A methodology development for the study of near surface stress gradients

Abstract

A modification of the geometry used in the sin 2 technique of X-ray diffraction is described. A modified equation for residual stress determination, including geometric adapted F ij , is presented. This method allows near surface stress gradients determination and is called pseudo-grazing incidence method. The limits of the new technique were first tested on different powder materials with X-ray radiation produced by conventional tubes and by a synchrotron radiation source. The technique was finally applied for the determination of a residual stress profile in a polished molybdenum surface before and after the deposition of a PVD chromium film.

Uncertainty of the X-ray Diffraction (XRD) sin2 ψ Technique in Measuring Residual Stresses of Physical Vapor Deposition (PVD) Hard Coatings

“…Therefore, the calculated residual stress value each represents an integrated stress value at certain coating thickness. Considering the fact that most hard coatings exhibit heterogeneous structure depending on the plasma-assisted growth [16][17][18][19][20][21]26,28,29], the GIXRD mode has provided an opportunity to analyze the depth profile of residual stresses, which also helps improve the understanding of the heterogeneous structure.…”

“…The increased residual stress with increasing Ω angle shows strong evidence of a stress profile along the depth direction. Because the X-ray penetration depth depends almost only on the applied Ω angle and each diffraction peak acquired at a certain Ω angle is actually the integration of diffractions of small volumes within a depth defined by the Ω angle, it is needed to consider a method of analysis to determine a depth profile of the actual residual stress, such as in literature [17][18][19]. Obviously, more extensive data processing is required, which is beyond the focus of this paper.…”

“…For the latter, because the nano-scale structure heterogeneity of PVD coatings has been experimentally approved as a result of microstructure evolution during their growth, a stress profile is expected to exist along the depth of such a coating. Related to this, theoretical and experimental approaches have been published for the measurement of stress profiles [17][18][19].…”

Structural modifications induced by swift heavy ions in cubic stabilized zirconia: An X-ray diffraction investigation

“…X-ray patterns were recorded in a range from 27°to 130°(2h) with steps of 0.02°; the acquisition time was 10 s per step. Residual macroscopic stresses induced by irradiation were determined by the sin 2 w method [9,10] which is based on the measurement of the shift of the diffraction peak position recorded for different angles w (w is the angle between the normal of the diffracting plane and the surface normal of the sample). In this approach, a specific diffraction plane (h k l) was selected and the residual strain, related to the stress by a linear elastic constitutive law, could be determined from a change in the interplanar spacing measured from a coupled h-2h scan.…”

Residual stresses in titanium nitride thin films obtained with step variation of substrate bias voltage during deposition

“…Brennan et al [26] and Leung et al [27] used a variation of the conventional sin 2 ψ method to determine stress as a function of penetration depths. Marques et al [28] and Peng et al [29] studied residual stress gradients by means of pseudo-grazing incidence X-ray diffraction method (PGIXRD), which is based on the conventional sin 2 ψ method in a 4-circle goniometer. In the method proposed by Kumar et al [30], the penetration depth is modified by employing a combination of χ and ω tilting.…”