Theoretical Strength Limit Research Articles

Exceptional strength and wear resistance in an AA7075/TiB2 composite fabricated via friction consolidation

The friction consolidation method successfully reinforced aluminum 7075 alloy (AA7075) with high-volume fractions (12 and 24 vol%) of titanium diboride (TiB2) by high pressure and severe plastic deformation at elevated temperatures. The consolidated AMCs have a uniform dispersion of submicron- and micron-sized TiB2 particles in the AA7075 matrix, with significant refinement of the matrix grain size and the particles. The addition of TiB2 significantly increases hardness by up to 50 %, Young’s modulus by up to 62 %, and ultimate tensile strength by up to 28 % to 672 MPa, while reducing ductility by 80 %. Wear resistance of 7075/24 vol% TiB2 improves seven-fold compared to baseline, making it comparable to that of carburized steels. Microstructure-based finite element modeling provided a theoretical strength limit of ∼730 MPa for the composites and indicated that high triaxiality in conjunction with severe equivalent plastic strain in a narrow area between the TiB2 particles led to early fracture initiations, limiting the ductility.

Strain-rate dependent mixed-mode traction laws for glass fiber-epoxy interphase using molecular dynamics simulations

In this paper, we establish a methodology to predict strain rate-dependent mixed-mode traction-separation responses (i.e., traction laws) for glass-epoxy composite interphase using molecular dynamics (MD) simulations. Glass-epoxy interphases with monolayer glycidoxypropyltrimethoxy silane are prepared by varying silane number density from 0.0 nm−2 to 3.9 nm−2 following the epoxy-amine diffusion and curing reactions. To established the effects of strain rate and mode-mixity on the interphase traction laws, the nano-meter size interphase domain is loaded in various mode-mixity (θ=0°(Mode−II),15°,30°,45°,60°,and90°(Mode−I)) with full range of strain rates from quasit-static to high strain rate (∼1e16/s) where a theoretical plateau strength limit is predicted. Following our previous work on Mode-I [Chowdhury et al., Composites Part B 237 (2022) 109877], mathematical model is developed for Mode-II as function of strain rate for different interphase structures (i.e., silane number density). The continuum equivalent bi-linear cohesive traction law is developed using the MD results to determine the mode-mixity quadratic functions and associated exponents for peak tractions, energy absorption, crack initiation and crack opening displacement from the mixed-mode simulations data. The MD predicted traction laws can be used to model interphase in micromechanics finite element analysis to bridge the length scale for the prediction of fiber-matrix debonding in composites.

Composite strut-plate lattice: A high-stiffness design of cellular metamaterial having excellent strength and energy absorption ability

Although the 3D-printed plate lattices have higher stiffness and strength than the strut lattices, the difficulty in fabricating the plate microlattices limited their potential application. The plate lattices require holes in the plates to remove the powder trapped inside, but introducing holes in plates in a lattice could reduce stiffness and strength. In general, to enhance the mechanical properties of a specific lattice for a particular mass, the size of the unit cell should be reduced. However, small plate unit cells require tiny holes on plates that may not be sufficiently large enough for post-fabrication powder removal. Thus, as an alternative design strategy, this work proposes a composite strut-plate lattice inspired by fiber-reinforced composite materials to achieve high stiffness, strength and energy absorption ability. Further, this study provides a methodology based on the classical rule of mixture for composite materials to determine the threshold volume fraction of the plate lattice reinforcement in the strut lattice matrix to attain a stiffness value that exceeds the maximum theoretical stiffness limit— the Hashin-Shtrikman upper bound. The finite element simulation results were corroborated by quasi-static compression tests on 3D-printed lattices made of polymer PA12 fabricated using multi jet fusion technique. Notably, the yield strength of the lattice exceeded the maximum theoretical yield strength limit— the Suquet upper bound. Also, the energy absorption ability was remarkably improved compared to the strut lattice and was close to that of the plate lattice. • Combined strut and plate unit cells that solve 3D printing's powder entrapment problem. • Stiffness and yield strength beyond their theoretical limits are achieved. • Mechanical properties are tailored using composite rule of mixture. • The designed composite lattice shows excellent energy absorption ability. • Mechanical properties are predicted by FEM and corroborated with experiments.

Strain-rate dependent mode I cohesive traction laws for glass fiber-epoxy interphase using molecular dynamics simulations

Using molecular dynamics (MD) simulations, we develop strain-rate dependent Mode-I cohesive traction laws for the glass fiber-epoxy interphase as a function of interphase structure. Interphase models with mono-layer glycidoxypropyltrimethoxy silane are prepared varying silane number density from 0.0 nm−2 to 3.9 nm−2. Interphase is formed through epoxy-amine diffusion in the silane layer followed by curing reaction. Traction laws are developed over a full range of strain rates from quasi-static to super-high strain rate (∼1e16/s) where a theoretical plateau strength limit is predicted. A stress-relaxation methodology is introduced to construct quasi-static traction-separation responses from high strain rate loading. Simulation results reveal that the interphase traction-separation responses are strain rate and silane number density dependent. Variations of peak traction and energy with strain rates show a characteristic S-shape pattern in a semi-log plot with a gradual increase in properties up to 1e12/s where a steep transition occurs between 1e13/s to 1e14/s followed by a strain rate independent plateau. Interphase properties (especially peak traction) increase almost linearly with silane number density for all strain rates. Mathematical correlations for the MD predicted traction versus strain rate and energy versus strain rate data are established to bridge length scales providing input micromechanics models for the prediction of fiber-matrix debonding in composites.

Centimetre-scale crack-free self-assembly for ultra-high tensile strength metallic nanolattices.

Nanolattices exhibit attractive mechanical, energy conversion and optical properties, but it is challenging to fabricate large nanolattices while maintaining the dense regular nanometre features that enable their properties. Here we report a crack-free self-assembly approach for fabricating centimetre-scale nickel nanolattices with much larger crack-free areas than prior self-assembled nanolattices and many more unit cells than three-dimensionally printed nanolattices. These nickel nanolattices have a feature size of 100 nm, a grain size of 30 nm and a tensile strength of 260 MPa, which approaches the theoretical strength limit for porous nickel. The self-assembly method and porous metal mechanics reported in this work may advance the fabrication and applications of high-strength multifunctional porous materials.

Plate-nanolattices at the theoretical limit of stiffness and strength

Though beam-based lattices have dominated mechanical metamaterials for the past two decades, low structural efficiency limits their performance to fractions of the Hashin-Shtrikman and Suquet upper bounds, i.e. the theoretical stiffness and strength limits of any isotropic cellular topology, respectively. While plate-based designs are predicted to reach the upper bounds, experimental verification has remained elusive due to significant manufacturing challenges. Here, we present a new class of nanolattices, constructed from closed-cell plate-architectures. Carbon plate-nanolattices are fabricated via two-photon lithography and pyrolysis and shown to reach the Hashin-Shtrikman and Suquet upper bounds, via in situ mechanical compression, nano-computed tomography and micro-Raman spectroscopy. Demonstrating specific strengths surpassing those of bulk diamond and average performance improvements up to 639% over the best beam-nanolattices, this study provides detailed experimental evidence of plate architectures as a superior mechanical metamaterial topology.

Mechanisms of micro-voids formation caused by optical breakdown in KCl single crystals

The phenomenon of optical breakdown has been studied experimentally for KCl single crystals exposed to laser emission focused on the neodymium glass with modulated quality-factor, pulse duration 5·10-8 s, wavelength λ= 1054 nm, and pulse energy of the order 1 J in the regime of local intrinsic absorption of the laser emission by the single crystal. Evaluations of local heat flash energetic constituents and characteristic durations for both local area heating and relaxation processes and following comparison with experimental results have shown that the relaxation process takes place in two stages: the first is fast phasefollowed by crowdion mass transfer with shock wave participation, and the second is slow phase with participation also dislocation mass transfer. The energy losses for heat radiation and thermal conductivity are found to be by orders of value less than the absorption energy flux Iabs that provides fast local heating and plasma formation. From the viewpoint of the mechanics of continua the process under study where the pressure achieves value exceeding the theoretical strength limit for the time less 10-6 s, should be considered as explosion-like or shock process. The general scheme of plastic deformation arising from abovementioned estimations and observations is seemed as follows. In the beginning, under action of the shock wave the crowdions are generated which carry the substance from the high pressure area and move along close-packed atomic rows (<110> type directions in KCl crystals); the void is formed almost completely during the shock wave passing the relaxation zone crosssection. This time is of the order of τrel, i. e. 10-9…10-8 s. After falling temperature and pressure and vapor condensation into liquid, at the end of relaxation process, the void boundaries expand already under liquid melt pressure, and the mass transfer dislocation mechanism comes into action providing additionally some enlarging the void volume. This process continues also after stopping the laser emission, during the crystal cooling down to the melt crystallization in the void and formation of a pore with size observed.

