Proceedings of OMAE 2006 Proceedings of OMAE 2006 25
25ththInternational Conference on Offshore Mechanics and Arctic EngineeringInternational Conference on Offshore Mechanics and Arctic Engineering June 4 - 9, 2006, Hamburg, Germany June 4 - 9, 2006, Hamburg, Germany
OMAE 2006 - 92268
OMAE 2006 - 92268
LOW CYCLE FATIGUE ANALYSIS OF MARINE STRUCTURES
LOW CYCLE FATIGUE ANALYSIS OF MARINE STRUCTURES
Xiaozhi Wang Xiaozhi Wang
American Bureau of Shipping American Bureau of Shipping 16855 Northchase Drive 16855 Northchase Drive Houston, TX 77060 Houston, TX 77060 USA USA [email protected] [email protected] Joong-Kyoo Kang Joong-Kyoo Kang
Daewoo Shipbuilding and Daewoo Shipbuilding and Marine Engineering Co., LTD Marine Engineering Co., LTD 1 Aju-dong, Geoje-si, 1 Aju-dong, Geoje-si, Gyeongsangnam-do Gyeongsangnam-do, , 656-714656-714 KOREA KOREA [email protected] [email protected] Yooil Kim Yooil Kim
Daewoo Shipbuilding and Daewoo Shipbuilding and Marine Engineering Co., LTD Marine Engineering Co., LTD 1 Aju-dong, Geoje-si, 1 Aju-dong, Geoje-si, Gyeongsangnam-do, 656-714 Gyeongsangnam-do, 656-714 KOREA KOREA [email protected] [email protected] Paul H. Wirsching Paul H. Wirsching Aerospace and Aerospace and Mechanical Engineering Mechanical Engineering University of Arizona University of Arizona Tucson, AZ 85721, USA Tucson, AZ 85721, USA [email protected] [email protected]
Originally published by American Society of
Originally published by American Society of Mechanical Engineers (ASME), New York, NY,Mechanical Engineers (ASME), New York, NY, and reprinted with their kind
and reprinted with their kind permission.permission.
ABSTRACT ABSTRACT
There are situations where a marine structure is There are situations where a marine structure is subjected to stress cycles of such large magnitude that subjected to stress cycles of such large magnitude that small, but significant, parts of the structural component small, but significant, parts of the structural component in question experiences cyclic plasticity. Welded joints in question experiences cyclic plasticity. Welded joints are particularly vulnerable because of high local stress are particularly vulnerable because of high local stress concentrations. Fatigue caused by oscillating strain in concentrations. Fatigue caused by oscillating strain in the plastic range is called “low cycle fatigue”. Cycles to the plastic range is called “low cycle fatigue”. Cycles to failure are typically below 10
failure are typically below 1044. Traditional welded joint. Traditional welded joint S-N curves do not describe the fatigue strength in the S-N curves do not describe the fatigue strength in the low cycle region (< 10
low cycle region (< 1044 number of cycles). Typicalnumber of cycles). Typical Class Society Rules do not directly address the low Class Society Rules do not directly address the low cycle fatigue problem. It is therefore the objective of cycle fatigue problem. It is therefore the objective of this paper to present a credible fatigue damage this paper to present a credible fatigue damage prediction method of welded joints in the low cycle prediction method of welded joints in the low cycle
fatigue regime. fatigue regime. INTRODUCTION INTRODUCTION
Certain duty cycles associated with operations of a Certain duty cycles associated with operations of a ship may produce
ship may produce oscillatory stresses whose magnitudesoscillatory stresses whose magnitudes exceed the yield strength of the material. For example, exceed the yield strength of the material. For example, the welded joints in certain members of tankers and the welded joints in certain members of tankers and FPSO’
FPSO’s during ths during the loading/offloading process for e loading/offloading process for whichwhich the total number of cycles during the service life is the total number of cycles during the service life is expected to be less than 10
expected to be less than 1044. Fatigue associated with. Fatigue associated with cyclic plasticity (“low cycle fatigue”) must be cyclic plasticity (“low cycle fatigue”) must be considered as a principal failure mode, yet the d
considered as a principal failure mode, yet the d esign S-esign S- N curves specified in typical class society rules are not N curves specified in typical class society rules are not
defined below 10
defined below 1044 cycles. To perform a safety check for cycles. To perform a safety check for low cycle fatigue, it is necessary to define the S-N low cycle fatigue, it is necessary to define the S-N curve, define the stress associated with the S-N curve curve, define the stress associated with the S-N curve (here the hot spot stress is used), and the process by (here the hot spot stress is used), and the process by which nominal stress is transformed to hot spot stress. which nominal stress is transformed to hot spot stress.
