Powder Metallurgy Progress, Vol.8 (2008), No 3 200

EFFECT OF TENSILE MEAN STRESSES ON FATIGUE STRENGTH OF Fe-Cu-C STEELS IN AS-SINTERED AND HEAT TREATED CONDITIONS

A. Zafari, P. Beiss

Abstract Smooth and notched (Kt = 1.8) specimens according to ISO 3928 were compacted from Fe - 1.5 Cu - 0.6 C to different densities and sintered in industrial furnaces at 1120°C. The majority of the samples were fatigue tested under plane bending in the as-sintered condition at different stresses ratios R = σmin / σmax (R = − 1, − 0.4, 0 and + 0.25) to establish Haigh diagrams. A smaller group of specimens was subjected to various heat treatments in order to study the effect of higher strength or brittle mechanical behaviour on the reaction to tensile mean stresses. In contrast to conventional structural steels or grey cast iron, porous PM steels seem to have linear Haigh diagrams, which permit us to determine the slope from only two fatigue strength values at different mean stresses or stress ratios. In this study the slope in the as-sintered state turned out to be rather well predictable for smooth and notched geometries, which enables fairly reliable inter- and extrapolations over a wide range of non-investigated loading conditions. After heat treatments, the behaviour turned out to deviate more from the anticipated functional relationships. Much more systematic work is needed to fully understand the material behaviour in the various heat treating conditions, because the scatter in the very few results of this study is too high to draw conclusions on quantitative relationships. Further areas of future research should be reliable axial tests also with compressive mean stresses, tests with stress ratios R > 0, the investigation of notched conditions with different notch geometries and the statistical size effect. Keywords: stress controlled fatigue, mean stress sensitivity, notches and heat treatments

INTRODUCTION Stress controlled fatigue strength of metals is not a single valued property but -

similar to wear - a complex multiparameter material response to external loading conditions. The number of independent variables in fatigue testing of porous sintered steels is much greater than for conventional steels or other structural materials. Therefore, a stress controlled fatigue characterisation of sintered steels requires presently a huge experimental effort, and even after years of work many questions remain unanswered. The amount of data on the fatigue strength of Fe-Cu-C steels is, however, high enough to establish first quantitative descriptive rules on the relationships between different fatigue characteristics. This could open the path to gradually replacing the costly and long lasting experimental Ali Zafari, Paul Beiss, Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Aachen, Germany

Powder Metallurgy Progress, Vol.8 (2008), No 3 201 investigations by educated guesses. This paper is meant to illustrate how far our present understanding reaches on the effect of mean tensile stresses on the endurable cyclic amplitude of a common Fe-Cu-C steel.

In fatigue design, the average or static mean stress in a service loading situation is often of concern, and for this reason the endurable fatigue strength amplitude is generally plotted versus the mean stress in Haigh diagrams. In fatigue testing, most of the time the stress ratio R = σmin / σmax of a loading cycle is kept constant during the test for better comparability of the results. At a given amplitude σA and stress ratio R, the corresponding mean stress σm can be determined from

R1R1

Am −+= σσ (1)

Fig.1. Definition of the stress ratio R = σmin / σmax.

Figure 1 illustrates schematically the effect of mean stress on the endurable amplitude. Positive mean stresses lower and negative mean stresses increase the endurable cyclic amplitude. The extent, to which the amplitude is changed, depends highly on the material strength or rather the brittleness. Figure 2 shows a linear Haigh diagram in which the fatigue strength amplitude σA is plotted versus the mean stress σm. The absolute slope tanα in this diagram is called mean stress sensitivity M. There are two limiting cases, the perfectly ductile material with M = 0 and the perfectly brittle material with M = 1. In reality mean stress sensitivities are found between the extremes 0 < M < 1. Ductile conventional steels exhibit usually degressive Haigh diagram slopes when the mean stress decreases. Grey cast iron has progressive slopes from the tensile stress level at least up to R = − 5, whereas porous PM steels show constant slopes M which can be determined from two fatigue strength values at different mean stresses or stress ratios. To this end often the fully reversed (R = − 1) and the pulsating (R = 0) fatigue strength amplitudes are chosen. According to Fig.2 the slope M becomes then

( )( ) 1

A

A −=

−==

0R

1R

M σσ

(2)

Powder Metallurgy Progress, Vol.8 (2008), No 3 202

Fig.2. Linear Haigh diagram and definition of the mean stress sensitivity M.

