Dynamic crack initiation toughness of 4340 steel at constant loading rates

Determination of fracture toughness for metals under quasi-static loading conditions can follow well-established procedures and ASTM standards. The use of metallic materials in impact related applications requires the determination of dynamic crack initiation toughness for these materials. There are two main challenges in experiment design that must be overcome before valid dynamic data can be obtained. Dynamic equilibrium over the entire specimen needs to be approximately achieved to relate the crack tip loading state to the far-field loading conditions, and the loading rate at the crack tip should be maintained near constant during an experiment to delineate rate effects on the values of dynamic crack initiation toughness. A recently developed experimental technique for determining dynamic crack initiation toughness of brittle materials has been adapted to measure the dynamic crack initiation toughness of high-strength steel alloys. A Kolsky pressure bar is used to apply the dynamic loading. A pulse shaper is used to achieve constant loading rate at the crack tip and dynamic equilibrium across the specimen. A four-point bending configuration is used at the gage section of the setup. Results are presented which show a monotonically increasing rate dependence of crack initiation toughness for 4340 high-strength steel.     

On higher order parameters in cracked composite plates under far‐field pure shear

This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress‐based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non‐zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non‐singular term, ie, the T‐stress. Unlike the isotropic materials, in which the T‐stress is zero under pure shear, it is found that the T‐stress is non‐zero for the case of anisotropic materials, being the only material‐dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T‐stress on stresses near the crack tip in composite plates under pure shear loads.     

Experimental study of crack propagation in polymethyl methacrylate material with double holes under the directional controlled blasting

The crack propagation behaviours of polymethyl methacrylate material with double holes under the directional controlled blasting are studied using dynamic caustic method. A series of dynamic caustic patterns at the propagating crack tip under the explosive loading are recorded using the digital high‐speed camera. Some important dynamic fracture characterizations and parameters about two main cracks are determined including the crack path, the propagating speed and the crack tip stress intensity factors. The fracture mechanisms of the double blasting holes are analysed. The results provide the important experimental basis for evaluating and designing the directional controlled blasting for the rock tunnel and the rock face excavation.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Modeling of the dynamic delamination of L-shaped unidirectional laminated composites

One of the widely used geometrically complex parts in advanced commercial aircraft is the L-shaped composite. Due to the sharp curved geometry, interlaminar opening stresses are induced and delamination occurs under considerable mode-mixities in L-shaped beams. Dynamic phenomena during delamination initiation and propagation of L-shaped beams are investigated using dynamic (explicit) finite element analysis in conjunction with cohesive zone methods. The 2-D model consists of 24 plies of unidirectional CFRP laminate with an initial 1 mm crack at the center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading type yields different traction fields and mode-mixities in the two sides of the crack in which delamination occurs under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed of the delamination under shear dominated loading at one side is 800 m/s and under normal stress dominated loading is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, a different failure mode is observed in which a secondary crack nucleates at the arm and propagates towards the center crack.     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.     

含倾斜裂纹三点弯动态断裂试验研究

为研究冲击荷载下巷道围岩不同角度径向裂纹的破坏机制,采用落锤冲击加载平台和数字激光动态焦散线实验系统,以有机玻璃为试验材料,设计冲击荷载下半圆孔上不同角度裂纹的三点弯动态断裂试验,记录预制裂纹的角度α的改变对裂纹动态力学行为的影响,通过分析动态应力强度因子和裂纹扩展轨迹的分形维数对实验现象进行归纳总结。研究发现:①预制裂纹角度对裂纹尖端应变能的积累和释放的快慢有较大影响,随着角度的增大,起裂时间变短,起裂更容易,裂纹尖端应变能积累的更快;②裂纹尖端应变能释放的快慢在α=45°两侧表现出不同的规律;③不同角度裂纹的Ⅰ型动态应力强度因子随时间的变化规律具有相似性,但最大值却具有差异性;④不同角度裂纹的扩展轨迹满足一定的分形规律。     

基于两种破裂判据的裂隙岩体单轴压缩起裂分析

该文引入Rankine最大拉应力准则和Mohr-coulomb剪切破坏准则分别作为岩石基质的拉伸和压剪破裂判据,分析了单轴压缩下裂隙岩体的起裂机制。根据含单个椭圆裂隙的无限域岩体在单轴压缩下的应力理论解,编制了Matlab程序,计算分析了不同短轴与长轴比k和倾角α(加载轴与裂隙长轴间的夹角)下的岩石基质应力集中系数、两种不同起裂机制的破裂函数值、开裂位置和开裂临界荷载。对多裂隙岩体,采用ABAQUS有限元软件进行了应力计算和起裂机制分析。计算结果表明:1)与单裂隙岩体相比,多裂隙岩体的岩石基质应力集中系数略大、起裂临界荷载略小,但起裂位置相同;2)随着裂隙倾角α的增大,岩石基质的主拉应力集中区由裂隙端部附近很小的区域逐渐变为裂隙中部的大面积区域,而主压应力集中区则反之;3)存在临界裂隙倾角α0,其值在45°附近。当裂隙倾角0<α≤α0时,在裂隙端部同时有拉应力和压剪应力集中,拉破裂临界荷载小于压剪破裂临界荷载,但随着裂隙轴比的增大二者逐渐相等,表明岩体受拉破裂和压剪破裂共同影响越来越明显;当α0<α≤90°时,尽管拉破裂临界荷载大于压剪破裂临界荷载,但首先发生在裂隙端部的压剪破裂区范围很小,而随后将在裂隙中部或端部发生大量的拉伸破裂。上述分析结果与实验现象较为吻合。     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

Effect of shear and rotary inertia on dynamic fracture of a beam or plate in tensile loading

The dynamic fracture response of a long beam of brittle material subjected to tensile loading is studied. If the magnitude of the applied tensile loading is increased to a critical value, a crack will propagate from one of the longitudinal surfaces of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the tensile loading and the induced bending moment at the fracturing section is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the bending moment effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded. The results also apply for plane strain fracture of a plate in tensile loading provided the value of the elastic modulus is appropriately modified.     

