Fracture initiation in elastic brittle materials having non-linear fracture envelopes

A theory is outlined for determining the initiation of fracture and initial fracture propagation in elastic brittle materials having non-linear Mohr fracture envelopes. This theory is applied to a specific boundary value problem, i.e. a truncated quarter plane with arbitrary traction distribution on the truncated boundary and varying confining pressure. This problem simulates the chipping phase of the penetration of a wedge shaped tool into an elastic brittle material. Numerical results are obtained for two rock materials, Blair dolomite and quartzite. Results indicate that for increasing confining pressure, a limit condition is reached for both fracture initiation location and force. This limit location is closer to the boundary than the fracture initiation points at lower confining pressures, indicating smaller chips. It is also found that initial fracture propagation is less clearly defined at higher confining pressures. Both of these results have been observed experimentally.     

Anomalous propagation of elastic waves through a boundary between liquid and magnetoacoustic material

We consider a longitudinal acoustic wave incident onto a plane boundary between a liquid and a magnetoacoustic medium representing an antiferromagnetic material with anisotropy of the easy plane type, occurring in the vicinity of an orientational phase transition with respect to magnetic field. The directions of propagation and the amplitudes of reflected and transmitted longitudinal and transverse waves are determined. The possibility of an effective field control for the refraction angle and the wave type transformation is demonstrated. Beginning with a certain critical angle of incidence, the longitudinal and, eventually, the transverse waves in the magnetic medium become inhomogeneous and slide along the interface. If the magnetic material is sufficiently close to the phase transition point, the waves can be reirradiated into the liquid medium.     

Nanoscale mechanisms for high-pressure mechanochemistry: a phase field study

Coupled evolution of a high-pressure phase (HPP) and dislocations, including dislocation pileups and dislocations generated due to phase transformation (PT), under compression and shear of a nanograined bicrystal, is considered as a model for high-pressure mechanochemistry. Recently developed phase field approach for the interaction between PTs and dislocations at large strains and a finite element analysis are utilized. Periodic boundary conditions for displacements are applied to the lateral surfaces. It is confirmed that the shear-induced dislocation pileups may reduce the PT pressure by an order of magnitude in comparison with hydrostatic loading, and even below phase equilibrium pressure, as it was observed in some experiments. In contrast to the formulation with boundary conditions for lateral stresses, which do not exhibit the sample size effect, periodic boundary conditions lead to some suppression of PT with decreased grain and sample sizes. The local transformation work-based phase equilibrium condition is met for most of the points of the stationary phase interfaces. The interface configurations also correspond in the most cases to the constant pressure contour but with different values for different loadings. Rarely, the same is true for the constant shear stress contours. Similar phase equilibrium conditions are satisfied for the transformation work expressed in terms of stresses averaged over the transformed grain and HPP. These conditions can be used to scale up results of the nanoscale studies to the coarse-grained microscale theory. During unloading, the PT, dislocations, and plastic shear are fully reversible. Even if one pins all the dislocations before unloading starts, still the entire HPP returns back. Thus, problem with modeling metastability of the HPPs still remains open. Obtained results are applicable for interpretation of experiments on high-pressure torsion with diamond or ceramic anvils, friction, surface processing, and probably on ball milling.     

Magnetofluiddynamic flow with a pressure gradient and fluid injection

Summary The nonlinear partial differential equation of motion for an incompressible fluid flowing over a flat plate under the influence of a magnetic field and a pressure gradient, and with or without fluid injection (or ejection) through the plate is transformed to a nonlinear, third order ordinary differential equation by using a stream function and a similarity transformation.The necessary boundary conditions are developed for flow with and without fluid injection (or ejection), and an example is presented to illustrate the solution to the flow problem.The controlling equation reduces to the well known Falkner-Skan equation when the magnetic field is zero, and if additionally the pressure gradient is zero, the equation reduces to the Blasius equation.     

Modelling of crack propagation in rocks under SHPB impacts using a damage method

Rock dynamic fracture is a complex problem and has received considerable attention during the last few decades. In this paper, tensile crack softening failure criterion is used to study impact‐induced crack initiation and propagation in rocks. In order to examine applicability of the criterion, under realistic loading and boundary conditions, three boundary conditions were analyzed in details and an impacting experiment using single cleavage semicircle compression (SCSC) specimens had been successfully simulated. A good agreement was achieved between the simulation and experimental results. It was concluded that the boundary conditions play an important role in rock dynamic fracturing. When a stress wave propagates from a material with low wave impedance to a material of high wave impedance, the compression wave is partially reflected back and the process of fast cracking is suppressed. In addition, with the change of the tensile strength and the fracture energy, the crack initiation modes can be divided into four types.     

