Threshold Strain Research Articles

Experimental Investigations on Crack Propagation Characteristics of Granite Rectangle Plate with a Crack (GRPC) under Different Blast Loading Rates

The experimental system of 3D digital image correlation (3D-DIC) is set up to eliminate a certain extent of out-of-plane motion for accurate measuring the full-field strain field during crack propagation, and the effect of blast loading rates of fracture behavior of granite rectangle plate with a crack (GRPC) is investigated. The experimental results indicated that the maximum values of the strain concentration zone do not fully represent the crack tip during the whole process of crack propagation. The axial strain threshold value tip (ASTVT) plotting with lines and coordinate contours corresponding with the actual crack at the shooting area can be used to describe the position of the crack. The axial strain 1.3% is more practical to obtain crack velocity and average crack velocity, and the average crack velocity decreases as the blast loading rates increase. Through observing the relationship between crack width and time, it can be found that there are three stages, and the crack width increases as the blast loading rates increase.

Onset of Mechanochromic Response in the High Strain Rate Uniaxial Compression of Spiropyran Embedded Silicone Elastomers.

The molecular processes that accompany dynamic mechanical response to large deformations at high strain rate (≈1000 s-1 or higher) underlie the early stages of damage in materials, but understanding of material response in this regime is typically limited to macroscopic constitutive equations. Here, spiropyran mechanophores are embedded in very short, stress-bearing strands in silicone elastomers, and their mechanochromic response to uniaxial compression is explored in a Split Hopkinson Pressure (or Kolsky) Bar. At strain rates of 1000 s-1 , the onset of mechanochromism occurs at lower strains, but higher stresses, than in the same materials under quasi-static loading. Similar to quasi-static loading, however, a negligible effect of mechanophore structure on the critical strain for colorimetric onset is observed. The results suggest that nonequilibrium, inhomogeneous local tension distributions in the elastomers lead to greater stress in individual strands than at the same strains under equilibrium loading, but that within the regions of force concentration, mechanochromic onset is determined primarily by a limiting local strain threshold.

Grain boundary engineering of AL6XN super-austenitic stainless steel: Distinctive effects of planar-slip dislocations and deformation twins

To explore the influence of deformation microstructures on the gain boundary engineering (GBE), a series of thermo-mechanical processes (TMPs) were performed on an AL6XN super-austenitic stainless steel (ASS). The deformation microstructures of cold-rolled samples and the TMPed microstructures were characterized by transmission electron microscopy and electron back-scatter diffraction, respectively. The results show that the deformation microstructures, including planar slip bands and deformation twins (DTs), play a distinctive role in the GBE treatment. Planar slip bands are in favor of the GBE treatment, since the migrating boundaries of twin related domains might generate “stacking accidents” in a sequence of closely packed atomic planes via absorbing the planar-slip dislocations, and thus derive the formation of annealing twins. In contrast, DTs are detrimental to GBE for they hinder the growth of twin related domains. Therefore, the optimal prior strain (namely cold-rolling reduction) of TMP for the GBE treatment of AL6XN super-ASS is suggested to be slightly less than the threshold strain for the appearance of DTs. The GBE-quantifying parameters are greatly improved by cold-rolling with 7% reduction and subsequently annealing at 1323 K for 12 h, and the fraction of special boundaries is increased up to 74.5%, thus effectively disrupting the connectivity of random high angle grain boundary network.

Metallization of diamond

Experimental discovery of ultralarge elastic deformation in nanoscale diamond and machine learning of its electronic and phonon structures have created opportunities to address new scientific questions. Can diamond, with an ultrawide bandgap of 5.6 eV, be completely metallized, solely under mechanical strain without phonon instability, so that its electronic bandgap fully vanishes? Through first-principles calculations, finite-element simulations validated by experiments, and neural network learning, we show here that metallization/demetallization as well as indirect-to-direct bandgap transitions can be achieved reversibly in diamond below threshold strain levels for phonon instability. We identify the pathway to metallization within six-dimensional strain space for different sample geometries. We also explore phonon-instability conditions that promote phase transition to graphite. These findings offer opportunities for tailoring properties of diamond via strain engineering for electronic, photonic, and quantum applications.

