Fatigue Under Mean Conditions

8/17/2019 Fatigue Under Mean Conditions

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Fatigue testing of materials and components under mean load conditions

F. Klubberga)

, I. Klopferb)

, C. Broeckmanna)

, R. Berchtoldb)

, P. Beissa)

a) Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Augustinerbach 4 – 52062 Aachen, Germany, e-mail: [email protected]

b)

RUMUL Russenberger Prüfmaschinen AG, Gewerbestrasse 10,– 8212 Neuhausen, Switzerland,e-mail: [email protected]

ABSTRACT

The fatigue behaviour of metallic materials and components is significantly influenced by superimposed static meanstresses, which must be taken into account in service life calculations or in structure design. For a particular given cyclic

life it is usually observed that the load amplitude of the endurance limits decreases with growing mean stress or staticload. This requires suitable investigations to determine the allowable stress amplitude for various stress ratios R

between the lowest and highest stress value during a loading cycle. Mean stress effects in fatigue are usually presentedas stress amplitude versus mean stress plot according to Haigh. The paper presents the working principle of high

frequency resonant testing machines and especially examples of applications in testing materials and components withrespect to non-zero mean stresses in tension and compression.

KEYWORDS: Fatigue, mean stress effect, metallic materials, component testing

1. INTRODUCTION

A major problem in fatigue design is the knowledge of

the effect of static mean stresses m on the endurablestress amplitude A. Accessible data have led to thegeneral observation that the endurable stress amplitude

S ≡ A drops with increasing static mean stress. Fig. 1 gives a schematic overview of the amplitude reduction

influenced by static compression or tension preloads.Although this effect has been known for hundred years,

occasional failures due to this cause are stillencountered based on only qualitative assumptions of

this kind.

The stress ratio R is defined as the quotient of minimumand maximum stress within a full sinusoidal loading

cycle (t) = m + a sin(t), Fig. 2.

am

am

max

minR

(1) (1)

with m and a: mean static stress and stress amplitude,respectively.

Figure 1: Mean stress effect in the S-N diagram

(schematic)

Figure 2: Definition of the stress ratio R and stress

amplitude at various mean stresses

2. FATIGUE TESTING MACHINES

In the current state of the art of testing technologyespecially designed testing machines can stress

specimens or structures with a dynamic loadsuperimposed onto a static load. Comparing costs high

frequency resonant testing machines have clear

advantages over servo-hydraulic machines. Forfrequencies in the range of 50 Hz rather efficientequipment has to be used. The testing load for each cycle

of the specimen has to be built-up by oil pressure of ahydraulic actuator which is operating in a servo-loop. The

shortcoming is, that practically all needed energy is

transformed into heat and has to be carried off by anadditional cooling system. The dynamic load of a

resonant testing machine is generated by a mechanicaloscillating system (resonator) which consists of masses

and springs. Also the specimen with its elasticity is partof this system. The RUMUL product family is shown in

Fig. 3.

Anales de Mecánica de la Fractura 28, Vol. 1 (2011)

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Figure 3: High frequency resonant testing machines,Type RUMUL

The machines discussed here are used at full resonance,e.g. the operating point is situated in the peak of the

resonance curve. The resonator is excited by anelectromagnet. Typical frequencies for such machines

are in the range of 50 - 250 Hz and due to the resonanteffect the needed energy consumption is very low, about

0.5 kW. The machine works subdivided into a separatestatic and dynamic part and allows to run any

combination of stress ratio with high accuracy. The loadis measured by means of RUMUL load cells. The

control unit is a compact adaptive testing system. A

twin computer concept allows a consequent separationin functions by avoiding the well known problem of

running process software on unstable PC operatingsystems. The host computer is a pure Windows-PC, theoperating system is PC-independent. The core is a

powerful process computer system. The online data

acquisition and the digital controllers register the data ofthe installed transducers. The control conception is used

for new testing machines as well as for modernisations

of older equipment, e.g. 100 kN high frequency pulsators of type Amsler 422 (Fig. 4).

