Fatigue design with cast magnesium alloys under constant...

Fatigue design with cast magnesium alloys under constant

and variable amplitude loading

C.M. Sonsino*, K. Dieterich

Fraunhofer-Institute for Structural Durability and System Reliability LBF, Bartningstraße 47, D-64289 Darmstadt, Germany

Received 15 November 2004; received in revised form 31 May 2005; accepted 23 June 2005

Available online 15 August 2005

Abstract

For a fatigue design of cast components of magnesium alloys AZ 91 HP, AM 50 HP and AM 20 HP strain and stress controlled fatigue

data, influence of notches, main stresses, elevated temperatures and at last but not least the knowledge of cumulative fatigue behaviour is

needed. This data is compiled in the presented paper and compared with cast aluminium alloys. The principles of component design are

discussed.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Cast magnesium; Fatigue; Constant amplitudes; Variable amplitudes; Cumulative damage; Mean-stress sensitivity; Notch sensitivity; Temperature

1. Introduction

The light weight of magnesium alloys make them

attractive especially for automotive applications which

require ecological contributions by saving of resources,

i.e. material and energy. However, for a broader use of these

materials, a good knowledge of fatigue design relevant

properties such as fatigue curves for constant and variable

amplitude loading, their scatters, influence of mean stresses

and notches on fatigue strength as well as the influence of

thickness and surface (casting skin) is necessary.

The following paper presents fatigue data, generated for

the die cast materials AZ 91 HP (MgAl9Zn1), AM 50 HP

(MgAl5Mn) and AM 20 HP (MgAl2Mn) to be used for the

design of components in different cycle regimes under

constant as well as under variable amplitude loadings

(Fig. 1).

The obtained data are compared with wrought steels,

cast-nodular iron, and cast aluminium alloys. This investi-

gation enlarges the existing data basis for fatigue

applications [1,2].

0142-1123/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2005.06.043

* Corresponding author. Tel.: C49 61 517 052 44; fax: C49 61 517

052 14.

E-mail address: [email protected] (C.M. Sonsino).

2. Materials and mechanical properties

The materials AZ 91 HP, AM 50 AP, and AM 20 HP

were die cast. Table 1 gives the chemical compositions and

Table 2 the mechanical properties. Fig. 2 shows the

dependencies between hardness and Sy, Su, and e. The

microstructures are presented in Fig. 3.

3. Fatigue test results

3.1. Strain-controlled fatigue data

The strain-controlled fatigue tests were carried out

under frequencies of fZ0.5–5 sK1 with unnotched speci-

mens (KtZ1.0, rectangular investigated section 8 mm!8 mm!14 mm) with different strain ratios R3ZK1 and

0), only with the alloys AZ 91 HP and AM 50 HP.

Fig. 4 shows an example of obtained cyclic and

monotonic stress–strain curves and the strain–cycle

curve of the alloy AZ 91 HP. The monotonic curves

were registered at the start of the strain-controlled tests.

The determined data for describing the elasto-plastic

material behaviour of the investigated alloys are

compiled in Table 3.

International Journal of Fatigue 28 (2006) 183–193

www.elsevier.com/locate/ijfatigue

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Nomenclature

K, K 0 strength coefficient, monotonic, cyclic

n, n 0 strain hardening exponent, monotonic, cyclic

b, c exponents of the Coffin–Manson–Basquin

equation

3 0f fatigue ductility coefficient

s 0f fatigue strength coefficient

e elongation

D damage sum

E Young’s modulus

HB Brinell hardness

Kt stress concentration factor

Kf fatigue stress concentration factor

M mean-stress sensitivity

P probability

js safety factor

s standard deviation

u0 normalized safety

s stress

3 strain

r density

m Poisson’s ratio

Sy, Su yield, tensile strength

Ls sequence length

I irregularity factor

Ts scatter width of stress amplitudes

R3 strain ratio

R, �R maximum stress ratio for constant, variable

amplitude loading

Ra, Rz, Rt roughness values

k, k 0 slopes of the Woehler curve

n cycles

N, �N fatigue life under constant, variable amplitude

loading

Indexes

a amplitude

m mean

n nominal

el elastic

pl plastic

f failure

s survival

Table 1

Chemical compositions of the investigated alloys

Chemical

comp. in

(wt%)

