Self-similar Crack Research Articles

Dynamic nucleation as a cascade-up of earthquakes depending on rupture propagation velocity

Earthquake dynamic rupture requires a nucleation process to provide sufficient energy to overcome the fracture energy. Large earthquakes may occur via a cascading rupture process, which includes many triggering processes that cascade from small to large sections of the fault system. During such a process, the nucleation of a large section of the fault plane may occur dynamically via the propagating rupture from a small section of the fault plane. A quasi-static view of seismic nucleation has been widely discussed in earthquake seismology; however, the dynamic nucleation process remains poorly known. Here, we investigate one aspect of the dynamic nucleation process by focusing on the rupture propagation velocity during the nucleation process. We simplify this process as self-similar crack propagation at a constant rupture velocity in a finite nucleation zone within a target region that possesses a uniform fracture energy. We numerically solve this elastodynamic problem in two dimensions for both the anti-plane and in-plane cases using the Boundary Integral Equation method. As the rupture velocity increases, the critical ratio of the fracture energy step to continue the rupture increases and the critical size of the dynamic nucleation zone decreases. The rapid increase in the ratio of the fracture energy step toward infinity could explain why earthquakes never propagate at slow rupture velocities. However, the effect on the size of the nucleation zone is rather limited, with the size of the dynamic nucleation zone decreasing to ~ 70% of the static nucleation zone size. However, such a small difference would result in a significant overall difference if such a dynamic nucleation process repeatedly occurred in the cascading rupture process of a large earthquake, which would be a difficult situation for earthquake early warning.Graphical

Theoretical analysis of self-similar crack propagation along viscoelastic and elasto–viscoplastic interface in a double cantilever beam test

Theoretical analysis of self-similar crack propagation along viscoelastic and elasto–viscoplastic interface in a double cantilever beam test

Self-similar crack propagation along a viscoelastic interface in a double-cantilever beam test

Self-similar crack propagation along a viscoelastic interface in a double-cantilever beam test

Cassette-like peeling system for testing the adhesion of soft-to-rigid assemblies

A novel cassette-like peeling system is developed to address the limitations of current peeling standards when evaluating bonding quality of soft-to-rigid assemblies. The system transforms the translation of a specimen in the conventional peeling configuration to rotation via a cassette-like spool clamping the specimen. The peeled film is loaded by tension to drive the winding of the spool, thus achieving self-similar crack propagation and a stationary peeling front unrelated to the stiffness of the film. These features enable the system’s compatibility with most universal testers and in situ observation of crack tip morphology with optical instruments. Analysis to derive the intrinsic fracture energy when peeling a soft film is conducted based on Griffith energy balance, making use of which, a parametric study is performed to clarify the related mechanisms. We carry out a comprehensive validation of the cassette-like peeling system by performing a series of peeling tests using our in-house prototype and by comparing the results with those from the conventional system. Owing to its universality and ease-of-use, the proposed cassette-like peeling system can potentially be applied to the development of the next generation of peel test standards.

Crack interaction and fracturing of geomaterials with multiscale cracks

Geomaterials contain numerous cracks whose interaction affects the macroscopic mechanical properties of the materials significantly. We propose a mechanical model of cracks of 3 scale levels to investigate the pattern of crack propagation and possible failure modes produced. For modelling crack interaction between different scale levels, we model the unloading domain of influence of a single crack as the sphere with the diameter being the crack size drawn around the crack center. When the tip of a lower scale crack propagates into the influence domain of a crack of a higher scale level, the propagating crack of a lower scale will be unloaded and never grow from this tip. Propagation and coalescence of cracks of different scale levels for different initial crack concentration result in different patterns of cracks propagation and failure. For relatively lower initial crack concentrations, the interaction of cracks of the first scale level dominates, producing failure due to the coalescence of cracks of the first scale level. With the increase of the initial crack concentration, the coalescence of cracks of the third scale level dominates leading to failure at a higher initial concentration. With the further increase of the initial crack concentration, the failure is produced by the coalescence of cracks of the second scale level. At even higher initial crack concentrations the failure is again produced by the coalescence of cracks of the first scale level. The dynamic strength decreases with the increase in the initial crack concentration. • A model of interaction, growth and coalescence of self-similar cracks of 3 scale levels is proposed. • The unloading effect of higher scale level cracks on the propagation of lower scale level cracks is considered. • Degradation of the effective deformation modulus is considered in solving crack-tip equations of motion. • The discreteness of crack propagation at the accelerating stage of loading is discovered. • At certain intervals of the initial crack concentration cracks of the lowest scale level will coalesce first.