The question must, however, been raised whether it is always necessary to measure two S-N curves for a linear Haigh diagram. To derive an answer, a look can be taken at Fig.3 where a typical fully reversed and the corresponding pulsation S-N curves are sketched schematically in double-logarithmic coordinates.

Fig.3. Fully reversed and pulsating S-N curves in double-logarithmic coordinates,

schematically.

In the finite life region the curves can be approximated by straight lines kaCN σ= (3)

where N is the number of cycles to failure, C the extrapolated abscissa intersection and k the slope. If the subscripts 1 and 2 refer to reversed and pulsation loading, respectively, at a given cycle number N in the finite life zone one can write

( ) k1/k2a1

1/k2a2

2k2a2

1ka11 or σσσσ ⋅== 21 / CCCC (4)

Powder Metallurgy Progress, Vol.8 (2008), No 3 203

Since Ci and ki are constants, after solving for σa2, with K = (C1/C2)1/k2 and q = k1/k2, the pulsating amplitude depends on the reversed amplitude as follows:

( ) ( )[ qaa RKR 10 −=== σσ ]

]

]

(5) If the knee point to more or less constant amplitudes occurs in both curves at about

identical cycle numbers, eqn. 5 stays valid also for so-called endurance limits σA

( ) ( )[ qAA RKR 10 −=== σσ (6)

K and q can be determined from well documented S-N curves or from a set of corresponding reversed and pulsating endurance limits of similar materials by regression analysis. If K and q are known for a family of similarly performing materials, a single S-N curve is sufficient to predict the Haigh diagram, because inserting eqn. 6 into eqn.2 delivers

( )[ ] 11 11 −−== −− qA RKM σ (7)

With an adjustment factor C3 eqn. 6 is also valid for local stress peaks KtσA in notched structures where σA is the nominal stress amplitude and Kt is the stress concentration factor

( ) ( )[ qAtAt RKKRKC 103 −=== σσ (8)

and M becomes ( )[ ] 11 1

31 −−== −− q

At RKCKM σ (9) This general consideration must now be tested experimentally.

EXPERIMENTAL PROCEDURE Smooth and notched fatigue testing specimens, Fig.4, according to ISO 3928 were

compacted to different densities from a water atomised pure iron powder (Hoeganaes Ancorsteel® 1000 BMN), 1.5% Hymod copper, 0.6% graphite (Kropfmühl UF4) and 0.8% Kenolube. The specimen thickness was increased from 5 mm as standardised to 7 mm to double the section modulus in bending which improves the relative precision during setting of the testing machines. The specimens were sintered at 1120°C for 20 minutes in an atmosphere of 95% N2 and 5% H2 in an industrial belt furnace.

Fig.4. Notched and smooth fatigue testing specimens according to ISO 3928 with 7 mm

height.

Powder Metallurgy Progress, Vol.8 (2008), No 3 204

A few samples were manufactured without graphite addition for carbonitriding, which took place in a two step processes. First, the material was carburised at 920°C for 30 minutes with 0.15% CO2 in endogas from methane, in the second step the temperature was lowered to 870°C with 0.22% CO2, corresponding to a carbon potential of 0.8%, for an additional 30 minutes. During the 870°C soak 0.2 Nm3/h NH3 was added which is about 4%. All carbonitrided samples were quenched in oil at about 60°C and tempered at 200°C for 30 minutes. Aside from the carbon-free specimens, also a series containing 0.6% C was carbonitrided for comparison purposes. A further series with 0.6% carbon was austenitised at 870°C for 40 minutes in endogas from methane at a carbon potential of 0.6%, quenched in oil and tempered at 180°C for 1 hour. The manufacturing and testing conditions are summarised in Table 1.

The specimens were loaded in four point bending about the direction of compaction up to 107 cycles. At R = − 1 and R = 0, sixty samples were tested in six stress levels of ten specimens each, at R = − 0.4 and R = + 0.25, thirty samples were tested by the staircase method with about fifteen or more samples in the staircase. Depending on strength level, the step heights were 2.5, 5 or 10 N/mm2. A commercial software (SAFD: statistical analysis of fatigue data) was applied for the data processing.

Tab.1. Manufacturing and testing conditions.

Stress ratios Material Heat treatment − 1 − 0.4 0 + 0.25

Fe-1.5Cu-0.6C Fe-1.5Cu-0.6C Fe-1.5Cu-0.6C Fe-1.5Cu

AS QT CH CH

x x x x

x

x x x x

x

AS: as-sintered; QT: quenched and tempered; CH: case hardened by carbonitriding Run-out specimens were used for density and hardness measurements. The density

was determined on small sections of about 2 g cut from the waist or from the centre between the lateral notches. For each material condition 10 parallel measurements were averaged. The apparent hardness was measured in the same area, where the fractures occur, with the Brinell method using a Ø 2.5 mm tungsten carbide ball. For the as-sintered specimens 20 indentations were made with a load of 613 N. For the heat treated materials a load of 1839 N was applied.

