Collapse strength prediction method
A collapse strength prediction method of a steel pipe includes deriving a prediction equation indicating a relationship among D/t obtained by dividing an outer diameter D (mm) by a thickness t (mm), material characteristics, a collapse strength dominant factor, and a collapse dominant proof stress (σ CDOS ) of the steel pipe using a plurality of reference steel pipes collapse whose strengths have been obtained in advance, obtaining D/t, material characteristics, a collapse strength dominant factor, and a predicted collapse strength of a steel pipe that is an evaluation subject, obtaining a compressive stress-strain curve in a circumferential direction of the steel pipe that is the evaluation subject, obtaining a stress that causes a permanent strain to be generated in the steel pipe that is the evaluation subject as the collapse dominant proof stress on the basis of the compressive stress-strain curve, and computing the predicted collapse strength of the steel pipe that is the evaluation subject from the D/t, the material characteristics, the collapse strength dominant factor, and the collapse dominant proof stress, which have been obtained, on the basis of the prediction equation, and the permanent strain is set according to a value of the D/t of the steel pipe that is the evaluation subject.
1. A collapse strength prediction method for predicting a collapse strength of a steel pipe, the method comprising:
deriving a prediction equation indicating a relationship among D/t obtained by dividing an outer diameter D (mm) by a thickness t (mm), material characteristics, a collapse strength dominant factor, a collapse dominant proof stress, and a predicted collapse strength of the steel pipe using a plurality of reference steel pipes collapse whose strengths have been obtained in advance;
obtaining D/t obtained by dividing an outer diameter D (mm) by a thickness t (mm), material characteristics, and a collapse strength dominant factor of a steel pipe that is an evaluation subject;
obtaining a compressive stress-strain curve in a circumferential direction of the steel pipe that is the evaluation subject;
obtaining a stress that causes a permanent strain to be generated in the steel pipe that is the evaluation subject as the collapse dominant proof stress on the basis of the compressive stress-strain curve; and
computing the predicted collapse strength of the steel pipe that is the evaluation subject from the D/t, the material characteristics, the collapse strength dominant factor, and the collapse dominant proof stress, which have been obtained, on the basis of the prediction equation,
wherein the permanent strain is set according to a value of the D/t of the steel pipe that is the evaluation subject.
2. The collapse strength prediction method according to claim 1 ,
wherein the collapse dominant proof stress is a 0.50% proof stress in a case in which the value of D/t of the steel pipe that is the evaluation subject is in a yield collapse region, is a 0.10% proof stress in a case in which the value of D/t is in a plastic collapse region, and is 0.05% proof stress in a case in which the value of D/t is in a transition collapse region or an elastic collapse region.
3. The collapse strength prediction method according to claim 1 ,
wherein the collapse dominant proof stress is a 0.50% proof stress in a case in which the value of D/t of the steel pipe that is the evaluation subject is 10, is a 0.10% proof stress in a case in which the value of D/t is 19, is a 0.05% proof stress in a case in which the value of D/t is 28 to 48, is obtained by interpolation calculation of the 0.50% proof stress and the 0.10% proof stress in a case in which the value of D/t is more than 10 and less than 19, and is obtained by interpolation calculation of the 0.10% proof stress and the 0.05% proof stress in a case in which the value of D/t is more than 19 and less than 28.
4. The collapse strength prediction method according to claim 1 ,
wherein the permanent strain is represented by Equation 1 or Equation 2,
in the case of D/t≤28:
CDOS (%)=exp(5.522)×( D/t ) −2.719+0.02 (Equation 1), and
in the case of D/t>28:
CDOS (%)=0.05 (Equation 2).
5. The collapse strength prediction method according to claim 1 ,
wherein the material characteristics include a Young's modulus and a Poisson's ratio of the steel pipe that is the evaluation subject; and
the collapse strength dominant factor includes one or more selected from an ovality, an eccentricity, and a residual stress in the circumferential direction of the steel pipe.
6. The collapse strength prediction method according to claim 2 ,
wherein the material characteristics include a Young's modulus and a Poisson's ratio of the steel pipe that is the evaluation subject; and
the collapse strength dominant factor includes one or more selected from an ovality, an eccentricity, and a residual stress in the circumferential direction of the steel pipe.
7. The collapse strength prediction method according to claim 3 ,
wherein the material characteristics include a Young's modulus and a Poisson's ratio of the steel pipe that is the evaluation subject; and
the collapse strength dominant factor includes one or more selected from an ovality, an eccentricity, and a residual stress in the circumferential direction of the steel pipe.
8. The collapse strength prediction method according to claim 4 ,
wherein the material characteristics include a Young's modulus and a Poisson's ratio of the steel pipe that is the evaluation subject; and
the collapse strength dominant factor includes one or more selected from an ovality, an eccentricity, and a residual stress in the circumferential direction of the steel pipe.
9. The collapse strength prediction method according to claim 5 ,
wherein the prediction equation is represented by Equation 3,
P c =γ(0.5( P E +P Y )−√{square root over (0.25( P E −P Y ) 2 +P E P Y H ))} (Equation 3)
where, P c in Equation 3 is the predicted collapse strength, P E and P Y are an elastic collapse strength and an entire surface yield strength respectively, and H and γ are correction terms and are computed using Equation 4 to Equation 15, provided that in Equation 4 to Equation 15, E is the Young's modulus, v is the Poisson's ratio, u is the ovality represented by Equation 11, e is the eccentricity represented by Equation 12, σ R0 is the residual stress in the circumferential direction, σ CDOS is the collapse dominant proof stress, and values represented by h α , h β , h γ , α,β, ζ, and η are coefficients that are obtained in advance,
P
E
=
2
(
E
1
-
v
2
)
(
1
D
/
t
(
D
/
t
-
1
)
2
)
F
E
(
D
/
t
)
G
E
(
σ
CDOS
)
(
Equation
4
)
P
Y
=
2
σ
CDOS
D
/
t
-
1
(
D
/
t
)
2
[
1
+
1.47
D
/
t
-
1
]
F
Y
(
D
/
t
)
G
Y
(
σ
CDOS
)
(
Equation
5
)
H
=
h
α
u
(
%
)
+
h
β
e
(
%
)
+
h
γ
(
σ
R
θ
σ
CDOS
)
(
Equation
6
)
F
E
(
D
/
t
)
=
∑
i
=
1
5
α
i
E
(
D
/
t
)
i
-
3
(
Equation
7
)
F
Y
(
D
/
t
)
=
∑
i
=
1
5
α
i
Y
(
D
/
t
)
i
-
3
(
Equation
8
)
G
E
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
E
(
σ
CDOS
)
i
-
3
(
Equation
9
)
G
Y
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
Y
(
σ
CDOS
)
i
-
3
(
Equation
10
)
ovality
u
(
%
)
=
(
maximum
outer
diameter
-
minimum
outer
diameter
)
/
average
outer
diameter
×
100
(
Equation
11
)
e
ccentricity
e
(
%
)
=
(
maximum
thickness
-
minimum
thickness
)
/
average
thickness
×
100
(
Equation
12
)
γ
=
F
(
u
,
D
/
t
)
-
f
(
u
)
g
(
D
/
t
)
(
Equation
13
)
f
(
u
)
=
∑
i
=
1
3
ξ
i
(
u
)
i
-
1
(
Equation
14
)
g
(
D
/
t
)
=
∑
i
=
1
3
η
i
(
D
/
t
)
i
-
1
(
Equation
15
)
10. The collapse strength prediction method according to claim 6 ,
wherein the prediction equation is represented by Equation 3,
P c =γ(0.5( P E +P Y )−√{square root over (0.25( P E −P Y ) 2 +P E P Y H ))} (Equation 3)
where, P c in Equation 3 is the predicted collapse strength, P E and P Y are an elastic collapse strength and an entire surface yield strength respectively, and H and γ are correction terms and are computed using Equation 4 to Equation 15, provided that in Equation 4 to Equation 15, E is the Young's modulus, v is the Poisson's ratio, u is the ovality represented by Equation 11, e is the eccentricity represented by Equation 12, σ R0 is the residual stress in the circumferential direction, σ CDOS is the collapse dominant proof stress, and values represented by h α , h β , h γ , α,β, ζ, and η are coefficients that are obtained in advance,
P
E
=
2
(
E
1
-
v
2
)
(
1
D
/
t
(
D
/
t
-
1
)
2
)
F
E
(
D
/
t
)
G
E
(
σ
CDOS
)
(
Equation
4
)
P
Y
=
2
σ
CDOS
D
/
t
-
1
(
D
/
t
)
2
[
1
+
1.47
D
/
t
-
1
]
F
Y
(
D
/
t
)
G
Y
(
σ
CDOS
)
(
Equation
5
)
H
=
h
α
u
(
%
)
+
h
β
e
(
%
)
+
h
γ
(
σ
R
θ
σ
CDOS
)
(
Equation
6
)
F
E
(
D
/
t
)
=
∑
i
=
1
5
α
i
E
(
D
/
t
)
i
-
3
(
Equation
7
)
F
Y
(
D
/
t
)
=
∑
i
=
1
5
α
i
Y
(
D
/
t
)
i
-
3
(
Equation
8
)
G
E
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
E
(
σ
CDOS
)
i
-
3
(
Equation
9
)
G
Y
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
Y
(
σ
CDOS
)
i
-
3
(
Equation
10
)
ovality
u
(
%
)
=
(
maximum
outer
diameter
-
minimum
outer
diameter
)
/
average
outer
diameter
×
100
(
Equation
11
)
eccentricity
e
(
%
)
=
(
maximum
thickness
-
minimum
thickness
)
/
average
thickness
×
100
(
Equation
12
)
γ
=
F
(
u
,
D
/
t
)
-
f
(
u
)
g
(
D
/
t
)
(
Equation
13
)
f
(
u
)
=
∑
i
=
1
3
ξ
i
(
u
)
i
-
1
(
Equation
14
)
g
(
D
/
t
)
=
∑
i
=
1
3
η
i
(
D
/
t
)
i
-
1
(
Equation
15
)
11. The collapse strength prediction method according to claim 7 ,
wherein the prediction equation is represented by Equation 3,
P c =γ(0.5( P E +P Y )−√{square root over (0.25( P E −P Y ) 2 +P E P Y H ))} (Equation 3)
where, P c in Equation 3 is the predicted collapse strength, P E and P Y are an elastic collapse strength and an entire surface yield strength respectively, and H and γ are correction terms and are computed using Equation 4 to Equation 15, provided that in Equation 4 to Equation 15, E is the Young's modulus, v is the Poisson's ratio, u is the ovality represented by Equation 11, e is the eccentricity represented by Equation 12, σ R0 is the residual stress in the circumferential direction, σ CDOS is the collapse dominant proof stress, and values represented by h α , h β , h γ , α,β, ζ, and η are coefficients that are obtained in advance,
P
E
=
2
(
E
1
-
v
2
)
(
1
D
/
t
(
D
/
t
-
1
)
2
)
F
E
(
D
/
t
)
G
E
(
σ
CDOS
)
(
Equation
4
)
P
Y
=
2
σ
CDOS
D
/
t
-
1
(
D
/
t
)
2
[
1
+
1.47
D
/
t
-
1
]
F
Y
(
D
/
t
)
G
Y
(
σ
CDOS
)
(
Equation
5
)
H
=
h
α
u
(
%
)
+
h
β
e
(
%
)
+
h
γ
(
σ
R
θ
σ
CDOS
)
(
Equation
6
)
F
E
(
D
/
t
)
=
∑
i
=
1
5
α
i
E
(
D
/
t
)
i
-
3
(
Equation
7
)
F
Y
(
D
/
t
)
=
∑
i
=
1
5
α
i
Y
(
D
/
t
)
i
-
3
(
Equation
8
)
G
E
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