Approaching diamond\u2019s theoretical elasticity and strength limits

Diamond is the hardest natural material, but its practical strength is low and its elastic deformability extremely limited. While recent experiments have demonstrated that diamond nanoneedles can sustain exceptionally large elastic tensile strains with high tensile strengths, the size- and orientation-dependence of these properties remains unknown. Here we report maximum achievable tensile strain and strength of diamond nanoneedles with various diameters, oriented in <100>, <110> and <111> -directions, using in situ transmission electron microscopy. We show that reversible elastic deformation depends both on nanoneedle diameter and orientation. <100> -oriented nanoneedles with a diameter of 60 nm exhibit highest elastic tensile strain (13.4%) and tensile strength (125 GPa). These values are comparable with the theoretical elasticity and Griffith strength limits of diamond, respectively. Our experimental data, together with first principles simulations, indicate that maximum achievable elastic strain and strength are primarily determined by surface conditions of the nanoneedles.

The effect of defects on strength of gold microparticles

Mechanical properties of solid-state-dewetted Au microparticles were characterized by microcompression tests. Our results revealed that large Au microparticles exhibit a strong size effect in yield strength, while the strength of their smaller counterparts reaches saturation and is size-independent. We discuss these two regimes in terms of source-controlled plasticity with a theoretical strength limit. Our calculations capture the particles behavior observed in the experiment, as well as predict the effects of sample geometry on the scaling law. This work shows that the microparticles produced by solid-state-dewetting method represent a convenient model system to study dislocation plasticity at small length scales.

Behaviour of pultruded GFRP truss system connected using through-bolt with mechanical insert

This paper presents the experimental and analytical studies of double-chorded composite truss system connected using stainless steel through-bolts with mechanical inserts. The composite trusses were assembled using rectangular hollow sections of pultruded glass fibre reinforced polymer (GFRP) where adhesively bonded mechanical inserts were introduced at the vicinity of the joining areas. The trusses were tested under 4-point bending (Load Case 1) and 3-point bending (Load Case 2). From this experimental program, the load-vertical deflection behaviour of the truss, internal forces distribution in the members and joint behaviour were investigated. The pultruded GFRP truss under Load Case 1 was capable of resisting the maximum load capacity of the testing equipment at 450 kN with the lowest factor of safety of 1.10 was attained by the external diagonal members. High axial compression forces experienced by the external diagonal members has exceeded the American pre-standard theoretical joint bearing capacity by 2%, and this was reflected by the minor bearing damage observed on the joints of these members. Meanwhile, the truss under Load Case 2 failed at 160 kN with the continuous top chords ruptured in flexural bending manner. The satisfactory comparisons between the Strand 7 truss model and experimental results demonstrated the validity of the adopted simplified numerical model. Additionally, the theoretical strength limits of pultruded GFRP truss members in tension, compression and flexural according to American pre-standard are in close agreement with the experimental results.

Elastomer-like deformation in high-Poisson's-ratio graphene allotropes may allow tensile strengths beyond theoretical cohesive strength limits

Phenomenological theories of deformation in brittle solids generally envisage fracture under tension as the breaking of atomic bonds perpendicular to the fracture plane, thereby ignoring the role of bond rotation. Using density functional theory calculations, we found that during the early stage of the uniaxial tension of graphene allotropes with high Poisson's ratios, bond rotation effectively lessens bond stretch and increases the fracture strain. Specifically, in the deformation of an allotrope, Gr10, with a Poisson's ratio of 0.8, bond rotation results in an S-shaped stress-strain curve, akin to those of elastomers. Moreover, the tensile strength (σth) and the Young's modulus (E) of Gr10 exceed the theoretical cohesive strength limit σth≈E/10, reaching σth≈E/1.7. However, a universal relationship between bond lengths and charge density distribution along bond paths was found to be suitable for all carbon-carbon covalent bonds. Consequently, all carbon-carbon bonds obey a common shape of bond-force vs. bond-strain curve, with bond strength, S, and bond stiffness, K, following S≈K/9; hence, σth≈E/10 remains valid for the low-Poisson's-ratio graphene allotropes whose deformation is dominated by bond stretch. Overall, we suggest the trade-off between bond stretching and bond rotation can be utilized to enhance the fracture strain of two-dimensional carbon structures.

