Mechanical Size Effects Research Articles

Size effect and underlying microstructural mechanism in cyclic deformation behavior of nickel-based superalloy sheet

The nickel-based GH4169 superalloy is widely used in the aerospace field, which has desirable oxidation resistance and strength in extreme environments. However, the size effect and underlying microstructural mechanism in the cyclic deformation of the GH4169 sheet are still not fully elucidated, which affects the forming accuracy precision of thin-walled components. To this end, the cyclic mechanical properties and microstructural evolution of the GH4169 sheets with different thicknesses and grain sizes were systematically investigated via cyclic shearing tests. The superalloy sheet exhibits obvious early re-yielding, instantaneous softening and permanent softening during the cyclic deformation and these cyclic deformation behaviors are obviously affected by size effect. To rationalize the cyclic mechanical responses and size effect, transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD) tests were conducted. The results indicated that the dislocation slip patterns are principally planar array slip and cross slip in the cyclic shearing deformation. Meanwhile, the annihilation of unstable dislocation and the presence of carbides led to the instantaneous softening. Moreover, the change of loading direction, the reduction of texture strength, the proportion of low-angle grain boundary (LAGB), and geometrically necessary dislocation (GND) density together result in the occurrence of permanent softening. Based on the comparative analysis of the microstructure evolution of superalloy sheets with different size factors, the underlying mechanism of size effect on cyclic deformation was clarified. The findings in the research combine the cyclic mechanical response and microstructure evolution closely in the cyclic deformation of superalloy sheets and deepen the understanding of size effect under complex loading paths.

Anisotropic size effect of 3D printed LC3-based engineered cementitious composites (LC3-ECC)

One of the critical factors affecting the development of 3D concrete printing (3DCP) is the challenging issue of in-situ reinforcement. Engineered Cementitious Composites (ECC) are printable self-reinforced materials, and their application in 3DCP technology can facilitate de-steelisation. However, traditional ECC materials pose certain concerns for sustainable environmental development. The integration of Limestone Calcined Clay Cement (LC3) suitable for 3DCP into ECC (LC3-ECC) presents an ideal solution to the aforementioned challenges. Moreover, conducting comprehensive research into its size effects is an essential step from experimentation to engineering application. A thorough exploration of the size effects of 3D printed LC3-ECC in compression, shear, and flexural fracture aspects is conducted to derive size effect laws. The relationship between the anisotropic mechanical properties and size effects has been established. The mold-cast LC3-ECC precisely follows the Bažant size effect law (SEL). The fiber orientation effect enhances bridging efficiency, leading to the fact that the mechanical properties of certain printed LC3-ECC are hardly affected by the size effect. The mechanical performance of some printed LC3-ECC depends on interlayer strength, making its primary reason for size effect not in the Fracture Process Zone (FPZ) energy release, hence closer to the Multifractal Scaling Law (MFSL). LC3-ECC exhibits weak anisotropy in mechanical properties, showing satisfactory stability. However, under flexural fracture behavior, the anisotropic size effect is higher, necessitating careful consideration in structural design.

Size effects in fatigue crack growth in confined volumes: A microbending case study on nanocrystalline nickel

Mechanical size effects are a well known phenomenon when the sample volume is reduced or the characteristic length of the microstructure is changed. While size effects in micropillar compression (smaller is stronger) or due to grain refinement (Hall-Petch) are well understood, this is less so in fracture mechanics. Given this lack of knowledge, the main question addressed in this work is: What happens to the fatigue crack growth properties when extrinsic size effects play a role? To answer this question, nanocrystalline nickel cantilevers, ranging in width from 5 to ▪, were subjected to fatigue crack growth. The crack growth rates and stress intensity factors were calculated and the Paris exponent in the stable crack growth regime was determined. It was found that the results scatter more strongly for the smaller cantilevers compared to the larger cantilevers. Results are interpreted in terms of plastic zone size and ligament size which are found to be critical for small cantilevers.

