Qualification Testing Phase of Satellite Structure - Finite Element Analysis for Satellite Structures - page 264

Fig. 6.10 Low fatigue FE

model [ 4 ]

boundary condi-
tions

Table 6.3 Mechanical properties of alloys AMg6 and titanium

q (kg/m 3 ) Material r u (MPa) r y E

72 9 10 3 AMg6 2,630 310 156

110 9 10 3

Titanium 4,430 923 903

component (which describes the translation of the yield surface in stress space)
and, for the nonlinear isotropic/kinematic hardening model, of an isotropic com-
ponent (which describes the change of the elastic range). The nonlinear isotropic/
kinematic hardening model provides more accurate predictions. Ratcheting and
relaxation of the mean stress are accounted for only by the nonlinear isotropic/
kinematic model. The kinematic hardening component is defined to be an additive
combination of a purely kinematic term (linear Ziegler hardening law) and a
relaxation term (the recall term), which introduces the nonlinearity. When tem-
perature and field variable dependencies are omitted, the hardening law is

e pl cae pl

1
r j o

a ¼ C r r y ð 6 : 2 Þ

where a is the translation of the yield surface in stress space through the back-
stress, e pl is the equivalent plastic strain rate, C is the initial kinematic hardening
modulus, and c determines the rate at which the kinematic hardening modulus
decreases with increasing plastic deformation. In this model the equivalent stress
defines the size of the yield surface, r j o defining the size of the yield surface at
zero plastic strain. C and c are material parameters that must be calibrated from
cyclic test data [ 5 ]. [C = 11,800 MPa, c = 103].
The isotropic hardening behavior of the model defines the evolution of the yield
surface size, r j o ; as a function of the equivalent plastic strain, e pl ; using the simple
exponential law