Size Effect In Strength Research Articles

Numerical modeling of size effect in shear strength of FRP-reinforced concrete beams

This study presents the numerical modeling of size effect in shear strength of FRP-reinforced concrete (RC) beams with and without stirrups by finite element analysis (FEA) model. The size effect was incorporated in the model by controlling the mesh size, softening tensile stress-strain response, and dilation angle. A new modification was suggested to represent the softening tensile strength of concrete for different size of beams. The calibrated FEA model for beams with and without stirrups showed great power and ability in simulating the experimental results in terms of ultimate shear capacity, ultimate deflection, flexural and stirrup strains, and crack patterns. Additionally, the calibrated model was then verified by thirteen experimental results from four different studies, as well as a parametric study was performed.

Strength size effect and post-peak softening in textile composites analyzed by cohesive zone and crack band models

In contrast to metals, the failure behavior of textile composites is quasibrittle, which entails salient structural behaviors such as the strength size effect and post peak softening. This paper presents a detailed account of numerical analysis of these aspects in woven textile composites undergoing translaminar tensile fracturing. Two of the most established fracture modeling techniques viz. the cohesive zone model (CZM) and the crack band model (CBM) are evaluated in this regard. The predictions from both techniques are compared to each other as well as to available test data on various woven composites. With a linear softening law CZM and CBM are seen to yield virtually identical results. A linear softening law is seen to be adequate to predict the strength size effect but it is not always able to accurately capture the full post-peak softening. Adapting a bilinear softening law, formulated via the R-curve approach, is seen to improve the post-peak softening predictions. Subsequently, it is shown that various numerical and physical parameters, such as the finite element type, manner of time integration (implicit vs explicit), mesh size, fracture energy, the crack band width, mass scaling, and stress state assumption could have a significant effect on the accuracy of the results, if set sub-optimally. Accordingly, recommendations for optimal settings are made.

Mesoscopic numerical simulation of dynamic size effect on the splitting-tensile strength of concrete

Under static loadings, concrete has been demonstrated to exhibit obvious size effect due to the heterogeneity of mesoscopic composition. Under dynamic loadings, the strain rate effect has a significant influence on the failure of concrete. It is therefore of great importance to explore the size effect of concrete under dynamic loadings. In this study, the focus is on the size effect in dynamic splitting-tensile strength of concrete. A mesoscopic numerical model for the simulation of the splitting-tensile failure and size effect at different strain rates (10−5/s ∼ 200/s) was established. The mesoscopic simulation results indicate that the size effect on the dynamic splitting-tensile strength of concrete has an obvious discrepancy with the static one. There is a critical strain rate in dynamic splitting-tensile strength of concrete. As the applied strain rate below the critical strain rate the size effect behavior is restrained and weakened gradually with the addition of strain rate. As the applied strain rate exceeds the critical strain rate the dynamic strength enhances linearly as the structural size increases. Furthermore, considering the contribution of strain rate on the dynamic size effect, a Static and Dynamic unified Size Effect Law (i.e. SD-SEL) for splitting-tensile strength of concrete was developed. The proposed SD-SEL was verified by the numerical results and the available test data.

Effect of Temperature on Small-Scale Deformation of Individual FCC and BCC Phases of Al0.7CoCrFeNi High Entropy Alloy

High Entropy Alloys (HEAs) represent an important class of structural materials because of their high strength, ductility, and thermal stability due to the solid solution nature of the multi-component metallic system. Understanding the mechanical response of isolated phases (FCC and BCC) of a dual-phase HEA is integral to understanding mechanical properties of these special alloys in bulk. We investigate the compressive response of single crystalline cylinders with diameters between 400 nm and 2 µm excised from individual grains within FCC and BCC phases of Al0.7CoCrFeNi HEA at 295 K, 143 K and 40 K. Micro-compression experiments were conducted in an in-situ SEM equipped with a custom-constructed cryogenic setup; FCC samples had a [324] crystallographic orientation, and those extracted from the BCC phase had a [001] orientation. We observed a smaller is stronger size effect in the yield strength as a function of pillar diameter, D, of both alloy phases for all temperatures, τ_y ∝D^m with a power law exponent, m, decreasing from -0.68 at 295K to -0.47 at 143K to -0.38 at 40K for FCC phase, and remaining constant at ~-0.33 for all temperatures for the BCC phase. We also observed reduced work hardening rates and more extensive strain bursts during deformation at lower temperatures in all samples. All deformed FCC samples contained multiple parallel slip offsets for all pillar sizes and temperatures; compressed BCC pillars had wavy slip traces, which are evidence of multiple intersecting slip systems. Transmission Electron Microscopy (TEM) microstructural analysis of the compressed FCC samples reveals parallel slip lines and distorted slip planes, while compressed BCC samples contained entangled dislocation networks, as well as several twinned regions in samples deformed at 40 K. Molecular dynamics (MD) simulations of representative FCC and BCC HEA compressions reveal that deformation in FCC HEAs is dominated by nucleation and propagation of partial dislocations along parallel slip planes but by partial dislocation/twinning in the BCC HEA at all temperatures. Simulations also predict a decrease in stacking fault energy with increased alloying. For example, a reduction in the stable stacking fault energy of the FCC HEA up to 55% with respect to pure constituents is observed. This reduction in stable stacking fault energy may drive the observed deformation mechanisms. We also discuss theories of low-temperature strengthening in HEAs, compare them to our experimental data and assess how they manifest in the observed temperature-dependent size effect.

