CONTENTS
ANNEX 2E – MATERIAL PROPERTIES FOR STRESS ANALYSIS ...2E-1 2E.1 GENERAL ... 2E-1 2E.1.1 Material Properties Required ... 2E-1 2E.1.2 Material Properties and In-Service Degradation ... 2E-1 2E.2 STRENGTH PARAMETERS ... 2E-2 2E.2.1 Yield and Tensile Strength... 2E-2 2E.2.2 Flow Stress ... 2E-3 2E.3 MONOTONIC STRESS-STRAIN RELATIONSHIPS ... 2E-4 2E.3.1 MPC Stress-Strain Curve Model ... 2E-4 2E.3.2 MPC Tangent Modulus Model ... 2E-5 2E.3.3 Ramberg-Osgood Model ... 2E-5 2E.3.4 Ramberg-Osgood Tangent Modulus Model... 2E-6 2E.4 CYCLIC STRESS-STRAIN RELATIONSHIPS ... 2E-6 2E.4.1 Ramberg-Osgood ... 2E-6 2E.4.2 Uniform Material Law... 2E-7 2E.5 PHYSICAL PROPERTIES ... 2E-7 2E.5.1 Elastic Modulus ... 2E-7 2E.5.2 Poisson’s Ratio ... 2E-7 2E.5.3 Coefficient of Thermal Expansion ... 2E-7 2E.5.4 Thermal Conductivity ... 2E-7 2E.5.5 Thermal Diffusivity ... 2E-7 2E.5.6 Density ... 2E-7 2E.6 NOMENCLATURE ... 2E-7 2E.7 REFERENCES ... 2E-9 2E.7.1 Strength Parameters ... 2E-9 2E.7.2 Cyclic Stress-Strain Relationships ... 2E-10 2E.7.3 Physical Properties ... 2E-10 2E.8 TABLES ... 2E-11 2E.1 General
2E.1.1 Material Properties Required
The information in this Annex is intended to provide guidance on the materials information required for the Fitness-For-Service (FFS) assessments covered in this Standard. Specific materials data are provided for strength parameters, monotonic stress-strain curve relationships, cyclic stress-strain curve relationships, and physical properties; however, some of the materials data are provided in terms of references to published sources. To include, and keep up to date, all of the property information required by all of the assessment methods in this Standard would be prohibitive. This is especially true of properties that are affected by the service environment.
2E.1.2 Material Properties and In-Service Degradation
The FFS assessment procedures in this Standard cover situations involving flaws commonly encountered in pressure vessels, piping and tankage that have been exposed to service for long periods of time. Therefore,
of equipment that has been in-service; the properties used in the assessment should reflect any change or degradation, including aging, resulting from the service environment or past operation.
2E.2 Strength Parameters 2E.2.1 Yield and Tensile Strength
2E.2.1.1 Estimates for the material yield strength and tensile strength to be used in an FFS assessment may be obtained as follows:
a) It may be necessary to obtain samples from a component and use a standard test procedure to directly determine the yield and tensile strength when accurate estimates of these properties can affect the results of an assessment. The yield strength and ultimate tensile strength for plate and pipe material can be determined in accordance with ASTM A370, ASTM E8, or an equivalent standard method, and reported on a mill test report for the particular heat of steel.
b) Hardness tests can be used to estimate the tensile strength(see Table 2E.1). The conversions found in this table may be used for carbon and alloy steels in the annealed, normalized, and quench-and- tempered conditions. The conversions are not applicable for cold worked materials, austenitic stainless steels, or for non-ferrous materials.
c) If the temperature for which a FFS assessment is to be made differs substantially from the temperature for which the yield and tensile strengths were determined, these values should be modified by a suitable temperature correction factor. The temperature correction factor may be derived from the Materials Properties Council (MPC) material data for the yield strength and ultimate strength given in paragraphs 2E.2.1.2 and 2E.2.1.3, respectively.
d) In the absence of heat specific data, mean values for the tensile and yield strength can be approximated using the following equations:
mean min 69
uts uts MPa
s = s + (2E.1)
10
mean min
uts uts ksi
s = s + (2E.2)
and,
mean min 69
ys ys MPa
s = s + (2E.3)
10
mean min
ys ys ksi
s = s + (2E.4)
2E.2.1.2 Analytical expressions for the minimum specified yield strength as a function of temperature and the applicable temperature range are provided in Table 2E.2. The minimum specified yield strength at a temperature is determined by multiplying the value at room temperature by a temperature reduction factor in these tables. The room temperature value of the minimum specified yield strength can be found in the applicable design code. The analytical expressions for the minimum specified yield strength for a limited number of materials are listed in terms of a material pointer, PYS, which can be determined for a specific material of construction using Table 2E.3.
