Size Effect In Strength Research Articles

Reverse Size Effect of the Unconfined Compressive Strength of Crystalline Rock: A Grain-Scale Perspective

Reverse Size Effect of the Unconfined Compressive Strength of Crystalline Rock: A Grain-Scale Perspective

Size effect on tensile bonding strength between new and old concrete

The interface between new and old concrete plays a significant role in reinforced concrete engineering due to its size effect and weak strength. To investigate the size effect of tensile strength in new-to-old concrete, splitting tensile tests and computed tomography (CT) scans on composite specimens were conducted. Specimen size, interface roughness, volume fraction of polyvinyl alcohol fiber and adhesive were considered. The tensile bonding strength initially increases and then decreases with interface roughness and fiber content, while size effect on the strength shows a downward trend before rising. The adhesive notably enhances the tensile bonding strength and weakens its size effect. The interface roughness, polyvinyl alcohol fibers and interface agents influence the size effect by modifying the bonding area, specimen uniformity, and characteristic structure of the interface region. At an interface roughness of 5.5 mm and a polyvinyl alcohol fiber content of 0.5 %, the maximum strength was achieved and the maximum attenuation of size effect occurred. The size effect laws of tensile bonding performance were presented based on the Weibull statistical theory, Bažant energy theory and Carpinteri multi-fractal theory. The experimental values exhibit good consistency with the predictions from the size effect models.

Specimen size effect on compressive strength of 3D printed concrete containing coarse aggregate with varying water to binder ratios

This study aims to investigate the specimen size effect of compressive strength in 3D printed concrete containing coarse aggregate (3DPCA). Firstly, we compare the specimen size effect of compressive strength in mold-cast concrete (CC) and 3DPCA. Through X-CT scans and image analysis, the underlying mechanisms of this specimen size effect in 3DPCA are revealed. The results indicate that 3DPCA exhibits a less pronounced specimen size effect on compressive strength when loaded along the Z direction compared to CC, due to the presence of interlayer weak zones that mitigate the influence of size variations. Specifically, when the water-binder ratio varies between 0.3 and 0.5, the size coefficient of printed sample is reduced by 0.01–0.07 compared to cast sample. Similarly, variations in coarse aggregate content result in a size coefficient for printed sample that is 0.01–0.05 lower than cast sample. Higher porosity increases the specimen size effect of 3DPCA, but good printing quality can mitigate this influence. A modified Weibull model integrating water-binder ratio and coarse aggregate content was proposed, providing precise predictions of the specimen size effect on 3DPCA's compressive strength, with a correlation coefficient exceeding 93 %.

The influence of initial static shear on the torsional performance of BFRP bars-RC beams with different sizes

To reveal the influence of the initial static shear on the torsional performance of Basalt Fiber Reinforced Polymer Bars-Reinforced Concrete (BFRP bars-RC) beams, in this study, 52 BFRP bars-RC beam models with geometric similarity using a three-dimensional mesoscale numerical simulation method were established. The effects of initial shear static loadings (F0 = 0, 0.25Vu, 0.5Vu, and 0.75Vu) on the failure modes, torsional strength, ductility, and size effect of BFRP bars-RC beams under various equivalent strain rates were quantitatively analyzed. The results show that, regardless of whether the beams have initial damage, their load-bearing capacity and deformation ability increase as loading strain rates increase. For beams with initial damage, the increased degrees in load-bearing capacity relative to their respective initial static shear decreases as the initial static shear level increases but then increases as the subsequent loading strain rate increases. Increasing the beams’ initial damage degree makes the beams’ ductility worse. In addition, the more severe the beams’ initial damage, the more significant the strength size effect. However, increasing the strain rate can weaken the beams’ strength size effect.

