1、CYCLIC STRESS-STRAIN CURVESSTP-PT-081STP-PT-081 CYCLIC STRESS-STRAIN CURVES Prepared by: Wolfgang Hoffelner RWH consult GmbH Date of Issuance: June 29, 2017 This report was prepared by ASME Standards Technology, LLC (ASME ST-LLC) and sponsored by the American Society of Mechanical Engineers (ASME) P
2、ressure Technology Codes solid line, incremental step (source 3) 3 Figure 1-4: Correlation between monotonic and cyclic yield strength for different alloys 4. 4 Figure 1-5: Correlation between monotonic and cyclic yield strength of carbon and low alloy steels used in automotive applications at room
3、temperature 6 . 4 Figure 2-1: The influence of very different K and n values on the calculated cyclic curves at low strain amplitudes (typical for LCF loading) 6 Figure 4-1: Relation between monotonic and cyclic yield stress for carbon steels 8 Figure 4-2: Cyclic hardening exponents for carbon steel
4、s 9 Figure 5-1: Relation between monotonic and cyclic yield stress for low alloy steels 10 Figure 5-2: Cyclic hardening exponents for low alloy steels 11 Figure 6-1: Relation between monotonic and cyclic yield stress for low alloy steels 12 Figure 6-2: Cyclic hardening exponents for martensitic 9-13
5、% Cr steels 13 STP-PT-081: Cyclic Stress-Strain Curves iv Figure 7-1: Cyclic yield stress as a function of monotonic yield stress for austenitic steels 14 Figure 7-2: Ratio between cyclic yield stress (YS) and monotonic yield stress at room temperature (YS(RT) as a function of temperature for austen
6、itic steels 14 Figure 7-3: Cyclic hardening exponent, n, as a function of temperature for austenitic steels . 15 Figure 8-1: Relationship between monotonic and cyclic yield stress for nickel-base alloys 16 Figure 8-2: Average cyclic hardening exponent for nickel-base alloys 17 Figure 9-1: Cyclic yie
7、ld strength as a function of monotonic yield strength for aluminum alloys . 18 Figure 9-2: Average cyclic hardening exponent for aluminum alloys 18 Figure 9-3: Monotonic and cyclic stress-strain curves for aluminum alloy A 6061 at 100 C 11 . 19 Figure 9-4: Monotonic and cyclic stress-strain curves f
8、or aluminum alloy A 6061 at 150 C 11 . 19 Figure 10-1: Cyclic yield stress as a function of monotonic yield stress for titanium alloys . 20 Figure 10-2: Average cyclic hardening exponent for titanium alloys . 20 Figure 13-1: Scheme for presentation of cyclic and monotonic data 23 Figure A-1: Screens
9、hot of the spreadsheet for determination of stress-strain curves . 26 Figure C-1: Cyclic curve for 9Cr-1Mo in Section VIII/2 showing temperature (C), n and K . 37 Figure C-2: Original NIMS data for Grade 91 37 Figure C-3: Comparison of cyclic and monotonic stress-strain curves for 9Cr-1Mo (grade 91)
10、 in current code edition . 38 Figure D-1: Comparison of the results of this investigation with literature data 40 Figure D-2: Comparison of the results of this investigation with literature data 41 Figure D-3: Monotonic and cyclic stress-strain curves of a grade 91 martensitic steel 41 Figure D-4: C
11、omparison of measured (at 593C) cyclic stress-strain values for 304 (exp) 13 with the prediction based on the current report (calc) . 42 STP-PT-081: Cyclic Stress-Strain Curves v FOREWORD The report develops rules for determination of cyclic stress-strain curves for materials contained in the ASME B
12、oiler and Pressure Vessel Code (BPVC), Section II, Tables IID from monotonic data. The following classes of materials were considered: Carbon steel (all strength levels) Chromium Molybdenum (Vanadium) steels (i.e., 1.25Cr-1Mo or 2.25 Cr-1Mo), includingenhanced alloys (all strength levels) Ferritic-m
13、artensitic steels (e.g., 9-12% Cr), including enhanced alloys Stainless steels (austenitic, ferritic-martensitic, duplex, precipitation hardening) Nickel-base alloys (e.g., N06600, N06625, N08800). Aluminum based alloys Titanium based alloys Copper based alloys Zirconium based alloysThe author ackno
14、wledges, with deep appreciation, the activities of ASME staff and volunteers who have provided valuable technical input, advice and assistance with review of, commenting on, and editing of, this document. Established in 1880, the ASME is a professional not-for-profit organization with more than 135,
15、000 members and volunteers promoting the art, science and practice of mechanical and multidisciplinary engineering and allied sciences. ASME develops codes and standards that enhance public safety, and provides lifelong learning and technical exchange opportunities benefiting the engineering and tec
16、hnology community. Visit https:/www.asme.org/ for more information. ASME ST-LLC is a not-for-profit Limited Liability Company, with ASME as the sole member, formed in 2004 to carry out work related to new and developing technology. The ASME ST-LLC mission includes meeting the needs of industry and g
17、overnment 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 technology development needed to establish and maintain the technical relevance of codes and standards. Visit
