1、STP-PT-022COMPARISON ANDVALIDATION OFCREEP-BUCKLINGANALYSIS METHODSSTP-PT-022 COMPARISON AND VALIDATION OF CREEP BUCKLING ANALYSIS METHODS Prepared by: Peter Carter Alstom Inc. D.L Marriott Stress Engineering Services, Inc Date of Issuance: September 3, 2008 This report was prepared as an account of
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9、ark Avenue, New York, NY 10016-5990 ISBN No. 0-7918-3174-4 Copyright 2008 by ASME Standards Technology, LLC All Rights Reserved Comparison and Validation of Creep-Buckling Analysis Methods STP-PT-022 iii TABLE OF CONTENTS Foreword v Abstract . vi 1 INTRODUCTION . 7 2 CREEP MODELS 9 2.1 Primary and S
10、econdary Creep. 9 2.2 Tertiary Creep 9 2.3 Isochronous Stress-Strain Curves 11 3 CREEP BUCKLING ANALYSIS TECHNIQUES. 12 3.1 Baseline Finite Element Creep Analyses with Initial Imperfections. 12 3.2 Critical Strain Technique. 12 3.3 Modified Modulus Technique . 13 3.4 Isochronous Stress-Strain Curve
11、Limit/Instability Analysis . 14 3.5 Effect of Tertiary Creep 14 4 EXAMPLE 1 LONG (2-D) CYLINDER UNDER EXTERNAL PRESSURE 16 4.1 Comparison between Shell and Solid Models. 17 4.2 Finite Element Creep Analyses with Initial Imperfections . 17 4.3 Critical Strain and Modified Modulus Calculations 18 4.4
12、Comparison between Shell Secondary Creep Analyses and Time-Independent Isochronous Limit Analyses 18 4.5 Effect of Primary Creep 20 4.6 Effect of Tertiary Creep 21 5 EXAMPLE 2 SPHERE UNDER EXTERNAL PRESSURE . 22 6 EXAMPLE 3 CYLINDER UNDER AXIAL LOAD . 24 7 CONCLUSIONS . 27 References 28 Acknowledgem
13、ents 29 LIST OF TABLES Table 1 - WRC Calculations of Buckling Stress 14 Table 2 - Comparison between Shell and Solid Models for Buckling Times of Cylinders under External Pressure 17 Table 3 - Comparison between Shell Model Buckling Times and Critical Strain Buckling Times. Effects of Initial Imperf
14、ection are Given 19 Table 4 - Comparison between Finite Element Buckling Pressures and Approximate Techniques 20 Table 5 - Comparison of Steady and Primary Creep Buckling Times . 20 Table 6 - Comparison of Isochronous Limit and Tangent Moduli Calculations 21 STP-PT-022 Comparison and Validation of C
15、reep-Buckling Analysis Methods iv Table 7 - Comparison of Finite Element and Isochronous Limit/Instability Analyses for Secondary and Tertiary Creep With Omega = 2000.21 Table 8 - Comparison of Finite Element, Constant Stress Isochronous Limit/Instability, Critical Strain and Tangent Modulus Predict
16、ions for Creep Rupture Model with Omega = 2000.21 Table 9 - Comparison of Finite Element Secondary Creep and Approximate Analyses for Sphere Creep Buckling .23 Table 10 - Comparison of Finite Element Secondary Creep and Approximate Analyses for Cylinder Axial Creep Buckling.26 LIST OF FIGURES Figure
17、 1 - Creep Strain with Steady (Original) and Time Hardening Models, 5 MPa And 20 MPa Stress, Respectively 9 Figure 2 - Creep Strain at Constant Stress for 42 MPa, Omega = 2000, Secondary and Tertiary Creep Models 11 Figure 3 - Isochronous Stress-Strain Curve and Tangent Modulus 13 Figure 4 - Isochro
18、nous Curves for 100,000 Hours for Secondary Creep and Creep Rupture at 44.6 MPa.15 Figure 5 - Undeformed and Buckled Shapes of a Row of Shell Elements .16 Figure 6 - Deflection in Part of Quarter Model Solid Section for R/T = 20 .17 Figure 7 - Displacement-Time Plot for Case 1 in Table 3 and Table 4
19、 18 Figure 8 - Displacement-Time Plot for Case 8 in Table 3 and Table 4 19 Figure 9 - First Elastic Buckling Modes for Sphere and Axisymmetric Model, with Buckling Stress = 1024 MPa. Typical Creep Buckling Mode22 Figure 10 - Creep Buckling for Sphere Case 1 .23 Figure 11 - Finite Element Axisymmetri
20、c Shell Model of Axially Buckled Cylinder: Mode 1.24 Figure 12 - Deflection History for Case 3 of Table 10 Below25 Figure 13 - Deflection History for Case 4 of Table 10 Below25 Comparison and Validation of Creep-Buckling Analysis Methods STP-PT-022 v FOREWORD This document was developed under a rese
21、arch and development project which resulted from ASME Pressure Technology Codes & Standards (PTCS) committee requests to identify, prioritize, and address technology gaps in current or new PTCS Codes, Standards and Guidelines. This project is one of several included for ASME fiscal year 2008 sponsor
