Interferometric grating method and its application in Fe-base shape memory alloy structure design

This paper presents an interferometric grating method used in measuring strain fields on a curved surface. This method can be used to determine the small and large strains with high sensitivity and has been applied successfully in Fe-base shape memory alloy (FSMA) structure design. In this study, five diffracted beam from the specimen surface produce the interferometric gratings through an optical system. Using image processing technique (fast Fourier transform with special interpolation and phase shifting technique), we have obtained the strain fields of outer surface of FSMA joint and contact pressure distribution on its inside surface which has mechanical deformation and transformation.     

Band gap of carbon nanotubes under combined uniaxial–torsional strain

Within tight-binding model, the band gaps of armchair and zigzag carbon nanotubes (CNTs) under both uniaxial tensile and torsional strains have been studied. It is found that the changes in band gaps of CNTs depend strongly on the strain type. The torsional strain can induce a band gap for armchair CNTs, but it has little effect on band gap of the zigzag CNTs. While the tensile strain has great effect on band gap of zigzag CNTs, but it has no effect on that of the armchair CNTs. More importantly, when both the tensile and torsional strains are simultaneously applied to the CNTs, the band gap changes of armchair CNTs are not equal to a simple sum over those induced separately by uniaxial tensile and torsional strains. There exists a cooperative effect between two kinds of strains on band gap changes of armchair CNTs. But for zigzag CNTs, the cooperative effect was not found. Analytical expressions for the band gaps of armchair and zigzag CNTs under combined uniaxial–torsional strains have been derived, which agree well with the numerical results.     

Spin-valley Hall conductivity of doped ferromagnetic silicene under strain

The spin-valley Hall conductivity(SHC-VHC) of two-dimensional material ferromagnetic graphene's silicon analog,silicene, is investigated in the presence of strain within the Kubo formalism in the context of the Kane–Mele Hamiltonian.The Dirac cone approximation has been used to investigate the dynamics of carriers under the strain along the armchair(AC) direction. In particular, we study the effect of external static electric field on these conductivities under the strain.In the presence of the strain, the carriers have a larger effective mass and the transport decreases. Our findings show that SHC changes with respect to the direction of the applied electric field symmetrically while VHC increases independently.Furthermore, the reflection symmetry of the structure has been broken with the electric field and a phase transition occurs to topological insulator for strained ferromagnetic silicene. A critical strain is found in the presence of the electric field around 45%. SHC(VHC) decreases(increases) for strains smaller than this value symmetrically while it increases(decreases) for strains larger than one.     

Piezoelectricity of the ice nanotube with odd side faces

The molecular dynamics (MD) simulations have been utilized to investigate the strain effect on the polarization distribution and piezoelectric coefficient of the ice nanotube (ice-NT) with odd side faces. It is found that the polarization of the system increases under the compressive strain, and decreases with the tensile strain. The piezoelectric coefficient is about 1.3 C/m² for a single 〈5, 0〉 ice-NT with its diameter of 4.34 Å, which is superior to BaTiO₃ nanowire, the ferroelectricity of the latter with the same diameter has been vanished owning to the depolarization effect. We have also considered the axial strain energy under the different strains, and found that most of the strain energy in the compressive process seems larger than that of the stretching case.     

Some effects of inhomogeneous strain on surface properties of metals: I. Flat surface

Jelium model calculations using the many electron formalism and a parameterized charge density distribution have been used to evaluate the change in surface energy, barrier height and work function due to the presence of a tensile and compressive strain gradient at the surface of Cs, Rb, K and Na. The method is useful for short range strain fields (? 4–5 atom spacings), but not for larger fields. The surface energy change due to inhomogeneous strain is almost twice as large as that due to homogeneous strain. The work function changes due to inhomogeneous strain are ~10–10² times larger than those due to homogeneous strains. The results are of considerable importance to general fracture and stress corrosion cracking studies.     