18、www.asmestllc.org for more information. STP-PT-081: Cyclic Stress-Strain Curves vi SUMMARY Monotonic strength values of materials like Yield Strength or Ultimate Tensile Strength are usually determined with well-defined and well-established testing equipment and sample geometries. For many materials
19、, a wide database exists which accelerates statistical analyses and determination of minimum values, however, cyclic stress-strain curves do not benefit from such an established knowledgebase. Fatigue testing is much more complex than tensile testing, and different approaches exist in determining th
20、e representative hysteresis loop. Figure S-1: Proposed procedures for determination of cyclic stress-strain curves for different materials Conservative Average Comments Carbon steels YS=YS for YS350 MPa YS=f1(YS) n= 0.167 Results compare well with literature Low alloy steels YS=YS for YS400 MPa YS=f
21、2(YS) n= 0.130 Results compare well with literature Martensitic 9-13% Cr YS=average YS=f3(YS) n= 0.116 Results compare well with literature Austenitic steels YS=YS YS=f4(YSRT, T) n=f5(T) Temperature is important Nickel-base alloys YS=YS YS=f6(YS) n= 0.150 Results compare well with literature Aluminu
22、m alloys YS=YS YS=YS for high strength temper (T4, T6) YS=f7(YS) for other alloys n= 0.086 Titanium alloys YS=average YS= f8(YS) n= 0.085 Only limited amount of data available Copper and Zirconium alloys N.A. N.A. Not sufficient data available Notes: YS=Yield stress, YS=Cyclic yield stress, n=cyclic
23、 strain hardening exponent, YS=K*0.002n, fi (i=1-8). Material dependent functions are derived in the body of this report. Cyclic stress-strain curves can therefore be only considered as an average description of a material. As materials can cyclic soften and cyclic harden, the relationship between m
24、onotonic and cyclic yield strength is of particular importance. The cyclic stress-strain curve for strain-controlled fatigue near zero mean stress is usually described by the following relationship: 2 =2 + (2)1 Where: =total strain range, =(representative) total stress range, E=Youngs modulus, K=cyc
25、lic strength coefficient, n=cyclic hardening exponent. STP-PT-081: Cyclic Stress-Strain Curves vii The cyclic stress range usually changes as a function of a number of cycles (hardening/softening) and therefore a “typical” stress range must be chosen. By convention, the stress range at Nf/2 is used
26、in almost all cases. Other definitions are occasionally used, but in this report the Nf/2 approach is used almost exclusively. K (YS) and n were determined by analysis of literature data for the different groups of materials. The results are summarized in Figure S-1. The procedures given are only va
27、lid for materials not hardened by cold deformation or yield stresses far outside the ASME code specifications. They should only be used for temperatures governed by time-independent properties. For higher temperatures, creep effects might impact the cyclic behavior. Within these limitations, it is p
28、ossible to determine representative cyclic stress-strain curves for several materials presented in the ASME BPVC Section II Tables IID. It is important to stress that, with this approach, only typical average values could be determined which allow an assessment of the cyclic response of a material (
29、e.g., for J-integral assessments). Excel worksheets for monotonic and cyclic stress-strain curves were developed. Raw data created during the project and literature used is also presented and discussed with respect to eventual implementation into the ASME Materials Database. In addition to the liter
30、ature cited in the document, the References section contains all literature used to establish the results of this report. Details are summarized in Appendices A-D: Appendix A: Description of the Excel Worksheet for determination of stress-strain curves Appendix B: Representation of cyclic data for e
31、ventual inclusion into the ASME database Appendix C: Example for inconsistencies once not well correlated monotonic and cyclic data areused Appendix D: Examples for validity of conceptImportant Remarks: In contrast to monotonic stress-strain curves, the procedure for determination of cyclic stress-s
32、train curves is not very well established, and large differences between the results of different investigations exist. For this investigation, results from single-specimen tests were used, and the representative hysteresis loop was the loop at half lifetime. The cyclic strains leading to fatigue fa
33、ilure are in the 1-2 percent range. Therefore, no discrimination between engineering and true stresses and strains is necessary. The spreadsheet for evaluation of stress-strain curves is not part of the report. Disclaimer: Results gained with the introduced worksheet can only serve as technical info
