PSI - Issue 12
Massimiliano Avalle et al. / Procedia Structural Integrity 12 (2018) 130–144 Massimiliano Avalle/ Structural Integrity Procedia 00 (2018) 000 – 000
136
7
100 120
100 120
σ_ r σ_ c σ_ z
σ_ r σ_ c σ_ z
20 40 60 80
20 40 60 80
Stress component (MPa)
-20 0
Stress component (MPa)
-20 0
6
7
8
9
6
7
8
9
Radius (mm)
Radius (mm)
Fig. 5. Comparison of the results in the numerical simulation of the elastic-perfectly plastic materials obtained with ANSYS (left) and the Nadai analytical model (right).
In this work, a simpler solution is proposed considering the solution of the rigid-perfectly plastic material plus a solution for a rigid-linearly hardening material. The stress state for the rigid-perfectly plastic material comes from the solution of the equation of equilibrium considering the hoop stress equal to the value of the yield strength when the axisymmetric solid is fully yielded:
e d d
i r ri d d p
i p d
1
r
i
i
d d
(3)
i
e
i p d
S
y d p S d i
1
c
i e
i
y
d d
i
e
The second contribution is related to the rigid-linearly hardening material, for which the stress distribution can be considered as:
2 2
2
2 d d d d e e
i d p d
i
r
2
i
(4)
2 2
2
2 d d d d e e
i d p d
i
c
2
i
1 d d d d d E 2 2 e e i y
2
i
2 d d d d 2 e e
2
2 1
2 E u u d d p d i i i i
p u
i
2
2
2 1
y
i
2
i
It is then possible to relate the internal pressure due to a given interference d ogive − d i as follows:
d E i y
1 1
d S d i e y
1 1
1
1
2 e d d d d d 2 i
p S
E i
1
r
y
y
2
2
2 1
2 1
i
i
(5)
2
2
e
i
r S t i y
2 r E i i y
d E i y
t
1
2 d
1
i t r t r 1 1 2 2
S
y
2
t d t d
1 1
2 1
1 2 1 2
1 1
2 1
i
i
i
2
i
i
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