A stress analytical solution for Mode III crack within modified gradient elasticity

The strain gradient exists near a crack tip may significantly influence the near-tip stress field. In this paper, the strain gradient and the internal length scales are introduced into the basic equations of mode III crack by the modified gradient elasticity (MGE). By using a complex function approach, the analytical solution of stress fields for mode III crack problem is derived within MGE. When the internal length scales vanish, the stress fields can be simplified to the stress fields of classical linear elastic fracture mechanics. The results show that the singularity of the shear stress is made up of two parts, r^−1/2 part and r^−3/2 part, and the sign of the stress σ_yz changes. With the increase of l_x, the peak value of σ_yz decrease and its location moves farther from the fracture vertex. The influence of strain gradient for mode III crack problem cannot be ignored.     

On the propagation and pulsation of Portevin-Le Chatelier deformation bands: An experimental study with digital speckle pattern metrology

The Portevin-Le Chatelier (PLC) effect is closely associated with inhomogeneous deformation, which is characterized by the band of strain localization. In this work, the spatio-temporal dynamics of the Portevin-Le Chatelier deformation bands are investigated by a novel digital speckle pattern metrology technique consisting of digital speckle pattern interferometry (DSPI) and digital speckle correlation (DSC). A series of tension process of a commercial aluminum alloy (A2017) under different imposed strain rates in a range from 10⁻⁶ to 10⁻³ s⁻¹ are monitored in real time with this technique. The formation of the PLC band, the evolution of the band structure and the propagation of the band are visualized and followed by fringe patterns. The distribution of the deformation in the specimen containing the band is measured precisely. It is shown that even for a tensile test, an elastic shrinkage deformation, which is caused by the avalanche-like shearing deformation within the band, occurs outside the band.     

Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers—polycarbonate and poly(methyl methacrylate)—at strain rates ranging from 10⁻⁴ to 10⁴ s⁻¹. This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on the servo-hydraulic machine (10⁻⁴ to 1 s⁻¹) and the split-Hopkinson pressure bar (10³ to 10⁴ s⁻¹) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the β-transition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.     

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10¹ s⁻¹ to 10¹⁰ s⁻¹ in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10⁶ s⁻¹, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10⁶ s⁻¹, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10⁸ s⁻¹, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10⁷ s⁻¹ homogeneous nucleation becomes the dominant generation mechanism.     

Biogenic synthesis of silver nanoparticles using Persicaria odorata leaf extract: Antibacterial,cytocompatibility, and in vitro wound healing evaluation

Biogenic synthesis of silver nanoparticles (b-AgNPs) utilising plant extract has gained the interest of researchers due to the environmentally friendly and cost-effective technique. However, the extent of its application in the biomedical field remains scarce. This study evaluates the antibacterial, cytocompatibility, and wound healing activities of synthesised AgNPs using Persicaria odorata leaves extract (PO-AgNPs). The formation of PO-AgNPs was observed by visual colour changes and verified by ultraviolet-visible (UV–vis) spectrophotometer, which revealed a surface plasmon resonance (SPR) at around 440 nm, and further confirmed by X-ray diffraction (XRD). Characterisation using Fourier transform infrared (FTIR) spectroscopy showed biomolecules from the leaves extract presented together on PO-AgNPs. Field emission scanning electron microscope (FESEM) and high-resolution transmission electron microscopy (HR-TEM) images revealed PO-AgNPs nanospheres with diameters of 11 ± 3 nm. Disc diffusion test (DDT) and minimum inhibitory concentration (MIC) analysis resulted in a dose-dependent inhibition of PO-AgNPs against tested Staphylococcus epidermidis and Methicillin-resistant Staphylococcus aureus (MRSA). These results were further corroborated by time-kill kinetic assay which revealed that PO-AgNPs were bactericidal against both strains 24 h post-treatment. Cytocompatibility and in vitro wound healing evaluation against normal human fibroblast cells, HSF 1184 inferred that PO-AgNPs are non-toxic to normal cells and able to enhance cell migration as compared to the non-treated cells. Therefore, PO-AgNPs are biocompatible and possess antibacterial and wound healing capabilities that are useful in biomedical applications.     

Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (−40 °C to 180 °C) and strain rates (0.0001 s⁻¹ up to 5000 s⁻¹). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the β mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.     

