Low Cycle Fatigue Analysis

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Proceedings of OMAE 2006 th 25 International Conference on Offshore Mechanics and Arctic Engineering June 4 - 9, 2006, Hamburg, Germany

OMAE 2006 - 92268 LOW CYCLE FATIGUE ANALYSIS OF MARINE STRUCTURES Xiaozhi Wang American Bureau of Shipping 16855 Northchase Drive Houston, TX 77060 USA [email protected]

Joong-Kyoo Kang Daewoo Shipbuilding and Marine Engineering Co., LTD 1 Aju-dong, Geoje-si, Gyeongsangnam-do, Gyeongsangnam-do, 656-714 KOREA  [email protected] 

Yooil Kim Daewoo Shipbuilding and Marine Engineering Co., LTD 1 Aju-dong, Geoje-si, Gyeongsangnam-do, 656-714 KOREA [email protected] 

Paul H. Wirsching Aerospace and Mechanical Engineering University of Arizona Tucson, AZ 85721, USA [email protected]

Originally published by American Society of Mechanical Engineers (ASME), New York, NY, and reprinted with their kind permission.

ABSTRACT There are situations where a marine structure is subjected to stress cycles of such large magnitude that small, but significant, parts of the structural component in question experiences cyclic plasticity. Welded joints are particularly vulnerable because of high local stress concentrations. Fatigue caused by oscillating strain in the plastic range is called “low cycle fatigue”. Cycles to failure are typically below 104. Traditional welded joint S-N curves do not describe the fatigue strength in the 4 low cycle region (< 10 number of cycles). Typical Class Society Rules do not directly address the low cycle fatigue problem. It is therefore the objective of  this paper to present a credible fatigue damage   prediction method of welded joints in the low cycle fatigue regime.

INTRODUCTION Certain duty cycles associated with operations of a ship may produce oscillatory stresses whose magnitudes exceed the yield strength of the material. For example, the welded joints in certain members of tankers and FPSO’s FPSO’s during the th e loading/offloading process for which the total number of cycles during the service life is expected to be less than 104. Fatigue associated with cyclic plasticity (“low cycle fatigue”) must be considered as a principal failure mode, yet the d esign S N curves specified in typical class society rules are not defined below 104 cycles. To perform a safety check for  low cycle fatigue, it is necessary to define the S-N curve, define the stress associated with the S-N curve (here the hot spot stress is used), and the process by which nominal stress is transformed to hot spot stress.

Cycle Fatigue Analysis of Marine

In this paper, a literature review of material  behavior and strength of marine steels is first presented. Characteristic parameter values of cyclic stress-strain curve and strain-life curve are established based on the literature study, experimental testing and nonlinear  FEA. An S-N curve is then proposed in order to define the fatigue strength in the low cycle regime. Finally, a fatigue damage calculation method is developed based on a hot spot stress approach.

MATERIAL BEHAVIOR AND STRENGTH UNDER LOW CYCLE CYCLIC LOADS For life prediction in welded joints, it is necessary to define fatigue strength. For fatigue strength within low cycle regime, the general strain-life curve will be employed. The general strain-life curve has the form, See Dowling (1999), ε a

= ε ea

ε  pa

The elastic strain-life curve is defined as ' 

ε ea

=

σ  f 

( 2 N  f  )b

 E  And the plastic strain-life curve is defined as ε  pa

where  N  f 

= ε  f '  ( 2 N  f  )c

= cycles to failure

ε a

= notch strain amplitude

ε ea

= elastic notch strain amplitude

ε  pa

= plastic notch strain amplitude

 E 

= modulus of elasticity

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'

σ  f 

= fatigue strength coefficient

b

= fatigue strength exponent '

ε  f 

= fatigue ductility coefficient

c

= fatigue ductility exponent

This is convenient when dealing with both high and low cycle fatigue as high cycle fatigue analysis is conventionally performed in terms of stress. 104 Open circles: base metal, Grade A Heo et al (2004)

Thus the total strain-life curve can be expressed as ε a

=

'  σ  f 

(2 N  f  )b +  f '  (2 N  f  )c ε 

 E  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, S  PR =  E ε  R

Solid circles: welded joint Heo et al (2004)

   )   a    P    M    (  ,    R

   S  ,   e   g   n   a    R   s   s   e   r    t    S   o    d   u   e   s    P

1000

Total strain-life SSC-346

Elastic strain-life SSC-346

Plastic strain-life SSC-346

Cycles to Failure, N 100 100

1000

104

105

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 nonconservative. 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 '  ~ σ  ≈ σ   f 

