Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading

A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases.     

Effects of pre-stress on crack-tip fields in elastic,incompressible solids

A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot's incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J₂-deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.     

Nano-ductile crack propagation in glasses under stress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip

Recent experiments have evidenced the existence of a ductile fracture mode at the nanometer scale in Aluminosilicate glass. The present study is designed to check whether such a ductile mode is inherent to the amorphous nature of glass. Therefore, the slow crack advance is observed in real time via an Atomic Force Microscope in a minimal glass, amorphous Silica, under stress corrosion. In this case, the Crack propagation proceeds by the nucleation, growth and coalescence of damage cavities as in the Aluminosilicate glass, but the cavity size is significantly larger. We focus here on the kinematics of crack propagation by looking at the spatio-temporal evolution of both the tip of the main crack and the cavity ahead. It is shown that the velocity of the main crack tip is significantly lower than the one of the cavity edge toward the main crack tip, like in metallic alloys. Moreover, the velocities of the different fronts (main crack, frontward and backward cavity tips) at these nanometric scales is one order of magnitude smaller than the crack tip velocity at the continuum scale. This has important consequences for the modelling of stress corrosion, especially at ultra-slow crack propagation.     

横观各向同性油气藏水力压裂裂纹扩展规律研究

针对横观各向同性与各向同性油气藏水力压裂裂纹扩展的差异性,基于扩展有限元法建立水力压裂力学模型,通过ABAQUS子程序开发了各向同性和横观各向同性岩体的起裂判据。在各向同性岩体数值模拟结果与解析解以及现场压裂典型曲线对比吻合的基础上,得到了包含层理构造的横观各向同性岩体水力压裂过程中裂纹扩展规律。层理类岩体水力压裂的裂缝扩展方向由地应力状态、层理方向以及岩体与层理界面抗拉强度共同决定;水力压裂过程中,注水压力在裂纹尖端产生应力集中,层理面法向分量先达到界面抗拉强度时,裂纹沿层理方向开裂,反之裂纹沿垂直最小地应力的方向扩展;裂纹扩展速度随层理抗拉强度的增加而降低;由于地层的滤失,随压裂液的注入,裂纹长宽尺度增长速率降低。     

水力压裂中裂纹扩展的数值模拟

水力压裂是在高压粘滞流体或清水作用下地层内裂缝起裂与扩展的过程。由于包含岩石断裂和流-固耦合等复杂问题,对该过程的数值模拟具有相当大的挑战性。本文建立基于有限元与离散元混合方法的裂纹模型,模拟岩石裂纹扩展,实现了连续向非连续的转化;建立双重介质流动模型,裂隙流作为孔隙渗流的压力边界,孔隙渗流反作用裂隙的压力求解,处理了流体在基岩与人工裂缝中的协调流动;将裂纹模型与流体流动模式进行结合,建立断裂-应力-渗流耦合形式的力学模型,进一步分析了水力压裂的基本过程,综合多种数值计算方法,编写程序,在验证岩体裂纹模型与双重介质流动模型有效性的基础上,对压裂过程进行复现,将模拟结果与文献结果进行了对比,并讨论了所构建模型的优缺点。     

Model of stepwise propagation of the tip of a hydraulic fracture in the absence of filtration

Quasi-static stepwise propagation of a hydraulic fracture in rock with a regular structure in the absence of filtration is considered. It is proposed to use a brittle fracture diagram taking into account the hydraulic fracturing fluid pressure and the confining pressure. Fracture curves describing the brittle rock fracture where the hydraulic fracturing fluid partially fills the fracture are constructed and used to predicted the possibility of stepwise propagation of hydraulic fracturing in the case where the fluid gradually flows into the fracturing crack. The regularity of the structure of the brittle rocks fracture is estimated from the results of two full-scale experiments: the critical stress intensity factor and the tensile strength limit of the rock. Experiments on pulsed loading of polymethylmethacrylate samples with stepwise crack propagation along concentric circular arcs were performed. The results of the experiments are consistent with theoretical predictions.     

