Residual stress analysis on metal surfaces
X-ray diffraction
X-ray diffraction is a method that allows the non-destructive detection, if limited to the surface, of residual and applied stresses. The measurement of residual stresses is fundamental for understanding the behaviour of mechanical components subjected to “fatigue” (see the controlled shot peening topic on the site to learn more about the concept of fatigue in materials).
X-ray diffraction was originated in 1912 by Lawrence Bragg, who won the Nobel Prize, with his father, for this discovery in 1915 at just twenty-five years old! The reason for the award was “for their services in the analysis of crystalline structure through of X-rays”.
It was thanks to Bragg’s Law that it was possible to determine the position and distance of the atoms in the crystalline lattices that characterize the solid state of most metals, and crystalline substances, at room temperature. In fact, only through the application of Bragg’s law was it possible to interpret the image relating to the interaction of monochromatic X-rays with a zinc sulphide crystal obtained shortly before by the German physicist Max Laue (next image).
Photo by Max Laue relating to the interaction of X-rays with zinc sulphide crystal"
In the following years, much research was carried out to solve the crystalline structure of most metals and chemical compounds, and a database was created on which most of our knowledge of crystallography is still based today.
In 1952, thanks to R. Franklin and R. Gosling, X-ray diffraction made it possible to understand the helical structure of DNA (next image).
Subsequently, the method that used X-ray diffraction was developed to determine the variations between the distances of the crystalline planes, in other words it became possible to evaluate the deformations, and therefore the residual or applied tensions that cause them.
The following pages show the principles on which the measurement of residual stresses using X-ray diffraction is based.
X-ray diffraction of DNA"
Introduction to the measurement of residual stresses by X-ray diffraction
The crystalline structure
In crystalline solids the atoms occupy positions in space that are repeated with geometric regularity, in fact a repetitive element is always identifiable, consisting of a variable number of atoms, this element is called an elementary cell.
Many materials used in the field of mechanics have crystalline structures. For example, iron and its alloys have a crystalline structure characterised, depending on the temperature, by body-centred cubic (bcc), face-centred (cfc) and body-centred cubic elementary cells. Many metallic alloys, based on various chemical elements, have a structure that depends on temperature and chemical composition. For example, pure copper has a face-centred cubic unit cell, but if zinc is added to copper, the resulting alloy can have, depending on the percentage of zinc present, a face-centred or body-centred cubic unit cell.
Face-centred cubic unit cell (cfc)
Body-centred cubic (bcc) unit cell
Fourteen elementary cells have been identified
In elementary cells it is possible to identify a series of planes, parallel to each other, which are characterised by Miller indices. These indices are defined as the reciprocal of the intercept with the crystalline axes, the following figure shows various examples. If we consider the plane characterised by the indices (0 1 0) it is defined as parallel to the x and z axes, while it intersects the y axis at a unit distance from the origin of the axes.
Elementary cells
Miller indices for the cubic unit cell
X-ray generation
Generally the X-rays used in the laboratory are produced by tubes. In a tube there is a filament that emits electrons due to the thermionic effect. The electrons emitted from the filament are accelerated towards a cathode by an electric potential imposed between the filament and the cathode.
X-ray tube
X-rays are emitted during the interaction between electrons and the cathode itself.
X-rays can be divided into two different groups, according to the process by which they are generated:
– braking radiation (bremsstrahlung): emitted by the electron beam, with energies greater than 100 eV, when they are abruptly braked by the impact with the atoms of the cathode
– X-rays characteristic of atoms: deriving from the excitation of the internal electrons of the cathode by bombardment with the incident electron beam.
Braking radiation
The first group is used in radiography, the second in diffraction or flurosescence X-ray. While for the first group the generated wavelength is distributed along a continuous spectrum (white radiation), the second group have intensity peaks at well-defined wavelengths and depend on the atoms of the cathode (characteristic radiation).
RX spectrum emitted by a tube as a function of potential
The characteristic radiation is generated when an electron accelerated by the potential hits the cathode and expels an electron from the hit atom
Diagram illustrating the collision between the incident electron and the ejected electron
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