Maan Jawad Global Engineering & Technology Camas, Washington, U.S.A.

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1 Proceedings of the ASME 018 Symposium on Elevated Temperature Application of Materials for Fossil, Nuclear, and Petrochemical Industries ETAM018 April 3-5, 018, Seattle, WA, USA ETAM ALLOWABLE COMPRESSIVE STRESS RULES IN THE ASME BOILER AND PRESSURE VESSEL CODE, SECTION VIII, IN THE CREEP REGIME Maan Jawad Global Engineering & Technology Camas, Washington, U.S.A. ABSTRACT This paper outlines several procedures for developing allowable compressive stress rules in the creep regime (time dependent regime). The rules are intended for the ASME Boiler and Pressure Vessel codes (Sections I and VIII). The proposed rules extend the methodology presently outlined in Sections I, II-D, and VIII of the ASME code for temperatures below the creep regime into temperatures where creep is a consideration. 1. INTRODUCTION The 017 edition of the ASME Boiler and Pressure Vessel Code Sections I, III, and VIII limits the calculations for allowable compressive stress to temperatures below the creep regime (timeindependent regime). However, a number of research articles recently published [1,, and 3] demonstrated the feasibility of extending the allowable compressive stress in the ASME code into the creep regime (time-dependent regime). Presently the ASME code is developing rules for allowable compressive stress in the creep regime and this paper summarizes some of the options available.. ISOCHRONOUS CURVES The buckling equations at temperatures below the creep regime are based on stress-strain curves. However, at temperatures in the creep range the stress-strain curves cannot be used since the stress relaxes at any given strain. Accordingly, isochronous curves form the bases for developing the buckling equations. The isochronous curves at a given temperature are obtained in a two step process. First, tensile specimens are stressed to a given level and strain is measured as a function of time. Different tensile specimens are used at various stress levels. Curves are then plotted in terms of time versus strain for various stress values. The second step is to enter the chart at a given time and plot stress versus strain. These pseudo stress strain curves [4, 5, and 6] are called isochronous curves. Figure 1 shows Average Isochronous Curves [3] for 9Cr-1Mo-V steel at 1000 o F. The isochronous curves are used as pseudo stress-strain curves [] to form the basis for developing compressive stress needed in the design of cylindrical and spherical shells under axial compression and external pressure. 1 Copyright 018 ASME

2 Calculations for allowable compressive stress require either External Pressure Charts or External Pressure Equations. There are three methods for developing external pressure charts/curves in the creep regime using the strain method. The first is plotting External Pressure Charts from the isochronous curves. The second is representing the charts with equations. And the third method is by representing the isochronous curves by equations then then taking the derivative of equations to obtain tangent moduli from which external pressure curves/equations are developed. Details of these three methods are discussed below. Figure 1. Average isochronous curves for 9Cr-1Mo- V at 1000 o F [3]. Two methodologies are being considered by ASME for obtaining equations and/or charts for use in compressive stress calculations. These are the Strain Method and the Remaining Life Method. Both of these methods are discussed next. 3. STRAIN METHOD FOR CALCULATING COMPRESSIVE STRESS This method is based on isochronous curves found originally in Section III-NH of the ASME code. Section III-NH has been deleted from ASME as of 017. The isochronous curves now reside in two placed. The first is in Division 5 of Section III for nuclear applications and the second is in Section II-D for nonnuclear applications. 3.1 Method 1. External Pressure Charts (EPC). The External Pressure Charts (EPC) are probably the most widely used method for determining compressive stress in shells. The EPC in the creep regime are constructed from isochronous curves. The ASME procedure for constructing the EPC consists of reducing the Average stress-strain Isochronous Curves by 0% to obtain Minimum Isochronous Curves. The resulting minimum curves are then used to plot external pressure curves by finding the tangent moduli, E t, from the relationship d /d at various stress values and then calculating corresponding strains, called Factors A, from the relationship A = /E t. The tangent modulus is normally obtained from the isochronous curves by either a graphical method or by a finite difference procedure. The resulting curves are plotted as compressive stress, S c, versus Factor A. Figure shows external pressure curves for 9Cr-1Mo-V steel at 1000 o F with various time periods. One advantage of using the EPC is it gives the designer an overall view of the trend of the stresses which helps in the design process. One disadvantage is the difficulty of interpolating between various points on the log-log chart. Copyright 018 ASME

