Appendices D-G

144 Pages·2015·5.64 MB·English

Appendix D
Fatigue Crack Growth
Analyses of Propeller Shaft
by Det Norske Veritas
D N V
ET ORSKE ERITASTM
REPORT

FATIGUE CRACK GROWTH
ANALYSES OF PROPELLER SHAFT

Interislander

DNV Doc. No./Report No.: 18Q5SWV-1/2014-3010
Date of Issue: 2014-01-17
Revision: 0

Project Name: Fatigue crack growth analyses of propeller shaft
Report Title:

Table of Contents

1  EXECUTIVE SUMMARY ........................................................................................................ 4 
2  INTRODUCTION ...................................................................................................................... 4 
2.1  Objective 4 
2.2  Assessment premises 4 
3  ABBREVIATIONS .................................................................................................................... 5 
4  THE PRINCIPAL OF FRACTURE INTEGRITY ASSESSMENTS ........................................ 6 
5  DESCRIPTION OF THE FRACTURE MECHANICS ANALYSES ....................................... 8 
5.1  Unstable fracture 8 
5.2  Fatigue crack growth analyses 9 
6  RESULTS ................................................................................................................................. 11 
6.1  Critical flaw height 11 
6.2  Fatigue life until 140.8mm flaw height 12 
7  CONCLUSIONS ...................................................................................................................... 14 
8  REFERENCES ......................................................................................................................... 14 

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1 EXECUTIVE SUMMARY
One of two propeller shafts of the Interislander’s vessel Arater has broken. Interislander is questioning
if the vessel may sail with the remaining propeller to Singapore or another port for repair.
DNV GL Materials Laboratory Section has performed fracture mechanics fatigue crack growth and
unstable fracture assessments to determine the remaining fatigue life time based on different input
assumptions.
A conclusion on the remaining fatigue life must be interpreted based on the NDT performed and the
findings in this report.

2 INTRODUCTION
One of two propeller shafts of the Interislander’s vessel Arater has broken. Interislander is questioning
if the vessel may sail with the remaining propeller to Singapore or another port for repair.
The remaining shaft has been subject to NDT inspection without any indication of fatigue cracks.
However, it is not possible to guarantee that there is no fatigue cracks in the shaft because limitations
with the NDT equipment. Hence, it has been assumed that the shaft may have up to 5-10mm deep
fatigue cracks.
DNV GL has been contracted by Interislander to perform fracture mechanics analyses in order to
evaluate the remaining fatigue life until unstable fracture or an unacceptable large fatigue crack has
developed.
Various levels of initial flaw sizes, different fracture toughness propertries, different crack growth
parameters and maximum stress levels have been assumed and the remaining service life until unstable
fracture have been calculated.
No calculations or evaluations of the fractured shaft are included in this report.

2.1 Objective
The objective of this report is to summarize the fracture integrity assessments performed for the
remaining shaft of Arater. The results may be used to give a robust evaluation of the remaining service
life based on information about cracks from NDT inspection.

2.2 Assessment premises
Information relevant for the fracture mechanics analyses are summarized in Table 2-1.
Table 2-1 Relevant input parameters
Parameter/description Value
Shaft diameter, D 352 mm
Shaft material C-Mn steel, similar to C40 or maybe S355J2G3+N
Specified minimum yield stress, SMYS Probably around 320-360MPa
Specified minimum tensile strength, SMTS Probably around 450-500MPa
E-modulus 207000 N/mm2
Poison’s ratio 0.3
Temperature range Not considered to affect material properties and the
assessments

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Project Name: Fatigue crack growth analyses of propeller shaft
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Fracture mechanics analyses are a valid tool for assessing the criticality of plan ar flaws and cracks.
DNV GL has no information about planar flaws or cracks in the remaining shaft, but it is understood
that NDT has been performed without findings. However, it is not for sure that the NDT technique
used is able to detect cracks with heights less than 5-10mm. Hence, various initial flaw sizes have been
assumed. The fatigue crack growth has been assessed for the initial crack sizes to grow to the critical
flaw size for different maximum stress levels and fracture toughness properties. For some of the
assessments the calculated fatigue life is not limited by unstable fracture, but geometry limitations for
the various formulas used in the assessments, i.e. those cases will be somewhat conservative.
DNV has currently no detailed information about the exact shaft material designation or the fracture
toughness properties of the propeller shaft, but different values have been assumed.

