•The energetic and statistical size effects in quasibrittle structures are critically analyzed.•Size Effect Law (SEL) is in excellent agreement with a large bulk of experimental data.•SEL agrees ...asymptotically with Cohesive Fracture Mechanics.•The main errors, weaknesses and inconsistencies of the Boundary Effect Model (BEM) are identified.•The BEM features incorrect large and small-size asymptotic size effects.•The BEM conflicts with broad-range comprehensive test data and with the cohesive crack model.•The BEM predicts an incorrect aggregate-size dependence of strength.•The BEM features an illogical dependence on the ligament stress profile.•The BEM cannot to capture the statistical part of size effect at large sizes.•The BEM does not capture the difference between type I and II size effects.
For several decades it has been clear that the size effect on structural strength, exhibiting a major non-statistical component, is a quintessential property of all quasibrittle materials. However, progress in design codes and practice for these materials has been retarded by protracted controversies about the proper mathematical form and justification of the size effect law (SEL). A fresh exception is the American Concrete Institute which, in 2019, becomes the first concrete code-making society to adopt the SEL based on quasibrittle fracture mechanics. This article begins by discussing several long-running controversies that have recently abated, and then focuses critically on the so-called Boundary Effect Model (BEM), promoted for concrete relentlessly for two decades, in ever-changing versions, by Xiaozhi Hu et al. The BEM is here compared to the quasibrittle SEL based on asymptotic matching. Its errors, weaknesses and inconsistencies are identified—including incorrect large- and small-size asymptotic size effects, conflicts with broad-range comprehensive test data and with the cohesive crack model, incorrect aggregate-size dependence of strength, illogical dependence on ligament stress profile, inability to capture the statistical part of size effect at large sizes, simplistic effect of boundary proximity, and lack of distinction between Type 1 and 2 size effects. In contrast to the SEL, the BEM is not applicable to mixed and shear fracture modes and to complex geometries of engineering structures, and is not transplantable from concrete to other quasibrittle materials.
The purpose of this critique is to help crystallize a consensus about the proper size effect formulation, not only for concrete structures but also, and mainly, for other quasibrittle materials and structures, including airframes made of fiber composites, ceramic components and micrometer-scale devices, and for failure assessments of sea ice, rock, stiff soils, bone, and various bio- or bio-mimetic materials, for all of which the non-statistical size effect is yet to be widely accepted in practice.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Dynamic compressive failures of 150 squared concrete specimens are simulated at meso-scale under dynamic loadings. (The applied strain rates are: 10–5/s, 10–3/s, 10–2/s, 10–1/s, 1/s, 10/s, 30/s, ...50/s, 100/s and 200/s. The widths of the specimens are: b = 100, 150, 300, 450 and 600 mm.)•The size effect in dynamic compressive strength of concrete under different strain rates is investigated.•The contribution of strain rate in dynamic compressive size effect can be divided into two parts: the strength enhancement, and the weakening and reverse enhancement of size effect.•The proposed Static and Dynamic unified Size Effect Law (SD-SEL) in this study can reflect the relation between dynamic size effect and static size effect, and it can well describe the size effect on the compressive strength of concrete under different strain rates of 10–5∼200/s.
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.
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In this paper, the governing equations of torsional porous flexoelectric microtubes made of functionally graded (FG) materials are investigated and obtained for the first time. First, the governing ...electromechanical coupling equations of the problem are extracted, and to achieve this goal, a modified non-classical flexoelectric theory has been used to derive these equations. The independent parameters of polarization in enthalpy relationships and the mechanical and electrical size effect are the important points in this theory. Noted that the independent parameter effects of polarization, mechanical and electrical size that is considered for the first time in this paper, are the capability of this theory, and the effect of these parameters is evaluated on direct and reverse flexoelectric. After that, the static analysis and free vibrations have been reviewed. And in the conclusion section interesting and valuable results have been obtained, that could help the torsional micro-sensors and torsional micro-actuators designers.