3 Figure 3. Comparison of Eq.(1) and actual compression curve for 9Cr-1Mo-V steel at 100F and 100,000 hours. The knee in Figure 3 is due to merging of the constant elastic modulus with the variable isochronous curve at 6 ksi. Figure. External Pressure Chart at 1000 o F [3]. 3.. Method. Equations Representing EPC The curves in the external pressure chart may be represented by equations. The advantage of using equations is the consistency of getting answers by bypassing the process of reading the log-log charts. As an example, the following equations are obtained by regression analysis for the 100,000 hour curve in Figure. 100,000 hour curve for 9Cr-1Mo-V steel = E 0 < (1a) = (G 1 + G + G 3 )/(1 + G 4 + G 5 ) < 0.1 (1b) G 1 = 4.11 G = 1, G 3 = 540,53.9 G 4 = G 5 = 5,414.4 A plot of Eq.(1) is shown in Figure 3 together with the actual curve for 100,000 hours Method 3. Equations Representing Isochronous Curves. Individual External Pressure Curves correlating A to S c may also be obtained directly from available Average Isochronous Curves. The procedure consists of starting with an Average Isochronous stress-strain Curve and reducing it by 0% to obtain a Minimum Isochronous Curve. Then regression analysis is used to find an equation simulating the minimum isochronous curve. The d /d derivative of this equation represents the tangent modulus E t from which Factor A is determined from the relationship A = /E t. An External Pressure Curve is then plotted as a function of A versus S c. This can be demonstrated by taking the 100,000 hour isochronous curve in Figure 1 and developing the following equations which represent the 80% stress level 3 Copyright 018 ASME

4 100,000 hour curve for 9Cr-1Mo-V steel = E 0 < (a) = (G 6 + G 7 + G 8 )/(1 + G 9 + G 10 ) < 0.09 (b) = < 0.1 (c) G 6 = G 7 = 46, G 8 = 841,80.0 G 9 = G 10 = 6, A plot of Equations () results in a curve that is identical to the curve in Figure 1 for 100,000 hours. The derivatives of Equations () are E t = E = 5,300 ksi 0 < (3a) E t = (G 13 / G 1 )- (G 11 G 14 / G 1 ) < 0.09 (3b) E t = < 0.1 (3c) G 11 = G 6 + G 7 + G 8 G 1 = 1 + G 9 + G 10 G 13 = G 7 + G 8 G 14 = G 9 + G 10 The factor A for the external pressure curve is obtained from A = /E t (4) The external pressure curve correlating Factor A to S t is obtained by calculating Factor A for various values of and plotting Factor A versus S c on a loglog graph. Figure 4 shows the result of the curve obtained from Equation (3) together with the curve from Figure for 9Cr-1Mo-V steel at 1000 o F and 100,000 hours. One advantage of using this method is it bypasses the laborious process of constructing an external pressure chart. Figure 4. Comparison of External Pressure Curves for 9Cr-1Mo-V steel at 1000 o F and 100,000 hours obtained from Equation (3) and from Figure. 4. REMAINING LIFE METHOD FOR CALCULATING COMPRESSIVE STRESS This methodology is based on Publication API 579-1/ASME FFS-1 [6] which list equations for constructing average isochronous curves for various materials at any time and temperature in the creep regime. One advantage of this method is the ability to draw isochronous curves at any given time and temperature compared to the Strain Method where only specific times and temperatures are listed. A brief description of this methodology is shown next. 4.1 Equations for Isochronous Curves The isochronous curves are generated from the following equations t = e + c + p (5) 4 Copyright 018 ASME

