-11
INTERNATIONAL COUNCIL
ON COMBUSTION ENGINESCONSEIL INTERNATIONAL
DES MACHINES A COMBUSTION

CO-ORDINATING WORKING GROUP"CLASSIFICATION SOCIETIES – DIESEL"(WG2)

Proposal by CIMAC WG4
3rd of December, 2010

IACS UR M53, Appendix V
Guidance for calculation ofSurface Treated Fillets
and Oil Bore Outlets

-22

Index
1.
2.

Introduction.......................................................................................................... 3
Definition of surface treatment ............................................................................. 3
2.1. Surface treatment methods .......................................................................... 3
3. Calculation principles........................................................................................... 4
3.1. Evaluation of local fillet stresses................................................................... 5
3.2. Evaluation of oil bore stresses...................................................................... 6
3.3. Acceptability criteria ..................................................................................... 8
4. Induction hardening ............................................................................................. 94.1. Local fatigue strength ................................................................................. 10
5. Nitriding ............................................................................................................. 11
5.1. Local fatigue strength ................................................................................. 12
6. Cold forming ...................................................................................................... 13
6.1. Stroke peening by means of a ball ............................................................. 13
6.2. Cold rolling ................................................................................................. 15

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1. Introduction
This appendix deals with surface treated fillets and oil bore outlets. The various
treatments are explained and some empirical formulae are given for calculation
purposes. Conservative empiricism has been applied intentionally, in order to be on
the safe side from a calculation standpoint.
Please note that measurements or more specific knowledge should be used if
available. However, in the case of a wide scatter (e.g. for residual stresses) thevalues should be chosen from the end of the range that would be on the safe side forcalculation purposes.

2. Definition of surface treatment‘Surface treatment’ is a term covering treatments such as thermal, chemical ormechanical operations, leading to inhomogeneous material properties – such as
hardness, chemistry or residual stresses – from the surface to the core.
2.1. Surface treatment methods
The following list covers possible treatment methods and how they influence theproperties that are decisive for the fatigue strength.
Table 2.1. Surface treatment methods and the characteristics they affect.
Treatment method
Induction hardening
NitridingCase hardening
Die quenching (no temper)
Cold rolling
Stroke peening
Shot peening
Laser peening
Ball coining

Affecting
Hardness and residual stresses
Chemistry, hardness and residual stresses
Chemistry, hardness and residual stresses
Hardness and residual stresses
Residual stresses
Residual stresses
Residual stresses
Residual stresses
Residual stresses

It is important to note that since only induction hardening, nitriding, cold rolling andstroke peening are considered relevant for marine engines, other methods are notdealt within this document. In addition die quenching can be considered in the same
way as induction hardening.

-44

3. Calculation principles
The basic principle is that the alternating working stresses shall be below the local
fatigue strength (including the effect of surface treatment) wherein non-propagatingcracks may occur, see also section 6.1 for details. This is then divided by a certain
safety factor. This applies through the entire fillet or oil bore contour as well as below
the surface to a depth below the treatment-affected zone – i.e. to cover the depth all
the way to the core.
Consideration of the local fatigue strength shall include the influence of the local
hardness, residual stress and mean working stress. The influence of the ‘giga-cycle
effect’, especially for initiation of subsurface cracks, should be covered by the choiceof safety margin.
It is of vital importance that the extension of hardening/peening in an area withconcentrated stresses be duly considered. Any transition where thehardening/peening is ended is likely to have considerable tensile residual stresses.
This forms a ‘weak spot’ and is important if it coincides with an area of high stresses.

Stress,Alternating and mean working stresses must be known for the entire area of thestress concentration as well as to a depth of about 1.2 times the depth of thetreatment. The following figure indicates this principle in the case of induction
hardening. The base axis is either the depth (perpendicular to the surface) or along
the fillet contour.

Fatigue strength R = -1
Dynamic working stress

Residual stresses

Figure 3.1. Stresses as functions of depth, general principles.
The acceptability criterion is to be applied stepwise from the surface to the core aswell as from the point of maximum stress concentration along the fillet surface
contour to the web.

-55
3.1. Evaluation of local fillet stresses
It is necessary to have knowledge of the stresses along the fillet contour as well as in
the subsurface to a depth somewhat beyond the hardened layer. Normally this will befound via FEA as described in Appendix III. However, the element size in thesubsurface range will have to be the same size as at the surface. For crankpin
hardening only the small element size will have to be continued along the surface tothe hard layer.
If no FEA is available, a simplified approach may be used. This can be based on theempirically determined stress concentration factors (SCFs), as in M53.3 if within its
validity range, and a relative stress gradient inversely proportional to the fillet radius.
Bending and torsional stresses must be addressed separately. The combination ofthese is addressed by the acceptability criterion.
The subsurface transition-zone stresses, with the minimum hardening depth, can be
determined by means of local stress concentration factors along an axis
perpendicular to the fillet surface. These functions B-local and T-local have different
shapes due to the different stress gradients.
The SCFs B and T are valid at the surface. The local B-local and T-local drop withincreasing depth. The relative stress gradients at the surface depend on the kind ofstress raiser, but for crankpin fillets they can be simplified to 2/RH in bending and
1/RH in torsion. The journal fillets are handled analogously by using RG. The nominal
stresses are assumed to be linear from the surface to a midpoint in the web between
the crankpin fillet and the journal fillet for bending and to the crankpin or journal
centre for torsion.
The local SCFs are then functions of depth t according to Equation 3.1 as shown in
Figure 3.2 for bending and respectively for torsion in Equation 3.2 and Figure 3.3.

B local

B

1 e

2t
RH

0.6

1

T

1 e RH

W2

B

S2

(3.1)

1

t
T local

2 t

1

2 t
D

T

(3.2)

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Stress gradient in bending
Stresses r elated to nomi nal stress

2

1.6

1.2

0.8

0.4

0

RH/2

De pth below surface, mm

W 2 S22
Figure 3.2. Bending SCF in the crankpin fillet as a function of depth. The
corresponding SCF for the journal fillet can be found by replacing RH with RG.
Stress gradient in torsion

Stress related to nominal stress

2.4

2

1.6

1.2

0.8

0.4

0

RH

Depth below surface, mm

D/2

Figure 3.3. Torsional SCF in the crankpin fillet as a function of depth. The
corresponding SCF for the journal fillet can be found by replacing RH with RG and Dwith DG.
If the pin is hardened only and the end of the hardened zone is closer to the fillet than
three times the maximum hardness depth, FEA should be used to determine theactual stresses in the transition zone.
3.2. Evaluation of oil bore stresses
Stresses in the oil bores can be determined also by FEA. The element size should beless than 1/8 of the oil bore diameter DO and the element mesh quality criteria should
be followed as prescribed in Appendix III. The fine element mesh should continue
well beyond a radial depth corresponding to the hardening depth.

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The loads to be applied in the FEA are the torque – see Appendix III item 3.1 – andthe bending moment, with four-point bending as in Appendix III item 3.2.
If no FEA is available, a simplified approach may be used. This can be based on theempirically determined SCF from M53.3 if within its applicability range. Bending andtorsional stresses at the point of peak stresses are combined as in M53.5.

Figure 3.4. Stresses and hardness in induction hardened oil holes.
Figure 3.4 indicates a local drop of the hardness in the transition zone between ahard and soft material. Whether this drop occurs depends also on the tempering
temperature after quenching in the QT process.
The peak stress in the bore occurs at the end of the edge rounding. Within this zone
the stress drops almost linearly to the centre of the pin. As can be seen from Figure
3.4, for shallow (A) and intermediate (B) hardening, the transition point practicallycoincides with the point of maximal stresses. For deep hardening the transition pointcomes outside of the point of peak stress and the local stress can be assessed as a
portion (1-2·tH/D) of the peak stresses where tH is the hardening depth.
The subsurface transition-zone stresses (using the minimum hardening depth) canbe determined by means of local stress concentration factors along an axis
perpendicular to the oil bore surface. These functions B-local and T-local have different
shapes, because of the different stress gradients.
The stress concentration factors B and T are valid at the surface. The local SCFs
B-local andT-local drop with increasing depth. The relative stress gradients at the-88
surface depend on the kind of stress raiser, but for crankpin oil bores they can be
simplified to 4/DO in bending and 2/DO in torsion. The local SCFs are then functionsof the depth t:

