Increasing Specimen Size Research Articles

Size Effect Analysis for the Characterization of Marcellus Shale Quasi-brittle Fracture Properties

Mechanical characterization of shale-like rocks requires understanding the scaling of the measured properties to enable the extrapolation from small scale laboratory tests to field study. In this paper, the size effect of Marcellus shale was analyzed, and the fracture properties were obtained through size effect tests. A number of fracture tests were conducted on Three-Point-Bending (TPB) specimens with increasing size. Test results show that the nominal strength decreases with increasing specimen size, and can be fitted well by Bazant's Size Effect Law (SEL). It is shown that SEL accounts for the effects of both specimen size and geometry, allowing an accurate identification of the initial fracture energy of the material, Gf, and the effective Fracture Process Zone (FPZ) length, cf. The obtained fracture properties were verified by the numerical simulations of the investigated specimens using standard Finite Element technique with cohesive model. Significant anisotropy was observed in the fracture properties determined in three principal notch orientations: arrester, divider, and short-transverse. The size effect of the measured structural strength and apparent fracture toughness was discussed. Neither strength-based criterion which neglects size effect, nor classic LEFM which does not account for the finiteness of the FPZ can predict the reported size effect data, and nonlinear fracture mechanics of the quasibrittle type is instead applicable.

Size and Temperature Effect of Compressive Strength and Deformation Modulus of Fly Ash Concrete Prism

In this paper, the prism specimens of fly ash concrete were tested under the axial compressive load, and the prism specimens were cast with different curing temperature in winter. The aim of this project is to find how section size, curing temperature and fly ash content influence the compressive performance of the long curing age prism specimens. The side length of prisms cross section have a total of 6 dimensions from 100mm to 500mm. Concrete mixtures were prepared by substituting 0, 25% and 50% fly ash respectively. The average curing age of specimens is 570 days. The results show that when the size of the specimens increases, the axial compressive strength of the prism specimen, modulus of elasticity, and the peak value of secant modulus increase as well. Replacing part of cement with fly ash and increasing specimen size are beneficial to the strength and elastic modulus growth of concrete under construction and low temperature curing conditions in winter.

Scale effects and strength anisotropy in coal

We explore microstructure-related effects of loading direction and specimen size on the anisotropy of uniaxial compressive strength in coal. We measure uniaxial compressive strength on coal samples of four different diameters (25 to 75 mm) and with varied dip of the bedding plane with respect to loading direction (0°, 15°, 30°, 45°, 60° and 90°) including characterizing the variation of microstructures in the specimens by X-ray imaging. The uniaxial compressive strength for each specimen size exhibits a unique U-shape curve against the angle of anisotropy (Jaeger, 1971). The degree of the strength anisotropy decreases with increasing specimen size, principally due to the enhanced microstructural volume of a larger specimen. The contribution of microstructures on uniaxial compressive strength differs for different orientations of loading relative to anisotropy. The rate of decline of the average uniaxial compressive strength with increasing specimen size is greatest when loading is parallel to bedding (anisotropic angle of 0°) and is the most moderate at 45°. An empirical equation relating specimen diameter with uniaxial compressive strength is proposed and verified against the experimental data. Based on this equation, the UCS of coal samples with different orientations relative to the anisotropy are predicted for the limiting sizes of zero and ∞. The anisotropy of the scale effect is also explored. Meanwhile, it is verified that a cosine relation between anisotropy angle and uniaxial compressive strength is applicable to coal specimens of different sizes. This demonstrates that the strength anisotropy in coal will remain constant when the specimen diameter is larger than a critical threshold. Based on these two observations/equations, a universal equation relying on the minimum strength angle, friction angle and Weibull coefficients is proposed and verified against experimental data to describe the relationship among anisotropy angle, specimen size, and uniaxial compressive strength in coal.

