X-ray Stress Determination Research Articles

Determination of Stress Values in the Surface Layer of Inconel 718 Samples Dedicated to Fatigue Tests

Abstract This work deals with the problem of X-ray stress determination on the samples dedicated to fatigue tests. A number of research studies point out the fact that the processing of hard, difficult to machine materials like nickel superalloys, reveals more than one trend of residual stress versus working parameters of behaviour (Lavella and Berruti, 2010). Many papers have shown that the residual stresses are dependent on a combination of a number of factors. When the above is taken into account simultaneously with the requirements of the internal General Electric specification for the fatigue tests samples preparation (Metallic test specimen preparation, low stress, 2017) the problem of turning and grinding parameters gathers significance. It is well known that the quality of the surface layer, produced during machining, is of vital importance for the fatigue life specially for the components of aircraft produced form nickel superalloys e.g. Inconel 718 (Kortabarri et al., 2011). That is why the surface layer’s properties are described in detail by the standards. The aim of the work is to determine one of the most influential features from the point of view of fatigue life, i.e. the stress state on the surface layer with one non-destructive method – the diffraction analysis.

The cos<i>α</i> method for X-ray residual stress measurement using two-dimensional detector

X-ray stress measurement is widely used as one of the most powerful nondestructive tools to measure residual stresses in polycrystalline solids. In most cases, the sin2Ψ method has been used to determine the stress. In recent years, however, the cosα method has attracted engineers as a new method to measure the stress using two-dimensional detectors, such as imaging plates. The present article is the review of the state of the art of the cosα method. For biaxial stress cases, the cosα method utilizes the whole Debye-Scherrer ring recorded on a two-dimensional detector taken by single exposure of X-rays, and normal and shear stresses are determined simultaneously. The accuracy of the stress measurement of the cosα method has been confirmed to be equivalent to that of the sin2Ψ method for various metals. The simple optical system of the cosα method makes stress analyzers smaller, lighter and more convenient to use for on-site or field measurements. A recent portable stress analyzer adopting the cosα method shortens the measurement time to 60 s. The method has been further developed to analyze triaxial residual stresses. Various advantages of the cosα method are highlighted in comparison with the other methods of X-ray stress determination. Applications of the cosα method to machines and engineering structures are presented, together with future perspectives of the method.

2次元検出器を用いたcos <i>α</i>法によるX線応力測定 その１ 測定の基礎

X-ray stress measurements are widely used as one of the most powerful nondestructive tools to measure residual stress in polycrystalline solids. In most cases, the sin2ψ method has been adapted to determine the stress. In recent years, the cos α method attracts engineers as a new method to measure the stress using two-dimensional detectors, such as imaging plates (IP). The present article is the part one of the review of state of the art of the cos α method. The principle of the method was originally proposed in Japan and has been developed in cooperative works in the Society of Materials Science, Japan. The strain is determined from the whole Debye-Scherrer ring recorded on IP by single exposure of X-rays as a function of the orientation angle α. In one measurement, the normal stress is determined by cos α diagrams and the shear stress by sin α diagrams, without knowing the exact value of stress-free diffraction angle. A commercial portable stress analyzer adapting the cos α method shortens the measurement time to about 1min. In the present article, the history of the development of the cos α method is covered and fundamentals of the method are presented. The advantages of the cos α method are highlighted in comparison with the other methods of X-ray stress determination.

Equivalence of Kröner and weighted Voigt-Reuss models for x-ray stress determination