Meso-scale modelling of the size effect on dynamic compressive failure of concrete under different strain rates

Great progresses have been made in static size effect of concrete, while almost no efforts have been conducted in dynamic size effect of concrete. The macro nonlinearity and size effect of concrete should be attributed to the inner heterogeneities. Herein, a meso-scale simulation method was built to study the dynamic failure and size effect of concrete. In the approach, the concrete heterogeneities were explicitly described, and the strain rate effect for the meso components were also taken into account. Taking squared concrete specimens as examples, the dynamic compressive failure and the size effect of concrete under different strain rates from 10−5/s to 200/s were modelled and investigated. The effect of strain rate on the size effect in compressive strength of concrete was also explored. The simulation results indicate that, there exists a critical strain rate (ɛ˙cr=1/s). When the applied strain rate is less than the critical strain rate, the compressive strength decreases with increasing the specimen size and the size effect on the dynamic compressive strength is weakened as the strain rate increases. The dynamic compressive strength turns to be independent on the structural size of the specimen for the critical strain rate. When the applied strain rate is more than the critical strain rate, the compressive strength increases with the increase of specimen size and the size effect on the dynamic compressive strength is enhanced as the strain rate increases. Finally, based on the influencing mechanism of strain rate effect to dynamic strength and size effect, a Static and Dynamic unified Size Effect Law (i.e. SD-SEL) for compressive strength of concrete was established. The proposed size effect law was also calibrated by the meso-scale simulation results.

Size Effect on Cracking Load of Recycled Aggregate Concrete Beam

Background: The cracking load is an important parameter in the design and testing of beam structures according to the recent patents. Compared to ordinary concrete, recycled aggregate concrete components are more prone to cracking. Methods: In this paper, the calculation method and the size effect of the cracking load for the recycled aggregate concrete beam were studied. Four recycled aggregate concrete beams with different sizes were tested by the four-point bending experiment to obtain their cracking loads. According to the comparison of the tested values and the calculated values by two existing methods, it was found that the existing calculation methods are only suitable for small-sized beam specimens. The main reason for the calculation error lies in the fact that the existing calculation method does not consider the size effect of tensile strength of recycled aggregate concrete. Results: It is very necessary to modify the existing formulas to calculate the cracking load more accurately for large-size beam specimens. Therefore, this paper presents an improved formula for the cracking load calculation by considering the size effect. The calculated results obtained by the proposed method are closer to the test values than those obtained by the original methods. Conclusion: It has been shown that it is necessary and reasonable to consider the size effect in the calculation of the cracking load of the recycled aggregate concrete beam.

Size effect on shear failure at core region of reinforced concrete connections: Experimental study

Fourteen geometrically-similar interior reinforced concrete (RC) beam-to-column connections whose maximum structural sizes were 700 mm ×700 mm were designed. The seismic performances of these RC beam-to-column connections subjected to monotonic and low-cycle loading were tested. The effects of loading type, structural size and stirrup ratio on the shear failure behavior at the core region of the connections were studied. Moreover, the size effect on the nominal shear strength of the core region of RC connections was examined, and the sources of size effect were also discussed. The test results and analyses indicate that: (1) all the RC beam-to-column connections under monotonic and low-cycle loading failed by shear; (2) due to the existence of low-cycle fatigue damage characteristics, the nominal shear strength of the joints under cyclic loading is lower, and the deformation capacity is weaker; (3) the nominal shear strength decreases with the increase of the structural size of RC connections, and size effect phenomenon is obvious; (4) with the increase of stirrups ratio, the shear bearing capacity and deformation capacity of RC connections increases, at the same time the size effect in shear strength is weakened. In this experiment, the dominant effect of concrete failure and the low-cycle fatigue characteristic of loading are the main reasons for the size effect of shear failure.

Mathematical Modeling of the Coupled Processes in Nanoporous Bodies

Abstract The methods of irreversible thermomechanics and functional analysis are used to formulate the mathematical model of thermoelastic solid body taking account of structural heterogeneity of the body material and geometric irregularity of its surface. The density and the chemical potential of skeleton among others are included into the state parameters space. The source of skeleton mass reconciles the actual and reference body states and may be associated with real surface forming method. The analysis of model problem solutions shows that the model is appropriate to describe coupled processes in porous and nanoporous bodies. It allows studying the size effects of strength, elastic moduli, etc. caused by near-surface non-homogeneity.