Experimental investigation of the size effect of layered roller compacted concrete (RCC) under high-strain-rate loading

The strain rate and specimen size are two main influential factors when measuring the compressive strength of concrete-like materials. Understanding the dynamic size effect of concrete is essential for better analysis and design of concrete structures. However, few systematic laboratory tests have investigated the dynamic size effect in layered roller compacted concrete (RCC) under various levels of high-strain-rate loading. In this study, three sizes of cylindrical RCC specimens with diameters of 50 mm, 75 mm and 100 mm are prepared and tested under high loading rates to directly investigate the size effects. The size dependence and strain rate sensitivity are characterized in terms of the failure pattern, dynamic compressive strength, ultimate strain, maximum strains, and toughness. The dynamic compressive strength increases with increasing specimen size under impact loading, which is opposite to the size effect under static loading. The statistical significance is further investigated in terms of the variation in the dynamic mechanical properties of the RCC material based on analysis of variance (ANOVA). A modified Weibull size effect law, which incorporates both the specimen size and strain rate, is proposed and verified to illustrate the underlying mechanism of the dynamic size effect for the RCC material under impact loading.

Scale Effect on the Anisotropy of Acoustic Emission in Coal

Acoustic emission (AE) in coal is anisotropic. In this paper, we investigate the microstructure‐related scale effect on the anisotropic AE feature in coal at unconfined loading process. A series of coal specimens were processed with diameters of 25 mm, 38 mm, 50 mm, and 75 mm (height to diameter ratio of 2) and anisotropic angles of 0°, 15°, 30°, 45°, 60°, and 90°. The cumulative AE counts and energy dissipation increase with the specimen size, while the energy dissipation per AE count behaves in the opposite way. This may result from the increasing amount of both preexisting discontinuities and cracks (volume/number) needed for specimen failure and the lower energy dissipation AE counts generated by them. The effect of microstructures on the anisotropies of AE weakens with the increasing specimen size. The TRFD and its anisotropy reduce as the specimen size increases, and the reduction of fractal dimension is most pronounced at the anisotropic angle of 45°. The correlation between TRFD and cumulative AE energy in the specimens with different sizes are separately consistent with the negative exponential equation proposed by Xie and Pariseau. With the specimen size gain, the reduction of the TRFD weakens with the increasing amount of cumulative absolute AE energy.

Size effect in circular concrete-filled steel tubes with different diameter-to-thickness ratios under axial compression

Axial compression tests of circular concrete-filled steel tubes with different diameters (219mm, 426mm, and 630mm) and ratios of tube diameter to steel thickness (55 and 88) were conducted to investigate the effect of size on the bearing capacity. The experimental results indicated that the peak nominal stress decreased as the size increased, and the decrease in the nominal stress due to the size effect increased at higher ratios of diameter to thickness. At the peak load moment, an increased specimen diameter corresponded to a decreased hoop stress in the steel tube as well as a decreased concrete strength due to the confinement effect of the steel tube. When the ratio of diameter to thickness increased, the extent of reduction of the hoop stress and the confining effect of the steel tube influenced by the increasing specimen size increased. However, the vertical stress in the steel tube was increased at increased size, and increases in the ratio of diameter to thickness improved the increase degree of the vertical stress of steel tube due to the enlargement of specimen size. Hence, the vertical bearing capacity of the steel tube was affected by both the specimen size and the ratio of diameter to thickness. Based on the size effect law (SEL) proposed by Bazant, and taken the effect of the ratio of diameter to thickness into consideration, a size-dependent formula to evaluate hoop stress in the steel tube was developed. A size-related model considering situations with different ratios of diameter to thickness was established in order to estimate the bearing capacity of large-size circular concrete-filled steel tubes. The model and experimental results showed good agreement.

Specimens size, aggregate size, and aggregate type effect on spalling of concrete in fire

SummaryThis paper attempted to isolate variables that govern concrete spalling when exposed to a hydrocarbon fire. The influence of specimen size was investigated by studying 4 specimen sizes consisting of cylinders, columns, and panels. Three aggregate sizes, 7 mm, 14 mm, and 20 mm were used in the concrete mixes to determine their effect on concrete spalling. Influence of aggregate type on concrete spalling was also investigated. Forty‐two different specimens were considered in this investigation. Concrete spalling was quantified as nominal spalling depth, which has been presented as a new way of quantifying the degree of concrete spalling. The results indicated that specimen size did have an effect on the spalling of concrete under hydrocarbon fire exposure and that nominal spalling depth of concrete increases as the specimen size increases. Aggregate size effect was evident when the maximum aggregate size increased from 7 mm to 20 mm, and explosive spalling was more severe for specimens with small size aggregates. Specimens with 14‐mm aggregate size showed inconsistent results and the spalling behavior witnessed was more random and sporadic. The type of aggregate used has no clear bearing on concrete spalling given both aggregates had similar linear expansion profiles.