Flutter analysis of cantilevered quadrilateral plates

In this paper, the title problem is solved by using a numerical method involving an integral equation technique and a normal mode method. Linear plate theory has been used for computing the strain energy and kinetic energy of the plate. Piston theory has been used to describe the aerodynamic pressure distribution. Numerical work has been done and convergence of the solution has been studied. Results have also been obtained for various cases and compared with those of other investigators.     

Automated fine grid technique for measurement of large-strain deformation maps

The fine grid technique has been a standard engineering tool for measuring large strains for many years. The sample surface is marked with a grid, and the deformation of this grid allows the deformation of the sample to be monitored. However, it has never been easy quantitatively to analyse the strain across the whole of a specimen's surface. We describe here an automated approach in which digitised images of a sample prepared with a grid are analysed by the Fourier transform method. This provides phase maps which, when unwrapped, yield planes representing the two in-plane specimen coordinates. An iterative technique follows these deforming planes from one frame to the next as the specimen deforms, allowing displacement fields to be calculated. Numerical differentiation gives strains across the specimen surface. Gerchberg iteration is used to provide immunity to errors resulting from holes or tears in the specimen surface. The method is demonstrated on a propellant simulant containing burn holes (a cylinder of diameter 10 mm; grid PITCH = 76 μm), loaded in compression across a diameter. All in-plane components of strain are calculated up to strains of approximately one-third. Displacement accuracy is of order 1 μm.     

Velocities of sound and the densities of phonon states in a uniformly strained flat graphene sheet

The effect of elastic strain on the mechanical and physical properties of graphene has been intensively studied in recent years. Using the molecular dynamics method, a surface has been built in the three-dimensional space of components of the plane strain tensor bounds the region of the structural stability of a flat graphene sheet without considering thermal vibrations and the influence of boundary conditions. The velocities of sound and the densities of phonon states in graphene subjected to an elastic strain within the region of the structural stability have been calculated. It has been shown that one of the velocities of sound becomes zero near the stability boundary of a flat graphene sheet. During biaxial tension of graphene, there is no gap in its phonon spectrum; however, it forms under uniaxial tension along the zigzag or armchair directions and also under combined tensile and compressive strains.     

Single-step scanner-based digital image correlation (SB-DIC) method for large deformation mapping in rubber

The incremental digital image correlation (DIC) method has been applied in the past to determine strain in large deformation materials like rubber. This method is, however, prone to cumulative errors since the total displacement is determined by combining the displacements in numerous stages of the deformation. In this work, a method of mapping large strains in rubber using DIC in a single-step without the need for a series of deformation images is proposed. The reference subsets were deformed using deformation factors obtained from the fitted mean stress-axial stretch ratio curve obtained experimentally and the theoretical Poisson function. The deformed reference subsets were then correlated with the deformed image after loading. The recently developed scanner-based digital image correlation (SB-DIC) method was applied on dumbbell rubber specimens to obtain the in-plane displacement fields up to 350% axial strain. Comparison of the mean axial strains determined from the single-step SB-DIC method with those from the incremental SB-DIC method showed an average difference of 4.7%. Two rectangular rubber specimens containing circular and square holes were deformed and analysed using the proposed method. The resultant strain maps from the single-step SB-DIC method were compared with the results of finite element modeling (FEM). The comparison shows that the proposed single-step SB-DIC method can be used to map the strain distribution accurately in large deformation materials like rubber at much shorter time compared to the incremental DIC method.     

Experimental determination of Representative Volume Element (RVE) size in woven composites

A systematic approach is proposed to estimate the length scales of the representative volume element (RVE) in orthogonal plain woven composites. The approach is based on experimental full-field deformation measurements at mesoscopic scales. Stereovision digital image correlation (DIC) is conducted to determine the full-field strain distribution in on- and off-axis specimens loaded axially in tension. A sensitivity analysis is carried out to optimize the image correlation parameters. Using the optimized set of image correlation parameters, full-field strains are measured and used in conjunction with a simple strain averaging algorithm to identify the length scales at which globally applied and spatially-averaged local strains converge in values. The size of a virtual window containing local strain data, the average of which has the same value as the global strain, is identified as the RVE dimensions for the examined material. The smallest RVE sizes found in this work are shown to be both strain and angle dependent. The largest RVE dimension obtained is reported as a unique, strain and orientation insensitive RVE size for the woven composite examined.     