定向断裂控制爆破爆生裂纹扩展机理的实验研究

采用新型数字激光动态焦散线实验系统,对缺陷介质双孔定向断裂控制爆破裂纹扩展的动态行为进行了研究。结果表明,预制斜裂纹阻断了爆生主裂纹的扩展,最终两条主裂纹分别与翼裂纹形成相互勾连的形状。爆生主裂纹尖端以张拉应力场为主,其断裂为近似I型断裂。当爆生主裂纹运动到预制裂纹附近时,主裂纹端部应力场与预制裂纹尖端奇异应力场相互叠加,在预制裂纹尖端形成较强的拉剪应力场,且受已有主裂纹面的影响,预制裂纹扩展表现为弯向主裂纹面的弯曲断裂。研究结果可为含节理岩体定向断裂控制爆破提供理论依据。     

Stress-Strain State and Energy Fluxes in a Plate Containing a Stationary Crack under Impulsive Loading

We study the stress-strain state and energy fluxes in a continuous infinite plate and in a plate containing a stationary crack of finite length under impulsive loading. For this purpose, we develop a model of formation of the zone of elevated stresses and the zone of unloading as well as a numerical procedure for the evaluation of their parameters. We deduce analytic expressions for the quantitative analysis of the stress-strain state and energy fluxes in the plate near the tip of the stationary crack under arbitrary impulsive loading. The theoretical results are compared with the experimental data on the initiation of main cracks in plane specimens made of solid polymers. We formulate a quantitative criterion for the difference between the dynamic and quasistatic loading of a crack and show that the dynamic and static fracture processes can be described within the framework of a single approach.     

A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture

This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly. The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.     

Effect of bending moment on the dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. As an extension of previous work, an induced bending moment generated during fracture is incorporated into the analysis and this improved formulation is presented. The crack length, crack tip speed, axial force and bending moment on the fracturing section are determined as functions of time after crack initiation. It is found that the bending moment has a significant effect on the fracture process in that it tends to retard fracture and causes a drastic change in the slope of the loading curve for large crack depths. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate in pure tensile loading.     

THE PROBLEM OF SCATTER OF FRACTURE TOUGHNESS DATA

The authors studied the influence of the conditions for growing an initial fatigue crack on the scatter of fracture toughness data determined under static loading. It was found that the values of static fracture toughness for cyclically softening steels at temperatures below the brittle-to-ductile transition are essentially dependent on the degree of the material fatigue damage in the vicinity of the crack tip during the final stage of crack initiation. A method is proposed for evaluating the fracture toughness under static loading which makes it possible to take into account the material damage in the vicinity of the crack tip.     

Experimental validation of large-scale simulations of dynamic fracture along weak planes

A well-controlled and minimal experimental scheme for dynamic fracture along weak planes is specifically designed for the validation of large-scale simulations using cohesive finite elements. The role of the experiments in the integrated approach is two-fold. On the one hand, careful measurements provide accurate boundary conditions and material parameters for a complete setup of the simulations without free parameters. On the other hand, quantitative performance metrics are provided by the experiments, which are compared a posteriori with the results of the simulations. A modified Hopkinson bar setup in association with notch-face loading is used to obtain controlled loading of the fracture specimens. An inverse problem of cohesive zone modeling is performed to obtain accurate mode-I cohesive zone laws from experimentally measured deformation fields. The speckle interferometry technique is employed to obtain the experimentally measured deformation field. Dynamic photoelasticity in conjunction with high-speed photography is used to capture experimental records of crack propagation. The comparison shows that both the experiments and the numerical simulations result in very similar crack initiation times and produce crack tip velocities which differ by less than 6%. The results also confirm that the detailed shape of the non-linear cohesive zone law has no significant influence on the numerical results.     

Fracture parameters for interfacial cracks: an experimental-finite element study of crack tip fields and crack initiation toughness

Crack tip measurements and analysis of interfacial parameters for PMMA-aluminum bimaterial system are presented. A variety of crack tip mode-mixities are obtained by subjecting asymmetric four-point-bend specimens to different boundary loads. The crack tip fields are mapped using the optical method of Coherent Gradient Sensing (CGS). The complex stress intensity factors and the associated crack tip mixities () are measured from CGS fringe patterns. The asymptotic expansion field for interface cracks is used for extracting fracture parameters by accounting for higher order contributions to the experimental data. The measurements are compared with complementary finite element computations. A linear relationship between crack tip mixity and the applied load mixity is experimentally demonstrated in this large elastic mismatch system. The fracture load and hence the energy release rate G _cr () at crack initiation is measured as applied load mixities are varied. Limited discussion on the influence of surface roughness prior to bonding on the fracture toughness is included. Positive and negative shear on the crack plane produce different failure responses in this bimaterial system and the observed asymmetry is akin to the one predicted by the T&H model that includes crack tip nonlinearty.     

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.