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.     

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     

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.     

Determination of thermal strains by moiré interferometry

An existing method is extended to measure thermal strain distributions on an absolute basis. Free thermal expansion and stress-induced deformations are separated, allowing the determination of coefficients of expansion, stress-induced strains, normal stresses and shear stresses. The method is applicable to many steady-state and transient thermal-strain problems. A crossed-line grating is replicated on the specimen at elevated temperature. A zero-expansion mold is used for the replication, so that the grating frequency at the replication temperature can be retained to null the moiré interferometer at room temperature. When the specimen is viewed in the moiré interferometer, the fringe patterns reveal theU andV displacements induced by any change from the replication temperature. In addition, carrier fringe techniques are introduced for steady-state problems to subtract off the free thermal expansion and produce fringe patterns of the stress-induced deformations themselves. The method is demonstrated by analysis of a bimaterial plate subjected to a uniform change of temperature. Paper was presented at the 1988 SEM Fall Conference on Experimental Mechanics held in Indianapolis, IN on November 6–8.     

Residual surface stresses in laminated cross-ply fiber-epoxy composite materials

Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [90₂₀/0₂₀/90₂₀] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.     

利用具有相位跳跃技术的阴影摩尔图测量电子组装元件的热翘曲

Phase-stepping technique is applied to the analysis of fringe patterns of shadow moiré of electronic packages.Sensitivity of the fringe pattern analysis is demonstrated to be significantly increased.Thermally induced warpage of electronic packages is successfully measured in real-time as the sample is driven through a simulated reflow process.The paper discusses the technique of phase stepping,noise filtering and its application to the shadow moiré method.Applications of the technology are presented.     

利用具有相位跳跃技术的阴影摩尔图测量电子组装元件的热翘曲

Phase-stepping technique is applied to the analysis of fringe patterns of shadow moiré of electronic packages. Sensitivity of the fringe pattern analysis is demonstrated to be significantly increased. Thermally induced warpage of electronic packages is successfully measured in real-time as the sample is driven through a simulated reflow process. The paper discusses the technique of phase stepping, noise filtering and its application to the shadow moiré method. Applications of the technology are presented.     

A finite-element technique to analyze the data measured by the hole-drilling method

A finite-element technique to analyze the data obtained by the hole-drilling strain-gage method is presented. In this study, residual stresses are assumed as initial stresses existing in the structural material or component. It is also assumed that the elimination of the initial stresses in the region of the drilled hole changes the measured strains. After putting initial stresses into displacement finite-element equations and comparing the stiffness matrix and the initial stresses matrix with those of the previous increment, equations relating unknown initial stresses and measured strains were obtained. By solving these equations, residual stresses were obtained. In this paper three examples are studied. In the first two examples, calibration constants C1 to be used in determining residual stress were calculated which varied with depth. In the third example, the data obtained by using the hole-drilling method are analyzed. All examples show good agreement with previous studies. Using the present method allows greater flexibility of choice of specimen shape, materials, and experimental procedure than would be possible if only analytic solutions were used.     

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.     

三层薄板的热屈曲测量及特征反演

The paper presents a new study on a tri-layer thin plate.Shadow moiré implemented with an advanced phase unwrapping technique is employed to obtain actual flexural deformation of a real-life plate sample subjected to thermal loads.An analytical model is re-formulated to provide the plate with global closed-form solutions of the plate deflection as well as the interfacial stress and strain.With the measurements and the solutions available,an inverse iterative approach is developed to evaluate and maximize th...     

Enhancement of the shadow-moiré method through digital image processing

Surface topography can be conveniently investigated by a well-known shadow-moiré technique. It is relatively free from stringent requirements on stability of instrumentation and quality of the light source. The main unresolved problem of the shadow moiré is its relatively low resolution. The digital-image-analysis enhanced shadow-moiré technique described here is based on the marriage of two well-known and developed methods: classical shadow moiré and contemporary digital image analysis. This combination allows a significant increase of the sensitivity of the classical shadow moiré by utilizing the ability of the digital-image-analysis system to acquire wholefield light-intensity information and process this information to yield the related displacement field. The suggested approach was utilized for a three-dimensional curved surface. The obtained topography of the three-dimensional specimen was compared to the one measured by a high precision dial gage and the differences were on average less than three percent between the two sets of data. The described combination of the shadow moiré and digital image analysis may prove as a useful tool for on-line quality control in a variety of manufacturing processes. Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

三层薄板的热屈曲测量及特征反演

The paper presents a new study on a tri-layer thin plate. Shadow moiré implemented with an advanced phase unwrapping technique is employed to obtain actual flexural deformation of a real-life plate sample subjected to thermal loads. An analytical model is re-formulated to provide the plate with global closed-form solutions of the plate deflection as well as the interfacial stress and strain. With the measurements and the solutions available, an inverse iterative approach is developed to evaluate and maximize the correlation between the measured and the predicted thermal flexure, leading to ascertained materials' constitutive and thermal behaviour. The inverse search algorithm starts with estimated ranges of material property parameters and progressively updates them to finally approach the respective true values. The established model solutions along with the optimized material properties matrix enable the prediction of the interfacial stresses/strains for the specific plate sample under evaluation.     

Separation of contact stress components by moire interferometry

A hybrid technique of combining moiré measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moiré interferometry offers the displacement fields near the deformed contact zone, from which the tangential strains and boundary slopes of the deformed configurations can be evaluated. Those experimental results provide boundary conditions for the discrete integration of Flamant’s solutions, to inversely compute the separated components of the contact stresses. The project supported by the National Basic Research Program (2007CB935602), the National Natural Science Foundation of China (90607004) and the ICM Fund of CAEP (42105080106).     

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.     

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.     

Recent research activities in experimental mechanics in China

A brief review is presented of the recent activities in the field of experimental mechanics in the People's Republic of China. The current research work covers the following subjects: (1) photoelastic phenomena, such as the classical three-dimensional photoelasticity, the scattered-light technique, birefringent coatings, birefringent materials; (2) holography, holographic interferometry, speckle interferometry and their applications; (3) moiré method; (4) strain-gage techniques and strain indicators.     

Z-pin复合材料细观模型固化残余应力研究

针对植入Z-pin后碳纤维增强复合材料的微观结构，通过施加Z-pin周期性边界约束条件，建立了Z-pin复合材料单层板单胞细观模型．考虑固化过程中树脂体积收缩、弹性模量随固化度变化和纤维因Z-pin进入偏转因素，运用有限单元法计算了单胞结构在固化成型工艺过程中树脂和纤维应力发展和分布，并研究了Z-pin直径和分布密度对单层板面内残余应力的影响．结果表明：凝胶点之前，树脂模量和残余应力很小，凝胶点之后，树脂模量和残余应力增加较快；残余应力分布与纤维偏转有关；Z-pin直径和分布密度增加会使固化残余应力增大．     

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.     

Geometric moiré methods with enhanced sensitivity by optical/digital fringe multiplication

A robust fringe-shifting and image processing scheme is applied to geometric moiré experiments. High quality contour maps ofU, V andW displacement fields are obtained with sensitivity enhanced by a factor of ten. The method is compatible with complicated intensity distributions, variable bar-to-space ratios of gratings, and optical noise. It is applicable to large fields for both in-plane moiré and shadow moiré measurements. Paper was presented at the 1992 SEM VII International Congress on Experimental Mechanics held in Las Vegas, NV on June 8.