annex 3.d strength parameters.pdf

8/10/2019 Annex 3.D Strength Parameters.pdf

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2010 SECTION VIII, DIVISION 2

3-100

ANNEX 3.D

STRENGTH PARAMETERS

(NORMATIVE)

3.D.1 Yield Strength

Values for the yield strength as a function of temperature are provided in Table Y-1 in the ASME B&PV Code,Section II, Part D.

3.D.2 Ultimate Tensile Strength

Values for the ultimate tensile strength as a function of temperature are provided in Table U in the ASMEB&PV Code, Section II, Part D.

3.D.3 Stress Strain Curve

The following model for the stress-strain curve shall be used in design calculations where required by thisDivision when the strain hardening characteristics of the stress-strain curve are to be considered. The yieldstrength and ultimate tensile strength in paragraphs 3.D.1 and 3.D.2 may be used in this model to determinea stress-strain curve at a specified temperature.

1 2t

t

yE

(3.D.1)

where

11 1.0 tanh2

H

(3.D.2)

22 1.0 tanh2

H

(3.D.3)

1

1

1

1

mt

A

(3.D.4)

1

1

1

ln 1

ys ys

m

ys

A

(3.D.5)

1

ln

ln 1ln

ln 1

p ys

p

ys

Rm

(3.D.6)

opyright ASME International

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Not for Resale, 08/14/2010 03:31:13 MDTo reproduction or networking permitted without license from IHS

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3-101

2

1

2

2

mt

A

(3.D.7)

2

2

2

2

exputs

m

mA

m

(3.D.8)

2t ys uts ys

uts ys

KH

K

(3.D.9)

ys

uts

R

(3.D.10)

0.002ys (3.D.11)

1.5 2.5 3.51.5 0.5K R R R (3.D.12)

The parameters 2m , and p are provided in Table 3.D.1.The development of the stress strain curve should

be limited to a value of true ultimate tensile stress at true ultimate tensile strain. The stress strain curvebeyond this point should be perfectly plastic. The value of true ultimate tensile stress at true ultimate tensilestrain is calculated as follows:

, 2exputs t uts m (3.D.13)

3.D.4 Cyclic Stress Strain Curve

The cyclic stress-strain curve of a material (i.e. strain amplitude versus stress amplitude) may be representedby the Equation (3.D.14). The material constants for this model are provided in Table 3.D.2.

1

cssna a

ta

y cssE K

(3.D.14)

The hysteresis loop stress-strain curve of a material (i.e. strain range versus stress range) obtained by scalingthe cyclic stress-strain curve by a factor of two is represented by the Equation (3.D.15). The materialconstants provided in Table 3.D.2 are also used in this equation.

1

22

cssnr r

tr

y cssE K

(3.D.15)

3.D.5 Tangent Modulus

3.D.5.1 Tangent Modulus Based on the Stress-Strain Curve Model

The tangent modulus based on the stress-strain curve model in paragraph 3.D.3 is given by the followingequation.




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3-102

11

1 2 3 4

1t tt

t t y

E D D D DE

(3.D.16)

where

1

1

11

1 1

1 12

m

t

m

D

m A

(3.D.17)

1 1

1

1 11

2

2 11

1

1 1 2 11 tanh tanh

2

m m

t t

uts ysm

D H HmK

A

(3.D.18)

2

2

11

3 1

2 22

m

t

m

D

m A

(3.D.19)

2 2

2

1 11

2

4 12

2

1 1 2 11 tanh tanh

2

m m

t t

uts ysm

D H HmK

A

(3.D.20)

The parameter Kis given by Equation (3.D.12)

3.D.5.2 Tangent Modulus Based on External Pressure Charts

An acceptable alternative for calculating the Tangent Modulus is to use the External Pressure charts inSection II, Part D, Subpart 3, including the notes to Subpart 3. The appropriate chart for the material underconsideration is assigned in the column designated External Pressure Chart Number given in Tables 1A or

1B. The tangent modulus,tE , is equal to 2B A , where A is the strain given on the abscissa and B is the

stress value on the ordinate of the chart.




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3.D.6 Nomenclature

A Section II, Part D, Subpart 3 external pressure chart A-value.1A curve fitting constant for the elastic region of the stress-strain curve.

2A curve fitting constant for the plastic region of the stress-strain curve.

B Section II, Part D, Subpart 3 external pressure chart B-value.

1D coefficient used in the tangent modulus.




p stress-strain curve fitting parameter.

t total true strain

ta total true strain amplitude.

tr total true strain range.

ys 0.2% engineering offset strain.

1 true plastic strain in the micro-strain region of the stress-strain curve.

2 true plastic strain in the macro-strain region of the stress-strain curve.

tE tangent modulus of elasticity evaluated at the temperature of interest.

yE modulus of elasticity evaluated at the temperature of interest, see Annex 3.E.

1 true strain in the micro-strain region of the stress-strain curve.

2 true strain in the macro-strain region of the stress-strain curve.

H stress-strain curve fitting parameter.K material parameter for stress-strain curve model

cssK material parameter for the cyclic stress-strain curve model.

1m curve fitting exponent for the stress-strain curve equal to the true strain at the proportional

limit and the strain hardening coefficient in the large strain region.

2m curve fitting exponent for the stress-strain curve equal to the true strain at the true ultimate

stress.

cssn material parameter for the cyclic stress-strain curve model.

a total stress amplitude.

r total stress range.

t true stress at which the true strain will be evaluated, may be a membrane, membrane plus

bending, or membrane, membrane plus bending plus peak stress depending on theapplication.

ys engineering yield stress evaluated at the temperature of interest, see paragraph 3.D.1.

uts engineering ultimate tensile stress evaluated at the temperature of interest, see paragraph

3.D.2.