Titanium Resistance to Deformation Near the Theoretical Strength Limit

In this paper, we studied the evolution of the compression wave in titanium films generated by femtosecond laser pulses by spectral interferometry with a picosecond resolution. At a submicron propagation length, splitting of the shock wave into an elastic and plastic shock is recorded with a compression stress of 8.4 GPa behind the front of the elastic precursor. The corresponding value of the maximum shear stress (2.7 GPa) is comparable to the calculated values of the ideal strength of titanium.

Dual phase amorphous carbon ceramic achieves theoretical strength limit and large plasticity

Ceramics are widely used as engineering materials due to their high strength; however, their lack of plasticity is a major drawback. We report that dual-phase amorphous carbon (a-C) reveals high yield strength of ∼E/11 (E is elastic modulus, and E/10 is theoretical limit for ideal material) and large plasticity of ∼70% at room temperature in uniaxial compression tests. To the best of our knowledge, this report describes the first time since 2006 that the experimental yield strength has been determined to agree with the theoretical prediction. Pillars with diameters smaller than 427 nm deform homogeneously and show plasticity comparable to that of metals. The mechanism for such unusual properties of a-C is explored using high-resolution transmission electron microscopy (TEM) and Raman spectroscopy. The results indicate that the near-ideal strength is ascribed to the limitation of both the size and the number of defects with the smaller sample size. Large plasticity is accompanied by material densification and phase transformation at compressive stress. This finding widens the possible application of strong-and-plastic ceramic films for both biomedical and micro/nano-electromechanical systems (MEMS/NEMS).

Extreme strength observed in limpet teeth.

The teeth of limpets exploit distinctive composite nanostructures consisting of high volume fractions of reinforcing goethite nanofibres within a softer protein phase to provide mechanical integrity when rasping over rock surfaces during feeding. The tensile strength of discrete volumes of limpet tooth material measured using in situ atomic force microscopy was found to range from 3.0 to 6.5 GPa and was independent of sample size. These observations highlight an absolute material tensile strength that is the highest recorded for a biological material, outperforming the high strength of spider silk currently considered to be the strongest natural material, and approaching values comparable to those of the strongest man-made fibres. This considerable tensile strength of limpet teeth is attributed to a high mineral volume fraction of reinforcing goethite nanofibres with diameters below a defect-controlled critical size, suggesting that natural design in limpet teeth is optimized towards theoretical strength limits.

Near-ideal theoretical strength in gold nanowires containing angstrom scale twins

Although nanoscale twinning is an effective means to enhance yield strength and tensile ductility in metals, nanotwinned metals generally fail well below their theoretical strength limit due to heterogeneous dislocation nucleation from boundaries or surface imperfections. Here we show that Au nanowires containing angstrom-scaled twins (0.7 nm in thickness) exhibit tensile strengths up to 3.12 GPa, near the ideal limit, with a remarkable ductile-to-brittle transition with decreasing twin size. This is opposite to the behaviour of metallic nanowires with lower-density twins reported thus far. Ultrahigh-density twins (twin thickness<2.8 nm) are shown to give rise to homogeneous dislocation nucleation and plastic shear localization, contrasting with the heterogeneous slip mechanism observed in single-crystalline or low-density-twinned nanowires. The twin size dependent dislocation nucleation and deformation represent a new type of size effect distinct from the sample size effects described previously.

Cyclic Cantilever Bending of Copper Nanowhiskers

AbstractA cyclic bending test with cantilever geometry is developed for probing local mechanical properties of single crystalline Cu nanowhiskers (NWs). A lower limit for the yield stress for such whiskers is derived at ≈5 GPa. Since all NWs exhibit the axis parallel to the 〈1 1 0〉 crystallographic direction, the resolved shear stress can be calculated. The values of ≈2 GPa lie close to the theoretical strength limit and predict partial dislocation nucleation as the governing mechanism at the onset of plastic deformation. The yield stress is practically independent of the whisker diameter.

Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals

A numerical model to estimate critical times required for nanovoid nucleation in high-purity aluminum single crystals subjected to shock loading is presented. We regard a nanovoid to be nucleated when it attains a size sufficient for subsequent growth by dislocation-mediated plasticity. Nucleation is assumed to proceed by means of diffusion-mediated vacancy aggregation and subsequent vacancy cluster coarsening. Nucleation times are computed by a combination of lattice kinetic Monte Carlo simulations and simple estimates of nanovoid cavitation pressures and vacancy concentrations. The domain of validity of the model is established by considering rate-limiting physical processes and theoretical strength limits. The computed nucleation times are compared to experiments suggesting that vacancy aggregation and cluster coarsening are feasible mechanisms of nanovoid nucleation in a specific subdomain of the pressure-strain rate-temperature space.

On the theoretical strength limit of the layered elastic and viscoelastic composites in compression

The theoretical strength limit in compression (TSLC) of composite material with two alternating isotropic homogeneous elastic and viscoelastic layers is studied. The investigation is made within the piecewise-homogeneous body model with the use of the Three-Dimensional Linearized Theory of Stability for elastic and viscoelastic materials. It is assumed that there is an initial imperfection in the local curving form of the reinforcing layers along the direction which is inclined to the layers. As the criterion for determination of the TSLC, the case is taken for which the aforementioned imperfections start to increase indefinitely. The numerical results for the TSLC are presented and discussed. According to these numerical results, in particular, the direction (or the surface) along which the fracture in compression takes place, is determined.

Determining the Elasticity of Materials Employing Quantum‐mechanical Approaches: From the Electronic Ground State to the Limits of Materials Stability

AbstractQuantum‐mechanical (so‐called ab initio) calculations have achieved considerable reliability in predicting physical and chemical properties and phenomena. Due to their reliability they are becoming increasingly useful when designing new alloys or revealing the origin of phenomena in existing materials, also because these calculations are able to accurately predict basic material properties without experimental input. Due to the universal validity of fundamental quantum mechanics, not only ground‐state properties, but also materials responses to external parameters can reliably be determined. The focus of the present paper is on ab initio approaches to the elasticity of materials. First, the methodology to determine single‐crystalline elastic constants and polycrystalline moduli of ordered compounds as well as disordered alloys is introduced. In a second part, the methodology is applied on α‐Fe, with a main focus on (i) investigating the influence of magnetism on its elasticity and phase stability and (ii) simulating extreme loading conditions that go up to the theoretical tensile strength limits and beyond.

Mechanical properties of ceria nanorods and nanochains; the effect of dislocations, grain-boundaries and oriented attachment

We predict that the presence of extended defects can reduce the mechanical strength of a ceria nanorod by 70%. Conversely, the pristine material can deform near its theoretical strength limit. Specifically, atomistic models of ceria nanorods have been generated with full microstructure, including: growth direction, morphology, surface roughening (steps, edges, corners), point defects, dislocations and grain-boundaries. The models were then used to calculate the mechanical strength as a function of microstructure. Our simulations reveal that the compressive yield strengths of ceria nanorods, ca. 10 nm in diameter and without extended defects, are 46 and 36 GPa for rods oriented along [211] and [110] respectively, which represents almost 10% of the bulk elastic modulus and are associated with yield strains of about 0.09. Tensile yield strengths were calculated to be about 50% lower with associated yield strains of about 0.06. For both nanorods, plastic deformation was found to proceed via slip in the {001} plane with direction <110>--a primary slip system for crystals with the fluorite structure. Dislocation evolution for the nanorod oriented along [110] was nucleated via a cerium vacancy present at the surface. A nanorod oriented along [321] and comprising twin-grain boundaries with {111} interfacial planes was calculated to have a yield strength of about 10 GPa (compression and tension) with the grain boundary providing the vehicle for plastic deformation, which slipped in the plane of the grain boundary, with an associated <110> slip direction. We also predict, using a combination of atomistic simulation and DFT, that rutile-structured ceria is feasible when the crystal is placed under tension. The mechanical properties of nanochains, comprising individual ceria nanoparticles with oriented attachment and generated using simulated self-assembly, were found to be similar to those of the nanorod with grain-boundary. Images of the atom positions during tension and compression are shown, together with animations, revealing the mechanisms underpinning plastic deformation. For the nanochain, our simulations help further our understanding of how a crystallising ice front can be used to 'sculpt' ceria nanoparticles into nanorods via oriented attachment.