2E.2.1.3 Analytical expressions for the minimum specified ultimate tensile strength as a function of temperature and the applicable temperature range are provided in Table 2E.4. The minimum specified ultimate tensile strength at a temperature is determined by multiplying the value at room temperature by a
temperature reduction factor in these tables. The room temperature value of the minimum specified ultimate tensile strength can be found in the applicable design code. The analytical expressions for the minimum specified ultimate tensile strength for a limited number of materials are listed in terms of a material pointer, PUS, which can be determined for a specific material of construction using Table 2E.5.
2E.2.1.4 A method to compute the yield and tensile strength as a function of temperature for pipe and tube materials is provided in Table 2E.6. The data used to develop these equations are from API Std 530, 6th Edition, September 2008. The yield and tensile properties of API Std 530 have been updated to reflect modern steel making practices for alloys currently produced and used for petroleum refinery heater applications (see Annex 10.B, paragraph 10B.2.3). The yield and tensile values from WRC Bulletin 541 are provided in Table 2E.7.
2E.2.1.5 Values for the yield and tensile strength below the creep regime for pressure vessel, piping, and tankage steels can be found in the ASME Code, Section II, Part D. Other sources for yield and tensile strength data for various materials are provided in paragraph 2E.7.1. These data sources provide values for the yield and tensile strength that are representative of those for new materials.
2E.2.2 Flow Stress
2E.2.2.1 The flow stress, sf, can be thought of as the effective yield strength of a work hardened material.
The use of a flow stress concept permits the real material to be treated as if it were an elastic-plastic material that can be characterized by a single strength parameter. The flow stress can be used, for example, as the stress level in the material that controls the resistance of a cracked structure to failure by plastic collapse.
2E.2.2.2 Several relationships for estimating the flow stress have been proposed which are summarized below. The flow stress to be used in an assessment will be covered in the appropriate Part of this Standard.
In the absence of a material test report for plate and pipe, and for weld metal, the specified minimum yield strength and the specified minimum tensile strength for the material can be used to calculate the flow stress.
a) Average of the yield and tensile strengths (recommended for most assessments):
( )
2
ys uts
f
s s
s = + (2E.5)
b) The yield strength plus 69 MPa (10 ksi):
69 MPa
f ys
s = s + (2E.6)
10 ksi
f ys
s = s + (2E.7)
c) For austenitic stainless steels, a factor times the average of the yield and tensile strengths:
( )
1.15 2
ys uts f
s s
s = ⋅ + (2E.8)
d) For ferritic steels and austenitic stainless steels, the maximum allowable stress (S) in accordance with the ASME Code, Section VIII, Division 2, multiplied by an appropriate factor:
f 2.4 S for ferritic steels
s = ⋅ (2E.9)
3 S for austenitic stainless steels s = ⋅
e) If Ramberg-Osgood parameters are available (see paragraph 2E.3.3), the flow stress can be computed using the following equation.
0.002 [ ]
2 1
exp
nRO ys RO
f
RO
n n s s
= +
(2E.11)
2E.3 Monotonic Stress-Strain Relationships 2E.3.1 MPC Stress-Strain Curve Model
The following model for the stress-strain curve may be used in FFS calculations where required by this Standard when the strain hardening characteristics of the stress-strain curve are to be considered.
