

Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

51, 2, pp. 439-446, Warsaw 2013

FRACTOGRAPHICALLY-AIDED ANALYSIS OF FISH-EYE CRACK

GROWTH IN NITRIDED STEEL

Karel Slámečka, Jaroslav Pokluda

Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czech Republic

e-mail: slamecka@fme.vutbr.cz

Marta Kianicová

Alexander Dubček University in Trenč́ın, Faculty of Industrial Technologies of Púchov, Púchov, Slovakia

e-mail: kianicova@tnuni.sk

An analysis of the internal fish-eye crack growth in a plasma-nitrided high-strength low-
alloy steel specimen has been performed. The study combines information obtained from
the fractographical observation of the striations field located near the centre of the fish-eye
crack on the specimen subjected to combined bending-torsion loadingwith the linear elastic
fracturemechanicsmodelling of the fatigue crack propagation. The results suggest that the
propagation stage constitutes only a minor part of the total fatigue life, the major part of
which is spent on the fatigue crack initiation. This conclusion is consistent with the high
cycle and very high cycle fatigue behaviour of specimens without any surface hardening
layer.

Key words: fish-eye, striations, fractography, nitrided steel

1. Introduction

Case hardening processes, such as nitriding, induction hardening, carburization or shot peening
are important technologies that are used to improve surface hardness, fatigue strength andwear
and corrosion resistances of crankshafts, gears, valve parts, extrusion and forging dies andmany
other engineering components (Agarwal et al., 2007;DeLaCruz et al., 1998; Dvořák andHanák,
1999; Genel et al., 2000; Pokluda et al., 2006; Shiozawa and Lu, 2001; Sirin and Kaluc, 2008;
Slámečka et al., 2010; Song and Choi, 2003). The nitriding procedure features adsorbtion of
nitrogen atoms in the form of N+ ions or NH+, NH2 andNH3 radicals and subsequent diffusion
of these species into the volume resulting in formation of a hard surface layer consisting of a
very thin compound layer (the so-called white layer) composed of different iron nitride phases
and an extensive subsurface diffusion zone.
The strong residual compressive stress field,which is introducedwithin thediffusion zone and

the near corematerial due to a lattice distortion, is themain cause of significant improvement of
fatigue limit of a component. Enhanced surface strength and diminishedmobility of dislocations
within the diffusion zone causes that the principal crack nucleation site is usually located at
some defect (mostly a non-metallic inclusion) in the core material in both the low cycle fatigue
(LCF) and the high cycle fatigue (HCF) regions. The initiation stage proceeds by decohesion of
the inclusion-matrix interface, after which the crack propagates in an elliptical manner forming
a distinct internal fracture pattern known as the “fish-eye”. When the crack front approaches
sufficiently close to the free surface, a rapid propagation through the low-toughness nitrided
layer occurs, which is followed by an accelerated atmosphere-assisted fatigue crack propagation
and subsequentfinal quasistatic failure (Dvořák andHanák, 1999; Pokluda et al., 2006; Slámečka
et al., 2010), Fig. 1. On the other hand, when the loading levels are high enough to damage the
nitrided layer (very low cycle fatigue), the failure occurs due to the fatigue fracture initiated


440 K. Slámečka et al.

at the surface. The existence of two characteristic failure modes is usually manifested in the
S-N curve as a change of the slope at stress levels corresponding to the onset of the internal
fatigue crack initiation or as the transitional plateau. Analogous fracture behaviour has also
been reported for other case hardening technologies (Agarwal et al., 2007; Shiozawa and Lu,
2001; Song and Choi, 2003).

Fig. 1. SEM image of the fish-eye crack in the specimen subjected to combined bending-torsion loading.
The bending and torsion amplitudes, σa, τa, and the number of cycles to fracture, Nf, were:
σa =850MPa, τa =310MPa and Nf =2.6×105 cycles. Numbers of cycles N1-N5 correspond to

individuals fracture process phases

In the very-high cycle fatigue (VHCF) region, the internal fish-eye crack initiation is almost
invariably observed even for specimens without any surface reinforcing layers. In this case, the
time span of crack propagation inside the fish-eye has been theoretically tackled by Wang et
al. (2002) and by Marines-Garcia et al. (2007) by using the Paris-Hertzberg-McClintock crack
growth rate law. Results of these calculations, which were experimentally confirmed by infrared
pyrometrymeasurements (Ranc et al., 2008), showthat the initiation stage constitutes themajor
part of the total fatigue life while the residual fatigue life is practically negligible.
Recently, we have identified a distinct striations field in the centre of the fish-eye crack

in Fig. 1. A simplified estimate of the residual life based on the striation spacing data was
attempted leading to a conclusion that the crack growth period constituted only 1-7% of the
total fatigue life in the HCF region (Slámečka et al., 2011). The aim of this paper is to present
an improved assessment of the time span of the crack propagation inside the fish-eye region by
using the striation-spacing data according to Slámečka et al. (2011) in combination with the
crack-propagation law based on the linear elastic fracture mechanics (Klesnil and Lukáš, 1992;
Ruckert et al., 2006).

