The fracture process zone in asphalt mixture at low temperature

The fracture process zone (FPZ) is a key factor to mechanistically characterize material fracture. This study investigates the FPZ of asphalt mixture at low temperature. The fracture process under a semi-circular bend (SCB) test of seven asphalt mixtures that represent a combination of different factors was monitored using an acoustic (AE) system with eight piezoelectric sensors. The size of FPZ was estimated by locating micro-cracks that correspond to 95% AE energy before peak load in the vicinity of the initial crack tip. The experimental data illustrates the significant influence of test temperature on the behavior of the asphalt mixture. Comparison results showed that the size of the FPZ significantly depends on air voids and aggregate type, but is less depend on the asphalt content. It was found that at a very low temperature, different loading rates produced very close FPZ, both for the width and length. No obvious difference was observed on the width of the FPZ for the three different initial notch lengths, whereas the length of the FPZ was found significantly increases with the decrease of the notch length. The size of FPZ was also numerically estimated for one case with the cohesive zone model (CZM) calibrated by experimental data from the same SCB test. The FPZ size obtained with both methods agrees reasonably with each other.     

Loading‐rate dependence of mode I crack growth in concrete

Mode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

用能量方法研究混凝土断裂过程区的力学性能

准脆性混凝土自由裂缝前缘断裂过程区的发展与其非线性断裂特征及尺寸效应现象密切相关。它的物理力学行为的量化分析对理解混凝土断裂破坏机理和建立适用于混凝土结构裂缝稳定分析和安全评估断裂准则尤为重要,一直是混凝土断裂力学研究的核心问题。该文依据Hillerborg给出的断裂能定义,给出了计算单位长度断裂过程区发展能量耗散的通用表达式。以三点弯曲梁为例,采用非线性软化本构关系,进一步给出了计算此平均能量耗散的具体步骤及对应的公式。在根据实测的三点弯曲梁的断裂能回归拟合了特征裂缝张开位移w0后,计算了每个试件整个断裂全过程中不同荷载时刻断裂过程区耗能的平均值。结果表明:随着裂缝扩展,断裂过程区能量耗散的变化和试件尺寸无关,可描述断裂过程区混凝土材料的力学性能。     

Efficient prediction of deterministic size effects using the scaled boundary finite element method

This paper develops an efficient numerical approach to predict deterministic size effects in structures made of quasi-brittle materials using the scaled boundary finite element method (SBFEM). Depending on the structure’s size, two different SBFEM-based crack propagation modelling methodologies are used for fracture analyses. When the length of the fracture process zone (FPZ) in a structure is of the order of its characteristic dimension, nonlinear fracture analyses are carried out using the finite element-SBFEM coupled method. In large-sized structures, a linear elastic fracture mechanics (LEFM)-based SBFEM is used to reduce computing time due to small crack propagation length required to represent the FPZ in an equivalent nonlinear analysis. Remeshing is used in both methods to model crack propagation with crack paths unknown a priori. The resulting peak loads are used to establish the size effect laws. Three concrete structures were modelled to validate the approach. The predicted size effect is in good agreement with experimental data. The developed approach was found more efficient than the finite element method, at least in modelling LEFM problems and is thus an attractive tool for predicting size effect.     

Boundary effect on concrete fracture and non-constant fracture energy distribution

This paper extends the local fracture energy concept of Hu and Wittmann [29] and [30], and proposes a bilinear model for boundary or size effect on the fracture properties of cementitious materials. The bilinear function used to approximate the non-constant local fracture energy distribution along a ligament is based on the assumption of the proportionality of the local fracture energy to the fracture process zone (FPZ) height and characterises the FPZ height reduction when approaching a specimen back boundary. The bilinear function consists of a horizontal straight line of the intrinsic fracture energy G_F and a declining straight line that reduces to zero at the back boundary. It is demonstrated that using the bilinear model, the size-independent fracture energy G_F can be estimated from the fracture energy data measured on laboratory-size specimens, and the intersection of these two linear functions, defined as the transition ligament, represents the influence of the back boundary on the fracture properties. It is also demonstrated that the specimen size alone is not sufficient to characterise the size effect in the fracture properties observed on laboratory-size specimens.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

A data reduction method based on the J-integral to obtain the interlaminar fracture toughness in a mode II end-loaded split (ELS) test

