金属试件变形断裂过程的计算模拟分析——组合功密度模型的应用

本文作者已建立了一个既适用于裂纹体亦适用于无裂纹体的统一损伤断裂模型——组合功密度模型。在本文中,作者应用该模型并结合大应变弹塑性有限元方法对40Cr制的圆棒光滑拉伸试件、圆棒切口拉伸试件和三点弯曲裂纹试件的变形和断裂过程进行了计算模拟。模拟结果很好地再现了两种圆棒拉伸试件的实验过程;而对于三点弯曲试件,模拟得到的载荷——加载位移关系曲线、裂纹扩展量——加载位移关系曲线、J_R阻力曲线和断裂韧性J_(IC)值等均与实测结果相当吻合。证实了该模型既能用于模拟预测无裂纹体中的裂纹萌生和扩展,也能模拟预测裂纹体中的裂纹起裂和稳定扩展过程。     

A STUDY OF FRACTURE OF UNIDIRECTIONAL CF/SiC SINGLE EDGE-NOTCHED BEAM UNDER THREE-POINT BENDING- MACRO/MICRO-NUMERICAL MONTE CARLO SIMULATION

In this paper, the fracture process of a unidirectional CF/SiC single edge-notched beam (SENB) under three-point bending (TPB) is studied by means of macro/micro-statistical Monte Carlo simulation. The simulatedP-Δ curves are in agreement with the experimental results before the peaks of curves, and the simulated microevolution patterns are in agreement with the patterns of the crack surfaces, which have verified this method. It is preliminarily demonstrated that the second turning point in the compliance changing rate curve corresponds to the fracture initiation for experiments on SENB under TPB of unidirectional CF/SiC composites.     

Experimental study and BEM analysis of fatigue crack growth in a cracked heterogeneous body

A model for analysing a soft-hard heterogeneous body with a crack in the hard region is presented in this paper. The result of fatigue experiments shows that mechanical heterogeneity affects the rate of propagation of fatigue crack. Meanwhile the results computed by BEM for cracked heterogeneous bodies under cycling loading indicate that the smaller the distance between the crack and the interface of hard and soft regions is, the smaller the amplitude of crack opening displacement, COD and ofJ-integral as well at the same step during the fatigue crack growth will be. The effect of heterogeneity on the rate of fatigue crack propagation is shown by the variation of J. The smaller the distance of the crack to the interface is, the smaller the rate of fatigue crack growth will be.     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

A novel method for measuring and characterizing dynamic fracture-initiation toughness of elastic-plastic materials

The characterization and testing methods of the dynamic fracture initiation toughness of elastic-plastic materials under tensile impact are studied. By using the self-designed bar-bar tensile impact apparatus, a novel test method for studying dynamic fracture-initiation has been proposed based on the one-dimensional test principle. The curve of average loadv. s. displacement is smooth until unstable crack propagation, and the kinetic energy which does not contribute to the crack growth can be removed from total work done by external-force to the specimen. The fracture-initiation point is determined by compliance-changing rate method. The results show that these methods are feasible and effective. Through the analysis of the conversion between work and energy of a fracture specimen, the dynamicJ-integral is adopted as a characteristic parameter for elastic-plastic materials under impact loading. TheJ-integral is calculated from and curves by using the formula proposed, by Rice. TheJ-integral at fracture initiation is employed to describe the dynamic fracture-initiation toughness of elastic-plastic materials and the experimental results indicate thatJ _ID can be regarded as a material constant.     

Analytical and experimental determination of dynamic impact stress intensity factor for 40 Cr steel

A linear elastic three-dimensional finite element analysis is made to analyze the near field stress behavior of an edge cracked rectangular bar simply supported and subjected to central impact at the back side of the crack. The material is made of 40 Cr steel. Determined numerically are the local time histories of the stress wave, displacement near load point, crack tip strain, and dynamic stress intensity factor K_(d)¹. The above quantities were also measured experimentally by performing impact tests; they agreed well with the analytical results and determine the load at fracture initiation and hence the critical dynamic stress intensity factor K_(d)^1c. The interaction effect between the loading bar and specimen appears to be negligible.     