34、rmation to assess materials properties. At the current stage they may not be used for any safety-relevant calculations or considerations. STP-PT-081: Cyclic Stress-Strain Curves 1 1 INTRODUCTION AND DESCRIPTION OF THE PROBLEM Cyclic stress-strain curves describe the stress-strain behavior under cycl
35、ic loads. Usually, the cyclic stress amplitude /2 is plotted as a function of the cyclic strain amplitude /2 for a defined cycle. The fact that the stress-strain response of a material is usually cycle-dependent requires a reference cycle which can be considered as representative for the cyclic stre
36、ss-strain curve. In contrast to monotonic stress-strain curves which deliver a unique relationship between the stress and strain of a material, the cyclic stress-strain relationships may undergo cycle-dependent changes. The material can be: Cyclic hardening Cyclic softening Cyclic stable Combination
37、s of cyclic softening and cyclic hardening This means that the stress-strain relationship determined in strain fatigue tests is usually cycle dependent. Figure 1-1 shows the change of stress amplitude with a number of cycles for a low carbon steel as an example 1. Figure 1-1: Cyclic hardening-soften
38、ing curves of a low carbon steel for different total strain amplitudes, . (Replotted from 1) STP-PT-081: Cyclic Stress-Strain Curves 2 Figure 1-2 shows the cyclic stress-strain response of IN 600 at a different number of cycles (replotted from 2. Figure 1-2: Cycle dependence of stress-strain curves
39、for IN 600 (replotted from literature 2) When a cyclic stable hysteresis loop is obtained, this stabilized loop can be used as a reference. If a cyclic stable hysteresis loop is not established, the cycle at half the time to rupture (Nf/2) is taken as a reference independent of whether the material
40、is cyclic softening, cyclic hardening or shows a mixed behavior. These cycles are usually obtained from reversed strain cycling tests on a number of companion specimens, but shortcut procedures are also used by various investigators. Such shortcut methods use only a single specimen, which is cycled
41、a certain number of times or until saturation is reached. The levels of cyclic straining are stepwise increased (incremental step test). This means that cyclic pre-deformed samples are used, which can lead to artifacts in cases where cycle-dependent microstructural changes can happen. It is also wor
42、th mentioning that low cycle fatigue (LCF) is primarily crack growth from short cracks, which can also affect the behavior of pre-deformed material. The fact that materials can cyclically harden or soften makes the relationship between cyclic and monotonic curves important. A cyclic stress-strain cu
43、rve alone, without any relation to the monotonic properties, is only of very limited use for design or safety considerations. An independent choice of a cyclic stress-strain curve without reference to the monotonic behavior might cause misleading results. Cyclic softening material can appear as cycl
44、ic hardening and vice-versa (an example from ASME BPVC Section VIII/2 is given in Appendix C:). Therefore, relationships between STP-PT-081: Cyclic Stress-Strain Curves 3 monotonic and cyclic properties are required. General trends for cyclic hardening/softening of different classes of materials are
45、 given in 3. Figure 1-3 illustrates typical examples of monotonic and cyclic stress-strain curves. Austenitic matrices tend towards cyclic hardening, whereas ferritic/martensitic materials tend towards cyclic softening. Figure 1-3: Monotonic and cyclic stress-strain diagrams for six different engine
46、ering alloys. , companion specimens; solid line, incremental step (source 3) A few attempts for the derivation of cyclic stress-strain curves exist (e.g., 4, 5, 6). Particularly, the relationships between monotonic and cyclic yield strengths were analyzed in these investigations. Results are shown i
47、n Figure 1-4 and Figure 1-5. Figure 1-4 shows data for ferritic/pearlitic, martensitic, and austenitic steels. Ferritic/pearlitic steels tend to behave cyclic stable to slight cyclic softening. The martensitic steels are cyclic softening. Austenitic steels show cyclic hardening behavior, however, a
48、wide scatter of data can be seen. This will be further discussed in section 7 concerning austenitic steels. The results shown in Figure 1-5 indicate that carbon and low alloy steels start cyclic stable at low yield strength and become cyclic softening at high yield strength. These results will also
49、be discussed later in the report. STP-PT-081: Cyclic Stress-Strain Curves 4 Figure 1-4: Correlation between monotonic and cyclic yield strength for different alloys 4 Figure 1-5: Correlation between monotonic and cyclic yield strength of carbon and low alloy steels used in automotive applications at room temperature 6 The exact shape of the cyclic curves depends on the material itself and its response to deformation (e.g., dynamic strain aging, deformation induced m
