A three-point bend specimen with partly tapered cross-section sides

The stress intensity factor and the J-integral have been derived analytically and numerically for a modified three-point bend specimen with partly tapered sides, for various crack lengths, taper and specimen cross-section proportions, in order to allow full-thickness testing of tapered samples, common in older steel structures, to obtain a fair effective fracture toughness value for a through thickness crack in inhomogeneous materials. The stress intensity factor is obtained with the approximate analytical method of Kienzler and Herrmann, based on the concept of material forces. The J-integral is calculated numerically with a 3D finite element model for a linear elastic material and an elastic ideal-plastic material. A simple single specimen fracture toughness evaluation procedure is proposed. It is found that the effect of taper in the range encountered in practice is small, of the order of a few percent.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

Effects of finite notch width on the fracture of chevron – notched specimens

The chevron notched three-point bend test specimen is often used for measuring the fracture toughness of brittle materials such as ceramics. Specimen sizes are often very restricted when testing advanced materials due to limited volume of material available or high material costs. Since the minimum chevron notch width is limited by the size of the cutting wheels or wire saw used to produce it, as the sample size gets small enough, the notch width becomes large in relation to the sample size. It is shown via finite element analysis that the notch width has an important effect on the stress intensity factors of short cracks. The minimum in the normalized stress intensity factor versus crack length is lost, rendering the usual analysis of the experimental results invalid and contributing greatly to decreased fracture stability of such specimens. Previous analytical and numerical studies do not take into account the width of the chevron notch. Based on the calculations, a guideline to permissible notch widths is introduced. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of the dynamic responses for a pre-cracked three-point bend specimen

In this paper, shear deformation and rotary inertia was introduced into the calculation of the dynamic stress intensity factor by means of solving the stiffness of a pre-cracked three-point bend specimen. A simple formula of dynamic stress intensity factor for a pre-cracked three-point bend specimen is derived using the vibration analysis method. Dynamic three-point bending tests were performed on a uniquely modified Hopkinson pressure bar, allowing the dynamic responses of the pre-cracked specimen, such as: the natural frequency, the period of apparent specimen oscillations, the dynamic loads, and the dynamic stress intensity factor to be analyzed experimentally and theoretically.     

纯弯曲Sandwich 梁试样界面裂纹扩展的应变能释放率

纯弯曲的Sandwich 梁试样在评价界面断裂抗力方面有重要作用。利用能量的叠加原理和截面转换方法, 本文导出了纯弯曲Sandw ich 梁试样界面裂纹扩展应变能释放率的显式解, 并根据实验测得的界面裂纹扩展的临界载荷, 用其计算出了四点弯曲Si₃N₄/Al/Si₃N 4试样Si₃N₄/Al 扩散连接界面的断裂韧度。      

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.     

Effects of microstructure, specimen and loading geometries on KIC of brittle honeycombs

Fracture toughness of brittle honeycombs depends on cell microstructure, specimen and geometries. A microstructure coefficient in the K_IC expression of brittle honeycombs can not be found analytically. In this paper, a finite element program is utilized to numerically determine the coefficient. In practice, fracture toughness can be measured from conducting a three-point bend or uniaxial tension test. Specimen geometry restrictions of three-point bend test for honeycombs are examined and proposed here. Meanwhile, fracture toughness of honeycombs under the two loading geometries is compared; results show that K_IC measured from uniaxial tension test is smaller than that from three-point bend test if the K_IC formulations for solid materials are employed. As a result of that, the K_IC formulation of three-point bend test is modified for honeycomb-like materials.     

The nonlinear and biaxial effects on energy release rate, J-integral and stress intensity factor

A nonlinear finite element analysis is performed for a finite center-cracked specimen subjected to biaxial loading. A Ramberg-Osgood type stress-strain relation is used to characterize the material property. It is found that the energy release rate, J-integral, stress intensity factor, strain intensity factor depend not only on applied stress perpendicular to the crack but also on applied stress parallel to the crack. Biaxial effects on fracture toughness parameters increase as applied stress increases. The coupling between biaxial effects and material nonlinearity has been indicated.     

