An experimental investigation on the FPZ properties in concrete using digital image correlation technique

This paper presents an experimental investigation on the properties of the fracture process zone (FPZ) in concrete using the digital image correlation (DIC) technique. Based on the experimental results, it is found that the FPZ length increases during crack propagation but decreases after the FPZ is fully developed. The FPZ length at the peak load and the maximum FPZ length increase with an increase in specimen height, but decrease by increasing the notch depth to specimen height ratio. It is also found that the crack extension length at the peak load is about 0.25 times the ligament length.     

Cohesive Modeling of Fracture in Asphalt Mixtures at Low Temperatures

Low temperature cracking is the major distress observed in asphalt pavements in the northern US and Canada. In the past years fracture mechanics concepts were introduced to investigate the fracture properties of asphalt mixtures at low temperatures. In this paper the cohesive zone model (CZM) is used to describe the fracture behavior of asphalt mixtures at low temperatures and the interface element is used to numerically simulate the material response under monotonic loading. The simulation is calibrated with the experimental results from a newly proposed semi circular bend (SCB) test. A parametric analysis of the input material properties indicates that the tensile strength has a significant effect on the peak load in the SCB configuration, the modulus has a strong effect on the calculated stiffness of the SCB specimen, and the fracture energy influences the post-peak behavior of the asphalt mixtures. The calibrated numerical model was applied to simulate the low temperature cracking in a simplified asphalt pavement and to study the influence of these material parameters on the performance of asphalt pavements.     

Estimation of width of fracture process zone in spruce wood by radial tensile test

Fracture behavior of spruce wood under radial tension was analyzed using nonlinear fracture mechanics as wood is classified as a quasi-brittle material. Stress-strain relationship with a strain-softening branch was obtained by digital image analysis and stress redistribution process, and the energy release rate of serial end-matched specimens was measured by performing a single-edge-notched tension test.The width of the fracture process zone (FPZ) was estimated by comparing two kinds of fracture energies. One was the dispersion energy per unit area to model strain localizations using a discontinuum model of damage theory, by integrating the stress-strain function with the strain-softening branch. The other was the energy release rate to determine crack growth. From this analysis, we determined that the width of the FPZ ranged from 0.3 mm to 0.5 mm in the radial direction. However, for a few specimens, the approximate stress-strain function could not be fitted into the stress-strain relationship obtained by the image analysis; it was observed that the fracture planes of these specimens tended to be more or less inclined.     

Experimental study of creep-damage coupling in concrete by acoustic emission technique

In order to design reliable concrete structures, prediction of long term behaviour of concrete is important by considering a coupling between creep and damage. An experimental investigation on the fracture properties of concrete beams submitted to creep bending tests with high levels of sustained load is reported. The influence of creep on the residual capacity and the fracture energy of concrete is studied. The progression of fracture is followed by the measurement of the crack mouth opening displacement during a three-point bending test. The sustained loading seems to increase the flexural strength of concrete, probably because of the consolidation of the hardened cement paste. The acoustic emission (AE) technique is used to perform the characterization of the influence of creep on the crack development. Results give wealth information on the fracture process zone (FPZ) and the propagation of the crack. A decrease in the amplitude distribution of AE hits is observed in the post-peak region for creep specimens. The width of the FPZ also decreases in this later indicating that the material has a more brittle behaviour which may be due to the development of microcracking under creep and the prestressing of the upper zone of the beam.     

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。     

Fracture behavior of concrete-concrete interface using acoustic emission technique

The fracture behavior of concrete-concrete interface is characterized using acoustic emission (AE). Beams of different sizes having jointed interface between two different strengths of concrete are tested. The results of load, displacement, CMOD, AE-events and AE-energy are analyzed. The width of fracture process zone and damage zone are computed using AE-data and are found to be independent of size. It is observed that, as the difference in compressive strength of concrete on either side of interface increases, the load carrying capacity, number of AE-events, AE-energy, width of fracture process zone and damage zone decreases.     

Notched strength of satin-woven Si-Ti-C-O fiber-bonded ceramic composite

The fracture behavior of Si-Ti-C-O fiber-bonded ceramic composite produced by hot-pressing oxidized 8 harness-satin-woven Si-Ti-C-O fibers was investigated by using unnotched and double edge notched tensile test specimens with different width (8 and 40 mm). The main results are summarized as follows. (i) The tensile strength of unnotched specimens for 8 mm width was higher than that for 40 mm width. Such a width-dependence of the unnotched strength could be described fairly well from the viewpoint of effective volume by application of the experimentally estimated Weibull's shape parameter. (ii) The applicability of the fracture toughness criterion (fracture arises when the stress intensity factor reaches the critical value) and net section stress criterion (fracture arises when the strength of the ligament reaches the unnotched strength) to the present composite was examined. The fracture strength of a notched specimen for 8 mm width was described by the net stress criterion. On the other hand, the strength for 40 mm width obeyed the net stress criterion for a small notch length but it shifted toward the fracture toughness criterion for large one. The shift of the fracture criterion from net strength- to fracture toughness-criterion arose around at the relative notch length 0.2 (notch length 8 mm), corresponding to periodical spacing of fiber strands (8 harness). (iii) The fiber pull-out length (0.4 mm on an average) was nearly the same as the half length of the fiber strand whose deformation is not constricted by the other strands in the satin-weave. (iv) The present fiber-bonded ceramic composite is insensitive to notch under the condition where the width of specimen is narrow and the notch length is smaller than 8 mm. This composite could be therefore applicable to industrial objects safely when the objects are designed as to satisfy the notch-insensitive condition.     

Scaling of the fracture process zone in rock

The zone of microcracks surrounding a notch tip—the process zone—is a phenomenon observed in fracture of quasi-brittle materials, and the characterization of the process zone is the topic of the paper. Specimens of different sizes with a center notch fabricated from a granite of large grain (Rockville granite, average grain size of 10 mm), were tested in three-point bending. Acoustic emissions were recorded and locations of microcracks were determined up to peak load. The results show that both the length and width of the process zone increase with the increase of the specimen size. Furthermore, the suitability of a proposed theoretical relationship between the length and width of the process zone and specimen size was studied experimentally and numerically. The discrete element method with a tension softening contact bond model was used to investigate the development of the process zone with the specimen size. A synthetic rock composed of rigid circular particles that interact through normal and shear springs was tested in the numerical simulations. It was shown that the limiting specimen size, beyond which no further noticeable increase in the length of the process zone is observed, is significantly larger than the limiting specimen size beyond which the width of the process zone shows no size effect.     

Cooling cycle effects on low temperature cracking characteristics of asphalt concrete mixture

The effect of cooling cycles on the low temperature behavior of asphalt concrete mixtures is investigated using a recently developed acoustic emission (AE) test device. In an attempt to link the local AE response of the asphalt mixtures to the pavement global response obtained through mechanical tests, the AE-based results were validated using traditional mechanical pavement performance testing methods namely, the disk-shaped compact tension [DC(T)] test and the indirect tensile test (IDT) method. Field-aged pavement cores, which were expected to have a gradient in binder aging properties (more aging near the surface of the pavement), were collected and tested. Test results revealed that significant damage resulted from cyclic cooling, effecting the fracture energy and stress relaxation ability of the asphalt mixture. The AE results collected were consistent with the results obtained using the DC(T) and the IDT test methods. The so-called Felicity effect was observed by evaluating AE activity occurring in a sample subjected to multiple cooling cycles and an AE based healing index was introduced to evaluate the amount of healing that resulted from warming cycles. Low temperature induced microdamage was also investigated using X-ray computer micro-tomography, in an effort to better understand the physical nature of microcracking in asphalt mixtures at low temperatures and the source of AE emissions detected.     

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.     

Measurements and Calculations of the Width of the Fracture Process Zones on the Surface of Notched Concrete Beams

Abstract: The paper presents the results of experimental and theoretical investigations of the width of the fracture process zone (FPZ) on the surface of notched concrete beams during quasi‐static three‐point bending. To measure two‐dimensional deformations on the surface of beams, a Digital Image Correlation (DIC) technique was used. Laboratory tests were performed with different notched concrete beams. The experiments were simulated with two different isotropic continuum crack models under two‐dimensional conditions: an elasto‐plastic and a damage one with non‐local softening.     

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.     

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.     

Size effect and quasi-brittle fracture: the role of FPZ

Fracture process zone (FPZ), or the crack-tip damage zone created by crack-bridging and micro-cracking activities, in a specimen of a concrete-like material is comparable to the crack size and un-cracked ligament, so fracture is typically quasi-brittle. Increasing or decreasing the specimen size, quasi-brittle fracture transition occurs towards the toughness-controlled or strength-controlled fracture, which is known as size effect (SE). In this study it is shown that the “size-dependent” quasi-brittle fracture transition is actually due to the interaction of FPZ with the nearest structure boundary rather than the size variation, and the widely-accepted SE for geometrically-similar specimens of different sizes is only a special case of quasi-brittle fracture controlled by the FPZ/boundary interaction. Relevant SE relations are critically reviewed and explained by emphasizing the key SE mechanism, FPZ/boundary interaction.     

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.     

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.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

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.     

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.