and nonlinear cohesive interface finite elements (CIEs), respectively. The CIEs are automatically inserted into the SBFEM mesh as the cracks propagate. The algorithm previously devised for single crack propagation is augmented to model problems with multiple cracks and to allow cracks to initiate in an un-cracked SBFEM mesh. It also addresses crack propagation from one subdomain into another, as a result of partitioning a coarse SBFEM mesh, required for some mixed–mode problems. Each crack in the SBFEM mesh propagates when the sign of the Mode-I stress intensity factor at the crack tip turns positive from negative. Its propagation angle is determined using linear elastic fracture mechanics criteria. Three concrete beams involving multiple crack propagation are modelled. The predicted crack propagation patterns and load–displacement curves are in good agreement with data reported in literature.

Vers un modèle probabiliste pour la formation de réseaux de fissures dans les roches lors de l’injection de CO2

Injection of CO 2 into geologic formations is being practiced today to decrease the greenhouse gas effect, but it is not yet possible to predict with confidence storage volume, formation integrity and long term reliability. Potential CO 2 leakage towards the surface is associated with the cracking state of caprocks through the permeability-fracturing state relationship. A probabilistic method based on the initial distribution of defects is proposed to describe different aspects of the formation of crack networks in rocks under CO 2 injection conditions. Propagation of single cracks is discussed by studying the stress intensity factor variation and the possibility of crack network formation is shown. The interaction between cracks is modelled by considering obscuration zones corresponding to shielding effects created by each crack.

On the mechanics of wire cutting of cheese

The wire cutting process is used in the food industry during the manufacture and testing of products. The cutting process involves fracture as well as large strain deformation and surface friction. This paper investigates the mechanics of the wire cutting process of cheese through a combination of experiments, theory and finite element simulations. The experiments revealed that there was secondary damage on the cut surface, thus a higher fracture energy would be consumed than the common assumption of a single crack propagation. The numerical simulations showed that there was a six-fold change in the strain rate when wire diameters of 0.25 to 2 mm are used. This strain rate effect was modelled through a modification of a previous theoretical analysis of the wire cutting process. The numerical models were also used to predict the cutting forces using two failure criteria: critical strain, which was applied to the initiation of cracking, and a cohesive zone model to simulate crack propagation. Both criteria showed reasonable success in predicting the cutting forces, particularly for cuts made with small wire diameters.

Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method

A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK, 1999]. The entire crack geometry, including one or more cracks, is represented by a single signed distance (level set) function. Merging of distinct cracks is handled naturally by the FMM with no collision detection or mesh reconstruction required. The FMM in conjunction with the Paris crack growth law is used to advance the crack front. In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity [Comput. Meth. Appl. Mech. Engng. 139 (1996) 289]. This enables the domain to be modeled by a single fixed finite element mesh with no explicit meshing of the crack surfaces. In an earlier study [Engng. Fract. Mech. 70 (1) (2003) 29], the methodology, algorithm, and implementation for three-dimensional crack propagation of single cracks was introduced. In this paper, simulations for multiple planar cracks are presented, with crack merging and fatigue growth carried out without any user-intervention or remeshing.

Finite volume analysis of dynamic fracture phenomena. I. A node release methodology

A novel node release numerical methodology based on the Finite Volume discretisation (Ivankovic et al., 1994) has been developed and applied for the simulation of (non-linear) elastic fractures where crack propagation velocities are not a priori known. The analysis is performed in two-dimensions by means of an unconditionally stable implicit time-marching scheme and a second order accurate conservative spatial differencing scheme. Application to single crack propagation problems has demonstrated the validity and accuracy of the proposed formulation for dynamic crack propagation. The results obtained by two examples of crack propagation in single edge notch tensile (SENT) and double cantilever beam (DCB) specimens show good agreement with selected numerical, experimental and analytical results. Based on these results, the formulation appears to be well suited to the study of rapid crack propagation (RCP) phenomena in brittle materials. This, combined with the simplicity and accuracy of the formulation, may provide a solid foundation for more physically realistic RCP computational methodologies other than that of the single linear elastic crack representation considered here.

岩盤 つくばでの最近の研究 （３） 砂岩のサブクリティカルなクラック成長とそれに基づく引張強度のひずみ速度依存性推定の試み

Double torsion tests in ambient air and liquid water have been used to establish stress intensity factor (KI )-crack velocity (V ) diagrams for propagation of single tensile crack in dry or water-saturated sandstones, Kimachi sandstone and Shirahama sandstone. The following main results were obtained: 1) All the experimental data for dry specimens in ambient air and water-saturated specimens in water pertain to region I of the typical KI-V curve, while even region II was clearly observed in KI-V curve of dry specimens tested in water. The appearance of region was particularly clear in Shirahama sandstone. 2) No stress corrosion limit was encountered in the specimens tested in water even at nearly 20 % of critical stress intensity factor (KIC ). But, dry Kimachi sandstone specimen tested in ambient air possibly exhibits the stress corrosion limit at nearly 50 % of critical stress intensity factor (KIC ). 3) The KI-V data of Kimachi sandstone were used to generate a diagram predicting the influence of strain rate on tensile strength. These predictions were in good agreement with the tensile strength determined by Brazilian experiments in ambient air and liquid water. Both the predictions and the experimental results are consistent with a monotonic reduction in tensile strength as strain rate is reduced from nearly 10-2 s-1 to nearly 10-8 s-1.

Analytical study on the cracking transition of concrete shear key

The objective of this paper is to study analytically the transition phenomenon between a large single curvilinear crack and diagnoal multiple cracks observed during the shear-off failure sequence of concrete shear key joints. Based on the principle of the conservation of strain energy, well-known elastic solutions are applied to analyze the principal strain distribution along the shear key base after a large single curvilinear crack propagation. The analytical prediction is compared with the principal strain distribution obtained by the smeared crack FEM analysis. The analytical model is found in relatively good agreement with FEM analysis, indicating that the nonlinear strain localization at the cracking transition could be quantified in a simple manner to a certain extent. In addition, it is analytically clarified that the cracking transition is induced by the change of the boundary condition.