Configuration of the ELS test for the determination of the mode II fracture toughness in adhesive joints

In order to obtain Mode II fracture toughness of unidirectional fiber composite materials, the End-Loaded Split (ELS) has enjoyed great success because of its higher stability. As a result, crack growth initiation and propagation values are obtained, the latter being especially used in interlaminar progressive damage models. The propagation values must be obtained when the Failure Process Zone (FPZ) has completely developed. In delamination tests of unidirectional composites, such as those contemplated in ISO 15114, the dimension of the FPZ can be neglected against the rest of the dimensions of the specimen, whereby the self-similar crack growth is reached just after the initiation of the crack propagation. However, in adhesive joints, the dimension of the FPZ increases significantly due to the plasticity of the adhesives. And even it can be larger than the entire length reserved for crack propagation. When this occurs, only initiation values are obtained, always inferior to the values of propagation, being these values too conservative to reproduce the behaviour of the joint. In this paper we present a methodology to define the configuration of the ELS test and the specimen dimensions required to obtain propagation results in adhesive joints. The methodology defined is based on two criteria that take into account the length of the FPZ and the stability of the test. As a result, a domain of validity of the test is obtained, which, for a certain type of adhesive and specimen configuration, it indicated is there will be propagation or not.

Verification of reinforcement isotropic solid model in conjunction with maximum shear stress criterion to anticipate mixed mode I/II fracture of composite materials

In the present research, a new criterion based on maximum shear stress (MSS) theory is developed for fracture investigation of orthotropic materials under mixed mode I/II loading. The crack is assumed to be embedded both along and across the fibers in the isotropic matrix. Self-similar crack propagation is assumed based on experimental observations and the reinforcement isotropic solid (RIS) concept is utilized for theoretical derivation of the criterion. In this model, an istropic crack tip stress field is assumed and the effects of fibers are supposed as stress reduction factors. The superiority of employing MSS theory in conjunction with RIS model is proved by derivation of a direct MSS-based mixed mode fracture criterion with respect to the orthotropic crack tip stress field. Verification of the results is performed by comparison of the fracture limit curves with available experimental mixed mode fracture data.

Parameter interdependence of dynamic self-similar crack with distance-weakening friction

SUMMARY In several analytical and numerical studies, the slip rate function and energy release rate for dynamic self-similar crack growth have been investigated, and the results obtained have contributed to a theoretical understanding and estimation of on-fault energetics. However, the relationships among physical parameters, including stress state, process zone size, rupture velocity, peak slip rate and energy release rate, are still unclear. Therefore, the aim of this study is to derive an analytical solution of the slip rate distribution of antiplane self-similar crack growth under distance-weakening friction that mimics slip-weakening friction. To satisfy the condition that the slip rate starts from zero at the rupture front, a trade-off relationship among rupture velocity, process zone size and breakdown stress-to-stress drop ratio is proposed. The peak slip rate, slip-weakening distance and fracture energy obtained using the proposed model provide a possible mechanism for the determination of the rupture velocity and the estimation of the fracture energy of the self-similar crack growth, based on the seismic observables.

Pure mode I and II interlaminar fracture characterization of carbon-fibre reinforced polyamide composite

In this work, interlaminar fracture characterization of carbon-fibre reinforced polyamide composite was studied experimentally and numerically. The double cantilever beam and end notched-flexure tests were performed to determine interlaminar fracture toughness under pure mode I and pure mode II, respectively. Equivalent crack length based procedures were used to assess the Resistance-curves, which allowed obtaining the fracture energies under self-similar crack growth. It was observed that toughness values are markedly higher than the ones obtained for typical carbon-epoxy composites and other thermoset based composites. A cohesive zone model with trapezoidal softening law was employed to simulate the fracture process in both tests. An inverse procedure was followed to determine cohesive parameters defining laws representative of the fracture process. Overall, good agreement was obtained revealing the suitability of the procedure and the appropriateness of the obtained laws. The obtained fracture energies for this thermoplastic composite are quite superior when compared to the thermoset based ones, making this material a promising candidate to replace thermoset matrices in many structural applications.

Mode I steady-state crack propagation through a fully-yielded ligament in thin ductile metal foils

Steady-state crack propagation is the advance of a self-similar crack tip with a constant driving force. Though steady-state growth is often described with analytical models, it is rarely experimentally observed or characterized under quasi-static loading conditions. Thin ductile metal sheets, such as the 25.4 μm, 50.8 μm, and 127 μm thick 1235 aluminum specimens used in this study, exhibit steady-state crack propagation but cannot be characterized by conventional linear-elastic (K) or elastic-plastic (J) crack tip parameters that require contained crack tip plastic zones. Instead we used a fully-yielded plastic crack growth resistance analysis (i.e., ligament stresses were above the tensile yield stress) to identify when cracks in thin aluminum sheet specimens reached steady-state propagation conditions. At steady-state a constant, characteristic crack growth resistance, σc was observed for each sheet thickness (σc25.4μm=60MPa,σc50.8μm=95MPa, and σc127μm=93MPa). This σc-controlled crack growth is dramatically different from conventional linear elastic and elastic plastic crack growth because the plastic zone is uncontained and extends across the remaining ligament.

Conditions of Self-Similarity of Edge Transverse Shear Cracks in a Square Plate

We determine the stress-strain state of a rectangular plate with edge crack under the conditions of transverse shear. The conditions of self-similar crack propagation are established. We deduce a formula for the evaluation of the stress intensity factors KII via the shear stresses.

Rolling disc model for rock cutting based on fracture mechanics

A rock cutting by a TBM's rolling disc model based on Linear Elastic Fracture Mechanics is considered in this study. From dimensional considerations the factors that primarily influence the normal force exerted by disc cutter mounted on the cutterhead of a rock TBM are: (i) the fracture toughness of the rock itself that controls the propagation of a critical initial crack leading to chipping, (ii) the disc's tip shape that also influences the ratio of normal force to the lateral force and the ratio of the normal force to the rolling force, and (iii) the disc's penetration depth that also depicts together with the disc radius the contact area, and (iv) the spacing between adjacent cuts. The hardness of the rock is then calculated by dividing the normal force with the contact area. These parameters are considered here as the main input parameters for the simulation of the quasi-static propagation of a lateral crack that gives a rock chip starting from the disc towards the adjacent kerf created by the neighboring cutter under the action of a concentrated load. In this first order approach we assume that the size of the starter crack over the penetration depth ratio remains constant. For the accurate computation of the mode-I and mode-II stress intensity factors at each crack growth increment, we have employed the displacement discontinuity numerical method equipped with a special crack tip element based on strain gradient or grade-2 (g2) elasticity theory. Mixed-mode crack growth obeys either the energy balance criterion or maximum tangential tensile stress criterion. The numerical results are then compared with published linear cutting rig test results on four rock types. The accuracy of the maximum tensile tangential stress criterion is better compared to the energy balance criterion. However, even with the simplest self-similar crack growth fracture criterion based on energy balance, we have found acceptable agreement of numerical with experimental results by assuming only one free parameter, namely the mode-I fracture toughness of the rock. It is thus recommended that the rock characterization for disc cutting processes should be done not only by the uniaxial compression and indirect tension tests, but also with a proper fracture mechanics test according to the ISRM Suggested Methods for the determination of the rock fracture toughness.

A study of mode-I self-similar dynamic crack propagation using a lattice spring model

The spontaneous crack growth in an infinite domain is studied using the distinct lattice spring model (DLSM). The kinetic energy, strain energy, crack opening, and crack branching during the crack growth are investigated numerically using a simple spring model. The discrete simulation satisfactorily reproduces the experimental observations and the theoretical predictions of the fracture energy increase even without considering the crack tip damage zone and crack bifurcation. Moreover, from analysis of the intrinsic fracture energy release rate, it was concluded that the observed fracture energy increase should originate from the distribution of kinetic energy during self-similar crack growth.

Stress distribution study on multi-holes configurations in woven fabric kenaf composite plates

In structures applications, composite components are joined by bolted connection is commonplace requires introduction of drilling multi-holes. In order to study the structures response of these material properly, a parametric study on stress analysis is required to take into account arrays of variation including lay-up types, multi-hole configurations, intensity of applied stress etc. The failure and fracture of composite plates is somewhat complex, stress analysis study from numerical modelling able to predict the location of crack exhibited. Current study implemented 2-D finite element analysis (FEA) modelling framework on various multi-holes configurations woven fabric kenaf composite (WFKC) plates, the findings are then compared with conducted experiment. It was found that in non-staggered holes, maximum stress occurred at the outer holes suggesting net-sectional failure to initiate and self-similar crack behaviour through plate thickness. On the contrary, net-sectional failure in staggered hole configurations are dependent upon smallest net-sectional area in any line perpendicular to plane axis. The stress analysis conducted provides good agreement with conducted experiment.

Cohesive zone and level set method for simulation of high cycle fatigue delamination in composite materials

This paper deals with high cycle fatigue delamination in composite materials. The cohesive zone approach along with the level set method is used to simulate fatigue-driven delamination growth. The cohesive zone method is used for calculation of the energy release rate at the crack front because of its superiority over the virtual crack closure technique (VCCT) for bi-material interfaces and non self-similar crack growth. Evolution of the crack front in 3D during fatigue growth is handled with the level set method. The damage variable in the cohesive zone formulation is changed according to the updated level set field. Benchmarks are used to evaluate the performance of the proposed approach in simulation of 3D delamination growth under fatigue loading.

Applicability of VCCT in mode I loading of yielding adhesively bonded joints—a case study

Virtual Crack Closure Technique (VCCT) is a fracture analysis method that is typically utilised when plastic dissipation does not exist. This paper studies the applicability of VCCT for crack growth analyses of an adhesively bonded joint with a ductile adhesive and self-similar crack growth. Analyses were performed for a Double Cantilever Beam (DCB) specimen with epoxy adhesive. Reference data for the analysis case existed. The precrack cycle of the DCB test was first analysed assuming linear elastic behaviour of the adhesive and by using the measured average fracture energy as a critical value. The computed force–displacement curve was noted to match well with the experimental data. In the next step, a nonlinear analysis was performed by using a linear elastic – ideally plastic material model for the adhesive and by selecting the critical energy release rate value so that the computed force–displacement curve fit the experimental and linear analysis data. The approach allowed for extracting plastic dissipation from the measured fracture energy to obtain an estimate for the critical energy release rate. The nonlinear analysis results were further studied using the Energy Derivate Technique (EDT) as a post-processing tool. The EDT analysis results confirmed that plastic dissipation remains at a constant level for the entire crack propagation phase of the precrack cycle analysis.

Mode I fracture characterization of human bone using the DCB test

Purpose – Fracture characterization of human cortical bone under pure mode I loading was performed in this work. The purpose of this paper is to validate the proposed test and procedure concerning fracture characterization of human cortical bone under pure mode I loading. Design/methodology/approach – A miniaturized version of the double cantilever beam (DCB) test was used for the experimental tests. A data reduction scheme based on crack equivalent concept and Timoshenko beam theory is proposed to overcome difficulties inherent to crack length monitoring during the test. The application of the method propitiates an easy determination of the Resistance-curves (R-curves) that allow to define the fracture energy under mode I loading from the plateau region. The average value of fracture energy was subsequently used in a numerical analysis with element method involving cohesive zone modelling. Findings – The excellent agreement obtained reveals that the proposed test and associated methodology is quite effective concerning fracture characterization of human cortical bone under pure mode I loading. Originality/value – A miniaturized version of traditional DCB test was proposed for cortical human bone fracture characterization under mode I loading owing to size restrictions imposed by human femur. In fact, DCB specimen propitiates a longer length for self-similar crack propagation without undertaking spurious effects. As a consequence, a R-curve was obtained allowing an adequate characterization of cortical bone fracture under mode I loading.

Dugdale model for a dynamically expanding crack in an orthotropic solid

The Dugdale model has been extended to a dynamically expanding crack in an orthotropic material. The stresses in the plastic zone as functions of applied stress, plastic zone tip speed and crack speed are derived. Expression for the energy release rate is obtained. The effects of plastic anisotropy and elastic anisotropy on ductile crack propagation are studied using a quadratic yield criterion and an admissible condition for self-similar crack expansion.

Investigation of Fracture in an Interface Crack Between Bone Cement and Stainless Steel

Interface strength is considered as one of the most influential factors in the long-term durability of the replaced joint in cemented total hip replacement. Several researchers have suggested that the damage initiation in a replaced joint is a mechanical phenomenon primarily taking place in the vicinity of cement-prosthesis interface. In this study, the fracture behavior of a crack at the interface of cement-prosthesis was investigated both experimentally and theoretically under static loading conditions. The finite element method, and then the maximum tangential stress (MTS) and the generalized MTS (GMTS) criteria were used for theoretical study of interface fracture. Some experiments were also carried out to investigate the effect of cement mixing methods (hand mixing and vacuum mixing) on crack growth pattern. The results showed that the vacuum-mixed cement led to self-similar crack growth along the cement-prosthesis interface, while the crack kinked into the cement in the samples prepared by hand-mixed cement. Then some experiments were performed to verify the theoretical results obtained for mixed mode fracture angles in the samples prepared by hand-mixed cement. The sandwich Brazilian disk model was used in both finite element and experimental approaches to simulate the cement-prosthesis interface. The experimental results were found to be in good agreement with those predicted by the GMTS criterion.

Dynamic cracking resistance of metallic materials during rapid propagation of a self-similar crack

A model is proposed to determine the dynamic cracking resistance KID of metals and alloys for the case of a rapidly moving fractal or self-affine crack. The values of this characteristic correlate with the fractal dimension Df of the future contour of a crack surface profile. KID is lower or higher than KIC depending on the fractal dimension.