Full-field strain measurements of the inside of an agricultural tyre using digital image correlation

This paper investigates strain measured on the inside of an agricultural tyre with large tread-blocks during a series of static tests using a novel measuring system. The full field strain measurements may be used in the development of a tyre which is capable of estimating tyre forces from strain measurements. The strain measurement system makes use of a calibrated stereo camera system on a mechanical stabilizing system that keeps the cameras pointed at the inside surface of the tyre in contact with the road while the wheel rotates. A static tyre test rig is used to displace the road surface relative to the tyre in the vertical and longitudinal direction. The large tread-blocks caused strain concentrations on the inner surface as the tyre deforms to comply with the road surface. Vertical and longitudinal tests each produce unique strain patterns in the contact patch region. Relationships between the applied forces and strain measurements were developed and showed that these relationships are near linear with R² values above 0.97. The strain measurements also show that the location where strain gauges, for single point strain measurements, are placed inside the tyre is very important on large lugged tyres.     

Compositional characteristics and toxicological responses of human lung epithelial cells to inhalable particles (PM10) from ten typical biomass fuel combustions

As the primary component of haze, atmospheric inhalable particulate matters (PM₁₀) are highly detrimental to human health. Biomass combustion is one of China's most pivotal sources to aerosols pollution, inducing non-negligible emissions and uncertain risks. PM₁₀ samples directly from 10 representative biomass fuel combustion sources (2 groups covering the reality widely: straws of rice, wheat, corn, corncob, soybean, peanut, rape, sesame; and branches of pine, peach) were collected using the dilution channel sampler and analyzed for chemical compositions and in vitro cytotoxicity to human lung epithelial cell lines A549. The components of PM₁₀ are dominated by organic carbon (OC), followed by water-soluble K⁺ and Cl⁻, and rich in metals Fe, Zn, Cr, and Ni. Generally, PM₁₀ emitted from biomass fuel combustions can weaken the antioxidant capacity of cells, and straws emissions, especially rape and peanut straws, show stronger ability to further induce oxidative stress and inflammatory damage than fuelwoods, owing to the key toxic roles of Cr, Ni, and Co. Therefore, reducing the specific source emissions of PM₁₀ from crop straw combustions rich in heavy metals could be an effective oriented strategy to improve environmental air quality and control aerosols pollution precisely for protecting public health.     

Size effects in generalised continuum crystal plasticity for two-phase laminates

The solutions of a boundary value problem are explored for various classes of generalised crystal plasticity models including Cosserat, strain gradient and micromorphic crystal plasticity. The considered microstructure consists of a two-phase laminate containing a purely elastic and an elasto-plastic phase undergoing single or double slip. The local distributions of plastic slip, lattice rotation and stresses are derived when the microstructure is subjected to simple shear. The arising size effects are characterised by the overall extra back stress component resulting from the action of higher order stresses, a characteristic length l_c describing the size-dependent domain of material response, and by the corresponding scaling law lⁿ as a function of microstructural length scale, l. Explicit relations for these quantities are derived and compared for the different models. The conditions at the interface between the elastic and elasto-plastic phases are shown to play a major role in the solution. A range of material parameters is shown to exist for which the Cosserat and micromorphic approaches exhibit the same behaviour. The models display in general significantly different asymptotic regimes for small microstructural length scales. Scaling power laws with the exponent continuously ranging from 0 to −2 are obtained depending on the values of the material parameters. The unusual exponent value −2 is obtained for the strain gradient plasticity model, denoted “curl H^p” in this work. These results provide guidelines for the identification of higher order material parameters of crystal plasticity models from experimental data, such as precipitate size effects in precipitate strengthened alloys.     

An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to graphene

Force multipoles are employed to represent various types of defects and physical phenomena in solids: point defects (interstitials, vacancies), surface steps and islands, proteins on biological membranes, inclusions, extended defects, and biological cell interactions among others. In the present work, we (i) as a prototype simple test case, conduct quantum mechanical calculations for mechanics of defects in graphene sheet and in parallel, (ii) formulate an enriched continuum elasticity theory of force dipoles of various anisotropies incorporating up to second gradients of strain fields (thus accounting for nonlocal dispersive effects) instead of the usual dispersion-less classical elasticity formulation that depends on just the strain (c.f. Peyla, P., Misbah, C., 2003. Elastic interaction between defects in thin and 2-D films. Eur. Phys. J. B. 33, 233-247). The fundamental Green's function is derived for the governing equations of second gradient elasticity and the elastic self and interaction energies between force dipoles are formulated for both the two-dimensional thin film and the three-dimensional case. While our continuum results asymptotically yield the same interaction energy law as Peyla and Misbah for large defect separations (∼1/rⁿ for defects with n-fold symmetry), the near-field interactions are qualitatively far more complex and free of singularities. Certain qualitative behavior of defect mechanics predicted by atomistic calculations are well captured by our enriched continuum models in contrast to classical elasticity calculations. For example, consistent with our atomistic calculations of defects in isotropic graphene, even two dilation centers show a finite interaction (as opposed to classical elasticity that predicts zero interaction). We explicitly find the physically consistent result that the self-energy of a defect is equivalent to half the interaction energy between two identical defects when they “merge” into each other. The atomistic, classical elastic and the enriched continuum predictions are thoroughly compared for two types of defects in graphene: Stone-Wales and divacancy.     