Highly tailorable thermomechanical properties of nanograined silicon: Importance of grain size and grain anisotropy

Nanocrystalline silicon can have unique thermal transport and mechanical properties governed by its constituent grain microstructure. Here, we use phonon ray-tracing and molecular dynamics simulations to demonstrate the largely tunable thermomechanical behaviors with varying grain sizes (a0) and aspect ratios (ξ). Our work shows that, by selectively increasing the grain size along the heat transfer direction while keeping the grain area constant, the in-plane lattice thermal conductivity (kx) increases more significantly than the cross-plane lattice thermal conductivity (ky) due to anisotropic phonon–grain boundary scattering. While kx generally increases with increasing ξ, a critical value exists for ξ at which kx reaches its maximum. Beyond this transition point, further increases in ξ result in a decrease in kx due to substantial scattering of low-frequency phonons with anisotropic grain boundaries. Moreover, we observe reductions in the elastic and shear modulus with decreasing grain size, and this lattice softening leads to significant reductions in phonon group velocity and thermal conductivity. By considering both thermal and mechanical size effects, we identify two distinct regimes of thermal transport, in which anisotropic phonon–grain boundary scattering becomes more appreciable at low temperatures and lattice softening becomes more pronounced at high temperatures. Through phonon spectral analysis, we attribute the significant thermal conductivity anisotropy in nanograined silicon to grain boundary scattering of low-frequency phonons and the softening-driven thermal conductivity reduction to Umklapp scattering of high-frequency phonons. These findings offer insights into the manipulation of thermomechanical properties of nanocrystalline silicon via microstructure engineering, carrying profound implications for the development of future nanomaterials.

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.

Suppressed Size Effect in Nanopillars with Hierarchical Microstructures Enabled by Nanoscale Additive Manufacturing.

Studies on mechanical size effects in nanosized metals unanimously highlight both intrinsic microstructures and extrinsic dimensions for understanding size-dependent properties, commonly focusing on strengths of uniform microstructures, e.g., single-crystalline/nanocrystalline and nanoporous, as a function of pillar diameters, D. We developed a hydrogel infusion-based additive manufacturing (AM) technique using two-photon lithography to produce metals in prescribed 3D-shapes with ∼100 nm feature resolution. We demonstrate hierarchical microstructures of as-AM-fabricated Ni nanopillars (D ∼ 130-330 nm) to be nanoporous and nanocrystalline, with d ∼ 30-50 nm nanograins subtending each ligament in bamboo-like arrangements and pores with critical dimensions comparable to d. In situ nanocompression experiments unveil their yield strengths, σ, to be ∼1-3 GPa, above single-crystalline/nanocrystalline counterparts in the D range, a weak size dependence, σ ∝ D-0.2, and localized-to-homogenized transition in deformation modes mediated by nanoporosity, uncovered by molecular dynamics simulations. This work highlights hierarchical microstructures on mechanical response in nanosized metals and suggests small-scale engineering opportunities through AM-enabled microstructures.

Specimen size effect on the strength of nickel-boron alloys

Nickel-boron alloys are prepared by an electrodeposition method. The as-deposited nickel-boron alloy is then annealed at 250 °C and 400 °C for 4 h. Their mechanical strengths and specimen size effects on the strength are evaluated by micro-compression test using pillar-type micro-specimens fabricated by focused ion beam system. In all as-deposited and annealed specimens, a smaller-is-stronger specimen size effect is confirmed. The compressive strength of the nickel-boron alloys reaches a maximum of 5.79 GPa with the smallest specimen size in this work.