The determination of stress in polycrystalline aggregates by diffraction-based methods relies on the proper choice of grain interaction model that links the observed strain to the elastic stress state in the ensemble. It is shown that for single-phase, polycrystalline samples composed of crystals with cubic symmetry, x-ray elastic constants (XEC) calculated under the Kröner model are equal to those from a weighted combination of Reuss and Voigt XEC, where the weighting factor is only a function of the single crystal elastic tensor coefficients. This weighting factor, xKr, generally scales with elastic anisotropy factor, A, with a value close to the Neerfeld limit for elastically isotropic materials (A = 1). Materials that possess large values of A, and correspondingly small xKr, exhibit a greater deviation between the Neerfeld and Kröner limit XEC. A dimensionless parameter, Q, based on a different combination of elastic coefficients than A, demonstrates a monotonic trend with respect to xKr and may serve as a better metric for describing the elastic response of a polycrystalline ensemble as interrogated by x-ray diffraction. For crystals possessing lower symmetry, a similar analysis reveals that Kröner XEC are not a unique combination of Voigt and Reuss limits. In the case of hexagonal crystal symmetry, xKr for a particular material varies as a function of the orientation parameter of the crystal, indicating that the degree of elastic anisotropy of the constituent crystals may impact the determination of stress depending on the choice of x-ray reflection.

Residual Stress Analysis of Textured Materials by X-Ray Diffraction Method

The residual stress measurement by the conventional X-ray diffraction was formulated on the assumption that a specimen from polycrystalline materials was quasi-isotropic and homogeneous, and the stress was biaxial and almost constant within the X-ray penetration depth. Therefore, it was not available to analyze the stress state of the textured materials by the conventional measurement as a general rule. In resent years, advanced methods have been proposed for the X-ray stress measurement of textured materials. In some methods, it is assumed that the X-ray elastic constant is derived from the crystallite orientation distribution function of textured materials for solving the first anisotropic problem. However, there is a nonlinear problem in the stress analysis from the measured lattice strain. In present study, the X-ray elastic constants were averaged as the expected value around the normal direction of the X-ray diffraction in a similar way. A stress analysis was proposed by differential calculus of the X-ray elastic constant in order to the avoidance of nonlinear problem. The stress analysis was applied to residual stress measurements of a titanium carbide coating film with preferred orientation and a cold-rolled steel with texture. The calculated values of the X-ray elastic constants showed the linearity on some condition for the film. The X-ray stress determination was carried out by the fitting the gradients of the measured lattice strain.

Why we should give up the sin2ψ method

The sin2ψ method can be formulated as a single system of simultaneous linear equations. Using this it is easy to show that the sin2ψ method is not a least-squares method. It further helps to compare the accuracies of the stress tensors obtained by the sin2ψ method and the method of least squares. Quantitative comparisons have been made for different fictitious measurements. It is shown that the unnecessary loss in accuracy by using the sin2ψ method is quite significant and by no means negligible. The same course of action has been applied to compare the so-called Dölle-Hauk method with a least-squares method; the result is similar. Some other methods for X-ray stress determination, most often similar to the sin2ψ method, and their shortcomings are also discussed briefly, together with the corresponding, more effective and more versatile least-squares method.

Effects of Temperature Fluctuations on X-Ray Stress Determination

The results presented in this paper are part of a process to analyse systematically the sources of uncertainty in X-ray stress determination. They concern one part of the effects of temperature variations which could intervene either as random fluctuations or as a monotonic drift during the acquisition. The proposed formulation is in agreement with the recommendations of the ISO guide on the expression of uncertainty (GUM). It was found that the effect is usually negligible for laboratory experiments which are often temperature controlled and for most materials. However the uncertainty can reach 20 MPa for austenitic steels and a temperature drift of 2 K.

Reference specimens for x-ray stress analysis: the French experience

The aim of this paper is to analyse the results obtained by a French workgroup that has been working on reference specimens for x-ray stress determination, to critically examine the procedure and to understand the factors that control the accuracy of the results. It is found that manufacturing of specimens with sufficient accuracy is possible and the paper shows how the embryo of a metrological system for x-ray stress analysis can be set up.

Influence of Annealing on the Residual Stress in Sputter-Deposited Platinum Films

The changes of residual stress in commercially produced platinum layers during heat treatment are studies in this paper. X-ray stress determination techniques yield, superimposed, both the thermal and intrinsic stresses in the layer. An analytical model, following the method of Tsui and Clyne, is used to separate these two stress contributions. This allows one to interpret the development of the intrinsic stress under thermal influence.

