DEFORMATION OF METALS AS SEEN BY NEUTRON DIFFRACTION

P.Lukáš¹, K.Macek², P.Mikula¹, D.Neov¹, G.M.Swallowe³, M.Vrána¹ and R.Wimpory⁴

¹Nuclear Physics Institute, 250 68 Oe? near Prague, Czech Republic
²Faculty of Mech. Eng., CTU Prague, Karlovo nám. 13, 121 35 Prague 2, Czech Rep.
³Dept. of Physics, Loughborough University, Leicestershire LE11 3TU, U.K.
⁴Institute Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France

Keywords: microstrains, elastic modulus, neutron diffraction

Because of their high penetration thermal neutrons have been found very useful probe in measurements of internal strains in polycrystalline materials. The neutron diffraction technique can provide information on both macro- and micro-strains. The determination of macrostrains (e=Dd/d_o) is based on the measurement of small angular shifts of diffraction peaks caused by small lattice-parameter variations Dd in a sampled volume with respect to the stress-free lattice spacing d_o. The magnitude of stress can be calculated by using appropriate elastic moduli. Investigation of microstrains is based on the analysis of the shape of broadened diffraction profiles. Recently, a lot of work has been done investigating the distribution of residual strains resulting from different technological treatments as well as phase specific strains in multiphase materials and in composites. Of special interest are deformation tests realized in situ at the neutron diffractometers. In this case, the precise angular position of the profile maximum provides information on an averaged elastic strain in the sampled specimen volume whereas the width and shape of the diffraction profile is related to the evolution of the plastic deformation.

Two high-resolution neutron diffractometers dedicated to strain investigations are available at the medium-power reactor LVR-15 in NPI Oe?. They are equipped with curved Si and Ge monochromators and with a high-resolution 1d-PSD for fast recording of diffraction profiles. The strain scanner SPN-100 using a two-crystal sandwich monochromator permits us to work with two different neutron wavelengths, simultaneously (Ge(311)- l=0.147 nm, Si(111)-l=0.27 nm) and thus to record more sample reflections with a sufficiently high Dd/d-resolution (»2x10^-3). While the SPN-100 scanner is mainly qualified for microstrain analysis, the scanner TKSN-400 is optimized for mapping macrostrains in small sample gauge volumes down to 1mm³ or investigating weakly reflecting materials. The scanner operates at the wavelength of 0.22 nm and the bent Si(111) monochromator provides an instrumental resolution Dd/d of about 5x10^-3, but with a luminosity about 20 times higher than that of the SPN-100 instrument. The strain diffractometers are equipped with a deformation rig enabling both tensile and compressive tests up to maximum loading of ±20 kN. The advantages of such instrumentation is illustrated by the following two examples of investigations of elastic and plastic deformation of steels.

The first example deals with the plastic deformation of low carbon steel. In this case, the width of the diffraction profile was used as a measure of plastic deformation. Using the integral breadth technique [1], a relatively simple method of profile analysis, mean-square microstrains were refined from diffraction profiles for different degrees of the plastic deformation. This structural parameter can be used for modelling the dislocation density [2]. The effect of dislocation strengthening can be thus studied by combining the results of mechanical tests (yield stress) and diffraction conclusions (dislocation density). The extended Hall-Petch equation [3] describes different mechanisms of strengthening, the increment of the yield stress DR_disl. due to dislocations can be related to the dislocation density as DR_disl. = a G b r^1/2; where is the dislocation density, G is the shear modulus, b is the Burgers vector and the constant a varies between 0.5 and 2. When the values of dislocation densities calculated from the peak breadth is compared to the measured yield stresses, very good agreement with the Hall-Petch model is obtained (Fig.1, fitted parameter a = 1.35). This illustrates that the neutron diffraction technique and the applied profile analysis method are appropriate tools for studying dislocation strengthening in metals.

The second example deals with the elastic properties of high-carbon steels. Carbon steels are essentially composites of hard cementite in a ferrite matrix. In principle, the diffraction technique can yield information on the elastic properties of the individual phases. Fig.2 shows the elastic loading and unloading behaviour of the ferrite phase. When the load exceeds the ferrite yield stress the unloading curve for ferrite is been found to be non linear. The presence of the relatively small amount of the cementite can thus significantly influence the elastic properties of the dominant phase. This behaviour in high-carbon steels was predicted by the finite element model of Zhonghua & Haicheng [4]. Due to the observed non-linearity of the unloading curve, a 30% variation in ferrite elastic moduli was measured. This effect can introduce significant errors in 'true' stress evaluation when using a single valued constant modulus to convert from strain to stress.

[1] D.Balzar, S. Popovie, J. Appl. Cryst. 29 (1996) 16.
[2] G.K.Williamson and R.E.Smallman, Phil. Mag. 1 (1955) 34.
[3] N.J.Petch, J. Iron Steel Inst. 174 (1953) 25.
[4] Li Zhonghua, Gu Haicheng, Metall. Trans. A, 21A, 717-732, 1990.