Multi-Scale White Matter Tract Embedded Brain Finite Element Model Predicts the Location of Traumatic Diffuse Axonal Injury.

Finite element models (FEMs) are used increasingly in the traumatic brain injury (TBI) field to provide an estimation of tissue responses and predict the probability of sustaining TBI after a biomechanical event. However, FEM studies have mainly focused on predicting the absence/presence of TBI rather than estimating the location of injury. In this study, we created a multi-scale FEM of the pig brain with embedded axonal tracts to estimate the sites of acute (≤6 h) traumatic axonal injury (TAI) after rapid head rotation. We examined three finite element (FE)-derived metrics related to the axonal bundle deformation and three FE-derived metrics based on brain tissue deformation for prediction of acute TAI location. Rapid head rotations were performed in pigs, and TAI neuropathological maps were generated and colocalized to the FEM. The distributions of the FEM-derived brain/axonal deformations spatially correlate with the locations of acute TAI. For each of the six metric candidates, we examined a matrix of different injury thresholds (thx) and distance to actual TAI sites (ds) to maximize the average of two optimization criteria. Three axonal deformation-related TAI candidates predicted the sites of acute TAI within 2.5 mm, but no brain tissue metric succeeded. The optimal range of thresholds for maximum axonal strain, maximum axonal strain rate, and maximum product of axonal strain and strain rate were 0.08-0.14, 40-90, and 2.0-7.5 s-1, respectively. The upper bounds of these thresholds resulted in higher true-positive prediction rate. In summary, this study confirmed the hypothesis that the large axonal-bundle deformations occur on/close to the areas that sustained TAI.

Expanded Byrne model for evaluating seismic compression

Seismic compression is the accrual of contractive volumetric strain in unsaturated or partially saturated sandy soils during earthquake shaking and has caused significant distress to overlying and nearby structures. The phenomenon can be well characterized by load-dependent, interaction macro-level fatigue theories. Toward this end, the Byrne cyclic shear-volumetric strain coupling model is expanded and calibrated for evaluating seismic compression for several soil types. In addition, the model was transformed to allow it to be implemented in a “simplified” manner, in addition to the original “non-simplified” formulation. Both implementation approaches are used to analyze a site in Japan impacted by the 2007, Mw6.6 Niigata-ken Chuetsu-oki earthquake. The results from the analyses are in general accord with the post-earthquake field observations and highlight the sensitivity of predicted magnitude of the seismic compression to the input variables used and modeling assumptions (e.g. relative density of the soil, magnitude of the volumetric threshold strain, orientation of the ground motions, settlement of soils below the ground water table, and accounting for multidirectional shaking). Although additional studies are needed to further validate the findings presented herein, estimation of relative density and threshold shear strain of the soil and ground motion orientation individually have moderate-to-significant influence on the computed magnitude of seismic compression, but they have a significant influence when taken in combination. Also, the seismic compression models can seemingly be used to predict the settlement in fully saturated sand when the excess pore water pressures are limited. Finally, accounting for multidirectional shaking has a significant influence on the computed magnitude of seismic compression.

Thermomechanical insight into the stability of nanoporous graphene membranes

Porous graphene (PG) is a graphene derivative endowed of nanoporous architectures. This material possesses a particular structure with interconnected networks of high pore volume, producing membranes with a large surface area. Experiments revealed that PG combines remarkable properties such as high mechanical strength and good thermal stability. In this work, we have carried out fully-atomistic reactive (ReaxFF) molecular dynamics simulations to perform a comprehensive study on the elastic properties, fracture mechanism, and thermal stability of 2D porous n-Benzo-CMPs (CMP and n refer, respectively, to π-conjugated microporous polymers and the pore diameter) membranes with distinct nanoporous architectures. For comparison purposes, the results were also contrasted with the ones for graphene sheets of similar dimensions. We adopted three different nanoporous diameters: small (3.45 Å), medium (8.07 Å), and large (11.93 Å). Results showed that PG is thermally stable up to 4660 K, about 1000 K smaller than the graphene melting point (5643 K). During the PG heating, linear atomic chains are formed combining carbon and hydrogen atoms. The fracture strains range between 15% and 34% by applying a uniaxial loading in both plane directions for temperatures up to 1200 K. The fracture strain increases proportionally with the nanoporous size. All the PG membranes go abruptly from elastic to completely fractured regimes after a critical strain threshold.