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•Dynamic splitting-tensile failure of concrete is simulated at the meso-scale.•Size effect on dynamic splitting-tensile strength of concrete is explored.•Dynamic size effect in concrete is obviously ...distinct with static one.•A static and dynamic unified size effect law is proposed.
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.
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•Dynamic tensile failure of 135 double-edge notched concrete specimens are simulated at mesoscopic under dynamic loadings.•The size effect in dynamic tensile strength of concrete under different ...strain rates is investigated.•The proposed Static and Dynamic unified Size Effect Law in this study can well describe the size effect on the tensile strength of concrete under different strain rates.
The macro nonlinearity and size effect of concrete are essentially attributed to the internal heterogeneity of concrete. Considering the heterogeneities and the strain rate effect of meso-components, the concrete was modelled as a three-phase composite composed of aggregate particles, mortar matrix and the interfacial transition zones (ITZs). Taking double-edge notched concrete specimens as examples, a meso-scale numerical model for the simulation of the failure and size effect of concrete under dynamic tensile loading with different strain rates from 10−5/s to 100/s was established. The effect of structural sizes on the dynamic tensile strength of concrete was explored. The numerical results indicate that dynamic size effect on tensile strength of concrete has an obvious discrepancy with the static one. There exists a critical strain rate (ε˙cr = 1/s), and at the strain rate the dynamic tensile strength turns to be independent on the structural size of the specimen. For the case less than the critical strain rate, the tensile strength decreases with increasing the specimen size, and the size effect on the dynamic tensile strength is weakened or suppressed as the strain rate increases. For the strain rate larger than the critical one, there is no obvious difference in the dynamic tensile strength of the concrete specimen having different structural sizes, and the corresponding size effect completely disappears. According to the influencing mechanism of strain rate effect and size effect, a Static and Dynamic unified Size Effect Law (i.e. SD-SEL) for tensile strength of concrete was built. The proposed SD-SEL was also verified by the mesoscopic numerical simulation results.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
As the NN bond in N2 is one of the strongest bonds in chemistry, the fixation of N2 to ammonia is a kinetically complex and energetically challenging reaction and, up to now, its synthesis is still ...heavily relying on energy and capital intensive Haber–Bosch process (150–350 atm, 350–550 °C), wherein the input of H2 and energy are largely derived from fossil fuels and thus result in large amount of CO2 emission. In this paper, it is demonstrated that by using Au sub‐nanoclusters (≈0.5 nm ) embedded on TiO2 (Au loading is 1.542 wt%), the electrocatalytic N2 reduction reaction (NRR) is indeed possible at ambient condition. Unexpectedly, NRR with very high and stable production yield (NH3: 21.4 µg h−1 mg−1cat., Faradaic efficiency: 8.11%) and good selectivity is achieved at −0.2 V versus RHE, which is much higher than that of the best results for N2 fixation under ambient conditions, and even comparable to the yield and activation energy under high temperatures and/or pressures. As isolated precious metal active centers dispersed onto oxide supports provide a well‐defined system, the special structure of atomic Au cluster would promote other important reactions besides NRR for water splitting, fuel cells, and other electrochemical devices.
Using Au sub‐nanoclusters anchored on TiO2 substrate as a heterogeneous electrocatalyst, the special Au active sites lead to the effective and stable electrochemical N2 reduction reaction with high NH3 yield (21.4 µg h−1 mg−1cat.) and Faradaic efficiency (8.11%) as well as 100% NH3 selectivity at ambient conditions.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
This paper presents a discussion on the subject of fracture energy of concrete and effective parameters. Therefore, it serves as an overview of the available approaches in determining the fracture ...energy. It also includes experimental methods which form the basis for measuring the fracture energies obtained from work of fracture (GF) and size effect models (Gf) and thus provides a comparison between different models. Furthermore, the behavior of the load-displacement curve, factors affecting the fracture energy and the crack path in the specimen are discussed. In order to build a background for the current understanding of fracture energy, references from both former and present authors are included to tie the subject together within the course of time.
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•A strain energy-based critical damage region is defined for fatigue modeling;•The effective strain energy density concept is utilized for fatigue analysis under notch and size effect;•A novel ...fatigue life prediction model combining weakest link theory with strain energy concept is proposed;•A general probabilistic procedure for notch fatigue modelling under size effect is presented;•Experimental data of GH4169, TC4 and TC11 alloys verified the model predictions accuracy.
Notch fatigue analysis is vital for structural integrity design, while efficient fatigue models coupling notch and size effect are still lacking, which are highly desired for fatigue design of critical components. Accordingly, this study proposes a new probabilistic fatigue model for life assessment by combining the weakest link theory with strain energy concept. Specifically, a novel effective strain energy density concept is developed herein to build the connection between experimental data of smooth specimens and strain energy density of notched ones within the critical damage region. Experimental data of GH4169, TC4 and TC11 alloys with different geometries are utilized for model validation and comparison. Results indicate that the proposed model show higher accuracy than the other four models; in addition, the P–Wa¯–Nf curves describe the experimental data scatter effectively.
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•The relationship among defects, fatigue strength and S-N curve are quantitatively analysed.•Proposed strength altering factor (SAF) for probabilistic fatigue assessment of AM ...materials under size effect.•SAF 1-3 characterize the influence of size effect, defect scatter and microstructure on fatigue strength of AM materials.•Proposed strategy for defect tolerant fatigue assessment of AM parts.
Despite the significant advantages such as rapid prototyping of complex structures, engineering application of Additive Manufacturing (AM) technique has been limited due to the weak fatigue performance and lacking of fatigue design rules of AM parts. Particularly, this application relies on the improvement of AM processing technique and integrity assessment of AM parts, the latter usually demands costly and time-consuming fatigue tests, especially for full-scale tests. Accordingly, the size effect and fatigue performance scatter in AM materials are explored on basis of defect data scanned by CT and experimental data in this work. Firstly, the distribution of maximum defects of AM materials under size effect is extrapolated via extreme value statistics theory; then a strength altering factor is proposed to characterize the effect of defects on fatigue scatter and size effect. From essential structure of fatigue curves, the relationship among defects, fatigue strength and fatigue curves are quantitatively analysed to extrapolate the probabilistic fatigue curves for AM materials; finally, three series of AlSi10Mg specimens with different processing parameters and gauge volumes prove the method effectiveness that the “location” and “scale” of fatigue curves is successfully predicted, and defect-tolerant assessment for AM parts is performed by employing the predicted fatigue curves.
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Micro- and nanolattices can achieve simultaneously both lightweight and ultra-high strength due to a combination of resilient architecture and enhanced mechanical properties of small-scale unit ...constituents. However, understanding the fundamental deformation mechanism for these novel materials remains intriguing due to the intricate interplay of various geometric characteristics and intrinsic microscopic defects. Here, we investigate the fundamental mechanism of plastic deformation in terms of dynamic evolution of defects and corresponding mechanical responses in aluminum nanolattices using a mesoscale defect dynamics model which couples three-dimensional dislocation dynamics and finite element method. Our concurrently coupled model could capture detailed dislocation motion under complex loading conditions and predict the plastic flow stress of the nanolattices. We demonstrate that the size of individual constituent beam plays a critical role in the properties of nanolattices through small-scale strengthening, showing the strength of the nanolattices increases with decreasing beam size with the scaling law of σ∝db−0.89. As a result, the scaling law of plastic yielding with material density drastically increases from the continuum prediction. In addition, our modeling could allow us to study the geometric effect with various nanolattices. These findings establish a foundation for the fundamental understanding of the governing mechanism of plastic deformation, allowing access to a new regime in designing optimal structures using nanolattices.
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