E
(
σ
CDOS
)
i
-
3
(
Equation
9
)
G
Y
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
Y
(
σ
CDOS
)
i
-
3
(
Equation
10
)
ovality
u
(
%
)
=
(
maximum
outer
diameter
-
minimum
outer
diameter
)
/
average
outer
diameter
×
100
(
Equation
11
)
eccentricity
e
(
%
)
=
(
maximum
thickness
-
minimum
thickness
)
/
average
thickness
×
100
(
Equation
12
)
γ
=
F
(
u
,
D
/
t
)
-
f
(
u
)
g
(
D
/
t
)
(
Equation
13
)
f
(
u
)
=
∑
i
=
1
3
ξ
i
(
u
)
i
-
1
(
Equation
14
)
g
(
D
/
t
)
=
∑
i
=
1
3
η
i
(
D
/
t
)
i
-
1
(
Equation
15
)
12. The collapse strength prediction method according to claim 8 ,
wherein the prediction equation is represented by Equation 3,
P c =γ(0.5( P E +P Y )−√{square root over (0.25( P E −P Y ) 2 +P E P Y H ))} (Equation 3)
where, P c in Equation 3 is the predicted collapse strength, P E and P Y are an elastic collapse strength and an entire surface yield strength respectively, and H and γ are correction terms and are computed using Equation 4 to Equation 15, provided that in Equation 4 to Equation 15, E is the Young's modulus, v is the Poisson's ratio, u is the ovality represented by Equation 11, e is the eccentricity represented by Equation 12, σ R0 is the residual stress in the circumferential direction, σ CDOS is the collapse dominant proof stress, and values represented by h α , h β , h γ , α,β, ζ, and η are coefficients that are obtained in advance,
P
E
=
2
(
E
1
-
v
2
)
(
1
D
/
t
(
D
/
t
-
1
)
2
)
F
E
(
D
/
t
)
G
E
(
σ
CDOS
)
(
Equation
4
)
P
Y
=
2
σ
CDOS
D
/
t
-
1
(
D
/
t
)
2
[
1
+
1.47
D
/
t
-
1
]
F
Y
(
D
/
t
)
G
Y
(
σ
CDOS
)
(
Equation
5
)
H
=
h
α
u
(
%
)
+
h
β
e
(
%
)
+
h
γ
(
σ
R
θ
σ
CDOS
)
(
Equation
6
)
F
E
(
D
/
t
)
=
∑
i
=
1
5
α
i
E
(
D
/
t
)
i
-
3
(
Equation
7
)
F
Y
(
D
/
t
)
=
∑
i
=
1
5
α
i
Y
(
D
/
t
)
i
-
3
(
Equation
8
)
G
E
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
E
(
σ
CDOS
)
i
-
3
(
Equation
9
)
G
Y
(
σ
CDOS
)
=
∑
i
=
1
5
β
i
Y
(
σ
CDOS
)
i
-
3
(
Equation
10
)
ovality
u
(
%
)
=
(
maximum
outer
diameter
-
minimum
outer
diameter
)
/
average
outer
diameter
×
100
(
Equation
11
)
eccentricity
e
(
%
)
=
(
maximum
thickness
-
minimum
thickness
)
/
average
thickness
×
100
(
Equation
12
)
γ
=
F
(
u
,
D
/
t
)
-
f
(
u
)
g
(
D
/
t
)
(
Equation
13
)
f
(
u
)
=
∑
i
=
1
3
ξ
i
(
u
)
i
-
1
(
Equation
14
)
g
(
D
/
t
)
=
∑
i
=
1
3
η
i
(
D
/
t
)
i
-
1
(
Equation
15
)
13. The collapse strength prediction method according to claim 9 ,
wherein Equation 7 is represented by
F E ( D/t )=9.39×10 −1 +3.37×10 −2 ×( D/t )−3.70×10 −4 ×( D/t ) 2 (Equation 16),
Equation 8 may be represented by
F Y ( D/t )=1.17−1.35×10 −2 ( D/t )−3.49×10 −5 ×( D/t ) 2 (Equation 17),
Equation 9 may be represented by
G E (σ CDOS )=9.54(σ CDOS ) −2 −1.85×10×(σ CDOS ) −1 +6.41×10 −1 +4.57×10 −5 ×(σ CDOS ) (Equation 18),
Equation 10 may be represented by
G Y (σ CDOS )=1 (Equation 19),
Equation 14 may be represented by
f ( u )=9.39×10 −1 +1.11×10 −2 ×( u )+2.15×10 −2 ×( u ) 2 (Equation 20), and
Equation 15 may be represented by
g ( D/t )=1.08+7.06×10 −8 ×( D/t )+7.85×10 −7 ×( D/t ) 2 (Equation 21).
14. The collapse strength prediction method according to claim 10 ,
wherein Equation 7 is represented by
F E ( D/t )=9.39×10 −1 +3.37×10 −2 ×( D/t )−3.70×10 −4 ×( D/t ) 2 (Equation 16),
Equation 8 may be represented by
F Y ( D/t )=1.17−1.35×10 −2 ( D/t )−3.49×10 −5 ×( D/t ) 2 (Equation 17),
Equation 9 may be represented by
G E (σ CDOS )=9.54(σ CDOS ) −2 −1.85×10×(σ CDOS ) −1 +6.41×10 −1 +4.57×10 −5 ×(σ CDOS ) (Equation 18),
Equation 10 may be represented by
G Y (σ CDOS )=1 (Equation 19),
Equation 14 may be represented by
f ( u )=9.39×10 −1 +1.11×10 −2 ×( u )+2.15×10 −2 ×( u ) 2 (Equation 20), and
Equation 15 may be represented by
g ( D/t )=1.08+7.06×10 −8 ×( D/t )+7.85×10 −7 ×( D/t ) 2 (Equation 21).
15. The collapse strength prediction method according to claim 11 ,
wherein Equation 7 is represented by
F E ( D/t )=9.39×10 −1 +3.37×10 −2 ×( D/t )−3.70×10 −4 ×( D/t ) 2 (Equation 16),
Equation 8 may be represented by
F Y ( D/t )=1.17−1.35×10 −2 ( D/t )−3.49×10 −5 ×( D/t ) 2 (Equation 17),
Equation 9 may be represented by
G E (σ CDOS )=9.54(σ CDOS ) −2 −1.85×10×(σ CDOS ) −1 +6.41×10 −1 +4.57×10 −5 ×(σ CDOS ) (Equation 18),
Equation 10 may be represented by
G Y (σ CDOS )=1 (Equation 19),
Equation 14 may be represented by
f ( u )=9.39×10 −1 +1.11×10 −2 ×( u )+2.15×10 −2 ×( u ) 2 (Equation 20), and
Equation 15 may be represented by
g ( D/t )=1.08+7.06×10 −8 ×( D/t )+7.85×10 −7 ×( D/t ) 2 (Equation 21).
16. The collapse strength prediction method according to claim 12 ,
wherein Equation 7 is represented by
F E ( D/t )=9.39×10 −1 +3.37×10 −2 ×( D/t )−3.70×10 −4 ×( D/t ) 2 (Equation 16),
Equation 8 may be represented by
F Y ( D/t )=1.17−1.35×10 −2 ( D/t )−3.49×10 −5 ×( D/t ) 2 (Equation 17),
Equation 9 may be represented by
G E (σ CDOS )=9.54(σ CDOS ) −2 −1.85×10×(σ CDOS ) −1 +6.41×10 −1 +4.57×10 −5 ×(σ CDOS ) (Equation 18),
Equation 10 may be represented by
G Y (σ CDOS )=1 (Equation 19),
Equation 14 may be represented by
f ( u )=9.39×10 −1 +1.11×10 −2 ×( u )+2.15×10 −2 ×( u ) 2 (Equation 20), and
Equation 15 may be represented by
g ( D/t )=1.08+7.06×10 −8 ×( D/t )+7.85×10 −7 ×( D/t ) 2 (Equation 21).