PSI - Issue 18

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Evgeny Lomakin et al. / Procedia Structural Integrity 18 (2019) 549–555 Evgeny Lomakin and Boris Fedulov / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 3. Diagrams of tension and compression for a sample of extruded rod (D16T alloy).

2. Constitutive equations Thus, the main problem to develop the mathematical model for such materials consists in that it is necessary to take into account the sensitivity of plastic material properties to the direction of the loading or their anisotropy and the sensitivity to the type of loading. In [4, 5], the elastic potential was proposed with the required characteristics. Its usage, but in the form of plastic potential and the associated plastic flow rule, is a logical extension of isotropic criteria described in [6], but allows us to take into account anisotropy of material properties. In general, the plasticity criterion for an anisotropic material can be formulated as follows [5]: ���� ( ) �� �� = � , (1) where � , �� , � = � 2 �� �� , �� = �� − �� , �� = 0 ( ), �� = ( ) . Coefficients ���� ( are the components of fourth rank tensor and have to satisfy the symmetry conditions [4, 5]: ���� = ���� = ���� = ���� = ���� = ���� = ���� . The main difficulty of practical dealing with this criterion of plasticity is a large number of unknown dependencies ���� ( or functions, in general case there are 13 of them. To determine all of these dependencies, an almost impractical experimental program has to be realized. To give the proposed set of coefficients a more understandable physical meaning, we can turn to Hill’s work [7] and simplify the general form of the criterion: ( )( �� − �� ) � + ( )( �� − �� ) � + ( )( �� − �� ) � + 2( ( ) �� � + ( ) � � � + ( ) � � � ) = � (2) In this case, the dependencies can be described with the use of special coefficients �� , which have understandable simple meaning: