PSI - Issue 32

A.Yu. Iziumova et al. / Procedia Structural Integrity 32 (2021) 93–100 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

97

5

Fedorov V.V. (1979) experimentally proved that the specific stored energy for various steels and modes of their heat treatment at various fixed stress amplitude is comparable to the enthalpy of iron melting. The specific stored energy is calculated for a unit volume of destroyed metal (the volume of metal with broken long-range order bonds). However, it is not indicated how exactly this volume was determined; therefore, it was not possible to construct a similar analogy between the specific stored energy and the enthalpy of titanium melting for the titanium alloy Ti 0.8Al-0.8Mn under study in this work. Nevertheless, the steady growth of the stored energy up to a certain critical value, which is approximately the same for different values of loading, suggests that such an analogy, possibly, also exists for the titanium alloy Ti-0.8Al-0.8Mn under study. 4. Modeling A combined hardening model (isotropic hardening and Chaboche’s kinematic hardening model) described by Jirasek and Bazant (2001) was used for the numerical calculation of the plastic work. Equilibrium equation: 0,    (4) where σ is the stress tensor. Hook’s law :

0 0 3 , e K   

(5)

2 , e

d S G  

(6)

e ε is the volumetric elastic strain tensor; S is the deviatoric stress, e d ε is

where 0 σ is the volumetric stress tensor, 0

the deviatoric elastic strain, K is the bulk modulus, G is the shear modulus. Geometric relation:   1 , 2 T u u    

(7)

ε is the total strain tensor, u is the displacement vector. Additive decomposition of total strain tensor: , e p     

(8)

e ε is the elastic strain tensor, p ε is the plastic strain tensor. Associated flow rule:



,

0,

k



p

k





(9)





k is the plastic multiplier,  is the yield function. Yield criterion: