Velocity Of Fracture Research Articles

Low-medium loading rate effect on dynamic fracture toughness of sandstone scaled model

To investigate the effects of loading rate on the dynamic fracture toughness of rock in a scaled system, a multi-scale experimental and numerical study is carried out with a single cleavage semi-circle (SCSC) specimen based on a new scaled modeling method. The loading curves of the scaled models are obtained by using the data recorded by an oscilloscope. The fracture time is monitored by the fracture propagation gauge (FPG) to calculate the propagation velocity of fracture. The dynamic fracture toughness of the propagation fracture can be obtained by combining experimental data with a finite-element method. The results show that the effects of loading amplitudes and model size on fracture toughness can be significantly eliminated by the scaled modeling method applied in this paper, which provides a prerequisite for a thorough analysis of the loading rate effect on scaled models. Furtherly, by introducing a new proportional coefficient factor, the scaled modeling method is confirmed to predict the dynamic fracture toughness effectively. The dynamic fracture toughness exhibits a non-linear increase with loading rate in both the fracture initiation and propagation stages. This increase is characterized by a rapid-growth in some middle range of loading rates, with a relatively slow-growth below or above that range. Furthermore, the propagation toughness is greatly affected by loading rate at low rates, whereas the initiation toughness is more significantly influenced by medium loading rates.

Finite element simulations of hydraulic fracturing: A comparison of algorithms for extracting the propagation velocity of the fracture

The finite element method is a powerful and general numerical method used to simulate subsurface processes. In this paper, we take recent hydraulic fracturing propagation algorithms and assess their performance when used within the finite element framework. In particular, we evaluate aperture and energy-based methodologies that are capable of extracting the propagation velocity of a hydraulic fracture propagating throughout the toughness and viscous regime. Such algorithms have the benefit of a quicker convergence on the fracture front. The aperture-based methodology consists of the multi-scale aperture asymptote that is yet to be applied with finite elements. On the other-hand, the energy-based methodology consists of a recently developed procedure for predicting the propagation velocity from the energy release rate, which is calculated using a J-integral devised for hydraulic fracturing. A comparison of the accuracy and the number of iterations required to converge on the fracture length is undertaken, and found to produce similar results for both methods. Consequently, we conclude that the higher accuracy of energy-based methods in extracting stress intensity factors does not immediately translate to a higher accuracy in extracting propagation velocities, most notably in the toughness-dominated propagation regime. Given the similar performance of the methods, and the simplicity of the aperture-based approach, we then extend the evaluation of the multi-scale aperture asymptote to the case of buoyancy-driven propagation. As a result, the aperture asymptote is shown to be a simple and efficient method for the simulation of subsurface processes using a finite element framework.

Migration and Distribution Characteristics of Proppant at the Corner of Horizontal Fracture Network in Coal Seam

A complex fracture network is composed of many similar structures. The migration law of proppant at each structure is the core and basic content of the migration law of proppant in complex fracture network, and there is little research. In this study, the EulerianEulerian method (TEM) is used to analyze the migration and distribution characteristics of solid–liquid two phases at the fracture corner according to different corner types of the fracture network. The results show that the migration characteristics of proppant in the corner area can be divided into the corner anomaly area, buffer area, and stability area; the influence of the turning angle on proppant migration is mainly concentrated at the corner and in the range of 4 times the fracture width after turning. The probability of sand plugging at the corner of the “Y → T” fracture is lower than that of “L → l”, higher than that of the “X → +” wing branch fracture, and lower than that of the main fracture. At the corner of the fracture network, after the solid flow turns, the proppant will form a high sand area on the side of the impact fracture surface, then rebound back to the fracture, form a sand-free area on the other side, and form a high-velocity core in the refraction interval. At the corner of the “L → l” fracture, there are one high sand area, one non-sand area, two low-velocity areas, and one high-velocity area; there are three low-velocity areas, two sand-free areas, and one high sand area at the corner of the “Y → T” fracture; at the corner of the “X → +” fracture, there is a high sand area and no sand-free area, and the flow velocity of the main fracture is much greater than that of the wing branch fracture.