Dynamic performance of energy-absorbing rockbolts based on laboratory test results. Part II: Role of inherent features on dynamic performance of rockbolts

Deep mining and the related dynamic loading are the critical challenges confronting the reinforcement system like energy-absorbing rockbolts, which plays a decisive role in the dynamic response of underground mine excavations. Over the past decades, various types of novel energy-absorbing rockbolts with different deformation mechanisms and dynamic characteristics have been invented. Meanwhile, the test methods and facilities to quantify the dynamic performance of rockbolts have been proposed, and a lot of test results are obtained. In the companion Part II, with comparative analysis of test results along with available data from literature, some inherent features related to the dynamic performance of bolts have been revealed. The research indicates that, for both shank stretching and ploughing/extrusion bolts, the energy absorption is approximately proportional to the displacement. For the shank stretching bolts, only when the impact energy is higher than a threshold value, yield and strain hardening occurs; in the case of strain hardening, even a low impact energy can roughly predict the dynamic response curve. The statistical analysis of test results indicates that, in laboratory dynamic tests, the strain rate of bolts varies between 0.5/s and 3/s, and the increments of dynamic capacity enhancement factor (DCEF) is 3.4%-10.5%. For a particular bolt, DCEF can be roughly viewed as a constant which is mainly dependent on the yield strength level of the shank. Therefore, dynamic impact load can be approximated as a constant; the dynamic load–displacement curve can be simplified into a unique polyline segment comprising two line segments; and the impact duration is linearly related to the input momentum. These findings could be used for the pre-evaluation of the dynamic performance of the candidate bolts before laboratory test and support scheme design.

Sub-trabecular strain evolution in human trabecular bone

To comprehend the most detrimental characteristics behind bone fractures, it is key to understand the material and tissue level strain limits and their relation to failure sites. The aim of this study was to investigate the three-dimensional strain distribution and its evolution during loading at the sub-trabecular level in trabecular bone tissue. Human cadaver trabecular bone samples were compressed in situ until failure, while imaging with high-resolution synchrotron radiation X-ray tomography. Digital volume correlation was used to determine the strains inside the trabeculae. Regions without emerging damage were compared to those about to crack. Local strains in close vicinity of developing cracks were higher than previously reported for a whole trabecular structure and similar to those reported for single isolated trabeculae. Early literature on bone fracture strain thresholds at the tissue level seem to underestimate the maximum strain magnitudes in trabecular bone. Furthermore, we found lower strain levels and a reduced ability to capture detailed crack-paths with increased image voxel size. This highlights the dependence between the observed strain levels and the voxel size and that high-resolution is needed to investigate behavior of individual trabeculae. Furthermore, low trabecular thickness appears to be one predictor of developing cracks. In summary, this study investigated the local strains in whole trabecular structure at sub-trabecular resolution in human bone and confirmed the high strain magnitudes reported for single trabeculae under loading and, importantly extends its translation to the whole trabecular structure.

Local deformation behaviour of saturated silica sand during undrained cyclic torsional shear tests using image analysis

A series of undrained cyclic torsional shear tests was conducted to investigate the development of local deformations of silica sand specimens directly using an image-based technique and a transparent membrane. The results for saturated sand specimens with varying densities showed that the vertical slippage of sand particles relative to the membrane was initiated at the liquefaction stage. Additionally, the quantity of vertical slippage of dense specimens was lower than that of loose specimens tested under the same conditions. Moreover, measured on the surface of the specimen, the large accumulated movement during cyclic shearing significantly increased the potential for inducing vertical slippage. A comparison of local deformation among the different tests revealed that the threshold of shear strain to generate non-uniform local deformations decreased with an increase in the relative density of the specimen. A lower liquefaction resistance layer, which formed at the upper part of the specimen after initial liquefaction, would accelerate the concentration of local shear strain; this was especially distinct when the specimen was completely liquefied.