Study on the size effect of rock burst tendency of red sandstone under uniaxial compression

The study of rock burst tendency of rock masses with different sizes plays a key role in the prevention of rock burst. Through theoretical analysis, it is proposed that uniaxial compressive strength and deformation modulus ratio are the key mechanical parameters affecting rock burst occurrence. In order to find out the size effect of uniaxial compressive strength and deformation modulus ratio, theoretical analysis and uniaxial compression experiment are carried out on rock samples with different heights, different cross-sectional areas and different volumes. The results show that the smaller the uniaxial compressive strength is, the larger the deformation modulus ratio is, and the more likely rock burst are to occur. On the contrary, rock burst is still not easy to generate. The uniaxial compressive strength of rock samples with different heights, different cross-sectional areas and different volumes increases with the increase of rock sample size. The deformation modulus ratio of rock samples with different heights and different volumes shows an upward trend on the whole, while that of rock samples with different cross-sectional areas shows a downward trend on the whole. The fracture forms of rock are analyzed using the energy conversion law in the process of deformation and failure for three kinds of rock with different shapes and sizes.

Analysis of strength size effect and failure mechanism of asphalt mixtures based on discrete element method

The purpose of this study is to further investigate the strength size effect and failure mechanism of asphalt mixtures and clarify the strength parameter conversion relationship between standard and non-standard size samples. The article established an improved microscopic model for uniaxial compression and indirect tensile testing of asphalt mixtures based on laboratory and discrete element simulation tests. The effects of thickness and gradation on the uniaxial compressive strength (UCS) and indirect tensile strength (ITS) of asphalt mixtures were studied. The loading rates of the UCS and ITS tests were set at 2 mm/min and 50 mm/min, respectively. Additionally, the tensile-compressive stress distribution, crack propagation, and strength contribution rates of different contact types within the sample were investigated during the virtual model loading process. The reliability of the model was validated through laboratory test results. Finally, the strength parameter conversion relationship between standard and non-standard size samples was investigated. The study found that the UCS of asphalt mixtures decreases with increasing thickness, while the ITS increases with increasing thickness, with average reduction and increase rates of 70.69 % and 24.18 %, respectively. The contact fracture ratio and the strength contribution rate of the aggregate-asphalt mortar contacts both exceed 50 %, indicating that the fracture of these contacts is the primary cause of asphalt mixture failure. The use of small-sized samples instead of standard samples in practical applications is promising. These research work outcomes can serve as a theoretical basis for designing asphalt pavement materials and acquiring existing asphalt pavement material parameters.

Study on the strength size effect of wastewater concrete under freeze-thaw cycles

In this study, the size effect on the strength of wastewater concrete under freeze-thaw cycles was evaluated. Cube specimens of wastewater concrete with side lengths of 40 mm, 100 mm, 150 mm, and 200 mm were prepared, and the resulting compressive and splitting tensile strengths after exposure to 0, 10, 20, 30, 40, and 50 freeze-thaw cycles were determined. The results show that the size effect is increasingly affected by freeze-thaw cycles with the increase in the number of cycles, while the corresponding specimen brittleness is gradually reduced, and the plasticity is enhanced. The modified Bažant size effect model considering the effect of freeze-thaw cycles on size effect was established. The modified size effect curve considering the freeze-thaw damage can be used to predict the initial strength of specimens after freeze-thaw cycles. The predicted data points were mainly distributed on the size effect curve and could directly reflect the size effect phenomenon of wastewater concrete without freeze-thaw cycles.

Study on the size effect of dynamic tensile strength in lightweight concrete using Leca aggregates at the mesoscopic level

To investigate the influence of volume fraction of lightweight aggregate concrete on dynamic tensile strength and size effect, theoretical derivation and microscopic numerical simulation are combined in this study, and a dynamic hybrid fracture cohesive zone constitutive model for lightweight aggregate concrete to characterize the tensile behavior considering strain rate at microscopic scale. The research reveals that, for geometrically similar specimens of various sizes, the direct tensile strength with different aggregate volume fractions exhibits differing degrees of improvement with increasing strain rates. The tensile strength gradually decreases as volume fraction increases. The established coupling function incorporating strain rate, specimen size, and aggregate volume fraction accurately characterizes the dynamic tensile strength variation. In addition, a theoretical framework is proposed to provide a microscopic understanding of the static-dynamic size effect. This framework facilitates the estimation of the dynamic tensile strength under specific volume fraction, specimen size and strain rate conditions.

Improved size effect law (SEL) considering size-dependent fracture process zone (FPZ) for quasi-brittle materials

Establishing a mechanistic model to simultaneously capture the descending size effect (DSE) and the change from DSE to the ascending size effect (ASE) remains a challenging issue for quasi-brittle materials. A size-dependent fracture process zone (FPZ) model is proposed and verified by experimental and simulative results. Subsequently, the size effect law (SEL) of unnotched specimens is improved by considering the size-dependent FPZ model, which is termed the improved SEL in this paper. Parametric studies are conducted for a better understanding of the improved SEL. It is found that the underlying mechanism of the DSE and the change from DSE to ASE is the competition between the relative rates of FPZ and specimen size change with respect to specimen size. The ASE is obtained when the relative rate of FPZ change is higher than that of specimen size. Conversely, the DSE is observed. No size effect exists when the relative rate of FPZ change is equal to that of specimen size. Experimental and simulative results are adopted to validate the improved SEL of unnotched specimens. The validation of the improved SEL indicates that the improved SEL not only accurately predicts the DSE, but also correctly captures the change from DSE to ASE. In addition, the size effect of nominal strength with different maximum aggregate size is well captured by the improved SEL. The fitting parameters of the improved SEL lie in the given interval. By comparing the determination coefficients R2 of the SEL, unified size effect law (USEL), and improved SEL, it is found that the R2 of the improved SEL is higher than that of the SEL for the DSE and is close to that of the IUSEL for the change from DSE to ASE. Therefore, it is recommended that engineers and researchers use the improved SEL to describe the DSE and the change from DSE to ASE of unnotched specimens.

A study of dimensional effects on the stress characteristics of Yunnan pine shafts considering seismic strain rates

Abstract The mechanical properties of wood are affected by member size and loading rate. Axial compression tests with different seismic strain rates and sizes of specimens were carried out to investigate the static and dynamic dimensional effects of Yunnan pine timber. And obtained load-displacement curves, compressive strength, modulus of elasticity, peak strain and Poisson’s ratio. Weibull’s weakest chain theory, Bazant’s law of dimensional effects and Carpinteri’s law of multiple fractal dimensional effects were used to analyze the dimensional effects on the compressive strength of wood, and to establish a wood strength model that takes strain rate effects and dimensional effects into account. The results showed that the compressive strength, elastic modulus, and Poisson’s ratio of Yunnan pine wood exhibit both size and strain rate effects. Under the coupling effect of strain rate effect and size effect, the size effect of Yunnan pine wood strength decreases with increasing strain rate, while the strain rate effect increases with increasing size. A size effect model for compressive strength of wood considering strain rate effect based on three theories and experimental data can well describe the dynamic size effect of Yunnan pine wood strength.

FE Analysis on Size Effect in Torsional Behavior of Rectangular RC Beams with and Without FRP Strengthening

Although torsion is usually considered a secondary consideration in structural design, it can lead to failures, especially in structures with irregular geometry exposed to seismic forces or in unique situations. While some studies have explored the size effect on the torsional behavior of RC beams, none have addressed the impact of reinforcement. This paper investigates the size effect on the torsional behavior of RC beams with varying reinforcement ratios, including both FRP sheets and steel rebars. In this study, the torsional behavior of reinforced concrete (RC) beams with and without FRP strengthening was investigated numerically. Modeling was carried out by Finite element (FE) software ABAQUS and validated using experimental data from literature. The torsional behavior of 24 models with differences in cross-section size and reinforcement ratio were investigated. Concrete damage plasticity, Hashin damage criteria, and von Mises stress were used to investigate the damage in concrete, FRP, and steel, respectively. The cracking torsional moment, ultimate torsional moment, and torque-twist curve of the beams were evaluated and presented. The results indicated the presence of a significant size effect in the torsional strength of beams. After reinforcing the beams with FRP fabrics, the average cracking moment increased by a range of 1.72% to 36% across different groups of beams. An 8.2% increase in ultimate strength is observed with just a 0.4% rise in the FRP strengthening ratio. Post-cracking behavior was seen in 8 models with adequate steel and FRP reinforcement ratio.

Experimental Investigation of the Size Effect on Roller-Compacted Hydraulic Asphalt Concrete under Different Strain Rates of Loading.

Asphalt concrete is widely used in hydraulic structure facilities as an impermeable structure in alpine cold regions, and its dynamic mechanical properties are influenced by the strain rate and specimen size. However, the specimen size has an important effect on mechanical properties; few systematic studies have investigated on the size effect of hydraulic asphalt concrete (HAC) under dynamic or static loading rates. In the present study, four sizes of cylindrical roller-compacted hydraulic asphalt concrete (RCHAC) specimens with heights of 50 mm, 100 mm, 150 mm, and 200 mm were prepared and tested under different loading rates ranging from 10-5 s-1 to 10-2 s-1 to investigate the size effects of mechanical properties and failure modes at the temperature of 5 °C. The effect of strain rate on the size effects of the compressive strength and the elastic modulus of RCHAC have also been explored. These tests indicate that when the specimen size increases, the compressive strength and failure degree decrease, while the elastic modulus increases. When the height increases from 50 mm to 200 mm, the compressive strength at different strain rates decreased by more than 50%. Furthermore, the elastic modulus increased by about 211.8% from 0.51 GPa to 1.59 GPa at a strain rate of 10-5 s-1, and increased by 150% from 5.08 GPa to 12.71 GPa at a strain rate of 10-2 s-1. As the strain rate increases, the variation trends with the size of the compressive strength, elastic modulus, and failure degree are distinctly intensified. A modified dynamic size effect law, which incorporates both the specimen size and strain rate, is proposed and verified to illustrate the dynamic size effect for the RCHAC under different loading rates.

Shear performance and size effect of CFRP strengthened RC beams

In this study, a 3D meso-scale numerical simulation method is established for analyzing the shear failure of carbon fiber reinforced polymer (CFRP) strengthened RC beams without stirrups. The inhomogeneity of concrete, the bond-slip relationship between steel bars and concrete, and the interaction between CFRP and concrete are considered. Based on this method, effects of shear-span ratio and CFRP fiber ratio on the shear performance and nominal shear strength size effect of CFRP strengthened RC beams are investigated. Results indicate that the size effect of CFRP strengthened RC beams is obvious, however, the shear-span ratio has little impact on the size effect of nominal shear strength of RC beams. The CFRP fiber ratio enhances the shear strength of RC beams on the one hand, while weakens the shear size effect of RC beams on the other hand. However, its influence on the shear performance of RC beams remains basically unchanged with varying shear-span ratios, indicating that there is no coupling effect between the shear-span ratio and CFRP fiber ratio. The shear-span ratio significantly influences both the shear bearing capacity of RC beams and the shear contribution of CFRP sheets, with the increase in the shear-span ratio, the shear bearing capacity of RC beams decreases to varying degrees, and the shear contribution of CFRP sheets increases initially and then decreases. Finally, the shear strength size effect law (SEL) of CFRP strengthened RC beams is proposed, which can quantitatively describe the effects of the shear-span ratio and the CFRP fiber ratio.