Various difficulties arise in the data reduction of the end-loaded split (ELS) test. On one hand, a small Fracture Process Zone (FPZ) at the crack front is assumed in the existing mode II end-loaded split test methodologies based on Linear Elastic Fracture Mechanics (LEFM). However, mode II fracture has been reported to involve large FPZ and a fuzzy crack tip. Furthermore, the ELS test, is usually affected by geometrical non-linearities.This work proposes a closed-form solution based on the J-integral to determine the interlaminar fracture toughness in an ELS test. This solution avoids the need to measure the crack length, and is applicable when a large FPZ is present, as occurs in adhesive bonded joints between CFRP. In addition, because the ELS test involves large vertical deflections, a correction of the formulation for large displacements has been implemented.This new methodology has been compared to other methods available in the literature based on LEFM by means of an experimental campaign of delamination tests using unidirectional CFRP specimens in order to make a first validation of the method.     

An experimental and theoretical comparison of CCNBD and CCNSCB specimens for determining mode I fracture toughness of rocks

The cracked chevron notched Brazilian disc (CCNBD) specimen, suggested by the International Society for Rock Mechanics for testing mode I fracture toughness of rocks, usually yields rather conservative toughness measurements, and the reasons have not been fully explored. In this study, the CCNBD method is compared with the cracked chevron notched semicircular bending (CCNSCB) method in the fracture process zone (FPZ) and its influence on the fracture toughness measurement. Theoretical analysis reveals that the FPZ is longer in the CCNBD specimen than in the CCNSCB specimen using a relatively large support span, the toughness measurement using the former is affected more seriously by the presence of FPZ, and thus the CCNBD method is usually, more or less, conservative compared with the CCNSCB method. These inferences are further validated by experimental results, which indicate that the CCNBD test indeed produces much lower fracture toughness values and even the results of 75‐mm radius CCNBD specimens are still lower than those of 25‐mm radius CCNSCB specimens. Consequently, due to smaller FPZ, the CCNSCB specimen with a relatively large span is more likely to produce comparably accurate or representative toughness value, and it may be more suitable than the CCNBD specimen for the engineering applications that require more representative or less conservative fracture toughness.     

Fracture behaviour of a TiAl alloy under various loading modes

Tensile tests, compression tests, in situ tensile tests, bending tests, tensile fatigue tests and bending fatigue tests were carried out for a TiAl alloy. Based on the global experimental results and microscopic observations of the fracture surfaces and cracking behaviour on the side surfaces of tested specimens, the fracture mechanisms of fully lamellar (FL) TiAl alloys under various loading modes are summarized as following: (1) Cracks initiate at grain boundaries and/or interfaces between lamellae. (2) When a crack extends to a critical length, which matches the fracture loading stress the crack propagates catastrophically through entire specimen. (3) The crack with the critical length can be produced promptly by the applied load in the tensile and bending test or be produced step-by-step by a much lower load in the fatigue tensile test. (4) For fatigue bending tests, the fatigue crack initiates and extends directly from the notch root, then extends step-by-step with increasing the fatigue bending loads. The fatigue crack maybe extends through entire specimen at a lower fatigue load or triggers the cleavage through the whole specimen at a higher load. (5) In compressive tests, cracks initiate and propagate in directions parallel or inclined to the compressive load after producing appreciable plastic strains. The specimen can be fractured by the propagation of cracks in both directions.     

粗骨料体积分数对混凝土Ⅱ型断裂参数的影响

对不同粗骨料体积分数下的混凝土Ⅱ型断裂性能进行了研究。根据最大泥浆厚度(Maximum paste thickness, MPT)理论,给出了断裂韧度K_{Ⅱ C}与粗骨料体积分数V_a之间的经验关系式。通过对含有四种粗骨料体积分数(19%、25%、31%、37%)的无切口试件开展半边加载断裂试验,测得相应的峰值荷载、断裂韧度、能量释放率等断裂参数,并分析了断裂韧带表面的裂纹分布规律。试验结果表明:随着粗骨料体积分数的增加,混凝土的Ⅱ型断裂韧度K_{Ⅱ C}和临界能量释放率G_{Ⅱ C}明显增加,名义断裂韧带处的裂纹轮廓线更长、更曲折;各配比试件的开裂模式基本一致,剪切裂纹主要集中在名义断裂韧带区域。同时,利用数字图像相关技术(Digital image correlation, DIC)对试件表面的损伤演化进行分析,结果表明,试件表面的应变局部化能够较好地表征断裂过程区(Fracture process zone, FPZ)的形态特征及演化过程。随着粗骨料体积分数的增加,FPZ的形态更不规则,分支更多。      

Size effect of concrete members applied with flexural compressive stresses

In this study, two types of special experiments are carried out to understand flexural compressive strength size effect of concrete members. The first type is an ordinary cylindrical specimen (CS) with a fully penetrated and vertically standing plate type notch at the mid-height of the specimen, which is loaded in compression at the top surface (e.g., in the parallel direction to the notch length). The second type is a general double cantilever beam (DCB), which is compression loaded in axial direction (e.g., in the parallel direction of the notch). For CS, an adequate notch length is taken from the experimental results obtained from the compressive strength experiment of various initial notch lengths. The trial tests to select the effective initial notch length show that CS with an initial notch length approximately greater than four times the maximum aggregate size fails without an additional increased load and in stable manner under Mode I failure mechanism. Therefore, the initial notch length to the maximum aggregate size ratio of 4.0 is used for all size specimens. For DCB, the eccentricity of loading points with respect to the axial axis of each cantilever and the initial notch length are varied. In both specimens, the compressive loads apply flexural compressive stresses on the crack tip region of the specimens. These two types of specimens fail by Mode I crack opening mechanism. By testing 3 geometrically proportional size specimens for CS and DCB, the experimental datum for flexural compression size effect of concrete are obtained. Using the obtained flexural compressive strength size effect datum, regression analyses are performed using Levenberg-Marquardt's least square method (LSM) to suggest new parameters for the modified size effect law (MSEL). The analysis results show that size effect is apparent for flexural compressive strength of specimens with an initial notch. For CS, the effect of initial notch length on flexural compressive strength size effect is apparent. For DCB, flexural compressive size effect is dependent on the eccentricity of loading points with respect to the axial axis of the cantilever beam. In other words, if DCB specimen is applied with greater tensile stress at the crack tip, the size effect of concrete becomes more distinct. The results show that the flexural compressive strength size effect of initial notch length variation of DCB exists but directly dependent on the loading location. This is due to the fact that the sizes of fracture process zone (FPZ) of all DCB specimens are similar regardless of the differences in the specimen slenderness ratio, but the flexural compressive and tensile stress combinations resulting in stress concentration at the crack tip region has direct effect on size effect of concrete members.     

Fully-developed FPZ length in quasi-brittle materials

This paper studies the development of fracture processes in quasi-brittle materials. We propose to use the length of the fracture process zone (FPZ) once it is fully developed as a material parameter. This assumption allows us to build an analytical formulation that reproduces the mechanical behavior of any specimen as a cohesive crack advances. Extensive comparisons with experimental results lead us to define a new characteristic length that commensurates with the fully-developed FPZ and that together with the new analytical model, is used to provide a complete and consistent study on the fracture process. In particular, the size-effect deriving from our formulation coincides with the statistical size-effect law of Ba?ant for small and medium sizes, whereas it smoothly converges to size-independent results as size increases. The analytical cohesive formulation developed here is validated against experimental results on various types of normal and high-strength concretes as well as construction ceramics for several experimental set-ups and test scales. Because of its simplicity as compared with numerical models for fracture, this analytical formulation constitutes a powerful tool for studying fracture processes in a wide variety of mechanical configurations. Meanwhile, analytical expression for a fully-developed FPZ length is given for a general type of cohesive law.     

Size effect in shallow and deep notched quasi-brittle structures

The nominal strength of a quasi-brittle structure is known to vary with its size. If the structure undergoes large stable crack growth prior to failure or if it contains a large pre-existing crack, then the failure load is known to approach the asymptotic limit of linear elastic fracture mechanics (LEFM) for large structures from below. In this paper, the size effect is studied on a particular structural geometry containing a crack which can be relatively shallow or deep. The study is conducted within the framework of the fictitious crack model for the fracture of quasi-brittle materials. By allowing for the redistribution of the stresses in the fracture process zone (FPZ), the essential result of the size effect is confirmed. However, it is shown that this result can only be obtained from tests on specimens whose size exceeds a certain minimum value depending on the material, so that at failure the fully developed FPZ is contained wholly within the test specimen. Moreover, the minimum size of the test specimen is shown to increase as the depth of the pre-crack is reduced, thus requiring specimens of very large sizes to obtain valid results from tests on specimens with very shallow pre-cracks. This revised version was published online in July 2006 with corrections to the Cover Date.     

