Single Edge Notched Beam Specimens Research Articles

Fracture Toughness of Ordinary Plain Concrete Under Three-Point Bending Based on Double-K and Boundary Effect Fracture Models.

Fracture tests are a necessary means to obtain the fracture properties of concrete, which are crucial material parameters for the fracture analysis of concrete structures. This study aims to fill the gap of insufficient test results on the fracture toughness of widely used ordinary C40~C60 concrete. A three-point bending fracture test was conducted on 28 plain concrete and 6 reinforced concrete single-edge notched beam specimens with various depths of prefabricated notches. The results are reported, including the failure pattern, crack initiation load, peak load, and complete load versus crack mouth opening displacement curves. The cracking load showed significant variation due to differences in notch prefabrication and aggregate distribution, while the peak load decreased nonlinearly with an increase in the notch-to-height ratio. The reinforced concrete beams showed a significantly higher peak load than the plain concrete beams, attributed to the restraint of steel reinforcement, but the measured cracking load was comparable. A compliance versus notch-to-height ratio curve was derived for future applications, such as estimating crack length in crack growth rate tests. Finally, fracture toughness was determined based on the double-K fracture model and the boundary effect model. The average fracture toughness value for C50 concrete from this study was 2.0 MPa·m, slightly smaller than that of lower-strength concrete, indicating the strength and ductility dependency of concrete fracture toughness. The fracture toughness calculated from the two models is consistent, and both methods employ a closed-form solution and are practical to use. The derived fracture toughness was insensitive to the discrete parameters in the boundary effect model. The insights gained from this study significantly contribute to our understanding of the fracture toughness properties of ordinary structural concrete, highlighting its potential to shape future studies and applications in the field.

Investigating the influence of various three-point bending specimen configurations on rock fracture parameters testing: an experimental study

The fracture parameters of rocks, including fracture toughness and fracture energy, represent their resistance to crack propagation under external stress. These parameters play a critical role in engineering design, construction safety, geological mechanics research, and rock material assessment. This study determined the fracture parameters of granite under Mode I loading conditions using notched semicircular bend (NSCB) and single-edge notched beam (SENB) specimens. Although there was little difference between the initial and unstable fracture toughness values of the two specimen configurations, significant differences were observed in the fracture process and other fracture parameters. For example, the NSCB specimen exhibits a higher elastic modulus, and it witnessed rapid failure after reaching the peak load, whereas the SENB specimen displayed a more gradual failure process with a distinct post-peak stage. This may be one of the reasons for the higher fracture energy in the NSCB specimen than in the SENB specimen. Based on finite element analysis and the extraction of the tangential stress at the crack tip region, the application of the maximum tangential stress fracture criterion provided a robust explanation for the coherence observed in the unstable fracture toughness test results between the two specimen configurations.

Influence of specimen size on granite fracture characteristics and acoustic emission phenomena under mode I loading conditions

The rock mode I fracture characteristics and the size effect are of great significance in understanding the crack initiation, nucleation, propagation, and characterizing the fracture toughness of rocks which is essential for predicting the behavior of rock masses and designing underground structures. In this paper, three-point bending fracture experiments were carried out using single-edge notched beam specimens of different sizes. The fracture characteristics of the entire loading stage, including the post peak stage, were analyzed using digital image correlation (DIC) technology and acoustic emission (AE) technology. Specifically, the calculation of the b value uses the Fisher optimal split and global search algorithm (FGS) method. The results show that both the Fracture process zone (FPZ) length and fracture toughness of granite are size-dependent parameters, and the FPZ length growth rate increases with increasing load level. The failure mode of the source during fracture is mainly tensile failure, and the proportion of tensile failure tends to increase with the increase of specimen size. The temporal b value, average AF value and RA value show corresponding stage changes with time, and the minimum b value, minimum AF value and maximum RA value can characterize the maximum of macroscopic growth rate.

Fracture Behavior of Concrete under Chlorine Salt Attack Exposed to Freeze-Thaw Cycles Environment.