1 2
t t
Ey
ε = s + + γ γ (2E.12)
where,
( [ ] )
1 1 1.0 tanh
2 H
γ = ε − (2E.13)
( [ ] )
2 2 1.0 tanh
2 H
γ = ε + (2E.14)
1 1
1 1 t m
A ε = s
(2E.15)
( )
( ) 1
1
1 ln 1
ys ys
m ys
A s ε
ε
= +
+
(2E.16)
[ ] ( )
1
ln ln ln 1
ln 1
p ys
p ys
m R ε ε
ε ε
+ −
= +
+
(2E.17)
2 1
2 2 t m
A ε = s
(2E.18)
[ ]
2 2 2
2 utsexp
m
A m
m
= s (2E.19)
( )
( )
( )
2 t ys uts ys
uts ys
H K
K
s s s s
s s
− + ⋅ −
= − (2E.20)
ys uts
R s
= s (2E.21)
0.002
εys = (2E.22)
1.5 2.5 3.5
1.5 0.5
K = R − R − R (2E.23)
The parameters m2, and εp are provided in Table 2E.8 and st is determined using Equation (2E.30).
2E.3.2 MPC Tangent Modulus Model
The tangent modulus based on the MPC stress-strain curve model in paragraph 2E.3.1 is given by Equation (2E.24).
1 1
1 2 3 4
t t 1
t
t t y
E D D D D
E
s ε
ε s
− −
∂ ∂
= ∂ = ∂ = + + + + (2E.24)
where,
1
1 1 1
1 1
1 1
2
m t
m
D
m A s
−
=
⋅
(2E.25)
( ) ( [ ] ) [ ]
1 1
1
1 1 1
2 1 2
1 1
1 1 2 1 tanh 1 tanh
2
m m
t t
uts ys
m
D H H
K m A
s s
s s
−
= − ⋅ ⋅ − ⋅ − + ⋅ ⋅
(2E.26)
2
2 1 1
3 1
2 2
2
t m
m
D
m A s
−
=
⋅
(2E.27)
( ) ( [ ] ) [ ]
2 2
2
1 1 1
4 1 2
2 2
1 1 2 1 tanh 1 tanh
2
m m
t t
uts ys
m
D H H
K m A
s s
s s
−
= ⋅ ⋅ − ⋅ − + ⋅ ⋅
(2E.28)
2E.3.3 Ramberg-Osgood Model
The stress-strain curve of a material can be represented by Equation (2E.29) known as the Ramberg-Osgood equation. The exponent used in this equation may be required for a J-integral calculation.
1 nRO
t t
t
y RO
E H
s s
ε = +
(2E.29)
where,
( 1 )
t es es
s = + ε s (2E.30)
( )
t ln 1 es
ε = + ε (2E.31)
If multiple data points for a stress-strain curve are provided, the data fitting constants can be derived using regression techniques. If only the yield and ultimate tensile strength are known, the exponent, nRO, can be computed using Equation (2E.32) (for the range 0.02 ≤ s sys uts ≤ 1.0). The constant HRO is computed using Equation (2E.33).
2 3
2
1 1.3495 5.3117 2.9643
1.1249 11.0097 11.7464
ys ys ys
uts uts uts
RO
ys ys
uts uts
n
s s s
s s s
s s
s s
+ − +
=
+ −
(2E.32)
[ ]
exp
RO
uts RO
RO n
RO
H n
n
= s (2E.33)
2E.3.4 Ramberg-Osgood Tangent Modulus Model
The tangent modulus based on the Ramberg-Osgood stress-strain curve model in paragraph 2E.3.3 is given by Equation (2E.34).
1 1
1 1
1 1 nRO 1
t t t
t
t t y RO RO RO
E E n H H
s ε s
ε s
− − −
∂ ∂
= ∂ = ∂ = + ⋅
(2E.34)
2E.4 Cyclic Stress-Strain Relationships 2E.4.1 Ramberg-Osgood
The cyclic stress-strain curve of a material (i.e. strain amplitude versus stress amplitude) may be represented by the Equation (2E.35). The material constants for this model are provided in Table 2E.9.
1 ncss
a usm a
ta
y css
C
E K
s s
ε = + ⋅
(2E.35)
The hysteresis loop stress-strain curve of a material (i.e. strain range versus stress range) obtained by scaling the cyclic stress-strain curve by a factor of two is represented by the Equation (2E.36). The material constants provided in Table 2E.9 are also used in this equation.
1
2 2
ncss
usm r
tr r
y css
C
E K
s ε = s + ⋅
(2E.36)
2E.4.2 Uniform Material Law
Baumel and Seeger developed a Uniform Material Law for estimating cyclic stress-strain curve and strain life properties for plain carbon and low to medium alloy steels, and for aluminum and titanium alloys. The method is shown in Table 2E.10. The Uniform Material Law provides generally satisfactory agreement with measured material properties, and may on occasion provide an exceptional correlation. It is the general method recommended for estimating cyclic stress-strain curves and strain life properties when actual data for a specific material are not provided in the form of a correlation or actual data points.
