Determining the double‐K fracture parameters for three‐point bending notched concrete beams using weight function

Parameters of universal form of weight functions having four terms and five terms are derived for edge cracks in finite width of plate. The standard Tada Green's function is taken as the basis for the derivation. The shape of universal form of weight functions considered enables closed form expressions for cohesive toughness of three‐point bending test geometry of notched concrete beams due to linear cohesive stress distribution in the fictitious fracture zone. This solution provides a viable method to determine the double‐K fracture parameters: the initiation toughness, and the unstable toughness for mode I fracture of concrete beam. A comparison with existing analytical method shows that the weight function method for determination of the double‐K fracture parameters yields results without any appreciable error. The use of weight function will not only simplify the calculation to obtain the double‐K fracture parameters, and but also it will avoid the need of skilled numerical integration technique due to singularity problem at the integral boundary.     

A simplified extreme method for determining double‐K fracture parameters of concrete using experimental peak load

A simplified approach to obtain the double‐K fracture parameters of concrete for three‐point bending beams was proposed based on the extreme method. With the proposed method, the double‐K parameters can be easily obtained by the experimental peak load. This method requires fewer parameters or tests than the double‐K method and the peak load method. It also avoids complicated numerical integral compared with the traditional extreme method. The double‐K parameters obtained by the proposed method are slightly smaller than those by the double‐K method, and they do not seem to be influenced by the initial crack length to depth ratio.     

Determination of the bilinear stress‐crack opening curve for normal‐ and high‐strength concrete

An improved version of the method proposed to ACI committee 446 and to RILEM TC 187‐SOC to determine the fracture parameters of concrete is applied in this study to several mixtures of normal and high‐strength concretes. The results are processed with a C++ program developed by the authors to automatise the mathematical operations required to obtain the bilinear softening curve of concrete from the experimental results. Numerical simulations of the tests are also carried out using finite elements with an embedded cohesive crack. The comparison between numerical and experimental results confirms that the experimental and numerical procedures are appropiate for normal‐strength concretes and high‐strength concretes.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

用应变片法确定混凝土动态起裂时间的研究

在混凝土等准脆性材料的动态起裂韧度K_(1d)测试中,准确确定试件裂尖的起裂时间是测试工作的关键。采用分离式霍普金森压杆系统,对圆孔裂纹平台巴西圆盘混凝土试件进行动态径向冲击试验,通过在裂尖粘贴应变片的方法来确定起裂时间。讨论了应变片在裂纹尖端的粘贴位置、粘贴方向等因素对起裂时间测试值的影响,结果表明裂尖应变片的最佳粘贴方式是:在裂纹延长线上或在裂尖并与裂纹垂直的线上,都距离裂尖3 mm左右,且粘贴方向与裂纹延长线垂直。给出了考虑贴片位置和试件厚度的起裂时间计算公式。     

Latent crack path and service life predictions for unnotched concrete under bending by digital speckle correlation method

The critical factor for flexural fracture of an unnotched concrete structure is the local damage with stress concentration. The latent critical crack path on the concrete surface is difficult to inspect using ordinary experimental methods. In the present paper, the digital speckle correlation method (DSCM) is employed to obtain the latent critical crack and to calculate the strain and displacement distributions on the surface of unnotched concrete under flexural load. The relationships of static flexural load versus longitudinal strain and load-direction displacement as well as fracture toughness are inherent material parameters. Furthermore, the cohesive energy density (CED) around the latent critical crack for unnotched concrete and the brittleness number are also determined by using the DSCM results. Then, the tensile performance of concrete and the residual service life are evaluated through the above material parameters. It is found that the latent crack path on the concrete surface depends on the strain fields after the bending force applied to the specimen reaches 30% of concrete flexural strength, and the cohesive stress does not rapidly increase until reaching 75% of concrete flexural strength. The service life of unnotched concrete without steel bars is dependent on the local cohesive performance around the latent crack path. Finally, the experimental results show that DSCM is useful to confirm the connection between the local damage of the material and the whole structure safety.     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.     

Comparison of three real time techniques for the measurement of dynamic fracture initiation toughness in metals

Three techniques for measuring dynamic stress intensity factor time histories of dynamically loaded stationary mode-I cracks are compared as applied to dynamically loaded pre-cracked 6Al-4V titanium alloy specimens. The three techniques are crack opening displacement (COD), dynamic strain gage measurement, and coherent gradient sensing (CGS). The stress intensity factor histories are inferred from each measurement technique and are used to obtain the critical dynamic initiation toughness as a function of loading rate (). There are significant differences in implementation and information obtained from each of the three measurement techniques, though for the tests performed all are found to yield very similar results.     