B localT local

B

T

1 e
1 e

4t
DO

2t
DO

1

(3.3)

1

(3.4)

3.3. Acceptability criteria
Acceptance of crankshafts is based on fatigue considerations; M53 compares theequivalent alternating stress and the fatigue strength ratio to an acceptability factor of
Q 1.15 for oil bore outlets, crankpin fillets and journal fillets. The term ‘safety factor’is intentionally not used, since the method contains several so-called hidden safeties.
Table 3.1. Some assumptions leading to so-called hidden safety.
I. Analytical equations do not cover complicated crank web
geometries or fillet shapes
II. Three-point bending applies on one crankthrow without
influence from adjacent cranks
III. Full torque applies on the crankpin, i.e. no restraint in main
bearings is included
IV. Stress concentration for torsion and bending occurs at thesame location in a fillet
V. Maximum torsion and maximum bending stresses are in phase
VI. Fatigue strength is assessed without the influence of meanstressFor calculations assuming I-III, even if SCFs are found by FEA, the acceptability
factor of 1.15 should remain. When more accurate calculations are made (e.g. when
one or more of the hidden safeties are bypassed) the acceptability factor turns more
toward the safety factor and a suitable value and approach should be applied.

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4. Induction hardening
Generally the hardness specification shall specify the surface hardness range i.e.
minimum and maximum values, the minimum and maximum extension in or throughthe fillet and also the minimum and maximum depth along the fillet contour.
The induction hardening depth is defined as the depth where the hardness is 80% of
the minimum specified surface hardness.

Figure 4.1. Typical hardness as a function of depth. The arrows indicate the defined
hardening depth. Note the indicated potential hardness drop at the transition to thecore. This can be a weak point as local strength may be reduced and tensile residual
stresses may occur.
In the case of crankpin or journal hardening only, the minimum distance to the fillet
shall be specified due to the tensile stress at the heat-affected zone as shown in
Figure 4.2.

End of thehardened layer

SurfaceHeat-affected
zone
UnheatedregionTensilesurface stresses

Compressive
surface stresses

Figure 4.2. Residual stresses along the surface of a pin and fillet.

-1010If the hardness-versus-depth profile and residual stresses are not known or specified,
one may assume the following:
The hardness profile consists of two layers (see figure 4.1):
o Constant hardness from the surface to the transition zoneo Constant hardness from the transition zone to the core material
Residual stresses in the hard zone of 200 MPa (compression)
Transition-zone hardness as 90% of the core hardness unless the local
hardness drop is avoided
Transition-zone maximum residual stresses (von Mises) of 300 MPa tension
If the crankpin or journal hardening ends close to the fillet, the influence of tensile
residual stresses has to be considered. If the minimum distance between the end of
the hardening and the beginning of the fillet is more than 3 times the maximum
hardening depth, the influence may be disregarded.
4.1. Local fatigue strength
Induction-hardened crankshafts will suffer fatigue either at the surface or at thetransition to the core. The fatigue strengths, for both the surface and the transition
zone, can be determined by fatigue testing of full size cranks as described inAppendix IV. In the case of a transition zone, the initiation of the fatigue can be either
subsurface (i.e. below the hard layer) or at the surface where the hardening ends.
Tests made with the core material only will not be representative since the tensile
residual stresses at the transition are lacking.
Alternatively, the surface fatigue strength (principal stress) can be determined
empirically as follows where HV is the surface (Vickers) hardness. The Equation 4.1
provides a conservative value, with which the fatigue strength is assumed to include
the influence of the residual stress. The resulting value is valid for a working stressratio of R = -1:
Fsurface

400 0.5 ( HV

400)

[MPa]

(4.1)

It has to be noted also that the mean stress influence of induction-hardened steels
may be significantly higher than that for QT steels.
The fatigue strength in the transition zone, without taking into account any possible
local hardness drop, shall be determined by the equation introduced in UR M53.6.
For journal and respectively to crankpin fillet applies:

Ftransitio n ,cpin

K (0.42B39.3) 0.264 1.073 Y 0.2

Where
Y = DG and X = RG
Y = D and X = RH

for journal fillet
for crankpin fillet

785
B
4900

196
B

1
X

(4.2)