Hydrogen-induced fast fracture in notched 1500 and 1700 MPa class automotive martensitic advanced high-strength steel

Hydrogen embrittlement of notched martensitic advanced high-strength steels was studied. Notched specimens had (i) higher tensile strength and lower ductility, and (ii) increased hydrogen sensitivity, manifested by reductions in ductility and strength. Hydrogen-induced fast fractures (HIFF) initiated when the load-controlled specimen became mechanically unstable. The HIFF velocity (61−130 m/s) was greater than the velocity of ductile fracture (46 m/s). HIFF susceptibility increased with increasing steel strength, increasing hydrogen fugacity, and decreasing stress rate. HIFF exhibited brittle features (quasi-cleavage, transgranular and intergranular fracture) in the initiation zone, suggesting hydrogen-enhanced plasticity-mediated decohesion (HEPD). These features increased in area with increasing hydrogen embrittlement.

Isogeometric analysis of fracture propagation in saturated porous media due to a pressurised non-Newtonian fluid

A model has been developed to simulate fractures which are pressurised using a non-Newtonian (power-law) fluid. The flow in the surrounding, deformable porous medium is described with a non-Newtonian fluid as well. The resulting model can represent the propagation of pressurised fractures, leak-off and the interstitial fluid pressure in a saturated porous medium. The resulting equations have been discretised using Non-Uniform Rational B-Splines (NURBS), cast into a traditional finite element datastructure using Bézier extraction. It is shown that lumped integration of the fracture inflow terms is needed to obtain non-oscillatory results for the fluid velocity normal to the discontinuity, and an integration scheme has been derived to prevent non-physical fluid leak-off from the fracture tips. Simulations have been carried out for a typical hydraulic fracture problem. The results show the dependence of the fluid leak-off and the fracture tip pressure on the power-law fluid index. Shear-thinning fluids result in a larger amount of fluid leak-off compared to Newtonian fluids, but their lower effective viscosity results in a higher pressure at the fracture tip. These effects influence the propagation velocity of the pressurised fracture, and thus demonstrate the importance of properly modelling the non-Newtonian character of pressurising fluids.

Dynamic fracture of Ti-6Al-4V alloy in Taylor impact test

The dynamic fracture behaviors of Ti-6Al-4V alloy at high strain rate loading were investigated systemically through Taylor impact test, over the range of impact velocities from 145 m/s to 306 m/s. The critical impact velocity of fracture ranges from 217 m/s to 236 m/s. Smooth surfaces and ductile dimple areas were observed on the fracture surfaces. As the impact velocity reached 260 m/s, the serious melting regions were also observed on the fracture surfaces. Self-organization of cracks emerges when the impact velocity reaches 260 m/s, while some special cracks whose “tips” are not sharp but arc and smooth, and without any evidence of deformation or adiabatic shear band were also observed on the impact end surfaces. Examination of the sections of these special cracks reveals that the cracks expand along the two maximum shear stress directions respectively, and finally intersect as a tridimensional “stagger ridge” structure.

The critical velocity of mode-I fracture in a non-linear lattice in the absence of viscosity

The high-velocity regime of mode-I fracture is interesting, especially because of the instability of the steady-state propagating crack to a more complex dynamics (such as micro-branching). In this article, we study mode-I fracture in a non-linear lattice in the absence of a viscous force. In earlier study, we had studied the effects of the bond potential parameters, including Kelvin viscous force, on the macroscopic behavior of the crack, including the high velocity regime instability. Recently, a new study has appeared using a very similar non-linear force but claiming quite different results. In this article, we seek to discover an explanation of these differences. We find that they do not result from the viscosity present in our previous study. At least part of the differences are attributable, rather, to the very wide system used in the recent study, which leads to long transients and a failure to probe the steady-state behavior. Our results confirm our previously claimed lack of agreement with the Yoffe prediction for the critical velocity of a steady-state crack, and neither do they match the predictions of Gao’s model.

