Crack Surface Friction Research Articles

Effect of crack surface friction on stress intensity factor for double-edge cracked Brazilian disk specimens under parabolic distribution load

The weight function method was employed to derive the closed-form solutions of stress intensity factors (SIFs) for double-edge cracked Brazilian disk (DECBD) specimens subjected to parabolic distribution loads, taking into account the influence of crack surface friction. Additionally, the accuracy and validity of these solutions were discussed in comparison with previous numerical results. Furthermore, the impact of friction coefficient and load distribution angle on SIFs was further investigated. The results indicate that the effect degree of load distribution angle on SIFs is closely correlated with both the loading angle θ and crack length α. Both the mode I and mode II SIFs increase with increasing load distribution angle γ for θ = 15° and α < 0.4. However, when α ≥0.60, the impact of load distribution angle γ on SIFs becomes negligible. Furthermore, the friction between crack surfaces of DECBD specimens significantly affects the dimensionless mode II SIF YII, leading to a decrease in dimensionless mode II SIF YII as the friction coefficient μ increases. Moreover, it further demonstrates that both the relative crack length α and friction coefficient μ play important roles in determining the critical loading angle θIIc for crack sticking. The critical loading angle θIIc for crack sticking increases with an increasing relative crack length; however, an increase in the friction coefficient leads to a reduction of this critical loading angle θIIc.

Phase‐field Fracture Based on Representative Crack Elements (RCE): Inelastic Materials, Friction, Finite Deformations, Multi‐physics

AbstractThe concept of representative crack elements has been successfully introduced to phase‐field fracture in previous publications, where anisotropic elasticity [1], visco‐elasticity [2], elasto‐plasticity and crack surface friction [3] are considered at small deformations. This framework allows to overcome unrealistic predictions for the crack kinematics, reported e.g. in Strobl and Seelig [4], and Steinke and Kaliske [5], known from phase‐field models with approximations for the crack closure behaviour based on volumetric‐deviatoric, spectral or similar splits of stress or strain tensors.In the current contribution to the method of phase‐field fracture, the framework for representative crack elements is shown for finite deformations and fully coupled thermo‐mechanics. The iterative solution scheme for the representative crack element and the variational homogenisation method are sketched. Applications to elasto‐plasticity, crack surface friction, finite deformations and thermo‐mechanics with heat radiation through the crack demonstrate the flexibility of the framework.

Investigation of the compression–shear fracture propagation for rocks accounting for confining pressure and crack surface friction

A series of fracture experiments were carried out to study the coupling effects of confining pressure and crack surface friction on the propagation of compression-shear fracture in a self-developed triaxial compartment. Meanwhile, a fracture propagation code (FPC) that can effectively simulate the initiation and propagation of closed cracks was developed for the corresponding numerical research. The results show that the crack of the centrally cracked Brazilian disc (CCBD) specimen is still mainly of tension-shear fracture in a certain range of crack inclination angle under a high confining pressure coefficient. Compared with confining pressure, the influence of crack surface friction on fracture propagation is more prominent after crack closure. In addition, the fracture mode for closed crack is determined by confining pressure, crack surface friction, relative crack length and crack inclination angle.

A complex analysis of stress intensity factors for two asymmetric and unequal collinear cracks in rocks subjected to compressive and shear loads

Crack in the rocks is an important factor of landslide disasters, and cracks may be interconnected to form a large gap under compressive and shear loads. Therefore, it is necessary to study the stability of cracks. In order to study the interaction between multiple cracks, a plane containing two asymmetric and unequal collinear cracks under compressive loads, shear loads and internal pressure was investigated. Complex functions were applied to derive the stress intensity factors (SIFs) of crack tips. The numerical simulation by using the ABAQUS code was conducted to validate the correctness of theoretical solutions, and the numerical results were in good agreement with the theoretical solutions. Then, the effects of outer shear stress, internal pressure, crack distance, crack surface friction and crack length on stress intensity factors of mode II were discussed. We thus can conclude that internal pressure will reduce the friction effect on the crack surface and cause the crack to initiate more easily; the maximum value of KII increases with the outer shear stress increase; the SIFs of internal crack tips are more easily affected by the distance of cracks than that of the external crack tips.