2. Biaxial fatigue of nitrided steel specimens: summary of main results

Thematerial used for biaxial fatigue experimentswas nitrided high-strength low-alloyCr-Al-Mo
steel (equivalent to EN37CrAlMo6) with the chemical composition [wt%] as follows: C: 0.357%,
Mn: 0.468%, Cr: 1.49%, Mo: 0.194%, V: 0.01%, Cu: 0.072%, Al: 1.4%, W: 0.032%, Si: 0.292%,
P: 0.006%, S: 0.006%, Fe: balance. Heat treatment of specimens consisted of annealing (920◦C,
25min, air), quenching (930◦C, 25min, oil) and tempering (650◦C, 25min, air). Themicropulse
plasmanitridingprocedure consisting of cleaning (510◦C,30min) andnitriding (515◦C, 8hours)
resulted in the formation of the nitrided layer of thickness hl ≈ 200µm.


Fractographically-aided analysis of fish-eye crack... 441

Biaxial fatigue experimentswere carried out on cylindrical specimensbymeans of the testing
stand MZGS-200. Sinusoidal symmetrical bending (5 specimens), torsion (3 specimens) and
synchronous in-phase bending-torsion loading combinations (15 specimens) were applied with a
frequency f ≈ 30Hz at room temperature. All specimens were fractured in the HCF domain
with the number of cycles to failure Nf found in the range of (2.0×105;6.1×106) cycles. The
results of extended experimental investigation on the influence of nitriding on the fatigue life
under biaxial fatigue loading and also under the conventional push-pull loading of different R-
ratios were presented elsewhere (Pokluda et al., 2006). It is sufficient to note that themicropulse
plasma nitriding procedure was found to increase the fatigue resistance by about 25% for all
loading regimes.

Detailed inspection of fracture surfaces was carried out by means of the scanning electron
microscopy (SEM), the optical profilometry and the stereophotogrammetry. The examination
revealed that all specimens failed due to the internal fish-eye crack nucleated on the inclusion
of some complex oxidic type (Al, Si, Ca, Mn) located bellow the diffusion zone at depth h
in the range of 420-1040µm. All fish-eye cracks were of a semi-elliptical shape. The fatigue
crack growth rate was always partially reduced in the direction towards the free surface due
to increasing residual compressive stresses. This retardation effect was prominent especially in
the case of fish-eye cracks initiated at inclusions at depths h< 0.7mm, e.g. the fish eye crack
shown in Fig. 1. The deflection of the fish-eye macroscopic plane from the plane perpendicular
to the specimen axis was almost negligible in the radial direction (αr always less than 5

◦). On
the other hand, the inclination angle in the tangential direction αt varied as a function of the
loading regime, with αt ≈ 0◦ for pure bending and αt ≈ 45◦ for pure torsion. Inmost cases, the
spatial orientation of fish-eye cracks corresponded well to the orientation of themajor principal
planemeaning that the crack front tended to propagate undermode I loading. For example, the
average inclination angles of profiles intercepting the centre of the fish-eye shown in Fig. 1 in
the radial and tangential directions weremeasured as αr ≈ 2◦ and αt ≈ 16◦, which is very close
to the orientation of the major principal plane at the inclusion at the maximum of the loading
cycle (αr ≈ 0◦ and αt ≈ 20◦).

Fig. 2. The striation field located near the centre of the fish-eye crack from Fig. 1

The predominant role ofmode Imicromechanism has also been confirmed by the presence of
the striations field located in the immediate vicinity of the inclusion in the centre of this fish-eye
crack, Fig. 2. The distinct striation pattern with a very low striation spacing (less than 100nm
close to the inclusion) reveals continuous crack front propagation, which probably occurred in a
partially softenedmaterial created by depletion of the alloying elements and carbon due to their


442 K. Slámečka et al.

diffusion towards the incoherent inclusion/matrix interface. This idea seems to be confirmed by
the energy dispersive X-ray analysis of locations inside/outside the striation field. Despite the
lower precision of measurements that were taken from the fracture surface, the content of most
elements is clearly lower inside the striation field,most notably the content of Al obtained as an
average from two point measurements drops from 1.50 to 1.35, Si shows drop from 0.48 to 0.43
and the content of Cr drops from 1.62 to 1.52wt%, respectively. The striation spacing datawere
used to simplified estimation of the time span of the crack propagationwithin the fish-eye region
leading to the conclusion that most of the fatigue life is spent on the fatigue crack initiation
period (Slámečka et al., 2011). In the following Section, these crack growth rate data are used
for the linear elastic fracture mechanics assessment of the fish-eye crack growth period.

