Increasing Specimen Size Research Articles

Evaluating the impact of specimen and punch sizes on the tensile strength of UHPC through double punch testing

Many studies have shown that direct tensile tests are fraught with numerous challenges. The Double Punch Test (DPT) is considered a more reliable alternative for evaluating tensile properties among the indirect tensile methods. While DPT is efficient and reliable, its size effect should not be overlooked. Previous studies on DPT size effects have primarily focused on specimen size, with little discussion on the impact of punch size variations. Additionally, with the evolution of construction materials, the applicability of the generalized DPT formula to new materials, such as Ultra-High-Performance Concrete (UHPC), with its exceptional strength, toughness, durability, and crack resistance, needs to be evaluated. This study conducts experimental research on UHPC, focusing on the relationship between specimen and punch sizes and their impact on tensile strength measurements. By designing experiments with 12 different specimen sizes and punch ratios, we explore the differences between actual experimental results and simplified formula calculations. Bažant's theoretical methods are also applied to analyze the size effects of specimen and punch dimensions on DPT. The results indicate that, with appropriate specimen size and punch ratio, DPT can provide tensile strength measurements closer to those of Direct Tensile Tests (DTT). It was also found that tensile strength, strain, and toughness decrease with increasing specimen size. When the ratio of UHPC specimen to punch size (d/D) is 1/3, the results align well with the predictions of the simplified formula. This indicates that the optimal punch ratio is not fixed for different specimen sizes. These findings offer valuable references for designing related experiments and improving quality control and structural performance in various engineering fields.

Effect of size and anisotropy on fracture process zone of coal: An experiment and numerical simulation

The size and properties of the fracture process zone (FPZ) have a significant impact on the fracture toughness of materials. Researching and understanding the characteristics of FPZ contribute to optimizing material performance and enhancing the reliability of engineering structures. In this study, the newly proposed modified semi circular bending (SCB) test method was used to carry out the pure mode I fracture test of coal samples with four sizes and four bedding angles, the development process of FPZ was obtained by using digital image correlation method, and the cohesive zone model considering the bedding plane was established. The influence of size and anisotropy on the development and size of FPZ was studied, and the influence mechanism of FPZ on the size effect and anisotropy of fracture toughness was revealed. The results show that the FPZ length of coal has obvious size effect and anisotropy. The FPZ length increases with the increasing specimen size, and increases first and then decreases with the increasing bedding angle. The FPZ relative length decreases with increasing specimen size, indicating that as the specimen size increases, the influence of specimen boundaries on PFZ gradually decreases, and the size effect of fracture toughness also gradually weakens. The competition between microcrack development driven by principal stress and microcrack development driven by bedding plane results in anisotropy in the development process of FPZ. The anisotropy of FPZ development process results in the anisotropy of FPZ length, fracture toughness and crack propagation path. The research findings can provide valuable guidance for the design of hydraulic fracturing in coal seams.

Investigation on the size effect of compacted clay mode I fracture based on NDB specimens

The size effect is closely related to the cracking resistance of compacted clay, which is crucial in engineering applications, but little attention has been given to it in previous studies. This study investigated the size effect on mode I fracture behaviors of compacted clay using single-edge notched deep beam (NDB) specimens. Through the digital image correlation (DIC) method, the crack initiation mechanism of compacted clay was analyzed. The results showed that the specimen size and dimensionless crack length did not change the failure pattern, while peak load, peak displacement, and fracture energy gradually increased with the increase of specimen size. Based on the load–displacement curves and the horizontal strain evolution laws, the three horizontal strain stages at the crack tip crack initiation point were defined, i.e., the steady strain growth stage, the nonlinear strain growth stage, and the nonlinear strain intensification stage. Through the Bažant size effect model (SEM), the fracture process zone length Cf and mode I fracture toughness KIC of compacted clay without the size effect were inferred. The separated form of SEM was applied, and the contribution ratios of the strength criterion and linear elastic fracture mechanics were quantitatively analyzed. Combing the characteristics of the NDB specimens, a prediction model considering the support spacing, specimen structure parameters, and fracture toughness was established.

Experimental investigation on the size-dependent CFRP shear contribution in CFRP-strengthened RC shear wall

Most of the current methods for estimating the shear contribution of CFRP are based on laboratory testing of small-sized specimens. The applicability of the current codes on large-sized FRP-strengthened shear walls remains debatable. The present study addresses the problem by investigating the combined effects of structural sizes and CFRP ratios on the shear contribution of CFRP. Through experiments, a series of geometrically similar CFRP-strengthened RC shear walls were designed and subjected to a cyclic horizontal loading. From the experiments, the following results can be obtained. The application of the externally bonded CFRP strips alters the failure mode and enhances remarkably the seismic resistance by suppressing crack propagation and increasing the energy dissipation. The increasing specimen size reduces the enhancement effects of CFRP on the nominal shear strength, ductility, and energy dissipation. These findings indicate that without considering the size effect, the effective strain that reflects the shear contribution of CFRP strips are greatly overestimated by the current codes. Therefore, the present study proposed and validated an effective strain factor capturing the combined effects of the structural size and the CFRP ratio on the shear contribution of CFRP strips, serving in assessing the shear strengthening effect of CFRP on shear walls.

A new probabilistic control volume scheme to interpret specimen size effect on fatigue life of additively manufactured titanium alloys

The effect of specimen size on the fatigue performance of additively manufactured (AMed) Ti-6Al-4V is investigated in this paper. The fatigue tests of Ti-6Al-4V specimens made by laser powder bed fusion were conducted via ultrasonic axial cycling up to very-high-cycle regime with stress ratio R = –1. The S-N data of five group specimens show an evident size effect, that is, with the increase of specimen size, the fatigue life or fatigue strength decreasing gradually. A new probabilistic control volume scheme is developed to evaluate the fatigue life of large sized specimens by the tested data of small sized specimens. The applicability of the proposed model is validated by the present data and those of our previous investigation. Moreover, a general form of probabilistic control volume model is derived to show the original and present models are the special cases for conventional cast and AMed alloys.

Mechanical and fracture characteristics in center cracked circular discs of coal specimens with different sizes: An experimental investigation

The propagation of cracks on a small scale can result in dynamic disasters, such as rock bursts induced by large-scale fractures in coal seams. To gain insights into the mechanism of fracture-induced disasters in deep coal seams, this study investigates the micro-process and size effect of crack propagation in coal specimens featuring different sizes of center-crack circular discs (CCCD). We conducted Brazilian splitting tests on coal samples with varying dimensions and employed acoustic emission (AE) and digital image correlation (DIC) techniques to quantitatively describe the crack propagation process. Additionally, coal specimens of different diameters were compared for the size effect characteristics of different fracture parameters during the tensile failure process. The results show that as the specimen size increases, quasi-brittle failure characteristics become pronounced, tensile strength gradually decreases and stabilizes, while fracture toughness and fracture process zone length gradually increase and tend to stabilize. The macroscopic cracks in the coal specimens generally extend from the centre of the specimen to both ends along the precracks. Large energy events are mainly concentrated at the lower end of the precracks. As coal specimen size increases, the number of AE events decreases, while the proportion of large energy events gradually increases, and the critical crack opening quantity exhibits a linear increase with specimen size. By conducting the fracture size effect experiment on coal specimens, we extend the relevant mechanical parameters from laboratory-scale tests to field engineering scales. This provides fundamental parameters for the analysis of large-scale fracture process of in-situ coal based on fracture mechanics.

Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture

A large structural size effect on brittle fracture energy was observed in studies of impact fracture of steels by Stanton, Batson and Docherty, nearly 100 years ago. The size effect was seen in macroscopically brittle fractures of geometrically similar specimens tested over a large size range. These historical findings have great significance in designing large-scale steel structures such as ships and bridges. However, there has been no physical principle or theory yet to explain the size effects observed by Stanton, Batson and Docherty. In the present work, a new approach based on net-section mechanics is used to explain the size effect. It is shown that the change in net-section strain energy predicts well the size effect on fracture energy , under the constant condition of cleavage crack initiation stress at the notch root. The spectacular decrease in specific fracture energy with increased specimen size is explained by noting the three-dimensional nature of stored strain energy and the two-dimensional nature of fracture energy dissipated in the crack layer. By scaling both energies to a reference cubic specimen volume and equating, an expression that describes the inverse size dependence of specific fracture energy has been formulated. The mechanics of the size effect is illustrated by assessing the theory with extensive experimental data. Further, scaling laws for fracture energy have been developed. This work honours the pioneering studies of Stanton, Batson and Docherty, which have been instrumental for the development of the present theory and analysis.