Method for slab track substructure design at a speed of 400 km/h

Abstract This paper presents a practical method for identifying the fundamental design parameters of a multilayered earth structure in ballastless tracks at an operational speed of 400 km/h. The properties of subgrade materials and layer thickness are determined based on vehicle–track coupled dynamic numerical analysis and integrated empirical models incorporating a threshold cyclic strain approach. The principle of the proposed method is to limit train-induced strain and deformation in the foundations in order to achieve satisfactory long-term track performance. Firstly, the critical velocity effect is introduced and briefly assessed for design purposes. Dynamic amplification factor (DAF) is obtained from the statistical analysis of simulated results of vertical vehicle–track coupled dynamic models. A trapezoidal stress pattern is used to characterize the mobilized stress distribution on the subgrade surface under two-axle moving loads of a vehicle on a slab track. The attenuation law of excess vertical soil stress in a substructure under traffic loads is consequently reproduced using Boussinesq’s equation. Next, two threshold strains are defined in accordance with the accumulation rate of residual subgrade settlement, predicted by empirical models as a function of the K 30 value (modulus of subgrade reaction) and plasticity index of the subgrade aggregate. Following this, the abovementioned results are synthesized into design criteria that can be readily utilized. The application of the proposed method is illustrated by an example of earthwork design. Field observations are finally presented for the validation of the developed approach. The design methodology will improve knowledge of slab track substructure design and is expected to extend the applicability of the current railway code to higher train speed conditions.

On the Mechanical Properties and Thermal Stability of a Recently Synthesized Monolayer Amorphous Carbon

Recently (C.-T. Toh et al., Nature 577, 199 (2020)), the first synthesis of free-standing monolayer amorphous carbon (MAC) was achieved. MAC is a pure carbon structure composed of five, six, seven and eight atom rings randomly distributed. MAC proved to be surprisingly stable and highly fracture resistant. Its electronic properties are similar to boron nitride. In this work, we have investigated the mechanical properties and thermal stability of MAC models using fully-atomistic reactive molecular dynamics simulations. For comparison purposes, the results are contrasted against pristine graphene (PG) models of similar dimensions. Our results show that MAC and PG exhibit distinct mechanical behavior and fracture dynamics patterns. While PG after a critical strain threshold goes directly from elastic to brittle regimes, MAC shows different elastic stages between these two regimes. Remarkably, MAC is thermally stable up to 3600 K, which is close to the PG melting point. These exceptional physical properties make MAC-based materials promising candidates for new technologies, such as flexible electronics.

Mechanoregulation modeling of bone healing in realistic fracture geometries.

In bone fracture healing, new tissue gradually forms, ossifies, and eventually remodels itself to restore mechanical stiffness and strength across injury site. Mechanical strain at the fracture site has been implicated in controlling the process of healing and numerical mechanoregulation models with strain-based fuzzy logic rules have been applied to simulate bone healing for simple fracture geometries. However, many of these simplified models cannot capture in vivo observations such as delays in healing with torsional instability or differences in healing rate between different fracture types. Accordingly, the purpose of this work was to apply a fuzzy logic mechanoregulation fracture healing simulation technique to 3D models representing a range of clinically inspired fracture geometries with intramedullary nail fixation and multiaxial loading conditions. The models predicted that the rate of healing depends on the geometry of the fracture and that all fracture types experience a small healing delay with torsional instability. The results also indicated that when realistic torsional loading and fixator mechanics are included, previously published strain-based rules for tissue destruction lead to simulated nonunions that would not be expected in vivo. This suggested that fracture healing may be more robust to distortional strain than has been previously reported and that fuzzy logic models may require parameter tuning to correctly capture clinically relevant healing. The strengths of this study are that it includes fracture morphology effects, realistic implant mechanics, and an exploratory adaptation of the upper distortional strain threshold. These findings may help future researchers extend these methods into clinical fracture healing prediction.