3. Analysis of the fish-eye crack growth

Asmentioned earlier, the HCF failure process of the investigated nitrided steel specimens com-
prises several phases. These are: (i) initiation of the internal fatigue crack, which usually occurs
by decohesion of the inclusion-matrix interface (the corresponding number of cycles denoted
as N1), (ii) its propagation within the fish-eye region (N2 cycles), (iii) breakage of the crack
through the lower-toughness nitrided zone (N3 cycles), (iv) accelerated atmosphere assisted
crack growth from the specimen surface, and (N4 cycles), (v) the final quasistatic fracture
(N5 cycles), Fig. 1. The total fatigue life can be thus written as a sum of five terms correspon-
ding to individual numbers of cycles

Nf =N1+N2+N3+N4+N5 (3.1)

Considering that N5 ≈ 1, N4 is in the order of hundreds of cycles in magnitude (estimated
by integration of the Forman formula) and N3 is easily negligible based on the fractographical
observations (Dvořák andHanák, 1999), themajority of the fatigue lifemust clearly be spent on
the fish-eye crack initiation and its propagation within the fish-eye region. Since the transition
short/long crack in high-strength steels is in the order of tens µm inmagnitude and, therefore,
the crack can be assumed to be a long one already after the initiation period, the number of
cycles N2 can be estimated by integrating the long fatigue crack growth rate formula. For this
purpose, the Klesnil-Lukš relationship for the long near-threshold fatigue crack propagating
under asymmetric loading has been adopted in the following form (Klesnil and Lukáš, 1992)

da

dn
=A((Pγ∆K)n− (Pγ∆Kth)n) (3.2)

where da/dn is the fatigue crack growth rate, ∆K is the stress intensity factor range, A and
n are constants dependent on thematerial and the ambient environment, γ≈ 0.7 and ∆Kth is
the threshold stress intensity factor range and the parameter P related to the stress ratio R as

P =
2

1−R
(3.3)

reflects the local loading asymmetry caused by the presence of residual stresses.

The considered fish-eye crack has been modelled as a circular crack in a shaft propagating
under the range of the bending stress equal to the range of the principal stress ∆σ1. The
employedmodel is a reasonable approximation of the real situation due to the spatial orientation
of the fish-eyemacroscopic plane (as discussed above) and the fact that the biaxiality of loading
could be neglected since the principal stress σ3 is almost an order of magnitude lower than
the principal stress σ1. Considering the geometry of the problem, the stress intensity factor


Fractographically-aided analysis of fish-eye crack... 443

range ∆K at thedeepest point on the crack frontpropagating fromthe central inclusion towards
the specimen centre is given as (Chen et al., 1992)

∆K =FB
( s√
2.464Rsp

−0.4246 a
Rsp

)

∆σ1
√
πa (3.4)

where a is the crack length, s ≈ 3.8mm is the distance of the inclusion from the specimen
centre, Rsp =4.25mm is the specimen radius, and

FB =1+0.018
[

1+
(Rsp−s
Rsp

)0.3]( a

Rsp−s
)2

tan
πa

2(Rsp−s)
(3.5)

The distribution of residual stresses in the specimen and the fitting curve used for the esti-
mation of the parameters of asymmetry R and P within the fish-eye region is shown in Fig. 3.
The data represented by the full square symbols were obtained by precise X-ray measurements

Fig. 3. The experimental profile and theoretical estimation of the residual stress σres as a function of
depth h. The scheme in the inset figure shows a general shape of the residual stress curve along the

specimen radius

of the specimensmade of an equivalent high-strength steel with the same depth of the nitrided
layer (Onuki et al., 1992). The empty circles show the data estimated by combined fractographi-
cal/strength analysis of our specimens subjected to pure bending (Slámečka et al., 2010). Note
that these results correctly predict small tensile stresses present at the depth h> 0.7mm com-
pensating for the compressive stress field.Byusing thefitting curve fromFig. 3, theparameter P
as a function of the crack length a may be expressed as

P =−61290a2+668.1a+0.865 (3.6)

