Classification of holographic fringe patterns inherent in through hole drilling in residual stress field

Comparative analysis of actual fringe patterns, which are induced by combined implementing the hole drilling method and reflection hologram interferometry for residual stresses determination, is presented. Involved considerations are related to plane thin-walled structural elements. A set of interferograms of perfect (ideal) form is selected proceeding from one-side measurements. A base for recognising each specific ideal configuration is a fine coincidence between actual interferograms and analogous reference fringe patterns constructed for the same stress state. Perfect (ideal) both actual and reference fringe patterns are defined as a response of pure membrane 2D stress field on through hole drilling between exposures. Main principles of creating the regular catalogue of reference fringe patterns inherent in through hole drilling in thin-walled components are formulated. Emphasis is made on a careful collecting and classifying actual interferograms with clear indications of bending stress presence in total residual stress field. Evidences needed for a reliable classification of the type of residual stresses field of interest are established and verified. A response of superimposed residual stress field, which consists of both membrane and bending components, is characterised by various deviations of each specific fringe pattern from an ideal form. More deep analysis of fringe patterns related to superimposed residual stress field is based on specially designed technique. The main essence of the approach developed is simultaneous measurements of through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Sophisticated optical set-up that is capable of obtaining high-quality fringe patterns in the course of two-side measurements is developed and implemented. Typical set of fringe patterns obtained for single probe hole on opposite specimen faces is presented.     

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.     

Combined implementing the hole-drilling method and reflection hologram interferometry for residual stresses determination in cylindrical shells and tubes

Main features inherent in simplified approach to residual stresses determination in cylindrical shells and tubes, external diameter of which is not less than 60 mm, by combing the hole-drilling method and reflection hologram interferometry are discussed in detail. Initial experimental information in a form of hole diameter increments in principal stress directions is derived from high-quality reflection holograms recorded near cylindrical objects of intermediate curvature value. Converting measured parameters into required stress values is based on the transition model that corresponds to plane stress conditions of pure membrane type. The technique developed is capable of determining residual stress component values within 5% accuracy in an absence of stress gradients over the probe hole diameter when a type of residual stress field corresponds to the transition model adopted. The accuracy analysis involved is based on matrix formulation of conventionally direct problem and an assumption on a pure membrane character of residual stress field under study for thin-walled shell. Required error estimations in a case of inspecting thick-walled cylindrical tube are obtained by combining the above-mentioned approach and an analogy of reconstructed fringe patterns with actual and artificial interferograms, which follow from drilling blind hole of the same geometrical parameters in thick-walled plates. Experimental verification of the developed approach is founded upon a determination of actual stresses in thin-walled cylindrical shell and obtaining residual stress distributions at the proximity of welded joint in thick-walled cylindrical tube.     

Holographic interferometry for measuring residual stresses by using probing holes

An original method of determining residual stresses by using probing holes and measuring the difference in the holographic interference fringe orders for two sets of pairs of points taken on the principal strain axes is suggested. The optical scheme of the interferometer is based on the use of reflection holograms. The principal residual strains are found by solving an overdetermined set of linear equations. The effect of rigid displacement on the fringe pattern is taken into account. The method is experimentally verified by measuring elastic stresses in uniaxially and biaxially strained specimens.     

A role of fringe pattern catalogue in the course of interferometrically based determination of residual stresses by the hole-drilling method

A further development of the technique for residual stresses determination in thick-walled structures, which is based on a combination of the hole-drilling method and reflection hologram interferometry, is presented. A plane specimen welded from two equal parts of dimensions 130×80 mm² in plane and thickness 12 mm is the object of investigation. Weld seam is performed along the shortest side of the specimen. Residual stress field of interest is formed by a superposition of initial welding-induced field and secondary stress field caused by plastic deformation of the specimen. A set of actual fringe patterns, which corresponds to a wide variety of residual stress components both ratio and sign, are reconstructed and presented as illustrations. A series of reference fringe patterns is simulated for the most typical cases inherent in residual stress field under study. It is shown that actual interferograms obtained belong to three main groups depending on a typical form of fringes configuration. On this base the main principles of creating the general catalogue of fringe patterns are established and the first version of this catalogue, which is related to reflection hologram interferometry, is developed. A structure of the catalogue that consists of both actual interferograms and reference fringe patterns is described. Possible ways of further catalogue completing and its direct implementing in the course of quantitative determination of residual stresses are discussed. It is shown that both experimental and numerical data aggregated into the first version of the catalogue can be effectively used for a verification of various coherent optics techniques with respect to a determination of residual stress components by means of hole drilling. An analysis of capabilities of reflection hologram interferometry in the field of residual stresses determination comparing with dual-beam speckle-interferometric techniques is presented. Superimposed residual stress field is quantitatively described in detail for both specimen sides of dimensions 260×80 mm². It is shown that fine nuances inherent in residual stress distributions over different specimen faces can be reliably derived from recorded fringe patterns of any type. This study serves as an example of residual stress components determination in real structure with a type of residual stress field to be investigated is unknown before the experiment.     

Determination of residual stresses using hole drilling and digital speckle pattern interferometry with automated data analysis

A digital speckle pattern interferometry and hole drilling combined system is developed to determine the magnitude of the residual stress in a aluminum thin plate subjected to an uniform uniaxial tensile load. Performing automated fringe analysis, the optical data contained in the speckle interferograms are quickly converted into values of residual stress. The evaluation is carried out through the measurement of the in-plane displacement field generated by the introduction of the small hole. The displacement field is determined from the calculation of the optical phase distribution by means of a phase shifting method. The magnitude of the residual stress is finally evaluated through a least-squares calculation and compared with the stress value applied to the specimen.     

