Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

水力压裂过程的扩展有限元数值模拟方法

建立了基于扩展有限元法的水力压裂数值模拟方法,使水力裂缝独立于网格存在,无需预设裂缝扩展方位。在扩展有限元计算框架下,将裂缝面处理为求解域内边界,将缝内水压力转化为相关单元等效节点力;运用考虑缝内水压力作用的相互积分法来数值求解缝尖应力强度因子;采用最大能量释放率准则确定裂缝是否继续扩展及扩展方位;最终编制了计算机程序。利用该方法数值模拟了单条水力裂缝在恒定水压力作用下作非平面扩展,所得结果分别与室内试验和解析模型相对比。结果表明,数值结果与室内试验和解析解吻合较好,缝尖应力强度因子最大相对误差不高于0.45%,验证了该方法的可行性和准确性。     

On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

Simulation of dynamic crack curving and branching under biaxial loading by a time domain boundary integral equation method

Bifurcation and trifurcation of a fast running crack under various biaxial loading conditions is investigated numerically. The solution procedure for the 2D model in the framework of linear elastodynamics employs a time-domain boundary element method and allows for arbitrary curvilinear crack propagation. Branching events are controlled by the criterion of a critical mode I stress intensity factor while the propagation direction and growth rate of each branch are determined from the criterion of maximum circumferential stress. Numerical results are compared with experimental findings and are discussed with respect to macroscopic and microscopic aspects of dynamic fracture.     

Simulation of craze failure in a glassy polymer: rate dependent drawing and rate dependent failure models

The failure of a craze ahead of a crack growing under steady state conditions in a glassy polymer is investigated by modeling the craze microstructure using a highly anisotropic network of springs. A rate dependent drawing law is used to determine the shape of the craze-bulk interface. Approximate analytical results are developed to link the normal stress on the craze-bulk interface, the thickness of the craze and the far field stress intensity factor to the crack propagating velocity, through the craze failure criterion and the craze microstructural parameters. The accuracy of the analytical results is examined using a detailed numerical simulation. Our analysis shows that the rate independent craze failure criterion, which assumes the failure stress for fibrils ahead of the crack tip to be a material constant independent of the crack growth rate, leads to predictions of the dependence of the craze thickness and the fracture toughness on crack growth rate that are contrary to what is found experimentally. Rate dependent craze failure criteria are then proposed. Specifically, we study a case where the crack tip fibril breaks down by rate dependent chain scission and a case where the crack tip fibril fails by rate dependent chain disentanglement. For the rate dependent chain scission criterion, the results given by the rate independent constant failure stress criterion are retrieved in the limit of low crack propagation velocity. Also, there exists a critical stress intensity factor below which steady state crack propagation is impossible, i.e., crack growth becomes unstable.     

Crack blunting mechanisms in polymers

A quantitative model has been developed to account for the degree of blunting that occurs at crack tips in epoxy materials prior to the onset of crack propagation. This mechanism controls the subsequent mode of crack growth and, to a large extent, the toughness as defined by the stress intensity factor for crack initiation. From this model a unique fracture criterion is derived which is applicable over all modes of crack propagation.     

Automated dynamic fracture procedure for modelling mixed-mode crack propagation using explicit time integration brick finite elements

Several fracture codes have been developed in recent years to perform analyses of dynamic crack propagation in arbitrary directions. However, general-purpose, commercial finite-element software which have capabilities to do fracture analyses are still limited in their use to stationary cracks and crack propagation along trajectories known a priori . In this paper, we present an automated fracture procedure implemented in the large-scale, nonlinear, explicit, finite-element code DYNA3D which can be used to simulate dynamic crack propagation in arbitrary directions. The model can be used to perform both generation- and application-phase simulations of self-similar as well as non-self-similar dynamic crack propagation in linear elastic structures without user intervention. It is developed based on dynamic fracture mechanics concepts and implemented for three-dimensional solid elements. Energy approach is used in the model to check for crack initiation/propagation. Dynamic energy release rate and stress intensity factors are determined from far-field finite-element field solutions using finite-domain integrals. Fracture toughness is input as a function of crack-tip velocity, and when the criterion for crack growth is satisfied, an element deletion-and-replacement re-meshing procedure is used along with a gradual nodal release technique to update the crack geometry and model the crack propagation. Direction of crack propagation is determined using the maximum circumferential stress criterion. Numerical simulations of experiments involving non-self-similar crack propagation are performed, and results are presented as verification examples.     