Boundary discretization based on the residual energy using the SGBEM

The paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the Symmetric Galerkin Boundary Element Method (SGBEM) and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization. The body, characterized by a domain Ω and a boundary Γ⁻, is embedded inside a complementary unlimited domain Ω_∞⧹Ω bounded by a boundary Γ⁺. In such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work, defined generalized, obtained as the product among nodal and weighted quantities on the actual boundary Γ⁻ and on the complementary boundary Γ⁺. In order to reduce the error in the analysis phases, the scattered energy has been computed as generalized work in each boundary element of Γ⁺ and an adequate node number has been introduced inside the boundary elements where this generalized work is higher. This strategy, made in a recursive way, has shown effectiveness whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in Ω_∞⧹Ω and the total work, both expressed in terms of generalized quantities.     

Thermomechanical behavior of casting sands: Experiments and elastoplastic modeling

The thermomechanical behavior of casting sands is discussed from an experimental and a theoretical point of view. Uniaxial compression tests at temperatures ranging from 20°C to 950°C and at different values of strain rate (ϵ = 10⁻² s⁻¹, ϵ = 10⁻³ s⁻¹ and ϵ = 10⁻⁴ s⁻¹) have been performed. They show that casting sands exhibit no strain rate effect in the temperature range 20–600°C, and that an elastoplastic model is well suited to describe the experimental results. Three thermoelastoplastic models, derived from Cam Clay and Hujeux models have been developed. These new models take into account the cohesion of the material. The physical parameters needed for these models have been obtained in the temperature range 20–300°C by using triaxial tests, uniaxial compression tests, isotropic compression tests and die pressing tests. An original triaxial apparatus has been built allowing a temperature of 800°C and a pressure of 4 MPa to be reached. In the temperature at which the parameters have been obtained (20–300°C), two additional triaxial compression tests at different confining pressures are used to check the validity of the thermoelastoplastic models used. The best quantitative results are obtained with the revised modified Cam Clay model.     

The interferometric strain gage

The interferometric strain gage consists of two very shallow grooves ruled on a highly polished surface. The grooves are cut with a diamond and are 4×10^?5 in. deep and 5×10^?3 in. apart. Coherent, monochromatic light from a He?Ne gas laser incident upon these grooves will produce fringe patterns. A fringe pattern with the fringes parallel to the grooves is formed on each side of the impinging beam. The position of these patterns in space is related to the distance between the two grooves. As this distance changes, the fringes shift. Measurement of these fringe shifts enables one to determine the local strain of the specimen. In this paper, the theory of the measurement is developed first. The strain, ∈, is given by ∈=ΔFλ/d _o sin α _o where ΔF is the average fringe shift of the two patterns, λ is the wavelength of light,d _o is the initial distance between grooves, and α _o is the angle between the incident light beam and the fringe patterns. A procedure for making static measurements with the interferometric strain gage is presented. The sensitivity for these measurements is 0.5 percent strain per fringe shift, and the maximum strain is 4 percent. The method is evaluated by comparing its results with other accepted means of measuring large plastic strain. These other techniques are: post-yield foil gages, a 2-in. clip gage, and an Instron testing machine. The average percent difference among these techniques is less than 0.4 percent based on a full-scale measurement of 4-percent strain. The interferometric strain gage has the following features: a gage integral with the specimen surface, a very short gage length, relatively easy application, and the ability to measure large strains.     

Semi-analytical solution of consolidation for composite ground

A number of consolidation solutions of composite ground which ignores the nonlinear character of soft soil and columns have been derived. In this paper, the e−log σ′ and e−log k relationship is used to describe the stress–strain and strain–permeability coefficient relationship of soft soil. The nonlinear compressive character of stone columns is considered. With the assumption that the initial stresses of soil and columns increase linearly along the depth, a semi-analytical method by dividing the computing unit and segmenting the consolidation time is introduced, and some nonlinear consolidation properties of composite ground are analyzed.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

On the interplay between material flaws and dynamic necking

In this paper we investigate the interplay between material defects and flow localization in elastoplastic bars subjected to dynamic tension. For that task, we have developed a 1D finite difference scheme within a large deformation framework in which the material is modelled using rate-dependent J₂ plasticity. A perturbation of the initial yield stress is introduced in each node of the finite difference mesh to model localized material flaws. Numerical computations are carried out within a wide spectrum of strain rates ranging from 500 s⁻¹ to 2500 s⁻¹. On the one hand, our calculations reveal the effect of the material defects in the necking process. On the other hand, our results show that the necking inception, instead of being a random type process, is the deterministic result of the interplay between the mechanical behaviour of the material and the boundary conditions. This conclusion agrees with the experimental evidence reported by Rittel et al. [1] and Rotbaum et al. [2].     

Dynamics as a mechanism preventing the formation of finer and finer microstructure

We study the dynamics of pattern formation in the one-dimensional partial differential equation $$u_u - (W'(u_x ))_x - u_{xxt} + u = 0{\text{ (}}u = u(x,t),{\text{ }}x \in (0,1),{\text{ }}t > 0)$$ proposed recently by Ball, Holmes, James, Pego & Swart [BHJPS] as a mathematical “cartoon” for the dynamic formation of microstructures observed in various crystalline solids. Here W is a double-well potential like 1/4((u _x )² ?1)². What makes this equation interesting and unusual is that it possesses as a Lyapunov function a free energy (consisting of kinetic energy plus a nonconvex “elastic” energy, but no interfacial energy contribution) which does not attain a minimum but favours the formation of finer and finer phase mixtures: $$E[u,u_t ] = \int\limits_0^1 {(\frac{{u_t^2 }}{2} + W(u_x ) + \frac{{u^2 }}{2})dx.}$$ Our analysis of the dynamics confirms the following surprising and striking difference between statics and dynamics, conjectured in [BHJPS] on the basis of numerical simulations of Swart & Holmes [SH]:

?While minimizing the above energy predicts infinitely fine patterns (mathematically: weak but not strong convergence of all minimizing sequences (u _nv_n) of E[u,v] in the Sobolev space W ^{1 p}(0, 1)×L²(0,1)), solutions to the evolution equation of ball et al. typically develop patterns of small but finite length scale (mathematically: strong convergence in W ₁ ^p(0,1)×L²(0,1) of all solutions (u(t),u_t(t)) with low initial energy as time t → ∞).

Moreover, in order to understand the finer details of why the dynamics fails to mimic the behaviour of minimizing sequences and how solutions select their limiting pattern, we present a detailed analysis of the evolution of a restricted class of initial data — those where the strain field u _x has a transition layer structure; our analysis includes proofs that

?at low energy, the number of phases is in fact exactly preserved, that is, there is no nucleation or coarsening

?transition layers lock in and steepen exponentially fast, converging to discontinuous stationary sharp interfaces as time t → ∞

?the limiting patterns — while not minimizing energy globally — are ‘relative minimizers’ in the weak sense of the calculus of variations, that is, minimizers among all patterns which share the same strain interface positions.

     

The plastic deformation of non-homogeneous polycrystals

To describe the work hardening process of polycrystals processed using various thermomechanical cycles with isochronal annealing from 500 to 900 °C, a dislocation based strain hardening model constructed in the basis of the so-called Kocks–Mecking model is proposed. The time and temperature dependence of flow stress is accounted via grain boundary migration, and the migration is related to annihilation of extrinsic grain boundary dislocations (EGBD’s) by climb via lattice diffusion of vacancies at the triple points. Recovery of yield stress is associated with changes in the total dislocation density term ρ^T. A sequence of deformation and annealing steps generally result in reduction of flow stress via the annihilation of the total dislocation density ρ^T defined as the sum of geometrically necessary dislocations ρ^G and statistically stored dislocations ρ^S. The predicted variation of yield stress with annealing temperature and cold working stages is in agreement with experimental observations. An attempt is made to determine the mathematical expressions which best describe the deformation behaviour of polycrystals in uniaxial deformation.     

Adiabatic shear localization in the dynamic punch test,part I: experimental investigation

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during a dynamic punch test is investigated. Specifically, the possibility and affects of adiabatic shear localization are examined. The three materials are chosen to encompass a wide range of physical properties. Punch tests are conducted at average shear strain rates from 10⁻³ to 10⁴ s⁻¹ on a servo-hydraulic compression machine, a mechanical press, and a Hopkinson bar apparatus. Experimental load displacement curves are obtained and fractographic and metallographic analysis is performed. Finite element simulations of punching operations are performed in the second part of this two part investigation to examine internal deformation not visible during experimental tests. More specifically, the role of adiabatic shear localization in burr formation is determined. Adiabatic shear localization occurs in the titanium alloy for the mechanical press and Hopkinson bar tests, while localization is not present for the 6061-T6 aluminum in any test. The 1018 steel begins to exhibit some transitional behavior toward shear localization in the Hopkinson bar experiments. It is seen that in the materials tested here, a combination of high strength and low strain hardening make a material more susceptible to adiabatic shear localization in punching operations.