实用断裂试验方法的意义与内容（一）

为了在材料性能检测中普遍、持久地应用断裂试验，推荐一种延性材料断裂韧性实用测试方法。该实用测试方法包括侧切三点弯曲试件、测量δｃ的两点位移法和测量ＪＩＣ的位称计法。该方法具有科学合理、通谷易懂、准确可靠、简便快捷、费用低廉等显著特点，适合普遍推广应用。     

Intralaminar toughness characterisation of unbalanced hybrid plain weave laminates

A numerical and experimental investigation on the mode-I intralaminar toughness of a hybrid plain weave composite laminate manufactured using resin infusion under flexible tooling (RIFT) process is presented in this paper. The pre-cracked geometries consisted of overheight compact tension (OCT), double edge notch (DEN) and centrally cracked four-point-bending (4PBT) test specimens. The position as well as the strain field ahead of the crack tip during the loading stage was determined using a digital speckle photogrammetry system. The limitation on the applicability of the standard data reduction schemes for the determination of intralaminar toughness of composite materials is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of the stress intensity factor for composites. The method accounts for material anisotropy and finite specimen dimension effects regardless of the geometry. The approach has been validated for alternative non-standard specimen geometries. A comparison between different methods currently available for computing the intralaminar fracture toughness in composite laminates is presented and a good agreement between numerical and experimental results using the proposed methodology was obtained.     

Prestressed fracture specimen for delamination testing of composites

The prestressed end-notched flexure fracture specimen is developed in the present work, which combines the traditional double-cantilever beam and the end-notched flexure specimens in a very simple way. The most important features of the new beam-like specimen are that it is able to provide any combination of the modes I and II strain energy release rates and it may be performed by using a simple three-point bending fixture. The mode-I part of the strain energy release rate is fixed by inserting a steel roller, which causes a fixed crack opening displacement. The mode-II part of the energy release rate is provided by the external load. A simple closed-form solution using beam theory is developed for the energy release rates of the new configuration. The applicability and the limitations of the novel configuration are demonstrated using unidirectional glass/polyester composite specimens. If only propagation onset is involved then the prestressed end-notched flexure specimen can be used to obtain the fracture criterion of transparent composite materials in a very simple way.     

Stress intensity factors for cracks in some fracture mechanics test specimens under displacement control

The stress intensity factors for cracks of varying length in some common fracture mechanics test specimens have been calculated when the displacement at the loading pins is held constant. For centre and edge cracked plates with a given crack length the stress intensity factor decreases with the decrearing separation of the loading pins. For a three-point bend specimen of span to width of 8 a plateau is observed in the stress intensity factory over a range 0.3< a/w <0.6. For CKS-type and T-type wedge-open-loaded specimens the stress intensity factor decreases monotonically with increasing crack length for a/w > 0.3. The implications of these results to fracture mechanics testing are discussed.     

Further studies on fracture process zone for mode I concrete fracture

The development of a fracture process zone associated with stable crack growth in single edge-notched (SEN), three-point bend concrete specimens of different tensile strengths was monitored with moire interferometry. The experimental data was then used to drive a finite element model of the fracture specimen in its generation/propagation mode and to determine the crack closure stress due to aggregate bridging, the energy release and dissipation rates and the resistance curve.     

钢纤维对水泥基复合材料抗起裂特性的影响

通过不同钢纤维体积分数及不同试件尺寸的预制缺口三点弯曲梁断裂试验,研究了普通乱向及定向钢纤维增强水泥基复合材料的抗起裂特性。利用试验测得的荷载-裂缝口张开位移曲线,分析了钢纤维对水泥基复合材料断裂性能的影响,并基于线性相关系数陡降法计算了起裂韧度。结果表明,定向钢纤维增强水泥基复合材料的起裂韧度明显高于普通乱向钢纤维增强水泥基复合材料;起裂韧度随钢纤维体积分数的增加而逐渐增大,当钢纤维体积分数达到0.9%左右时,定向钢纤维增强水泥基复合材料的起裂韧度值趋于稳定;在本试件高度范围内(40~100mm),起裂韧度随试件尺寸增加而逐渐增大,且定向钢纤维增强水泥基复合材料的增长趋势较为平缓。此外,从裂缝尖端夹杂改变其应力强度因子的角度解释了钢纤维的掺入及定向对起裂韧度的提高作用。     

Transferability of Charpy Absorbed Energy to Fracture Toughness Based on Weibull Stress Criterion

