On the determination of the sum of the principal stresses in two-dimensional problems

The well-known principle of the determination of the sum of principal stresses in plates by measuring thickness changes is applied in this paper to “frozen” plates and to models made with low-modulus materials, such as rubbers, deformed inside portable frames. It is shown that a sufficiently precise measurement of thickness changes is possible with a machine-shop comparator, rather than with the more delicate laboratory-type instruments. The necessary corrections to be introduced to the comparator readings when rubber models are used are described in the Appendix. Two other methods based on moiré fringes, using the same two kinds of models, are also presented. The use of moiré on “frozen” specimens yields patterns of large response. Gratings on rubber models also yield precise moiré patterns that can be combined with isochromatics to separate the principal stresses. Two ways of conducting the moiré analyses are presented. The advantages and limitations of the several alternative methods are pointed out, and applications are given.     

A moiré microscope for finite deformation micro-mechanical studies

A new version of a moiré microscope is presented that embodies the theory of optical moiré interferometry. To interrogate the deformed specimen grating, the device uses a transmission diffraction grating that allows for a simple and quick change of the virtual reference grating vector without disturbing the optical alignment of the other components in the optical train. To analyze deformation from the acquired moiré interference fringe patterns, the displacement light-itensity moiré optical law introduced by Sciammarella is revisited. The analysis of deformation is consistent with the continuum principles of finite deformation and can readily be used to obtain micro-mechanical quantities of interest such as the local strains, stretches and rotations.     

Developments in the optical spatial filtering of superposed crossed gratings

It is shown in this paper how the whole field of displacement components and of their time and space derivatives (isothetics, isotachics and isoparagogics) can be obtained individually, as separate patterns in a simple and precise manner using spatial-filtering techniques. This result can be obtained even when crossed gratings are used on the deformed body. A method for achieving fringe multiplication in moiré patterns produced by superposed, crossed gratings is also demonstrated. It is also shown that displacement components and their time and space derivatives in directions diagonal to the crossed-grating lines can be obtained by proper handling of grating transparencies and spatial-filtering techniques. Hence, the moiré equivalent of a whole field of rosette-strain-gage measurements is obtained from a single photograph of a deformed crossed grating. A disk compressed between two wedges is used as an example. Important applications will be found in the fields of dynamics, nonlinear elasticity and plasticity.     

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.     

The micro-connection of the second-order moiré fringes and its order determination,and the determination of the boundary strains

The micro-connection method for determining the centre lines of second-order moiré fringes presented in this paper can enhance the accuracy in measuring strain fields, and generally can determine the absolute order of the second-order moiré fringes. The strain data obtained from curved beam experiment are in good accordance with theory. The relationship between the second-order moiré fringe and the strains at the specific points of the specimen is derived. Hence a reciprocate shift method is presented for determining strain distributions in the non-overlapping region of the shifted moiré patterns, (usually in the region of specimen where no second-order moiré fringes occur is the boundary region).     

Solution of the moiré hole drilling method using a finite-element-method-based approach

The moiré hole drilling method in a biaxially loaded infinite plate in plane stress is an inverse problem that exhibits a dual nature: the first problem results from first drilling the circular hole and then applying the biaxial loads, while the other problem arises from doing the opposite, i.e., first applying the biaxial load and then drilling the circular hole. The first problem is hardly ever addressed in the literature but implies that either separation of stresses or material property identification may be achieved from interpreting the moiré signature around the hole. The second is the well-known problem of determination of residual stresses from interpreting the moiré fringe orders around the hole. This paper addresses these inverse problem solutions using the finite element method as the means to model the plate with a hole, rather than the typical approach using the Kirsch solution, and a least-squares optimization approach to resolve for the quantities of interest. To test the viability of the proposed method three numerical simulations and one experimental result in a finite width plate are used to illustrate the techniques. The results are found to be in excellent agreement. The simulations employ noisy data to test the robustness of this approach. The finite-element-method-based inverse problem approach employed in this paper has the potential for use in applications where the specimen shape and boundary conditions do not conform to symmetric or well-used shapes. Also, it is a first step in testing similar procedures in three-dimensional samples to assess the residual stresses in materials.     

A new optical system for moiré methods

A new optical system for moiré methods is proposed in which the light path from the model grating and that from the master grating are diffent. They are combined by mirrors to form moiré patterns. Its application to Ligtenberg's reflective moiré method extends the method to dynamic problems and also facilitates the use of linearmismatch fringes. It can also be applied to in-plane moiré method in cases where deformation is large and diect contact with model grating is to be avoided.     

An electron moiré method for a common SEM

In the electron moiré method, a high-frequency grating is used to measure microscopic deformation, which promises significant potential applications for the method in the microscopic analysis of materials. However, a special beam scanning control device is required to produce a grating and generate a moiré fringe pattern for the scanning electron microscope (SEM). Because only a few SEMs used in the material science studies are equipped with this device, the use of the electron moiré method is limited. In this study, an electron moiré method for a common SEM without the beam control device is presented. A grating based on a multi-scanning concept is fabricated in any observing mode. A real-time moiré pattern can also be generated in the SEM or an optical filtering system. Without the beam control device being a prerequisite, the electron moiré method can be more widely used. The experimental results from three different types of SEMs show that high quality gratings with uniform lines and less pitch error can be fabricated by this method, and moiré patterns can also be correctly generated.The project supported by the National Natural Science Foundation of China (10662005) and JSPS fellowship in Japan. The English text was polished by Keren Wang.     

Residual strain measurement in composites using the cure-referencing method

This paper describes the details of a novel procedure called the cure-referencing method (CRM) to measure the strains associated with residual stresses on the surface of composite panels. The CRM involves the replication of diffraction gratings onto the surface of composite specimens during the autoclave during cycle. Residual strains associated with the curing process are measured using moiré interferometry at room temperature after the specimens have been taken out of the autoclave. The procedures for both the grating replication and the moiré interferometry experiment are described in detail. A method of high-temperature moiré interferometry was developed to resolve the residual strains due to thermal expansion from those due to chemical matrix shrinkage and stress relaxation. These procedures are demonstrated on unidirectional and multidirectional laminates and on woven textile composites.     

Investigation of shrinkage-induced stresses in stereolithography photo-curable resins

An experimental study has been undertaken to investigate the shrinkage characteristics of acrylic-based and epoxy-based stereolithography (SL) photopolymer resin systems after they have been laser cured and post-cured under ultraviolet (UV), and thermal exposure. The induced residual stresses and strains were determined by the shadow moiré and the hole-drilling strain-gage methods. Out-of-plane displacements (warpage) of acrylic-based post-cured resin plates were recorded by means of the shadow moiré method and correlated to the shrinkage strains by theoretical analysis. The induced residual stresses in the epoxy-based cylindrical resin specimens were determined from strains of three-element strain-gage rosettes of the blind-hole drilling method. Results are presented for the shrinkage stresses and strains for both material systems as a function of the post-curing process (UV, thermal). It was found that the shrinkage strains in the acrylic-based photopolymer resin were of considerable magnitude, while thermal post-curing resulted in higher shrinkage stresses for both material systems. The values of the shrinkage stresses compare well with those of the existing literature.     

Photography without lenses

Good photographic records fo brittle coating, photoelasticity and moiré patterns can be obtained in certain cases by direct contact of the specimen and the photographic film. No lenses are required. Several examples of application of the technique are given. The method is particularly useful when brittle coating or moiré are applied to transparent curved developable surfaces.     

On replication for moiré-fringe multiplication

A modified casting method is described for forming replicas of deformed moiré grids for subsequent fringe multiplication. The technique, which is believed to be simpler, faster and more convenient than previous procedures, is demonstrated by application to a fiber-reinforced interlaminar shear-strength specimen.     

Non-linear least-squares solution to the moiré hole method problem in orthotropic materials. Part 1: Residual stresses

The hole method problem relates to two inverse problems of interest: the first, most commonly addressed by practitioners, is to obtain residual stresses; the other, generally neglected, inverse problem can be posed as either a stress separation problem or a material elastic properties identification problem. In both this Paper I and Paper II, we pose and solve this dual hole method problem in an orthotropic plate, using computer generated moiré isothetics, by means of a non-linear least-squares approach. In Paper I we address the residual stress problem. In Paper II we pose the use of moiré isothetics as a means to achieve separation of stresses, but we deal with the determination of the five orthotropic elastic constants, four of which are independent.     

Study of three-dimensional deformation of a pallet using phase-shiff shadow moiré and finite-element analysis

We present the results of a comparative study on the static deformation of a pallet, made from oil-palm fiberreinforced composite material, using the phase-shift shadow moiré method and finite-element analysis (FEA). The pallet was designed and analyzed using a commerical software package. The effect of various joint types on the deformation profile was studied to obtain a simplified model to represent the actual design. A one-fifth scale model of the pallet was fabricated and the deformation due to static loading was measured using the phase-shift shadow moiré method. The comparison between the measurement and FEA results on the deformed profile showed a maximum difference of 13.7% at the center of the some of the deck boards, but a smaller difference at other deck boards. The FEA results also produced a larger deformation gradient compared to the measurements.     

The moiré method—A review

The paper focuses on the moiré phenomenon as a tool of experimental mechanics. The properties of moiré patterns are outlined. The application of these properties to the measurement of displacements of the points of a surface (intrinsic moiré), contours or deflections (projection moiré) and slopes (reflection moiré) is discussed. Observation methods, recording methods, data-processing techniques are outlined and practical aspects are stressed. Sensitivities and precisions that have been achieved are reviewed. Finally, some typical applications to problems in areas of interest are briefly described.     

Experimental analysis of the deformation of convex cylindrical surfaces

The described method is based on the moiré technque. By applying a special stripping film with a copied grid to a convex cylindrical surface, it is possible to express the equations of the deformed as well as the undeformed grid. By using the double-exposure photographic technique, a field of moiré fringes will be obtained, which gives information of the component perpendicular to the direction of observation of the deformation vector in the plane perpendicular to the axis of revolution. By observing two different directions α₁ and α₂, the experimental data yield the calculation of the displacement vector. The application of the derived method and its reliability will be demonstrated by several examples. The method does not require highly expensive laboratory equipment and is especially useful for engineers in consulting and structural design.     

The transfer-grid method,a practical Moiré stress-analysis tool

A practical and simple moiré stress-analysis technique is described. The grid is applied to any part by a transfer method, like a decal, not necessitating mechanical engraving or photoetching nor any special environmental care. The moiré fringes are observed remotely from the part without master contact. This is done through the use of a projection device and a master held in a plane where the projected image of the working grid is formed. Limitations of the method, as well as its applications, are discussed.     

Thermal stresses at high temperatures in stainless-steel rings by the moiré method

The research presented in this paper is a continuation of previous work published by one of the authors. Improvements in the techniques of recording and processing moiré data in thermal-strain fields have extended the maximum temperature at which useful information can be obtained from 400 to 1600° F. It has been found that the strains obtained experimentally do not depart very much from the values predicted by the theory of elasticity, although the stresses at some points of the model exceed the yield limit at the corresponding temperature. These results prove that the moiré method can be used with advantage to obtain experimental information in an area where experimental data are scarce if not nonexistent.     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP     

The moiré method for the study of explosions

Explosives have been used to produce weak shock waves in central cavities of Plexiglas spheres. Shock pressures engendered were less than the so-called stable shock threshold and they resulted in a decomposition of the shock wave into an elastic precursor preceding the so-called plastic shock wave. The differential moiré method has been used to measure simultaneously the precursor and shock-wave velocities, as well as the velocity of the cavity interface. Moreover, the displacement field given by the moiré pattern yields the components of strains and the particle velocity behind each shock.