Critical J-integral and tearing energies for fracture of reinforced natural rubber

The critical tearing energy and J-integral for initiation and rapid crack propagation at 22°C were determined for carbon black reinforced natural rubber. Tearing energies were 20 per cent and up to 100 per cent greater for initiation and rupture, respectively, and more scattered than the J values. Specimen geometry affects both fracture characterizing parameters because of the energy dissipated during deformation. However, the J-integral analysis can partition this energy between the crack tip region and the bulk of the specimen. Therefore, application of the J-integral concept for characterizing fracture of elastomers is promising.     

Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method

Polymer bonded explosives (PBXs) are highly particle-filled composite materials. This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test. The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera. The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method. The crack opening displacement is calculated from the displacement fields, the initiation and propagation of the crack are analyzed. In addition, the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and the correlation coefficient fields at different loading steps.     

A damage model for crack initiation and growth

A damage accumulation model is presented for the study of the problem of crack initiation and stable growth in an elastic-plastic material. A centre-cracked specimen subjected to a uniform stress perpendicular to the crack plane is considered. A coupled stress and failure analysis is performed by using a finite element computer program based on J₂-plasticity theory in conjunction with the strain energy density theory. After initial yielding, each material element follows a different equivalent uniaxial stress-strain behavior depending on the amount of energy dissipation by permanent deformation. A host of uniaxial stress-strain curves constituting parts of the same stress-strain curve were assigned to material elements for each increment of loading. The path-dependent nature of the onset of crack initiation and growth was revealed. The proposed model predicts faster crack growth rates than those obtained on the basis of a single uniaxial stress-strain curve and is closer to experimental observation.     

Initiation and arrest of cracks on two pipeline steels at low temperature

Dynamic fracture toughness at initiationK _1d and fracture toughness at arrestK _1a were measured on two pipeline steel grades. Dynamic fracture toughness was measured at a very high loading rate with the help of split Hopkinson pressure bars. The values ofK _1d andK _1a are compared. The purpose of this work is to examine the possibilities of using dynamic fracture toughness at crack initiation as a lower bound of crack arrest toughness. This work has practical applications because crack arrest tests are difficult to perform, give scattered results and are costly and time consuming. This procedure shows that it is possible to economize and rationalize using intelligent technology.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

Some recent developments on integrity assessment of pipes and elbows. Part I: Theoretical investigations

Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a system oriented methodology for integrity assessment of pipes and elbows, mainly for application to nuclear power plants. However, there is a scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of pipings. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part I of the paper, the theoretical investigations are discussed. Part II will cover the experimental investigations. The theoretical investigations considered the following issues: new plastic (collapse) moment equations of defect-free elbow under combined internal pressure and in-plane closing/opening moments; new plastic (collapse) moment equations of throughwall circumferentially cracked elbow, which are more accurate and closer to the test results; new ‘η_pl’ and ‘γ’ functions of pipes and elbows with various crack configurations under different loading conditions to evaluate J–R curve from test data; and the effect of deformation on the unloading compliance of TPB specimen and throughwall circumferentially cracked pipe to measure crack growth during fracture experiment. These developments would also help to study the effect of stress triaxiality in the transfer of material J–R curve from specimen to component.     

Edge fracture in cone-plate and parallel plate flows

Edge fracture is an instability of cone-plate and parallel plate flows of viscoelastic liquids and suspensions, characterised by the formation of a `crack' or indentation at a critical shear rate on the free surface of the liquid. A study is undertaken of the theoretical, experimental and computational aspects of edge fracture. The Tanner-Keentok theory of edge fracture in second-order liquids is re-examined and is approximately extended to cover the Criminale-Ericksen-Filbey (CEF) model. The second-order theory shows that the stress distribution on the semi-circular crack is not constant, requiring an average to be taken of the stress; this affects the proportionality constant, K in the edge fracture equation −N _2c = KΓ/a, where N _2c is the critical second normal stress difference, Γ is the surface tension coefficient and a is the fracture diameter. When the minimum stress is used, K = 2/3 as found by Tanner and Keentok (1983). Consideration is given to the sources of experimental error, including secondary flow and slip (wall effect). The effect of inertia on edge fracture is derived. A video camera was used to record the inception and development of edge fracture in four viscoelastic liquids and two suspensions. The recorded image was then measured to obtain the fracture diameter. The edge fracture phenomenon was examined to find its dependence on the physical dimensions of the flow (i.e. parallel plate gap or cone angle), on the surface tension coefficient, on the critical shear rate and on the critical second normal stress difference. The critical second normal stress difference was found to depend on the surface tension coefficient and the fracture diameter, as shown by the theory of Tanner and Keentok (1983); however, the experimental data were best fitted by the equation −N _2c = 1.095Γ/a. It was found that edge fracture in viscoelastic liquids depends on the Reynolds number, which is in good agreement with the inertial theory of edge fracture. Edge fracture in lubricating grease and toothpaste is broadly consistent with the CEF model of edge fracture. A finite volume method program was used to simulate the flow of a viscoelastic liquid, obeying the modified Phan-Thien-Tanner model, to obtain the velocity and stress distribution in parallel plate flow in three dimensions. Stress concentrations of the second normal stress difference (N ₂) were found in the plane of the crack; the velocity distribution shows a secondary flow tending to aid crack formation if N ₂ is negative, and a secondary flow tending to suppress crack formation if N ₂ is positive. Received: 4 January 1999 Accepted: 19 May 1999     