The relationship between Charpy absorbed energy and the fracture toughness by means of the (crack tip opening displacement (CTOD)) method was analyzed based on the Weibull stress criterion. The Charpy absorbed energy and the fracture toughness were measured for the SN490B steel under the ductile-brittle transition temperature region. For the instrumented Charpy impact test, the curves between the loading point displacement and the load against time were recorded. The critical Weibull stress was taken as a fracture controlled parameter, and it could not be affected by the specimen configuration and the loading pattern based on the local approach. The parameters controlled brittle fracture are obtained from the Charpy absorbed energy results, then the fracture toughness for the compact tension (CT) specimen is predicted. It is found that the results predicted are in good agreement with the experimental. The fracture toughness could be evaluated by the Charpy absorbed energy, because the local approach give     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Fracture mechanics of idealised bituminous mixes

The durability of asphalt pavements is strongly impaired by cracks, caused primarily by traffic loads and environmental effects. In this work, fracture behaviour of idealised asphalt mixes is investigated. Experiments on idealised asphalt mixes under pure-tension mode (mode I cracking) were performed and fracture parameters were evaluated. In these three-point bend fracture tests, the test variables were temperature and load rate. The test data were stored in an asphalt materials database and special-purpose tools were implemented to analyse and handle the laboratory data automatically. Fracture mechanism maps were constructed, showing the conditions associated with ductile, brittle and ductile–brittle transition regimes of behaviour. The mechanism maps show the failure response of the material in terms of the stress intensity factor, strain energy release rate and J-integral as a function of the temperature-compensated crack mouth opening strain rate. Fracture behaviour of asphalt mix specimens was simulated by cohesive zone model in conjunction with a novel material constitutive model for asphalt mixes. The finite element model agrees well with the experimental results and provides insights into fracture response of the notched asphalt mix beam specimens.     

Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen

Experimental and numerical analyses are performed to determine the translayer mode-I fracture toughness of a thick-section fiber reinforced polymeric composite using the eccentrically loaded, single-edge-notch tension, ESE(T) specimen. Finite element analyses using the virtual crack closure technique were performed to assess the effect of material orthotropy on the mode-I stress intensity factors in the ESE(T) specimen. The stress intensity factors for the proposed ESE(T) geometry, are calculated as a function of the material orthotropic parameters. The formula is validated for a class of thick composite materials. The thick composite tested in this study is a pultruded composite material that consists of roving and continuous filament mat layers with E-glass fiber and polyester matrix materials. Data reduction from the fracture tests was performed using two methods based on existing metallic and composite ASTM [ASTM E 1922, Standard Test Method for Translaminar Fracture Toughness of Laminated Polymer Matrix Composites, Annual Book of ASTM Standards, 1997; ASTM E 399, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, 1997] fracture testing standards. Criteria for assessing test validity and for determining the critical load used in calculating the fracture toughness were examined. Crack growth measurements were performed to determine the amount of stable crack growth before reaching critical load. The load versus notch mouth opening displacement, for different crack length to width ratios is affected by material orthotropy, nonlinearity, and stable crack propagation. The mode-I translayer fracture toughness and response during crack growth is reported for ESE(T) specimen with roving layers oriented both, transverse and parallel to the loading direction.     

MODAL APPROACH FOR PROCESSING ONE- AND THREE-POINT BEND TEST DATA FOR DSIF-TIME DIAGRAM DETERMINATION PART I—THEORY

A hybrid experimental/numerical method for the determination of the variation in the dynamic stress intensity factor (DSIF) with time during one- or three-point bend impact tests is presented. According to the concept of hybrid methods, a DSIF–time diagram is calculated for a particular mathematical model for the specimen using experimentally registered loading as the model excitation. The simple expression for the impact DSIF–response function is derived for an arbitrary linear model of the specimen, using the modal superposition method. Finally, formulae for DSIF calculations for different types of loading approximation are derived.     

The room temperature fracture strength of sintered UO2 rings containing deliberately introduced impurities

A ring test has been used to measure the room temperature fracture strength of sintered UO₂ and of UO₂ deliberately doped with either silica, calcium oxide or iron oxide. The maximum observed flaw size and the minimum measured fracture strength in a group of nominally identical specimens was found to be related for some of the materials tested. It is shown that the additions of silica and calcium oxide do not appear to alter the energy for fracture initiation. Fracture strength measurements obtained using the ring test, where the applied stress is relatively uniform over the specimen cross-section, and the three-point bend test where it is not, fit the same strength/flaw size relationship provided minimum measured strength is associated with maximum flaw size.