Calculation of natural frequencies of fixed-free circular cylindrical shells

A theoretical analysis is discussed here in detail which is used to investigate the natural frequencies of fixed-free circular cylindrical shells. The results are compared with the experimental observations of other workers. Analytical results are, in general, in reasonably good agreement with the experimental results.The effect of the simplifying assumption of zero hoop and shear strains has been studied carefully. It is shown that for shells of large length-to-radius ratio this assumption can be incorporated resulting in a major simplification of the analysis involved without significantly affecting the accuracy of the results, whereas for shells of small length-to-radius ratio and for higher axial modes the simplified analysis must be used with care, especially for the low circumferential wave numbers because the effect there is to significantly increase the natural frequencies. In an attempt to understand the physical significance of this assumption, calculations were made to estimate the proportion of strain energy due to bending and stretching actions for various modal arrangements with and without this assumption. It was found that the effect of the assumption is to increase considerably the strain energy due to extension with little effect on the strain energy due to bending and thus increase the total strain energy, substantially in case of the shells with small length-to-radius ratio and for higher axial modes with consequent increase in the natural frequencies. In such cases the analysis without making this assumption is to be used and it is shown that this can quite easily be handled.The integrals involving characteristic beam functions have been derived in closed form.     

A new paradigm for the molecular basis of rubber elasticity

The molecular basis for rubber elasticity is arguably the oldest and one of the most important questions in the field of polymer physics. The theoretical investigation of rubber elasticity began in earnest almost a century ago with the development of analytic thermodynamic models, based on simple, highly-symmetric configurations of so-called Gaussian chains, i.e. polymer chains that obey Markov statistics. Numerous theories have been proposed over the past 90 years based on the ansatz that the elastic force for individual network chains arises from the entropy change associated with the distribution of end-to-end distances of a free polymer chain. There are serious conceptual objections to this assumption and others, such as the assumption that all network nodes undergo a simple volume-preserving linear motion and that all of the network chains have the same length. Recently, a new paradigm for elasticity in rubber networks has been proposed that is based on mechanisms that originate at the molecular level. Using conventional statistical mechanics analyses, Quantum Chemistry, and Molecular Dynamics simulations, the fundamental entropic and enthalpic chain extension forces for polyisoprene (natural rubber) have been determined, along with estimates for the basic force constants. Concurrently, the complex morphology of natural rubber networks (the joint probability density distributions that relate the chain end-to-end distance to its contour length) has also been captured in a numerical model (EPnet). When molecular chain forces are merged with the network structure in this model, it is possible to study the mechanical response to tensile and compressive strains of a representative volume element of a polymer network. As strain is imposed on a network, pathways of connected taut chains, that completely span the network along strain axis, emerge. Although these chains represent only a few percent of the total, they account for nearly all of the elastic stress at high strain. Here we provide a brief review of previous elasticity theories and their deficiencies, and present a new paradigm with an emphasis on experimental comparisons.     

Static-geometric analogy in the micropolar theory of elasticity

For a micropolar elastic medium with distributed dislocations and disclinations, an analogy has been established between the equilibrium equations for force and couple stresses and the reduced incompatibility equations for metric and bending strains. The strain boundary conditions have been derived. The physically different but mathematically equivalent boundary-value problems of the three-dimensional micropolar theory of elasticity have been formulated.     

New studies of X-ray diffraction line profiles from aggregates of distorted crystallites I

The fourth central moment of an X-ray diffraction profile from an aggregate of distorted crystallites has been expressed by Mitra (1964a) as a function of the crystallite size, strain and strain gradients in the specimen. While the usual methods of line profile analysis yield information regarding either the apparent strain or the rms strain, the present study provides additional information regarding strain distribution in the form of strain derivatives and rms displacements of atoms over a given distancet in the direction of study. The strain parameters like 〈ee′〉, 〈ee″〉 have been obtained from fourth moment of the strain profile against range plots. The strain parameters thus obtained have subsequently been used to determine the rms displacements of the atoms. Alloys of copper and zinc at different stages of cold working and annealing have been studied by this method. The results have been discussed in the light of dislocation distribution, polygonisation and grain growth as well as distortion waves in the distorted crystals.     