A generalized force measure of conditions at crack tips

A tentative measure of the forces tending to cause crack growth—the apparent crack extension force—is defined within the framework of continuum mechanics. By an associated fracture criterion initiation of growth may be predicted as well as the direction of preferred growth. The theory is specialized to elastic, viscoelastic and elastic-plastic materials. Under specified conditions the apparent crack extension force may be expressed by surface integrals over the boundary of an arbitrary part of the body for quasi-static deformation and for steady-state propagation of the crack. For plane deformation and for infinitesimal deformation under plane stress conditions these surface integrals reduce to path independent line integrals which include the J integral by Rice[1] and the G integral by Sih[2] as special cases.     

The application of Moire interferometry in the measurement of displacement field and strain field at notch-tip and crack-tip

This paper presents the application of Moire interferometry in measuring the displacement and strain field at notch-tip and crack-tip before and after crack propagation. The experiment is carried out using a three point bending beam with a notch. TheN _x andN _y fringe patterns representing displacement field, and the ΔN _x/Δx and ΔN _γ/Δγ fringe patterns representing the strain field are obtained. The sensitivity of the measured displacement is 0.417 μm per fringe order. The displacement and strain distribution along the sectionx=0 have been worked out according toN _x andN _γ fringe patterns. The project supported by Chinese Academy of Sciences and National Natural Science Foundation of China     

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt∼10⁸ MPa m^1/2s⁻¹. With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the “momentum trap” technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model. The project supported by the National Natural Science Foundation of China (No. 19672066 and 18981180-4) and the Key Project of Chinese Academy of Sciences (No. KJ951-1-20)     

The interaction between crack and electric dipole of piezoelectricity

Discrete dipoles located near the crack tip play an important role in nonlinear electric field induced fracture of piezoelectric ceramics. A physico-mathematical model of dipole is constructed of two generalized concentrated piezoelectric forces with equal density and opposite sign. The interaction between crack and electric dipole in piezoelectricity is analyzed. The closed form solutions, including those for stress and electric displacement, crack opening displacement and electric potential, are obtained. The function of piezoelectric anisotropic direction,p _a (θ)=cosθ+p _a sinθ, can be used to express the influence of a dipole's direction. In the case that a dipole locates near crack tip, the piezoelectric stress intensity factor is a power function with −3/2 index of the distance between dipole and crack tip. Supported by National Natural Science Foundation of China(No. 10072033)     

致密砂岩巷道模型试件动态起裂及止裂全过程分析

为了开展在不同冲击载荷作用下巷道围岩内裂纹的起裂、扩展及止裂等问题,以可调速冲击试验机进行动态加载试验,采用致密青砂岩制作裂纹巷道模型试件,并利用裂纹扩展计分别记录了动态起裂、扩展、止裂等时刻,对裂纹扩展速度的变化规律进行分析;随后采用AUTODYN有限差分法软件进行相应的数值模拟,数值模拟得到的裂纹扩展路径与试验结果基本一致。经过两者对比分析可知:随着冲击载荷作用的增加,裂纹平均扩展速度逐渐增大,随后趋于稳定值;预制裂纹的起裂时间随着冲击速度载荷的增加而逐渐降低,并在稳定值上下波动;随着冲击速度载荷的增加,裂纹扩展路径过程中的止裂时段逐渐变短。     

Damage accumulation and crack growth in bilinear materials with softening: Application of strain energy density theory

A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)_c and the strain energy density factor S_c.