In this paper, a literature review of material In this paper, a literature review of material behavior and strength of marine steels is first presented. behavior and strength of marine steels is first presented. Characteristic parameter values of cyclic stress-strain Characteristic parameter values of cyclic stress-strain curve and strain-life curve are established based on the curve and strain-life curve are established based on the literature study, experimental testing and nonlinear literature study, experimental testing and nonlinear FEA. An S-N curve is then proposed in order to define FEA. An S-N curve is then proposed in order to define the fatigue strength in the low cycle regime. Finally, a the fatigue strength in the low cycle regime. Finally, a fatigue damage calculation method is developed based fatigue damage calculation method is developed based on a hot spot
on a hot spot stress approach.stress approach.
MATERIAL BEHAVIOR AND STRENGTH MATERIAL BEHAVIOR AND STRENGTH UNDER LOW CYCLE CYCLIC LOADS UNDER LOW CYCLE CYCLIC LOADS
For life prediction in welded joints, it is necessary For life prediction in welded joints, it is necessary to define fatigue strength. For fatigue strength within to define fatigue strength. For fatigue strength within low cycle regime, the general strain-life curve will be low cycle regime, the general strain-life curve will be employed.
employed.
The general strain-life curve has the form, See The general strain-life curve has the form, See Dowling (1999), Dowling (1999), pa pa ea ea a a ε ε ε ε ε ε
==
The elastic strain-life curve is defined as The elastic strain-life curve is defined as
b b f f ' ' f f ea ea ( ( N N ) ) E E 22 σ σ ε ε
==
And the plastic strain-life curve is defined as And the plastic strain-life curve is defined as
cc f f ' ' f f pa pa ε ε ( ( 22 N N ) ) ε ε
==
where where NN f f = cycles to failure= cycles to failure
a a
ε
ε = notch strain amplitude= notch strain amplitude
ea ea
ε
ε = elastic notch strain amplitude= elastic notch strain amplitude
pa pa
ε
ε = plastic notch strain amplitude= plastic notch strain amplitude
E
' f
σ = fatigue strength coefficient
b = fatigue strength exponent
' f
ε = fatigue ductility coefficient
c = fatigue ductility exponent
Thus the total strain-life curve can be expressed as
( ) ( )
c f ' f b f ' f a N N E 2 2 ε σ ε=
+
The strain-life curve is defined by the last five parameters of the list. Because E is well known, the focus of this study will be on the last four. It is expected that the fatigue crack will form in the heat affected zone (HAZ) so that special attention will be given to the HAZ.
To obtain the strain-life curve, three approaches are possible:
- Direct measurement from testing.
Unfortunately there is little data available in the general literature, see Park and
Lawrence(1998), and therefore other
methods may be employed
- Use of published fatigue parameters of steels having similar monotonic properties. There exists a large catalog of fatigue parameters for a wide variety of steels. It is argued that parameters for welded joints should be
similar to those of steels having roughly the same monotonic properties
- Empirical relationships for parameters based on monotonic tests. Experience from extensive fatigue testing of steels has led to empirical forms in which the parameters can be established from such monotonic properties as ultimate strength and Brinnel
hardness
Park and Lawrence (1988) reporting in SSC-346 provide the strain-life parameters for HAZ and for weld material as relating to a specific detail. One of the details consists of a center plate and two loading plates welded to the center plate by all around fillet welds. The base material is ASTM A-36. The Shielded Metal Arc Welding (SMAW) process and E7018 electrodes were used. Another series of tests were made on this cruciform joint using the Gas Metal Arc Welding (GMAW) process. The base metal was 12.7 mm plates of ASTM A441 Grade 50 steel.
The Park and Lawrence parameters for HAZ (SMAW; 12.7 mm plate) produce the strain-life curves shown in Figure 1.
Note that the S-N curve of Figure 1 is given in terms of pseudo stress. Low cycle fatigue involves strain cycling and a strain-life relationship to define fatigue strength. However for engineering purposes it is useful to define pseudo stress range, S PR, as the modulus
of elasticity, E , times strain range,ε R,
R PR E
S
=
εThis is convenient when dealing with both high and low cycle fatigue as high cycle fatigue analysis is conventionally performed in terms of stress.
Open circles: base metal, Grade A Heo et al (2004)
Solid circles: welded joint Heo et al (2004) Total strain-life SSC-346 Plastic strain-life SSC-346 Elastic strain-life SSC-346 Cycles to Failure, N 1000 100 100 1000 104 105 104 P s e u d o S t r e s s R a n g e , S R , ( M P a )
Figure 1: Strain-life curve
Heo et al (2004) report the results of a fatigue test on 11 dogbone specimens of Grade A steel (base metal) having an upper bound yield and ultimate strength of 320 and 460 MPa. These data are plotted as the open circles in Figure 1. It should be noted that base metal data is being compared to the HAZ curves of SSC-346. Heo et al (2004) report the results of a fatigue test on 16 welded specimens; non load carrying partially penetrated cruciform fillet welded joints. Stress-life data is shown in Figure 1. Assuming that the fatigue cracks originated in the HAZ, this data is comparable to the SSC-346 total strain-life curve. On the basis of this data, it appears that the SSC-346 HAZ curves are non-conservative.
While it is argued by Boardman (1982) and Dowling (1999) that estimates of fatigue properties by empirical forms should never be substituted for full scale testing of actual parts under service conditions, the fact remains that these forms are useful in those cases where data collection is impractical.
Empirical relationships that will be useful are summarized as follows:
- The fatigue strength coefficient is
approximately equal to the true fracture stress from a tension test
f ' f σ ~
σ
≈
- The fatigue ductility coefficient is
approximately equal to the true fracture strain from a tension test
f ' f ε ~
ε
≈
- Strain-life curves for a wide variety of engineering metals tend to all pass near the strain
ε
a= 0.01 for a life Nf = 1000 cycles- Strain-life curves for a wide variety of engineering metals tend to all pass near the strain
ε
a= 0.01 for a life Nf = 1000 cycles- Ultimate strength can be approximated from Brinell hardness
σ u= 3.45 BHN (MPa)
- The fatigue strength coefficient can be estimated from ultimate strength
345
+
≈
u ' f σ σ MPa- For steels having an ultimate strength below aboutσ u = 1400 MPa, a fatigue limit occurs near 106 cycles at a stress amplitude around
σ
a =σ u/2. From the elastic strain-life curve, itfollows that
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
u ' f log . b σ σ 2 3 6 1- A typical value of the fatigue strength exponent b is -0.085. For soft metals, values of around b equals to -0.12 are common as are values of b equals to -0.05 for hardened materials
- Values around c = -0.60 are common for the
fatigue ductility exponent. A relatively narrow range of c in the range of 0.50 to -0.80 appears to include most engineering materials
- The transition fatigue life can be
approximated from the Brinnel hardness 2 N t = exp( 13.6 – 0.0185 BHN)
This is the value of life, N, for which the elastic and plastic-strain life curves are the same, i.e., the point where the curves cross. This relationship can be used to estimate the fatigue ductility exponent
PSEUDO HOT SPOT STRESS RANGE CALCULATION
Both ABS existing ship rules and upcoming IACS Common Structural Rules for tankers use the hot spot stress approach for fatigue assessment for only high cycle fatigue. It is therefore consistent to develop low cycle fatigue assessment procedure based on hot spot stress approach. Although some fatigue testing measurements, as shown in Figure 1, are based on notch stress, the geometry of the local notch at a weld varies along the weld profile, and it may be difficult to find a geometry on which to base the analysis.