Accuracy and sensitivity of a hole drilling and digital speckle pattern interferometry combined technique to measure residual stresses

This paper reports on the accuracy and sensitivity of digital speckle pattern interferometry (DSPI) when it is combined with the hole drilling technique for measuring residual stresses. The in-plane displacement field generated by the introduction of a small hole is determined using an automated data analysis approach. This method is based on the calculation of the optical phase distribution through a phase-shifting method and the application of a robust iterative phase unwrapping algorithm. It is experimentally demonstrated that residual stresses can be measured with a relative uncertainty of 7.5%. It is also shown that the minimum value of residual stress that can be determined with the DSPI and hole drilling combined technique is about 10% of the yield stress of the material.     

A least-squares method to cancel rigid body displacements in a hole drilling and DSPI system for measuring residual stresses

This paper presents the evaluation of a method to cancel rigid body displacements that can be introduced when a hole drilling and digital speckle pattern interferometry (DSPI) combined system is used to measure residual stresses. The proposed method is based on a least-square calculation of three correction parameters determined from two evaluation lines located near the edge of the phase map where the displacement field generated by the drilling process is supposed to be negligible. The errors introduced by the method for different residual stress levels and rigid body displacements are analysed using a numerical simulation. An application of the method to experimental data is also presented.     

Hybrid investigation on residual stresses induced by self-drilling screw on polycarbonate plates

The residual stresses induced by using self-drilling screws on polycarbonate plates were investigated by the hybrid method which incorporates the digital photoelastic method and finite element method (FEM). Different types of screws lead to different photoelastic fringe patterns, which provide the boundary conditions needed in the numerical simulation. By changing the two main parameters (pressure and temperature), the FEM results can be matched well with the experimental results for drilling at 0° tilt angle. For drilling at other tilt angles, the photoelastic fringe patterns provide useful information for failure analysis.     

An analysis of residual stress patterns resulting from hole expansion in an infinite plate, a thick cylinder, and an asymmetric lug

Residual stresses were induced in three specimen geometries: a quasiinfinite plate, a thick cylinder and an asymmetric lug. In each case, a hole expansion process was used, whereby the bore was expanded into the plastic regime; this in effect left residual compression at the bore and residual tension in the far field. In view of the symmetry, the stress patterns in the quasi-infinite plate were measured by a hole drilling method, using an interferometric moiré method to measure the resulting strain patterns. In the case of the thick cylinder and the asymmetric lug, the residual stresses were evidenced by a dissection method. A comparison with theoretical treatments shows that the theory predicts an approximate upper bound to the actual stress levels in the quasi-infinite plate. In the lug geometry, there was a similar systematic difference between theory and experiment.     

Determination of residual stress by use of phase shifting moiré interferometry and hole-drilling method

A phase-shifting moiré interferometry and hole-drilling combined system was developed to determine residual stresses. The relationship between the 2D displacement data of three points around the drilled hole and the residual stresses relieved by hole-drilling was established. The experimental setup consisted of a four-beam moiré interferometer and a computer-controlled hole-drilling system. Two phase shifters controlled by computer were fixed in two of the four optic paths to directly get the displacement data. With special residual stresses calculation software, the phase distributions of the u and v field obtained by moiré interferometry were quickly converted into values of residual stresses. To analyze the accuracy of this experimental system, an aluminum specimen with a blind hole in the center was real-time tensioned in this system. The displacement field obtained by phase shifting moiré interferometry was compared with the finite element method solution. Good agreement was found with respect to each other. As an application, the in-depth residual stresses of a shot-peened aluminum plate were measured by this method, and possible error sources were discussed.     

Stress evaluation of Through-Silicon Vias using micro-infrared photoelasticity and finite element analysis

The Through-SiliconVias (TSV) is a key component of three dimensional electronic packaging. Obtaining its stresses is very important for evaluating its reliability. A micro-infrared photoelasticity system with a thermal loading function was built and applied to characterize the stresses of the TSV structure. Through testing it was found that the stress of each TSV is different even if their fabrication technology is exactly the same, that different TSVs obtain their stress free states at different elevated temperatures, and that their stress free states are maintained even when the temperature is further elevated. A finite element model was used to quantitatively determine the stresses of a TSV under different stress-free temperatures. Different virtual photoelasticity fringe patterns were then created based on the principle of photoelasticity and the simulated stresses. Comparing the virtual fringe patterns with the experimental pattern, an appropriate virtual photoelasticity fringe pattern and the corresponding stresses of TSV were determined     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

A novel fringe adaptation method for digital projector

Aimed to obtain high-quality sinusoidal fringe projection, a new method to correct the output fringe of digital projector is presented. The method is based on the proposed fringe transform model, which describes the relationship of the input and output fringe pattern. Firstly, a series of fringe patterns are projected and from the fringe images, the transform function is calculated by the pattern shifting method. At last, by modifying the input fringe pattern, a standard sinusoidal output fringe can be achieved. Different from the previous methods, the waveform nonlinearity is estimated by varying the intensity of the projected fringe pixel by pixel; thus the waveform nonlinearity can be estimated precisely and the time cost is considerably reduced. Experimental results show that by modification of the input projection patterns the projector can project fringe with high-quality sinusoidal waveform leading to high performance of the projection system.     

基于Gabor滤波的散斑条纹图平滑方法

提出了一种基于伽博(Gabor)滤波的散斑条纹图平滑方法.通过加窗傅里叶运算提取散斑条纹图的条纹频率和条纹梯度方向,并利用它们确定具有频率和方向选择性的Gabor滤波器对散斑条纹图进行Gabor滤波.数值模拟和实验结果表明,该方法在滤除散斑噪声的同时能够有效的保留散斑条纹图的条纹结构,为从单幅散斑条纹图中进一步提取条纹相位场奠定了良好的基础.