Moiré analysis of thick composites with embedded optical fibers

Moiré interferometry is used with Fourier transform fringe analysis to investigate the strain fields in a region local to 125-m uncoated silica optical fibers embedded in a quasi-isotropic graphite/PEEK thick composite compression specimens. Analysis of several regions in several specimens showed no measurable strain concentrations resulting from the embedded optical fibers, even though the optical fibers clearly alter the local microarchitecture of the host material system.Paper was presented at the 1993 SEM Spring Conference on Experimental Mechanics held in Dearborn, MI on June 7–9.     

Recent Applications of Moiré Interferometry

Moiré interferometry has been a valuable experimental technique for the understanding of the mechanical behavior of materials and structures. Over the last decade less emphasis has been placed on the development of the technique and more towards applications. This paper is a review article on recent applications using moiré interferometry in the fields of microelectronics devices, material characterization, micromechanics, residual stress, composite materials, fracture mechanics, and biomechanics. The general principles of moiré interferometry and advancement of techniques will not be discussed in this text, but references will be provided.     

Bulge Testing Transparent Thin Films with Moiré Deflectometry

The problem that is addressed here is the measurement of the mechanical properties of very thin, transparent films using bulge tests. All existing techniques make use of reflection from the film surface, but they can be difficult or impossible to apply to very thin, transparent films. Consequently, a novel approach based on the formation of a lens structure and using transmitted light is developed. In this technique, the focal length of the lens structure formed by the bulged film and the pressurizing medium is determined by moiré deflectometry with a corrected governing equation. The resulting curvature of the bulge film is used in the stress analysis of the bulge-test. By combining circular and rectangular configurations, the Young’s modulus and Poisson’s ratio of a 3 μm PET film were 4.65 ± 0.11 GPa and 0.34 ± 0.01, respectively. Consistent residual stresses were obtained from both configurations.     

Measurements of Deflection and Residual Stress in Thin Films Utilizing Coherent Light Reflection/Projection Moiré Interferometry

Thin film technology is an area of great importance in current applications of opto-electronics, electronics, MEMS and computer technology. A critical issue in thin film technology is residual stresses that arise when the coating is deposited onto a substrate. Residual stresses can be very large in magnitude and have detrimental effects on the role that the thin film must play. To save development time on coating deposition processes it is important to perform accurate residual stresses measurements in situ in real time where the deposition is made. A novel optical set up is developed in this study to measure deflections and residual stresses generated in coated specimens that can be applied directly in the reactor utilized in the deposition process. Experimental results are in good agreement with other measurements carried out independently and other data reported in literature for thin films like those tested in the experiments.     

Mechanical Characterization of Biological Membranes with Moiré Techniques and Multi-Point Simulated Annealing

This paper describes an hybrid procedure for mechanical characterization of biological membranes. The in-plane displacement field of a glutaraldehyde treated bovine pericardium patch obtained with an equi-biaxial tension test is measured with intrinsic moiré and then compared with finite element predictions. Preliminary analysis of moiré patterns observed in the experiments justifies the assumption of the constitutive model based on transversely isotropic hyperelasticity. In order to determine the 16 hyperelastic constants included in the constitutive model and the fiber orientation, the difference Ω between displacement values measured with moiré and their counterpart determined numerically is minimized by means of multi-level and multi-point simulated annealing. Results clearly demonstrate the efficiency of the identification procedure presented in this research: in fact, residual difference between experimental data and numerical values of in-plane displacements is less than 2%. In order to validate the entire identification process, another experimental test is conducted by inflating the same specimen. Out-of-plane displacements, now measured with projection moiré, are compared with predictions of a new finite element model reproducing the experimental test. The 16 hyper-elastic constants previously determined are given in input to the inflation test FE model. Remarkably, experimental and numerical results are again in excellent agreement: maximum percent error on w-displacement is less than 3%.     

Automatic Full Strain Field Moiré Interferometry Measurement with Nano-scale Resolution

Moiré Interferometry (MI) theoretically can provide real-time full strain field measurements in dynamic environment. So it’s extensively used in reliability analysis of electronic packaging. Due to the nature of specimen preparations procedure, the optical noise is usually too strong so that an accurate phase-based information processing is not possible. In this paper, a 164 nm/pixel spatial resolution Moiré Interferometer with automated full strain field calculation is proposed. Provided by two-level zooming system, the high spatial resolution increase the signal intensity and eliminate some optical noise which allows accurate full strain field map generated automatically by the combination of phase shifting technique and continuous wavelet transform (CWT). Furthermore, the calculation procedure of CWT proposed here does not require unwrapping and differentiation, which avoid the possible numerical noise introduced in these two steps. In the proposed system, pixel by pixel in-plane strain tensors will be calculate from the intensity map of interferograms using phase-based method. The resulting strain tensor can be used to model constitutive relationship or compare with finite element analysis results. A thermal experiment on BGA packaging is used to demonstrate the advantages of the proposed new design.     