5 t is total strain, e is elastic strain, c is creep strain, and p is plastic strain. The equation for creep strain c may be written as [7] = ċo e (m+p+c) (6) m is a modified Norton s component relating stress to strain, p represents microstructural damage, and c represents other factors. The quantity ċo is initial strain rate. Define = m+p+c (7) Then Equation (6) becomes = ċo e (8) This equation can be rearranged as d /(e ) = ċo dt (9) Integrating this equation using the limits 0 to and 0 to T gives T = [1/ ( ċo ( 1- e - ) (10) or, in terms of creep strain, c = - (1/ ) ln( 1- ċo T) (11) Equation (8) is used by FFS1 to construct isochronous curves. The quantities and ċo define isochronous curves for various materials at various temperatures and times. FFS1 uses the following polynomials for and ċo to define the isochronous curves Log 10 ( ċo ) = - [ (A o + sr ) + (A 1 + A S 1 + A 3 S 1 + A 4 S 1 3 )/(460 + T e )] (1) Log 10 ( ) = [ (B o + cd ) + (B 1 + B S 1 + B 3 S 1 + B 4 S 3 1 )/(460 + T e )] (13) S 1 = log 10 ( ) (14) Constants A i and B i are based on actual data and are tabulated in Reference [6] for various materials. It must be noted that the data base for these materials may be different than that in Section II-D of ASME. The quantities sr and cd are material scatter and material ductility factors listed in Reference [6]. Various evaluations made by the author for.5cr- 1Mo annealed steel at 1000 o F have shown that the external pressure curve obtained from API 579-1/ASME FFS-1 [6] data base is essentially the same as that obtained from the ASME III-NH [5] data base when sr is taken as and cd is taken as 0.0. The equation for elastic strain e is defined by e = /E y (15) E y is modulus of elasticity and is stress. The equation for plastic strain p is expressed as p = 1 + (16) The expressions for 1 and are fairly lengthy and involve many constants as a function of yield and tensile given in FFS1. Substituting the various constants in the expression of 1 gives 1 = 0.5( t / 3 ) (1/ ) { 1 tanh[( t 5 )/ 6 ]} (17) 1 = R = ys / ult = m 1 = [ln(r) + ( p ys )]/{ln[(ln(1 + p ))/(ln(1 + ys ))]} 3 = A 1 = [ ys (1 + ys )]/[ ln(1+ ys )] m1 4 = K = 1.5R R.5 R = ys + K( ult ys ) 6 = K( ult ys ) Similarly the expression for is = 0.5( t / 8 ) (1/ 7) { 1 tanh[( t 5 )/ 6 ]} (18) 7 = m 8 = A = uts e m /(m m ) There is a temperature limitation on p and m. For example, the values for p and m for ferrous steels are limited to 900 o F. Hence, isochronous curves may be drawn from Equation (5) where c is obtained from Equations (11) (14), e is obtained from Equation (15), and p is obtained from Equations (16) (18). 4. Equations for External Pressure Lines The equations for external pressure lines are obtained by taking the derivative of Equation (5) to find the tangent modulus E t. The tangent modulus is obtained from Eq.(5) as follows d t /d = d e /d + d c /d + d p /d 5 Copyright 018 ASME

6 and E t = d /d t = 1/( d t /d ) = 1/( d e /d + d c /d d p /d ) (19) The quantity d e /d is calculated from Eq.(15) as d e /d = 1/E y (0) The quantity d c /d is obtained by taking the derivative of Eq.(11) using a recursive computer program with symbolic solution. The result is d c /d = C 10 /C 7 + C 8 /K 1 (1) where, A 00 = A 0 + sr B 00 = B 0 + cd K 1 = T e S 1 = log 10 (0.8 ) C 1 = B 00 +(B 1 + B *S 1 + B 3 *S 1 + B 4 *S 1 3 )/K 1 C =A 00 +(A 1 + A *S 1 + A 3 *S 1 + A 4 *S 1 3 )/K 1 C 3 = B + *B 3 *S 1 + 3*B 4 *S 1 C 4 = A + *A 3 *S 1 + 3*A 4 *S 1 C 5 = 10 C1 *(1/10 C )*T*ln(10)*C 3 C 6 = ln(10)*ln[ 1-10 C1 *(1/10 C )*T] C 7 = 10 C1 *(1/10 C )*T - 1 C 8 = (1/10 C1 )*C 6 *C 4 C 9 = C 5 /K 1-10 C1 *(1/10 C )*T*ln(10)*C 4 )/K 1 C 10 = (1/10 C1 )*C 9 C i are terms of the strain derivative d /d. The quantity d p /d is obtained by taking the derivative of Eq.(16) using a recursive computer program with symbolic solution. The result is d p /d = d 1 /d + d /d () where, d 1 /d = ( 6 t ) -1 {( t / 3) (1/ ) [ tanh(( 5 t )/ 6 )+ 1][ 6 t + t tanh(( 5 t )/ 6 )]} d /d = (- 6 7 t ) -1 {( t / 8) (1/ 7) [ tanh(( 5 t )/ 6 ) - 1][ t + 7 t tanh(( 5 t )/ 6 )]} Equations (0) through () are substituted into Equation (19) to determine the tangent modulus E t for various t values. Factor A for constructing external pressure line is obtained from Equation (4) as A = /E t The external pressure curve correlating A to S t is obtained by calculating A for various values of and plotting the result on log-log graph correlating S c and Factor A. This remaining Life method has a great advantage over the Strain Method in that the External Pressure Curve can be drawn directly for any given time and temperature in the creep range. For example, the External Pressure Curve for 304 type stainless steel at 87,600 hours (ten years) at 138 o F is obtained from Equation () and is shown in Figure 5. And while such a curve may be obtained from the Elastic method, its development will require extensive timeconsuming interpolations and the results will not be as accurate. Figure 5. External pressure chart for 304 type stainless steel at 138 o F and 87,600 hours. 5. PROPOSED PROCEDURE FOR CALCULATING ALLOWABLE AXIAL COMPRESSION IN CYLINDRICAL SHELLS IN THE CREEP RANGE The elastic critical in-plane buckling equation for long cylindrical shells [] under axial compression is given by 6 Copyright 018 ASME