R-curve behavior in fracture of notched porous ceramics

Notched specimens of porous silicon carbide (SiC) with porosity 37% were fractured under four-point bending. A single edge notch with six depths ranging from 0.1 to 2.8 mm was introduced to the specimen with a height of 7 mm. The fracture of specimens with a notch depth of 0.1 mm did not start from the notch, but from the intrinsic defect. The size of the non-damaging notch is about 0.1-0.2 mm and roughly equal to the size of SiC particles. When the notch depth was larger than 0.4 mm, the fracture started from the notch for all specimens. The record of the strain gage glued on the compression surface of the specimen as a function of the load showed nonlinearity before reaching the maximum load. The critical stress intensity factor was nearly constant for crack initiation from the notch. The resistance curve was constructed by estimating the crack length from the compliance change of the specimen, and was used for determining the maximum load point in bending tests. Fractographic observations showed the fracture path along the binder phase between silicon particles.     

Experimental investigation of fracture damage of notched granite beams under cyclic loading using DIC and AE techniques

Fracture experiments of three‐point bending notched granite beams were performed under cyclic loading using digital image correlation (DIC) and acoustic emission (AE) techniques. The damage evolution process of the specimen under cyclic loading was analysed on the basis of AE ring count and b value. The strain and displacement fields and the fracture process zone (FPZ) ahead of the crack tip were revealed by DIC. The results showed that the AE characteristics of rock fracture indicated a noticeable Kaiser effect in the stage of cyclic loading and unloading. Moreover, when the loading force reached 70% of its peak value, the AE characteristics showed the Felicity effect. The damage produced during the loading‐unloading process contributed to the development of the cracks leading to the catastrophic fracture. Besides, a relatively high loading rate was found to help to suppress the development of the FPZ at the crack tip.     

Comparison of cohesive zone parameters and crack tip stress states between two different specimen types

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.     

Fracture mechanic modeling of fiber reinforced polymer shear-strengthened reinforced concrete beam

A numerical method is developed to model shear-strengthening of reinforced concrete beam by using fiber reinforced polymer (FRP) composites. Tensile crack is simulated by a non-linear spring element with softening behavior ahead of the crack tip to model the cohesive zone in concrete. A truss element is used, parallel to the spring element, to simulate the energy dissipation rate by the FRP. The strain energy release rate is calculated directly by using a virtual crack closure technique. It is observed that the length of the fracture process zone (FPZ) increases with the application of FRP shear-strengthening. The present model shows that the main diagonal crack is formed at the support in the control beam while it appears through the shear span in the shear-strengthened beam. Another important observation is that the load capacity increases with the number of CFRP sheets in the shear span.     

基于显微CT的泥岩单轴压缩破坏特征的声发射表征

研制了基于实时声发射采集和实时加载CT扫描同步进行的加载控制系统,组建了对岩石损伤、破坏过程进行声发射表征的实验系统和实验方法。研究表明:①在峰值载荷28%前,原生裂纹宽度基本无变化,而后经历先变窄再变宽的过程。在峰值载荷47%前,原生裂纹长度基本无变化,而后开始增长,原生裂纹在宽度上先进行扩展从而引起原生裂纹在长度上的增长;②在峰值载荷65%前,裂纹的延伸发生在裂纹尖端的软弱介质中,而后才是真正的原生裂纹起裂,并快速延伸扩展;③新生裂纹易产生在软硬夹层交界处,新生裂纹产生时的载荷约为峰值载荷的56%～75%,在峰值载荷84%前,裂纹处于稳定扩展阶段,三条裂纹同时各自发展;④裂纹宽度变大、原生裂纹在其尖端软弱介质中延伸、软硬交界处新生裂纹的产生过程中声发射较少,当这些过程连在一起时,便形成了声发射平静期;⑤建立了岩石孔隙率、裂纹长度和宽度与声发射能量、振铃计数之间的表征方程,并提出不同加载阶段岩石状态评价的判据。     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.