Size-dependent fracture toughness of tungsten

In order to understand the size-dependent fracture behaviour of tungsten at the microscale, micro-cantilever tests were performed on single crystalline and ultrafine grained tungsten. The elastic-plastic fracture behaviour and crack tip plasticity were found to be strongly influenced by the sample size. The smallest cantilevers with dimensions below one micron failed by pure cleavage fracture at a fracture toughness of 1.5 MPa m1/2, which agrees well with the Griffith theory for brittle fracture. With increasing specimen size crack tip plasticity was observed, leading to a successive increase in fracture toughness and crack resistance behaviour. Using scanning transmission electron microscopy and electron backscatter diffraction, dislocation densities were analysed and measured. Pronounced plastic strain gradients were found at the crack tip for an intermediate specimen size, which also showed the highest crack resistance. When further increasing the specimen size, large plastic zones were still observed but the gradients in plastic strain vanished, leading to a reduction in the crack resistance behaviour. For those samples, a size independent fracture toughness of ca. 7 MPa m1/2 was found, which is close to macroscopic literature data. Increasing the initial dislocation density in the single crystals through plastic pre-straining led to a reduced stable crack growth behaviour but did not affect the fracture toughness. Furthermore, the effect of grain boundaries on the fracture behaviour was studied by means of ultrafine grained tungsten. A fracture toughness lower than the one reported in literature was found, which is explained by the higher susceptibility to failure once a crack propagates at the micro-scale.

Failure behavior and scaling of graphene nanocomposites

This work proposes an investigation on the scaling of the structural strength of polymer/graphene nanocomposites. To this end, fracture tests on geometrically scaled Single Edge Notch Bending (SENB) specimens with varying contents of graphene were conducted to study the effects of nanomodification on the scaling.It is shown that, while the strength of the pristine polymer scales according to Linear Elastic Fracture Mechanics (LEFM), this is not the case for nanocomposites, even for very low graphene contents. In fact, small specimens exhibited a more pronounced ductility with limited scaling and a significant deviation from LEFM whereas larger specimens behaved in a more brittle way, with scaling of nominal strength closer to the one predicted by LEFM.This behavior, due to the significant size of the Fracture Process Zone (FPZ) compared to the specimen size, needs to be taken into serious consideration. In facts, it is shown that, for the specimen sizes investigated in this work, neglecting the non-linear effects of the FPZ can lead to an underestimation of the fracture energy as high as 113%, this error decreasing for increasing specimen sizes.

Size-dependent impact resistance of ultra-high-performance fiber-reinforced concrete beams

This study examines the rate dependent flexural behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) beams with three different sizes. Two different loading rates (static and impact), fiber aspect ratios (lf/df of 65 and 100), and fiber types (straight and twisted) were considered. Test results indicated that the static flexural performance, including the flexural strength and toughness, were improved by increasing the fiber aspect ratio or through the use of twisted steel fibers. The static flexural strength clearly decreased with an increase in specimen size due to a decrease in the number of fibers at the crack surface. The use of straight steel fibers with a higher aspect ratio of 100 provided the best impact resistance in terms of the highest post-cracking flexural strengths and the largest normalized energy dissipation rates, compared to those of twisted steel fibers and straight steel fibers with a reduced aspect ratio of 65. Thus, the use the straight steel fibers with high aspect ratios was recommended to improve the impact resistance of UHPFRC. Dynamic increase factor (DIF) on the flexural strength of UHPFRC beams was properly investigated with strain-rate, regardless of specimen size. In addition, there were no effects with regard to the fiber aspect ratio and type on the relationship between the DIF of the first-cracking flexural strength and the stress- (or strain-) rate.

Experimental and numerical investigation of intra-laminar energy dissipation and size effect in two-dimensional textile composites

Design of large composite structures requires understanding the scaling of their mechanical properties, an aspect often overlooked in the literature on composites.This contribution analyzes, experimentally and numerically, the intra-laminar size effect of textile composite structures. Test results of geometrically similar Single Edge Notched specimens made of [0∘]8 epoxy/carbon twill 2 × 2 laminates are reported. Results show that the nominal strength decreases with increasing specimen size and that the experimental data can be fitted well by Bažant's size effect law, allowing an accurate identification of the intra-laminar fracture energy of the material, Gf.The importance of an accurate estimation of Gf in situations where intra-laminar fracturing is the main energy dissipation mechanism is clarified by studying numerically its effect on crashworthiness of composite tubes.Simulations demonstrate that, for the analyzed geometry, a decrease of the fracture energy to 50% of the measured value corresponds to an almost 42% decrease in plateau crushing load. Further, assuming a vertical stress drop after the peak, a typical assumption of strength-based constitutive laws implemented in most commercial Finite Element codes, results in an strength underestimation of the order of 70%.The main conclusion of this study is that measuring accurately fracture energy and modeling correctly the fracturing behavior of textile composites, including their quasi-brittleness, is key. This can be accomplished neither by strength- or strain-based approaches, which neglect size effect, nor by LEFM which does not account for the finiteness of the Fracture Process Zone.

Improved compressive fracture models for self-consolidating concrete (SCC)

This paper investigates the size effect phenomena in compressive strength of self-consolidating concrete (SCC) with different water to cement ratios, and attempts to model the experimental data coming from a series of laboratory unconfined compression tests. To this aim, several concrete cylinders having a constant slenderness ratio of two and diameters ranging from 50mm to 200mm were prepared, and tested under uniaxial compression. In addition, four theoretical models (i.e. size effect law (SEL), modified size effect law (MSEL), Sim et al.’s model, and multifractal scaling law (MFSL)) were investigated on their ability to catch this size effect by regression analysis using the nonlinear least squares method. The experiments indicated a pronounced strength reduction as the specimen size increases. The comparison of the goodness of fit between the models was quantified by using correlation coefficient R which provides that the models can interpret satisfactory the observed size effect.

Size effect on axial stress-strain behavior of CFRP-confined square concrete columns

Research published on the axial compressive behavior of fibre-reinforced polymer (FRP)-confined concrete columns has been generally based on small-sized specimens. There have been limited studies published on large-sized columns and there have also been limited studies on the validity of upscaling results obtained from small-sized specimens. On account of such knowledge gap, this paper presents the test results of 23 carbon FRP-confined square concrete columns of varying sizes subjected to monotonic axial compression. The specimens were sorted into 10 groups based on (i) specimen size, (ii) theoretical lateral FRP confining pressure, (iii) number of layers of FRP wrap, and (iv) inclusion and exclusion of internal steel reinforcement. In each group, the specimens consisted of different cross-sectional sizes but the same theoretical lateral confining pressure. The experimental results showed that specimen size had no significant effect on the axial stress-strain behavior of FRP-confined medium- and small-sized columns (i.e. sections defined herein equal to and less than 300mm in width). The axial stress-strain responses exhibited differences as the specimen size increased. This was especially the case for FRP-confined large-sized columns (i.e. sections defined herein equal to and larger than 350mm in width). The rupture strain of the FRP wrap at the corner regions is proposed to be defined as the effective lateral rupture strain of FRP, and this strain was shown to decrease with an increase of specimen size. Based on the test results, a modified FRP effective strain factor model considering the influence of size effect is proposed.

Numerical investigation of the influence of specimen size on the unconfined strength of defected rocks

A grain-based distinct element model (GBM) is used to investigate the influence of specimen size on the strength of intact (not defected) and defected rocks. The defected specimens are simulated by integrating a previously calibrated GBM with Discrete Fracture Network models representing defect geometries. The results of scale effect analysis conducted on synthetic specimens show that the strength of intact specimens is independent of specimen size. However, depending on the orientation of defects relative to the loading direction, the strength of defected specimens may decrease, increase or fluctuate with increasing specimen size.

Fracture initiation in cavity expansion of rock

Initiation of fracture from a cylindrical opening in blocks of Berea sandstone under plane strain was monitored with a cavity expansion apparatus. Using the particle tracking technique called digital image correlation, a discontinuity in the displacement field near the cavity boundary was identified at 80% of the peak internal pressure, which meant that a process zone developed prior to peak. To investigate the effect of scaling on fracture, a two dimensional bonded particle model was validated, and several specimens sizes with different borehole and tension softening characteristics were tested numerically. It is demonstrated that with increase in specimen size or with increase in borehole size, the peak pressure decreases, and these size effects are governed by both material and structural length scales.

