Neuber method
In: Notch effect
The Neuber method allows a conversion of fictitious wholly elastic stress values obtained from a FEM to “real” elastic-plastic values. This is the basic condition for any computation done through the local elastic-plastic strain analysis, with the only exception is the use of transient analysis.
The basic assumption of the method looks like this:
The fictitious state of the left hand side is purely elastic and allows a use of Hooke’s law. The right hand side respects the real elastic-plastic work diagram, which can be described by the Ramberg-Osgood equation. Thus we get:
,
where the cyclic hardening koefficient K’ and cyclic hardening exponent n’ are introduced. The user should be notified, that the plastic part of strain in PragTic is in all cases described by parameters of Basquin-Manson-Coffin curve, since it can be proved that:
.
Thus the final non-linear equation for determination of elastic-plastic stress state is:
Pospíšil later stated that the equation should be rewritten and equipped with a further parameter m (NEUBER material parameter in PragTic) in order to include all possible types of component shapes and loading:
This is the version implemented in PragTic. The implementation uses a loop of Newton-Raphson iterative method to derive the elastic-plastic stress from the right-hand side part.
The method is usable for uniaxial calculations only, since it relates scalar values. The other restriction is clear from the explanation – the m (NEUBER) parameter is more related to load conditions of the locality examined than to material properties. This clearly decreases potential for any real and fast use on complicated structures.
If the parameter m = 0.5 is used in the original Neuber relation, an equality of area of the triangles bordered by appropriate stress and strain values should be valid – see the picture below. There is also Glinka method depicted.
Nomenclature:
|
Mark |
Unit |
PragTic variable |
Meaning |
|
b |
[-] |
EXP_B |
fatigue strength exponent |
|
c |
[-] |
EXP_C |
fatigue ductility exponent |
|
E |
[MPa] |
E |
elastic modulus |
|
|
[-] |
|
strain |
|
|
[-] |
EPS_F |
fatigue ductility coefficient |
|
K’ |
[MPa] |
K’ |
cyclic hardening coefficient |
|
m |
[-] |
NEUBER |
Pospisil’s exponent in Neuber method |
|
n’ |
[-] |
N’ |
cyclic hardening exponent |
|
|
[MPa] |
|
stress |
|
|
[MPa] |
SIG_F |
fatigue strength coefficient |
|
|
|
|
|
|
|
|
|
fictitious elastic value of x retrieved from a linear FE-computation |
More:
local elastic-plastic strain analysis
© PragTic, 2007
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