Figure 4: Amsler HFP 422 upgraded

A great number of different data is recorded during afatigue test. The user can determine the type of data and

the intervals for reading data. These data includeinformation related to the damage process of thespecimens or components and allow a more extensive

analysis than a standard fatigue test. A history function

with graphic display records continuously data andshows the user the immediate state of test. All test data

are in ASCII-files.

A lot of special tools, i.e. hydraulic gripping heads forsheet metal samples, for torsion and 4-point-bending,

furnace up to 900 °C, corrosion chamber and lowtemperature chamber ensure a universal application.

Resonant testing machines are predestined for tests withlarge number of load cycles, therefore, the main

applications are fatigue tests for material investigations.

3. GENERAL DESCRIPTION OF MEAN

STRESS EFFECT

Mean stress effects in fatigue are usually presented as

plots of the stress amplitude A versus thecorresponding mean stress m according to Haigh, withthe life to failure N as a parameter, particular thelimiting value of stress cycle NG in the fatigue tests in

case of the endurance limit with the average failure probability P = 50 %. With the exception of aluminium

alloys, the fatigue endurance limit or the knee in thefatigue curve usually occurs between 10

6 and 10

7 cycles

at a given stress. In axial testing, for instance, an

absolutely limiting engineering stress would be thetensile strength R m of the material. For the sake of better

comparison and - if possible - generalization, Haighdiagrams can be presented in a dimensionless version by

normalizing the stress amplitude to the fully reversed

amplitude at m = 0 and formulating a stress ratio alsofor the mean stress on the abscissa, e.g. in axial tests by

dividing the mean stress by the tensile strength. A

schematic example is given in Fig. 5 for endurance

limits A.

Figure 5: Mean stress effect for endurance limits in non-dimensional form of the amplitude versus mean stress

plot according to Haigh and general description models

For generalization purposes several types of equationshave been proposed. Goodman suggested to estimate the

endurable amplitude by a straight line through A/A (R =1) = 1 and m/R m = 1 which gives reasonable results for

partly brittle materials, yet, underestimates the

behaviour of ductile materials. Gerber introduced a

parabola through A/A(R = 1) = 1 and m/R m = 1 whichwas in fair agreement with experimental observations of

ductile materials with positive mean stresses. AdditionalSmith proposed a progressive description for extremely


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brittle materials. In general, however, the fatigue performance of materials is not sufficiently described in

the form of these simple theoretically models. They are

not intended for precise use, but rather to give a pictureof the relations involved. In further approaches the

endurable amplitude is discontinuously described by

straight line segment between certain defined stressratios R [1] but there are much more flexible relations

by higher order polynomials proposed [2, 3] considering

material specific mean stress sensitivity, e.g.:

,R

)p1(R

p1

2

m

m

m

m

W

A

(2)

with respect to the sensitivity parameter p [2]. For p = 1in eq. (2) the linear relation by Goodman (line “a” in

figure 5) and for p = 0 the Gerber parabola relation (“b”

in figure 5) are resulting. The sensitivity parameter p

can be calculated from ultimate tensile strength UTS R m, reversed axial and pulsating axial endurance limitsA (R = 1) W and 2·A (R=0) Sch respectively, basedon constant-load amplitude tests at R = –1 and R = 0:

.

R2

R

24

p

m

)0R(A

m

)0R(A

2

)1R(A

)0R(A

)1R(A

)0R(A

(3)

Unfortunately, however, only very few results of goodreliability are reported in the literature. For a given

material, there are often no pulsating fatigue strengthresults at hand. Therefore a statistically backed estimate

of the pulsating fatigue strength dependence on thealternating strength amplitude by a two parameter

power law was proposed [4, 5]:

qAAA 1RK)0R( (4)

with material group specific parameters K A and q,which can be gained by regression analysis on basis of a

sufficient number of available data pairs. Especially K A

in eq. (4) is affected by the material ductility and

indicates the declining, straight line or progressivecharacter of mean stress influence. The accuracy of the

proposed eq. (4) was tested by comparing the calculatedwith the predicted pulsating stress amplitude for about

1700 pairs of data [5].