Size effect on the cyclic deformation behavior of superalloy ultrathin sheet: Characterization and multiscale modelling

Superalloy ultrathin sheets have high strength, outstanding oxidation resistance, corrosion resistance and fatigue performance, and its thin-walled components occupy a considerable proportion in aeroengines. In the microforming process of aeroengine thin-walled components, the superalloy ultrathin sheet is often deformed under complex loading states and shows obvious springback. However, the forming and springback laws of superalloy ultrathin sheet in the microforming process are not clear and often affected by size effect. In addition, the existing nonlinear kinematic hardening models cannot accurately forecast the deformation and springback of superalloy ultrathin sheets. To address this issue, the cyclic shearing tests were performed to systemically explore the size effect on Bauschinger effect, permanent softening, transient hardening and work hardening stagnation of superalloy ultrathin sheets under cyclic loading states. The mechanism of size effect on cyclic mechanical response was systematically revealed through microstructure evolution combined with surface layer effect. In addition, a new multiscale cyclic hardening model was proposed based on the Y-U model and size effect on cyclic deformation behavior of superalloy ultrathin sheets. The new multiscale cyclic hardening model coupling surface layer effect and grain boundary strengthening effect was constructed by modeling the relationship between the cyclic mechanical response and size effect. Comparisons between the original Y-U model and the new proposed model on the characterization effect of shear stress-strain curves demonstrated that the proposed cyclic hardening model can accurately present the cyclic deformation behavior. To further verify the prediction capability of the proposed cyclic hardening model, the springback behavior of superalloy ultrathin sheet in U-bending test and hydroforming of seal ring was predicted via the proposed model combined with the decrease of elastic modulus and Yld2000–2d yield criterion, and the predicted results were compared with experimental ones. Comparative research revealed that the proposed cyclic hardening model can accurately describe the cyclic deformation behavior and springback of superalloy ultrathin sheets affected by size effect.

Study on mechanical properties and size effect of coal gangue concrete at mesoscale

Using solid waste coal gangue as building materials, especially the coarse aggregate of concrete, conforms to the concept of environmental protection and saves natural resources, such as sand and gravel. The traditional numerical model cannot describe the heterogeneous characteristics of coal gangue concrete. A numerical model of coal gangue concrete based on a mesoscale was established to study the influence of the internal component properties on the mechanical properties and size effect of the compressive strength of coal gangue concrete. The results show that the mesoscopic model can better describe the mechanical properties, failure modes and internal damage evolution process of the coal gangue concrete. With the increase of ITZ strength, the peak stress of coal gangue concrete increases first and then decreases, but the residual strength tends to be consistent. Improving the mortar strength can increase the peak stress and brittleness of coal gangue concrete. The degree of influence is related to the strength of the three-phase mechanical properties. When ƒcp-ITZ<ƒcp-M<ƒcp-Agg, the influence is the largest. When ƒcp-Agg<ƒcp-ITZ<ƒcp-M, the influence is weaker than the former case. When ƒcp-ITZ<ƒcp-Agg<ƒcp-M, the influence is small. The increase in the aggregate strength improve the peak stress of the concrete. When ƒcp-Agg<ƒcp-M, the peak stress of concrete can be effectively increased, and when ƒcp-Agg>ƒcp-M, the increase rate will decrease rapidly. Increasing the strength of the aggregate improves the brittleness of concrete. The size effect of coal gangue concrete is more significant than that of ordinary concrete, and it is recommended to consider conversion factors of 0.9 and 1.15 for cube sizes of 100 mm and 200 mm, respectively. Increasing the mortar strength made the size effect more pronounced. The size effect rate model based on the Bažant theory can describe the relationship between the nominal strength and the size of coal gangue concrete.

