Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

An analysis of the crack tip fields in a ductile three-point bend specimen subjected to impact loading

Analyses of an impact fracture test of a precracked, three-point beam of HY100 steel were performed to determine the dynamic fracture toughness. During impact, the crack tip opening displacement (CTOD) 100 μm behind the crack tip was measured using an optical measuring device called the interferometric strain/displacement gage. Since fracture initiates when stress wave effects dominate, a numerical simulation of the fracture event was conducted to obtain relevant near crack tip field parameters. The specimen was modeled by a plane stress finite element simulation using a rate sensitive elastoplastic material law. Since the simulated CTOD was to be compared with the measured CTOD in a region of residual strains due to crack closure, this effect was included in the model. The simulation produces a CTOD versus time response within 10% of the observed response, indicating that the other field quantities (such as the J-integral) should also be reliable. The loading rate /.K₁ was approximately 8 × 10⁶MPa√m/sec. If the fracture initiation time is assumed to coincide with the time at which the simulated and observed CTOD curves diverge, then the impact fracture toughness is 56% higher than the static fracture toughness.     

Measuring Crack Length in Coarse Grain Ceramics

Due to a coarse grain structure, crack lengths in precracked magnesium aluminate (MgAlO₄) spinel specimens could not be measured optically, so the crack lengths and fracture toughness were estimated by strain gage measurements. An expression was developed via finite element analysis to correlate the measured strain with crack length in four-point flexure. The fracture toughness estimated by the strain gaged samples and another standardized method were in agreement.     

A method for testing interlaminar dynamic fracture toughness of polymeric composites

Static and dynamic Mode I delamination fracture in two polymeric fiber composites was studied using a WIF test method. The dynamic test was conducted on a Split Hopkinson Pressure Bar apparatus. Crack speeds up to 1000 m/s were achieved. Dynamic fracture and crack propagation were modeled by the finite element method. Dynamic initiation fracture toughness of S2/8552 and IM7/977-3 composites were obtained. The dynamic fracture toughness of IM7/977-3 associated with the high speed propagating crack was extracted from the finite element simulation based on the measured data. It was found that the dynamic fracture toughness of the delamination crack propagating at a speed up to 1000 m/s approximately equals the static fracture toughness.     

Dynamic response of bimaterial and graded interface cracks under impact loading

The interfacial fracture in bimaterial and functionally graded material (FGM) under impact loading conditions is investigated using experimental and numerical techniques that are valid for both type of interfaces. Experiments are conducted on epoxy based specimens in three point bend configuration and the complex SIF is measured using an electrical strain gage mounted close to the crack-tip. A complementary two-dimensional finite element simulation is performed using tup force and support reactions as input tractions, and the SIF-time history is determined using a displacement extrapolation technique. The experimentally determined SIF-histories match closely with numerical simulation up to the time of fracture initiation. The test results show that the mode-mixity remains nearly constant through out the test in both the materials, and the mixity values correspond to their respective static counterparts. The general dynamic response of the bimaterial and FGM specimens in terms of impact load, support reaction and the magnitude of complex SIF are comparable, and the mode-mixity is the parameter that distinguishes the graded interface from the bimaterial case.     

Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA

To investigate the effects of loading rate and plate thickness on the fracture toughness of PMMA (polymethyl methacrylate) under impact loading, two methods, A method and B method, are applied as follows. In the A method, a dynamic finite element method and a strain gage method are applied to measure the dynamic fracture toughness in the fracture test using an air gun. In the B method, a single axis strain gage method is applied to measure the critical dynamic stress intensity factor, namely dynamic fracture toughness, in the fracture test using a weight dropping type apparatus. The dimensions of the PMMA specimen are L = 140 mm length and W = 30 mm width. Three values of the plate thickness B, 15.0 mm, 10.0 mm and 5.0 mm, are selected to investigate the plate thickness effect in the fracture test. Both results by the A and B methods precisely indicated the minimum value and the loading rate effect on the dynamic fracture toughness.     

Application of incubation time approach to simulate dynamic crack propagation

The incubation time criterion for dynamic fracture is applied to simulate dynamic crack propagation. Being incorporated into ANSYS finite element package, this criterion is used to simulate the classical dynamic fracture experiments of Ravi-Chandar and Knauss on dynamic crack propagation in Homalite-100. In these experiments a plate with a cut simulating the crack was loaded by an intense pressure pulse applied on the faces of the cut. The load consisted of two consequent trapezoidal pulses. This, in the experimental conditions used by Ravi-Chandar and Knauss, resulted in a crack initiation, propagation, arrest and reinitiation. Dependence of the crack length on time was measured in those experiments. The results for crack propagation obtained by FEM modelling are in agreement with experimental measurements of crack length histories. This result shows the applicability of the incubation time approach to describe the initiation, propagation and arrest of dynamically loaded cracks.     