Behavior of High Strength Reinforced Cement Concrete with Polypropylene and Steel Fibres

The robustness, hardness, and longevity of high strength conventional concrete have long been sought after qualities. Fibre reinforced concrete (FRC) was created to address shortcomings. The purpose of fibres used is to control cracking and to enhance tensile strength, flexural strength, toughness, impact strength, and failure mode by enhancing post-cracking ductility. To study the influence of specimen size on the flexural behavior of high strength reinforced cement concrete of 60 MPa with hybrid fibres . The current work aimed to investigate the size effect of high strength, polypropylene and steel fibre reinforced RC beams under flexure loading more realistically in addition to that how specimen size affects the flexural behaviour of 60 MPa high strength hybrid fibre reinforced cement concrete. Correspondingly three cubes of size 150 mm x 150 mm x 150 mm and the cylinders of size 100 mm diameter, 200 mm height are also cast. Three RC beams of size 150 mm x 200 mm x 1000 mm (1A), 150 mm x 300 mm x 1500 mm (2A) and 150 mm x 400 mm x 2000 mm (3A) are cast. Three hybrid fibre reinforced concrete beams (HFRC) of size 150 mm x 200 mm x 1000 mm (1B), 150 mm x 300 mm x 1500 mm(2B) and 150 mm x 400 mm x 2000 mm(3B) are cast. All beams are provided with HYSD longitudinal reinforcement of 0.52% of the cross section at 0% and 1% fibres were added. Tests Such as Compressive strength test ,Split tensile strength test and Flexural strength test was conducted.

Modelling of Size Effect in Fatigue Strength for Welded Joints using Effective Notch Stress and Probabilistic Methods

Modelling of Size Effect in Fatigue Strength for Welded Joints using Effective Notch Stress and Probabilistic Methods

Structural size effect in the mode I and mixed mode I/II fracture of strain-hardening cementitious composites (SHCC)

The size effect in the fracture of solids represents a highly critical issue with a prolonged history of research. The size effect of traditional quasi-brittle materials can already be well described through the size effect model. However, there is still a lack of research on the size effect of strain-hardening cementitious composites (SHCC), a special type of fibre-reinforced concrete with macro-scale strain-hardening behaviour after first cracking. Being distinct from traditional quasi-brittle materials with softening nature, SHCC is thus expected to behave differently in terms of size effect. In this research, the structural size effect problem of SHCC is comprehensively studied by experimental investigation and theoretical analysis. Geometrically similar notched three-point bending specimens were tested in mode I and mixed mode I/II fracture condition. The whole-process of failure and matrix cracking zone around the main crack was captured with high resolution by digital image correlation technology. Experimental results showed that apparent fracture energy, nominal strength, structural ductility and fracture resistance curve are all structural size-dependent. The apparent fracture energy was shown to arise with specimen size within the tested range. This is related to large-scale pseudo yielding, i.e., enlargement of matrix cracking zone (like the yielding zone in metals) with increasing structural size. It thus provides an indirect method for the estimation of cohesive fracture energy of single crack with constitutive nature. Due to the scaled matrix cracking zone, an intermediate asymptote exists in the size effect curve of nominal strength, in addition to the plastic and LEFM asymptotes in the Bažant original size effect law. This resembles the recent finding of intermediate asymptote in plastic-hardening metal. The size-dependence of R-curve was also examined. Though size-dependent, the equivalent LEFM-based R-curves are shown to have three common stages reflecting different cracking processes. Based on experimental results, the size effect of fracture energy and nominal strength are finally modelled theoretically in the Bažant’s framework of equivalence between energy release and fracture resistance.

Study on pure-torsional size effect of CFRP-strengthened RC beams using a 3D meso-scale numerical model