Experimental simulation investigation on rockburst induced by spalling failure in deep circular tunnels

Spalling and rockburst are two common failure modes in deep hard-rock tunnels and they exhibit a strong correlation. In this paper, the process of rockburst induced by spalling is investigated. The uniaxial compressive strength and rockburst tendency of red sandstone are measured. Four different initial stress conditions are set up, and cubic red sandstone samples with a prefabricated hole are tested by a true-triaxial test system. During the experimental process, the failure of the hole sidewall is monitored and recorded in real time by a micro-camera. The process of rockburst induced by spalling damage in deep hard-rock tunnels is reproduced, and the mechanism by which spalling damage on induces rockburst is revealed. In addition, the evolution process and failure characteristics of rockburst induced by spalling damage are analysed. The experimental results indicated that the red sandstone has a moderate rockburst tendency, and its rockburst process can be divided into four periods: the calm period, the small grain ejection & spalling damage period, the slab buckling & fragment ejection period and the violent ejection period. The mechanism of spalling damage on inducing rockburst is mainly embodied in two aspects: promoting large buckling deformations (providing energy for rockburst) and to weakening the strength of the rock mass (creating conditions for the suddenly release of energy). The effect of lateral stress on spalling damage and rockburst is more obvious than that of axial stress, and the severity of rockburst can be significantly reduced by increasing the lateral stress. The diameter of the hole has a strength size effect on the sidewall damage, producing a certain inhibitory effect on the spalling damage and rockburst. Smaller lateral stress corresponds with greater depths of the V-shaped notch and much smaller width-to-length ratios in the rock fragments.

Investigation of Size Effects in Slip Strength of Titanium Alloys: α Nodule Size Dependence of the Critical Resolved Shear Stress

Reported critical resolved shear stress (CRSS) values for basal and prismatic slip of titanium alloys are presently reviewed. Despite different average compositions, CRSS variations appear as mostly related to the α nodule size. Investigations of tensile tests performed in a scanning electron microscope reveal that the underlying size effect results from back stress generated by dislocations piling up at nodule boundaries. A relationship is proposed to predict CRSS for alloys with a given nodule size.

On the size effect of interfacial fracture between concrete and fiber reinforced polymer

In this study, the size effect of the nominal interfacial strength between concrete and fiber reinforced polymer (FRP) is investigated by integrating fracture tests and computational simulations. Three-point bending fracture tests are performed with geometrically similar specimens to demonstrate the size effect, and to measure fracture parameters for mode-I. Based on the measured fracture parameters, the crack-growth behavior is predicted using the finite-element-based cohesive zone model. Computational results predict accurately the experimental results of the load versus crack mouth opening displacement (CMOD) curves. Furthermore, both the computational and experimental results illustrate that the nominal interfacial strength decreases with increases in the specimen size, i.e., the size effect of the interfacial fracture. Because of the size effect, fracture parameters, such as the fracture energy, should be measured and evaluated to predict the interfacial fracture between concrete and FRP.

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.

3D-printed polymers exhibit a strength size effect

This study is an investigation on the size dependence of strength of a 3D printed acrylic polymer. 3D printed beams are used in three-point bend fracture experiments. Three print modes of the PolyJet process are used to manufacture beams of dimensions commonly considered in 3D printed structures (1–5 mm). It is found that for that range of dimensions, the fracture response is in the nonlinear size-strength domain and specimens neither follow the limiting linear elastic fracture mechanics nor the strength criterion. Consequently, strength and toughness are size dependent. Moreover, a strong interaction between specimen dimensions and print layer thickness was found. A size threshold exists below which there appears to be an interaction between specimen dimensions and print layer thickness, and for specimens of dimension below that threshold exhibit a declining strength with size. From the present experiments, the size threshold is estimated to be 50 times the print layer thickness. The finding of a maximum strength relative to geometric dimensions should be accounted for in designing with 3D printed materials.