3 ABBREVIATIONS
CDF Crack driving force, term used to describe how “loaded” the crack tip
is. The measure for CDF in ductile materials under static loading is
the applied J or CTOD and K for dynamic loading

CTOD Crack tip opening displacement. A measure describing how much a
crack opens during loading. CTOD is used both as a measure for
CDF (CTOD ) and a measure for the fracture toughness property of
app
a material (CTOD )
mat

J The J- integral. This is a measure that similarly to CTOD describes
the fracture toughness properties of a material or the CDF

K, K Stress intensity factor. Parameter describing the fracture toughness
properties or the CDF considering quite low loading, brittle materials
or dynamic loading (fatigue crack growth)

J R- curve, CTOD R- curve Describes a material’s resistance to crack growth either expressed in
terms of J or CTOD

NDT Non-Destructive Testing

OD Outer diameter

P , P Bending stress and bending stress range in accordance with BS7910
b b

a Flaw height (surface breaking flaw)

2SD Two standard deviations

WT Wall thickness

RPM Revolutions per minute

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4 THE PRINCIPAL OF FRACTURE INTEGRITY ASSESSMENTS
The principle of fracture integrity assessments are simple and are in general an equilibrium evaluation
between the conditions trying to open up a flaw in a structural part and the materials resistance to open
up. These parameters are normally referred as the Crack Driving Force (CDF) and the fracture
toughness/tearing resistance if static loads are considered. Similarly if dynamic stresses are considered
the crack driving force is normally described by K which is calculated based on the dynamic stress
I
ranges and geometry and the materials resistance to fatigue crack growth described by fatigue crack
growth parameters. The principal of fracture mechanics are illustrated in Figure 4-1.
Crack Driving Force (CDF) Fracturetoughness (materials resistance)

Who is the
strongest?
Analyses/Calculations Testing

Figure 4-1 The principal of fracture mechanics analyses
Considering static loads the crack driving force is normally assessed according to formulas in specific
rules and standards or directly by FE analyses. For normal ductile metallic materials and static loads
the CDF is normally characterized by J or CTOD and the fracture toughness is characterized as
app app
J or CTOD or, J R- or CTOD R- tearing resistance curves, in case of tearing assessment. Both the
mat mat
fracture toughness and tearing resistance must be established by testing.
For dynamic loads where the crack driving force typically is lower the linear-elastic stress intensity
factor K is normally used both for applied K (for a given stress range) and for describing the
I
materials fatigue crack growth properties, da/dN = A(K)m referred as the Paris equation. K is
I
calculated according to BS7910 given the applied stress range and geometry of the structural detail and
flaw. The fatigue crack growth parameters are established from testing, but normally values according
to BS7910 are used.
In many cases it is necessary to consider both fracture given a maximum stress condition and the crack
growth considering fatigue loading as illustrated in Figure 4-2.

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Critical flaw length
Initial flaw length
Initial flaw
Fatigue height Critical
crack growth flaw height
Fatigue life
e
iz Critical flaw size or through thickness flaw (leakage)
s
w
a
l - Increased max applied stress
F
- Reduced fracture toughness
Time to initiate a fatigue Initial flaw size
crack (not known)
Number of cycles or time
Fatigue life until “failure”

Figure 4-2 Illustration of fatigue crack growth until unstable fracture
The accuracy of the fracture integrity assessments are depending on many factors as for instance:
─ Description of global static and dynamic loads
─ Local geometry and local stress conditions
─ Materials stress-strain curve
─ The flaw size
─ How accurately the CDF is calculated (both statically and dynamically)
─ How representative the fracture toughness/tearing resistance properties are
─ How accurate the fatigue crack growth properties are specified
─ The failure criterion used (critical flaw size, specified flaw size, leakage etc.)
─ How the effect of weld residual stresses are implemented
A good tool for evaluating how important the different inputs are is to establish a good probabilistic
model or to perform several input sensitivity analyses.