The transformation from elastic hot spot stress range to pseudo hot spot stress range is now considered. The procedure is described by Dowling (1999).
The stress range S E for any of the j loading/offloading
cycles is assumed to be constant amplitude. The following discussion applies to any of the loading cycles.
First define the cyclic stress-strain curve the form of which is [Dowling (1999)], ' n / ' K E 1
⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
+
=
σ σ εwhere, for this application, = hot spot stress,ε = hot
spot strain, K’ = cyclic strength coefficient, n’ = cyclic hardening exponent, E = modulus of elasticity; for steel, E = 206,850 MPa
The parameters K’ and n’ are provided in Table 1 for four types of ship steel, based on DSME testing results.
Table 1: Parameters for the cyclic stress-strain curve
Material A AH32 AH36 DH36
K’ (MPa) 592 669 694 739
N’ 0.114 0.108 0.112 0.106
The cyclic stress-strain curves are plotted in Figure 2.
DH36 AH36 AH32 A 0.005 0 0.01 0.015 0.02 0 100 200 300 400 500 Strain S t r e s s ( M P a )
Figure 2: Cyclic stress-strain curves for different steel grades
The second step is to employ Neuber’s rule which relates the actual stress
σ
and strainε
in the material, in both the elastic and plastic states, to the nominal orelastic stress S. In terms of stress amplitude: E S a a a 2
=
ε σwhere
σ
a andε
a are stress and strain amplitudesrespectively. The elastic stress amplitude is Sa= SL/2
σ
a andε
a is then be determined based on thesimultaneous solution of the above two equations. Material strain range,ε R, is then computed as:
ε R= 2ε a
and the pseudo hot spot stress range is obtained by S L= E ε R
The subscript “L” implies stress associated with low cycle fatigue. Using this procedure, the relationship between the elastic hot spot stress range and pseudo hot spot stress range is derived and presented in Figure 3 for the four materials under consideration.
S-N CURVE APPLIED FOR LOW CYCLE FATIGUE
Figure 4 shows pseudo hot spot stress vs. number of cycles to failure, with TWI (1974) and Heo et. al. (2004) data based on a Neuber correction. The specimen used in TWI (1974) is shown in Figure 5 with a longitudinal non-load carrying fillet welds. As stated in TWI (1974), the final failure which was taken being the point at which a sudden drop occurred in the cyclic tensile load. A SCF of 1.55 is applied.
DH36 AH36 AH32 A Elastic Behavior 2000 2500 1500 1000 500 0 0 1000 2000 3000 4000 5000 6000
Elastic Hot Spot Stress Range, SE(MPa) P s e u d o H o t S p o t S t r e s s R a n g e , S L ( M P a )
Figure 3: Pseudo hot spot stress range as a function of elastic hot spot stress range
The D curve is also plotted in Figure 4 for reference. The median of the pooled TWI and DSME data is calculated based on least square fit. A design curve is normally defined as the median curve minus two standard deviations. It is seen that for low cycle region, N < 104, using D curve, as a design S-N curve for low cycle fatigue, will yield conservative results.
Cycles to Failure, N 1000 100 100 1000 104 104 P s e u d o H o t S p o t S t r e s s R a n g e , ( M P a ) 105
Median (least squares line) m = 2.43
Median - 2*sigma m = 2.43
TWI and DSME based on Neuber analysis
triangles = TW I circles = DSME
Extended D-Curve m = 3
Figure 4: S-N curve in low cycle region
c) 100 mm gauge length 12 mm 900 mm 403 mm 152 mm 102 mm
Profile flame cut, ground and polished, corners radiused to 1.5 mm 38 mm 152 mm 8 mm fillet weld Ground end 12 mm
Figure 5: Test specimen from TWI (1974)
Heo et. al. (2004) test data is based on fatigue testing of a non-load-carrying partially penetrated cruciform fillet joint, as shown in Figure 6. Test was carried out under stain control condition and strain ratio was set to be zero which means strain value fluctuates between zero and specified maximum value. Test was topped when the load dropped down to 50% of initial value which corresponded to small amount of crack propagation. A SCF of 1.28 is applied.