From dipolar interactions of a random distribution of ferromagnetic particles to magnetostriction

The magnetostriction of a soft matrix, nonmagnetic, randomly filled by ferromagnetic particles is measured and calculated. Dipolar forces between particles have been calculated using a simple model of particles with the same permanent magnetic moment. Forces are injected in an FEM software to evaluate the strain of the composite. The longitudinal strain calculated for a cylinder-shape distribution is positive. A sample with the same shape has been prepared and shows the same strain.     

Reduction of elastic strains in directly-bonded silicon structures

The elastically strained state of the interface in directly-bonded silicon structures has been studied by x-ray diffraction topography and IR spectrometry. The pattern of the contrast observed in the x-ray topographs and the intensity oscillations in the IR spectra indicate a periodic strain distribution caused by the long-period surface microroughness on the plates to be bonded. The local microroughness did not exceed 2 Å, and it did not noticeably affect the interface structure. Two types of the structure were subjected to a comparative analysis, (i) with a smooth interface prepared by standard direct-bonding technology, and (ii) with an interface displaying a regular relief. The strain level in type-II structures was found to be lower by more than an order of magnitude. A model is proposed to account for the observed reduction of elastic strains at the bonded sections of the interface in terms of elastic relaxation of the free surfaces in the relief voids through their deflection and displacement.     

Method for monitoring slow dynamics recovery

Slow Dynamics is a specific material property, which for example is connected to the degree of damage. It is therefore of importance to be able to attain proper measurements of it. Usually it has been monitored by acoustic resonance methods which have very high sensitivity as such. However, because the acoustic wave is acting both as conditioner and as probe, the measurement is affecting the result which leads to a mixing of the fast nonlinear response to the excitation and the slow dynamics material recovery. In this article a method is introduced which, for the first time, removes the fast dynamics from the process and allows the behavior of the slow dynamics to be monitored by itself. The new method has the ability to measure at the shortest possible recovery times, and at very small conditioning strains. For the lowest strains the sound speed increases with strain, while at higher strains a linear decreasing dependence is observed. This is the first method and test that has been able to monitor the true material state recovery process.     

Three-dimensional strain localization of water-saturated clay and numerical simulation using an elasto-viscoplastic model

Since strain localization is a precursor of failure, it is an important subject to address in the field of geomechanics. Strain localization has been analysed for geomaterials by several researchers. Many of the studies, however, treated the problems brought about by strain localization as two-dimensional problems, although the phenomena are generally three-dimensional. In the present study, undrained triaxial compression tests using rectangular specimens and their numerical simulation are conducted in order to investigate the strain localization behaviour of geomaterials under three-dimensional conditions. In the experiments, both normally consolidated and over-consolidated clay samples are tested with different strain rates. Using the distribution of shear strain obtained by an image analysis of digital photographs taken during deformation, the effects of the strain rates, the dilation, and the over-consolidation on strain localization are studied in detail. The analysis method used in the numerical simulation is a coupled fluid-structure finite element method. The method is based on the finite deformation theory, in which an elasto-viscoplastic model for water-saturated clay, which can consider structural changes, is adopted. The results of the simulation include not only the distribution of shear strain on the surfaces of the specimens, but also the distributions of strain, stress, and pore water pressure inside the specimens. Through a comparison of the experimental results and the simulation results, the mechanisms of strain localization are studied under three-dimensional conditions.     

Internal strain in elastically strained germanium and silicon

The general relations between the internal strain vector and the strain tensor are used to derive the conditions for internal strain, in the diamond structure. Both the transverse and longitudinal internal strains have been measured, and the results of Part I improved. The experimental results on germanium and silicon are in good agreement with the theory of internal strain.