Determination of residual stresses by an optical correlative hole-drilling method

In conjunction with the incremental hole-drilling method, a new evaluation procedure is presented for determining the residual stress state in components. In contrast to the classical method, the whole displacement field around the drilled hole is measured using the electronic speckle pattern interferometry technique. The displacement patterns, measured without contact to the surface, are then correlated with those obtained by finite-element simulations using statistical methods. The simulated displacement patterns, used for calibration purposes, result from the application of properly defined basic loads. In this way, the values and the orientation of the residual stresses can be determined by superposition of these properly scaled and shifted basic loads. Even complex states of stress can be evaluated. The theoretical background and experimental results are presented.     

Full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data

A mathematical method is proposed for calculating residual stresses from hole drilling electronic speckle pattern interferometry (ESPI) data, independent of rigid-body motions. Even though the signal-to-noise ratio of typical ESPI data is modest, the method achieves good computational stability by averaging a large amount of data. It does this without excessive numerical effort by exploiting known trigonometric relationships among the data. The resulting stress calculations are very rapid, and are well suited for future application to non-uniform stress measurements.     

Modifications to the hole-drilling technique of measuring residual stresses for improved accuracy and reproducibility

The hole-drilling technique is a relatively well established and straightforward semidestructive method for measuring residual stresses in fabricated components. However, a number of factors can have a marked influence on the accuracy of this technique. Some of the factors evaluated in the present work were the method of drilling the hole, the size and shape of the hole, and the equations used to calculate the principal residual stresses from the relaxed-strain measurements. In this investigation, air-abrasive hole drilling using a 0.062-in.-ID stationary nozzle gave the most reproducible and accurate results. Of the three approaches used to calculate the residual stresses, one method proved to be superior, especially in a biaxial-stress field.     

A general form for calculating residual stresses detected by using the holographic blind-hole method

A general form used for analyzing residual stresses measured using the holographic blind-hole method is introduced in this paper. Adopting the general form presented, the residual stresses can be obtained using three relative displacements measured from a single interference fringe pattern. Even for the case in which phase-shifting holographic interferometry is not employed, interpolating calculations for determining the fringe orders are not needed, since the choice of data points becomes more flexible when using this general form. Two experiments, the first one carried out by the authors and the second one published previously, are used to illustrate the applicability and usefulness of this general form. Suggestions for the applications of this general form are also established via the upper bound error estimations.     

Assessing the effect of residual stresses on the fatigue behavior of integrally stiffened structures

Residual stresses emerge quite often in real structures due to the various manufacturing processes such as, welding, forming, cutting, milling, etc. In such cases, development of cracks at regions influenced by manufacturing operations demand additional attention. In the present work a numerical methodology has been developed, based on three-dimensional Finite Element Analysis, for the calculation of Stress Intensity Factors at cracks in welded components. The residual stress fields, which are used in SIF calculations, have been computed by the numerical simulation of the thermo-mechanical process. A numerical algorithm based on interpolation principles is developed, in order to introduce the three-dimensional field in the computational model of the cracked structure. The SIF calculation methodology is initially validated for the case of a welded plate by comparison of numerical results with existing analytical solutions. A cracked stiffened panel is analysed afterwards and the calculated fatigue crack propagation results are compared to experimentally measured data. Finally, the numerical procedure is applied to study the effect of more complicated residual stress fields on SIF values developing at cracks located in stiffened panels.     

An acoustoelastic method for measuring residual stresses in slightly orthotropic materials

An acoustoelastic method for residual stress measurement in slightly orthotropic materials by using ultrasonic longitudinal and shear waves is presented. A shear transducer with small vibrator 2 × 2mm² is developed and described, and the measurement of 2-D residual stresses in a seam welded plate was carried out by this method with the shear transducer developed.This project was supported by National Natural Science Fundation of China     

An investigation of the hole-drilling technique for measuring planar residual stress in rectangularly orthotropic materials

The applicability of the semidestructive holedrilling technique to the experimental determination of residual stresses in relatively thin rectangularly orthotropic materials was investigated. From the exploratory work, it was determined that the similitudes, for measurements at a particular ratio of hole depth to diameter, which exist for thick materials are not present in relatively thin materials. This implies that calibration tests must be made for each combination of strain-gage size and plate thickness. As a consolation, however, it was found that there is no need to drill to an optimum depth for thin materials. That is, one may simply drill a small hole completely through the material to obtain the desired strain change.     

Micromechanics of residual stress and texture development due to poling in polycrystalline ferroelectric ceramics

This paper presents micromechanics based analysis of elastic strain and changes in the texture of poled polycrystalline ferroelectric PZT ceramics for direct comparison with synchrotron X-ray measurements. The grains are modelled as spherical inclusions, to which transformation strains are assigned depending on the fractions of different ferroelectric domains. Eshelby's inclusion problem with the classical self-consistent method is applied to evaluate the elastic state of the grains. In particular, the elongation due to lattice elastic strain is calculated as a function of inclination Ψ relative to the polar axis. The ratio of diffraction peak intensities, corresponding to the domain fractions, is also expressed as a function of Ψ. This analysis identifies the special character of the reflection, for which the lattice strain along in the stress free state is independent of ferroelectric domain population and hence unaffected by poling. The elongation due to the lattice strain parallel to and peak intensity ratio are expressed in terms of the overall macroscopic strain of a poled specimen, each having a dependence.     

A new approach for determining the induced drilling stresses in the hole-drilling method of residual-stress measurement

Experimental Techniques -     

The effect of the Reynolds number on the Reynolds stresses and vorticity in a turbulent far-wake

Using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane, the effect of the Reynolds number in a turbulent plane far-wake has been investigated for two values of Re_θ (based on the free stream velocity and the momentum thickness), i.e. 1350 and 4600. It is observed that as the Reynolds number increases the magnitudes of the measured Reynolds stresses increase, as does the size of two-point vorticity correlation iso-contours. Discernible differences are also observed in probability density function, spectra and three-dimensional topologies. The Reynolds number dependence seems to vanish when Re_θ5000.     

A smoothed inverse eigenstrain method for reconstruction of the regularized residual fields

A smoothed inverse eigenstrain method is developed for reconstruction of residual field from limited strain measurements. A framework for appropriate choice of shape functions based on the prior knowledge of expected residual distribution is presented which results in stabilized numerical behavior. The analytical method is successfully applied to three case studies where residual stresses are introduced by inelastic beam bending, laser-forming and shot peening. The well-rehearsed advantage of the proposed eigenstrain-based formulation is that it not only minimizes the deviation of measurements from its approximations but also will result in an inverse solution satisfying a full range of continuum mechanics requirements. The smoothed inverse eigenstrain approach allows suppressing fluctuations that are contrary to the physics of the problem. Furthermore, a comprehensive discussion is performed on regularity of the asymptotic solution in the Tikhonov scheme and the regularization parameter is then exactly determined utilizing Morozov discrepancy principle. Gradient iterative regularization method is also examined and shown to have an excellent convergence to the Tikhonov–Morozov regularization results.     

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.     

Elastic waves in compressible materials with initial stresses and a nondestructive ultrasonic method for the determination of biaxial residual stresses

Concise information is given on the theory of the propagation of elastic waves in bodies with initial stresses. This information provides the basis of a nondestructive ultrasonic method for the determination of biaxial residual stresses in isotropic and quasiisotropic materials. The basic acoustoelasticity relation for biaxial stresses is analyzed, and an instrument for the determination of biaxial residual stresses in electric welding is described, along with examples of its application.Adapted from the complete text of a paper submitted to the 18th International Congress on Theoretical and Applied Mechanics, Haifa, Israel, August 22–28, 1992, Session B-A2: Waves in Solids (August 24, 1992).S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 3–17, January, 1994.     

A residual method of finite differencing for the elliptic transport problem and its application to cavity flow

A residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one-dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term-by-term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method.     

Size effect in the initiation of plasticity for ceramics in nanoindentation

The indentation size effect has been observed for many years and is usually associated with increasing hardness as the depth of indentation is reduced for pyramidal indenters. The indentation size effect for spherical indenters has recently been associated with an increase in the yield stress of metals proportional to the inverse cube root of indenter radius [Spary, I.J., Bushby, A.J., Jennett, N.M., 2006. On the indentation size effect in spherical indentation. Philos. Mag. 86 (33), 5581-5593]. Here we investigate ceramic materials where the yield point is high enough to be easily distinguished in nanoindentation tests. A robust method for determining the yield point from a nanoindentation test with spherical indenters is presented. The results for a range of ceramics confirm that the increase in yield pressure is directly proportional to the inverse cube root of indenter radius. Furthermore, the yield pressure is also shown to be proportional to the inverse square root of the contact radius. Revisiting data in the literature shows that this inverse square root relationship is also true for pyramidal indenters. This implies that the indentation size effect is driven by the contact area rather than by the depth of indentation or by the indenter radius.     

Use of Synchrotron Tomographic Techniques in the Assessment of Diffusion Parameters for Solute Transport in Groundwater Flow

This technical note describes the use of time-resolved synchrotron radiation tomographic energy dispersive diffraction imaging (TEDDI) and tomographic X-ray fluorescence (TXRF) for examining ion diffusion in porous media. The technique is capable of tracking the diffusion of several ion species simultaneously. This is illustrated by results which compare the movement of Cs⁺, Ba²⁺ and La³⁺ ions from solution into a typical sample of English chalk. The results exhibited somewhat anomalous (non-Fickian) behaviour and revealed heterogeneities (in 1D) on the scale of a few millimetres.     

Uniaxial extension and shear in combination with cyclic straining as a promising method for studying the viscoelasticity of polymers over a wide range of stresses and strains atT > T g

Simple relations are found between the fracture strains, the long-term durability and the initial values of parameters characterizing polymer rheology at deformation rates and stresses approaching zero. Fracture regimes are determined by two groups of parameters. One includes critical values of stresses. They are invariant with repect to temperature and molecular weight of the polymers; the values of critical stresses for different polymer compositions differ by a factor of 10 to 20. The second group of critical parameters includes the rates of deformation determined by the initial viscosity. The latter may vary by many orders of magnitude. There exists a universal critical value determining polymer fracture independent of linear macromolecule composition, its molecular weight, the temperature and the way of attaining a given state. This value is the recoverable strain and is equal to 0.5 according to Hencky. There exists a relation between the maximum value of recoverable strain in the transition region from the rubbery to the leathery state and the extensibility of macromolecules for polymers with various molecular weights. Quenching of the polymer near the maximum recoverable strain makes it possible to obtain high strength samples. Overspurt regimes for polymer flow have also been studied. It has been shown that this causes polymer static electrification. Simple and unique dependences of the charge density on temperature and polymer molecular weight have been established.Presented at the 28th IUPAC International Symposium on Macromolecules, June 1982, Amherst, Mass. (USA)Dedicated to Prof. Dr. Josef Schurz on the occassion of his 60th birthday