Characterization of crack-bridging and size effect on ultra-high performance fibre reinforced concrete under fatigue loading

The use of ultra-high performance fibre-reinforced concrete (UHPFRC) has become popular owing to its high strength, durability and toughness characteristics compared to conventional concrete. In this work, experimental investigations have been carried out to examine the fracture behaviour of UHPFRC beam specimens under static and fatigue loading with an emphasis on understanding the size effect. Experimental results of both monotonic and fatigue have been utilized to develop a mathematical formulation for predicting crack bridging degradation considering the fatigue loading history. Subsequently, the size effect behaviour on the crack-bridging strength of UHPFRC beams under fatigue loading conditions has been explored. An algorithm has been developed to predict crack propagation as a function of load cycles and to estimate the fatigue life corresponding to any load amplitude, accounting for the size effect. The crack-bridging strength has been observed to decrease with an increase in specimen size, lowering the fatigue life.

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.

A theoretical model for the prediction of fracture process zone in concrete under fatigue loading: Energy based approach

Characterizing the fracture behaviour of concrete and accurately predicting its service life under fatigue loading poses a significant challenge due to its heterogeneous nature and complex fracture mechanisms. The proposed study focuses on developing an energy based theoretical formulation for predicting the evolution of the fracture process zone throughout repetitive loading cycles. A stiffness degradation approach has been adopted for developing the formulations for the critical energy dissipation and fully developed fracture process zone. Subsequently, the proposed analytical expressions have been calibrated and validated by performing experiments under centre point bending and using available experimental results in the literature. Experiments have been conducted on a centre-point bend beam with varying aggregate size in conjunction with the digital image correlation (DIC) technique to estimate the fracture characteristics. The influence of specimen size and heterogeneity has been discussed in the context of predicting the fracture behaviour, critical dissipated energy, and process zone length of plain concrete beam specimens under fatigue loading. The results indicate that the process zone length and critical energy release rate increase with an increase in specimen size, while the same decreases with an increase in aggregate size.

Effect of size and anisotropy on mode I fracture toughness of coal

Obtaining the accurate fracture toughness of coal considering bedding angle and independent of size is of great significance to the evaluation of the initiation pressure in the hydraulic fracturing of coal seam. In this study, the newly proposed modified semi-circular bending test was used to conduct mode I fracture testing of coal samples with different sizes and bedding angles. A four-dimensional lattice spring model (4D-LSM) was established based on the cohesive zone model considering bedding planes to study the effects of specimen size and bedding angle the fracture toughness and fracture pattern of coal. The size effect and anisotropy characteristics of fracture toughness of coal were analyzed by using linear elastic fracture mechanics and Bazant size effect law (SEL) theory. The results show that the fracture toughness of coal has obvious size effect and anisotropy. In quasi-brittle materials, the fracture toughness increases with the increase of specimen size due to the fracture process zone (FPZ). However, the fracture toughness of coal affected by microcracks generally decreases with the increase of specimen size. The size effect of fracture toughness of coal is jointly determined by the FPZ with increasing effect and the microcrack with reducing effect. The fracture toughness of coal increases with the increase of bedding angle. The bedding angle has no influence on the fracture toughness size effect of coal, but the microcracks associated with the bedding plane have a greater influence on the fracture toughness size effect. The specimen size only affects the fracture toughness value, but has no obvious effect on the fracture toughness anisotropy. Based on Bazant SEL theory, a fracture toughness size effect model considering microcracks and bedding angles was established. The research results have reference significance for crack initiation and propagation in hydraulic fracturing of coal seam.

Fracture process zone in crystalline rock: effect of specimen size and shape

Ability to predict fracture properties of granular materials based on their size and loading conditions needs rigorous experimental evidence. Charcoal granite specimens of various sizes and geometries are tested under three- and four-point bending to investigate the effect on the fracture toughness of rock and size of the fracture process zone calculated using Digital Image Correlation (DIC), with validation provided by Acoustic Emission (AE). Two different methods to evaluate the length of the fracture process zone using DIC are adopted: the first one assumes that a traction free crack does not propagate in the pre-peak regime, while the second one hypothesizes that a cohesionless crack may exist at peak load before unstable crack growth. The effects of specimen size, geometry, and loading conditions are found to be more prominent for the specimen sizes used in the laboratory but are predicted to become less significant and eventually negligible as the specimen size increases. DIC results are in general agreement with localization of AE events, but the former technique is suggested due to greater resolution and ability of continuous measurements of the fracture process zone dimensions.

