Norio Hosokawa

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

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 eψ was calculated from the measurement of the diffraction angle of intensity distribution curve by using an automatic recorder. From the slope of eψ-sin2ψ diagram for several applied stresses, the eψ/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 eψ/σ calculated by the unniform local stress model (Reusss model) and the uniform local strain model (Voigts and Nagashimas model). According to the uniform local stress model, eψ/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

On the X-Ray Stress Analysis of Metals by the Oscillating Crystal Method

The principle of stress measurement by X-rays is based on the Hooks law which consists in the relation between the peak shift of the X-ray diffraction line and the magnitude of the stress, applied or internal. It has been noted as a unique method of nondestructive stress measurement of local stress. The X-ray stress measurement is applied in very wide fields of material engineering studies.The stress measured by X-rays, however, depends on the local value of the lattice strain observed in the certain diffracted crystal plane satisfying the Braggs condition. In this connection, there are some problems regarding the character of X-ray stress measurement, for example, the generation of the lattice strain obtained from the peak shift of certain diffraction line is closely related to the crystal grain size, the deformation mechanism, the crystal anisotropy and other complicated factors. As mentioned above, the X-ray stress measurement of coarse grained materials is inadequate sometimes for the ordinary way as offered by Glocker and Macherauch etc. In other words, the stress measurement of coarse grained specimens is essential from the standpoint of the practical application of the X-ray method.For these reasons, the authors attempted to measure the lattice strain and analyse the stress with coarse grained crystal of aluminum, using the oscillating crystal method, and discussed the errors in the measured value. In this paper, the practical significance of the oscillating crystal method is made clear, and besides, it is concluded that the method is more useful than the divergent X-ray method for the stress measurement with coarse grained materials in the engineering sense. Moreover, when the micro-beam technique is introduced to this method, it is possible to measure the extremely localized stress such as tip of crack or one grain in industrial material.The results are as follows.(1) This camera can be applied to any size of grain under suitable geometrical conditions.(2) To correct systematic errors, it is necessary to use the standard specimens which have two or more diffraction lines on a film.(3) The errors of lattice strain were less than 6×10-5 for undeformed Aluminum.(4) The principal residual stress of a coarse grain in the specimen of 7% deformed Aluminum is σ1=2.5kg/mm2, σ2=0.1kg/mm2 and σ3=-1.7kg/mm2, and their directions agree respectively with that of the tensile axis, of the thickness and of the width.