Al Zn Mn Cu Si Fe Ni Pb Be Mg

AZ 91 HP 9.0000 0.8100 0.1500 0.0064 0.0310 0.0010 0.0006 0.0050 0.0003 Balance

AM 50 HP 4.7000 0.0000 0.3100 0.0060 0.0030 0.0010 !5 ppm 0.0040 0.0002 Balance

AM 20 HP 1.9000 0.0200 0.4100 0.0011 0.0070 0.0020 0.0008 0.0070 0.0003 Balance

Fig. 1. Partition of fatigue strength.

C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193184

Table 2

Conventional mechanical properties

Properties Sy (MPa) Su (MPa) e (%) E (GPa) r (g/cm3) HB 2.5/31.25/20 m

AZ 91 HP 129 197 3.8 38 1.76 77 0.28

AM 50 HP 83 144 5.0 38 1.74 62 0.28

AM 20 HP 62 121 5.0 38 1.73 54 0.30

Fig. 2. Dependency between mechanical properties.

C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193 185

3.2. Load-controlled fatigue data under constant

and variable amplitude loading

The unnotched and notched specimens (Fig. 5) were

tested under the stress ratios RZK1 and 0 and axial

loading. The variable amplitude loading was carried out

using a Gaussian amplitude distribution with a sequence

length of LSZ5!104 cycles (Fig. 6). Obtained Woehler-

and Gassner-curves are presented for the alloy AZ 91 HP in

Figs. 7–9 and endurable stress amplitudes are compiled in

Table 4.

For the investigated alloys following characteristic

behaviours were observed:

– The knee point of the Woehler-curves, i.e. the transition

from medium to high-cycle fatigue, is around 105

cycles.

– The steep slope of kZ(D log N)/(D log sa)Z5 for N!105 cycles becomes after NO105 cycles extremely

shallow, kZ45, which means a drop of the stress

amplitude of 5% from one decade to the next one.

– The results are covered by the uniform scatter of the

stress amplitudes TsZ1: [sa(10%)/sa(90%)]Z1: 1.30

between the probability of survivals PsZ10 and 90%.

This value is also found for other cast materials.

– The curves for pulsating loading (RZ0) lie in a

lower level compared with fully reversed loading

(RZK1) due to the mean-stress sensitivity.

– The stresses of the notched specimens, presented by

nominal stress amplitudes sa,nZFa/Anetto, are lower

than the values of the unnotched ones due to the

existing notch sensitivity.

– The level of the Gassner-curves presented by the

maximum amplitude of the spectrum lie above the

level of the Woehler-curves.

– However, the exceedance diminishes with increasing

fatigue life.

The fatigue curves for the alloys AM 50 HP and AM

20 HP exhibit the same characteristics found for AZ 91

HP. The crack initiation site of these materials was

always microshrinkages (Fig. 10). The stress amplitudes

of these materials for NZ105 and 5!106 cycles with

PsZ50% are compiled in Table 4.

3.3. Mean-stress and notch sensitivity

From the given values in Table 4, the mean-stress

sensitivity

M Z ½saðR ZK1Þ=saðR Z 0Þ�K1 (1)

and the fatigue notch factor

Kf Z sa;nðKt Z 1:0Þ=sa;nðKt Z 2:5Þ; (2)

were calculated. The mean-stress sensitivity is presented in

Fig. 11 for constant and variable amplitude loading; it is not

significantly affected by the constant and variable amplitude

loading, but by the material [4]. AZ 91 HP has the highest

mean-stress sensitivity, AM 50 HP and AM 20 HPP reveal

comparable values.

3.4. Influence of temperature

For determining the influence of the temperature, some

investigations were carried out only with the creep resistant

alloy AZ 91 HP under 130 8C, fully reversed and pulsating

constant and variable amplitudes loadings (Fig. 12). In

contrast to room temperature, the knee point lies at 1!106

instead of 1!105 cycles. This results at 130 8C a higher

exceedance of the constant amplitude fatigue strength by

variable amplitude loading (compare Figs. 9 and 12). The

temperature of 130 8C decreases the fatigue strength at room

temperature in average by 36% (Fig. 13).