Permanent Deformation Evaluation and Instability Prediction of Semi-rigid Pavement Structure Using Accelerated Pavement Testing and Finite Element Method

Abstract A rutting prediction method for semi-rigid pavement structures using accelerated loading tests and finite element analysis was proposed in this study. Firstly, dynamic modulus and creep tests of three pavement materials were performed by changing sizes and temperatures. The prediction equation was obtained and verified using the falling weight deflectometer test and back-calculation modulus, and it was coupled into a modified Burgers model for rutting simulation for full-scale pavement structures. Results showed that the dynamic modulus of pavement materials increased with increasing specimen sizes and decreased with increasing temperature. SUP-25 had an enormous fatigue damage value (0.419) after 5,400 times repeated loading. The error between the rutting simulation and test results was 2.87 %, indicating that the model effectively applies to multilayer composite materials. Rutting deformation at one million loading times in summer was 4.6 times that in winter. From 22 to 120 km/h, rutting deformation decreased by 72.6 %. Axle load increased by 100 %, and rutting depth increased by 46.9 %, indicating that vehicle overload should be restricted, especially in low-speed sections in high-temperature areas. Rutting deformation entered the accelerated accumulation stage when the cumulative action times were more than 25 million, which requires timely maintenance and repair of pavement structures.

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.

Long-term strength and deformation size effect of gangue cemented backfill in acid mine water

The mine water environment can seriously affect the long-term strength and deformation of the backfill body, thereby affecting the stability of the goaf. In this study, the gangue cemented backfill (GCB) of different sizes were placed in different environments (air, water, single H2SO4 solution, and H2SO4 solution coupled with load), the deformation and ultrasonic pulse velocity (UPV) of specimens were recorded with age. The compressive strength, acoustic emission (AE), and resistivity of GCB during the uniaxial compression at 360 days were monitored. In addition, the microscopic morphology of GCB was observed by scanning electron microscopy (SEM), and the damage model of GCB in the process of uniaxial compression was established. The research showed that: the deformation of GCB was fast in the first 90 days and gradually slowed down. The bigger the size was, the greater the instantaneous creep of the GCB was, and the faster the increase rate of the initial deformation was. The UPV of eroded GCB experienced three stages of growth-stability-decrease. The UPV of the smaller GCB increased rapidly in the early stage and decreased rapidly in the later stage. At 360 days, the order of compressive strength of GCB in different media is: water > air > single H2SO4 solution > H2SO4 solution coupled with load, and the compressive strength decreases with the increase of specimen size. In the process of uniaxial compression, the larger the size of the GCB, the larger the number of AE rings detected. The smaller the size of GCB, the stronger the AE characteristics appeared in the initial compaction stage. During the loading process, the resistivity curve of GCB changed approximately in a “U” shape. The smaller the size of GCB, the slower the increasing rate of resistivity in the post-peak failure stage. The abrupt change in the AE ring and the stable resistivity stage could be used to predict the failure of the GCB. The research could provide a reference for the design of the erosion resistance of GCB.

Scaling effects on the strain rate sensitivity of unidirectional and [+45/−45]s laminates under tensile loading

The effects of geometric scaling on the strain rate sensitivity of unidirectional and [+45/−45]s laminates under uniaxial tensile loading has been investigated experimentally. Two material systems, Toray T800/3900-2B carbon/epoxy unitape and Newport NB321/7781 fiberglass/epoxy fabric, were used in the study. The nominal strain rates investigated ranged from quasi-static (0.0002 s−1) to moderate strain rates of 50 s−1 across the scaled specimen geometries. The geometric scaling effects at different strain rates were quantified in terms of the Weibull modulus. At each strain rate, the average failure stress of [0]4 carbon, [0]4 fiberglass, and [±45]s fiberglass showed a declining trend with increasing specimen size. However, the percentage of the strength reduction was less significant at higher strain rates compared to the quasi-static strain rate. In contrast to the other stacking sequences, [+45/−45]s carbon specimens showed a maximum percentage in strength reduction at a high strain rate compared to the quasi-static strain rate, indicating increased scaling effect with strain rate. The magnitude of Weibull modulus ( m) for the specimens increased with strain rate indicating diminishing scaling effects, while [+45/−45]s carbon specimens exhibited an opposite trend.

