US 2009/0211366 A1 · Fatigue life estimating method for spot welded structure

Abstract

A fatigue life estimating method for a spot welded structure is provided comprising the steps of providing a shell model of a spot welded structure for a finite element method analyzing process, calculating the nominal structural stress on a nugget as the center of the spot welded structure using a disk bending theory and a two-dimensional elastic theory of the elastodynamics with the partial loads exerted on the nugget and the deflection on the circumference of a circle, D in diameter, in which the nugget is located, which have been calculated by the finite element method analyzing process of the shell model, and estimating the fatigue life of the spot welded structure from the nominal structure stress. According to the method, the fatigue life of the spot welded structure can be estimated easily, readily, and accurately.

A fatigue life estimating method for a spot welded structure comprising the steps of:

preparing a spot welded structure consisting of two or more plates joined together;
providing a shell model from the spot welded structure for a finite element method analyzing process;
subjecting the shell model to the finite element method analyzing process to calculate the peel load, the bending moment, the shear force, and the torsional moment as partial forces exerted on a nugget at the center of the spot welded structure as well as the deflection on the circumference of a circle which is D in the diameter and defined to have the nugget at the center;
calculating the nominal structural stress responsive to the peel load, the bending moment, the shear force, and the torsional moment using a disk bending theory and a two-dimensional elastic theory of the elastodynamics with the calculations of the partial loads and the deflection,
where components σr, σθ, and τrθ of the nominal structural stress responsive to the shear force and the torsional moment are calculated using a two-dimensional elastodynamics formula
σ
r
=
a
0

r
-
2
+
2

b
0
+
(
a
1
r
+
2

b
1

r
-
2

a
1
′

r
-
3
+
b
1
′

r
-
1
)

cos


θ
+
(
c
1
r
+
2

d
1

r
-
2

c
1
′

r
-
3
+
d
1
′

r
-
1
)

sin


θ
+
∑
n
=
2
∞

{
a
n

n

(
1
-
n
)

r
n
-
2
+
b
n

(
n
+
2
-
n
2
)

r
n
-
a
n
′

n

(
1
+
n
)

r
-
n
-
2
+
b
n
′

(
-
n
+
2
-
n
2
)

r
-
n
}

cos


n


θ
+
∑
n
=
2
∞

{
c
n

n

(
1
-
n
)

r
n
-
2
+
d
n

(
n
+
2
-
n
2
)

r
n
-
c
n
′

n

(
1
+
n
)

r
-
n
-
2
+
d
n
′

(
-
n
+
2
-
n
2
)

r
-
n
}

sin


n


θ
σ
θ
=
-
α
0

r
-
2
+
2

b
0
+
(
6

b
1

r
+
2

a
1
′

r
-
3
+
b
1

′

r
-
1
)

cos


θ
+
(
6

d
1

r
+
2

c
1

′

r
-
3
+
d
1
′

r
-
1
)

sin


θ
+
∑
n
=
2
∞

{
a
n

n

(
n
-
1
)

r
n
-
2
+
b
n

(
n
+
2
)

(
n
+
1
)

r
n
+
a
n
′

n

(
n
+
1
)

r
-
n
-
2
+
b
n
′

(
-
n
+
2
)

(
-
n
+
1
)

r
-
n
}

cos


n


θ
+
∑
n
=
2
∞

{
c
n

n

(
n
-
1
)

r
n
-
2
+
d
n

(
n
+
2
)

(
n
+
1
)

r
n
+
c
n
′

n

(
n
+
1
)

r
-
n
-
2
+
d
n
′

(
-
n
+
2
)

(
-
n
+
1
)

r
-
n
}

sin


n


θ
τ
r


θ
=
(
2

b
1

r
-
2

a
1
′

r
-
3
+
b
1
′

r
-
1
)

sin


θ
-
(
2

d
1

r
-
2

c
1
′

r
-
3
+
d
1
′

r
-
1

)

cos


θ
+
∑
n
=
2
∞

{
a
n

n

(
n
-
1
)

r
n
-
2
+
b
n

n

(
n
+
1
)

r
n
-
a
n
′

n

(
n
+
1
)

r
-
n
-
2
-
b
n
′

n

(
n
-
1
)

r
-
n
}

sin


n


θ
-
∑
n
=
2
∞

{
c
n

n

(
n
-
1
)

r
n
-
2
+
d
n

n

(
n
+
1
)

r
n
-
c
n
′

n

(
n
+
1
)

r
-
n
-
2
-
d
n
′

n

(
n
-
1
)

r
-
n
}

cos


n


θ
(where a0 to d′n are unknown coefficients determined by the loading condition and the boundary condition) and components σr, σθ, and τrθ of the nominal structural stress responsive to the bending moment and the peel load are calculated from
σ
r
=
-
D
p

6
t
2

[
M
r


0
+
∑
n
=
1
∞

M
rfn

cos


n


θ
+
∑
n
=
1
∞

M
rgn

sin


n


θ
]
σ
θ
=
-
D
p

6
t
2

[
M
θ


0
+
∑
n
=
1
∞

M
θ


fn

cos


n


θ
+
∑
n
=
1
∞

M
θ


gn

sin


n


θ
]
τ
r


θ
=
(
1
-
v
)

D
p

6
t
2

[
∑
n
=
1
∞

M
r


θ


fn

sin


n


θ
+
∑
n
=
1
∞

M
r


θ


gn


cos


n


θ
]
where
M
r


0
=

2

f
0

r
2
+
v
r


f
0

r
M
r


n
=

2

f
n

r
2
+
v
r

(

f
n

r
-
f
n
r

n
2
)
(
i
≧
1
)
M
rgn
=

2

g
n

r
2
+
v
r

(

g
n

r
-
g
n
r

n
2
)
(
i
≧
1
)
M
θ


0
=
v


2

f
0

r
2
+
1
r


f
0

r
M
θ


n
=
v


2

f
n

r
2
+
1
r

(

f
n

r
-
f
n
r

n
2
)
(
i
≧
1
)
M
θ


gn
=
v


2

g
n

r
2
+
1
r

(

g
n

r
-
g
n
r

n
2
)
(
i
≧
1
)
M
r


θ


fn
=
-
n
r

(

f
n

r
-
f
n
r
)
(
i
≧
1
)
M
rgn
=
n
r

(

g
n

r
-
g
n
r
)
(
i
≧
1
)
f
0
=
A
o
+
B
0

r
2
+
C
0

ln


r
+
D
0

r
2

ln


r
f
1
=
A
1

r
+
B
1

r
3
+
C
1

r
-
1
+
D
1

r


ln


r
f
n
=
A
n

r
n
+
B
n

r
-
n
+
C
n

r
n
+
2
+
D
n

r
-
n
+
2
g
1
=
A
1
′

r
+
B
1
′

r
3
+
C
1
′

r
-
1
+
D
1
′

r


ln


r
g
n
=
A
n
′

r
n
+
B
n
′

r
-
n
+
C
n
′

r
n
+
2
+
D
n
′

r
-
n
+
2
(where r and θ are the polar coordinates, E is the Young's modulus, v is the Poisson's ratio, t is the thickness, and A0 to D′n are unknown coefficients determined by the loading condition and the boundary condition);
and estimating the fatigue life of the spot welded structure from the nominal structure stress.

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Fatigue life estimating method for spot welded structure

Life of this patent

Fatigue life estimating method for spot welded structure

Life of this patent

Abstract

Claims4