In this paper, a 3D meso-scale numerical model for pure-torsional failure analysis of carbon fiber reinforced plastic (CFRP)-strengthened reinforced concrete (RC) beams is established. Three main aspects regarding the establishment of the numerical model are thoroughly considered, including the heterogeneity of concrete, the bond-slip relationship between steel bars and concrete, and the nonlinear interaction between CFRP and concrete. Effects of CFRP fiber ratio and span-height ratio on pure-torsional performances and size effect behaviors of CFRP-strengthened RC beams are analyzed. With the increase of CFRP fiber ratio, the cracks spacing decreases, the number of cracks increases, and the strain of CFRP decreases. With the increase of the span-height ratio, the inclination angle of the oblique crack decreases, and the strain of CFRP increases. It is found that CFRP-strengthened RC beams have an obvious torsional size effect. Furthermore, CFRP fiber ratio and span-height ratio not only have a coupling enhancement effect on the nominal torsional strength, but also have a coupling weakening effect on the size effect behavior. Based on the simulation results, a CFRP-related Torsional size effect law (SEL), which can quantitatively describe the influences of CFRP fiber ratio and span-height ratio on the size effect of nominal torsional strength of CFRP-strengthened RC beams, is established.

Size effect on tensile strength of interface between coarse aggregate and mortar under freeze-thaw cycle

Through the cleavage tensile test and freeze-thaw cycle experiment, the variation of tensile strength of mortar and interfacial bond-splitting tensile strength of coarse aggregate-mortar interface with different specimen sizes under freeze-thaw cycle was studied. The results indicate that the splitting tensile strength of the mortar specimen and the interfacial bond-splitting tensile strength of the coarse aggregate-interface specimen have a significant size effect, and the splitting tensile strength of the coarse aggregate-mortar interfacial specimen is significantly lower than that of the mortar specimen. At the same time, it is found that the statistical size effect model, the multifractal size effect model, and the fracture mechanics size effect model all can well describe the size effect of the split tensile strength of mortar specimens. Finally, considering the splitting tensile strength of standard mortar and the number of freeze-thaw cycles, a two-parameter size effect calculation model for the interfacial bond-splitting tensile strength of the coarse aggregate-mortar interface was established, basing on the Bažant-Xi statistical theory size effect correction formula, which was verified to be universal by experimental data.

Influence of heterogeneity on size effect models and fracture characteristics of plain concrete

Material heterogeneity strongly influences the fracture process zone in concrete, which is responsible for the exhibition of size effect in the nominal strength. The fundamental aspect in deriving the size effect law lies with the non-negligible process zone, which strongly correlates with the material heterogeneity size. Therefore, it is essential to establish the correlation between the size effect parameters and the heterogeneity size to predict fracture behaviour. In this work, detailed experimental investigations have been performed under the centre point loading of beams to evaluate the influence of heterogeneity on the fracture performance of plain concrete members through the DIC and AE techniques. A new definition of fully developed FPZ under monotonic loading has been proposed to occur between 95%–75% of the post-peak load. The effects of aggregate size on the fracture characteristics of concrete have been observed with reference to the work of fracture method (WFM), size effect law (SEL), and boundary effect method (BEM) and found in agreement with the existing literature. The existing size effect models, such as the size effect law and boundary effect model, have been modified by establishing the correlations between the model material parameters, namely, D0 and a∞ and the material heterogeneity. Finally, regression-based equations have been developed to establish the correlation between Lch, predicted through WFM, the effective lengths of fracture process zone, Cf of SEL, and Lch and a∞ of BEM. The applicability of the developed equations has been verified with the available experimental data from the literature.

DEM investigation on the size effect in the fragmentation of intact aggregates

In this work, the size effect in the fragmentation strength of cylindrical alumina aggregate under quasi-static diametrical loading is investigated by performing Discrete Element Method (DEM) simulations. It is found that tensile stress concentration develops in the inner margin of the damage zone, ultimately leading to the emergence and propagation of diametrical crack and thus the catastrophic splitting of the compressed aggregate. Both the fragmentation strength and the dimensionless damage zone size (normalized by aggregate diameter) decrease to limit values, and the latter is around 0.1. It is found that the obtained limit value of fragmentation strength is approximately equal to the tensile fracture strength of the corresponding rectangular sample having two equal-length side cracks with length being 0.1 times the sample width. The DEM simulations thus suggest that the formation of damage zones adjacent to the loading points would induce the size effect in the fragmentation of intact aggregate.