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5 DESCRIPTION OF THE FRACTURE MECHANICS ANALYSES
The analyses are in general performed in accordance with BS7910, ref. /1/, and the Crakwise software,
ref. /2/, has been used.

5.1 Unstable fracture
The unstable fracture is mainly depending on the maximum stress normal to the crack that needs to be
considered and the fracture toughness property of the material.
Hence, it is difficult to predict the fracture capacity of the shaft when theses input parameters are
uncertain. However, some values which are believed to be representative have been assumed. The
inputs are summarized in Table 5 -1.
As long as the fracture toughness properties are not significantly lower than normally expected and/or
the maximum stress is not very high, the unstable fracture is typically not important for the remaining
fatigue life considering relatively small initial cracks.
A shaft speed of 160 RPM and 5200 kW has been estimated to give bending moment of 165 kNm
which gives a bending stress P equal to 38.6 MPa. The shaft speed is now specified to be 140 RPM
b
and using the propeller low the bending moment is calculated as 1402/1602 = 0.77x165 = 126.3 kNm.
According to propeller experts a 50% increase on that is a conservative estimate of the extreme
bending stress in the shaft. Hence, a reasonable extreme bending stress is 44.4MPa.

Table 5-1 Inputs applied in the fracture mechanics analyses to assess the critical flaw size
Parameter Value(s)
Analysis approach BS7910, Level 2B
Stress-strain curve Assumed, based on SMYS 350MPa and SMTS 500MPa with yield
plateau (conservative assumption). See Figure 5-1
Stress intensity factor (SIF) solution Semi-circular surface flaw in round bar, BS7910 M.6.2
Reference stress solution Straight-fronted and semi-circular flaws in round bar/bolt, BS7910
P.6.1
Diameter, D 352mm
Maximum bending stress, P 44.4MPa. This will normally allow large flaws before unstable
b
fracture and in general unstable fracture will not influence on the
fatigue life assessed. However, larger bending stresses have also been
assessed.
Fracture toughness values Not known, CTOD = 0.05, 0.1 and 0.2mm assumed for the
calculations
Fracture toughness conversion factor, 1.0 (conservative assumption)
X (constraint factor ref. BS7910)

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Project Name: Fatigue crack growth analyses of propeller shaft
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600
Assumed stress-strain curve
500
400
a
p
M
s,
s
e
r
st300
g
n
ri
e
e
n
gi
n200
E
100
0
0 1 2 3 4 5 6 7 8 9 10
Engineering strain, %

Figure 5-1 Assumed stress-strain curve representative for the shaft material
The fracture mechanics model describing a semi-circular surface flaw in a round bar has geometry
limitations and it is not possible to calculate a fatigue crack through the whole thickness. The results
are shown in Section 6.

5.2 Fatigue crack growth analyses
It has been assumed that Arater will sail at 160 RPM at power 5200 kW, i.e. 8400 revolutions per hour
and 201,600 revolutions (load cycles) per day. According to rough estimated performed by the
Machinery Section at DNV GL the dynamic stress range is P = 77.1MPa based on 160 RPM and
b
5200 kW.
Normally the shaft will be covered in oil and the fatigue crack growth parameters for air environment
in accordance with BS7910 should be applicable. However, some extent of seawater cannot be ruled
out and crack growth parameters for marine environment and free corrosion have also been assessed.
The mean crack growth parameters (expected values) and the crack growth parameters for mean plus
two standard deviations (characteristic design values) have been used. The parameters are in
accordance with BS7910 and are summarized in Table 5-2.

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