PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 334–340 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

337

4

with two material parameters, where the starting creep stress and the break creep stress can either be measured experimentally or calculated. Nazarov (2019) had been calculated creep ultimate stresses for various metallic materials. 3. Complex stress As a rule, the creep characteristics are measured either on thin-walled tubular specimens Himeno et al. (2016) and Nazarov (2014) or on plane specimens Kobayashi et al. (2017) and Sakane et al. (2019). These specimens can be tested under plane stress, where an elementary planar element can either be biaxially tension at the principal stresses 0 0 and 3 1 2       (biaxial tension of rectangular plates or loading of tubular specimens by internal pressure), or simultaneously tension and compressed at the principal stresses 0 0, 0 and 3 2 1       (loading of tubular specimens by torque and tensile axial force) in two perpendicular directions. In addition, there are unique mechanical tests Kobayashi et al. (2017) and Sakane et al. (2019) in which cubic specimens have been subjected to triaxial tension at the principal stresses 0 1 2 3       . Two different approaches (kinetic and criteria) are used for describing the creep and creep rupture processes. In the kinetic approach, various variants of the damage accumulation equations had been considered Lokoshchenko et al. (2005) and Lokoshchenko et al. (2009), where the damage value of the material is used as the main structural parameter. Different representations of the damage value are used, which can be a scalar, a vector, or a tensor. In the criterion approach, various invariant characteristics of the stress tensor are considered. These invariant characteristics of the stress tensor are called equivalent stresses. The maximum normal stress max  , the Mises stress mises  , the doubled maximum tangential stress max 2  , and their linear combinations with the parameter are considered as equivalent stress e  . All equivalent stresses e  are equal to the nominal tensile stress nom  at uniaxial tension, which means nom max mises max eq 2          . For describing the creep rupture under equal triaxial tension, one can either use kinetic equations with a vector representation of the damage value, or use a complex equivalent stress with two material parameters in the form Kobayashi et al. (2017) and Sakane et al. (2019). The vector value ( ) t   of damage had been considered Lokoshchenko et al. (2005) and Lokoshchenko et al. (2009), the absolute value ( ) t  of which takes the form where in thin walled tubular specimens the radial stress 0    , 1  and 2  are projections of the damage vector ( ) t   on the directions of the principal stresses, f is given function. The rupture time rupt t is determined from the integration of expressions (5), taking into account the initial condition (0) 0   at the initial time of force action and the final condition ( ) 1 rupt  t  at the rupture time. From the analysis of the total errors in the form of the difference between the experimental and approximating values of the rupture time it have been shown that taking into account the phenomenon of strength anisotropy allows us to better describe the creep rupture process under biaxial tension. The value equal to the ratio of the axial stress z  and the tangential stress   was considered as the strength anisotropy coefficient ( ) / ( ) rupt rupt t t z      , where each of the stresses z  and   individually lead to fracture along principal axe (in cylindrical coordinate axes z or  ) in the same time rupt t . Lokoshchenko et al. (2009) had been presented the model for describing the creep rupture process on the type of short term loading program, where this model takes into account the accumulation of damage both in the short term loading process and in the creep. The equivalent stress is used to describe the secondary creep and the creep rupture under complex stress. Two models for describing the secondary creep have been considered by Nazarov (2015) 0  r  , the axial stress 0  z  and the tangential stress ( , ( )) 2 2 t   / ( , ( )) 1 1 t   ( ) / f dt t d t   ( ) ( ) t ( ) t 2  1 2  1  f dt  d    (5)