French round-robin test of X-ray stress determination on a shot-peened steel

A round-robin test of X-ray residual stress determination was performed by the Groupement Francais d'Analyse des Contraintes and involved 16 laboratories. The standard deviation of the measurements was about 36 MPa, but a posttreatment of the raw data with the same soft-ware reduced the dispersion to 19 MPa. Analysis of the uncertainty sources (goniometer alignment, operator, counting statistics, nonlinearity of the material, etc.) revealed that the main sources come from the data treatment and the operator.

Two Parameters Characterizing Superficial Mechanical Features

Abstract Two parameters, surface yield strength and surface work hardening exponent, have been newly suggested in this paper to characterize the superficial mechanical features in engineering metallic materials. Emphasis was placed on the method by which the two parameters are determined. X-ray stress determination and strain gage techniques were employed to measure stress and strain. The Mises effective stresses at a sample surface under different loading conditions were then calculated with the measured data; hence, the relationship between stress and strain was available. Consequently, with the data processing procedure for general yield point and work hardening exponent of uniaxially loaded materials, the yield point and work hardening exponent at the sample surface can thereby be obtained. Experimental studies on a shot-peened surface showed satisfactory results when the described method was used.

Inhomogeneous Deformation in Thin Films

Residual stresses are a major factor in the reliable operation of multi-layer thin film structures. These stresses may form due to defect incorporation during deposition, recrystallization, second-phase precipitation, thermal coefficient of expansion (TCE) mismatch, etc., as well as local plastic flow, delamination or cracking. In the literature, residual stresses are usually assumed to be constant in the plane of the film. This assumption is sometimes implicitly made, as in the cases where only two psi-tilts are used in the stress determination with the sin2Ψ analysis.In this paper, we will review the possible causes of heterogeneous stress distributions in thin films and discuss their impact on x-ray stress determination techniques using some new data from W films.

Stress Correction for Removal of Material in X-Ray Stress Determination

Abstract To determine residual stresses in a (flat) plate or bar with a rectangular cross-section by X-ray diffraction after removal of material, we can sectionally approximate the measured stress curve with depth using power series, then consequently evaluate the additional stresses created by removal, and finally obtain the true stress distribution with depth before the layers were removed. Formulas to evaluate corrections for stress have been derived. Two examples demonstrate that power series with few terms can provide us with an approximation good enough for the measured stress curve, and that the influence of the approximation on the corrective result is far less than that of the errors arising from the X-ray stress determination itself.

Oscillations in Interplanar Spacing Vs. sin2ψ a FEM Analysis

AbstractRecent studies indicate that, if the stress/strain field within the irradiated volume in an x-ray stress determination experiment is inhomogeneous, oscillations occur in the interplanar spacing vs. sin2ψ plots. There is, however, little work on the degree of inhomogeneity required to cause a given oscillation, the uniqueness of the stress fields that can cause a given set of oscillations, or the error caused by applying the traditional methods currently in use to oscillatory data.In this paper, numerical modeling and eiasto-plastic finite element analysis was used to determine the strain fields in the diffracting volume of a polycrystalline sample under load. The elastic strain fields obtained from the analysis were then averaged over the regions that would diffract in an x-ray experiment/and then correlated to x-ray strain data to obtain an idea of the problems described ahove.

Energy band‐gap in elastic‐strained heteroepitaxial layers

AbstractThe effect of internal elastic stress on energy band‐gap shift in the A3B5 heteroepitaxial layers was investigated. The possibilities to get higher accuracy of divergent beam X‐ray stress determination method, designed in the scanning electron microscope (SEM), was presented. X‐ray topography method in the SEM with X‐ray magnification from 2 up to 10 was for the first time described.The epilayer photoluminescence (PL) peak energy shift as a function of internal elastic stress was measured on the GaInP/GaAs, GAInAsP/InP heterostructures and the influence of different factors on the accuracy of the results was discussed.

X-ray stress determination in austenitic steel

X-ray stress determination in austenitic steel