Propagation Criterion Research Articles

Propagation Effect Analysis of Existing Cracks in Box Girder Bridges Based on the Criterion of Compound Crack Propagation

Cracking in concrete box girder bridges will have a significant impact on the safety and durability of the structure, and many box girder bridges which are in service have undergone varying degrees of cracking. Currently, the safety design of actual bridge projects place an emphasis on the stress or the load value of a cross section at the limit value specified in the code for safety control. This design method assumes that the member itself is of uniform and continuous material and is internally undamaged. However, the bridge structure is more or less cracked to varying degrees during the period from casting to construction to operation of the concrete members. In this paper, a finite element computational model of a three-span prestressed concrete box girder bridge with existing cracks is established based on the fracture mechanics theory, and the critical parameters of crack extension are introduced to evaluate the extension state of cracks. At the same time, the extended stability of the existing cracks of the box girder bridge is analyzed by considering the temperature effect, vehicle loading, and prestressing loss, and the sensitivity of crack extension under each working condition is investigated. The results show that, with the increase in crack length and depth, the crack expansion is promoted, but the effect is relatively small, and the maximum stress intensity factor is only 6.48 MPa mm1/2. Under the multi-factor coupling effect, the cracks show a composite crack expansion dominated by type I cracks, the longitudinal cracks of the existing base plate are in a stable state, the maximum value of the crack expansion critical parameter of the vertical cracks of the webs reaches 1.087, and there is a tendency to expand locally. The maximum value of the critical parameter for crack extension of the vertical crack in the web plate reaches 1.087, and there is a tendency towards local expansion. The crack extension evaluation criteria proposed in this paper have a certain reference value for crack extension research on similar concrete box girder bridges and provide a scientific basis for the optimized design of similar bridges.

Experimental and numerical investigations on rate-dependent fracture behavior of concrete-rock interface

To ensure the safety and stability of the concrete gravity dams built in the seismic regions, this study investigated the rate-dependent fracture behavior of the concrete-rock interfaces with different roughness degrees. Firstly, direct tensile tests and three-point bending tests were conducted to measure the mechanical and fracture properties of the concrete-rock interface with three roughness degrees, i.e. the 4 × 4 interface, natural interface, and 7 × 7 interface, and under four strain rates, i.e. 10-5/s, 10-4/s, 10-3/s, and 10-2/s. By employing the fictitious crack model and initial fracture toughness-based crack propagation criterion, numerical simulations were conducted to analyze the crack propagation processes of the concrete-rock interfaces under different strain rates. The results indicated that the tensile strength and initial fracture toughness exhibited an obvious increasing tendency with the increase of the strain rates, and they showed a nearly linear relationship with the logarithms of the strain rates. Prediction models were proposed to calculate the tensile strength and initial fracture toughness of the concrete-rock interface under different strain rates. In addition, the initial fracture toughness-based crack propagation criterion was proved to be applicable to analyze the crack propagation processes of the concrete-rock interfaces under both quasi-static and seismic strain rates. It was found that the fully-formed fracture process zone lengths and the corresponding crack length decreased obviously with the increase of the strain rates, indicating that the boundary effect of the concrete became stronger under the higher strain rates, which approached to the fracture behaviors of the large-size specimens.

Characterization of low-frequency distributed acoustic sensing signals in hydraulic fracturing stimulation – A coupled flow-geomechanical simulation approach

Low-frequency distributed acoustic sensing (LF-DAS) is one of the promising diagnostic techniques for detecting and characterizing hydraulic fractures. LF-DAS signals can capture fracture hits and the strain field around the hydraulic fracture. However, the interpretation of field LF-DAS data can be challenging due to the complexity of the underground conditions. This study develops a fracture propagation model to simulate the hydraulic fracturing process. The modelling results are analyzed to examine patterns and trends observed in interpreting field LF-DAS data. The fracture propagation model, coupled with the flow and geomechanical computations, is implemented in the MATLAB Reservoir Simulation Toolbox (MRST). The flow and geomechanical calculations are discretized by the finite volume and the virtual element methods, respectively. The hydraulic fracture is set to propagate along a prescribed path with a specific propagation or activation criterion. The accuracy of our model is validated against the KGD analytical solutions for the leak-off-viscosity, storage-viscosity and leak-off-toughness dominated regimes. The simulated stress and strain features are consistent with those interpreted from field LF-DAS signals. Several case studies and sensitivity analyses demonstrate the approach's utility and examine fracture interference, closure, and stress shadowing effects. The modelling work facilitates interpreting field measurement data by investigating characteristics of fracture hits from adjacent wells. The modelling method provides insights into fracture interference and its implications on optimal designs during hydraulic fracturing stimulation.