Dynamic Analysis of Scarf Adhesive Joints in Carbon-Fiber Composites at Different Temperatures

The dynamic performance of scarf adhesive joints (SAJs) in fiber-reinforced polymer composites is a new topic that is not available in the literature yet; introducing it is one of the objectives of this study. Changes in stiffness, ratcheting strain, loss factor (), loss modulus (), storage modulus (), dissipated energy (), and potential energy () with the number of fatigue cycles were measured at room temperature (RT), , and 50°C. It was found that fatigue lives were longer at than at RT and 50°C. Fatigue life at plastic strain threshold was decreased by about 98% of the joint lifetime at 50°C. The behavior of agrees qualitatively with and . The improved ductility of the SAJs at 50°C induces significant changes in and , and hence they can be used to monitor the integrity of the SAJs and early prediction of fatigue failure. At , the and behave approximately in a linear constant manner up to sudden failure without warning. Accordingly, safe design fatigue life based on time to first failure was applied to evaluate the stress versus number of cycles to failure curves of the SAJs at different reliabilities.

Long-term dynamic stability of improved loess subgrade for high-speed railways

Loess material requires improvement before being used as a filler for the bottom layer of the subgrade bed and substructure of a high-speed railway. Currently, cement and lime are often used to improve loess in engineering. However, whether improved loess material and the solution of key problems of the different types of improved loess can meet the long-term dynamic stability requirements of the bottom layer of a high-speed railway subgrade needs further study. Dynamic triaxial tests on cement-improved (CI) and lime-improved (LI) loess specimens were conducted to study the cyclic shear strain threshold and critical dynamic stress and to evaluate the long-term dynamic stability of CI and LI loess as fillers for the bottom layer of a subgrade bed. The results showed that the two improved loess materials can meet the long-term dynamic stability requirements when used as the bottom layer of a high-speed railway subgrade. After comprehensive consideration, 5% cement or 6% lime is recommended, with the CI soil prioritised. Compared with the critical dynamic stress method, the dynamic shear strain evaluation method is a more systematic and comprehensive method for evaluating the long-term dynamic stability of roadbeds. The research results can provide a technical reference for subgrade filler selection and subgrade design in a loess area.

Phase diagrams of single-layer two-dimensional transition metal dichalcogenides: Landau theory

Single layer (SL) two-dimensional transition metal dichalcogenides (TMDs), such as MoS2, ReS2, WSe2, and MoTe2 have now become the focus of intensive fundamental and applied researches due to their intriguing and tunable physical properties. These materials exhibit a broad range of structural phases that can be induced via elastic strain, chemical doping, and electrostatic field effect. These transitions in turn can open and close the band gap of SL-TMDs, leading to metal-insulator transitions, and lead to emergence of more complex quantum phenomena. These considerations necessitate detailed understanding of the mesoscopic mechanisms of these structural phase transitions. Here we develop the Landau-type thermodynamic description of SL-TMDs on example of SL-(MoS2)1-x-(ReS2)x system and analyze the free energy surfaces, phase diagrams, and order parameter behavior. Our results predict the existence of multiple structural phases with 2-, 6- and 12-fold degenerated energy minima for in-plane and out of plane order parameters. This analysis suggests that out-of-plane ferroelectricity can exist in many of these phases, with the switchable polarization being proportional to the out-of-plane order parameter. We further predict that the domain walls in SL-(MoS2)1-x-(ReS2)x should become conductive above a certain strain threshold.

Finite Element Analysis of Changes in Tensile Strain by Airsoft Gun Impact on Eye and Deformation Rate in Eyes of Various Axial Lengths.