On computational homogenization of microscale crack propagation

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

各向异性弹性层中SH波传播的边界元方法

本文利用坐标变换下的映象法求出了底部为刚性边界的各向异性弹性层中SH波传播问题的格林函数,并由此建立了求解分层介质问题的边界元方法。文中给出了在稳态线荷载作用下带有圆孔的弹性层中反应的计算实例。     

Analytical modelling of dynamic fracture and crack arrest in DCB specimens under fixed displacement conditions

An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded double cantilever beam (DCB) specimen. Fixed displacement condition is prescribed at the pin location under which crack arrest occurs. In the static case, at first, the compliance function of a DCB specimen is obtained and shows good agreement with the experimental results cited in the literature. Afterward, the stress intensity factor is determined at the crack tip via the energy release rate formula. In the dynamic case, the obtained governing equations for the model are solved supposing quasi‐static treatment for unstable crack propagation. Finally, a closed form expression for the crack propagation velocity versus beam parameters and crack growth resistance of the material is found. It is shown that the reacceleration of crack growth appears as the crack tip approaches the finite boundary. Also, the predicted maximum crack propagation velocity is significantly lower than that obtained via the Euler–Bernoulli theory found in the literature.     

Crack growth in the process of unstable brittle fracture

We suggest a model of the transition of a crack from stable to unstable propagation with subsequent growth in the supercritical state. By using the energy balance equation for propagating cracks, we estimate the specific surface energy and crack growth rate under the conditions of unstable propagation. Unstable propagation starts with a rate which is lower than the maximum crack growth rate in the material. The specific surface energy and kinetics of the crack undergoing unstable fracture depend both on the maximum crack growth rate in the material and on the initial rate υ₀ of its unstable propagation. The rate υ₀ is largely determined by the critical size of the crack (critical stresses). Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 6, pp. 81–86, November–December, 1996.     

水下耐压结构拓扑优化设计方法探究

探究了拓扑优化设计方法在水下耐压结构设计中的应用。与固定载荷作用下结构的优化设计相比,此类问题需要正确地确定压力作用面。在拓扑优化过程中,利用变密度法得到的中间结构拓扑实际上可以看成是灰度图。基于此,提出了基于图像分割技术的压力加载面搜索方法,并利用距离正规化水平集方法(DRLSE)检测图像边界。利用数值算例验证了方法的有效性,并研究了静水压力作用下结构的拓扑优化设计问题。在给定材料约束的前提下,研究了不同边界条件下耐压壳体的最小柔顺度及最优结构拓扑形式。优化结果说明了该方法在多球交接耐压壳结构形式优化设计及复杂边界条件下耐压结构新形式探索中的工程应用价值。     

Thermal fracture as a framework for quasi-static crack propagation

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.     

Elastic plastic mode III crack under internal shear

A complete solution is presented for the problem of a mode III crack in an infinite elastic perfectly-plastic solid under internal shear stress. This problem is the anti-plane strain equivalent of a mode I crack with internal pressure. The problem is transformed into a boundary value problem for a potential function. The particular case when the applied stress σA is equal to the yield stress σ0 is solved analytically, and the distance to the elastic-plastic boundary is obtained in closed form. The general case when σA σ0 is solved numerically by using the Boundary Element Method for potential problems. Numerical results are given for the distance to the elastic-plastic boundary and the crack tip opening displacement. The extent of the plastic zone ahead of the crack tip is shown to vary linearly with the ratio σA/σ0) when 0.5 ≤ (σA/σ0) ≤ 1. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fracture behaviour of C–Mn steel multipass MMA weld metals at −60°C in Charpy V testing

Abstract

By observation of the fracture surfaces and of appropriate metallographic sections of C–Mn steel multipass MMA (manual metal arc) weld metals and simulated weld specimens which were fractured at ?60°C in Charpy V tests, it was found that the impact toughness of the specimen could be correlated with the length of the fibrous crack which was limited by unstable propagation of the cleavage crack; the latter could be initiated at a type of second phase particle transformed from carbon rich regions or non-metallic inclusions. The weakest zone in which the cleavage crack initiated was characterised by coarse grains of ferrite and the critical event which gave rise to unstable propagation of a cleavage crack was a crack in the ferrite grain larger than 30 μm cutting through the boundary and extending over the specimen. On the basis of these results, a model of the fracture mechanism is proposed and the effect of Mn content on increasing toughness is explained using the model.