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

A method for modelling arbitrarily shaped delamination fronts with large and distorted elements

The simulation of delamination in layered composites is currently limited for large structures. Typically, the use of Cohesive Zone Modelling leads to a requirement of keeping the elements smaller than 1.0 mm. As an alternative, this article presents an Energy Release Rate-based cohesive method enabling the use of elements significantly larger (up to 5 mm). A novel algorithm is presented to use the Virtual Crack Closure Technique with distorted elements not aligned with the delamination front. When the propagation criterion is met, a cohesive law is introduced to model the progressive crack growth along the newly created crack surface, ensuring to dissipate the correct amount of energy. The method is validated for different propagation tests. Notably, Double Cantilever Beam and End-Notched Flexure tests are accurately modelled with large and distorted elements. Finally, a partially reinforced DCB test demonstrates the ability of the method in representing an evolving delamination front.

Hybrid equilibrium formulation with adaptive element side orientation for cohesive crack prediction

AbstractThe present article proposes an hybrid equilibrium element (HEE) formulation for the prediction of cohesive fracture formation and propagation with the crack modelled by extrinsic interface embedded at element sides. The hybrid equilibrium element formulation can model high order (quadratic, cubic and quartic) stress fields which strongly satisfy homogeneous equilibrium equations, inter‐element and boundary equilibrium equations. The HEE can implicitly model both the initially rigid behaviour of an extrinsic interface and its debonding condition with separation displacement and softening. The extrinsic interface is embedded at the element sides and its behaviour is governed by means of the same degrees of freedom of HEE (generalized stresses), without any additional degree of freedom. The proposed extrinsic cohesive model is developed in the thermodynamic framework of damage mechanics. The proposed crack propagation criterion states that crack grows when the maximum principal stress reaches the tensile strength value, in a direction orthogonal to the principal stress direction. The crack is embedded at an element side and the mesh around crack tip is adapted, by rotation of the element sides, in order to have the interface aligned to the crack growth direction. Three classic two‐dimensional problems of fracture propagation are numerically reproduced and the results compared to the experimental data or to the other numerical results.

A novel strength-energy criterion for bimaterial interface crack propagation

This paper aims to propose a novel fracture criterion to predict complex propagation behaviors of a bimaterial interface crack, either delaminating along the interface or kinking out of the interface into one of the adjoining materials. A strength-based criterion is used to predict the crack deflection, and an energy-based criterion is adopted to assess delamination along the interface. To determine the competition between these two cracking modes, a competing strategy is developed by comparing the strength-based and energy-based criteria. This coupled strength-energy fracture criterion eliminates the disadvantages arising from a criterion based solely on strength or energy, and is convenient to be calculated and embedded into numerical models. As practice, we embed the criterion into a homemade extended finite element model to simulate bimaterial interface crack propagation. Several numerical examples are performed to verify the effectiveness and accuracy of the developed model. Finally, this model is applied to simulate an interface crack propagation in a sandwich structure that has a specially designed peel-stopper. Parametric studies reveal that the material and interface toughness as well as geometrical dimensions of the structure have significant effects on the propagation mode of the interface crack. The results provide practical suggestions on the optimal design of peel-stopper in sandwich structures.

Optimal design of electromagnetic field exposure maps in large areas

The mapping of electromagnetic field (EMF) exposure over large areas is a very useful tool for the analysis of epidemiological data and risk assessment. Its production requires a costly measurement process. To optimize the effort and ensure the representativeness of the exposure map, criteria for the selection of the sites to be measured must be established. This paper presents a methodology for conducting EMF exposure maps suitable for risk assessment evaluation in large areas. The proposal combines radio wave propagation criteria and GIS methods to optimize the sampling effort. The design criteria are based on the determination of a rectangular grid of 250 m side and the identification of the emitters within the area under study. Both urban and rural sites are analysed in the proposal and line of sight conditions (LOS) are considered to reduce the number of points required and thus optimize the measurement effort. Depending on the extent and regularity of the surface, the density of measurement points has been estimated to be between 8 and 10 points per square kilometre in the urban area. The proposed methodology has been applied to a case study of a 2.8 km2 urban area within a 35.11 km2 municipality, obtaining an average point density of 9.64 points/km2 in the urban area. The differences in exposure depending on the application of the criteria have been analysed by means of the statistical values of the sets and the subtraction of the maps generated using kriging techniques. According to our results, if LOS measurements are not properly incorporated, the mean value of the EMF is underestimated in the area under study.

The effects of non-inverse-square-root stress singularity on some crack propagation criteria in hydraulic fracturing

The effects of non-inverse-square-root stress singularity on some crack propagation criteria in hydraulic fracturing

Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements

Abstract The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.

Rock Breaking Mechanism and Process Optimisation of Jet Cutting Basic Roof Rock under Submerged Jet Condition

The destruction of rock under the condition of a close submerged jet has become a hot topic of scientific research and engineering application in the past decade. With the unremitting efforts of a large number of experts and scholars around the world, gratifying progress has been made in the research of computational fluid dynamics (CFD) on the internal and external flow fields of the jet nozzle, the theoretical derivation of rock mechanics on the fracture initiation and propagation criteria of hydraulic fracturing, and the numerical simulation of jet erosion mechanism under the coupling of fluid and solid fields, however, for the rock mechanics hydraulic fracturing cutting engineering scale of non-oil drilling fracturing technology, the research on the fluid-solid coupling boundary conditions of fracturing fluid and hard dense rock under the flow state conditions of the submerged field inside and outside the borehole is not sufficient. In the calculation of the fluid-solid coupling boundary flow field under the non-submerged jet state, the control equation with Reynolds number between 2300-4000 shall be selected, while it belongs to the laminar flow state in the stage of hole sealing and pressurised fracturing. Therefore, Von-Mises equivalent plastic stress is selected in the mechanical model to calibrate the failure state of the rock-solid boundary, and the control equations of laminar flow and turbulent flow are selected to calibrate the fluid boundary. The mechanism of different stages of rock breaking by hydraulic fracturing jet can be further analysed in detail, and Comsol 6.0 multi-physical field simulation software is selected for verification. The research results will help deepen the understanding of rock breaking mechanism by jet and optimise the selection of parameters for field construction.

Wmic-GMTS and Wmic-GMERR criteria for micron-scale crack propagation in red-bed soft rocks under hydraulic action

Micron-scale crack propagation in red-bed soft rocks under hydraulic action is a common cause of engineering disasters due to damage to the hard rock–soft rock–water interface. Previous studies have not provided a theoretical analysis of the length, inclination angle, and propagation angle of micron-scale cracks, nor have they established appropriate criteria to describe the crack propagation process. The propagation mechanism of micron-scale cracks in red-bed soft rocks under hydraulic action is not yet fully understood, which makes it challenging to prevent engineering disasters in these types of rocks. To address this issue, we have used the existing generalized maximum tangential stress (GMTS) and generalized maximum energy release rate (GMERR) criteria as the basis and introduced parameters related to micron-scale crack propagation and water action. The GMTS and GMERR criteria for micron-scale crack propagation in red-bed soft rocks under hydraulic action (abbreviated as the Wmic-GMTS and Wmic-GMERR criteria, respectively) were established to evaluate micron-scale crack propagation in red-bed soft rocks under hydraulic action. The influence of the parameters was also described. The process of micron-scale crack propagation under hydraulic action was monitored using uniaxial compression tests (UCTs) based on digital image correlation (DIC) technology. The study analyzed the length, propagation and inclination angles, and mechanical parameters of micron-scale crack propagation to confirm the reliability of the established criteria. The findings suggest that the Wmic-GMTS and Wmic-GMERR criteria are effective in describing the micron-scale crack propagation in red-bed soft rocks under hydraulic action. This study discusses the mechanism of micron-scale crack propagation and its effect on engineering disasters under hydraulic action. It covers topics such as the internal-external weakening of nano-scale particles, lateral propagation of micron-scale cracks, weakening of the mechanical properties of millimeter-scale soft rocks, and resulting interface damage at the engineering scale. The study provides a theoretical basis for the mechanism of disasters in red-bed soft-rock engineering under hydraulic action.

