The equation ε(φ, ψ, hkl)=Fij(φ, ψ, hkl)σij can be directly deduced from Hooke’s law. It is shown that the matrix Fij(φ, ψ, hkl) which is usually called X-ray elastic factors, behaves as a second rank tensor. Since this behaviour is the only criterion for the question of whether or not it is a tensor, the F-matrix must be regarded as a second rank tensor. This allows us to make some statements about the structure of the F-matrix on the basis of Neumann’s principle, to find relationships among F-matrices in different measurement directions, and to apply the methods and strategies for the measurement of a second rank tensor. All this is shown in a few examples. It is further shown that a consistent use of the F-matrix can replace all methods for data evaluation which makes use of linear regressions and, in addition, avoids all difficulties and disadvantages of these methods. One of these disadvantages is that the sin2 ψ-method, as well as its derivatives, is generally not correct least square fits of the measured data. This is also shown in an example. The more complicated cases with stress or constitution gradients in the range of the probed volume or stress measurement after plastic deformation are not discussed.
Elastic plastic deformation of TC6 titanium alloy analyzed by in-situ synchrotron based X-ray diffraction and microstructure based finite element modeling