RESULTS AND DISCUSSION All major results are summarised in Table 2. In the as sintered condition three

different densities were tested which permits us to estimate the density dependence and extrapolate to full density by eqn. 10:

( ) mAA 00 / ρρσσ = (10)

with ρ: density, m: empirical exponent and subscript 0 denoting full density. σA0 and m were calculated by regression analysis from the measured data in Table 2 on the base of ρ0 = 7.85 g/cm3. σA0 and m are listed as separate lines in Table 2. The fatigue strength at Kt = 1.8, ρ = 5.91 g/cm3 and R = − 0.4 was not taken into account in the evaluation because of obvious deviation from the remaining data. Also the experimental results at R = 0.25 sometimes do not fit into straight line Haigh diagrams and can be questioned as to their trustworthiness. The regression coefficients of the lines in Figs.5 and 6 were, therefore, calculated with weighting factors of 10 for R = − 1 and R = 0, 5 for R = − 0.4 and 1 for R =

Powder Metallurgy Progress, Vol.8 (2008), No 3 205 0.25. This yields the mean stress sensitivities in Table 2. The deviating data are presently subject to further investigations.

Fig.5. Haigh diagram for smooth specimens.

Fig.6. Haigh diagram for notched specimens.

Tab.2. Densities, hardness and fatigue strengths at 107 cycles and 50% survival probability.

Carbon Heat Density Kt Hardness Fatigue strength [N/mm2] Mean

Powder Metallurgy Progress, Vol.8 (2008), No 3 206

R content [%]

treatment [g/cm3]

− 1 HBW

− 1 − 0.4 0 +0.25

stress sensitivity

0.6 0.6 0.6 0.6

AS AS AS AS

7.85 6.95 6.36 5.83

1 1 1 1

235 152 100 77

324 176 113 73

286 158 109 69

252 144 97 64

194 112 86 53

0.306 0.246 0.179 0.157

m 5.005 4.729 4.589 4.226 0.6 0.6 0.6 0.6

AS AS AS AS

7.85 6.94 6.47 5.91

1.8 1.8 1.8 1.8

235 154 123 93

235 125 93 57

195 108 77

(35)

155 85 65 40

153 75 60 32

0.461 0.459 0.412 0.427

m 4.955 4.759 4.714 5.345 0.6 0.6 0 0

QT CH CH CH

6.81 6.91 6.47 6.90

1 1 1 1

373 412 ≈ 250 349

280 328 225 323

188 179 137 216

0.494 0.827 0.647 0.493

Fig.7. Relationship between pulsating and fully reversed fatigue strengths of predominantly

soft microstructures [1-8].

According to eqn. 6 and 8 there should be a parabolic relationship between pulsating and fully reversed stress amplitudes. Evaluating the literature on data pairs of at least 40 specimens per S-N curve, two well defined material groups can be distinguished, steels without larger amounts of martensite or bainite, Fig.7, and steels with predominantly hard microstructural constituents, Fig.8. The measured data of the present study are part of Figs.7 and 8. For the behaviour of the soft as-sintered steels in the unnotched condition in Fig.7, eqn. 6 delivers an almost perfect match with K = 1.35 and q = 0.90. Yet, the results from the notched geometries in Table 2 deviate systematically from this relationship and eqn. 8 must be applied with C3 = 1.18. For the heat treated or sinter hardened steels in Fig.8, which exhibit more scatter than the soft materials in Fig.7, a systematic deviation of data from notched geometries cannot be recognised. All notched data in this graph were generated with a 1.5% Mo prealloyed steel to which graphite was mixed and 4% Ni and 2% Cu were diffusion bonded. Depending on the

Powder Metallurgy Progress, Vol.8 (2008), No 3 207 cooling rate after sintering, this steel contains normally larger portions of martensite, bainite ad retained austenite. In this case an adjustment to eqn. 8 in order to determine pulsating amplitudes from fully reversed fatigue strengths is not necessary, C3 = 1.0 applies. The reason for this difference between soft and hard notched geometries is not known and must attract more attention in the future. In view of the very limited experimental evidence of higher reliability, C3 in eqn. 8 is presently treated as a material specific constant.