Computational analysis of dynamically propagating cracks in axisymmetric solids

Dynamic crack propagation behavior in axisymmetric solids is investigated using an effective computational procedure. First, an accurate method to extract energy release rate of a dynamically propagating crack from finite element solutions is formulated for axisymmetric geometries. The method is applied to an analysis of a radially growing circular crack under remote tension in an infinite medium. The computed dynamic energy release rate shows an excellent agreement with the exact solution. Next, we have developed an iterative technique to propagate a crack whose velocity history is initially unknown. With the iterative procedure, the crack propagates according to a condition specified by a dynamic fracture criterion. At each increment of crack growth, an optimum velocity at which the crack growth condition satisfies is obtained by the iterative scheme. This procedure requires no artificial input or no preset crack tip speed in a simulation study. The iterative scheme is employed in a dynamic fracture analysis of ceramics. The computational analysis is carried out for simulation of fracture experiments using circumferentially notched round bars. In the test, a ceramic specimen is subjected to tensile stress wave loading and after crack growth initiation, the external crack propagates to tear the specimen. The computational simulation is carried out for the entire fracture process including the crack growth initiation and the dynamic propagation. The iterative procedure enables us to predict the crack tip velocity which is unmeasurable in the experiment. Suitabilities of proposed fracture toughness criteria for the ceramics are investigated by comparing measured and computed transmitted pulses through the uncracked ligament. This study proves the usefulness of the computational procedures for dynamic fracture analysis. It is most effective in characterizing dynamic fracture toughness where determination of every relevant parameter is difficult in the experiments.     

Application of finite element method for determination of stress intensity factor and plastic zone geometry in an aluminium alloy sheet under uniaxial tension

High strength materials have gained prominence in the fields of aero-structures, space missiles, ship-building, pressure vessels etc. However, high strength materials are often characterised by low values of crack resistance or fracture toughness. Knowledge of stress intensity factor (SIF) is essential to predict their fracture toughness. SIF values can be obtained both theoretically and experimentally. Theoretical methods include analytical techniques as well as the finite element method (FEM). The former is used for simpler geometries and the latter for complicated geometries of engineering structures. The SIF as a function of crack size in an aluminium alloy 2024-T₃ (Al-4·5% Cu, 1·5% Mg, 0·6% Mn) sheet was determined by a computer method. These values were obtained directly from the stresses as well as indirectly from strain energy release rateG andJ integral. The results agree well with the normalised values obtained from an ASTM formula. The size and shape of the plastic zone at the crack tip have been determined as a function of nominal stress for a fixed crack length. The plastic zone has the form of two ellipsoids with their maximum spreads oriented around 69° to the crack axis.     

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。     

霍普金森杆冲击压缩单裂纹圆孔板的岩石动态断裂韧度试验方法

对压缩单裂纹圆孔板(single cleavage drilled compression--SCDC)砂岩试样,利用分离式霍普金森压杆(SHPB)冲击加载,进行了岩石张开型(I型)动态断裂实验。分别采用2种方法确定砂岩的动态断裂韧度,第1种方法是实验-数值法:由SHPB弹性杆上应变片获得作用在试件上的加载力,然后输入有限元分析程序求得试样裂尖动态应力强度因子,对应于裂尖起裂时刻的动态应力强度因子即为材料动态断裂韧度值;第2种方法是准静态法:将载荷峰值代入静态应力强度因子公式确定动态断裂韧度。2种方法的结果差异较大,对无量纲裂纹长度a/R= 0.64(A组)试样,准静态方法确定的断裂韧度值要比实验-数值法确定的断裂韧度值平均要小35%~62%;对无量纲裂纹长度a/R=1.61(B组)试样,准静态方法的计算结果比实验-数值法的计算结果平均要小72%~83%。从原理上讲,实验-数值法比准静态法能更合理地测定岩石的动态断裂韧度。     

Fracture Analysis of Concrete Structural Components Accounting for Tension Softening Effect

This paper presents methodologies for fracture analysis of concrete structural components with and without considering tension softening effect. Stress intensity factor (SIF) is computed by using analytical approach and finite element analysis. In the analytical approach, SIF accounting for tension softening effect has been obtained as the difference of SIF obtained using linear elastic fracture mechanics (LEFM) principles and SIF due to closing pressure. Superposition principle has been used by accounting for non-linearity in incremental form. SIF due to crack closing force applied on the effective crack face inside the process zone has been computed using Green's function approach. In finite element analysis, the domain integral method has been used for computation of SIF. The domain integral method is used to calculate the strain energy release rate and SIF when a crack grows. Numerical studies have been conducted on notched 3-point bending concrete specimen with and without considering the cohesive stresses. It is observed from the studies that SIF obtained from the finite element analysis with and without considering the cohesive stresses is in good agreement with the corresponding analytical value. The effect of cohesive stress on SIF decreases with increase of crack length. Further, studies have been conducted on geometrically similar structures and observed that (i) the effect of cohesive stress on SIF is significant with increase of load for a particular crack length and (iii) SIF values decreases with increase of tensile strength for a particular crack length and load.     

Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions

Stress singularity of a transverse crack normal to ply-interface in a composite laminate is investigated using analytical and finite element methods. Four-point bending tests were performed on single-notch bend specimens of graphite/epoxy laminates containing a transverse crack perpendicular to the ply-interface. The experimentally determined fracture loads were applied to the finite element model to estimate the fracture toughness. The procedures were repeated for specimens under cryogenic conditions. Although the fracture loads varied with specimen thickness, the critical stress intensity factor was constant for all the specimens indicating that the measured fracture toughness can be used to predict delamination initiation from transverse cracks. For a given crack length and laminate configuration, the fracture load at cryogenic temperature was significantly lower. The results indicate that fracture toughness does not change significantly at cryogenic temperatures, but the thermal stresses play a major role in fracture and initiation of delaminations from transverse cracks.     

Crack arrest in rupturing steel gas pipelines

Failure incident investigations and full-scale experiments of pipelines rupturing indicate that the original methods in predicting arrest are no longer reliable when applied to high toughness pipelines. The cause of the phenomenon is analyzed in this paper through a macroscopic and phenomenological method by referring to the energy balance equation, by that is established the iterative algorithm used in finite element method (FEM) simulation of crack deceleration. This simulation, in combination with the two-specimen drop weight tear test (DWTT), provides a broad prediction of the dynamic fracture process. In addition, the crack tip opening angle (CTOA) criterion is consummated through the comparison between CTOA in FEM calculation and the critical value of (CTOA)_C obtained in the two-specimen DWTT. Thus, the avoidance of both the dimensional effect and the dissipation of irrelevant energy common in small-scale tests are achieved.     

An experimental cum numerical technique to determine dynamic interlaminar fracture toughness

A method combining experimental and finite element analysis is developed to determine interlaminar dynamic fracture toughness. An interlaminar crack is propagated at very high speed in a double cantilever beam (DCB) specimen made of two steel strips which are bonded together by epoxy with a precrack of about 40 mm length. The face of the front cantilever is bonded to a large solid block and a special fixture is designed to apply impact load to the rear cantilever through a load bar. In the load bar, a compressive square shaped elastic stress pulse is generated by impacting it with a striker bar which is accelerated in an air gun. The rear cantilever is screwed to the load bar; when the incident compressive pulse reaches the specimen, a part of the energy is reflected into the load bar and the rest of it passes to the specimen. By monitoring the incident and the reflected pulses in the load bar through strain gauges, deflection of cantilever-end is determined. The crack velocity is determined by three strain gauges of 0.2 mm gauge length bonded to the side face of the rear cantilever. Further, the first strain gauge, bonded very close to the tip of the precrack, and the crack velocity determine the initiation time of crack propagation.

The experimental results are used as input data in a finite element (FE) code to calculate J-integral by the gradual release of nodal forces to model the propagation of the interlaminar crack. The initiation fracture toughness and propagation fracture toughness are evaluated for an interlaminar crack propagating with a velocity in the range of 850 to 1785 m/s. The initiation toughness and propagation toughness were found to vary between 90–200 J/m² and 2–13 J/m², respectively.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

锌漆薄膜/钢基底系统界面断裂韧性的试验与模拟

以锌漆薄膜与304不锈钢基底之间的界面裂纹为研究对象,采用声发射与显微镜实时检测技术与三点弯曲试验相结合的方法,测量了锌漆涂层的界面断裂韧性。同时将界面裂纹长度的有限元模拟结果和实验结果相比较,结果较为吻合。通过ABAQUS有限元模拟发现,界面断裂韧性与多种影响因素有关,界面裂纹扩展长度随薄膜厚度和外荷载的增加而增加,随界面断裂韧性和薄膜弹性模量的增大而减小,而泊松比对其影响不大。     

双悬臂梁试件裂纹动态扩展的准静态数值分析

本文采用双悬臂梁（DCB）试件研究了复合材料层合板层间插入韧性胶膜（Interleaf）层的Ⅰ型断裂行为。试验结果表明,含和不含Interleaf层试件分别呈现脆性非稳态和脆性稳态分层扩展特性。针对非稳定裂纹扩展问题,依据动态断裂力学中应变能释放率与动能变化率的关系,提出了以断裂韧性值G_IC变化来抵消动能变化对裂纹扩展过程影响的准静态分析方法,根据试验中裂纹扩展的韧性变化,推导出适用于准静态裂纹扩展模拟的等效韧性G_IC*,利用ABAQUS平台和虚裂纹闭合技术（VCCT）建立了三维有限元计算模型;实现了从起裂到止裂的整个裂纹动态扩展过程的数值模拟,揭示了非稳定裂纹扩展过程中一些复杂的力学现象。      

西气东输管道裂纹的韧性减速机理研究

将动态断裂力学的基本原理、基本方法和止裂判据与壳体动力学的有限元方法相结合,形成了求解输气管道裂纹扩展问题的数值分析方法。对于高韧性钢,塑性功卸载引起的热耗散不可忽略。为此根据瞬态裂纹扩展条件下的整体能量平衡方程,在有限元中构造了求解瞬时速度的迭代算法。其中以材料的热耗散比率为主要构成的动态断裂韧性由实验测得,在计算中作为裂纹扩展速度的函数代入,形成韧性减速机理。为了给出计算需要的参数,推导了双试件DWTT法测定热耗散比率的公式。     

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.