Mechanical size effect and serrated flow of various Zr-based bulk metallic glasses

Despite superior mechanical properties, the cross-scale mechanical properties of Zr-based bulk metallic glasses (BMGs) are urgent to be revealed. Depth-sensitive nanoindentation technique was employed to directly investigate the significant depth-dependent mechanical properties of three kinds of Zr-based BMGs. Specifically, the surface hardness H and elastic modulus E are verified to increase with the decrease of indentation depth while the fracture toughness KIC decreases with the indentation depth. The mechanical size effect is closely related to the evolution of shear bands at various indentation depths, which can be equivalently revealed by the distribution of serrated flow. Based on a relatively shallow indentation depth, the comparatively minor stress gradient established inside the micro-region underneath the indenter tip induces insufficient activation energy of shear bands, which prevents the nucleation of shear bands and further restricts plastic deformation, and ultimately results in enhanced surface hardness and elastic modulus but reduced fracture toughness. In addition, the shear band morphology of residual indentation and the stress distribution obtained from the finite element simulation provide integral evidence in support of the depth-induced mechanical size effect.

Modelling dynamic failure of geometrical-similar concrete subjected to tension-compression loads: Effect of strain rate and lateral stress ratio

Concrete materials are widely acceptable to practical structural buildings exposed to not only uniaxial loads but also complicated stress states. Additionally, concrete structures under quasi-static loads may suffer from inevitable occasional dynamic loads. In this study, mesoscopic modelling on geometrical-similar concrete was conducted. Numerical experiments were performed under dynamic biaxial Tension-Compression loads with different strain rates (ranging from 10−5 s−1 to 1 s−1) and lateral stress ratios (ranging from −1.00 to 0). The effect of lateral stress ratio and strain rate on the mechanical damage behavior and size effect of geometrical-similar concrete was discussed. The numerical results indicate that the size effect on dynamic spindle compressive strength and dynamic lateral tensile strength are weakened with the increasing strain rate. However, the increasing lateral stress ratios bring different impacts on the size effect, namely enhancing the size effect on dynamic spindle compressive strength and weakening the size effect on dynamic lateral tensile strength. Moreover, considering the coupling effects between lateral stress ratio and strain rate, a dynamic Tension-Compression failure criterion for concrete was proposed. Finally, a static-dynamic universal size effect formula on the lateral tensile strength of concrete under dynamic Tension-Compression loading was established and verified.

Micro/nano-mechanical behaviors of individual FCC, BCC and FCC/BCC interphase in a high-entropy alloy

• Micro-pillar compression tests were carried on a multiple high-entropy alloy. • Deformation behaviors of FCC, BCC and their interphase pillars were analyzed. • The strain bursts weakened with increasing strain in interphase pillar. • Interphase pillar exhibited better mechanical properties compared with FCC and BCC. • Revealed the relation between small scale deformation and interphase strengthening. Here, a systematic investigation was made on the interphase strengthening effects induced superior mechanical performances of multiphase high-entropy alloys (HEAs) at micro/nano-scale, compared with single phase HEAs. A pillar compression test under a scanning electron microscope (SEM) was performed on the individual face centered cubic (FCC), body centered cubic (BCC), and mixed-phases with different diameters in a Fe 24 Co 25 Ni 24 Cr 23 Al 4 HEA using focused ion beam (FIB) milling and a nanoindenter equipped with a flat punch. The stress-strain response of pillar underneath the indenter was selected to explore the diameter/phase-dependent size effect, the periodically fluctuation of local stress, and strain hardening. It was revealed that the pillars at the interphase exhibited significantly higher strength, compared with the FCC and BCC pillars. An experiment also verified the coincident mechanical size effects independent with the type of phases. The stress responses in the mixed-phase pillars manifested as a distinct transition from the dramatic drop to the minor fluctuation during the post-yield stages with the increasing strain, indicating the propagation of Al-Ni enriched solid solution phase (BCC1) under compression. Except the BCC1 phase, numerous dislocations were observed in the post-deformed pillars, particularly serving as the major source to enhance the strain hardening of BCC pillars.