Fig.8. Relationship between pulsating and fully reversed fatigue strengths of predominantly

hard microstructures [8-11].

With the aid of eqn. 2 and 8, the mean stress sensitivity can be estimated from eqn. 9 as depending on the nominal fully reversed fatigue strength amplitude, Fig.9. The agreement is close to perfect for the smooth specimens. Because of the irregularities with the notched fatigue strength results, especially the M value from the extrapolation to full density is not so well in line with eqn. 9.

Fig.9. Mean stress sensitivity according to eq. 9 and comparison with results in Table 2 of

the non-heat treated steels.

Powder Metallurgy Progress, Vol.8 (2008), No 3 208

As can be seen from Figs.5 and 6, it is justified to assume a linear relationship between σA

and σm for porous sintered steels: ( ) mAA MRR σσσ −−== 1)( (11)

From the definition of the mean stress, σm in eq. 11 can be expressed as a function of σA(R) and R, eqn. 1, and M can be inserted into eqn. 11 from eqn. 8. This yields the relationship particularly between σA0 and R:

( )( )[ ]

KKRKC

RR

RR q

At

AA −−=

⋅−++

−== −1

03

00 1

111

1)(

σσσ (12)

Figure 10 proves that the σA0 values from Table 2 are well described by eqn. 12, again with the exception of the notched series at R = 0.25.

Fig.10. Effect of stress ratio R on the fatigue strength at full density according to eqn. 12

and comparison with the results in Table 2.

SUMMARY In the case of iron-copper-carbon steels the available amount of data is large

enough to formulate first quantitative estimates for fatigue strength predictions. With soft microstructure and unnotched geometry the quality of predictions is very good. With the notched samples of this study some scatter spoils the picture, nevertheless the errors are easy to identify from plausibility checks. Presently the pulsating fatigue strength amplitude can be determined from fully reversed values. Since Haigh diagrams of sintered porous steels are straight lines, this is sufficient to predict the Haigh diagram for Kt values that were investigated. A reliable and generally applicable prediction of the strength reduction by external notches is not yet possible. For the material investigated here the slope of Haigh diagrams of notched specimens in the as-sintered state is significantly higher than that of smooth specimens. The mean stress sensitivity of heat treated or sinter hardening steels generally surpasses the results in the as-sintered state. With the limited volume of available data, however, trends cannot yet be distinguished from experimental scatter.

Other areas of future research should be reliable axial testing over wide ranges of stress ratios, torsion tests and investigations with different stress concentrations.

Powder Metallurgy Progress, Vol.8 (2008), No 3 209 The statistical size effect on the fatigue of sintered steels has so far not been seriously treated, and many variables in surface modifications and heat treatments would deserve more attention.

REFERENCES [1] Sonsino, CM.: Ermittlung anwendungsrelevanter Kenngrößen für Sintermetalle; Report

No. FB 158, Frauenhofer-Institut f. Betriebsfestigkeit, Darmstadt, 1981 [2] Sintermetallwerk Krebsöge, unpublished results, 1990 [3] Beiss, P., Dalgic, M.: Mat. Chem. Phys., vol. 67, 2001, p. 37 [4] Dalgic, M., Lindlohr, S., Beiss, P. In: Proc. Euro PM 2001, Nice. Vol. 3. Shrewsbury :

EPMA, 2001, p. 292 [5] Beiss, P. In: Proc. Euro PM 2003, Valencia. Vol. 1. Shrewsbury : EPMA, 2003, p. 363 [6] Namazov, SN., Abdalla, G., Dalgic, M., Gudenau, HW., Beiss, P.: Z. Metallkd., vol.

94, 2003, p. 737 [7] Zafari, A., Beiss, P. In: Proc. PM Auto 2008, Isfahan. Mashad Powder Metallurgy and

Techn. Univ. Vienna, 2008 [8] Beiss, P. In: Proc. PM Auto 2008, Isfahan. Mashad Powder Metallurgy and Techn.

Univ. Vienna, 2008 [9] Wassenberg, RB., Nurol, OF., Beiss, P. In: Proc. 2004 PM World Congr. Vienna. Vol.

3. Shrewsbury : EPMA, 2004, p. 133 [10] Wassenberg, RB., Beiss, P. In: Proc. Euro PM 2005, Prague. Vol. 1. Shrewsbury :

EPMA, 2005, p. 357 [11] Zafari, A., Beiss, P. In: Proc. Euro PM 2007, Toulouse. Vol. 1. Shrewsbury : EPMA,

2007, p. 175