Dynamic Process Of Crack Propagation Research Articles

Investigation of dynamic fracture behavior and energy dissipation of water-bearing coal under impact load

The stability of residual coal pillar in coal mine is significantly affected by the ponding in goaf and the dynamic disturbances such as blasting vibration and mine tremor activity in the production process of surrounding coal mines. In this paper, the effects of different loading pressure and water-bearing state on the dynamic fracture mechanical properties and energy dissipation law of coal samples were studied. The dynamic fracture characteristics of dry, natural and water-saturated notched semi-circular bending (NSCB) coal samples were tested under different loading pressure by using the impact loading system of split Hopkinson pressure bar (SHPB). A high-speed camera was used to record the dynamic crack propagation process. Combined with image processing method and fractal dimension calculation software, the influence of loading pressure and water-bearing state on fractal characteristics of crack propagation in coal specimens was further analyzed. The results show that at the beginning of crack initiation, water-saturated coal samples are easy to fracture compared to dry and natural coal samples. During the crack propagation, the dry and natural coal samples have a shorter crack penetration time compared to the water-saturated samples. The fracture toughness of the saturated coal sample is sensitive to the loading pressure and there is a threshold value. When the loading pressure is lower than 0.483 MPa, the dynamic fracture toughness of the dry coal sample is greater than the saturated coal sample. While the loading pressure is higher than 0.483 MPa, the dynamic fracture toughness of the saturated coal sample is greater than the dry coal sample. The fractal dimension of the crack propagation path of the coal sample changed as a “V” shape with the loading pressure. The fractal dimension of the crack propagation path of the dry coal sample is always higher than the water-saturated coal sample. The fracture energy of the coal sample meets the y=a·bx exponential growth relationship with the loading pressure. The fracture energy of water-saturated coal sample is the largest and the natural state is the least during the fracture process. The research results can provide theoretical guidance for the stability assessment of residual coal pillar as well as the safe and efficient mining of deep coal resources.

Double cantilever beam test and micro-computed tomography as evaluation tools for self-healing of CFRPs loaded with DCPD microcapsules

In the present study, the healing efficiency of microcapsules containing dicyclopentadiene (DCDP) was investigated on carbon fibre reinforced polymers (CFRPs) via morphological and mechanical characterisation. Micro-computed tomography (m-CT) has been used to observe in three dimensions (3D) the dynamic process of crack propagation and give CFRPs qualitative and quantitative structural and compositional information. Microcapsules with Poly(urea-formaldehyde) as shell and DCPD as healing agent in core were prepared by in situ polymerization in an oil-in-water emulsion. The morphology and thermal properties of microcapsules were examined via Optical Microscopy, Scanning Electron Microscopy (SEM), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Vacuum bagging was proved an efficient technique for the CFRPs’ manufacturing that microcapsules can endure. The morphology of heal progression of cracks, induced at the surface of microplastics, was observed through SEM, while for the mechanical response double cantilever beam (DCB) test was selected to evaluate heal efficiency. The reduction of the crack volume in the CFRPs internal structures was up to 45%, while the mechanical restoration exceeded 50% proving microcapsules’ efficiency.

Experimental and numerical study on the fracture characteristics of concrete under uniaxial compression

Since concrete infrastructure may lose its expected physical and functional properties over time, accurate inspection and assessment of such infrastructure systems is necessary to ensure safety and serviceability and prevent unsafe working conditions and the occurrence of hazards. In this paper, an experimental investigation was conducted on several concrete specimens under uniaxial compression to fully explore the fracture process and mechanical characteristics of concrete materials under compressive loading conditions. More specifically, a high-resolution industrial camera and a real-time geophysical acquisition system were employed to capture the fracture process and the microseismic (MS) and electromagnetic emission (EME) signals simultaneously. Based on digital image processing, a robust crack extraction algorithm was proposed for automatically identifying cracks on a concrete surface at the pixel level, and then two novel crack features were introduced to depict the dynamic crack propagation process quantitatively. Then, the correlation between MS, EME, stress drop and dynamic crack evolution characteristics was analyzed. The results indicate that: (1) the MS and EME signals of the concrete specimens have good consistency in the time domain, especially in the fully fractured stage; (2) the crack area, to a certain extent, can reflect the stress drop of a concrete specimen under the compression fracture process; (3) the crack propagation velocity parallel to the loading axis (along the vertical direction) is faster than that the perpendicular one to the loading axis (along the horizontal direction); and (4) the crack area, stress, MS signal, and EME signal reach their peak values nearly simultaneously. Finally, a novel mesh-free numerical model based on peridynamic (PD) theory was established to simulate the fracture process, and the displacement fields were presented to further reveal the failure mechanism of concrete under compressive loading.

Instability effects of the dynamic crack propagation process

Dependencies and parameters describing the crack propagation process can often exhibit unstable behavior which is not predicted by classic fracture mechanics. Here such phenomena as the crack velocity oscillations and floating stress intensity factor (SIF) values for the initiation of a pulse loaded crack can be mentioned. This paper considers SIF – crack velocity dependence (KI-ȧ dependence, mode-I fracture is considered in the paper) for dynamically propagating cracks as another example of instabilities observed in the crack propagation. Uniqueness, related to a given material, and even existence of this dependence has been a matter of discussion among researchers, since contradicting experimental results were reported in the literature over the last decades. Experiments with different loading regimes and specimen types demonstrated various shapes of the KI-ȧ curve for a particular material. However, common theoretical tools for the crack propagation prediction and simulation imply the KI-ȧ dependence to be a material property and thus suppose it to be unique for a particular material. In this work crack propagation is simulated using incubation time fracture criterion, which provides possibility to avoid the a priori given KI-ȧ dependence. A computational scheme based on finite element method and the incubation time fracture criterion was developed and various types of the KI-ȧdependence were numerically obtained for various loading conditions and materials.

Lab-Supported Hypothesis and Mathematical Modeling of Crack Development in the Fluid-Soaking Process of Multi-Fractured Horizontal Wells in Shale Gas Reservoirs

The objective of this study is to develop a technique to identify the optimum water-soaking time for maximizing productivity of shale gas and oil wells. Based on the lab observation of cracks formed in shale core samples under simulated water-soaking conditions, shale cracking was found to dominate the water-soaking process in multi-fractured gas/oil wells. An analytical model was derived from the principle of capillary-viscous force balance to describe the dynamic process of crack propagation in shale gas formations during water-soaking. Result of model analysis shows that the formation of cracks contributes to improving well inflow performance, while the cracks also draw fracturing fluid from the hydraulic fractures and reduce fracture width, and consequently lower well inflow performance. The tradeoff between the crack development and fracture closure allows for an optimum water-soaking time, which will maximize well productivity. Reducing viscosity of fracturing fluid will speed up the optimum water-soaking time, while lowering the water-shale interfacial tension will delay the optimum water-soaking time. It is recommended that real-time shut-in pressure data are measured and shale core samples are tested to predict the density of cracks under fluid-soaking conditions before using the crack propagation model. This work provides a shut-in pressure data-driven method for water-soaking time optimization in shale gas wells for maximizing well productivity and gas recovery factor.

Instabilities encountered in the dynamic crack propagation process under impact loading as a natural consequence of the dynamic fracture discreetness

Dependence of stress intensity factor (SIF) on crack velocity (KI−ȧ dependence) in Homalite-100 specimens subjected to pulse loading was numerically studied. The numerical scheme is based on finite element method and incubation time fracture criterion. Experimental results from works by Ravi-Chandar and Knauss (1984a,b,c) were used. Experimentally obtained KI−ȧ dependence is characterized by considerable scatter of the SIF values.Application of the incubation time based approach made it possible to qualitatively describe scattering of the SIF values since the used fracture condition does not rely neither on critical SIF value, nor on a a priori given KI−ȧ dependence.

Effect of the Preexisting Fissure with Different Fillings in PMMA on Blast‐Induced Crack Propagation

In order to study the dynamic crack propagation law in fissured rock under the different fillings, a borehole with 7 mm diameter was processed in the center of a polymethyl methacrylate (PMMA) specimen. The preexisting fissure with different angles (θ = 0°, 45°, and 90°) and different distances (L = 20, 30, 40, 50, and 60 mm) was prefabricated around the borehole. Air, soil, and water were employed as fillings in the fissure, respectively. The experiment of explosive loading was carried out by a single detonator, and the dynamic crack propagation process of the experimental specimens was simulated by nonlinear dynamics software AUTODYN. The results show that the blast‐induced cracks are the most favorable and unfavorable to propagate when θ = 0° and θ = 45°, respectively. The length of the far‐end wing crack decreases with the increase of the distance L, and the length of the far‐end wing crack in the air‐filled specimens is larger than those in soil‐filled and water‐filled specimens. The damage‐pressure curve of the far‐end wing crack initiation point shows “S”‐type change, and the damage‐pressure curve shows two obvious damage evolution processes of initial nonlinear and later linear stages. With the increase of the angle, the distance from the borehole to the crack initiation point decreases and the compressive stress wave peak value should increase, but the tensile force peak value decreases. Meanwhile, the relationships between pressure and average velocity of the initiation point and L, θ, and fillings are established, respectively. The numerical simulation agrees with the experimental results well. It can be seen that the fillings types, angle, and distance have a mutual restraint relationship with the reflected and absorbed stress wave energy. The phenomenon of crack propagation under different fillings can be explained well from the viewpoint of discontinuity degree and stress wave energy, which reveals the general law of blast‐induced crack propagation.