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

In 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.     

Crack propagation in elastic solids using the truss-like discrete element method

The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out.     

用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。     

Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.     

Numerical analysis of the crack growth path in the cement mantle of the reconstructed acetabulum

In this study, we use the finite element method to analyze the propagation's path of the crack in the orthopedic cement of the total hip replacement. In fact, a small python statement was incorporated with the Abaqus software to do in loop the following operations: extracting the crack propagation direction from the previous study using the maximal circumferential stresses criterion, drawing the new path, meshing and calculating again (stresses and fracture parameters). The loop is broken when the user's desired crack length is reached (number of propagations) or the value of the mode I stress intensity factor is negative. Results show that the crack propagation's path can be influenced by human body posture. The existing of a cavity in the vicinity of the crack can change its propagation path or can absolutely attract it enough to meet it. Crack can propagate in the outward direction (toward the acetabulum bone) and cannot propagate in the opposite direction, the mode I stress intensity factor increases with the crack length and that of mode II vanishes.     

Simulation of crack propagation in porous compacted specimens of aspirin

A model originally developed to simulate crack propagation in structural steel has been evaluated for porous compacted specimens of aspirin. The fracture mechanism is assumed to consist of hole growth and coalescence. The program allows both visualization of crack growth and the calculation of crack velocity. Simulations to investigate the effect of stress intensity factor indicate that the critical stress intensity factor for sustained growth for aspirin is of the order of 0.15 MPa m^1/2 consistent with experimental findings. The program is easy to use enabling many simulations to be performed with minimum effort.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

动焦散线在爆炸裂纹扩展试验研究中的应用

爆炸裂纹的动态扩展问题是爆炸力学研究的热点。本文建立了爆炸加载的动焦散线测试系统,解决了试验中的有效光学图片获取、精确同步控制等问题,为进一步定量分析爆炸裂纹扩展规律提供了一种新的有效实验方法。采用爆炸加载的透射式动焦散实验系统,初步研究了爆炸载荷下的裂纹起裂、发展和止裂的动态扩展行为,分析其破坏模式和动态应力强度因子、裂纹扩展速度的变化,并研究了爆炸裂纹穿过有机玻璃板的人工层理的规律。     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

动焦散线在爆炸裂纹扩展试验研究中的应用

爆炸裂纹的动态扩展问题是爆炸力学研究的热点。本文建立了爆炸加载的动焦散线测试系统,解决了试验中的有效光学图片获取、精确同步控制等问题,为进一步定量分析爆炸裂纹扩展规律提供了一种新的有效实验方法。采用爆炸加载的透射式动焦散实验系统,初步研究了爆炸载荷下的裂纹起裂、发展和止裂的动态扩展行为,分析其破坏模式和动态应力强度因子、裂纹扩展速度的变化,并研究了爆炸裂纹穿过有机玻璃板的人工层理的规律。     

7050铝合金Ⅰ-Ⅱ复合型疲劳裂纹研究

为研究7050铝合金在Ⅰ-Ⅱ型复合加载下疲劳裂纹扩展规律,在Amsler HFP5000高频试验机上利用Richard加载装置,完成紧凑拉剪(CTS)试样疲劳裂纹扩展试验,利用有限元对Ⅰ-Ⅱ复合型裂纹进行数值模拟,采用APDL命令流计算不同裂纹长度的应力强度因子,并引入最大周向应力准则计算裂纹扩展角,用有限元计算等效应...