Choice of standard fracture test for concrete and its statistical evaluation

The main characteristics of the cohesive (or fictitious) crack model, which is now generally accepted as the best simple fracture model for concrete, are (aside from tensile strength) the fracture energies G _F and G _f corresponding to the areas under the complete softening stress-separation curve and under the initial tangent of this curve. Although these are two independent fracture characteristics which both should be measured, the basic (level I) standard test is supposed to measure only one. First, it is argued that the level I test should measure G _f, for statistical reasons and because of relevance to prediction of maximum loads of structures. Second, various methods for measuring G _f (or the corresponding fracture toughness), including the size effect method, the Jenq-Shah method (TPFM), and the Guinea et al. method, are discussed. The last is clearly the most robust and optimal because: (1) it is based on the exact solution of the bilinear cohesive crack model and (2) necessitates nothing more than measurement of the maximum loads of notched specimens of one size, supplemented by tensile strength measurements. Since the identification of material fracture parameters from test data involves two random variables, f_t (tensile strength) and G _f, statistical regression should be applied. But regression is not feasible in the original Guinea et al.'s method. The present study proposes an improved version of Guinea et al.'s method which reduces the statistical problem to linear regression thanks to exploiting the systematic trend of size effect. This is made possible by noting that, according to the cohesive (or fictitious) crack model, the zero-size limit _N0 of nominal strength _N of a notched specimen is independent of F _f and thus can be easily calculated from the measured f_t. Then, the values of _N0 obtained from the measured f_t values, together with the measured _N-values of notched specimens, are used in statistical regression based on the exact size effect curve calculated in advance from the cohesive crack model for the chosen specimen geometry. This has several advantages: (1) the linear regression is the most robust statistical approach; (2) the difficult question of statistical correlation between measured f_t and the nominal strength of notched specimens is bypassed, by virtue of knowing the size effect trend; (3) the resulting coefficient of variation of mean G _f is very different and much more realistic than in the original version; (4) the coefficient of variation of the deviations of individual data from the regression line is very different from the coefficient of variation of individual notched test data and represents a much more realistic measure of scatter; and (5) possible accuracy improvements through the testing of notched specimens with different notch lengths and the same size, or notched specimens of different sizes, are in the regression setting straightforward. For engineering purposes where high accuracy is not needed, the simplest approach is the previously proposed zero-brittleness method, which can be regarded as a simplification of Guinea et al.' method. Finally, the errors of TPFM due to random variability of unloading-reloading properties from one concrete to another are quantitatively estimated.     

An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete*

An embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi‐brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well‐known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete.     

方钢管混凝土柱-外环板式组合梁节点在地震损伤后的耐火性能分析

为研究FRP增强混凝土梁失稳前断裂过程,该文基于混凝土断裂力学理论和非线性FRP-混凝土界面粘结滑移规律,建立了一个跨中裂缝导致界面脱粘的粘聚区模型,采用解析方法推导了FRP增强混凝土梁界面剪切应力、FRP拉应力以及失稳前断裂韧度的公式,为分析FRP-混凝土界面脱粘提供了一种有效的方法,并开展了动态荷载下4种不同初始缝高比(0.2、0.3、0.4和0.5)的FRP增强混凝土梁三点弯曲试验。结果表明,FRP增强混凝土梁的起裂荷载和阻裂荷载随着初始缝高比的增大而逐渐减小,但初始缝高比为0.4时,试件起裂最晚;起裂韧度和阻裂韧度不随初始缝高比的变化而变化,表现出与其他文献类似的规律,验证了断裂韧度解析解的正确性。     

The Identification of a Hidden Long‐Term Plastic Damage Stage During Splitting Tensile Loading of Concrete: A Fracture Mechanics Approach

Abstract: A new method for the determination of fracture toughness K_IC, fracture energy G_F and critical crack tip opening displacement CTOD_c of mortars and concretes with maximum size of aggregates up to 8 mm is presented. This was achieved by using a suitable modification of the conventional splitting tensile test. The values that were obtained are in accordance with those of other researchers. On the basis a clear‐cut fracture mechanics analysis, we extract a set of equations that correlates the above quantities with the crack rate. Specific plastic damage stages that accompany the crack growth were thus easily identified. A pre‐peak damage process of a characteristic bandwidth of 0.1–1 μm and length from a few micrometres to a few millimetres appears first. Damage process of this kind can be diffused and dispersed in bulk of the loading component or it can also be localised and formed into an active attractor cracking path through its chain accumulation. Then another damage stage, coming directly through the formation of the well‐known fracture process zone near the crack tip of 10 μm in bandwidth and a few tens of millimetres in length, must be added. Finally, a large‐scale stage involving the influences of composition and texture of stressed components as well as their loading and geometry conditions must be superimposed on the first two. This third damage process comes directly through the reordering and redistribution of the aforementioned features, during the evolution of fracture, giving an effective length that varies from few tens of millimetres to some metres. All these effective lengths could easily be extracted from the calculated concrete fracture quantities.     

Transferability of the two‐parameter fracture criterion for 2219 aluminium alloy cracked configurations

Two‐dimensional elastic–plastic finite‐element fracture simulations with the critical crack‐tip‐opening‐angle fracture criterion were used to evaluate the two‐parameter fracture criterion (TPFC). Three different crack configurations under tension and bending loads made of thin‐sheet 2219‐T87 aluminium alloy were analysed. A very wide range of widths (w = 76 to 2440 mm) and initial crack‐length‐to‐width ratios (c_i/w = 0.05 to 0.95) were considered. A relation from the original TPFC was shown to fit the simulated fracture behaviour fairly well for the three different specimen types for net‐section stresses less than the yield stress (σ_y) of the material. Comparisons were also made on measured and simulated fracture tests on middle‐crack‐tension specimens. A relation between the elastic stress‐intensity factor, K_Ie, and net‐section stress, S_n, at failure was found to be linear for S_n < σ_y. The results demonstrated the transferability of the TPFC for different crack configurations for S_n < σ_y, but further study is needed for S_n > σ_y.     