Fracture behavior is one of the key properties to study concrete cracking under sodium chloride attack exposed to the freeze-thaw cycles environment, which is frequently neglected. In this paper, 24 single edge notch beam specimens and 24 cubes were poured. The corresponding freeze-thaw cycles test in sodium chloride solution, standard cube compressive strength of concrete test, and three-point-bending tests were carried out. The research revealed that the fracture toughness, fracture energy, relative dynamic modulus of elasticity, and standard cube compressive strength were decreased by increasing freeze-thaw cycles under sodium chloride attack, and the damage degree of concrete caused by sodium chloride solution was deeper than that of pure water. In particular, there existed good linear correlation between the fracture behavior and imposed freeze-thaw damage for various solution. Accordingly, a more reliable damage model using fracture control parameters as damage factors was proposed.

Effect of ribose incubation on physical, chemical, and mechanical properties of human cortical bone

Raman spectroscopy (RS) is sensitive to the accumulation of advanced glycation end-products (AGEs), and it measures matrix-sensitive properties that correlate with the fracture toughness of human cortical bone. However, it is unclear whether sugar-mediated accumulation of AGEs affects the fracture toughness of human cortical bone in a manner that is consistent with the negative correlations between amide I sub-peak ratios and fracture toughness. Upon machining 64 single-edge notched beam (SENB) specimens from cadaveric femurs (8 male and 7 female donors between 46 years and 61 years of age), pairs of SENB specimens were incubated in 15 mL of phosphate buffered saline with or without 0.1 M ribose for 4 weeks at 37 °C. After acquiring 10 Raman spectra per bone specimen (n = 32 per incubation group), paired SENB specimens were loaded in three-point bending at a quasi-static or a high loading rate approximating 10−4 s−1 or 10−2 s−1, respectively (n = 16 per incubation group per loading rate). While 2 amide I sub-peak ratios, I1670/I1640 and I1670/I1610, decreased by 3–5% with a 100% increase in AGE content, as confirmed by fluorescence measurements, the ribose incubation to accumulate AGEs in bone did not affect linear elastic (KIc) nor non-linear elastic (KJc) measurements of bone's ability to resist crack growth. Moreover, AGE accumulation did not affect the change in these properties when the loading rate changed. Increasing the loading rate increased KIc but decreased KJc. Ribose incubation did not affect mineral-related RS properties such as mineral-to-matrix ratios, Type B carbonate substitutions, and crystallinity. It did however increase the thermal stability of demineralized bone (differential scanning calorimetry), without affecting the network connectivity of the organic matrix (i.e., maximum slope during a hydrothermal isometric tension test of demineralized bone). In conclusion, RS is sensitive to AGE accumulation via the amide I band (plus the hydroxyproline-to-proline ratio), but the increase in AGE content due to ribose incubation was not sufficient to affect the fracture toughness of human cortical bone.

The theory of critical distances applied to fracture of rocks with circular cavities

This work presents experimental and theoretical analyses of the fracture behavior of different rocks containing circular holes subjected to uniaxial compressive uniform loads. The experimental critical loads are compared with those derived from the Theory of Critical Distances (TCD) and finite element simulations. The rocks being analyzed are Floresta sandstone, Moleanos limestone, Macael marble and Carrara marble. They were previously characterized under compressive and tensile conditions, obtaining their corresponding Poisson's ratios, Young's moduli and ultimate tensile and compressive strengths. Besides, their fracture properties, specifically their fracture toughnesses and critical distances, were also available from a previous experimental campaign on Single Edge Notched Beam specimens with different notch radii and tested under 4-point-bending conditions. In this paper, prismatic specimens (9 per each type of rock) containing a cylindrical cavity at their center were uniaxially compressed until failure. The fracture pattern was revealed and agrees with previously published cases. The TCD, specifically the Point Method, was applied with the aim of comparing the corresponding fracture load predictions with the experimental ones. Three-dimensional finite element analyses were used to calculate the stress fields. The application of the TCD on the Floresta sandstone and the Moleanos limestone provides reasonable predictions of fracture loads, given their linear-elastic behavior. For the two studied marbles, the resulting predictions are overly conservative despite their quasi-brittle behavior. This may be attributed to complex process zones with intense microcracking that are revealed as white patches prior to failure and generate dust and small fragments after failure.

Indices-Based Healing Quantification for Bituminous Materials

AbstractIn the present study, three-point bending tests are carried out using single-edge notched beam specimens of bitumen and mastic to quantify healing. Experiments are conducted at a controlled...

Experimental study on fracture toughness of a compacted clay using semi-circular bend specimen

Single-edge notched beam specimens have been used widely to determine the fracture toughness KIC of compacted clays under three-point bending loading. However, this specimen type is not very suitable for the material with low strength. In this study, notched semi-circular bend specimens were employed to determine the KIC of a compacted clay, the effects of initial notch length, specimen thickness, moisture content and dry density on KIC were investigated. Based on the testing results, the ratio of initial notch length to specimen radius a0/R = 0.3–0.5 was suggested. There was no remarkable thickness-dependent size effect for the compacted clay. To investigate the relationship between the KIC and tensile strength σt of the compacted clay, unnotched semi-circular bend specimens were employed for determining the σt. It is concluded that there is a good linear relationship between these two parameters. According to the discussion on the testing results of different compacted clays, an empirical formula KIC = 0.3283σt was obtained, which can be used to estimate the KIC with σt of directly compacted clays. Additionally, the size of fracture process zone of the compacted clay was calculated by an estimation method.

Investigating the effect of heat treatment on the fracture toughness of a hot extruded Al–Ti composite produced by powder metallurgy route

An Al-5 wt% Ti composite was fabricated via powder metallurgy technique and hot extrusion. The produced composite samples were heat-treated subsequently at 600 °C for various time durations of 0, 4 and 10 h to achieve different volume fractions of the intermetallic Al3Ti phase. Pure aluminum sample was produced as a benchmark specimen to be compared to the composite samples. SEM studies were used to investigate the microstructure of the composite samples, and it was revealed that core-shell structured particles were formed in the composite heat-treated for 4 h. Triple point bending test was performed on the single edge notched beam specimens of the heat-treated Al-5 wt% Ti composite and the pure aluminum sample to investigate the bending strength and the fracture toughness. Two different methods of Kee and the fracture energy were implemented to evaluate the toughness of the Al-5 wt% Ti composites and the pure aluminum sample; the results indicated raising the heat treatment duration caused the fracture toughness (Kee) of the composite samples to decline, and the same trend was observed for the initiation and propagation fracture energies as well. By increasing the heat treatment time from 0 to 10 h, the fracture toughness of the composite dropped from 20.1 MPa m to 10.2 MPa m, while the pure aluminum sample had the greatest value of 25.6 MPa m. The SEM images of the fractured surface of the composite samples elucidated the effect of heating time on the fracture mechanism of the composites; the governing fracture mechanism changed from particle fracture for the composite heat-treated for 4 h to the particle decohesion for the one heat-treated for 10 h.

Effects of Na2O/SiO2 molar ratio on properties of aggregate-paste interphase in fly ash-based geopolymer mixtures through multiscale measurements

This paper presents a multiscale experimental study on the influence of different Na2O/SiO2 molar ratios on the mechanical and microstructural characteristics of the aggregate-paste interphase in fly ash-based geopolymer mixtures. By analyzing the scanning electron microscope images, the solid phases present in the microstructure were identified, and the frequency of occurrence of each phase was quantified. In addition, the porosity and pore size distribution of geopolymer specimens were measured by mercury intrusion porosimetry. By conducting nanoindentation tests on a large array of indentations and subsequent statistical analysis of the test results, the elastic moduli of individual phases were extracted. The bond behavior between aggregate and paste was also investigated by conducting the three-point bending test of single edge notched beam specimens. Integration of test results in different length scales showed that interphase region generates more sodium aluminosilicate hydrate (i.e., N-A-S-H) gel than the adjacent paste region regardless of the Na2O/SiO2 ratios used in this study. In addition, the mixture prepared with the higher Na2O/SiO2 molar ratio exhibited more N-A-S-H gel in the interphase zone, which led to increased bonding strength between aggregate and paste.

Comparative Evaluations and Microstructure: Mechanical Property Relations of Sintered Silicon Carbide Consolidated by Various Techniques

A comparative evaluation between pressureless or self-sintered silicon carbide (SSiC), hot-pressed silicon carbide (HP-SiC), and spark plasma-sintered silicon carbide (SPS-SiC) has been carried out with emphasis on examination of their microstructures and mechanical properties. The effect of sample dimensions on density and properties of SPS-SiC has been also examined. Elastic modulus, flexural strength, and fracture toughness measured by indentation or testing of single-edge notched beam specimens have been found to follow the following trend, HP-SiC > SSiC > SPS-SiC. The SPS-SiC samples have shown size-dependent densification and mechanical properties, with the smaller sample exhibiting superior properties. The mechanical properties of sintered SiC samples appear to be influenced by relative density, grain size, and morphology, as well as the existence of intergranular glassy phase. Studies of fracture surface morphologies have revealed the mechanism of failure to be transgranular in SSiC or HP-SiC, and intergranular in case of SPS-SiC, indicating the dominating influence of grain size and α-SiC formation with high aspect ratio.

Design of four-point SENB specimens with stable crack growth

A four-point single-edge-notch-beam (SENB) test specimen loaded in displacement control (fixed grip) is proposed for studying crack deflection at bi-material interfaces. In order to ensure stable crack growth, a novel analytical model of the four-point SENB specimen in fixed grip is derived and compared with numerical models. Model results show that the specimen should be short and thick, and the start-crack length should be deep for the crack to propagate stable towards the bi-material interface. Observations from experimental tests of four-point SENB specimens with different start-crack lengths, confirmed that the crack grows stable if the start-crack length is deep and unstable if not.

Prevalent role of porosity and osteonal area over mineralization heterogeneity in the fracture toughness of human cortical bone

Changes in the distribution of bone mineralization occurring with aging, disease, or treatment have prompted concerns that alterations in mineralization heterogeneity may affect the fracture resistance of bone. Yet, so far, studies assessing bone from hip fracture cases and fracture-free women have not reached a consensus on how heterogeneity in tissue mineralization relates to skeletal fragility. Owing to the multifactorial nature of toughening mechanisms occurring in bone, we assessed the relative contribution of heterogeneity in mineralization to fracture resistance with respect to age, porosity, and area fraction of osteonal tissue. The latter parameters were extracted from quantitative backscattered electron imaging of human cortical bone sections following R-curve tests of single-edge notched beam specimens to determine fracture toughness properties. Microstructural heterogeneity was determined as the width of the mineral distribution (bulk) and as the sill of the variogram (local). In univariate analyses of measures from 62 human donors (21 to 101 years), local but not bulk heterogeneity as well as pore clustering negatively correlated with fracture toughness properties. With age as covariate, heterogeneity was a significant predictor of crack initiation, though local had a stronger negative contribution than bulk. When considering all potential covariates, age, cortical porosity and area fraction of osteons explained up to 50% of the variance in bone׳s crack initiation toughness. However, including heterogeneity in mineralization did not improve upon this prediction. The findings of the present work stress the necessity to account for porosity and microstructure when evaluating the potential of matrix-related features to affect skeletal fragility.

High temperature digital image correlation evaluation of in-situ failure mechanism: An experimental framework with application to C/SiC composites

A high temperature digital image correlation (DIC) technique was developed, which was applied to study the in-situ fracture behavior of a carbon fibre reinforced silicon carbide matrix (C/SiC) composite. The displacement distribution and cracking information of the C/SiC single edge notched beam specimen can be monitored real-time, thanks to the improved DIC technique with special speckle patterns that can reach up to 1600°C. The results showed that the brittle to ductile transition temperature of C/SiC composites is about 1300°C. The new failure mechanisms of C/SiC composites at different experimental temperatures were further verified with the aid of X-ray diffraction and scanning electron microscope (SEM) techniques. In addition, the relationships between the fracture toughness, first-crack strength of C/SiC composites and environmental temperature were deduced. The proposed experimental method and testing results may shed some light on assessing the reliability and durability of C/SiC composites at high temperatures.

Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria

A numerical parametric study on the crack growth direction under mixed mode conditions (I+II) is introduced. An eccentric asymmetric four-point bending of a single edge notched beam specimen is considered as an example, since various levels of mode mixity can be thus obtained. The crack growth direction is estimated using the maximum tangential stress (MTS) criterion, the strain energy density (SED) criterion and the crack tip displacement (CTD) criterion. Multi-parameter fracture mechanics based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series is employed. It was found out that whereas the use of the CTD and SED criteria should be accurate enough even in their classical (or two-parameter) form for most geometries and distances of their application from the crack tip, the generalized form of the MTS criterion with at least four terms of the series should be applied, if the distance of its application is not less than 0.01 of the specimen width. Moreover, it is able to describe the typical dependence of the initial kink angle on the distance from the crack tip where the criterion is applied.

Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

The presented work introduces a numerical parametric study on the crack propagation direction under mixed-mode conditions (mode I + II). It is conducted for the geometry of an eccentric asymmetric fourpoint bending of a single edge notched beam specimen; various levels of mode-mixity are ensured by modifications in the crack length and crack eccentricity. The direction of crack propagation is estimated semianalytically using both the maximum tangential stress criterion and the strain energy density criterion (implemented as a procedure within the used finite element computational code) as well as numerically (from verification reasons). Multi-parameter fracture mechanics is employed in the presented work for precise analytical evaluation of the stress field in the cracked specimen. This theory is based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series. Recent studies show that utilization of only first term of the series, which corresponds to the stress intensity factor (SIF), the single controlling parameter for the crack initiation and propagation assessment in brittle materials, is insufficient in many crack problems. It appears also in this study that the higher-order terms of the asymptotic crack-tip field are of great relevance for the conducted analysis, similarly to a number of other fracture phenomena (near-crack-tip stress field approximation, non-linear zone extent estimation, etc.).

Influence of the notch root radius on the fracture toughness of brittle metals: Nanostructure tungsten alloy, a case study

Tungsten and tungsten-based alloys are considered to be candidate materials for next-generation nuclear fusion reactors. Unfortunately, their use in structural applications is compromised due to their inherent brittleness. To improve this crucial feature, it is necessary to accurately measure their fracture toughness as a real property independent of geometrical parameters and the method used to introduce the induced crack. This goal is the objective of this work; where the notch tip radius influence on the fracture toughness of a brittle nanostructured tungsten alloy is analyzed in depth.Three-point bending tests at room temperature were performed on four types of notch geometries in which the notch root radius was gradually reduced. The notches were introduced using four different methods: with a classical diamond disc, a diamond wire, a razor blade and an ultra-short pulsed laser. The results showed that single edge notched beam specimens overestimate the fracture toughness values and introduce some deformation into the notch root grains. However, the razor blade yields very good results with a low dispersion, but is only suitable for coarse grain materials since the size effect appears as the grain size decreases. Therefore, for nanostructured materials such as in this case, the notch root radius is still too large (several times the grain size), requiring the implementation of a new method. Very sharp single edge laser-notched beam specimens with a 5–20nm root radius were accordingly produced by using ultra-short pulsed laser ablation. This method has been previously used on ceramics but no evidence of its use was found on metals.

PS34 微粒等方性黒鉛の破壊靱性に及ぼす切欠き先端形状の影響

In order to investigate the effect of notch-tip geometry on the fracture toughness of fine-grained isotropic graphite ETU-10, three-point-bending fracture toughness tests have been performed by using two types of single-edge notched beam specimens with different notch angles of approximately 15° and 30°. In this test, the load-displacement curve was measured by using the load cell and the laser displacement sensor. The values of the fracture toughness were calculated based on linear elastic fracture mechanics by using the maximum force which could be obtained by the load-displacement curve. As a result, the values of the fracture toughness of the specimens with the notch angles of approximately 15° and 30° were 0.933 MPa m^<1/2> and 0.926 MPa m^<1/2>, respectively. This suggested that the values of the fracture toughness were not affected between the notch angles. Further work has been ongoing to discuss the effect of the notch-tip geometry such as angle and root radius of notch in terms of finite element analysis.

Fracture Behavior of SiC-TiB&lt;sub&gt;2&lt;/sub&gt; Composite Measured by Different Test Methods

SiC-TiB2composite was prepared by boron (B) and carbon(C) as sintering additive via presureless sintering in 2180°C. Fracture toughness of SiC-TiB2measured by indentation method and single edge notched beam specimen tenichques were analyzed and compared, and the most suitable indentation method equation was confirmed. Results revealed that the fracture toughness and flexure strength of the materials were influenced at varied degree by the content of TiB2, which had no effect on the selection of the most suitable equation for calculating the fracture toughness of the materials by indentation method. The fracture toughness decreases with the increasing TiB2content. When the TiB2content was 30%, SiC-TiB2composite had the best fracture toughness.

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.