Unified fatigue life evaluation method for welded structures
View Patent ↗Due to geometric discontinuities introduced by welding and joining processes, stresses or strain cannot be calculated reliably calculated using modern analytical and computer methods as result of stress or strain singularity at joint locations, which leads to severe mesh sensitivity. Design and fatigue evaluation of these structures remain empirical. This disclosure addresses mesh insensitivity of stress/strain calculations for welded structures through a cut-plane traction stress method through a novel post processing of conventional finite element computation results, as well as provides a unified fatigue evaluation procedure for fatigue design and structural life evaluation for both low-cycle and high cycle fatigue regime subjected to either proportional or non-proportional multiaxial fatigue loading, as well as a simple and reliable method for treating spot welds.
1. A method for calculating structural strain for a structure under load, comprising:
generating a finite element model for a given structure;
calculating a distribution of structural stress within the given structure using the finite element model and while the given structure is under a given load, where the distribution of stress is determined in relation to a plane intersecting the given structure;
calculating a distribution of structural strain experienced within the given structure while the given structure is under the given load, where the distribution of structural strain is calculated in part from the calculated distribution of structural stress and the distribution of structural strain is defined in relation to the plane by two closed-form expressions which account for stress that exceeds yield strength of material comprising the structure; and
calculating a fatigue life for the given structure using a structural strain range, wherein the structural strain range is defined in terms of
Δ
E
s
=
Δ
ε
NP
t
2
-
m
2
m
I
(
r
′
)
1
m
where Δε 0 represents uniaxial fatigue loading induced structural strain range for which Δε NP =ΔΣ AB (1+α ϵ ·g NP ) where Δε AB =Δε 0 and g NP =0, leading to Δε NP =Δε 0 , t is material thickness, m is an exponent derived crack growth data, r′ is a bending ratio, and I(r′) is a dimensionless polynomial function of the bending ratio r′.
2. The method of claim 1 wherein the given structure is defined as a plate and, when strain exceeds yield strain of non-hardening material at one surface of the plate, the distribution of strain is defined at the plate surfaces by
ε
o
=
S
Y
E
+
k
(
t
-
2
c
)
ε
i
=
S
Y
E
-
2
kc
where ε 0 is a top surface value, ε i is a bottom surface value, S Y is yield strength of the material, E is Young's modulus of the material, c is elastic core and k is the slope of the inclined deformation line across plate thickness t.
3. The method of claim 1 wherein the given structure is defined as a plate and, when strain exceeds yield strain of material on two surfaces of the plate, the distribution of strain is defined at the plate surfaces by
ε
o
=
k
(
e
+
t
2
)
ε
i
=
k
(
e
-
t
2
)
where ε 0 is a top surface value, ε i is a bottom surface value, t is thickness of the plate, E is Young's modulus of the material and k is the slope of the deformation line across plate thickness.
4. The method of claim 1 wherein the given structure is defined as a pipe and, when strain exceeds yield strength of non-hardening material in one side of the plane, the distribution of strain is defined
ε
o
=
[
k
(
R
-
y
Y
)
+
S
Y
]
/
E
ε
i
=
[
k
(
R
-
y
Y
)
+
S
Y
]
/
E
where ε 0 is an exterior surface value, ε i is an interior surface value, R is an outer radii of the pipe, r is an inner radii of the pipe, E is Young's modulus of the material, k is slope of the inclined deformation line with the elastic core, y Y is distance for plastic deformation boundary to neutral axis and S Y is yield strength of material.
5. The method of claim 1 wherein the given structure is defined as a pipe and, when strain exceeds yield strength of material on two sides of the plane, the distribution of strain is defined
ε
0
=
S
Y
(
R
-
e
)
cE
ε
i
=
-
S
Y
(
R
+
e
)
cE
where ε 0 is an exterior surface value, ε i is an interior surface value, R is an outer radii of the pipe, E is Young's modulus of the material, c is distance for plastic deformation boundary to neutral axis and S Y is yield strength of material.
6. The method of claim 5 wherein the distribution of structural strain is determined numerically.