Meso-Mechanical Characteristics of Granite with Natural Cracks after Mud Acid Corrosion

Most of the discovered high-temperature geothermal energy systems are often related with granite that is characterized by natural faults, fractures and cracks of different size. However, the porosity and permeability of the granite matrix is very low, greatly limiting the efficiency of heat extraction in granitic rock. Chemical stimulation, which is regarded as one of the most important means of reservoir stimulation, has consequently received more and more attention. In this paper, a Triassic granite obtained from the eastern region of Liaoning Province in China was reacted with three different concentration of mud acid solution (8% HCl + 1% HF, 10% HCl + 2% HF, 12% HCl + 3% HF) and the resulting microstructure changes studied by scanning electron microscopy (SEM) and nuclear magnetic resonance (NMR). The experimental results show that the number of micropores in the granite increases after chemical corrosion by mud acid solution. A higher mud acid solution concentration results in a much higher pore volume. Triaxial compression tests on the granite before and after chemical corrosion were carried out to study the effect of acidification on the mechanical characteristics of granite, showing that the peak stress and elastic modulus of granite decreases 25.7% and 16.5%, respectively, after exposure to mud acid solution (12% HCl + 3% HF) corrosion for three weeks at room temperature. The particle flow program PFC2D based on discrete element method was used to investigate the mechanical response before and after the chemical corrosion. Considering that the granite is rich in microcracks, the study is simplified by considering them all grouped into one main closed fracture. The influences of main crack inclination angle, crack length, friction coefficient and confining pressure on the mechanical response were investigated. Under the triaxial compression loading state, wing cracks appear at the initial crack tip, then secondary cracks begin to appear. The sensitivity analysis shows that three characteristic strengths (crack initiation strength, damage strength and peak strength) are strongly correlated with crack length, crack inclination angle, crack surface friction coefficient and confining pressure. These three characteristic strengths decrease 60%, 59% and 53%, respectively, compared with their initial values with the increase of main crack length from 6 mm to 22 mm, while they present positive correlation with the fracture friction coefficient from 0 to 1.0 and confining pressure from 10 to 50 MPa. There is a critical inclination angle of the main crack (i.e., 45°), meaning that these three characteristic strengths of granite decrease with inclination angles smaller than 45°, while they increase with an inclination angle larger than 45°. After the corrosion effect of mud acid solution on granite, the pore structure was changed and mechanical properties was damaged, which further affect the failure mode and failure process of granite samples affected by mud acid solutions. This paper provides a theoretical reference for evaluating the effect of chemical stimulation technology on the mechanical characteristics of granite, serving for the continuous hydraulic stimulation design after the chemical stimulation.

Phase‐field Fracture with Representative Crack Elements for Non‐linear Material Behaviour

AbstractThe mechanical energy potential of phase‐field fracture models is subdivided into a portion which (actively) drives the crack and a passive portion. This decompositions depends further on the crack state (opened, closed) in order to consider the re‐contact of the crack surfaces. The identification of the crack state and the decomposition is mostly approximated based on splits of the deformation or stress tensor. Stobel and Seelig [1], and Steinke and Kaliske [2] have shown unrealistic predictions for the crack kinematic for those models in quasi‐static and dynamic analyses. The approach proposed by these authors allows to predict the crack kinematic consistently. Nevertheless, this model is restricted to linear, isotropic elasticity and small deformations.In Storm et al. [3], the underlying concept is generalised. The crack kinematics is consistently obtained from a representative, discrete crack model and coupled to the phase‐field model by means of a variational homogenisation formulation. Thus, the crack driving force is a unique result of the framework of Representative Crack Elements. Analytical solutions for the mechanical problem of the representative crack element applied to linear, anisotropic elasticity and linear thermo‐elasticity at small deformations are presented there.In the current contribution to the method of phase‐field fracture, the framework for Representative Crack Elements is applied to non‐linear bulk materials. The iterative solution scheme for the representative crack element is presented and applied to elasticity with crack surface friction, visco‐elastic and elasto‐plastic materials.