The constants A and n can be foundby fitting the ∆K−da/dn data by formula (3.2). Since
the striations clearly occurred in apartially softenedmaterial, we considered ∆Kth =6MPa

√
m

corresponding to amild steel (Lampman, 1996). The values of both fitting parameters A,n and
their uncertaintieswere obtained by the nonlinear least-squaresMarquardt-Levenberg algorithm
as follows: A = 1.19× 10−13 ± 1.05× 10−13 and n = 7.12± 0.53 (for the crack growth rate
da/dn in m/cycle and stress intensity factor ranges ∆K, ∆Kth in MPa

√
m units), Fig. 4. In

comparison with atmosphere fracture behaviour of tempered (A ≈ 2.2× 10−11, n ≈ 2.6) and
an ion-nitrided material (A ≈ 6.8× 10−14, n ≈ 4.3), the results shows a higher exponent n.
This could probably be attributed to the uncertainties in the stress intensity factor range ∆K


444 K. Slámečka et al.

Fig. 4. The striation data fitted by crack growth rate formula (3.2)

caused by the circular approximation of the fish-eye crack in this early stage and uncertainty in
the value of ∆Kth.

The number of cycles related to fatigue crack propagation within the fish-eye region reads

N2 =

af
∫

ai

da

A((Pγ∆K)n− (Pγ∆Kth)n)
(3.7)

By using the initial crack length ai =13.6µm (half-size of the inclusion) and the final crack
length af =450µm (distance from the inclusion to location of themaximum fish eye depth) as
the integration bounds, the number of cycles for the fish-eye crack growth N2 was calculated as
N2 ∈ 〈59;6655〉 cycles. The most probable (mean) value of the number of cycles N2 is several
thousand cycles and, even for themost extremevalues of theparameters A and n, thenumberof
cycles N2 is always less than 3% of the total fatigue life Nf. In spite of an estimative character
of the performed analysis (several numerical approximations, assumption of a circular shape,
limited crack growth rate data from the locally differentmaterial), these results suggest that the
major part of the total HCF fatigue life in the nitrided steel specimen was spent in the fatigue
crack initiation phase. This behaviour is consistent with the high-cycle and the ultra-high-cycle
fatigue behaviour of smooth specimens without any surface hardening treatment.

4. Conclusions

An analysis of the fish-eye crack growth in the plasma-nitrided high-strength low-alloy steel
specimen subjected to symmetrical in-phase bending-torsion loading has been performed. By
combining the local crack growth rate data obtained from the fractographical observation of
the striations field found near the inclusion in the centre of the fish-eye crack with the linear
elastic fracture mechanics modelling of the long fatigue crack growth in the near-threshold and
the Paris regions, the number of cycles for the fish-eye crack growth was estimated to be in the
order of thousands of cycles inmagnitude. This result suggests that the total crack propagation
stage constitutes only a minor part of the fatigue life, which is in a qualitative agreement with
both the high-cycle and the ultra-high-cycle fatigue behaviour of specimens without reinforced
surface layers.


Fractographically-aided analysis of fish-eye crack... 445

Acknowledgements

We thank Prof. A. Shanyavskiy from the State Center for Civil Aviation Flights Safety, Moscow,

for fruitful discussions concerning the studied topic. The work was supported by Brno University of

Technology (project FSI-S-11-18) and Czech Science Foundation (project P108/10/0698).

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17. SongS.-H.,Choi B.-H., 2003,Fatigue characteristics and fatigue limit prediction of an induction
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446 K. Slámečka et al.

Fraktograficznie wspomagana analiza wzrostu pęknięć typu rybie oczy w stali azotowanej

Streszczenie

W pracy przedstawiono analizę wzrostu wewnętrznego pęknięcia typu „rybie oko” w plazmowo azo-
towanej, niskostopowej próbce wykonanej ze stali o wysokiej wytrzymałości. W badaniach powiązano
dane otrzymane z obserwacji fraktograficznej pola prążkowanego w pobliżu środka pęknięcia w próbce
poddanej złożonemu stanowi obciążenia giętno-skręcającemuzmodelowaniemmechanicznymprocesupę-
kania i propagacji szczeliny zmęczeniowej.Otrzymanewynikiwskazują, że fazapropagacji stanowi jedynie
drobną część całego procesu pękania zmęczeniowego, którego dominującym etapem jest inicjacja pęknię-
cia. Wniosek ten pozostaje w zgodzie z badaniami nad wysoko- i bardzo wysoko-cyklowym zmęczeniem
próbek bez powierzchni utwardzanych.

Manuscript received January 3, 2012; accepted for print September 5, 2012