X-Ray Investigation on the Elastic Deformation Behaviour of Two Phase Alloys

Abstract

It is well known that the constituent crystals of polycrystalline metals are anisotropic in the elastic and plastic deformation, on which various theories have higherto been proposed. Recently, some studies on the relation between the practical deformation behaviour of engineering materials and these theoretical models have been attempted. From this point of view, the authors have carried out their analytical investigations for the purpose of elucidating the deformation behaviour of the polycrystalline metals, and measured the X-ray elastic constants and changes in the integral breadth of carbon steels, copper and alluminium.
There are practically, on the other hand, metallic materials of two phase alloys, such as carbon steels, α+β brasses, Al-Si alloys and titanium alloys. These alloys contain, however, pearlite in the case of carbon steel, the second phase that has different crystal structure, physical or mechanical properties as compared with the matrix phase. Consequently, it seems that the deformation behaviour of each crystal is closely related to the deformation mechanism of metallic materials which is too complicated to be thoroughly understood. For clarifying the strength of materials, it is necessary first to investigate how the second phase will affect the first during the deformation, and then to measure the elastic constants of each phase.
The authors carried out a series of experiments using several kinds of two phase alloys for industrial use in order to clarify the essentials of the above-mentioned mechanism of deformation. In this paper, the results of the following experiments are reported. First the elastic constants of annealed 7-3 brass, 6-4 brass and Al-Si alloys were measured by using various kinds of X-rays, and then they were compared with the analytical results based on the elastic anisotropy of single crystals in connection with the mechanism of elastic deformation.
Five kinds of materials were used in this experiment, that is annealed plate specimens of 7-3 brass, 6-4 brass, 90Al-10Si, 80Al-20Si and 70Al-30Si alloys. The characteristic X-rays were irradiated on the specimen surface through parallel beam slit with divergent angle of 0.25 degree, and the strains were measured by using the diffraction from (100), (110) and (111) atomic planes or equivalent ones. The specimens were stressed stepwise by the tensile testing machine, and at the several stages of applied stress, the X-ray beams were radiated to the center of the specimen surface in vertical and oblique incidence with several angles ψ. The strain was measured by the conventional sin²ψ method using counter technique. The value of the lattice strain ε_ψ was calculated from the measurement of the diffraction angle of intensity distribution curve by using an automatic recorder. From the slope of ε_ψ-sin²ψ diagram for several applied stresses, the ε_ψ/σ-sin²ψ curve was drawn. by using the method of least square. From these slopes the elastic constants were calculated for each diffraction planes.
The summaries of the present study are as follows.
Fig. 5 shows ε_ψ/σ calculated by the unniform local stress model (Reuss's model) and the uniform local strain model (Voigt's and Nagashima's model). According to the uniform local stress model, ε_ψ/σ and sin²ψ are in linear relationship in full range and under no influence of volume fraction on the second phase. According to the uniform local strain model, however, deviation from the linear relationship is considerable in the small range of sin²ψ. This tendency is more conspicuous as the volume fraction of second phase is increased.
On the α-phase of 7-3 and 6-4 brasses, in our experimental results, it means that the mechanism of elastic deformation is very close on