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The strains of a curvilinear surface are determined using holographic interferometry. Equations are derived to interpret the interference fringes for a shell of revolution.

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A new experimental method for analysis of the mechanical properties of crystal materials is proposed. The method combines the advantages of holographic interferometry and the contact method of fixing a recording medium. The proposed approach is shown to be effective in determining the surface displacements and strains.Introduction. The behavior of loaded polycrystalline bodies is modelled numerically in [1][2][3]. Since numerical modeling of the anisotropy of the physicochemical properties of crystals and the conditions at their boundaries involves some difficulties, it is necessary to develop experimental methods of analysis of displacement fields, in particular, optical methods. The results of application of the speckle-photography method to investigation of the displacement fields on a surface of plane polycrystalline specimens are known [4,5]. The pointwise scanning method used in these studies to interpret specklograms is labor-consuming and does not allow one to obtain the fields of isolines of constant phase difference on the surface of a specimen. In contrast to the speckle-photographic method, the superimposed holographic interferometry makes it possible to visualize the displacement fields with higher spatial resolution and sensitivity [6].1. Preparation of Specimens. Specimens of working length 100 mm and cross section 16.2 • 1.5 mm were milled from commercial aluminum. Then, they were extended on a TsDM-5/91 testing machine, since it has been found experimentally that upon annealing and recrystallization the maximum grain size in a specimen is obtained for a 3% initial strain of the specimen. The elongation of the specimens was measured by a V-630 cathetometer. Annealing was performed for three hours at 630~ in a quartz tube inserted into the working zone of an SUOL muffle furnace. The specimens were cooled for 14 h in the furnace switched off. The specimens were pickled in a strong solution of sodium hydroxide NaOH for 40-60 min. Pickling was terminated if a white film separated independently from the surface of the specimens when they were taken out from a dish.To determine the grain boundaries on the surface, the specimens were photographed before the experiment for various directions of their illumination (the optical axis of the camera was perpendicular to the specimen surface). Then, the metallized crossed rasters with the line frequency ~bz = ~by --~b = 840 mm -1 were deposited on the specimen surface. The arrangement of the grains on one of the specimen surfaces is shown in Fig. 1. 2. Strains in Metal Grains under Static Loading. Physical Modeling. The experimental technique is outlined in [6]. Holographic interferograms were recorded at each of 11 stages of specimen loading by a tensile force P. The specimen elongation A1 was monitored by a clock-type indicator whose division was 0.01 mm. The hologram numbers n, the loads P applied to a specimen, and its elongations Al are listed in Table 1.