Mixed-Mode Dynamic Crack Growth in Functionally Graded Glass-Filled Epoxy

Compositionally graded glass-filled epoxy sheets with edge cracks initially along the gradient are studied under dynamic loading conditions. Specimens with monotonically varying volume fraction of reinforcement are subjected to mixed-mode loading by eccentric impact relative to the crack plane. The optical method of Coherent Gradient Sensing and high-speed photography are used to map transient crack tip deformations before and after crack initiation. Two configurations, one with a crack on the stiffer side of a graded sheet and the second with a crack on the compliant side, are examined experimentally. To elucidate the differences in fracture behavior due to functional grading, a homogeneous sample is also tested. The differences in both pre- and post-crack initiation behaviors are observed interms of crack initiation time, crack path, crack speed and stress intensity factor histories. When a crack is situated on the compliant side of the sample, it kinks significantly less compared to when it is on the stiffer side. Crack tip mode mixity histories show small but positive values during crack growth from the stiffer side of the sample towards the compliant side whereas a small but negative mode mixity prevails for the opposite configuration.     

Dynamic fracture parameters and constraint effects in functionally graded syntactic epoxy foams

Functionally graded syntactic foam sheets are developed by dispersing microballoons in epoxy for studying dynamic fracture behavior under low velocity impact loading. The volume fraction of microballoons is graded linearly over the width of the sheets. The mode-I crack initiation and growth behaviors are studied using reflection coherent gradient sensing technique and high-speed photography in samples with crack on the compliant and stiff sides and oriented along the compositional gradient. Crack growth along the gradient in each case shows sudden acceleration followed by steady state growth and deceleration during the window of observation. In both cases, the crack accelerations are similar while crack decelerations show differences. The dynamic stress intensity factor history prior to crack initiation in each case shows a rapid increase at different rates with the crack on the compliant side of the graded sheet experiencing higher rate of loading relative to the one with the crack on the stiffer side. Post-crack initiation stress intensity factor histories suggest increasing fracture toughness with crack growth in the graded sample with the crack on the compliant side while a decreasing trend is seen when the crack is on the stiffer side.Optical measurements are supplemented by finite element simulations for studying crack tip constraint effects on fracture behavior of graded foam sheets. Computed plane strain constraints in graded configurations are essentially identical to the homogeneous counterpart and the computed stress intensity factors obtained from plane stress elasto-dynamic analyses of the graded foams correlate well with the experimental measurements prior to crack initiation. The computed T-stress histories however, show an earlier loss of negative crack tip constraint in case of the graded foam sample with a crack on the compliant side. This correlates well with the higher crack tip loading rate and earlier crack initiation suggesting a possible role of in-plane constraint on fracture of graded foam. The coincidence of the time rate of change of in-plane constraint parameter becoming stationary close to experimentally observed crack initiation times are noted.     

预置圆孔膨胀环动态断裂行为研究

利用中心线起爆膨胀环加载技术,采用分幅摄影技术观测了20号钢圆环在准一维拉伸作用下,预置圆孔缺陷临近区域的动态断裂特征。获得了高应变率下圆孔的变形、裂纹的萌生及扩展过程。并采用LS-DYNA3D有限元程序分步建模,将驱动器对膨胀环的冲击压力简化为直接作用于圆环内壁的压力历史,以此模拟了整个断裂过程。通过实验图像,得到裂纹尖端的位移以及速度随时间变化的曲线。结果表明,宏观可见裂纹出现于应力集中最大处,裂纹扩展速度随时间振荡,数值模拟与实验结果吻合较好。     

Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads

Mixed-mode fracture problems of orthotropic functionally graded materials (FGMs) are examined under mechanical and thermal loading conditions. In the case of mechanical loading, an embedded crack in an orthotropic FGM layer is considered. The crack is assumed to be loaded by arbitrary normal and shear tractions that are applied to its surfaces. An analytical solution based on the singular integral equations and a numerical approach based on the enriched finite elements are developed to evaluate the mixed-mode stress intensity factors and the energy release rate under the given mechanical loading conditions. The use of this dual approach methodology allowed the verifications of both methods leading to a highly accurate numerical predictive capability to assess the effects of material orthotropy and nonhomogeneity constants on the crack tip parameters. In the case of thermal loading, the response of periodic cracks in an orthotropic FGM layer subjected to transient thermal stresses is examined by means of the developed enriched finite element method. The results presented for the thermally loaded layer illustrate the influences of the material property gradation profiles and crack periodicity on the transient fracture mechanics parameters.     

Poroelastic behaviors of the osteon: A comparison of two theoretical osteon models

In the paper, two theoretical poroelastic osteon models are presented to compare their poroelastic behaviors, one is the hollow osteon model (Haversian fluid is neglected) and the other is the osteon model with Haversian fluid considered. They both have the same two types of impermeable exterior boundary conditions, one is elastic restraint and the other is displacement constrained, which can be used for analyzing other experiments performed on similarly shaped poroelastic specimens. The obtained analytical pressure and velocity solutions demonstrate the effects of the loading factors and the material parameters, which may have a significant stimulus to the mechanotransduction of bone remodeling signals. Model comparisons indicate: (1) The Haversian fluid can enhance the whole osteonal fluid pressure and velocity fields. (2) In the hollow model, the key loading factor governing the poroelastic behavior of the osteon is strain rate, while in the model with Haversian fluid considered, the strain rate governs only the velocity. (3) The pressure amplitude is proportional to the loading frequency in the hollow model, while in the model with Haversian fluid considered, the loading frequency has little effect on the pressure amplitude.     

Propagation of a plane-strain hydraulic fracture with a fluid lag: Early-time solution

This paper studies the propagation of a plane-strain fluid-driven fracture with a fluid lag in an elastic solid. The fracture is driven by a constant rate of injection of an incompressible viscous fluid at the fracture inlet. The leak-off of the fracturing fluid into the host solid is considered negligible. The viscous fluid flow is lagging behind an advancing fracture tip, and the resulting tip cavity is assumed to be filled at some specified low pressure with either fluid vapor (impermeable host solid) or pore-fluids infiltrating from the permeable host solid. The scaling analysis allows to reduce problem parametric space to two lumped dimensionless parameters with the meaning of the solid toughness and of the tip underpressure (difference between the specified pressure in the tip cavity and the far field confining stress). A constant lumped toughness parameter uniquely defines solution trajectory in the parametric space, while time-varying lumped tip underpressure parameter describes evolution along the trajectory. Further analysis identifies the early and large time asymptotic states of the fracture evolution as corresponding to the small and large tip underpressure solutions, respectively. The former solution is obtained numerically herein and is characterized by a maximum fluid lag (as a fraction of the crack length), while the latter corresponds to the zero-lag solution of Spence and Sharp [Spence, D.A., Sharp, P.W., 1985. Self-similar solution for elastohydrodynamic cavity flow. Proc. Roy. Soc. London, Ser. A (400), 289–313]. The self-similarity at small/large tip underpressure implies that the solution for crack length, crack opening and net fluid pressure in the fluid-filled part of the crack is a given power-law of time, while the fluid lag is a constant fraction of the increasing fracture length. Evolution of a fluid-driven fracture between the two limit states corresponds to gradual expansion of the fluid-filled region and disappearance of the fluid lag. For small solid toughness and small tip underpressure, the fracture is practically devoid of fluid, which is localized into a narrow region near the fracture inlet. Corresponding asymptotic solution on the fracture lengthscale corresponds to that of a crack loaded by a pair of point forces which magnitude is determined from the coupled hydromechanical solution in the fluid-filled region near the crack inlet. For large solid toughness, the fluid lag is vanishingly small at any underpressure and the solution is adequately approximated by the zero-lag self-similar large toughness solution at any stage of fracture evolution. The small underpressure asymptotic solutions obtained in this work are sought to provide initial condition for the propagation of fractures which are initially under plane-strain conditions.     

