Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure
We present the results of experimental work carried out in order to analyze the initiation and propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis of the tested mater...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2008
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irk-123456789-484372013-08-19T18:19:49Z Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure Rozumek, D. Научно-технический раздел We present the results of experimental work carried out in order to analyze the initiation and propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis of the tested material microstructure were observed. Представлены экспериментальные результаты анализа зарождения и распространения усталостных трещин в стали FеР04. Испытания выполнены на плоских образцах при циклическом растяжении и постоянном номинальном коэффициенте асимметрии цикла R = 0. Рассмотрены пути распространения трещин, исходя из микроструктуры материала. 2008 Article Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure / D. Rozumek // Проблемы прочности. — 2008. — № 1. — С. 121-124. — Бібліогр.: 7 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48437 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Rozumek, D. Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure Проблемы прочности |
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We present the results of experimental work carried out in order to analyze the initiation and propagation of fatigue cracks in FeP04 steel. The tests were performed in plane specimens under cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis of the tested material microstructure were observed. |
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Rozumek, D. |
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Rozumek, D. |
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Rozumek, D. |
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Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure |
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Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure |
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Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure |
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Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure |
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Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure |
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crack growth in fep04 steel under cyclic tension for different notches on the basis of its microstructure |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2008 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/48437 |
| citation_txt |
Crack growth in FeP04 steel under cyclic tension for different notches on the basis of its microstructure / D. Rozumek // Проблемы прочности. — 2008. — № 1. — С. 121-124. — Бібліогр.: 7 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT rozumekd crackgrowthinfep04steelundercyclictensionfordifferentnotchesonthebasisofitsmicrostructure |
| first_indexed |
2025-07-04T08:56:39Z |
| last_indexed |
2025-07-04T08:56:39Z |
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1836706066565431296 |
| fulltext |
UDC 539.4
C r a c k G r o w th in F e P 0 4 S te e l u n d e r C y c lic T e n s io n f o r D if f e r e n t N o tc h e s on
th e B a s is o f it s M ic r o s tr u c tu r e
D . R o zu m ek 1,a
1 Opole University o f Technology, Department o f Mechanics and Machine Design, Opole, Poland
a d.rozumek@po.opole.pl
We present the results o f experimental work carried out in order to analyze the initiation and
propagation o f fatigue cracks in FeP04 steel. The tests were performed in plane specimens under
cyclic tension by keeping constant the nominal load ratio R = 0. Crack paths on the basis o f the
tested material microstructure were observed.
K e y w o rd s : crack path, microstructure, fatigue crack growth rate, notches, /-in tegra l range.
In trod u ction . In steels and alloys, tw o basic crack growth m echanism s can be
distinguished: brittle and ductile [1]. In case o f brittle cracking, intercrystalline cracking
(so-called fissile cracking) is usually observed. For ductile cracking, disintegration o f the
specim en surface in pure m etals is caused by successive slip bands; in com m ercial alloys
cracking begins in harder elem ents (non-m etallic inclusions), w here the developing voids
cause failure. During fatigue crack growth in m etal alloys, the fo llow ing three stages can
be distinguished [2]. The first stage includes generation o f microcracks or form ation o f
voids and is connected w ith phenom ena occurring in the d islocation structure o f the
material. The second stage includes crack growth in the plane o f m axim um principal
stresses. The final fracture causes the grow ing crack to reach its critical length, or the
stress reaches the tensile strength level, and the elem ent fails.
The aim o f this study is determ ination o f the fatigue crack growth in FeP04 steel,
used in car industry, taking into account the influence o f microstructure and different
notches on the steel life (fatigue crack growth rate).
M ateria ls and Test P rocedure. Sta tic P roperties an d F atigue Tests o f N otched
Specim ens. Tests were carried out on plates made o f FeP04-U N I 8092 deep-drawing steel,
w eakened by sym m etric lateral notches o f varying acuity. The tests were perform ed using
a M TS 809 servo-hydraulic device at the Department o f M anagem ent and Engineering in
V icenza (Padova U niversity) [3]. Chem ical com position (wt.%) o f the FeP04 steel tested
are 0.05 C, 0 .30 Mn, 0.05 Si, 0 .032 P, 0 .02 S, 0.043 A l, and 0.07 Cu. M echanical
properties o f FeP04 steel are as follow s: o y = 210 MPa, o u = 330 MPa, E = 191 GPa,
v = 0.3. C oefficients o f the R am berg-O sgood equation describing the cyclic strain curve
under tension-com pression conditions w ith R s = —1 for FeP04 steel are the fo llow ing
[4]: the cyclic strength coefficient K ' = 838 M Pa and the cyclic strain hardening exponent
n' = 0 .2 2 A ll fatigue tests w ere performed under force control, by im posing a constant
value o f the nom inal load ratio R = 0 w ith load amplitudes P a = 6 and 7 kN (w hich
corresponded to the nom inal amplitude o f normal stresses o a = 100 and 117 M Pa before
the crack initiation). The test frequency ranged from 13 to 15 Hz. The specim ens were
characterized by double sym metric lateral notches w ith a notch root radius ranging from
0.2 m m to 10 m m (Fig. 1). The theoretical stress concentration factor in the specim en
under tension K t = 9 .61 ,4 .30 , 3 .23, and 1.85 w as estim ated w ith use o f the m odel [5]. In
a number o f fatigue tests, fatigue crack initiation and propagation phases were controlled
by m eans o f an optical m icroscope (X 20).
