PSI - Issue 18

Evgeny Lomakin et al. / Procedia Structural Integrity 18 (2019) 549–555 Evgeny Lomakin and Boris Fedulov / Structural Integrity Procedia 00 (2019) 000–000 5 with the same, as in (1), conditions of symmetry ���� = 0 if index ≠ , and ���� = 0 if ≠ , ≠ и ≠ . Then the expression for the increments of plastic deformation components takes the following form: � � � = ���� ( ) �� �� �� = = �� ���� ( ) 1/3 �� �� − 3/2 �� � � � �� �� + (6) +2 ���� � �� �� − 1 3 �� �� � �� �, where dλ depends on the function of hardening. The incremental change for plastic volume deformations has the following expression: � = 1 3 � � � = � ���� ( ) � �� �� 3 � , (7) It can be seen, that the plastic volume deformations equal to zero only in the case of absence of the dependence of the coefficients on the parameter or if ���� ( ) ≡ . Further, the increment dλ can be determined from the condition ( ���� ( ) �� �� − ) = 0 : ���� ( ) �� �� �� �� − � � � � � � = 0. Eventually the expression for the increment of λ can be written in the following form: = ���� ( ) �� �� �� �� � � � ���� ( ) �� �� �� . (8) The challenging problem of modelling of such materials is that for simple loading experimental methods, which can be obtained with the use of ordinary one-component testing machines: tension, compression, shear and bending, these materials do not show their complex properties. It may seem that anisotropy can be neglected. Compression experiments, as a rule, give slightly larger values in uniaxial experiments due to barrel effect. The impression may be that the usual von Mises plastic surface is sufficient to assess the strength of more complex structural elements. However, in expensive field-tests of structures the unusual failures for the Mises model appear, and usually with a brittle type of damage. This can be explained by the fact, that even for not complex structures, complex stress state types can appear especially in concentrator areas. 3. Experiments and validation As an example, we consider the tests of tubular specimens of AD33 alloy under biaxial combined loading [8]. Fig. 5 shows the chart with values of the von Mises-equivalent stresses at the point of starting plastic deformations and the corresponding values of the triaxiality parameter on the horizontal axis. Here � - is the stress along the tubular line, and � corresponds to circumferential stress. Points 1 - 6 correspond to different ratios of loading stresses. It can be seen that the difference in the values of uniaxial tensile experiments (ξ = 0.333) characterizes the anisotropy of plastic properties. The difference in the values corresponding to experiments 1, 2, on the one hand, and 3,4,5,6 on the other, indicates a significant sensitivity of material to the type of loading. At the same time, the experiment corresponding to point 3 shows the minimum plastic deformations at the load of failure [8]. Considering the criterion of plasticity in the form (2), we can take into account all the described effects of such behavior of the material. Fig. 6 shows the diagrams of the coefficients �� ( ) depending on the parameter of the stress triaxiality. This choice of coefficients performs the yield surface with minimum discrepancy for experimental points. 553