22、ship which are intended to establish and maintain the technical relevance of ASME codes & standards products. The specific project related to this document is project 07-11 (BPVC#5), entitled “Comparison and Validation of Creep-Buckling Analysis Methods.” Established in 1880, the American Society of
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25、lated to newly commercialized technology. The ASME ST-LLC mission includes meeting the needs of industry and government by providing new standards-related products and services, which advance the application of emerging and newly commercialized science and technology and providing the research and t
26、echnology development needed to establish and maintain the technical relevance of codes and standards. Visit www.stllc.asme.org for more information. STP-PT-022 Comparison and Validation of Creep-Buckling Analysis Methods vi ABSTRACT This report provides comparisons of creep-buckling calculations an
27、d provides guidance on approximate methods which are feasible for design. This report includes a discussion of the various creep models, presents creep buckling analysis techniques, and provides several comparative example calculations. The techniques discussed in this report include: 1. Baseline an
28、alysis. Finite element creep analysis with different creep models and full non-linear strain-displacement (geometrical) analysis. 2. Critical strain technique. Elastic buckling strain defines the creep buckling strain. 3. Tangent/secant modulus approaches. Combinations of tangent and secant moduli o
29、f the isochronous stress-strain curve are used in calculations that reduce to elastic buckling calculations in the elastic case. 4. Use of an isochronous stress-strain curve in a limit/instability analysis of the imperfect structure. An instability (buckling) analysis would be in principle the same
30、as Technique 3, and should generate the same answer. Adding plastic collapse as a failure mode ensures that the yield strength of the structure is not exceeded. This analysis therefore reflects the failure modes which are covered by the baseline technique. Comparison and Validation of Creep-Buckling
31、 Analysis Methods STP-PT-022 7 1 INTRODUCTION This report provides comparisons between approximate and detailed creep-buckling calculations. The objective is to provide guidance on approximate methods which are feasible for design. This requires the efficient calculation of structural strength and t
32、ime to (buckling) failure, so that calculation of margins between design and failure boundaries does not require multiple trial and error creep calculations. The definition of creep buckling is taken to be wide, including elastic and inelastic instability, bifurcation and acceleration of strain and
33、deflection rates due to non-linear geometrical reduction in structural strength. The techniques used in this report are: 1. Baseline analysis. Finite element creep analysis with different creep models and full non-linear strain-displacement (geometrical) analysis. 2. Critical strain technique. Elast
34、ic buckling strain defines the creep buckling strain. (1, 2, 3) 3. Tangent/secant modulus approaches. Combinations of tangent and secant moduli of the isochronous stress-strain curve are used in calculations that reduce to elastic buckling calculations in the elastic case. (4, 5, 6) 4. Use of an iso
35、chronous stress-strain curve in a limit/instability analysis of the imperfect structure. An instability (buckling) analysis would be in principle the same as technique 3, and should generate the same answer. Adding plastic collapse as a failure mode ensures that the yield strength of the structure i
36、s not exceeded. This analysis therefore reflects the failure modes which are covered by the baseline technique. Techniques 2 and 3 do not have an explicit treatment of initial imperfection or out-of roundness. For simple structures such as cylinders and spheres, Technique 1 requires an initial imper
37、fection to give a reasonable result. With no defined initial imperfection it may or may not give a result, and if there was a result, it may or may not bear any resemblance to reality. Technique 4 requires the same initial imperfection as 1 to give a reasonable result. The selection of the initial i
38、mperfection is simple for the cases considered in this report. It is the first elastic buckling mode shape with a defined magnitude. For more complex structures, it may be necessary to examine a number of possible imperfection mode shapes, and to base the strength prediction on the mode which gives
39、the most conservative result. This is conveniently done by using a range of elastic buckling mode shapes, but other plausible or defined imperfection shapes can easily be used. A 0.5 mm radial imperfection with 100 mm radius corresponds to the ASME definition of 1% maximum acceptable out-of-round. T
40、his and 0.1 mm imperfections are considered in this report. Plasticity is not included. The cases to be analyzed will represent reasonable design conditions in terms of stress, temperature and life. Under these circumstances significant plasticity would not be expected for the simple structures in t
41、his report, unless it occurred due to severe distortions late in life. It would be difficult to load these structures so that initial yielding occurred which did not lead to instantaneous elastic-plastic buckling. In this case there is no difference between the technique 4 limit/instability analysis
42、 and the Technique 1 baseline analysis. However, plasticity may be readily included in all the analyses if necessary. There is no reason why isochronous stress-strain curves constructed from tests or from full elastic-creep-plasticity properties should present any difficulties over and above those i
43、n this report. Inclusion of plasticity in the full inelastic analysis and in the three approximate methods is not expected to change the conclusions based on the creep models. The ability of the approximate STP-PT-022 Comparison and Validation of Creep-Buckling Analysis Methods 8 methods to capture
44、time-dependent strength and instability is being tested. Plasticity adds another variable but no extra complexity to the problem. Any realistic or practical creep-buckling assessment should use full elastic-inelastic isochronous data. This report distinguishes between primary, secondary and tertiary
45、 creep only to prove this. Comparison and Validation of Creep-Buckling Analysis Methods STP-PT-022 9 2 CREEP MODELS 2.1 Primary and Secondary Creep For modeling primary and secondary creep, for convenience with the Abaqus options, the time-hardening power law model for creep strain rate is used. cnm
46、At=& (1) where A = 1.26 x 10-15n = 4.0 m = 0 for secondary creep stress is in MPa time t is in hours. This secondary creep law with m = 0 is an approximate model for Grade 22 steel at 515C. To account for primary creep we use the form of the creep model in equation 1, with the following constants. A
47、 = 1.26 x 10-12n = 4.0 m = 0.51 for primary and secondary creep up to 1 x 106hours stress is in MPa time t is in hours. Figure 1 shows creep strain as function of time for 5 and 20 MPa. 0.0E+002.0E-044.0E-046.0E-040.0E+00 5.0E+05 1.0E+06Time (hours)CreepstrainSteadyTime hardening0.0E+006.0E-071.2E-0
48、61.8E-060.0E+00 5.0E+05 1.0E+06Time (hours)CreepstrainSteadyTime hardeningFigure 1 - Creep Strain with Steady (Original) and Time Hardening Models, 5 MPa And 20 MPa Stress, Respectively 2.2 Tertiary Creep To account for tertiary creep, the “Omega” model in API 579-1/ASME FFS-1 1 is used in this stud
49、y. This model for creep gives the classical tertiary creep behavior, with creep strain rate STP-PT-022 Comparison and Validation of Creep-Buckling Analysis Methods 10 increasing significantly and asymptotically for strains greater than 1/, the Monkman-Grant strain. In this approach, a model (or data) for steady creep is modified as follows. Creep strain rate is 0exp( )cc c = & (2) where 0c&= secondary creep rate from equation (1), with m = 0 For constant stress, creep strain at time t is 01ln(1 )cct=& (3) The isochronous secant modulus is csE =/+(4) The