2E.5 Physical Properties 2E.5.1 Elastic Modulus
The elastic or Young’s modulus is required to perform stress analysis of a statically indeterminate component.
Values for the elastic modulus for a full range in temperatures can be found in WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D. Additional reference sources for the elastic modulus of various materials are provided in paragraph 2E.7.3.
2E.5.2 Poisson’s Ratio
The value of Poisson’s ratio in the elastic range, ν, can normally be taken as 0.3 for steels. Data for specific steels can be found in WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D.
2E.5.3 Coefficient of Thermal Expansion
The coefficient of thermal expansion is required to perform a thermal stress analysis of a component. Values for the thermal expansion coefficient for a full range in temperatures can be found in the WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D. Additional reference sources for the thermal expansion coefficient of various materials are provided in paragraph 2E.7.3.
2E.5.4 Thermal Conductivity
The thermal conductivity is required to perform a heat transfer analysis of a component. The results from this analysis are utilized in a thermal stress calculation. Values for the thermal conductivity for a full range in temperatures can be found in WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D.
2E.5.5 Thermal Diffusivity
The thermal diffusivity is required to perform a transient thermal heat transfer analysis of a component. The results from this analysis are utilized in a transient thermal stress calculation. Values for the thermal diffusivity for a full range in temperatures can be found in WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D.
2E.5.6 Density
The material density is required to perform a transient thermal heat transfer analysis, and in cases where body force components are to be considered in a stress analysis of a component. The results from this analysis are utilized in a transient thermal stress calculation. Values for the density for a full range in temperatures can be found in WRC Bulletin 503 or the ASME B&PV Code, Section II, Part D.
2E.6 Nomenclature
a parameter used in the Uniform Material Law.
A → A curve-fit coefficients for the yield strength data from API Std 530.
b fatigue strength exponent (Basquin’s exponent).
0 5
B → B curve-fit coefficients for the tensile strength data from API Std 530.
c fatigue strength exponent (Coffin-Manson exponent) in the Uniform Material Law.
Cusm conversion factor coefficient, 1.0 for units of ksi, (1.0/6.894) for units of MPa.
0 5
C → C material coefficients for the yield strength or ultimate tensile strength data, as applicable.
1 4
D → D material coefficients used in the tangent modulus calculation.
Et tangent Modulus.
Ey Young’s Modulus at the temperature of interest.
εes engineering strain.
εp 0.2% engineering offset strain for the proportional limit, other values may be used.
εt true strain or total true strain.
εta total true strain amplitude.
εtr total true strain range.
εys 0.2% engineering offset strain.
ε1 true plastic strain in the micro-strain region of the stress-strain curve.
ε2 true plastic strain in the macro-strain region of the stress-strain curve.
*
εf fatigue ductility coefficient.
γ1 true strain in the micro-strain region of the stress-strain curve.
γ2 true strain in the macro-strain region of the stress-strain curve.
H Prager doctor factor.
HRO constant in Ramberg-Osgood Stress Strain Model.
K elastic crack driving force parameter,stress intensity factor, or a parameter in the MPC stress- strain curve model, as applicable.
Kcss material parameter for the cyclic stress-strain curve model.
m1 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.
m2 curve fitting exponent for the stress-strain curve equal to the true strain at the true ultimate stress.
ncss material parameter for the cyclic stress-strain curve model.
nRO material parameter for Ramberg-Osgood stress-strain curve model.
Nf number of cycles to failure in accordance with the Uniform Material Law.
R the ratio of the engineering yield stress to engineering tensile stress evaluated at the assessment temperature, as applicable.
S allowable stress.
sa total stress amplitude.
sr total stress range.
st true stress.
sf flow stress.
sr applied stress range.
sys yield stress at the temperature of interest.
suts engineering ultimate tensile stress evaluated at the temperature of interest.
utsrt
s minimum specified ultimate tensile strength at room temperature.
rtys
s minimum specified yield strength at room temperature.
Tmin
sys ultimate tensile strength at Tmin.