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The influence of the residual stress is not included in 4.2.
For the purpose of considering subsurface fatigue, below the hard layer, thedisadvantage of tensile residual stresses has to be considered by subtracting 20%
from the value determined above. This 20% is based on the mean stress influence ofalloyed quenched and tempered steel having a residual tensile stress of 300 MPa.
When the residual stresses are known to be lower, also smaller value of subtraction
shall be used. For low-strength steels the percentage chosen should be higher.
For the purpose of considering surface fatigue near the end of the hardened zone –i.e. in the heat-affected zone shown in the Figure 4.2 – the influence of the tensile
residual stresses can be considered by subtracting a certain percentage, in
accordance with Table 4.1, from the value determined by the above formula.
Table 4.1. The influence of tensile residual stresses at a given distance from the endof the hardening.
I.
II.
III.
IV.

0 to 1.0 of the max. hardening depth: 20%
1.0 to 2.0 of the max. hardening depth: 12%
2.0 to 3.0 of the max. hardening depth: 6%
3.0 or more of the max. hardening depth: 0%

5. Nitriding
The hardness specification shall include the surface hardness range (min and max)
and the minimum and maximum depth. Only gas nitriding is considered.
The depth of the hardening is defined in different ways in the various standards andthe literature. The most practical method to use in this context is to define thenitriding depth tN as the depth to a hardness of 50 HV above the core hardness.
The hardening profile should be specified all the way to the core. If this is not known,
it may be determined empirically via the following formula:t

HV (t )

HVcore ( HVsurface

HVcore )tN

50
HVsurface

HVcoreWhere:t=
HV(t) =
HVcore =HVsurface =tN=

2

The local depth
Hardness at depth t
Core hardness
Surface hardness
Nitriding depth as defined above(5.1)

-12125.1. Local fatigue strength
It is important to note that in nitrided crankshaft cases, fatigue is found either at thesurface or at the transition to the core. This means that the fatigue strength can be
determined by tests as described in Appendix IV.
Alternatively, the surface fatigue strength (principal stress) can be determined
empirically and conservatively as follows. This is valid for a surface hardness of
600HV or greater:
Fsurface(5.2)

450 MPa

Note that this fatigue strength is assumed to include the influence of the surface
residual stress and applies for a working stress ratio of R = -1.
The fatigue strength in the transition zone can be determined by the equation
introduced in UR M53.6. For crankpin and respectively to journal applies:

Ftransitio n ,cpin

K (0.42B39.3) 0.264 1.073 Y 0.2

785
B
4900

196
B

1
X

(5.3)

Where
Y = DG and X = RG
Y = D and X = RH

for journal fillet
for crankpin fillet

Note that this fatigue strength is not assumed to include the influence of the residual
stresses.
In contrast to induction-hardening the nitrited components have no such distinct
transition to the core. Although the compressive residual stresses at the surface are
high, the balancing tensile stresses in the core are moderate because of the shallow
depth. For the purpose of analysis of subsurface fatigue the disadvantage of tensile
residual stresses in and below the transition zone may be even disregarded in viewof this smooth contour of a nitriding hardness profile.
Nevertheless, in principle the calculation should be carried out along the entire
hardness profile and it can be limited to a simplified approach of examining thesurface and an artificial transition point. This artificial transition point can be taken at
the depth where the local hardness is approximately 20 HV above the core hardness.
In such a case, the properties of the core material should be used. This means thatthe stresses at the transition to the core can be found by using the local SCF
formulae mentioned earlier when inserting t=1.2 tN.

-1313Figure 5.1. Sketch of the location for the artificial transition point in the depth
direction.