20 mm
11 mm 20 mm
400 mm
Figure 6: Testing specimen presented in Heo et. al. (2004)
The inverse slope of the median-2 standard deviation curve is 2.43. It is observed from Figure 1
showing the Park-Lawrence model and the
experimental data in Figure 4, that there is a tendency for the S-N curve to have a curvature that bends upwards in the area where cycle to failure is below 1000. It will be ideal that this tendency be reflected in the design S-N curve for low cycle fatigue, although using D curve would be conservative. However, modifying D curve for cycles to failure less than 1000 may complicate the damage model calculation.
FATIGUE DAMAGE CALCULATION SUBJECTED TO LOW CYCLE LOADS
In the following, the assumptions are made that the linear damage accumulation rule (Miner’s rule) applies, that rainflow analysis is used to identify stress cycles, and that the material at the hot spot of the weld will experience cyclic plasticity under stress cycles SLj as
shown in Figure 7. General methods of such analyses to produce a damage index are described in detail in the books by Dowling (1999) and Lee et al (2005). The damage model proposed here uses linear damage accumulation and implicitly, rainflow analysis, and is
based on the assumption that static and wave stresses are constant amplitude. Damage due to the low cycle static stresses is described in the following.
Basic application of Miner’s rule produces the expression of static stress damage,
∑
==
k j q Lj j B n S K D 1 1 Let, n n f j=
jf i = (number of the jth loading-offloading cycles)/
(number of wave induced cycles) at any life. Then the total damage associated with the high stress duty cycles is,
∑
==
k j q Lj j B f S K n D 1 S pj S j(t) SLj SBj ttj tcj SvjFigure 7: A single loading/offloading cycle of the jth type
CONCLUSIONS
Low cycle fatigue failure is a relatively new area of concern in modern marine industry, especially the application of FPSOs with frequent loading/unloading operations. In this paper, typical material behavior under low cycle large stress range is first investigated. Characteristic material parameters are recommended based on experimental test data. The pseudo hot spot
stress range can be calculated based on elastic hot spot stress range and material stress-strain curve with the application of Neuber’s rule. A suitable design S-N curve is derived with reference to the available test data. Fatigue damage can then be expressed in terms of Miner’s rule. The procedure in this paper could be used as a basis for authorities to establish the design criteria for better control marine safety due to cracks from low cycle fatigue and eventually the combination of low cycle fatigue and high cycle (considering dynamic hull girder loads, dynamic wave pressure and dynamic tank pressure loads resulting from ship motions) fatigue.
REFERENCES
Boardman, B.E., (1982), “Crack Initiation Fatigue – Data, Analysis, Trends, and Estimation”, Proceedings of the SAE Fatigue Conference, P-109, SAE, Warrendale, PA.
DEn, (1995), “Offshore Installations, Guidance on Design, Construction and Certification”, Department of Energy, UK, Amendment to the Fourth Edition, London, HMSO.
Dowling, N.E., (1999), Mechanical Behavior of Materials, Prentice-Hall, Upper Saddle River, NJ.
Heo, J.H., Kang, J.K, Kim, Y., Yoo, Y.S., Kim, K.S., and Urm, H.S., (2004), “A Study on the Design Guidance for Low Cycle Fatigue in Ship Structure”, Proceedings of the 9th Symposium of Practical Design of Ships and Other Floating Structures, Luebeck-Travemunde, Germany.
Lee, Y.L., Pan, J., Hathaway, R., and Barkey, M, (2005), “Fatigue Testing and Analysis”, Elsevier Butterworth – Heinemann, Oxford, UK.
Park, S.K. and Lawrence, F.V., (1988), “Fatigue Characterization of Fabricated Ship Details for Design – Phase II”, Ship Structures Committee, SSC-346.
TWI (1974), “Fatigue Performance of Welded High Strength Steels”, A compendium of reports from a sponsored research programme, The Welding Institute, Abington Hall, Abington, Cambridge CBI 6AL, England.