MST/647     

基于XFEM的RC梁静态破碎研究

建筑基坑内支撑的拆除是影响施工进度的重要因素之一。为提高施工效率,提出一种在钢筋混凝土支撑梁内部沿着梁轴线预埋大直径孔道进行静态破碎的拆除方案。在此基础上,通过扩展有限元方法(Extended Finite Element Method,XFEM)建立含预埋静态破碎孔(孔径为90 mm)的钢筋混凝土梁(截面尺寸为500 mm×500 mm)模型,并对其在静态膨胀压力作用下的破碎及裂缝扩展过程进行了模拟分析。模拟结果表明:内支撑梁的静态破碎过程可分为弹性变形、裂缝稳定扩展和裂缝失稳扩展3个阶段;基于虚拟闭合技术,进一步计算得到了复合开裂模式下的应变能释放率,计算结果显示:裂缝扩展以Ⅰ型裂缝为主,当膨胀压力达到19.4 MPa时,可实现破碎钢筋混凝土内支撑梁的目的。     

基于XFEM的RC梁静态破碎研究

建筑基坑内支撑的拆除是影响施工进度的重要因素之一。为提高施工效率,提出一种在钢筋混凝土支撑梁内部沿着梁轴线预埋大直径孔道进行静态破碎的拆除方案。在此基础上,通过扩展有限元方法(ExtendedFiniteElementMethod,XFEM)建立含预埋静态破碎孔(孔径为90mm)的钢筋混凝土梁(截面尺寸为500mm ×500mm)模型,并对其在静态膨胀压力作用下的破碎及裂缝扩展过程进行了模拟分析。模拟结果表明:内支撑梁的静态破碎过程可分为弹性变形、裂缝稳定扩展和裂缝失稳扩展3个阶段;基于虚拟闭合技术,进一步计算得到了复合开裂模式下的应变能释放率,计算结果显示:裂缝扩展以Ⅰ型裂缝为主,当膨胀压力达到19.4MPa时,可实现破碎钢筋混凝土内支撑梁的目的。     

Analysis of Elastic-PlasticWaves in a Thin-Walled Tube By a Novel Lie-Group Differential Algebraic Equations Method

In this paper, we adopt the viewpoint of a nonlinear complementarity problem (NCP) to derive an index-one differential algebraic equations (DAEs) system for the problem of elastic-plastic wave propagation in an elastic-plastic solid undergoing small deformations. This is achieved by recasting the pointwise complementary trio in the elastic-plastic constitutive equations into an algebraic equation through the Fischer-Burmeister NCP-function. Then, for an isotropicallyhardening/ softening material under prescribed impulse loadings on a thin-walled tube with combined axial-torsional stresses, we can develop a novel algorithm based on the Lie-group differential algebraic equations (LGDAE) method to iteratively solve the resultant DAEs at each time marching step, which converges very fast. The one-dimensional axial-torsional wave propagation problems under different imposed dynamical loading conditions and initial conditions are solved, to assess the performance of the LGDAE.     

高压水射流破碎胎面胶的脆化效应与胶粉形成

采用霍布金森压杆试验模拟子午线轮胎胎面胶的破碎回收过程,分析高压水射流冲击下胎面胶材料受力及响应状态,试验表明材料存在韧脆转变现象,进而发生脆性断裂。橡胶断口与胶粉微观形貌表明,裂纹扩展区呈现典型的放射状脆性断面形貌,并形成大量与胶粉尺寸匹配的平整光滑区域,直接验证了脆性断裂的存在并阐述其发生过程。然后利用应力波传播判据和脆断力学分析解释了胎面胶材料出现脆化效应的原因。对材料韧脆转变的影响因素进行分析后可知,高压水射流冲击过程中,材料质点变形速度远大于韧脆转变临界速度,在力学性能上表现为断裂应力小于屈服应力,致使材料发生脆性断裂并形成精细胶粉。     

Mechanical metamaterials with negative compressibility transitions

When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilizations of (meta)stable equilibria of the constituents. These destabilizations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micromechanical controls, and protective devices.