Carrier fringe method of moiré interferometry for tiny strain measurements in micro-field

In this paper, we demonstrate a new optical method for tiny strain measurements based on the principle of carrier fringes of moire interferometry. A cross-line grating with frequency of 1200 lp/mm is replicated on the specimen surface, and the strain can be deduced from the changes in carrier fringes before and after the deformation of an object. Four coherent laser beams are used to obtain the carrier fringe patterns of field U and V. Both theoretical analysis and numerical simulation indicate that the ideal accuracy of strain can be controlled within a range of ±1με. Case study of a plane extension experiment shows that the measurement accuracy of strain can be controlled within the range of ±10με. The average strain values of every row of field U and every column of field V can be obtained by using this method, and approximated strain of every pixel in the whole-field can be further acquired, and thus it is possible to measure tiny strains occurred in a micro-field. The technology in this paper can provide comprehensive information for analyzing related mechanical content in the field of MEMS.     

A multilevel treatment of moiré fringe data using finite elements

Finite element procedures are applied to the modeling, analysis and visualization of experimental moiré data. Smoothing elements are introduced and evaluated with respect to data sparseness and error. A one-dimensional smoothing element is uniquely coupled with the method of principal curves to extract moiré fringe centers. A two-dimensional smoothing element is then used to produce a full-field representation given the fringe locations. The moiré technique is applied to the four-point bend experiment, and the surface-modeling technique is used to obtain displacement and gradient (strain) information.     

Measurement of bending stresses in shells of arbitrary shape using the reflection moiré method

The basic equation for fringe formation in the case of reflection moiré applied to surfaces of arbitrary curvatures is derived. A practical point-by-point solution for the application of this method is introduced, and the corresponding simplified equations are given. The technique is applied to an industrial problem, the stress analysis of a shell-shaped door.     

High-magnification moiré interferometer for crack tip analysis of steels

A high-magnification moiré interferometer, particularly suitable for near-tip field analysis in cracked materials, is described. It has a submillimeter field of view, a high-resolution image sensor (1.4 million pixels), X-Y-Z translation stage and an optical fiber light delivery system. These features enable the microscope head to observe the crack tip while the specimen is loaded in a standard tensile test machine. Automated fringe pattern analysis, using temporal phase shifting and spatial phase unwrapping, enables thex ory displacement component to be measured and the corresponding in-plane strain component computed. The displacement placement accuracy is better than 40 nm, and the effective strain gage dimension is ∼ 25 μm. Furthermore, the interferometer has a built-in white light microscope that allows the observation of the specimen granular microstructure in exact registration with the displacement field. The interferometer has hence been employed to investigate the near-tip fields of a precracked stainless steel specimen under load. The influence of the grain boundaries on the measured displacement fields was relatively minor. The near-tip strain field shows a significant asymmetrical behavior despite pure mode lloading conditions.     

Identifying traction–separation behavior of self-adhesive polymeric films from in situ digital images under T-peeling

In this paper procedures are developed to identify traction–separation curves from digital images of the deformed flexible films during peeling. T-peel tests were performed for self-adhesive polymeric films. High quality photographs of the deformed shape within and outside the zone of adhesive interaction were made in situ by the digital light microscope. The deformed line is approximated by a power series with coefficients computed by minimizing a least squares functional. Two approaches to identify the traction–separation curve for the given deformation line are proposed. The first one is based on the energy integral of the non-linear theory of rods and allows the direct evaluation of the adhesion force potential. The second one utilizes the complementary energy type variational equation and the Ritz method to compute the adhesion force. The accuracy of both approaches is analyzed with respect to different approximations for the deformed line and the force of interaction. The obtained traction vs. axial coordinate and the traction–separation curves provide several properties of the adhesive system including the maximum adhesion force, the length of the adhesive zone and the equilibrium position, where the adhesive force is zero while the separation is positive.     

Fabrication of micro-scale gratings for moiré method with a femtosecond laser

Fabrication of micro gratings using a femtosecond laser exposure system is experimentally investigated for the electron moiré method. Micro holes and lines are firstly etched for parameter study. Grating profile is theoretically optimized to form high quality moiré patterns. For a demonstration, a parallel grating is fabricated on a specimen of quartz glass. The minimum line width and the distance between two adjacent lines are both set to be 1 μm, and the frequency of grating is 500 lines/mm. The experimental results indicate that the quality of gratings is good and the relative error of the gratings pitch is about1.5%. Based on moiré method, scanning electron microscope(SEM) moiré patterns are observed clearly,which manifests that gratings fabricated with the femtosecond laser exposure is suitable for micro scale deformation measurement.     

The moiré method and the evaluation of principal-moment and stress directions

This paper discusses, in relation to the moiré method as used for the solution of plate bending and two-dimensional stress problems, two graphical techniques for the determination of the directions of principal moments and stresses.The so-called isoclinic method and the point method are described.The application of these new techniques on three different models—a circular disk under diametrically opposite loads and two different circular plates subjected to a lateral load—are fully discussed.The graphically determined principal-stress and moment directions show excellent agreement with analytically determined comparable values.Paper was presented at 1963 SESA Annual Meeting held in Boston, Mass., on November 6–8.     

Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.     