Fig. 3. Microstructures of investigated alloys.

Fig. 4. Elasto-plastic material data of AZ 91 HP.


3.5. Comparison with other alloys

In Figs. 14 and 15, the mean-stress sensitivity M and the

notch sensitivity, which corresponds to the inverse value of

the fatigue notch factor, are compared with other materials

[5]. It can be concluded that the increase of ultimate tensile

strength also increases the mean-stress sensitivity. The

values are on a comparable level with cast aluminium alloys

(Fig. 14). Fig. 15 shows that the decrease of fatigue strength

with the increase of the stress concentration is much lower

for the investigated alloys than for aluminium, cast-nodular

iron or wrought steels. Despite the axial loading, the notch

Table 3

Cyclic material data

Alloy R3 Su

(MPa)

Sy

(MPa)

Sy in

(MPa)

A5 (%) E

(GPa)

m Stre

Mo

K

(MP

AZ 91

HP

K1 197 129 138 3.8 38 0.28 380

0 128 109 502

AM 50

HP

K1 144 83 98 5.0 38 0.28 314

0 79 89 331

sensitivity of magnesium is lower than that of cast-nodular

iron or wrought steels under bending. This means that under

bending the notch sensitivity of magnesium alloys will be

even lower and therefore more advantageous for fatigue

design.

As magnesium alloys are an alternative to aluminium

alloys, a comparison of the fatigue strength of both alloys is

necessary. In Fig. 16, the investigated alloys are compared

with the mostly used aged cast aluminium alloy

G-AlSi7Mg0.6 T6 [7] for a porosity degree PZ0 [6].

Fig. 16 reveals comparable high-cycle fatigue strength

amplitudes. The comparable fatigue strengths explain why

ss–strain curve Strain–cycle curve

notonic Cyclic s 0f

(MPa)

30f Kb Kc

a)

n K 0

(MPa)

n0

0.1740 496 0.2057 598.5 0.0402 0.1785 0.4927

0.2196 251 0.1336 417.7 0.0468 K0.1789 K0.5025

0.2133 440 0.2415 488.8 0.0578 0.1773 0.4954

0.2317 388 0.2366 510.7 0.0661 K0.2010 K0.5497

Fig. 5. Unnotched and notched specimens (units in mm) for load controlled

tests.

Fig. 6. Gaussian spectra for variable amplitude loading.


magnesium can be a good alternative to aluminium,

providing that corrosion and creep effects can be avoided

by good design and manufacturing.

3.6. Cumulative damage

The calculation of fatigue life under variable amplitude

loading requires the application of an appropriate damage

Fig. 7. Fatigue behaviour of AZ HP 91 unde

accumulation hypothesis and a real damage sum. The

present results were evaluated using the linear damage

accumulation hypothesis of Palmgren–Miner with the

modification according to Haibach [8], where after the

knee point the Woehler-curve is continued with the slope

k 0Z2kK 2 for cast materials (Fig. 17).

From the comparison of experimentally obtained and

calculated fatigue lives with DZ1.0 the real damage sum is

determined:

Dreal Z Nexp=NcalðD Z 1:0Þ (3)

In Fig. 18, the determined real damage sums for the

investigated alloys are displayed. The fatigue life calcu-

lation was carried out for each pair of Woehler- and

Gassner-curves on the stress level, resulting in NZ5!106

cycles under spectrum loading.

All real damage sums are below DZ1.0, indicating that a

calculation with DZ1.0 will overestimate the fatigue life,

especially for pulsating loading and 130 8C. An influence of

the material composition on the results is not observed. The

determined real damage sums under fully reversed loading

are comparable with other published data obtained under

bending [9]. However, the values obtained for 130 8C are

lower than other published data.

The results presented in Fig. 18 suggest for fully reserved

spectrum loading to perform cumulative damage calcu-

lations with DrealZ0.65 and 0.14 for pulsating loading at

room temperature and for 130 8C with the half of these

values.