Ultimate bearing capacity analysis of a reactor pressure vessel subjected to pressurized thermal shock with XFEM

Abstract Under pressurized thermal shock (PTS), the structure integrity of reactor pressure vessel (RPV) meets a potential challenge. The vicinity of inlet nozzle is the weak link and hazardous area of the vessel. Once crack initiation occurs here, the stress concentration around the crack tip would lead to plastic deformation, crack propagation, and even the failure of the whole structure. Based on ABAQUS, the beltline region around the inlet nozzle was modeled to calculate the response of the transient temperature field and stress strain field. In order to demonstrate the ultimate bearing capacity of the RPV with the critical crack sizes, the dynamic process of crack propagation was simulated with the XFEM. Through the quantitative analysis of the Mises stress and circumferential stress through the wall thickness, the crack propagation paths in different directions were confirmed. The above analysis and calculation provide an important reference for the safety and reliability assessment of RPV.

A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis

Peridynamics is a new nonlocal theory that provides the ability to represent displacement discontinuities in a continuum body without explicitly modeling the crack surface. In this paper, an explicit dynamics implementation of the bond-based peridynamics formulation is presented to simulate the dynamic fracture process in 3D elastic solid. Based on the variational theory, the Discontinuous Galerkin (DG) approach is utilized to formulate the classic peridynamics governing equation. As a result, the spatial integration can be carried out through finite element approach to enforce the boundary conditions, constraints, contacts as well as to handle the non-uniform mesh in the engineering practices. The classic material parameters, such as the elastic modulus and fracture energy release rate are employed for the determination of material response and failure in brittle material. Several numerical benchmarks are conducted to invest the convergence and mesh sensitivity of simulations of dynamic crack propagation process with different refinements. The results demonstrate that the proposed peridynamics formulation can capture the 3D dynamic crack process in brittle material effectively and accurately including multi-crack nucleation, propagation and branching.

R-curve behaviour in weak interface-toughened SiC-C laminates by discrete element modelling

Abstract Tough ceramics can be made by introducing weak interfaces which deflect a growing crack. A simple discrete element model was employed to study crack growth in SiC-C laminate with graphite as weak interfaces. By modelling the three-point-bending test of the notched laminate, de-bonding, de-lamination and crack deflection were observed dynamically. The fracture features of the laminate as like “graceful failure” and R-curve behaviour were replicated both qualitatively and quantitatively. It has been revealed that the strength of the weak interface should be in a certain range to assure the appearance of the toughening effect. A minimum presence of the weak interface is required to increase the strength of the laminate. The employed model is explicit and simple, it can be used to reproduce the dynamic process of crack propagation in ceramic laminates and guide the design of the laminate's structure in the future.

Finite element simulation of dynamic crack propagation process using an arbitrary Lagrangian Eulerian formulation

ABSTRACTIn this paper, the arbitrary Lagrangian Eulerian formulation is employed for finite element modelling of dynamic crack propagation problem. The application phase simulation of computational dynamic fracture is applied to model by which the crack propagation history and variation of crack velocity are predicted using the material dynamic fracture toughness. The dynamic solution of problem is accomplished using the implicit time integration method. The convective terms due to mesh‐material motion are taken into account via the convection equation. A robust and efficient mesh motion technique, that its equations need not to be solved at every time step, is employed in Eulerian phase. The mesh connectivity is preserved during the analysis. So, the successive remeshing of model is eliminated. When the dynamic fracture criterion is satisfied for crack growth, the presented algorithm allows the crack to advance by splitting the material particle at the crack tip. The dynamic energy release rate is calculated at each time step to determine dynamic stress intensity factor. The predicted results are compared with those obtained through the experimental study and remeshing technique cited in the literature. The proposed computational algorithm leads to an accurate and efficient simulation of dynamic crack propagation process.

Limitation on crack speed for a strip-craze model applied to PMMA

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ ns0. When σ ns0<60 MPa, the crack speed a ̇ <10 −8 mm/s and the crack is basically stationary; when 60 < σ ns0<95 MPa, then 10 −8< a ̇ <10 −2 mm/s the crack is in slow propagation; when σ ns0>95 MPa, then a ̇ >10 −2 mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.

Observation of fracture features in fused quartz with laser-induced internal flaws

Pulsed-laser light was used to generate internal flaws in fused quartz. The size of the flaw was proportional to the laser pulse energy above a threshold value of 2.5 mJ. Specimens which fractured under four-point bending, either from surface origins or from the internal flaws with a size less than 0.25 mm, exhibited the commonly observed fracture features of sequential mirror, mist, hackle and branching, and the transition from the mirror to other features was gradual. However, in specimens with internal flaws of a size greater than 0.25 mm, a new “demarcation” line (a smoothly curved boundary line between the mirror and other fracture features) was observed. Its characteristic varied with the flaw size and the relative position along the line. It is suggested that the formation of the demarcation line is caused by the combination of the dynamic process of crack propagation and environmental effects.