About Compression Fracture

The paper discusses fracture processes occurring under compressive loads. The processes are considered from two points of view: (i) compression fracture mechanisms and their effect on the strength and fracture resistance of the material, and (ii) the effect of geometric constraints on the stress-strain state and fracture conditions of bodies (natural objects) with cracks and crack-like defects. These are particularly the effects associated with crack surface contact, friction, and loading history. Fracture structures are described which form in the conditions of high-rate compression under extreme loads typical of tectonic processes and deep hydrocarbon production. The structures include crack-like compaction regions in highly porous brittle materials (rocks) formed under compression, which present a new form of quasi-brittle mode I fracture (a compression crack). A method is proposed for estimating the effective strength of compressed bodies with one dimension (thickness) being much smaller than the other two and that have through-thickness variable properties and/or composition. As an example, the ice cover strength with respect to longitudinal compression is considered taking into account a partial loss of the ice bearing capacity. The influence of geometric constraints on the fracture mechanisms in fractured thin bodies is discussed. It is shown that the compression fracture of bodies with elongated through holes (or crack-like defects), whose length is much larger than the body thickness, occurs by a mechanism induced by the overlapping of crack surfaces.

Direct Shear Behavior of Fiber Reinforced Concrete Elements

Improving the accuracy of load-deformation behavior, failure mode, and ultimate load capacity for reinforced concrete members subjected to in-plane loadings such as corbels, wall to foundation connections and panels need shear strength behavior to be included. Shear design in reinforced concrete structures depends on crack width, crack slippage and roughness of the surface of cracks.&#x0D; This paper illustrates results of an experimental investigation conducted to investigate the direct shear strength of fiber normal strength concrete (NSC) and reactive powder concrete (RPC). The tests were performed along a pre-selected shear plane in concrete members named push-off specimens. The effectiveness of concrete compressive strength, volume fraction of steel fiber, and shear reinforcement ratio on shear transfer capacity were considered in this study. Furthermore, failure modes, shear stress-slip behavior, and shear stress-crack width behavior were also presented in this study.&#x0D; Tests’ results showed that volume fraction of steel fiber and compressive strength of concrete in NSC and RPC play a major role in improving the shear strength of concrete. As expectedly, due to dowel action, the shear reinforcement is the predominant factor in resisting the shear stress. The shear failure of NSC and RPC has the sudden mode of failure (brittle failure) with the approximately linear behavior of shear stress-slip relationship till failure. Using RPC instead of NSC with the same amount of steel fibers in constructing the push-off specimen result in high shear strength. In NSC, shear strength influenced by the three major factors; crack surface friction, aggregate interlock and steel fiber content if present. Whereas, RPC has only steel fiber and cracks surface friction influencing the shear strength. Due to cementitious nature of RPC in comparisons with NSC, the RPC specimen shows greater cracks width.&#x0D; It is observed that the Mattock model gives very satisfactory predictions when applied to the present test results with a range of parametric variations; ranging from 0 % to 0.5 % in steel fibers content; from 0 % to 0.53 % in transverse reinforcement ratio; from 15 to 105 MPa in compressive strength of concrete. While it gives a poor prediction for a specimen with 1% steel fiber.&#x0D;

Quantification method for parameters affecting multi-scale roughness-induced fatigue crack closure

Our challenge is to clarify the relationship between crack roughness and microstructure. Roughness-induced crack closure (RICC) is known to be one of the main factors decelerating fatigue crack growth. Two factors trigger RICC: 1) nanometer-scale roughness on the crack surface (nano-roughness) and 2) degree of crack deflection (micro-roughness). These factors affect the friction stress acting on the crack planes and the stress intensity factor range for crack closure. For instance, S. Suresh and R. O. Ritchie discussed the effects of geometrical mismatch between fatigue crack planes on crack closure. We further attempt to measure multi-scale crack roughness to quantitatively estimate RICC with respect to both friction and crack closure effects. In this study, we examine the multi-scale crack roughness of a lamellar-structured Fe-9Mn-3Ni-1.4Al-0.01C steel sample as a case study. We verify the effect of crack surface friction. Here, we assume that the basic effect of nano-roughness on friction is significant when the inclination angle of micro-roughness against the loading direction is less than the angle of nano-roughness. If the inclination angle of micro-roughness against the loading direction is larger than the angle of nano-roughness, the nano-roughness effect does not occur because the crack surfaces do no contact with each other. To further discuss the underlying effects of multi-scale roughness, we will present more details on the microstructure- and mechanical condition-related roughness parameters and their quantification techniques.