High-precision and Arbitrary Arranged Projection Moiré System Based on an Iterative Calculation Model and the Self-calibration Method

Experimental Mechanics - Background As a full-field optical metrology, projection moiré approach has been widely used in many engineering applications. The modeling of moiré system and...     

Characterization of the arrangement feature of copper interconnects by Moiré inversion method

This paper explores the planar arrangement feature of the copper interconnects in a view field of several millimeters by the focused ion-beam (FIB) Moiré inversion method quantitatively. The curved FIB Moiré patterns indicate that the copper interconnects are a series of curves with continuous variations instead of beelines. The control equation set of the copper interconnects central lines is attained through the Moiré inversion method. This work can be extended to inspect the structural defects and provide a reliable support for the interconnects structure fabrication.     

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moiré method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moiré fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moiré fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moiré fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moiré method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moiré method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moiré method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.     

Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields

The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E ₁ , E ₂ , ν ₁₂ , G ₁₂ ) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moiré interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article).     

Micro-deformation Study of Stainless Steel Impacted by Ceramic Particle Using Electron Moiré Method

Background

High-velocity oxy-fuel (HVOF)-sprayed metallic coating can be used to create a surface layer that plays a significant role in enhancing the overall strength, stiffness, and fatigue life of the treated material. The micro-deformation around a single impacted particle is a critical factor that must be considered for the optimization of the HVOF process.

Objective

In this study, the micro-deformation field of stainless steel impacted by a ceramic particle was characterized at the micro-scale.

Method

A grid with a frequency of 1200 lines/mm was fabricated on the surface of stainless steel specimen. The microscopic deformation field formed on the substreate surface, induced by the impact of micro-particles with a diameter of 18 µm, was determined using the electron moiré method and numerical simulations.

Results

The in-plane plastic strain around the impacted particle was found to be as high as 9.1%, and the value sharply decreased with the increase of the distance to the edge of the impacted particle. The diameter of the plastic area was about 40 µm, which was approximately 2.2 times larger than the particle size. The experimental results were compared with numerical simulation results, and good agreement between the results was found.

Conclusions

The electron moiré technique can be a useful tool for the measurement of the deformation field induced by an impacted particle in a very local area with a size on the order of microns.

     

Deflection Measurement and Determination of Young’s Modulus of Micro-cantilever Using Phase-shift Shadow Moiré Method

The deflection of micro-structures have been previously measured using optical interferometry methods. In this study, the classical phase-shift shadow moiré method (PSSM) was applied to measure the deflection of a silicon micro-cantilever and to determine the Young’s modulus of the cantilever material. The modulus value was determined from the profile based on deflection equation. A normal white light source and a grating of 40 line pairs per mm were used to generate the moiré fringes. Since the use of white light and high-resolution grating produces low contrast moiré fringes, the fringe visibility was enhanced by applying contrast enhancement and filtering techniques. The Young’s modulus of the silicon cantilever material was estimated to be 165.9 GPa with an uncertainty of ±11.3 GPa (6.8%). The experimental results show that the PSSM method can be successfully applied for characterizing micro-cantilevers. Comparison of the deflection profile from the proposed method and a commercial 3-D optical profiler showed that the measurement range and sensitivity of PSSM are not affected by the poor contrast images.     

Numerical—Experimental Investigation of the Elastic Deformation of a Polymeric Pipeline under Impact

The paper reports results of numerical—experimental investigation of the hydroelastic process in a polyimide pipeline filled with a fluid. The propagation of small perturbations in the fluid is considered in an acoustic approximation based on wave equations. The equations are integrated using the method of characteristics and a two–layer difference scheme. The elastic problem is solved by the finite element method and the Newmark difference –method. The stress—strain state of the pipeline is defined by a superposition of fast rod modes of motion and slow shell modes of motion. Satisfactory agreement between calculated and experimental data is obtained.     

Mechanical Characterization of Angle-Ply Composite Laminates by Differential Moiré Method: The Influence of Specimens' Length-to-Width Ratio

The influence exerted by the specimen proportions on the measured performance of angle-ply [+45°/–45°]_s composite laminates is studied. Three kinds of specimens are considered, having different length-to-width ratios, made with glass/epoxy unidirectional or fabric laminae. The static tensile characteristics are measured by means of load cells, electric strain gauges and through the Moiré fringes method. The strain fields are analysed and the effects of stress concentration at the laminate-free edges are evaluated, as well as their influence on the strain distribution and the measured strength and stiffness. The results are summarized as diagrams of ultimate load and elastic modulus versus length-to-width ratio of the different specimens investigated. These diagrams allow the designer to evaluate the influence exerted by specimen proportions on the measured performance, as well as to compare characteristics which are heterogeneous, as obtained with different kinds of specimen.     