Effect of constraint on void growth near a blunt crack tip

The growth of a single cylindrical hole ahead of a blunt crack tip was studied using large deformation finite element analysis in three-point bend specimens with different precrack depth. The effect of small second phase particles was taken into account by incorporating Gurson's constitutive equation. The effects of strain hardening and the initial distance from the hole to the crack tip were also investigated. The results show that the variation of crack tip opening displacement with load is not sensitive to constraint level. The effects of constraint on the growth of hole and ductile initiation toughness are diminished with decreasing initial distance from the hole to the blunt crack tip. This revised version was published online in August 2006 with corrections to the Cover Date.     

Application of fracture mechanics for weld integrity assessment

The structural integrity assessment of a weld joint by conventional techniques is inadequate, because of unavoidable defects in the weld composite. The stress situation in a component having a defect is quite different from that of a homogeneous material. The significance of fracture mechanics to deal with such integrity assessments is brought out. A brief review on the basic formulations in the application of fracture mechanics is followed by established guidelines for evaluating the integrity of engineering components containing crack-like defects.     

Crack Tip Opening Angle Measurement Methods and Crack Tunnelling in 2024‐T351 Aluminium Alloy

Abstract: The crack tip opening angle (CTOA) fracture criterion is one of the most promising fracture criterion used to characterise the stable tearing process in metallic materials. Traditional methods used for the experimental characterisation of the CTOA involve accurate identification of the crack tip at each tearing event. Recently alternative methods have been proposed that reduce the necessity of accurately defining the current crack and rely more on the shape of the crack flanks to define the CTOA. In addition, these methods define an ‘apparent crack tip’, which may be different from the actual surface crack tip and may provide insight into the amount of crack‐front tunnelling that is occurring. In the current research, compact tension specimens fabricated from 6.35 mm thick 2024‐T351 aluminium alloy plate were evaluated to investigate different CTOA measurement methods and their potential for estimating crack‐front tunnelling. In addition to characterizing the CTOA, fatigue marker bands were employed to map the evolution of crack‐front tunnelling. The experimental critical CTOA values obtained from the alternative methods were noticeably lower than that obtained from the traditional approach and showed noticeably more scatter. When compared to the experimentally obtained marker bands, the alternative methods indicated limited potential for predicting crack‐front tunnelling.     

泵头体高强钢材料的力学性能

为了进一步研究泵头体高强钢25Cr2Ni4MoV和30CrNi2MoV的力学性能,采用拉伸、冲击和裂纹尖端张开位移(CTOD)试验对其进行测试。结果表明:材料在常温下具有较好的综合力学性能;在静载荷条件下,具有优良的断裂韧度。     

Artificial neural network‐based analysis of effective crack model in concrete fracture

Many non‐linear fracture models have been proposed by design codes and investigators to determine fracture parameters of cement‐based materials. To characterise failure of concrete structures, the effective crack model (ECM) needs two fracture parameters: the effective crack length a_e and the critical stress intensity factor . Nevertheless, ECM requires a closed‐loop testing system and the calculation of a_e needs considerable computational effort. For this reason, ECM is simulated with an artificial neural network (ANN) in this study. The main benefit of using an ANN approach is that the network is built directly on experimental data by using the self‐organizing capabilities of the ANN. The presented fracture model was developed by utilising 464 noisy test data taken from the literature, which were obtained via different test methods in different laboratories. The results of an ANN‐based ECM look viable and very promising.     

Numerical and experimental investigation of mixed‐mode fracture parameters on silicon nitride using the Brazilian disc test

Engineering applications of ceramics can often involve mixed‐mode conditions involving both tensile and shear loading. Mixed‐mode fracture toughness parameters are evaluated for applicability to ceramics using the Brazilian disc test on silicon nitride. Semi‐elliptical centrally located surface flaws are induced on the disc specimens using Vickers indentation and compression loaded to fracture with varying levels of mode mixity. The disc specimens are modelled via 3D finite element analysis and all three modes of stress intensity factors computed along the crack front, at failure load. We present a numerical and experimental investigation of four widely used mixed‐mode fracture criteria and conclude that the critical strain energy release rate criterion is simple to implement and effective for silicon nitride under mixed‐mode conditions.     

Embedded representation of fracture in concrete with mixed finite elements

As an alternative to the smeared and discrete crack representations, an embedded representation of fracture for finite element analysis of concrete structures is presented. The three-field Hu–Washizu variational statement is extended to bodies with internal discontinuities. The extended variational statement is then utilized for formulating elements with a discontinuous displacement field. The new elements are capable of modelling different deformation modes of an internal discontinuity at the element level. The satisfactory performance of the embedded crack representation is verified by several case studies on concrete fracture.