PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 348–353 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

349

2

complex stress had been listed in the review Lokoshchenko (2012). These two approaches are used depending on the type of complex stress taking into account the main stresses 1 2 3      . The kinetic approach is used for describing the creep rupture at two axis tension at 0 1 2     and 0 3   of the elementary plane element (tests Himeno et al. (2016) on internal pressure and tension of the tubular specimen or biaxial tension Kobayashi et al. (2017) of the plane specimen) and three axis tension at 0 1 2 3       of the elementary volume element (tests Kobayashi et al. (2017) on three axis tension of the cubic specimen). The scheme of the testing machine, which allows testing plane specimens under biaxial tension, is given Kobayashi et al. (2017). The essence of the kinetic approach is that damages only can accumulates on the sites perpendicular to the main tensile stresses, where the damage rates are proportional to the corresponding main stresses

d

 

1 

 

3

2

(1)

f ( ), d

f ( ), d

f ( ) 







1

2

3

dt

dt

dt

The absolute value of the damage vector

2

2

2

(2)

3 1        2

is considered as the characteristic of the damaged state with two time conditions

0

1

(3)

, 







0

t

 t t



rupt

Nomenclature 

damage creep time rupture time tensile stress

t

rupt t





tangential stress 1 2 3 , ,    principle stresses max  mises  Mises stress max  equivalent stress eq 

maximum normal stress

maximum tangential stress

2 eq 2 eq ,   complex equivalent stresses  total error

The kinetic approach is not suitable for describing the creep rupture under tension and compression at 0 1   , 0 2   and 0 3   of the elementary plane element in two mutually perpendicular directions (tests on torsion and tension Dyson et al. (1977) and Cane (1981) and Nazarov (2014a) and Kowalewski (1996) and Stanzl (1983) for the tubular specimen). At principle stresses 0 1   , 0 2   and 0 3   a criterial approach is used. This approach considers ( ) eq rupt  t g  . As a rule, the scalar characteristic of the stress tensor is considered as the equivalent stress, which, under conditions of uniaxial tension, takes the value of the nominal stress (the exception of the equivalent stress Nazarov (2014b)). The basic equivalent stresses are considered normal stress max  , Mises stress mises  and doubled maximum tangential stress max 2  . In addition to these three simple equivalent stresses, complex equivalent stresses are considered.