,uts t true ultimate tensile stress evaluated at the true ultimate tensile strain

R engineering yield to engineering tensile ratio.




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3.D.7 Tables

Table 3.D.1 Stress-Strain Curve Parameters

Material Temperature Limi t 2m p

Ferritic Steel 480C (900F) 0.60 1.00 R 2.0E-5

Stainless Steel andNickel Base Alloys

480C (900F) 0.75 1.00 R 2.0E-5

Duplex Stainless Steel 480C (900F) 0.70 0.95 R 2.0E-5

PrecipitationHardenable Nickel

Base

540C (1000F) 1.90 0.93 R 2.0E-5

Aluminum 120C (250F) 0.52 0.98 R 5.0E-6

Copper 65C (150F) 0.50 1.00 R 5.0E-6

Titanium andZirconium

260C (500F) 0.50 0.98 R 2.0E-5




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3-105

Table 3.D.2 Cyclic Stress-Strain Curve Data

Material Description Temperature (F) cssn cssK (ksi)

Carbon Steel (0.75 in. base metal)

70 0.128 109.8

390 0.134 105.6

570 0.093 107.5

750 0.109 96.6

Carbon Steel (0.75 in. weld metal)

70 0.110 100.8

390 0.118 99.6

570 0.066 100.8

750 0.067 79.6

Carbon Steel (2 in. base metal)

70 0.126 100.5

390 0.113 92.2

570 0.082 107.5

750 0.101 93.3

Carbon Steel (4 in. base metal)

70 0.137 111.0

390 0.156 115.7

570 0.100 108.5

750 0.112 96.9

1Cr1/2Mo (0.75 in. base metal)

70 0.116 95.7

390 0.126 95.1

570 0.094 90.4

750 0.087 90.8

1Cr1/2Mo (0.75 in. weld metal)

70 0.088 96.9

390 0.114 102.7

570 0.085 99.1

750 0.076 86.9

1Cr1/2Mo (0.75 in. base metal)

70 0.105 92.5

390 0.133 99.2

570 0.086 88.0

750 0.079 83.7

1Cr1Mo1/4V

70 0.128 156.9

750 0.128 132.3

930 0.143 118.2

1020 0.133 100.5

1110 0.153 80.6

2-1/4Cr1/2Mo

70 0.100 115.5

570 0.109 107.5

750 0.096 105.9

930 0.105 94.6

1110 0.082 62.1




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Table 3.D.2 Cyclic Stress-Strain Curve Data

Material Description Temperature (F) cssn cssK (ksi)

9Cr1Mo

70 0.177 141.4

930 0.132 100.5

1020 0.142 88.3

1110 0.121 64.3

1200 0.125 49.7

Type 304

70 0.171 178.0

750 0.095 85.6

930 0.085 79.8

1110 0.090 65.3

1290 0.094 44.4

Type 304 (Annealed) 70 0.334 330.0

800H

70 0.070 91.5

930 0.085 110.5

1110 0.088 105.7

1290 0.092 80.2

1470 0.080 45.7

Aluminum (Al4.5Zn0.6Mn) 70 0.058 65.7

Aluminum (Al4.5Zn1.5Mg) 70 0.047 74.1

Aluminum (1100-T6) 70 0.144 22.3

Aluminum (2014-T6) 70 0.132 139.7

Aluminum (5086) 70 0.139 96.0

Aluminum (6009-T4) 70 0.124 83.7Aluminum (6009-T6) 70 0.128 91.8

Copper 70 0.263 99.1




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Table 3.D.2M Cycl ic Stress-Strain Curve Data

Material Descript ion Temperature (C) cssn cssK (MPa)

Carbon Steel (20 mm base metal)

20 0.128 757

200 0.134 728

300 0.093 741

400 0.109 666

Carbon Steel (20 mm weld metal)

20 0.110 695

200 0.118 687

300 0.066 695

400 0.067 549


20 0.126 693

200 0.113 636

300 0.082 741

400 0.101 643


20 0.137 765

200 0.156 798

300 0.100 748

400 0.112 668

1Cr1/2Mo (20 mm base metal)

20 0.116 660

200 0.126 656

300 0.094 623

400 0.087 626

1Cr1/2Mo (20 mm weld metal)

20 0.088 668

200 0.114 708

300 0.085 683

400 0.076 599

1Cr1/2Mo (50 mm base metal)

20 0.105 638

200 0.133 684

300 0.086 607

400 0.079 577

1Cr1Mo1/4V

20 0.128 1082

400 0.128 912

500 0.143 815

550 0.133 693

600 0.153 556

2-1/4Cr1/2Mo

20 0.100 796

300 0.109 741

400 0.096 730

500 0.105 652

600 0.082 428

9Cr1Mo

20 0.117 975

500 0.132 693

550 0.142 609

600 0.121 443




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Table 3.D.2M Cycl ic Stress-Strain Curve Data

Material Descript ion Temperature (C) cssn cssK (MPa)

650 0.125 343

Type 304

20 0.171 1227

400 0.095 590

500 0.085 550

600 0.090 450

700 0.094 306

Type 304 (Annealed) 20 0.334 2275

800H

20 0.070 631

500 0.085 762

600 0.088 729

700 0.092 553800 0.080 315

Aluminum (Al4.5Zn0.6Mn) 20 0.058 453

Aluminum (Al4.5Zn1.5Mg) 20 0.047 511

Aluminum (1100-T6) 20 0.144 154

Aluminum (2014-T6) 20 0.132 963

Aluminum (5086) 20 0.139 662

Aluminum (6009-T4) 20 0.124 577

Aluminum (6009-T6) 20 0.128 633

Copper 20 0.263 683




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annex 3.d strength parameters.pdf

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