Multi-fractal scaling law for split strength of concrete cubes

Experiments on concrete members indicate that the nominal strength of a specimen decreases with increasing specimen size for the same specimen geometry. This phenomenon is known as the size effect in the fracture mechanics of plain and reinforced concrete. Although nominal strength is also highly affected by the width of the distributed load in split-tension cylinder and cube specimens, this effect can be negligible within the practical range of the load-distributed width in diagonal cubes. However, the number of reported theoretical and experimental studies on cube and especially diagonal cube split-tension specimens is much more limited than those on cylindrical specimens. Therefore, in this study, six series of cube and diagonal cube specimens, with three different sizes and with two different maximum aggregate sizes (4 mm and 16 mm) but similar geometries, were tested under different load-distributed widths. The peak loads obtained from the test results were analysed using the multi-fractal scaling law. Subsequently, two prediction formulae are proposed for the design of torsional concrete/reinforced concrete members.

Bearing Capacities of Different-Diameter Concrete-Filled Steel Tubes under Axial Compression

The bearing capacities of concrete-filled steel tubes are normally derived through experiments with small-scale specimens, but it is uncertain whether such derivations are appropriate for the much larger components used in practical engineering. This study therefore investigates the effect of different diameters (219, 426, 630, and 820 mm) on the axial compression of short concrete columns in steel (Q235) tubes. It is found that the peak nominal stress decreases with increasing specimen size and that the axial bearing capacity is determined by three separate components: the cylinder compressive strength of the concrete, the improvement in strength due to the confining effect of the steel tube, and the longitudinal strength of the steel tube. At peak load, increases in the specimen diameter reduce the hoop stresses in the steel tube, thereby reducing the strengthening effect of confinement. Vertical stress in the steel tube is increased with diameter; therefore, the axial bearing capacity of the steel tube is directly related to the specimen size. Size effect coefficients for these three aspects of bearing capacity are defined and used to develop a size-dependent model for predicting the axial bearing capacity of large, concrete-filled steel tubes. The model is then validated against experimental data.

Experimentally informed multi-scale modelling of mechanical properties of quasi-brittle nuclear graphite

Nuclear graphite has a complex microstructure and displays quasi-brittle fracture characteristics. Multi-scale experimental characterisation (micrometre-scale to centimetre-scale) and numerical modelling were performed for (i) PG25 filter graphite with pores only (52vol.%); and (ii) Gilsocarbon nuclear graphite with pores and aggregates. Modelling results show that the average mechanical properties and the scatter of the data both decrease monotonically with increase in specimen size. Strain fields and crack patterns were modelled and fit with experimental observations. The benefits of the model as a valuable tool in studying the influence of microstructural parameters on the fracture of nuclear graphites are discussed.

Influence of different sizes of concrete and roller compacted concrete on double-K fracture parameters

Affected by physical properties of various components, characteristics and stress states of junction surface and other multiple factors, concrete, as a kind of multi-phase composite material, has complicated failure mechanism, thus making its fracture mechanism research difficult. But concrete has been widely used in engineering construction, so research on concrete fracture theory is of important realistic significance and construction value. This study discusses influence rule of specimen size and crack-depth ratio (?0/h) on doubleK fracture parameters (initial fracture toughness ini ICK and unstable fracture toughness un ICK ) and its size effects by using fracture test. Different sizes of concretes and roller compacted concrete (RCC) specimens are adopted to explore influence of specimen size on concrete double-K fracture parameters. Results reveal that initial fracture toughness ini ICK and unstable fracture toughness un ICK increase as specimen size enlarges, showing a size effect; besides, subcritical crack extends with the increase of specimen size. With regard to specimens with different crack-depth ratios, its unstable fracture toughness un ICK is unrelated to initial crack-depth ratio when crack-depth ratio is more than or equal to 0.4, while initial fracture toughness ini ICK is correlated with initial crack-depth ratio, which indicate that double-K fracture parameters can be considered as material constants describing concrete initial fracture, stable expansion and whole process of stability failure.

Determination of double-K fracture parameters using semi-circular bend test specimens

The present research was conducted to evaluate the double-K fracture parameters using semi-circular bend test. Fracture tests were carried out on semi-circular bend specimens with three different diameters with a range from 200mm to 500mm and four different concrete strengths. The results indicated that double-K fracture parameters KIcini and KIcun values for semi-circular bend specimens were size and strength dependent. All the fracture parameters such as critical effective crack length, critical crack mouth opening displacement and unstable fracture toughness increased as the specimen size increased; while, initial fracture toughness decreased with the increase of specimen size.