M icrostructure an d F atigue C rack p a th in F eP 04 Steel. Steel FeP04 can be easily
subjected to cold working, it belongs to ferritic steels. Since amount o f carbon in ferrite is
low , ferrite properties are very similar to those o f pure iron a. The considered steel is
© D. RO ZU M EK , 2008
ISSN 0556-171X. Проблемы прочности, 2008, № 1 121
mailto:d.rozumek@po.opole.pl
D. Rozumek
applied for deep drawing. Fig. 2b show s microstructure o f FeP04 steel, containing the
ferrite (light) and numerous non-m etallic inclusions. The structure exhibits a distinct
rolling texture. N um erous non-m etallic inclusions, m ainly chains o f oxides about 1 fxm
(black) are visib le against the background o f long ferrite grains. The coalesced cementite
can be seen at the ferrite grain boundaries in Fig. 2b. Figure 2 presents the surface o f a
specim en tested under loading P a = 6 kN and w ith the radius o f notch root p = 0 .2 mm
after N f = 2 2 ,7 0 0 cycles to failure. D ifferent m agnifications were chosen so as to present
a path o f the m ain crack, about 0.9 m m in length (Fig. 2a). Figure 2b show s a crack course
taken from Fig. 2a, for m agnification X 2000, in order to analyze the crack growth. Here,
transcrystalline cracks through the grains o f a-phase are dom inating, but cracks along the
grain boundaries are also observed. The m ain cracks propagate in direction perpendicular
to the loading action, but secondary cracks are also visible.
n
O
n
220
I
Fig. 1. Geometry o f the specimen characterized by notches.
Fig. 2. The fatigue crack path in the FeP04 steel, magnification: (a) X200; (b) X2000.
Initiation and growth o f short (secondary) fatigue cracks can be seen in grains or at
the boundaries o f a-phase (Fig. 2b). In m ost cases, the secondary cracks grow ing in the
ferrite grains are blocked in the places w here coalesced cem entite and the non-m etallic
inclusions are present. Further characteristic o f the considered cracks, including short
cracks, is that they grow in different directions in relation to the specim en axis. The main
cracks grow in the p lanes o f the m axim um normal stresses. There are short lateral cracks
inclined to the m ain crack at the angle o f 30 and 40°. B ecause o f h igh p lasticity o f the
tested material, ductile cracking is observed. It is characterized by voids (black fields in
Fig. 2) after the material stratification observed in the cracking path. Stress concentration
and intensification o f p lastic flow occur around the voids. In Fig. 2a, asym metric pits can
be found, w hich are caused by the m ean loading and located in the perpendicular plane or
at a certain angle (up to 30°) to direction o f the external loading action. Stratification o f
the material can be seen at a certain distance from the m ain crack. The fatigue crack
growth rate in the ferrite grains is dependent on the stress value. Sim ilar crack growth was
observed in case o f specim ens w ith the notch root radii p = 125 , 2 .5 , and 10 mm.
Test R esu lts and A n alysis. In double logarithmic coordinates, Fig. 3 g ives the
number o f cycles to initiation and to failure for different notch root radii. The cracks (o f
m inim al observable crack length about 0.1 to 0.2 m m ) initiated at the same tim e on the
left and on the right o f the slot. A s seen from curves crack length a v s number o f cycles
122 ISSN 0556-171X. npo6n.eMH npounocmu, 2008, N 1
Crack Growth in FeP04 Steel under Cyclic Tension
N in Fig. 4, after changing the notch root radii p from 0.2 to 10 mm, fatigue life
increases. It is evident that w ith the h ighest radii, the initiation phase, w hich depends on
the stress conditions at the notch tip, prevails.
Fig. 3 Fig. 4
Fig. 3. Comparison between crack initiation points (open symbols) and final failures (solid
symbols), as a function o f different values o f the notch root radius.
Fig. 4. Dependencies o f fatigue crack length versus number o f cycles for different values o f the
notch root radius.
