Розрахунок критичного приведеного напруження зсуву для полікристалічного титану

Abstract

Запропоновано модель для розрахунку дійсних величин критичного приведеного напруження зсуву (КПНЗ) для необоротного ковзання в системах ковзання різного типу, які притаманні титановим сплавам. Показано, що різна величина КПНЗ для різних систем ковзання залежить від модуля пружнос-ті і величини вектора Бюргерса.

The onset of plastic deformation, i.e., the onset of irreversible slip of dislocations in different slip systems of certain metal crystals is determined numerically by the critical resolved shear stress (CRSS). However, in the case of polycrystals, it is impossible to determine accurately the CRSS value, since the dislocation motion is retarded by the gain boundary. For this reason, the grain size of a polycrystal affects the CRSS value. Based on this assumption, the paper presents a model for calculating the CRSS in a polycrystalline α-titanium, because titanium alloys belong to such class of materials in which the local plastic deformation due to a monotonic or cyclic loading is initiated on shear planes, most preferably located with respect to the loading direction. In hexagonal close-packed crystal structure (hcp) of α-titanium with lattice parameters a=0.295 nm and c=0.468 nm the following four types of slip systems can be activated: 1) < > in the basal plane (0002) with a slip direction  ; 2) < > in the prismatic plane { } with a slip direction  ; 3) < > in the pyramidal plane { } with a direction   and < > first order pyramidal slip in the same plane with a direction  ; 4) second order pyramidal < > slip in the plane { } with a direction  . The easiest system is the slip system with the Burgers vector in the prismatic plane. To calculate the CRSS using the proposed model, it is necessary to know the modulus of elasticity and the proportionality limit of the material, which are determined from the results of the short-term tensile tests of standard specimens. Besides, from the metallographic analysis, it is required to determine the mean linear size of the structural element (in the case of titanium alloys, this is the size of α-globules for globular and bimodal structures and the thickness of α-lamellae for lamellar structures) and the preferred direction of crystals with respect to the load direction, that is, the Schmid factor and the Burgers vector. The testing of the proposed model using the experimental results taken from the literature for single crystals of commercially pure α-titanium has shown a good coincidence between the calculated and experimental results. An error in determination of the CRSS is -3.3...+0.8%. In the paper it is also shown that for different slip planes in the hcp crystal lattice of α-titanium, the ratio of the CRSS values is determined by the ratio between elasticity moduli and the Burgers vectors for the corresponding planes. Basing on it, the ratios between the CRSS for the prismatic and basal < > slips and first order pyramidal < > slip are found. They are 1:1:2.6, respectively, i.e. they virtually coincide with the experimentally obtained by different authors for various titanium alloys. The proposed computational model can be used as express-evaluation of the characteristics of the static and fatigue strength in the development of new materials, since it enables one to obtain the value for CRSS without time-consuming and long-term experimental investigations.