Propagation velocity of a natural hydraulic fracture in a poroelastic medium: C. E. Renshaw & C. F. Harvey, Journal of Geophysical Research, 99(B11), 1994, pp 21,667-21,677

Propagation velocity of a natural hydraulic fracture in a poroelastic medium: C. E. Renshaw & C. F. Harvey, Journal of Geophysical Research, 99(B11), 1994, pp 21,667-21,677

Propagation velocity of a natural hydraulic fracture in a poroelastic medium

The propagation rate of a natural hydraulic fracture is limited by the rate that fluid flows from the saturated rock into the void space created by fracture growth. Unlike induced hydraulic fractures, natural hydraulic fractures can not be modeled by specifying rates of fracture growth or fluid flow into the fracture as boundary conditions. Numerical solutions of the governing equations for natural hydraulic fracture growth in a poroelastic medium indicate that growth rates are primarily controlled by the hydraulic conductivity κ, the storage Sp′ and the initial flaw length 2αo. Computationally more efficient models which partially and completely decouple material stresses from fluid pressures give similar results. Results for several rock types indicate that, although the rate of fracture propagation is limited by fluid flow, fracture growth still accelerates. Results are generalized in dimensionless plots of fracture length versus time for various values of the dimensionless parameter ϕ = (1‐ν)/(GSp′), where G is the shear modulus and ν is the drained Poisson's ratio.

Effect of Material Degradation on Impact Damage of Cast Ni-Base Superalloy IN738LC.

Nickel-base superalloy IN738LC is widely used for heavy-duty gas turbine buckets. But the buckets in current advanced gas turbines are exposed to extremely high temperature, which induces significant material degradation during service. Therefore an evaluation of the resistance against damage caused by foreign objects is required to establish a material degradation assessment system. In order to investigate the damage caused by impact from a projectile, the long-time aged material at 750°C-900°C up to 24000h of IN738LC are artificially produced and the single-particle fracture test was made on a particle impact test rig. In this study, introducing the fracture model, in which the strain rate controlling process is that dislocations move past γ' precipitates by looping, the critical velocity of impact fracture is explained as a function of projectile size, target thickness, mechanical property such as material elongation and the microstructural parameter of a ratio of the second power of the γ' interparticle distance to the γ' mean diameter. Furthermore, using measured impact loads, the relationship between normalized deformation work induced by impact projectile and impact velocity is discussed.

Transition of hertzian fracture to flexure fracture produced in glass plates by impact

The strength and fracture of a glass plate in a three-dimensional state of stress produced by the transverse impact of a spherical body is investigated. The plate is supported by a ring foundation whose radius is comparable to the thickness of the plate. A general impact theory is developed to determine the critical stresses in the plate as a function of impact velocity, plate thickness, and support span. Impact experiments were carried out to measure the impact velocity required to fracture a glass plate specimen as a function of support span. Hertzian fracture was observed at a short span of support whereas flexure fracture was observed at a larger support span. The impact velocity of fracture was measured to be increasing with increasing support span and its corresponding critical stress of fracture was also determined.

Limit velocity of fracture front and dynamic strength of brittle solids

The theories of propagation of brittle fracture fronts in solid materials are compared with experimental data. Instead of the well-known theory of the limit fracture stress the theory of limit velocity of fracture front is developed. Accordingly between the moving boundary at which the static strength is attained and the front of fracture the material can stand essential dynamic over-loadings. The experimental data on contained explosions in optically transparent intact blocks show that the limit velocity of brittle cracks front takes place immediately after the separation of the shock front and the front of brittle fracture. The hypothesis of the existence of limit front velocity leads to the conclusion that in the two-front structure of plane shock waves the amplitude of elastic precursors, known as “the Hugoniot elastic limit”, exceeds the value of ultimate static strength of a solid material and has to increase with increasing of a finite shock pressure. This effect is justified by a number of experiments with brittle materials. The analogue with the plane problem of a self-supporting brittle burst is shown. The explanation of exceeding of the ultimate static strength and of “the delay time” of fracture under the spall condition is given. The increasing of internal fractures, which is described by the dilatancy loosening of materials is discussed. The well-known laws of “the geometrical similarity” of contained explosions are in accordance with expression of the strength in terms of the ultimate stress but not in terms of Griffith's energy for creating of new cracks. The possibility of the regime of a limit front velocity of fracture at explosion motions in real rocks, for which the dilatancy has place, is discussed.