On the basis o f the results presented in Figs. 3 and 4 it can be stated that w ith the
increase o f notch root radii the number o f cycles to initiation and failure o f specim ens also
rises. Fig. 5a show s the fatigue crack growth rate d a /d N versus A K relations under
different notch root radii and load amplitude conditions. For different notches, under
P a = 7 kN , w ith the notch radius change (from p = 1.25 to p = 10 m m in the range
1 /27 6 < A K < 100 M Pa -m ) the crack growth rate increases. Figure 5b show s the fatigue
crack growth rate d a /d N versus A J relations. These relations show alm ost the same
tendency as the d a /d N versus A K relations. In Fig. 5 and for p = 0 .2 and 10 mm, at the
initial stage o f the crack growth, there is the influence o f plasticity v isib le (displacem ent
o f sym bols O to the right in relation to sym bols □ ) .
In the elastic-plastic range, stresses and strains were calculated by m eans o f the finite
elem ent F R A N C 2D software. In the m odels six-node triangular elem ents were used. The
test results show n in Fig. 5a were described by the Paris equation [6] and in Fig. 5b by the
m odified equation
d a /d N = B (A K ) n and d a /d N = B 1(A J ) " \ (1)
where A J = J max — J min, B , B 1 and n, n 1 are em pirical coefficients. The A J value in
Eq. (1) w as calculated by using the fo llow ing relationship [7], w hich is for slightly
hardening and cyclica lly stable materials
„ , A K 2 . A oA e p
A J = ----------+ n Y — 1= — a, (2)
E Vn'
w here A K = K max — K min = YAo^jn (a + a 0 ) and A o is the stress range corresponding
to the plastic strain range A e p , both ranges evaluated ahead o f the notch (stress and strain
fields by FEM for slot w ere calculated the near crack tip about 0.1 to 0.5 m m - local
approach), a 0 is notch depth, Y is correction factor [4], Y = 112+ 0.203(2(a + a 0 ) / w ) —
1197(2(a + a 0 ) / w )2 + 1 9 3 (2 (a + a 0 ) / w ) 3 , and w is specim en w idth. The em pirical
coefficients B , B 1 and n, n 1 occurring in Eq. (1) and the correlation coeffic ien ts r were
ISSN 0556-171X. Проблемы прочности, 2008, № 1 123
D . Rozumek
T a b l e 1
Coefficients B and n in Eq. (1) and Correlation Index r for the Curves in Fig. 5
Figures,
graphs
B,
m / (MPaVm)n, cycle
n r
m / (MPaVm)n1, cycle
n1 r1
5a-1, 5b-1 2.377-10“ 10 1.808 0.89 1.950 •Ю“6 0.453 0.89
5a-2, 5b-2 1.722-10“ 12 2.954 0.82 2.636 •Ю“6 0.467 0.87
5a-3, 5b-3 3.069 • 10“ 14 3.802 0.94 5.346 •Ю“6 0.889 0.94
5a-4, 5b-4 2.917 •Ю“ 9 1.166 0.74 1.050 •Ю“6 0.304 0.80
SiI . 4
z
%
- 0 І P = [].2 rn n
- £ ß p = 1 .25птп
p = 2 .5 i m
Г~ 1 ^Р = 10 mm
FeP04 STEEL 2
a s m ) \ ±
AK (MPa-mia ) A J (MPa-m)
a b
Fig. 5. Crack growth rate behavior da/dN versus AK (a) and dajdN versus AJ (b).
determ ined w ith the least square m ethod for a confidence level a = 0 .05 and they were
show n in Table 1.
C on clusions. In the considered material, ductile cracking is observed and in such
cracking voids occur after material lam ination. A t the specim en fractures, it w as possible
to find transcrystalline cracks through the grains o f a-phase and cracks along the grain
boundaries. The notch root radius rises together w ith increase number o f cycles to
initiation and failure o f specim ens. A fter com parison o f the influence o f notches w ith
p = 0 .2 and 10 m m on the crack grow th rate, at the initial cracking period larger plastic
w ere observed for p = 0 .2 (see displacem ent o f sym bols in Fig. 5).
1. S. Kocanda, Fatigue Failure o f Metals, Sijthoff& Noordhoff Int. Publishers (1985), p. 441.
2. D. Rozumek amd E. Macha, A Description o f Fatigue Crack Growth in Elasto-Plastic
Materials under Proportional Bending with Torsion [in Polish], Opole University of
Technology (2006), p. 198.
3. P. Lazzarin, R. Tovo, and G. Meneghetti, Int. J. Fatigue, 19, 647-657 (1997).
4. D. Rozumek, E. Macha, P. Lazzarin, and G. Meneghetti, J. Theor. Appl. Mech., 44, 127-137
(2006).
5. A. Thum, C. Petersen, and O. Swenson, Verformung, Spannung, und Kerbwirkung, VDI
(1960).
6. P. C. Paris and H. Tada, Int. J. Fracture, 11, 1070-1072 (1975).
7. D. Rozumek, Proc. 12th Int. Conf. on Experimental Mechanics (ICEM12), Politecnico di Bari
(2004), pp. 275-276.
Received 28. 06. 2007
124 ISSN 0556-171X. Проблемы прочности, 200S, № 1
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