4. RESULTS OF EXPERIMENTAL MATERIAL

INVESTIGATIONS

Caused by the lack of fatigue test data there are onlyvery few Haigh diagrams which take into account

compressive mean stresses. Examples of reliable test

results on smooth specimens and the description of theirfailure limit as parabolas of second order are given in

this paper, at first in Fig. 6 for a high strength alloy steel[6] and a pearlitic grey cast iron [7,8] with flake

graphite morphology. The curve of the endurable stress

amplitude resembles the Smith model for brittlematerials in figure 5. With other metallic materials there

is no such progressive amplitude increase with

compressive mean stresses, and on the other hand nosuch clear amplitude decrease with tensile mean

stresses. The fatigue properties of grey cast irons areaffected by their microstructures and the strength

depends on the amount, shape, size and distribution ofthe free graphite in their matrices. Flaky graphite might

be considered as an inherent notch that increases stress

concentrations for fatigue failure under tensile mean

stresses. The average compressive strength of grey castiron is roughly three and a half times the ultimate tensile

strength R m. For grey cast irons the general sensitivity

parameter in eq. (2) is p = 1,6 [7]. Extracted out offigure 6, Fig. 7 shows three S-N curves of this cast iron,

one for specimens with cast skin and one for smoothlongitudinally polished laboratory specimens, bothtested at the pure pulsating stress ratio R = 0 quantifying

the technological surface effect, and the third one incomparison to the second S-N curve, demonstrating thedrop of the endurance limit under high tension mean

stresses at R = 0,5.

Figure 6: Effect of mean stress on the endurance limit of brittle materials [6, 7, 8]

Figure 7: S-N lines of pearlitic flake-graphite cast iron

[7]

The endurance limit lines of two heat-treated steels,

earlier investigated [6, 9], are shown in Fig. 8. For eachdata point in the two steel curves in Fig. 8, e.g. each


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related S-N curve, about 30 smooth specimens wereavailable. The resulting curves correspond both to the

Gerber parabola distinctive for ductile materials. It is

striking that the allowable axial stress amplitude of2.5CrMo4V [9] decreases under compression mean

loading nearly in the same manner as for tension

conditions.

Figure 8: Effect of mean stress to the endurance limit of

ductile materials [6, 9, 10]

In the same figure a collection of curves for some

extruded aluminium alloys [6, 10] is given, alsoshowing ductile fatigue behaviour. The investigated

DISPAL alloys S230 and 232 are high performancespray-compacted aluminium alloys and hot extruded

[10]. The mechanical properties of these alloys must betailored by heat treating. The fatigue tests were

performed under axial loading with three different stressratios. The focus of all tests was the very high cycle

fatigue performance beyond 107

cycles. To this end 50 ·107 survived cycles were specified as run-out criterion.

Mainly several 100 kN - HFP type Amsler resonancetesting machines equipped with RUMUL upgrades were

used in parallel work over years for a total of 370smooth longitudinally polished specimens tested at

room temperature and 150 °C. In figure 8 only two of

the three investigated material conditions are shown.Figure 4 shows the arrangement for room temperature

testing. Fig. 9 gives a view into the opened shell furnaceafter fracture of a specimen had occurred in addition to

typical S-N diagrams of the PEAK aluminium alloyDISPAL S232 T6X under alternating stress amplitude

(R = –1) and compression mean stress(R = –2,3) at anelevated temperature of 150 °C. In comparison to the

fatigue strength under fully reversed loading the applied

compression load condition allows a higher stress levelof 6 %. Owing to the high alloy content and the uniform

segregation-free fine phase distribution, the fatiguestrength drop between room temperature and 150 °C

stays surprisingly moderate. Therefore this alloy has ahigh potential for oscillating load applications at

elevated temperatures e.g. for connecting rods [10].

