Page 266 - Marine Structural Design

242 Part N Ultimate Strength

0 A

Figure A.5 Uniaxial Stress and Strain Relation Based on Isotropic
Hardening Rule.

the yield criterion becomes,
-
o=ao (A. 16)
the multi-axial stress condition can then be corresponded to the uniaxial stress condition.
When the stress is larger than the yield criterion of the material, the hardening and plastic
deformation occur, and the yield function f =O must be satisfied. However, if f <O .
unloading occurs, the material is in elastic region.
12.5.4 Plastic Strain Increment
When plastic deformation occurs, the shape of yield surface may change following the
hardening rule. Here, the isotropic hardening rule and the kinematic hardening rule are
described in below.
Isotropic Hardening Rule
As shown in Figure A.4, in the hardening process, the size of the yield surface may increase
but no change to the position and shape of the yield surface. Figure AS shows the relationship
between uniaxial stress and strain. After loading along with the curve OYA, and unloading to
----
point B, and then continue in reverse direction to point C, AE%=BC, BC >OY. If the strain
hardening is considered, the yield function in Eq. (A. 13) becomes,
f=J3J,-ao =a-a, (A.17)
-
E
where, EP is the equivalent plastic strain, and may be expressed as,
-P
E =Id.’ (A. 18)
dZp in the above equation may be estimated as below,