Prediction on residual flexural fatigue life of rock-concrete interface based on a deformation-controlled fatigue crack propagation criterion

To assess the cracking resistance of rock-concrete interface, three-point bending tests were carried on composite rock-concrete specimens under the monotonic and high flexural fatigue loading. The crack opening displacements along the ligament of the beam were continuously recorded in the whole test process. According to the measured crack mouth opening displacements (CMODs), the correlation between the monotonic and fatigue deformations at different cracking statuses was discussed. It has been shown that the deformation development of composite specimens under flexural fatigue loading was mainly caused by the propagation of interfacial crack. The P-CMOD curve under monotonic loading was the envelope curve of those under the different maximum fatigue loads. There were three CMOD control points in the monotonic deformation response to indicate the fatigue crack propagation states, which corresponded to the initial cracking load, the ultimate load and the applied maximum fatigue load in the post-peak part of the monotonic response, respectively. Correspondingly, they manifested the fatigue crack initiation, the inflection point of the fatigue crack propagation rate from deceleration to acceleration and the fatigue failure of the rock-concrete interface. Based on the three CMOD control points, a deformation-controlled fatigue crack propagation criterion was proposed to assess the cracking state of the rock-concrete interface under fatigue loading. Accordingly, a theoretical prediction model, termed as fatigue deformation evolution law, was established to predict its residual flexural fatigue life. This method was verified by the reasonable agreements between experimental and predicted results in the residual fatigue life.

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

Statistical modeling of microstructurally short crack growth in high cycle fatigue

Capturing the behavior of short cracks under fatigue conditions has become a challenge for researchers. The early stage of crack propagation is influenced by microstructural features, such as grain boundaries and orientations, which leads to significant statistical variations. Models such as the ones developed by Navarro and De Los Rios have been able to describe the process by considering the average properties of the material and estimating the number of cycles related to the short crack stage. However, fatigue should be seen as an extreme value process. In the present work, a more realistic model was developed to consider the statistical nature related to grain orientations to estimate fatigue life dispersion. Eleven crack propagation criteria have been used to compute the number of cycles spent in the short crack stage. Parameters such as the Schmid factor, the potential crack length, and the various angles describing the misorientation between adjacent grains were considered. One thousand random scenarios for short crack growth were studied for each propagation criterion and some statistical analyzes were run to estimate the worst-case scenario out of one million. Results can be well described using the generalized extreme value distribution, capturing the stochastic nature of the fatigue life.

Experimental and computational failure analysis of hydrogen embrittled steel cords in a reinforced thermoplastic composite pipe

Reinforced thermoplastic pipes (RTPs) have attracted considerable attention lately in the oil and gas sector as potential alternative to carbon steel pipes. However, some RTP systems have been experiencing failures as a result of deficient design and inadequate operation practices. This study presents a comprehensive assessment of the failure of a steel-reinforced flexible thermoplastic composite layered pipe in a sour environment characterized by hydrogen sulfide (H2S) exposure. Utilizing scanning electron microscopy (SEM) and electron dispersive spectroscopy (EDS), the investigation conclusively attributes the failure of the RTP to hydrogen embrittlement of the carbon steel cords and wires in the reinforcement layer. Finite element models at both meso-scale and full RTP scale were developed, incorporating a novel damage initiation and propagation criterion for failure prediction of embrittled and non-embrittled (e.g. ductile) reinforcement steel cords. The numerical models consistently predicted a reduced burst pressures of the hydrogen embrittled case of the RTP, with a close match with field observations. They also predicted failure modes that closely matched the SEM findings, hence highlighting the unsuitability of the existing steel cords in RTPs for use in sour service environments. Additionally, the presence of moisture in the annular space was identified as an exacerbating factor. This investigation provides important insights for the future design and operation of RTPs susceptible to hydrogen embrittlement, paving the way for improved structural integrity and safety measures. Further research avenues may involve modeling hydrogen diffusion in the thermoplastic layers, simulating the movement of moisture in the annulus through the capillary effect, and incorporating fracture toughness degradation for a more thorough understanding of the interplay between mechanical and environmental factors in the hydrogen embrittlement of steel-reinforced RTP composite pipes.

