The program for macroscopic stress analysis

J. Drahokoupil

Faculty of Nuclear Science and Physical Engineering in Prague; Trojanova 13, 120 00 Prague 2, Czech Republic

jan.drahokoupil@fjfi.cvut.cz

Keywords: Macroscopic stress, Computer program

The program, written in Microsoft Excel, is based on “General least-square analysis” [1]. The general equation (1) for macroscopic stress is used. Thus, no limitations for angles φ, ψ, θ are used as is for example in method sin²ψ plot or its modification [2].

(1)

The program features can be summarized as:

· Data from different diffractometers with various wavelengths can be used together in one computation of stress tensor. The correction for sample displacement and zero shift errors are also included.

· The program is very appropriate for description of strain depth gradients. All stress tensor component are described by polynomial representation (to fourth order) as function of depth.

· The program also enable to determinate the lattice parameter also with it depth evolution. The polynomial representation (to second order) for lattice parameter is used. See section deep averaging in chapter 3.10.

· The elastic anisotropy is described by Neerfeld-Hill model with weight factor between Reuss and Voight models. The weight factor can be also determined from refinement. For cubic symmetry is enough to enter only the elastic constants c₁₁, c₁₂ and c₁₄ and the X-ray elastic constants are computed on the base of hkl. For non-cubic symmetry for every used hkl the X-ray elastic constants has to be entered.

· If experimental data was collected at various temperatures the program enables correction for it using linear coefficient of temperature expansion.

· The data collected from different depth can be used for the stress tensor determination with depth gradients.

· Two kind of graphical output are pre-constructed. The sin²ψ plot is used for visual comparison between measured and computed experimental data. For review of correctness all components of stress tensor are plotted as function of depth.

· The program is connecting strain, stress and temperature effect on inter-planar distance and as such is not only limited to macroscopic stress analysis but it can work in opposite way or the material constant can be variables (e.g.: from known stresses and strains the elastic constants can be determined; from known temperatures and inter-planar distances the linear coefficient of thermal expansion can be determined).

The program is relatively complex and is not suitable for beginners in macroscopic stress analysis since the number of refinable parameters is larger than information given by position of usually measured peaks. Nevertheless, for experienced user can offer very appropriate tool for his research. Moreover, the big advantage of the program is that it can be easily modified by user with standard knowledge of Microsoft Excel program.

1. R.A. Winholtz, J.B. Cohen,  Aust. J. Phys., 41, (1988), pp. 189-199.

2. V. Hauk, Editor., Structural and Residual Stress Analysis by Nondestructive Methods. Amsterdam: Elsevier, (1997).

Acknowledgements.

This research was supported by the project FR-TI3/814 of Ministry of Industry and Trade of the Czech Republic.