The unusual size effect of eutectic Sn/Pb alloys in the micro regime: Experiments and modeling

Eutectic alloys are widely used as solder-joint materials due to their suppressed melting points, but when used in micro-devices with small dimensions, their characteristic lamellar microstructure may lead to an internal length scale that affects strength. Here, we report an unusual ‘smaller-being-weaker’ phenomenon in eutectic Sn/Pb alloys with fine lamellar microstructure, namely, in the specimen-size regime close to and slightly larger than the interphase lamellar spacing, the strength decreases with decreasing size, while above this regime the strength tends towards the bulk value. Theoretical modeling indicates that in a fine lamellar microstructure, high contents of dislocations are retained, so that strength is governed by mutual dislocation interactions, rather than by dislocation starvation. Therefore, in smaller samples, fewer interphase lamellar boundaries are present to block dislocations, thus resulting in a ‘smaller-being-weaker’ behavior. In samples a lot larger than the lamellar spacing, significant strengthening arises from Taylor hardening and mutual dislocation interactions as a result of significant dislocation retention by the interphase boundaries, so that strength does not depend on specimen size anymore. In a course lamellar microstructure, however, even a larger micro-specimen may contain insufficient interphase boundaries to significantly retain dislocations, and strength may be governed by the starvation effect due to significant loss of dislocations at free surfaces. In this case, the size effect of strength may become a lot milder, or even exhibit the conventional “smaller-being-stronger” behavior. The results here supplement conventional knowledge on size effects in micro-scaled crystalline materials, and provide important implications on solder-joint design in micro-devices.

DEM modeling of hydraulic fracturing in permeable rock: influence of viscosity, injection rate and in situ states

Hydraulic fracturing in permeable rock is a complicated process which might be influenced by various factors including the operational parameters (e.g., fluid viscosity, injection rate and borehole diameter) and the in situ conditions (e.g., in situ stress states and initial pore pressure level). To elucidate the effects of these variables, simulations are performed on hollow-squared samples at laboratory scale using fully coupled discrete element method. The model is first validated by comparing the stress around the borehole wall measured numerically with that calculated theoretically. Systematic parametric studies are then conducted. Modeling results reveal that the breakdown pressure and time to fracture stay constant when the viscosity is lower than 0.002 Pa s or higher than 0.2 Pa s but increases significantly when it is between 0.002 and 0.2 Pa s. Raising the injection rate can shorten the time to fracture but dramatically increase the breakdown pressure. Larger borehole diameter leads to the increase in the time to fracture and the reduction in the breakdown pressure. Higher in situ stress requires a longer injection time and higher breakdown pressure. The initial pore pressure, on the other hand, reduces the breakdown pressure as well as the time to fracture. The increase in breakdown pressure with viscosity or injection rate can be attributed to the size effect of greater tensile strength of samples with smaller infiltrated regions.

The effect of matrix shear strength on the out-of-plane compressive strength of CFRP cross-ply laminates

The failure mechanism of ‘indirect tension’ is explored for cross-ply IM7/8552 carbon fibre/epoxy laminates subjected to quasi-static, out-of-plane compressive loading. The sensitivity of compressive response to strain rate and to the state of cure is measured, motivated by the hypothesis that the out-of-plane compressive strength is sensitive to the matrix shear strength. A pressure-sensitive film is placed between specimen and loading platen, and reveals that a shear lag zone of reduced compressive traction exists at the periphery of the specimen, giving rise to a size effect in compressive strength. The width of the shear lag zone reduces with increasing shear strength of the matrix. The laminates fail by the indirect tension mechanism: out-of-plane compressive loading generates tension in the fibre direction for each ply and ultimately induces fibre tensile failure. Finite element (FE) simulations and an analytical model are developed to account for the effect of matrix shear strength, specimen geometry, and strain rate on the out-of-plane compressive strength. Both the FE simulations and the analytical model suggest a recipe for increasing the through-thickness compressive strength.

Scatter prediction and size effect of ceramics strength by finite element analysis

Scatter prediction and size effect of ceramics strength by finite element analysis

Prediction of notch size effect in tensile strength of carbon/epoxy quasi-isotropic laminates

Prediction of notch size effect in tensile strength of carbon/epoxy quasi-isotropic laminates

A generalized weakest-link model for size effect on strength of quasi-brittle materials

The work contributes to the statistical approach to unitedly characterize the random variation and size effect of brittle fracture strength of materials. Current practices rely on the conventional Weibull statistics and more recently on the weakest-link statistical model conforming to the uniform spatial distribution of microcracks. Based on the understanding that the weakest-link postulate is built on the mutual independence of microcracks and is not necessarily bounded to the uniform spatial distribution of microcracks, this work develops a generic weakest-link statistical formulation pertaining to a power-law spatial distribution of mutually non-interactive microcracks to synchronize the random variation and size effect of brittle fracture strength. The formulation encompasses both Weibull statistics and the uniform spatial distribution law-based weakest-link model as its subordinate members. A resultant master curve behavior between a compound parameter and the nominal fracture strength is identified for size scaling of strength and is validated by the strength data of a wide spectrum of quasi-brittle materials including wood, concrete, coal, gamma titanium aluminum alloy, nuclear-grade graphite and aluminum foam on geometrically self-similar specimens under same loading conditions.

The size effect in the mechanical strength of semiconductors and metals: Strain relaxation by dislocation-mediated plastic deformation

Abstract