4. Component design

The assessment of a specific design is based on an

appropriate transformation of material data obtained

experimentally from specimens to components. The

r fully reversed axial loading RZK1.

Fig. 8. Fatigue behaviour of AZ 91 HP under pulsating axial loading RZ0.

Fig. 9. Comparison of the Woehler- and Gassner-curves under fully reversed and pulsating loading of AZ 91 HP under room temperature.


important issue is the assessment of local stresses in critical

areas of the component. The stresses and their distributions

can be obtained by finite-elemente-calculations (Fig. 19)

[10] or by strain gauges. The multiaxial stress state of a

Table 4

Fatigue strength amplitudes at NZ1!105 and 5!106 cycles with PsZ50%

Loading Constant am

Stress concentration factor, Kt 1.0

AZ 91 HP

(MgAl9Zn1)

sa,n, �sa;n (MPa)

K1 84/77

0 52/48

AM 50 HP

(MgAl5Mn)

K1 70/64

0 51/46

AM 20 HP

(MgAl2Mn)

K1 61/56

0 43/39

a TZ130 8C.

critical area must be transformed into an equivalent state.

For low ductility materials, the principal (normal) stress

hypothesis can be applied [5]. This is also valid for cast

magnesium with elongations e between 3 and 5%.

plitude (NZ1!105/5!106) Variable amplitude ( �NZ1!105/5!106)

2.5 1.0 2.5

61/56 (48/34)a 163/101 132/77 (95/55)a

38/35 (36/25)a – 91/46 (62/36)a

49/45 157/88 101/60

36/33 – 82/41

43/39 126/78 85/53

32/29 – 72/37

Fig. 10. Crack initiation sites of the investigated alloys.

Fig. 11. Mean-stress sensitivities of different die cast magnesium alloys.


For almost all parts in mechanical engineering, neither

a nominal section nor a notch factor can be defined. The

use of strain-controlled data determined from unnotched

specimens is not appropriate, because they do not contain

the influence of stress gradients on fatigue life. However,

Fig. 12. Comparison of Woehler- and Gassner-curves under fully rev

for assessing the local stresses Woehler-curves obtained

from tests on notched specimens in the nominal stress

system can be transformed into the local stress system.

This approach is closer to reality than data obtained from

unnotched specimens. The local Woehler curve is

ersed and pulsating axial loading of AZ 91 HP under 130 8C.

Fig. 13. Decrease of the fatigue strength of AZ 91 HP at TZ130 8C.

0 500 1000 1500 200020000

0.2

0.4

0.6

0.8

1.0

MPa

Ps= 50 %

Scatter band of flat specimens under

constant amplitude axial loading

Scatter band of round specimens

under constant amplitude bending

Steel

Cast steel

Cast iron

Aluminium

Cast aluminiumand magnesium

AM

20

HP

NiC

oMo

GS

NiC

oMo

AM

355

PH

15-

7 M

o

1.77

04.6

1.66

04.6

Ti-a

lloye

d

NiC

oMo

anne

alde

d

41 C

r 4

GG

G-1

00 z

w.

GG

G-7

0G

S 2

5 C

rMo

4

GT

S-7

0

SA

E 41

30

Ck

45

St

52

St

37G

GG

-40

GT

S-3

5A

lMg

Si 1

AlM

g 5

3.43

64.7

3.43

54.7

3.12

54.7

3.13

54.5

G-

AlS

i 7 M

g w

a

G -

AlS

i 11

MgS

r

Mea

n st

ress

sen

sitiv

ity M

Tensile strenght Rm

G -

AlC

u 4

Ti w

a

AZ

91

HP

AM

50

HP

Fig. 14. Mean-stress sensitivity of different metallic materials.

Fig. 15. Decrease of fatigue strength by increased stress concentration.


obtained by multiplying the nominal stress by the notch

factor of the notched specimens (seqZs1ZKtsn, princi-

pal stress hypothesis) (Fig. 20) [11].