6. Cold forming
The advantage of stroke peening or cold rolling of fillets is the compressive residual
stresses introduced in the high-loaded area. Even though surface residual stresses
can be determined by X-ray diffraction technique and subsurface residual stresses
can be determined through neutron diffraction, the local fatigue strength is virtually
non-assessable on that basis since suitable and reliable correlation formulae are
hardly known.
Therefore the fatigue strength has to be determined by fatigue testing; see also
Appendix IV. Such testing is normally carried out as four-point bending, with aworking stress ratio of R = -1. From these results the bending fatigue strength –surface- or subsurface-initiated depending on the manner of failure – can be
determined and expressed as the representative fatigue strength for applied bending
in the fillet.
In comparison to bending, the torsion fatigue strength in the fillet may differ
considerably from the ratio 3 (utilized by the von Mises criterion). The formingaffected depth that is sufficient to prevent subsurface fatigue in bending, may stillallow subsurface fatigue in torsion. Another possible reason for the difference inbending and torsion could be the extension of the highly stressed area.
The results obtained in a full size crank test can be applied for another crank size
provided that the base material (alloyed Q+T) is of the same type and that theforming is done so as to obtain the same level of compressive residual stresses atthe surface as well as through the depth. This means that both the extension and thedepth of the cold forming must be proportional to the fillet radius.
6.1. Stroke peening by means of a ball
The fatigue strength obtained can be documented by means of full size crank tests orby empirical methods if applied on the safe side. If both bending and torsion fatigue
strengths have been investigated and differ from the ratio 3, the von Mises criterion
should be excluded.

-1414
If only bending fatigue strength has been investigated, the torsional fatigue strength
should be assessed conservatively. If the bending fatigue strength is concluded to be
x% above the fatigue strength of the non-peened material, the torsional fatigue
strength should not be assumed to be more than 2/3 of x% above that of the nonpeened material.
As a result of the stroke peening process the maximum of the compressive residual
stress is found in the subsurface area. Therefore, depending on the fatigue testing
load and the stress gradient, it is possible to have higher working stresses at thesurface in comparison to the local fatigue strength of the surface. Because of thisphenomenon small cracks may appear during the fatigue testing, which will not beable to propagate in further load cycles and/or with further slight increases of thetesting load because of the profile of the compressive residual stress. Put simply, thehigh compressive residual stresses below the surface ‘arrest’ small surface cracks.
This is illustrated in Figure 6.1 as gradient load 2.

Figure 6.1. Working and residual stresses below the stroke-peened surface. Straightlines 1…3 represent different possible load stress gradients.
In fatigue testing with full-size crankshafts these small “hairline cracks” should not be
considered to be the failure crack. The crack that is technically the fatigue crack
leading to failure, and that therefore shuts off the test-bench, should be considered-1515for determination of the failure load level. This also applies if induction-hardened
fillets are stroke-peened.
In order to improve the fatigue strength of induction-hardened fillets it is possible toapply the stroke peening process in the crankshafts’ fillets after they have been
induction-hardened and tempered to the required surface hardness. If this is done, it
might be necessary to adapt the stroke peening force to the hardness of the surface
layer and not to the tensile strength of the base material. The effect on the fatigue
strength of induction hardening and stroke peening the fillets shall be determined bya full size crankshaft test. See Appendix IV.
Fatigue results from tests on one crankshaft may be used for a similar crankshaft if
all of the following criteria are fulfilled:
Ball size relative to fillet radius within 90 ± 5%
At least the same circumferential extension of the stroke peening
At least the same angular extension of fillet contour stroke-peened
Similar base material, e.g. alloyed quenched and tempered
Forward feed of ball of the same proportion of the radius
Force applied to ball proportional to base material hardness (if different)
Force applied to ball proportional to square of ball radius
6.2. Cold rolling
The fatigue strength can be obtained by means of full size crank tests or by empiricalmethods if these are applied so as to be on the safe side. If both bending and torsion
fatigue strengths have been investigated, and differ from the ratio 3, the von Mises
criterion should be excluded.
If only bending fatigue strength has been investigated, the torsional fatigue strength
should be assessed conservatively. If the bending fatigue strength is concluded to be
x% above the fatigue strength of the non-rolled material, the torsional fatigue strength
should not be assumed to be more than 2/3 of x% above that of the non-rolledmaterial.
Fatigue test results from testing of a crankshaft may be applied to another crankshaft
if that crankshaft is similar and all of the following criteria are fulfilled:
At least the same circumferential extension of cold rolling
At least the same angular extension of fillet contour rolled
Similar base material, e.g. alloyed quenched and tempered
Roller force to be calculated so as to achieve at least the same relative (to fillet
radius) depth of treatment