Evaluation of strongly non-linear surface-stress fields σxx(z) and σyy(z) from diffraction experiments

Abstract

H. RUPPERSBERG et al. : Non-Linear Surface-Stress Fields o,,(z) and uyy(z) 68 1 phys. stat. sol. (a) 116, 681 (1989) Subject classification: 62.20 and 68.25; S1.2 For single-phase polycrystalline materials the relation is discussed between the elastic strain ~( y , p) obtained from X-ray diffract'ion experiments and the polynomial expansion of the stress components oJo) and O~+ Q O ( Z ) with respect to the distance z from the external surface of the specimen. -1 universal plot is proposed for F(y, to, (hkl)) = +(c(p) + ~( p + 90)) curves measured for different penetration depths t o of the radiation and for different reflecting lattice planes. This expression also allows absolute scaling of the E values. The formalism is applied for discussing s(y, p, to, (hkl)) curves obtained with synchrotron radiation from a cold-rolled nickel plate. They indicate strongly non-linear variations of stress in a surface layer about two pm thick. F u r einphasige vielkristalline Werkstoffe wird der Zusammenhang zwischen rontgenographisch ermittelten Dehnungen ~( y , p) und den nach dem Xbstand z von der Grenzflache in Reihe entwikkelten Spannungskomponenten oB(z) und O~+ Q O ( Z ) erortert. Es wird eine universelle Auftragung fur E(y, to, (hkl)) = -;-(e(p) + ~( p + 90))-Kurven vorgeschlagen, die fur beliebige Eindringtiefen t o und reflektierende Netzebenen ermittelt werden. Es ergibt sich daraus auch die Moglichkeit, E absolut zu bestimmen. Der Formalismus wird auf c ( y , p, to, (hk2))-Kurven angewendet, die mittels Synchrotronstrahlung fur ein kaltgewalztes Pu'ickelblech erhalten wurden. Es ergeben sich stark nichtlineare Spannungsanderungen in einer etwa 2 pm dicker, Oberflachenschicht.

A methodology development for the study of near surface stress gradients

“…In our present study the lower mean penetration depth is in the order of 100 nm. The surface effect can therefore be neglected, as others authors had done [5,15,23]. A general overview of problem in the case of near surface XRD analysis is mentioned by Ruppersberg et al in [6] and by Genzel in [12].…”

“…Predecki et al proposed in [4] two methods based on the grazing incident X-ray diffraction for the asymmetric geometry in order to obtain the depth profiles of strains and stresses as a function of the penetration depth. Ruppersberg et al proposed in [5] the universal-plot method, which can combine the | ii (~)-profiles obtained in C-mode and V-mode for different radiations and reflections in a 'master-curve' [6]. Their results indicated a strongly non-linear stress variation in a surface layer about 2 mm thick.…”

“…(4) imposes analytical assumptions for the m ij (z) profiles. Usually exponential or polynomial functions are used [5,6,10,11]. Recently, it has been developed a numerical procedure in order to solve Eq.…”

Energy-Dispersive Residual Stress Analysis under Laboratory Conditions: Concept for a New Type of Diffractometer

“…In only relatively few papers the white beam technique in reflection geometry for depth resolved residual stress analysis in the subsurface layer region is used. In this regard, pioneering work was supported by the universal plot method (UVP) applied to the case of ED diffraction [6]. In [7,8], the bremsstrahlung of a conventional tungsten laboratory X-ray source was used in the early 90s to demonstrate on a polished steel plate, that the values determined from different diffraction interference E hkl are assigned to different levels of information depth and can fit together to one master curve yielding a complete residual stress depth profile.…”

Depth resolved near-surface residual stresses in γ-based TiAl before and after high-temperature exposure

“…The curved shape of the plot, especially at high values of sin 2 results from high non-linear surface stresses. The "universal plot" procedure [19] was thus used to obtain the stress profiles. The value of d 0 hkl is interpolated from the two data points adjacent to the value of …”