Study of different initiation and propagation criteria in the XFEM modelling of scarf adhesive joints

Scarf adhesive joints, characterized by an end-to-end connection between tapered adherents at a given scarf angle (α), are applicable in structural applications, e.g., fiber-reinforced structures, owing to their efficiency. This work presents an analysis on the tensile strength of scarf adhesive joints, considering a and the adhesive type as design parameters. A detailed numerical evaluation is presented, based on the eXtended Finite Element Method (XFEM), following the technique validation with experimental data, for adhesives with different characteristics. The XFEM technique was tested with varying damage initiation and propagation criteria. The XFEM technique was positively validated for specific damage initiation and propagation criteria.

Распространение магнитогидродинамических волн и гравитационная неустойчивость в астрофизической анизотропной и теплопроводной плазме

The hydrodynamic instability of a magnetised, self-gravitating rotating anisotropic plasma is analysed in the collisionless approximation and taking into account the heat flux vector on the basis of the modified Chew-Goldberger-Low equations. The dispersion relation is derived and simplified cases of propagation of small-amplitude perturbation waves are discussed, with modified analytical criteria for hydrodynamic instability obtained. In accordance with the general dispersion relation, three cases when the propagation of the perturbation wave passes across, along, and obliquely to the magnetic field vector are specifically considered. It is shown that anisotropic pressure and heat flux not only modify the classical Jeans instability criterion but also induce new unstable regions. It is found that the presence of uniform plasma rotation reduces the critical wave number and has a stabilising effect on the gravitational instability criterion for transverse propagation of the perturbation wave and has no effect in the case of its longitudinal propagation. The inclusion of thermal flows leads to the appearance of two additional wave modes. The results obtained are important for the construction of evolutionary magnetohydrodynamic models of collisionless astrophysical plasma.

Моделирование упругопластического разрушения компактного образца

The strength of a compact specimen under normal fracture (fracture mode I) is studied within the framework of the Neuber-Novozhilov approach. A model of an ideal elasto-plastic material with limiting relative elongation is chosen as the model of the deformable solid. This class of materials includes low-alloy steels that are used in structures operating at temperatures below the cold brittleness threshold. The crack propagation criterion is formulated using the modified Leonov-Panasyuk-Dugdale model, which uses an additional parameter, i.e., the diameter of the plasticity zone (the width of the prefracture zone). In the case of stress field singularity occurring in the vicinity of the crack tip, a two-parameter (coupled) criterion for quasi-brittle fracture is developed for type I cracks in an elastoplastic material. The coupled fracture criterion includes the deformation criterion attributed to the crack tip and the force criterion attributed to the model crack tip. The lengths of the original and model cracks differ by the length of the prefracture zone. Diagrams of the quasi-brittle fracture of the specimen under plane strain and plane stress conditions are constructed. The constitutive equations of the analytical model are analyzed in terms of the characteristic linear dimension of the material structure. Simple formulas applicable to verification calculations of the critical fracture load and pre-fracture zone length for quasi-brittle and quasi-ductile fractures are obtained. The parameters in the presented model of quasi-brittle fracture are analyzed. It is proposed to select the parameters of the model according to the approximation of the uniaxial tension diagram and the critical stress intensity factor.

A hot tearing propagation model for steel

Hot tearing is a significant challenge in material preparation process, including high-performance alloy casting, large ingot production and additive manufacturing, etc. However, the propagation process of hot tears, especially in steel, is still unclear at present. This study proposed a new model for hot tearing propagation that considers the energy balance, the relationship between the propagating mode and the growth rate of hot tears when they undergo irreversible and rapid propagation. To evaluate this model, a new testing device was developed and the hot tearing behaviors of low and high carbon steels were observed. The tests demonstrated a notable correlation with the model. Furthermore, a new criterion for propagation of hot tearing was put forward. This work provides a more comprehensive physical model and criteria for simulating and predicting the formation of hot tears.