Some characteristics of thermal fracture in glass

Techniques for obtaining controlled fractures in sheet glass by means of thermal stress are outlined. The velocity behavior of fracture under different stress configurations is analyzed, and it is seen that the nature of crack is strongly influenced by the ambient stress field. The peak velocity of a typical free-running fracture is observed to be 1450 m/sec and the corresponding crack opening to be 4 microns.

Determination of the Cleavage Velocity in Tungsten using Ultrasonic Fractography

A CLEAVAGE crack propagating through a solid will also cut through the strain field associated with microscopic surface flaws, and this releases energy in the form of a stress pulse. If the material is elastically isotropic, this pulse will travel outwards from each flaw at a constant velocity in all directions, and the interaction of the stress pulse with the moving crack front will cause a slight localized deflexion of the crack. Thus a series of curved “Wallner lines”1 are produced, and these are easily visible on the fracture surface. Because the velocity of the stress pulse is a known constant for materials such as glass, the presence of these lines provides a simple method of measuring the cleavage velocity2,3. Kerkhof4 was the first to point out that, because the fracture surface can be modulated by a single stress pulse, it should also be possible to produce a series of faint permanent ripples on the fracture surface using ultrasonics. Knowing the frequency of oscillation, the velocity of fracture is obtained directly from the spacing between the ripples. This technique has been used successfully on glass5 and a polymer (polymethyl methacrylate (ref. 6 and private communication from K. Saito)), but its application to crystals with well defined cleavage planes is less obvious, for a large energy is then necessary to force the crack to deviate slightly from this plane. The method can be used on ionic crystals (magnesium oxide7, potassium chloride (private communication from M. Schinker)), and we report here the successful application of the technique to a metal.

The velocity of shear fracture

abstract The maximum velocity of fracture in an homogeneous isotropic elastic medium under pure shear stress and with an added compressive stress is computed by an extension of Yoffe's method. The maximum velocity of shear fracture is smaller than the velocity of transverse waves in the medium. It increases as Poisson's ratio increases and decreases as the compressive stress increases. The maximum velocity of pure shear fracture is higher than the velocity of pure tensile fracture in the same medium. For a medium with Poisson's ratio of 0.25 the former is 0.775 and the latter is 0.631 of the transverse wave velocity.

Fracture Velocity and Fracture Energy of Glass in the Fatigue Range

A method is developed for determining crack velocities from the stress‐time curve of fracture. Velocities of glass broken in air and in vacuum converge at a value between 1 and 10 mm. per second. This convergence is considered to be the upper limit of the fatigue range. Fracture energy has been computed in terms of strain energy release rates. For glass broken in air under low stresses this energy is about equal to the surface energy of the glass, but when in vacuum it is fifteen times greater. At the upper limit of the fatigue range it is thirty times greater, whereas at the terminal velocity of fracture it is of the order of fifty times greater. It is concluded that surface energy must constitute only a small part of the energy absorbed in the fracture process. This excess energy has a pronounced influence on the fracture process and on the measured strength of glass.

Glass Cracking Caused by Underwater Spark

Using a Beckman & Whitley high-speed framing camera, the velocity of glass fracture caused by an underwater disruptive electric spark was measured. The observed maximum velocity was about 2.4 km/sec, 60% higher than the usually accepted normal limiting value. A gradual decrease of fracture velocity was also observed. From these observations it has been deduced that the maximum fracture velocity is, contrary to the hitherto assumed theory, dependent on the increasing rate of applied stress.

Variation, with Temperature, of the Cracking Velocity of Glass

The limiting velocity of fracture for a soda‐lime glass was measured as a function of temperature over the range of 80° and 475°K. The value of the fracture velocity was obtained by electronically measuring the time necessary for the crack to travel between two platinum lines fired into the surface of the glass specimen. The value of the fracture velocity for this glass was found to be 1485 m. per second at 300°K. with the velocity decreasing slightly with increasing temperature over the range studied. The results indicate a temperature coefficient on the order of –0.15 m. per second per °K.