Tmin
suts yield strength at Tmin.
utsmean
s mean value of the ultimate tensile strength.
utsmin
s minimum specified ultimate tensile strength from the original construction code.
ysmean
s mean value of the yield strength.
min
sys minimum specified yield strength.
*f
s fatigue strength coefficient.
T temperature.
Tmin minimum temperature for applicability of material data from API Std 530.
Tmax maximum temperature for applicability of material data from API Std 530.
2E.7 References
2E.7.1 Strength Parameters
1. ASME, Boiler and Pressure Vessel Code, Section II, Part D – Properties, ASME Code Section II, Part D, ASME, New York, N.Y.
3. Kim, Y., Huh, N., Kim, Y., Choi, Y., and Yang, J., “On Relevant Ramberg-Osgood Fit to Engineering Nonlinear Fracture Mechanics Analysis,” ASME, Journal of Pressure Vessel Technology, Vol. 126, August, 2004, pages 277-283.
4. Holt, J.M., Mindlin, H., and Ho, C.Y., Structural Alloys Handbook, Volumes 1, 2 and 3, CINDAS/Purdue University, Potter Engineering Center, West Lafayette, IN, 1995.
5. Neuber, H., “Theory of Stress Concentrations for Shear Strained Prismatic Bodies with Arbitrary Non- linear Stress-Strain Law,” Trans. ASME Journal of Applied Mechanics, 1969, p. 544.
6. Prager, M, Osage, D.A., and Panzarella, C.H., Evaluation Of Material Strength Data For Use In API Std 530, WRC Bulletin 541, The Welding Research Council, New York, N.Y., 2015.
2E.7.2 Cyclic Stress-Strain Relationships
1. Draper, J., Modern Metal fatigue Analysis, EMAS Publishing, FESI-UK Forum for Engineering Structural Integrity, Whittle House, The Quadrant, Birchwood Park, Warrington, WA3 6FW, UK, 2008.
2. Baumel A. Jr and Seeger, T., Materials Data for Cyclic Loading – Supplement 1, Elsevier Science Publishing BV, 1987.
2E.7.3 Physical Properties
1. Osage, D.A. and Prager, M. Compendium of Temperature-Dependent Physical Properties for Pressure Vessel Materials, WRC 503, Welding Research Council, New York, N.Y., In Progress.
2. Avallone, E.A., and Baumeister, T, Marks’ Standard Handbook for Mechanical Engineers, Ninth Edition, McGraw-Hill, New York, N.Y., 1978.
3. ASME, Boiler and Pressure Vessel Code, Section II, Part D – Properties, ASME Code Section II, Part D, ASME, New York, N.Y.
4. ASME, Subsection NH – Class 1 Components in Elevated Temperature Service, ASME Code Section III, Division 1, ASME, New York, N.Y.
5. Holt, J.M., Mindlin, H., and Ho, C.Y., Structural Alloys Handbook, Volumes 1, 2 and 3, CINDAS/Purdue University, Potter Engineering Center, West Lafayette, IN, 1995.
2E.8 Tables
Table 2E.1 – Approximate Equivalent Hardness Number and Tensile Strength for Carbon and Low Alloy Steels in the Annealed, Normalized, and Quenched-and-Tempered Conditions Brinell Hardness No.
(3000 kg load) Vickers Hardness No. Approximate Tensile Strength
(MPa) (ksi)
441 470 1572 228
433 460 1538 223
425 450 1496 217
415 440 1462 212
405 430 1413 205
397 420 1372 199
388 410 1331 193
379 400 1289 187
369 390 1248 181
360 380 1207 175
350 370 1172 170
341 360 1131 164
331 350 1096 159
322 340 1069 155
313 330 1034 150
303 320 1007 146
294 310 979 142
284 300 951 138
280 295 938 136
275 290 917 133
270 285 903 131
265 280 889 129
261 275 876 127
256 270 855 124
252 265 841 122
247 260 827 120
243 255 807 117
238 250 793 115
233 245 779 113
228 240 765 111
219 230 731 106
209 220 696 101
200 210 669 97
190 200 634 92
181 190 607 88
171 180 579 84
162 170 545 79
152 160 517 75
143 150 490 71
133 140 455 66
124 130 427 62
114 120 393 57
Table 2E.2 – MPC Minimum Specified Yield Strength as a Function of Temperature Material
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