Application of Moiré Interferometry to the Characterization of Orthotropic Materials in the Antisymmetric Configuration using the Virtual Fields Method

Moiré interferometry is an effective full-field deformation measurement technique and has been utilized for mechanical behavior analysis of materials and structures. For isotropic materials, Moiré patterns can be obtained by performing standard tests, such as, tensile and bending tests, to calculate the displacement and strain. Then, the mechanical properties can be characterized. However, standard tests are not sufficient to characterize the mechanical parameters of anisotropic materials due to the complexity of their material properties. Thus, in this work, Moiré interferometry was combined with the Virtual Fields Method to obtain the four in-plane elastic constants (Q₁₁, Q₂₂, Q₁₂, and Q₆₆) of orthotropic materials in the form of a diametrically compressed disk. Firstly, according to finite element method simulation results, optimized parameters can be achieved when the principal direction of the material does not coincide with the loading direction, making the loading configuration antisymmetric. Therefore, Moiré interferometry experiment was simulated to demonstrate the feasibility of measurement in the antisymmetric configuration. Finally, the Q₁₁, Q₂₂, Q₁₂ and Q₆₆ values of a unidirectional carbon fiber composite were measured in a real Moiré interferometry experiment using the proposed method, yielding results that agreed closely with those obtained using the strain gauges.     

Electrical Characteristics of Three‐Component Dielectric Composites with Close‐Packed Inclusions

The electric field and effective permittivity are calculated for a twodimensional threecomponent dielectric material reinforced by cylindrical fibers. A composite material with a square close packing of inclusions is considered. The field in the periodic system is investigated using the exact solution of the model problem of interaction of two dissimilar cylindrical inclusions in an external homogeneous electric field. A diagram of the relative effective permittivity is constructed.     

On the performance of truss panels with Kagomé cores

The performance characteristics of a truss core sandwich panel design based on the 3D Kagomé has been measured and compared with earlier simulations. Panels have been fabricated by investment casting and tested in compression, shear and bending. The isotropic nature of this core design has been confirmed. The superior performance relative to truss designs based on the tetrahedron has been demonstrated and attributed to the greater resistance to plastic buckling at the equivalent core density.     

The Residual Strain Measurement of Thin Conductive Metal Wire after Electrical Failure with SEM Moir

In this study, the residual strain of a thin conductive metal wire on a polymer substrate after electrical failure is measured with SEM moir′e. Focused ion beam(FIB) milling is applied to fabricate micron moir′e gratings on the surfaces of constantan wires and the random phase shifting technique is used to process moir′e fringes. The virtual strain method is briefly introduced and used to calculate the real strain of specimens. In order to study the influence of a defect on the electrical failure of the constantan wire, experiments were conducted on two specimens, one with a crack, while the other one without any crack. By comparing the results, we found that the defect makes the critical beam current of electrical failure decrease. In addition, the specimens were subjected to compression after electrical failure, in agreement with the observed crack closure of the specimen. The successful results demonstrate that the moir′e method is effective to characterize the full-field deformation of constantan wires on the polymer membrane, and has a good potential for further application to the deformation measurement of thin films.     

Development of Solute-solvent Separation Soft Lithography Grating for Measuring High-temperature In situ Deformation Using Scanning Electron Microscope Moiré Method

In this study, a technique is developed for fabricating high-temperature solute-solvent separation soft lithography (HSS-SL) grating for metallic materials. Using this technique, a 150 lines/mm crossing-type grating is directly fabricated on the surface of a miniaturized single edge notch tension (SENT) specimen. Further, the microstructure of the grating is analyzed using scanning electron microscope (SEM) and atom force microscope. The grating is found to be highly suited for forming high-contrast SEM moiré fringes. In addition, the chemical composition of the grating is characterized using energy dispersive X-ray spectroscope (EDS), whose results indicate that the grating exhibits good resistance to high-temperature oxidation owing to the high heat endurance of its constituent materials, SiO and SiO₂. With respect to high-temperature applications, the HSS-SL grating is employed successfully for measuring the linear thermal expansion coefficient of GH2036 alloy at temperatures of 25-600 °C. Moreover, the high-temperature displacement and strain fields around the semicircular notch of the SENT specimen are determined based on the SEM moiré. These results confirm that thus-fabricated HSS-SL gratings show high potential for use in high-temperature in situ deformation measurements using the SEM moiré method.

     

A Study of Crack–inclusion Interactions and Matrix–inclusion Debonding Using Moiré Interferometry and Finite Element Method

Failure behavior of composite materials in general and particulate composites in particular is intimately linked to interactions between a matrix crack and a second phase inclusion. In this work, surface deformations are optically mapped in the vicinity of a crack–inclusion pair using moiré interferometry. Edge cracked epoxy beams, each with a symmetrically positioned cylindrical glass inclusion ahead of the tip, are used to simulate a compliant matrix crack interacting with a stiff inclusion. Processes involving microelectronic fabrication techniques are developed for creating linear gratings in the crack–inclusion vicinity. The debond evolution between the inclusion–matrix pair is successfully mapped by recording crack opening displacements under quasi-static loading conditions. The surface deformations are analyzed to study evolution of strain fields due to crack–inclusion interactions. A numerical model based on experimental observations is also developed to simulate debonding of the inclusion from the matrix. An element stiffness deactivation method in conjunction with critical radial stress criterion is successfully demonstrated using finite element method. The proposed methodology is shown to capture the experimentally observed debonding process well.