Numerical investigations on the strain-rate-dependent mechanical behavior and size effect of RC shear walls

For accurately simulating the dynamic mechanical behavior of Reinforced Concrete (RC) shear walls subjected to dynamic loads, in this paper, a two-dimensional meso‑scale numerical model is proposed to capture the heterogenous nature and strain rate effect of concrete structure. The impacts of shear span ratio and strain rate on the dynamic mechanical properties and size effect law of the RC shear walls are investigated. The results indicate that: 1) the bearing capacity, ductility, and energy dissipation capacity of the RC shear walls increase with an increasing strain rate; 2) the failure mode of the RC shear walls is affected by the shear span ratio, while the bearing capacity decreases with an increasing shear span ratio; 3) both the increased strain rate and shear span ratio weaken the size effect of the RC shear wall. Based on these results, the dynamic size effect formula of the RC shear wall is proposed to quantitatively describe the influence of strain rate on the size effect. The proposed formula is validated by comparing both simulation and experimental results.

Size dependent coupled electromechanical torsional analysis of porous FG flexoelectric micro/nanotubes

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.

Size dependent torsional electro-mechanical analysis of flexoelectric micro/nanotubes

The free vibration and static torsion of a coupling electromechanical flexoelectric micro/nanotube have been investigated, in the present study. Using the non-classical theory of continuum mechanics which is based on a strain gradient, the coupling governing equations of torsional flexoelectric micro/nanotubes have been developed. To derive the coupling governing equations the variational method has been used and the formulation with the classical and non-classical boundary conditions is generally derived for torsional flexoelectric micro/nanotubes. For the first time, the formulation of micro/nanotube torsional flexoelectric coupling with independent polarization effect is presented in this paper which can be used for specific applications. At last, the static analysis and free vibrations results are presented for specific mechanical and electrical boundary conditions. The parameter of mechanical and electrical size effect changes has a great effect on the results. However, the effect of the mechanical and electrical size effect parameter on direct flexoelectric torsion is also opposite, but the effect of mechanical and electrical size effect parameter on reverse flexoelectric torsion is similar. Polarization is also introduced as a new variable in the equations and its effect is investigated as an independent variable of the electric field in the results, in this paper. As a significant parameter, the results show that polarization plays an important role to simulate the torsional electromechanical structures.

Mechanical Size Effect of Freestanding Nanoconfined Polymer Films

While elastic properties of nanoconfined polymer films have been recognized to show departures from bulk behavior, a careful understanding of the origins of mechanical size effects remains weak. Here, we report a significant mechanical stiffening of freestanding ultrathin poly(methyl methacrylate) films of varying thicknesses (6–200 nm) through atomic force microscopy deflection measurements at ambient conditions. After excluding the substrate influence, the stiffening mechanism is linked to extended chain conformations based on small-angle X-ray scattering and infrared nanoscopic characterization. We advocate that the entropic elasticity of individual chains plays a significant role in polymer mechanics in nanoscale thickness films, where the entanglement density is apparently low, with chains oriented in the plane of the film, unlike a bulk polymer. Molecular dynamics simulations further unveil the dominance of entropic contributions over enthalpic contributions to the chain stiffness that endows polymer films with higher load-bearing capacity and accounts for the stiffening at the nanoscale. The results presented herein provide a mechanistic understanding of molecular origins of the size effect, serving as a potent design strategy for accessing high-performance polymer-based devices.

Influence of dimensionality and specimen size on dynamic fracture

AbstractIn this contribution, we investigate the dynamic fracture process in Polymethyl Methacrylate (PMMA) plate specimens using a peridynamic computational model [2, 6]. We employ two as well as three dimensional peridynamic simulations in order to analyze the influence of dimensionality on the characteristics of the fracture process. The predicted crack speeds for the various levels of the initially stored energy, also known as the velocity toughening behavior, are compared with the experimentally observed crack velocities for PMMA specimens. The influence of the specimen size on the dynamic fracture process is investigated using 2D peridynamic simulations. The fracture strengths and the velocity toughening relationship obtained from different specimen sizes are compared with the Linear Elastic Fracture Mechanics (LEFM) size effect relationship and with results from the experiments [1], respectively.

