# Residual stress measurement using X-ray diffraction

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## Date

2005-02-17

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## Publisher

Texas A&M University

## Abstract

This paper briefly describes the theory and methods of x-ray residual stress
measurements.
Residual stresses can be defined as the stresses which remain in a material in the
absence of any external forces. There are many stress determination methods. Some of
those methods are destructive and some are nondestructive. X-ray residual stress
measurement is considered as a nondestructive method.
X-ray diffraction together with the other diffraction techniques of residual stress
measurement uses the distance between crystallographic planes as a strain gage. The
deformations cause changes in the spacing of the lattice planes from their stress free
value to a new value that corresponds to the magnitude of the residual stress. Because of
Poissons ratio effect, if a tensile stress is applied, the lattice spacing will increase for
planes perpendicular to the stress direction, and decrease for planes parallel to the stress
direction. This new spacing will be the same in any similarly oriented planes, with
respect to the applied stress. Therefore the method can only be applied to crystalline,
polycrystalline and semi-crystalline materials.
The diffraction angle, 2θ, is measured experimentally and then the lattice spacing
is calculated from the diffraction angle, and the known x-ray wavelength using Bragg's
Law. Once the d-spacing values are known, they can be plotted versus 2 sin ψ, ( ψ is the
tilt angle). In this paper, stress measurement of the samples that exhibit a linear behavior
as in the case of a homogenous isotropic sample in a biaxial stress state is included. The
plot of d vs. 2 sin ψ is a straight line which slope is proportional to stress. On the other
hand, the second set of samples showed oscillatory d vs. 2 sin ψ behavior. The oscillatory
behavior indicates the presence of inhomogeneous stress distribution. In this case the xray
elastic constants must be used instead of E and ν values. These constants can be
obtained from the literature for a given material and reflection combination. It is also
possible to obtain these values experimentally. Calculation of the residual stresses for
these samples is beyond the scope of this paper and will not be discussed here.

## Description

## Keywords

x-ray diffraction, residual stress