Fatigue design with cast magnesium alloys under constant...
Transcript of 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
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193186
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193 187
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193188
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193 189
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193190
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193 191
Fig. 19. Finite-elemente model of a bolted fastening.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193192
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.
C.M. Sonsino, K. Dieterich / International Journal of Fatigue 28 (2006) 183–193 193
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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