-

The fatigue ductility coefficient is approximately equal to the true fracture strain from a tension test '  ~ ε  ≈ ε   f 

-

-

 f 

 f 

Strain-life curves for a wide variety engineering metals tend to all pass near strain εa = 0.01 for a life Nf = 1000 cycles Strain-life curves for a wide variety engineering metals tend to all pass near strain εa = 0.01 for a life Nf = 1000 cycles

Cycle Fatigue Analysis of Marine

of  the of  the

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-

-

Ultimate strength can be approximated from Brinell hardness σ u= 3.45 BHN (MPa) The fatigue strength coefficient can be estimated from ultimate strength ' 

σ  f 

-

≈ σ u + 345

MPa

For steels having an ultimate strength below about σ u = 1400 MPa, a fatigue limit occurs near 106 cycles at a stress amplitude around σa = σ u/2. From the elastic strain-life curve, it follows that

⎛ 2σ  f '  ⎞  ⎟  b=− log ⎜ ⎜ σ u ⎟  6.3 ⎝  ⎠  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

where, 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 K’ (MPa)   N’

A 592

AH32 AH36 DH36 669 694 739 0.114 0.108 0.112 0.106

The cyclic stress-strain curves are plotted in Figure 2.

-

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)], ' 

⎛  σ  ⎞ 1 / n + ⎜⎜ ⎟  ε  = ⎟   E  ⎝  K '  ⎠  σ 

Cycle Fatigue Analysis of Marine

500 DH36 AH36

400

AH32 A

   )   a    P    M    ( 300   s   s   e   r    t    S 200

100

0 0

0.005

0.01

0.015

0.02

Strain

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 strain ε in the material, in   both the elastic and plastic states, to the nominal or  elastic stress S. In terms of stress amplitude: σ a ε a

=

S a2  E 

where σa and εa are stress and strain amplitudes respectively. The elastic stress amplitude is Sa = SL/2 σa and εa is then be determined based on the simultaneous solution of the above two equations. Material strain range, ε  R, is then computed as: ε   R = 2 ε 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.

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S-N CURVE APPLIED FOR LOW CYCLE FATIGUE

100 mm gauge length

Profile flame cut, ground and polished, corners radiused to 1.5 mm

12 mm

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.

AH32

6000

5000

   )   a    P    M    (    L    S  ,   e   g   n   a    R   s   s   e   r    t    S    t   o   p    S    t   o    H   o    d   u   e   s    P

4000

3000

2000

102 mm

152 mm

403 mm 900 mm Ground end

38 mm

c)

8 mm fillet weld

12 mm

152 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.

AH36

DH36 A

Elastic Behavior 

20 mm

1000

11 mm Elastic Hot Spot Stress Range, S E (MPa)

20 mm

0 0

500

1000

1500

2000

2500

400 mm

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.

104

Median (least squares line) m = 2.43

TWI and DSME based on Neuber analysis triangles = TW I circles = DSME

   )   a    P    M    (  ,   e   g   n   a    R   s   s 1000   e   r    t    S    t   o   p    S    t   o    H   o    d   u   e   s    P

Extended D-Curve m=3

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

Median - 2*sigma m = 2.43

100 100

Figure 6: Testing specimen presented in Heo et. al. (2004)

104

1000 Cycles to Failure, N

Figure 4: S-N curve in low cycle region

105

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

Cycle Fatigue Analysis of Marine

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  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,  D B

k 

∑= n S   K  1

=

q  j  Lj

Let,

=

n j n

Dowling, N.E., (1999), Mechanical Behavior of  Materials, Prentice-Hall, Upper Saddle River, NJ.

 f 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,  D B

=

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.

 j 1

 f  j

REFERENCES

k 

∑=  f  S   K  n

q  j  Lj

 j 1

Lee, Y.L., Pan, J., Hathaway, R., and Barkey, M, (2005), “Fatigue Testing and Analysis”, Elsevier  Butterworth – Heinemann, Oxford, UK.

S pj

S j(t)

SLj SBj

Park, S.K. and Lawrence, F.V., (1988), “Fatigue Characterization of Fabricated Ship Details for Design  – Phase II”, Ship Structures Committee, SSC-346.

tcj

ttj

Svj

Figure 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.

Cycle Fatigue Analysis of Marine

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, LuebeckTravemunde, Germany.

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.