Nanomechanical tests on continuous near-field electrospun PAN nanofibers reveal abnormal mechanical and morphology size effects

Polyacrylonitrile (PAN) nanofibers have long been the subject of studies as precursor for high performance materials such as carbon nanofibers. Here, we present the first effort to study the mechanical properties of PAN nanofibers fabricated via near field electrospinning, in which bending instability was completely suppressed. The method allowed for the collection of continuous single-strand PAN nanofibers with aspect ratios exceeding 106 on a spool (rotating target). By controlling the electrospinning parameters, such as solution concentration, voltage and distance, we demonstrated that the morphology and diameter of the PAN nanofiber were well controlled. We also realized that slight changes in the distance can significantly change the shape of the cross section of the fibers, from a circular cross section to oval shaped (ribbons), which was explained in terms of solvent residues in the jet and momentum transfer between the fibers and the target, as the fibers reach the target. Our studies on individual PAN nanofibers revealed a strong mechanical size effect, in which reducing the diameter of the nanofibers from ∼290 nm to ∼200 nm, led to a large increase in modulus to as high as ∼9 GPa, among the highest in as-electrospun PAN nanofibers. The strong size effect was attributed to a loss in chain alignment in thicker electrospun nanofibers facilitated by the plasticizing effect of residual solvent. In comparison to conventional electrospinning, the NFES led to a significantly narrower diameter distribution. The demonstrated size-dependent morphology, mechanical properties of NFES PAN nanofibers provides a solid foundation for fabricating polymer nanofiber with controllable patterning and properties through NFES.

Physical and numerical evaluation of effect of specimen size on dynamic tensile strength of rock

It is well known that both the specimen size and the loading rate can affect the tensile strength of rock specimens. In this study, the combined effect of loading rate and specimen size on tensile strength was investigated by performing some physical and numerical Brazilian tests on specimens with notch and without notch. The dynamic tests were performed using the Split Hopkinson Pressure Bar apparatus. A type of dental gypsum commercially known as Snow Rock was used to prepare the molded gypsum specimens for the physical tests. The CA3 computer program was utilized for the numerical simulation. The bonded particle model for simulation of the rock together with the implemented micromechanical model was able to capture many features of the physical test results. It was shown that the notched specimens were much more sensitive to the loading rate. Furthermore, the results suggested that there is a critical stress rate at which the specimen size has no effect on the specimen strength. For loading rates greater than the critical one, with the increase in the specimen size, greater tensile strength was obtained. Fracture mechanics size effect was partially observed for the applied loading rates smaller than the critical rate.

Aggravated stress fluctuation and mechanical size effects of nanoscale lamellar bone pillars

The size effects of mechanical properties influence the microdeformation behaviors and failure mechanisms of hierarchical lamellar bones. Investigations of the continuous deformation behaviors and structure–behavior–property relationships of nanoscale lamellar bones provide essential data for reducing the risk of fracture. Here, five pillars with diameters ranging from 640 to 4971 nm inside a single lamella were fabricated. In situ pillar compressive tests inside a scanning electron microscope directly revealed the diameter-dependent enhanced strength, ductility, and stress fluctuation amplitude. Real-time observations also revealed the segmented deformation and morphological anisotropy of pillars with smaller diameters and the slight elastic recovery of pillars with larger diameters. The critical diameter leading to the brittle-to-ductile transition was confirmed. The “analogous to serrated flow” stress fluctuation behaviors at the nanoscale exhibited a significant size effect, with coincident fluctuation cycles independent of diameter, and each cycle of the fluctuation manifested as a slow stress increase and a rapid stress release. The discontinuous fracture of collagen fibrils, embedded enhancement of hydroxyapatite crystals, and layered dislocation movement on the basis of strain gradient plasticity theory were expected to induce cyclical stress fluctuations with different amplitudes.