For a correct assessment using the local stress system, a

Woehler-curve in the nominal system must be selected in

such a way, that the stress gradient and the maximum

stressed material volume of both specimen and critical area

of the component are the same [12]. Otherwise, the local

Woehler curve determined from specimens must be shifted

with regard to the stress gradient and maximum stressed

volume of the component. If, for example, the stress

gradient at the specimens is steeper than the stress gradient

at the critical point of the component, then the fatigue

strength of the specimens must be reduced by the

consideration of the size effect according to the concept of

the maximum stressed material volume [12]. The position of

the Woehler curve is also influenced by the surface state,

anisotropy, and residual stresses.

0

50

100

150

200

250

300

350

G-MgAl2Mn (AM20HP)G-MgAl5Mn (AM50HP)G-MgAl9Zn1 (AZ91HP)

R =

0R =

-1

Sy

Su

Axial loading

N = 5· 106, Ps = 50%

R =

0R =

-1

Solidified cross section:s = 2 mm (magnesium alloys)s = 20 mm (aluminum alloy)

Thickness of the specimen:d = 2 mm ( magnesium alloys)d = 5 mm (aluminum alloy)

MPa

Kt 1.0 1.0 2.5 1.0 1.0 2.5 1.0 1.0 2.5 1.0 1.0 2.5G-AlSi7Mg0.6 T6

Str

engt

h an

d st

ress

am

plitu

deσ a

Fig. 16. Comparison of fatigue strengths of cast aluminium and magnesium alloys.

Fig. 17. Cumulative fatigue damage calculation.

1.0

0

0.5

0-1R: -1

2.52.5Kt : 1.0

Ps = 50%

RT

130˚C

AM

20

HP

AM

20

HP

AM

20

HP

AM

50

HP

AM

50

HP

AM

50

HP

AZ

91

HP

AZ

91 H

P

AZ

91

HP

Rea

l dam

age

sum

Dre

al

Fig. 18. Real damage sums for cast magnesium alloys.


Fig. 19. Finite-elemente model of a bolted fastening.


Thus, a component related Woehler curve for local

allowable stress amplitudes can be derived starting from

the curve with a probability of survival PsZ50%. For a

demanded theoretical probability of failure Pf (Table 5),

a design Woehler-curve must be derived [3]. For this, the

following scatters need to be considered:

– The standard deviation of endurable stress around its

mean value sPsZ50% with

ss Z 0:39 lgð1=TsÞ; (4)

– the standard deviation of mean value of stress sM, if

it undergoes scattering,

– the standard deviation of load sB; if maximum load is

assumed, then sBZ0 must be considered. The

Table 5

Theoretical probability of failure Pf and normalized safety factor u0 for Gaussian

Pf 10K1 10K2 10K3

Ku0 1.28 2.33 3.09

Fig. 20. Principle of deriving of allowable local stresses starting from a Woehler-c

statistically based safety factor is determined by

lg js ZKu0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2

s Cs2M Cs2

B

qZKu0s (5)

Finally, the allowable stress for a theoretical prob-

ability of failure Pf is obtained:

sal Z sPsZ50%=js (6)

Fig. 20 displays a schematical example of how to

assess the service fatigue life, when the local service

stress is calculated.

5. Conclusions

Presently used cast magnesium alloys reveal sufficient

high fatigue strength to be considered for a substitution of

cast aluminium alloys, and for taking advantage of the lower

density. However, for time and environment dependent

effects more knowledge and feed-back from field appli-

cations are necessary. With regard to fatigue design with

cast magnesium alloys same fatigue design principles as for

other metallic materials can be applied [11]. Thus, particular

properties of magnesium alloys such as low Young’s

modulus, tendency to creep, mean-stress, temperature and

corrosion sensitivity and continuous fatigue strength

decrease in high-cycle fatigue must be considered and

compensated by a magnesium-adjusted design.

logarithmic distribution

10K4 10K5 10K6

3.72 4.27 4.75

urve in the nominal stress system obtained by tests with notched specimens.


Acknowledgements

The presented results were obtained within a research

project funded by the Community of Industrial Research

Associations (AiF), Koln, (Funding No. 11 726) and

supported by the Working Group ‘Light Metal Casting’ of

the Association of German Casters (VDG), Dusseldorf,

chaired by R. Woltmann and managed by L. Wenk. The

authors acknowledge the mentioned supporters of this

investigation.

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