A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing

This paper presents a hybrid procedure for mechanical characterization of hyper-elastic materials based on moiré, finite element analysis and global optimization. The characterization process is absolutely general because does not require any assumption on specimen geometry, loading or/and boundary conditions.The novel experimental approach followed in this research relies on a proper combination of intrinsic moiré and projection moiré which allows 3D displacement components to be measured simultaneously and independently using always the same experimental setup and just one single camera. In order to properly compare experimental data and finite element predictions, 3D displacement information encoded in moiré patterns which are relative to the deformed configuration taken by the specimen are expressed in the reference system of the unloaded state.A global optimization algorithm based on multi-level and multi-point simulated annealing which keeps memory of all best records generated in the optimization is used in order to find the unknown material properties through the minimization of the Ω functional built by summing over the differences between displacements measured experimentally and those predicted numerically.Feasibility, efficiency and robustness of the proposed methodology are demonstrated for both isotropic and anisotropic specimens subject to increasing pressure loads: a natural rubber membrane and a glutaraldehyde treated bovine pericardium patch, respectively. Remarkably, the results of the characterization process are in very good agreement with target data independently determined. For the isotropic specimen, the maximum error on hyper-elastic constants is less than 1% and the residual error on displacements is less than 3.5%. For the anisotropic specimen, the maximum error on material properties is about 3.5% while the residual error on displacements is less than 3%. The identification process fails or becomes less reliable if “local” displacement values are considered.     

Whole-field residual stress measurement in rail using moiré interferometry and twyman/green interferometry via thermal annealing

A novel whole-field residual stress measurement technique is developed using moiré interferometry and Twyman/Green interferometry coupled with thermal annealing. The technique is successfully applied to residual stress measurement in rail. In the measurement, a high temperature resistant 1200-lines/mm cross grating is made on a rail transverse slice surface. The whole-field residual stress relief is achieved by thermal annealing. Moiré interferometry and Twyman/Green interferometry are employed to obtain the in-plane and out-of-plane deformations generated by the residual stress relaxation. The whole-field strain redistribution due to the residual stress relief is calculated, and the whole-field residual stress distribution, including the possible stress concentration, is then obtained. Because of the three-dimensional nature of the residual stress relaxation and the measurement, the three-dimensional residual stress reconstruction sometimes becomes possible based on some plausible assumptions. In this paper, the principle of the experimental theory, technique and procedures are described. Three-dimensional residual stress reconstruction in a rail using a transverse slice is shown. Its comparison to the hole-drilling method with moiré interferometry is also presented.     

Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation

The new (2+1)-dimensional generalized KdV equation which exists the bilinear form is mainly discussed. We prove that the equation does not admit the Painlevé property even by taking the arbitrary constant a=0. However, this result is different from Radha and Lakshmanan??s work. In addition, based on Hirota bilinear method, periodic wave solutions in terms of Riemann theta function and rational solutions are derived, respectively. The asymptotic properties of the periodic wave solutions are analyzed in detail.     

On the bifurcations of the Lamé solutions in plane-strain elasticity

We consider the in-plane bifurcations experienced by the Lamé solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro–Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.     

Flow patterns and pressure drop of ionic liquid–water two-phase flows in microchannels

The two-phase flow of a hydrophobic ionic liquid and water was studied in capillaries made of three different materials (two types of Teflon, FEP and Tefzel, and glass) with sizes between 200 μm and 270 μm. The ionic liquid was 1-butyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide, with density and viscosity of 1420 kg m⁻³ and 0.041 kg m⁻¹ s⁻¹, respectively. Flow patterns and pressure drop were measured for two inlet configurations (T- and Y-junction), for total flow rates of 0.065–214.9 cm³ h⁻¹ and ionic liquid volume fractions from 0.05 to 0.8. The continuous phase in the glass capillary depended on the fluid that initially filled the channel. When water was introduced first, it became the continuous phase with the ionic liquid forming plugs or a mixture of plugs and drops within it. In the Teflon microchannels, the order that fluids were introduced did not affect the results and the ionic liquid was always the continuous phase. The main patterns observed were annular, plug, and drop flow. Pressure drop in the Teflon microchannels at a constant ionic liquid flow rate, was found to increase as the ionic liquid volume fraction decreased, and was always higher than the single phase ionic liquid value at the same flow rate as in the two-phase mixture. However, in the glass microchannel during plug flow with water as the continuous phase, pressure drop for a constant ionic liquid flow rate was always lower than the single phase ionic liquid value. A modified plug flow pressure drop model using a correlation for film thickness derived for the current fluids pair showed very good agreement with the experimental data.     

Space–time evolution of optical breathers and modulation instability patterns in metamaterial waveguides

We present numerical and theoretical investigations of the spontaneous emergence of noise-driven modulation instability patterns in a metamaterial waveguide, which involves the generation of optical breather waves such as the Peregrine soliton, Akhmediev breathers and Kuznetsov–Ma breathers. We show that the intrinsic properties of the metamaterial waveguide, e.g. self-steepening and the magnetooptic effects, offer the potential to control the formation and subsequent spectral and temporal dynamics of these localized nonlinear waves. Such internal or external perturbations break the symmetry of the spectrum of nonlinear waves, thus leading to the existence of a controllable characteristic group velocity in their space–time evolution.