7 crl = 0.63 E/(R o /t) (3) R o is the outside radius. Experimental data have shown [] that buckling may occur at a value of one-tenth of that calculated from Equation (3) for large R/ t ratios. Accordingly, a knock-down factor of 5.0 is used by ASME for the effect of geometrical imperfections on axial compression and Equation (3) becomes = 0.15 E/(R o /t) (4) The elastic strain is then given by e = /E = 0.15 /(R o /t) (5) For inelastic buckling, the classical equation for buckling stress [] is of the form crl =[E s E t /(3(1 ))] 0.5 /(R o /t) (6) = 0.5 (0.5 )(E s /E) For design purposes Equation (6) is simplified by conservatively letting E = E s = E t. This results in the equation pcrl = 0.63 E t /(R o /t) (7) Using a knock-down factor of 5.0, Equation (7) can be written as p = 0.15 /(R o /t) (8) In addition to the knock-down factor of 5, a design factor, D F, of.0 is used in order to take into account such items as reduced modulus in the inelastic regime and variation of material properties that cause tests to deviate from theory. In temperatures below the creep regime the design factor is set to.0. In the creep regime it has been suggested to use a design factor that varies with time [] in accordance with the following relationship D F =.0 T 1.0 hour (9a) D F = ln(t) 1 < T 100,000 hours (9b) D F = 1.0 T > 100,000 hours (9c) The allowable compressive stress in long cylindrical shells for a given temperature, outside radius R o, and operating time T is obtained by assuming a thickness t and calculating factor A based on Equations (5) and (8) from the equation A = 0.15/(R o /t) (30) With a known value of A, compressive stress, S c, is calculated at a given temperature from any of the methods given in Sections 3 and 4 for two time periods. The first time period is at hot tensile (HT is equal to or less than one hour) and the second is at the operating time period specified. Then for each of the two time periods calculated the allowable compressive stress B using the smaller value obtained from the equations B = AE/(D F ) (31) and B = S c /(D F ) (3) The applied compressive stress shall be less than the lower value of allowable compressive stress B. If not, a new thickness and/or operating time are chosen and the above procedure is repeated. Equation (3) assumes a long cylinder. A more accurate equation that takes length, L, into consideration is presently in ASME Section VIII, Division, for the time-independent regime. Various ASME committees are presently evaluating this equation for use in the creep regime. 6. PROPOSED PROCEDURE FOR CALCULATING ALLOWABLE EXTERNAL PRESSURE ON CYLINDRICAL SHELLS IN THE CREEP RANGE The allowable external pressure in the creep range can be obtained for any cylindrical shells with a given temperature, operating time T, outside diameter D o, and given length L. The thickness t is assumed and Factor A is obtained from the geometric Figure G of ASME BPV II, Part D or from equations simulating the chart. With Factor A known, the compressive stress S c is determined from any of the methods discussed in Sections 3 and 4 7 Copyright 018 ASME

8 above for two time periods. The first time period is at less than one hour and the second is at the operating time period specified. Then the design factor D F is determined from the equations D F = 3.0 T 1.0 hour (33a) 3 D F = ln(t) 1 < T 100,000 hours (33b) D F =.0 T > 100,000 hours (33c) For each of the two time periods mentioned above, the allowable external pressure P is calculated from Equations (34) and (35). AE P = (34) (D F )(D o /t) and, S c P = (35) (D F )(D o /t) The actual external pressure shall be less than the lowest value of calculated external pressure. If not, a new thickness and/or operating time are chosen and the above steps are repeated. 7. PROPOSED PROCEDURE FOR CALCULATING AXIAL COMPRESSION IN COLUMNS (EULER BUCKLING) IN THE CREEP RANGE. The allowable axial stress on a column with an effective length L, outside radius R o, thickness t, and operating time T e is obtained by first calculating factor A from the equation A = / (L/r) (36) The compressive stress, S c, is calculated from any of the methods given in Sections 3 and 4 above for two time periods. The first time period is for less than one hour and the second at the operating time period specified. The suggested design factor D F is taken as For each of the two time periods above, the allowable compressive stress c is calculated from Eqs. (3) and (33) and the smaller value is used. c = AE/(D F ) (37) and c = S c /(D F ) (38) The actual calculated compressive stress shall be less than the lowest value of allowable compressive stress c. If not, a new thickness and/or operating time are chosen and the steps above are repeated. 8. EXAMPLE A stainless steel cylindrical shell has D o = 100 inch, L = 160 inch, and t = 0.5 inch. What is the allowable external pressure for a life service of 87,600 hours at 138 o F? Solution: L/D o = 1.60 D o /t = 400 From the Geometric Chart in ASME Section II, Part D, A = From Figure 5, S c = 1000 psi From Equation (33b), 3 D F = = ln(87,600) From Equation (35), the allowable external pressure is S c (1000) P = = =.5 psi (D F )(D o /t) (.01)(400) It is of interest to note that existing EPC in ASME Section II, Part D, based on Hot Tensile tests with no consideration to operating life gives an allowable external pressure value of about 3.3 psi at 138 o F. Hence, about 30% reduction in the allowable 8 Copyright 018 ASME

9 external pressure must be considered when the shell is operating in the creep regime for an extended period of time. 9. ACKNOWLEDGEMENT Special thanks to Dr. Kevin Jawad for supplying the derivatives in Section NOMENCLATURE A = factor in External Pressure Charts A o A 4 = material factors i = values of various stress and strain functions of various materials B = allowable compressive stress B o B 4 = material factors C i = terms of the creep strain derivative d c /d. c = constant representing various factors in the Norton equation. D o = outside diameter cd = material ductility factor. It ranges from to sr = material scatter factor. It ranges from to E = Young s modulus of elasticity E s = secant modulus, / E t = tangent modulus, d /d = strain c = creep strain e = elastic strain p = inelastic strain t = total strain = strain rate ċo = initial strain rate 1, = components of plastic strain L = length of cylinder m = modified Norton s component relating stress to strain =Poisson s ratio p = constant representing microstructural damage in the Norton equation. R = ys / ult R o = outside radius r = radius of gyration S 1 = log 10 ( ) S c = compressive stress = stress crl = elastic buckling stress pcrl = inelastic buckling stress ult = tensile strength ys = yield stress T = time, hours T e = temperature, F t = thickness 11. REFERENCES [1] P. Carter and D. Marriott, 008. Comparison and validation of creep buckling analysis methods STP- PT-0. ASME Standards Technology, LLC. [] M. Jawad and D. Griffin, 011. External pressure design in the creep range STP-PT-09. ASME Standards Technology, LLC. [3] M. Jawad, R. Swindeman, M. Swindeman, and D. Griffin, 016. Development of average isochronous stress-strain curves and equations and external pressure charts and equations for 9Cr-1Mo- V steel STP-PT-080. ASME Standards Technology, LLC. [4] M. Jawad and R. Jetter, 011, Design and analysis of ASME boiler and pressure vessel components in the creep range. ASME Press. [5] ASME Boiler and Pressure Vessel Code, Section III, Subsection NH, 015. Class 1 components in Elevated Temperature Service. American Society of Mechanical Engineers. [6] Fitness-for-Service, 016. API 579-1/ASME FFS-1. American Society of Mechanical Engineers. [7] M. Prager, Development of the MPC Omega Method for Life Assessment in the Creep Range Journal of Pressure Vessel Technology, Volume 117. American Society of Mechanical Engineers. 9 Copyright 018 ASME