PurposeWe have carried out three-dimensional finite element analysis (FEA) to determine the physical and mechanical response in several ocular injuries. We applied this FEA model to evaluate an airsoft gun impact on an eye and the deformation rate of eyes of various axial lengths at various velocities.MethodsThis study was carried out on a human eye model using an FEA program created by Nihon, ESI Group. The airsoft gun pellet was set to impact the eye at initial velocities of 45, 60 and 75 m/s with the addition of variation in axial length of 20 mm (hyperopia), 22 mm (emmetropia), 24 mm (myopia) and 26 mm (high myopia). Deformation of the eye was calculated as the decrease rate of the volume of the eyeball and the decrease rate of the axial length.ResultsIn all emmetropic cases, the cornea reached its strain threshold during the impact, and scleral strain showed a patchy strength distribution in the simulation. The deformation was most evident in the anterior segment, while deformation of the posterior segment was less. The decrease rate of the volume of the eyeball and decrease rate of the axial length were highest in the hyperopic eye, followed by the emmetropic eye and myopic eye, and the high myopic eye showed the lowest decrease rates among the four axial lengths in all impact velocity simulations.ConclusionThese results suggest that hyperopic eyes are most susceptible to deformation by an airsoft gun impact compared with other axial length eye models in this simulation. The considerable deformation by an airsoft gun impact shown in this study might indicate the necessity of ocular protection to avoid permanent eye injury. FEA using a human eyeball model might be a useful method to analyze and predict the mechanical features of ocular injury by an airsoft gun.

Comparison of cracking sensitivity between high-permeability 1.5 wt% Si steel and 6.5 wt% Si steel in mushy zone

Twin-roll thin strip casting process (SC) has been utilized in laboratory to fabricate typical high-permeability electrical steel (HPES) such as 1.5 wt% Si and 6.5 wt% Si steel with ideal crystallographic orientation and excellent permeability after a series of heat treatments. Whereas, there exists a problem associated to the cracking sensitivity in high temperature mushy zone, which further restricts the industrial application of SC to produce HPES. Mechanical behavior of 1.5 wt% Si and 6.5 wt% Si steels in high temperature mushy zone were comparatively studied by Gleeble-3800 physical simulation system under strain rate 3 s−1, systematically. The high temperature brittle region composed of zero strength temperature (ZST) and zero ductility temperature (ZDT) in the mushy zone were quantitatively determined, and the critical strain threshold associated to hot crack initiation in the brittle region were further evaluated following empirical model proposed by Y Won. Results show that the tensile strength and fracture ductility in the mushy zone are both closely associated with the varying volume fraction of network-shaped structure during solidification, and are decreased with decreasing solid fraction concerning studied 1.5 wt% Si and 6.5 wt% Si steels. The high temperature brittle region corresponding to the studied 1.5 wt% Si and 6.5 wt% Si steels in mushy zone are separately confirmed to be 1459 ~ 1465℃ and 1390 ~ 1427℃, and the thresholds of critical strain for hot cracks initiation in high temperature brittle region are calculated to be ~ 1.18% and ~ 0.24%, respectively. Considering from perspective of width of high temperature brittle region and critical strain threshold for hot crack initiation, the cracking sensitivity of 6.5 wt% Si steel in the mushy zone is more serious compared to 1.5 wt% Si steel.

Nonlinear quasilocalized excitations in glasses: True representatives of soft spots.

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations-often called "soft spots"-that are believed to play a key role in various thermodynamic, transport, and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multidimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g., phonons. In this series of papers we reintroduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes-coined here nonlinear quasilocalized excitations (NQEs)-that are defined via an anharmonic (nonlinear) analysis of the potential-energy landscape of a glass, and do not hybridize with other low-energy excitations. In this paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, nonhybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential-energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

Dynamic properties of a sand–nanoclay composite

The paper describes the influence of 1–3% (by dry mass of sand) Laponite, a highly plastic synthetic nanoclay, on the dynamic properties of Ottawa sand, based on undrained resonant column tests. The effect of Laponite depends on the amount added, the confining stress and consolidation time. With 1% Laponite, there is an increase in the very small-strain shear stiffness at all confining stresses, which increases with extended consolidation time, reflecting the thixotropic nature of the nanoclay. Added Laponite also produces an increase in small-strain damping, an extension of the linear strain threshold; and it delays the generation of excess pore pressure, degradation of shear modulus and increase in damping with shear strain. These effects, which become more significant with increasing Laponite content, can be attributed to the impact of the clay on the fabric and grain-to-grain contacts. Evidence is provided that Laponite interferes with direct interaction between the sand grains, and the thickness of the clay layer present at the contacts appears to control the small-strain behaviour of the sand–Laponite mixtures. The formation of a gel-like pore fluid from the hydration of Laponite in the voids, and the degree to which it occupies the pore space, are responsible for the behaviour in the non-linear region.