Crack deflection in brittle media with heterogeneous interfaces and its application in shale fracking

Driven by the rapid progress in exploiting unconventional energy resources such as shale gas, there is growing interest in hydraulic fracture of brittle yet heterogeneous shales. In particular, how hydraulic cracks interact with natural weak zones in sedimentary rocks to form permeable cracking networks is of significance in engineering practice. Such a process is typically influenced by crack deflection, material anisotropy, crack-surface friction, crustal stresses, and so on. In this work, we extend the He-Hutchinson theory (He and Hutchinson, 1989) to give the closed-form formulae of the strain energy release rate of a hydraulic crack with arbitrary angles with respect to the crustal stress. The critical conditions in which the hydraulic crack deflects into weak interfaces and exhibits a dependence on crack-surface friction and crustal stress anisotropy are given in explicit formulae. We reveal analytically that, with increasing pressure, hydraulic fracture in shales may sequentially undergo friction locking, mode II fracture, and mixed mode fracture. Mode II fracture dominates the hydraulic fracturing process and the impinging angle between the hydraulic crack and the weak interface is the determining factor that accounts for crack deflection; the lower friction coefficient between cracked planes and the greater crustal stress difference favor hydraulic fracturing. In addition to shale fracking, the analytical solution of crack deflection could be used in failure analysis of other brittle media.

Stress Intensity Factors Evaluation for Rolling Contact Fatigue Cracks in Rails

ABSTRACTThe stress intensity factors (SIFs) for multiple rolling contact fatigue cracks of a network in the Iran railway under vehicle dynamic load are evaluated in this article. Stress intensity factor evaluation under dynamic loading is simulated in three dimensions using a linear elastic boundary element code. For this purpose, a UIC60 rail with accurate geometry using a boundary element method is studied. A three-dimensional model in Franc3D is provided. Finally, the influence of the friction coefficient between the wheel and rail, crack surface friction, trapped fluid, and initial crack length on SIFs are investigated in detail.

Effect of the Crack Surface Friction on the Field Strength of Bi-Material-Interfacial Crack

The stress field, displacement field and stress intensity factor are discussed based on elastic theory in this paper. The finite element model for interface crack of bi-material is set up, the friction phenomena of interface between two materials is simulated. The effect of crack size ratio and friction factor of crack surface on crack tip displacement, equivalent effective stress and stress intensity factor are analyzed. The results show that with the increase of the crack surface friction coefficient, the displacement and equivalent effective stress of the crack tip, and stress intensity factor will also increase under the condition of the same crack size. If the crack surface friction is ignored, the results will be not precise and are not in conformity with the practical engineering, even the significant impacts will disappear in the research for crack initiation, extension and fracture.

The mutual effects between two unequal collinear cracks under compression

For two unequal collinear cracks under compression, which crack would propagate first, the longer one or the shorter one, and how they affected each other was studied. By using complex stress function theory and considering crack surface friction, the analytical formula of stress intensity factors (SIFs) for an infinite plane containing two unequal collinear cracks was obtained and the analytical results have been validated through numerical simulation by employing ABAQUS code, photoelastic experiments, and compressive tests. The results show that the numerical, photoelastic, and compressive test results agree well with the analytical result. Finally, the effects of crack length, crack surface friction, and crack interval distance between two crack tips on SIFs were analyzed, and the results show that the SIF values at the longer crack tips are always higher than those at the shorter crack tips; for each crack, the SIF value at the internal tip is always larger than that at the external tip.

Influence of crack surface friction on crack initiation and propagation: A numerical investigation based on extended finite element method

Rock strengths are directly influenced by the open or closed flaws widely distributed in rock masses. Extensive studies have been conducted on the propagations of open flaws in rocks. However, few concerns are paid on the propagation of closed flaws, the influence of the surface friction on the initiation and propagation of closed flaws should be investigated systematically. In present article, the crack initiation and propagation in rock like material subjected to compressive loads have been investigated. The effects of crack surface friction on crack initiation and propagation have been quantified with the help from extended finite element method which is efficient and accurate. Based on the analysis on stress distribution and propagation patterns, following results are obtained: Firstly, minor effects are exerted by crack surface friction on the stress distribution around the flaws when the flaws inclination angle is 30° and 45°. However, as the inclination angle increases to 60°, the effects are much more significant. Secondly, as the inclination angle ranges from 30° to 60°, the most favorable angle for crack propagation is 45°. Thirdly, the initiation location and angle of the wing cracks will not be influenced by the frictions. However, the propagation length will be greatly influenced by the friction and the inclination angle.