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.     

A variational approach to analyze a natural fault with hydraulic fracture based on the strain energy density criterion

A simplified analytical model of the interaction between a hydraulic fracture and an existing natural fault is developed. The mechanical activation of the natural fault as a result of contact with a pressurized fracture is described for plane strain conditions and quasi-static fracture propagation approximation. Using a variational approach, the normal and shear stresses, as well as the boundaries of the open and sliding zones along the fault, are predicted for three stages of the fracturing process (fracture approaching, coalescence, and fluid penetration). An accumulated concentration of shear stress at the tip of the fault’s sliding zone is shown to create sufficient tensile stress to initiate a new tensile crack on the opposite side of the fault, provided either the differential in situ stress is low or the friction coefficient is sufficiently large. The results of direct numerical simulation of the fracture interaction fit the model predictions made from the strain energy density fracture criterion.     

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

压应力场中爆生裂纹分布与扩展特征实验分析

采用动静组合加载实验装置和数字激光焦散线实验系统,进行了0、3、6、9 MPa等4种压应力场中PMMA试件的爆破致裂实验,分析了沿静态主应力方向扩展的裂纹运动学和力学行为。实验结果表明:首先,静态竖向载荷在预制炮孔周围产生应力集中,在炮孔壁上下端部处出现最大拉应力;随后,在动态爆炸载荷的叠加作用下,裂纹优先在炮孔壁上最大拉应力位置处起裂,并沿最大主应力方向扩展;裂纹扩展过程中,静态竖向载荷越大,裂纹扩展速度越大,且裂纹尖端应力强度因子值越大。     

Dynamic stress intensity factor KⅢ and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials,the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated.Stress,strain and displacement around the crack tip are expressed as an analytical complex function,which can be represented in power series.Constant coefficients of series are determined by boundary conditions.Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained.Components of dynamic stress,dynamic strain and dynamic displacement around the crack tip are derived.Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials,i.e.,crack propagation velocity M and the parameter α.The faster the crack velocity is,the greater the maximums of stress components and dynamic displacement components around the crack tip are.In particular,the parameter α affects stress and dynamic displacement around the crack tip.     

无限冰介质中爆炸裂纹扩展机理与数值模拟

根据冰体力学性能,提出了无限淡水冰介质在爆炸冲击载荷下的压碎区及裂隙区的理论计算方法.利用大型有限元软件ANSYS/LS-DYNA模拟了爆炸载荷下无限区域冰体内裂纹扩展过程,模拟结果与实验结果基本一致,表明采用的损伤断裂模型能够较准确的反映无限冰介质动态力学性能及裂纹成形过程.数值模型可近似计算冰体中裂隙区的半径.数值计算值与理论计算值误差不超过5%,数值模拟结果与实验结果吻合,从而确定了无限区域冰体在-15℃时的基本破坏特征及范围.     

Enriched kinematic fields of cracked structures

Far from the crack tip process zone where non-linear phenomena take place, the mechanical behavior of a cracked medium can be analyzed within the framework of elasticity. Apart from the classical singular stress field associated with the elastic behavior, the effect of a confined process zone is decomposed over a set of (super-singular) fields. Because these fields are indexed by the exponent of their decay with distance from the crack tip, the dominant effect of non-linear mechanisms is characterized by the amplitudes of the first super-singular fields (modes I and II). This approach provides a macroscopic characterization of crack tip non-linearities and describes accurately the displacement field. As an application, the cyclic loading of a cracked elasto-plastic medium is discussed.     

A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature

Viscoplastic crack-tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack-growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack-growth criterion based on strain accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilized in the prediction of crack-growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.