Assessing CO2 uptake of CO2-cured cement mortar through theoretical modeling and experimental validation

CO2 curing of cement-based materials is considered a promising carbon–neutral technology for large-scale storage of CO2, and CO2 uptake is the key parameter for evaluating CO2 storage capacity. This study assessed the CO2 uptake of cement mortar subjected to flue gas curing through theoretical modeling and experimental validation. It is found that the CO2 uptake for the high-concentration group is higher at early stages but becomes the same after sufficient curing, asthe higher CO2 concentration accelerates the diffusion process but has little effect on the carbonation process. Meanwhile, although the initial CO2 uptake for the smaller specimens is larger, the difference gradually decreases with curing time after overall curing. Achieving overall curing is an effective way to ensure high carbonation rate and CO2 uptake. The CO2 uptake at overall curing increases with increasing specimen size or decreasing CO2 concentration. For fixed-depth CO2 curing, the CO2 uptake decreases significantly with increasing specimen size, while the curing time and carbonation degree change little. The findings of the present work will be beneficial to improve the CO2 storage capacity of cement-based materials and push forward the application of CO2 capture, utilization and storage (CCUS) technology in the construction industry.

Experimental assessment on the size effects of square concrete-filled steel tubular columns under axial compression

In this study, eight specimens with the sectional widths (B) of 200–1000 mm and the width-to-steel tube thickness ratios (B/t) of 40 and 50 were tested to failure under axial compression to investigate the size effects of square concrete-filled steel tubular (CFST) short columns, specifically those on the failure mode, composite elastic modulus, peak axial strain, peak axial stress, ductility index, strength index, and stress development. The test results indicate that the peak axial stress, ductility index, and strength index decrease with the increasing specimen size, while the failure mode and composite elastic modulus maintain relatively steady. Under the peak axial load, the longitudinal to yield stress ratio of steel tubes increases with the increasing specimen size, while the trend of transverse to yield stress ratio is opposite. The size effect on the transverse stress in the steel tube reduces the tube confinement effect, thus degrades the compressive strength of the core concrete. Compared to the test results, both the EC4 and the GB50936 codes are unconservative in predicting the strength of large square CFST columns. Therefore, a model considering the ratio of width to thickness (B/t) and specimen size is proposed to evaluate the axial bearing capacity of square CFST short columns.

Hierarchical scaling model for size effect on tensile strength of polycrystalline rock

Here, we proposed an analytical model for quantifying the intriguing size-dependent tensile strength of polycrystalline rock, i.e. first ascending then descending with the increase of specimen size. The meso‑structure of polycrystalline rock was firstly degraded to a hierarchical arrangement of regularly cuboid mineral grains. The tensile strength distribution of mineral grain interface (GI) is modeled by Weibull distribution, and the stress state near the failed GI is analytically calculated. Then a probabilistic analysis of the failure evolution in hierarchical mineral grain sets (sets of sets) was performed by considering the meso crack initiation at the GI to their propagation at macro scale, so that the tensile strength distribution and the meso crack accumulation in the rock specimen can be derived. The consistency between the model predictions and experimental results demonstrates the proposed model is valid. In addition, the results revel that the size effect trend, ascending or descending, is determined by the dispersion degree of structure strength distribution.

Experimental study of bamboo scrimber-filled steel tube columns under axial compression

A new bamboo scrimber-filled steel tube (BSFST) structure consisting of a steel tube with bamboo scrimber is presented. The proposed structure can be used as an alternative to nonrenewable construction materials. To investigate the axial behavior of the structure, thirty bamboo scrimber and thirty BSFST columns were tested under axial compression. Specimen size and steel tube thickness were used as the test parameters. The results showed that for the unconfined bamboo scrimber, the failure mode changed from shear failure to split failure, and the ultimate stress decreased gradually with increasing specimen size. Based on the test results, the ultimate stress relationship between different sizes of bamboo scrimber was clarified, and a formula for the size effect was proposed. For the BSFSTs, the main damage mode was shear damage. With increasing steel tube thickness, the mechanical properties of the specimens increased greatly. Formulas for the calculation of the ultimate stress and ultimate strain of BSFST were proposed. According to the stress–strain curves of the BSFSTs, the characteristic points were defined, a formula for the calculation of characteristic points was suggested, and models of complete stress–strain curves BSFSTs were proposed. The proposed models accurately predicted complete stress–strain curves of the specimens used.