Stress intensity factor for an infinite plane containing three collinear cracks under compression

AbstractThe fracture behaviour of multi‐cracked materials has become a key issue in fracture mechanics and has received large attention recently. In this paper, an infinite plane containing three collinear cracks under biaxial compression has been investigated. Considering crack surface friction and using complex stress function theory, the exact analytical solution of stress intensity factors (SIFs) for an infinite plane containing three collinear cracks is obtained. The corresponding finite element code of Abaqus is employed to validate the theoretical results, and its results agree very well with the theoretical results. The effects of confining stresses, crack distances and the crack surface frictions on SIFs are analyzed through the theoretical results and the Abaqus code. A photoelastic experiment was conducted to validate the theoretical result about the effect of confining stresses.

The Cohesive Zone Model for Fatigue Crack Growth

In the past decade, the cohesive zone model has been receiving increasing attention as a powerful tool for the simulation of fatigue crack growth. When applying cohesive zone model to fatigue fracture problem, three aspects should generally be taken into account, that is, unloading-reloading path, damage evolution during cyclic loading, and crack surface contact and friction behavior. This paper addresses the critical views of these aspects. Before that, the formulation of cohesive zone model and identification of cohesive zone model parameters and its numerical implementation have been reviewed.

A Plasticity Criterion for Mixed Mode Fracture Initiation with Crack Surface Frictional Characteristics Under Compression

A new plasticity criterion for mixed mode crack initiation angles under compression is presented, based on the characteristics of the plastic core region surrounding the crack tip with crack surface friction. The shape and size of the plastic core region were thoroughly analyzed under compression and the non-dimensional variable radius of the plastic core region for mixed mode compressive fracture was considered. Obviously, the mixed mode fracture initiation under compression is influenced by the frictional characteristics of the crack surface and the external compressive loading state. The loading ratio, Poisson's ratio and the influence of the friction coefficient on the crack tip plastic radius were analyzed. The proposed criterion shows that the crack extends in the direction of the global minimum of the plastic core region boundary. The presented criterion was simulated for various compressive loads and was compared, with other available criteria, against the laboratory experimental data. It can be seen that the presented criterion provides a better agreement with the experimental data.

A Failure Criterion for Cracked Rock Mass under Seepage Pressure and Confining Pressure

The existence of water affects the mechanical properties of cracked rock mass. Taking into account the friction generated by the crack closure, the stress intensity factor of the center cracked plate subjected to compression and seepage pressure was obtained through the theoretical analysis and numerical calculation of the boundary collocation method. The results show that crack tip stress intensity factor increases with the increasing of the seepage pressure, but decreases with the increasing of crack surface friction and the confining pressure. Finally a failure criterion for cracked rock mass under seepage pressure and confining pressure is developed.

An Alternative Form of Propagation Criterion for Two Collinear Cracks under Compression

Under compression, cracks extend, branch and coalesce. These fracturing processes have received much attention recently. In this paper, an attempt is made to find the analytical solution of stress intensity factors for the special case of cracks situated along a straight line, and to set up a fracture criterion. Under compression, cracks close and the crack surface friction can resist crack surface sliding. Considering crack surface friction, a set of complex stress functions is proposed for the special case of cracks situated along a straight line. The analytical solution is formulated, and for the case of only two collinear cracks inside an infinite plate, the exact analytical solution of stress intensity factor is presented. Finally, an alternative form of crack propagation criterion for two collinear cracks under compression is developed, which is expressed in terms of principal stresses. For the case of materials without pre-existing macrocracks, this new propagation criterion becomes the well known Coulomb—Mohr criterion.

Elastic-Plastic Partial Slip Rolling Wheel-Rail Contact with an Oblique Rail Crack

This study employs an elastic-plastic finite element model to investigate the effect of oblique rail surface crack on the wheel-rail contact stress distribution under partial slip rolling conditions. Numerical simulations are performed to explore the effects of the contact distance and tractive force on the contact pressure and tangential stress distributions, tip plastic energy, and critical wheel applied load. Contact elements are used to simulate the interaction between the surfaces of the wheel rail and the crack. The numerical results indicate that the contact stress distributions are influenced significantly by the presence of oblique cracks in the rail. The results also indicate that a higher friction force is induced on the crack surfaces when a greater tractive force is applied to the wheel. This increased crack surface friction force reduces the sliding between the crack surfaces and hence causes a reduction in the tip plastic energy.