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ELSEVIER

Materials Scienc e and Engineering A234G236 (1997) 393-396

Calculation method for the fatigue limit of parts of case hardened

steels

H. Bomas *, P. Mayr, M. Schleicher

Stiftung Institut fir Werkstofftechnik, Badgasteiner StraJe 3, D-28359 Bremen, Germany

Received 31 January 1997

Abstract

Based on the weakest link concept a method is developed, from which the surv ival probability of every surface and volume

element of a case hardened part, which is loaded near the fatigue limit, can be calculated. Prerequisite of the calculation is the

knowledge of the hardness and residual stress distribution, the surface roughness, and the surface oxidation depth. By

multiplication of the surv ival probabilities of neighboured elements the surv ival probability of a limited region or of the whole

part can be calculated, which includes a fatigue limit determination. It is shown, that this method can be applied successful ly to

unnotched specimens o f case hardened steels. The necessary calculation parameters can be gained from a set of reference parts.

Because of the possibil ity to formulate a surv ival probability for every volume and surface element, there are no geometrical

restrictions to the parts which shall be calculated. 0 1997 Elsevier Science S.A.

Keywords: Case hardening; Fatigue limit; Calculation; Weakest link concept

1. Introduction

The here presented calculation method for the fatigue

limit of parts of case hardened steel is based on the

weakest link concept which was developed by Weibull

[l] for the strength of brittle materials and later trans-

ferred to fatigue behaviour by Heckel and co-workers

[2-61. The principles of this concept were also applied

to the calculation of the fatigue limit of homogeneous

materials by several other authors [7-lo]. Only a few

people showed the physical nature of the weakest links

and the correlation between their size distribution and

the fracture probability [ll]. The application of the

weakest link concept to inhomogeneous materials like

case hardened steel is new and needs additional devel-

opments considering different crack initiation mecha-

nisms and the role of local strength and residual

stresses.

* Corresponding author. Tel.: + 49 421 2185350; fax: + 49 421

2185333; e-mail bomas@iwt.uni-bremen.de

0921-5093/97/ 17.00 0 1997 Elsevier Scienc e S.A. All rights reserved.

PIISO921-5093(97)00159-7

2. Calculation principles

The failure of casehardened parts under loading near

the fatigue limit is a problem of crack initiation. This is

the condition under which the weakest link concept can

be applied to describe fatigue failure. Two main sites of

fatigue crack initiation and different reasons have to be

considered in case hardened parts:

l

crack initiation at the surface A) due to surface

roughness R) or due to surface oxidation SO)

l

crack initiation in the volume v>

According to the rules of probability mathematics,

the survival probability P, of a case hardened part can

be calculated as the product of the survival probabili-

ties of the surface P, A) and the volume P, V):

ps = Ps A).Ps V 1)

The weakest link concept is based on the assumption

that material strength is determined by bulk or surface

imperfections which are equally distributed in the

stressed egion. Fracture is caused by the weakest link,

which means the worst imperfection with respect to

crack initiation. Thus, the fracture probability near the

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H. Bomas et al. /Materials Scienc e and Engineering A234-236 (1997) 393-396 395

400 600 800 1000

Measured Fatigue Limit [N/mm21

1200

Fig. 1. Measured and calculated fatigue limits o f case hardened,

unnotched specim ens under rotating bending, push-pull and plane

bending.

ized by an equivalent short or long crack, depending on

its depth xso and a fit parameter x0. Considering this, a

factor Yso after Topper and El Haddad [16] is used to

describe the effect of surface oxida tion:

y,,= x,

J---

x0 + Go

(12)

The Weibull exponents

mA and m, are determined by

reference specimens.

By multiplication of the survival probabilities of

neighboured elements, the survival probability of lim-

ited regions or of the whole part can be calculated. The

fatigue limit is the nominal stress amplitude with the

total survival probability 0.5.

3. Application to unnotched, case hardened specimens

In order to study the described method with easy

calculations procedures, it was applied to unnotched,

case hardened specimens of two steel grades under

rotating bending RB), plane bending PB), and push-

pull loading PP) including different mean stressesand

different case hardening processes. Table 1 shows the

most important data of the examined specimens rom

the steels 16MnCr5 and 16MnCrS5 steels for case

hardening after German standard DIN 17 210), which

have partially been published before.

The specimens of charge I are cylindric with a net

diameter of 6 mm. The material is 16MnCrS5. The

specimensA and X were chosen as reference becauseA

exhibits crack initiation at the surface and X shows

crack initiation in the volume. The specimensof charge

II [17] are also cylindric with a net diameter of 12 mm.

The material is 16MnCr5. The specimensof charge III

[18] are bars with rectangular cross section and were

loaded by plane bending with a stress atio R = 0. The

bending height is 17 mm. Specimen H2 was taken as

additional reference in order to determine the parame-

ter Ho describing the mean stresssensitivity. The speci-

mens of charge IV [19] are cylindric with a net diameter

of 12 mm. The steel is 16MnCrS5.

The hardness and residual stress distribution of all

specimens is known, so that the survival probability

could be calculated. The calculation parameters de-

scribed in chapter 2 were optimized until the calculated

and measured fatigue limits of the reference specimens

were identical. Table 2 shows the optimized parameters,

which were used to calculate the fatigue limits shown in

Table 1 and Fig. 1. It can be seen, that the involved

effects on the fatigue limit of the examined unnotched

specimens, concerning their manufacturing, geometry,

and loading, are well described by the presented calcu-

lation method. Further work will show the applicability

of this method to notched specimens.

References

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