Fig 9: S-N curves of the spray-compacted PEAK

aluminium alloy DISPAL S232 T6X for fully reversedloading (R = –1) and compression mean stress

(R = –2,3) at a temperature of 150 °C [10]

Figure 10: Effect of mean stress to the endurance limit

of ductile materials [6, 11, 12]

Test results subjected to repeated and static load ofaluminium alloys for cylinder head die castings [6] are

shown in Fig. 10, together with a nanostructured highstrength powder metallurgy aluminium alloy [11, 12].

The permissible stress amplitudes decreases with

greater mean stresses according to the Goodmanstraight line for fatigue behaviour of partly brittle

materials. The PLM aluminium alloy MS-N4 is a newhigh performance Al-Ni-Fe based alloy, which has

been developed by applying melt spinning technologyon an industrial scale and downstream processing via

HIP and hot extrusion. The material has a nano-crystalline microstructure with an excellent thermal

stability up to 400°C. A plot of the summarized resultsof all the tests on smooth polished specimens of the

MS-N4 material performed under axial loads with

various combinations of alternating and mean stressesat room temperature and elevated temperatures is

shown in Fig. 11. Note the small reduction of fatiguestrength due to temperature. This alloy shows superior

static and dynamic mechanical properties without anyadditional heat treatment. This leads to new engine

applications for nanostructured P/M Al alloys liketappets, lightweight valves, pistons compressor wheels,

etc. [11, 12].


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Figure 11: Influence of temperature on fatigue strength

on a nanostructured high strength powder metallurgy

aluminium alloy in the Haigh diagram [11, 12]

Figure 12: Features of the evaluation software SAFD

developed by IWM

All fatigue test data handled in this work were statistical

evaluated using the Software SAFD© (Statistical

Analysis of Fatigue Data) [13, 14], Fig. 12. The samples

of component fatigue tests or the samples of materialfatigue tests as well as stored and reloaded samplings of

a fatigue data base can be evaluated to S - N lines. Thissoftware works in an efficient and practice oriented

manner. A complete analysis example for a fatigue test

case of figure 11, stress ratio R = –2,3 at elevatedtemperature of 250 °C, in form of the resulting S-N

diagram and the probability plots for the range of finitelife (high cycle fatigue regime) and the transition range

to infinite endurance is shown in Fig. 13. The

illustration demonstrates the statistical nature of fatiguedata by the experimental scatter inherent to fatigue

testing.

Figure 13: Statistical evaluation of fatigue tests with theSAFD software, S-N diagram (top), probability plots for

the HCF-regime (center) and long life fatigue region(bottom)

5. COMPONENT TESTING UNDER MEAN

STRESS CONDITIONS

With specially designed fixtures different components

can be adapted to resonance machines to test their

strength limits in the vicinity of the service loads.Several typical component applications are shown in

Fig. 14.


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Figure 14: Examples of component test applicationsunder typical static load conditions

6. SUMMARY AND CONCLUSIONS

Resonance fatigue testing machines are comparably

inexpensive, fast and reliable equipment for highnumbers of cycles at very moderate energy

consumptions. The loading modes can be plane

bending, torsion or axial in nature with or withoutsuperimposed mean stresses. Under axial conditions the

mean stresses can be positive and negative. This way,resonance machines are mainly used to characterise the

performance of materials under cyclic loading. In manysimpler loading situations also components can be

realistically tested under accelerated conditions to gainan overview of the behaviour when exposed to cyclic

service.

Examples are given under axial load for differentmaterial responses to mean stresses. Metallic materialswith limited ductility, e.g. grey cast iron, exhibit a

progressively increasing endurable stress amplitudewith decreasing mean stresses. Many more ductile

engineering materials, like low alloy steels or wroughtaluminium alloys, show a degressive slope in Haigh

diagrams or can even lose endurable stress amplitudewith higher compressive mean stresses, which is to say

that this material group has superior cyclic load bearing

capacity at positive mean stresses than the first group.And, thirdly, there are intermediate cases with a more or

less linear relationship between endurable amplitude

and mean stress, e.g. extremely alloyed nanostructuredaluminium alloys or cast aluminium.

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Fatigue Under Mean Conditions