endurance limit and threshold stress intensity of die...
TRANSCRIPT
Endurance limit and threshold stress intensity of die cast magnesium
and aluminium alloys at elevated temperatures
H. Mayera,*, M. Papakyriacoub, B. Zettla, S. Vacica
aInstitute of Physics and Materials Science, BOKU, Peter-Jordan-Str. 82, A 1190 Vienna, AustriabARC Leichtmetallkompetenzzentrum Ranshofen GmbH, Ranshofen A 5282, Austria
Received 23 August 2004; received in revised form 25 January 2005; accepted 10 February 2005
Available online 25 April 2005
Abstract
High cycle fatigue properties of the high-pressure die-cast magnesium alloys AZ91 hp, AS21 hp and AE42 hp and of the aluminium alloy
AlSi9Cu3 are investigated at elevated temperatures. Fatigue tests are performed at ultrasonic cyclic frequency and load ratio RZK1.
Compared with ambient air environment, the S–N curves determined in warm air of 125 8C (magnesium alloys) and 150 8C (aluminium
alloy) are shifted towards lower cyclic stresses. The mean endurance limits at 109 cycles of 41 MPa (AZ91 hp), 27 MPa (AS21 hp), 35 MPa
(AE42 hp) and 61 MPa (AlSi9Cu3) are 70–90% of the respective stresses found in ambient air, and fracture mechanics tests delivered
threshold stress intensities at elevated temperature of about 80% of the respective values at 20 8C. Fatigue cracks initiate, nearly, exclusively
at casting porosity and fracture surfaces appear similar at low and elevated temperatures. Fatigue cracks may form at voids at stresses below
the endurance limit, and non-propagating fatigue cracks of considerable length (greater 1 mm) are found in runnout specimens. Considering
porosity as an initial crack, critical stress intensity, Kcrit is evaluated, which quantifies the sensitivity of a material to defects. Materials can
sustain cyclic stresses without fatigue failure, if the cyclic stress intensity determined for their most damaging porosity is lower than Kcrit.
q 2005 Elsevier Ltd. All rights reserved.
Keywords: Cast magnesium; Cast aluminium; Porosity; High-cycle fatigue; Endurance limit; Threshold stress intensity; Ultrasonic fatigue
1. Introduction
Magnesium alloys have received increased interest as
possible construction materials in the automotive industry
due to their low mass density, the possible benefit of weight
reduction and consequently fuel saving. The rather high
specific strength, the good castability and damping property,
the improved corrosion resistance of high purity alloys
and the possibility of recycling are additional advantages of
these materials [1–3]. Today, cast magnesium alloys are
used in several automotive applications like covers and door
structures and heavier stressed components like wheels,
housings and frames, for example. Effective weight
reduction is possible using cast magnesium alloys progress-
ively more often in load bearing components. Vehicles
0142-1123/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijfatigue.2005.02.002
* Corresponding author. Tel.: C43 1 47654 5161; fax: C43 1 47654
5159.
E-mail address: [email protected] (H. Mayer).
components are subjected to vibrations and repeated
mechanical straining, and the number of load cycles may
be very high, such as several 108 cycles in car wheels.
When magnesium alloys are considered for powertrain
components, like crank case or gearbox casing, fatigue
properties at elevated temperatures are of great interest
and have to be compared to the cyclic properties of well-
established cast aluminium.
Fatigue stress amplitudes in the range of 80 MPa at
108 cycles and room temperature are reported for several
cast magnesium alloys [4], which is closely comparable to
cast aluminium alloys. These high fatigue strengths,
however, are obtained with separately cast specimens,
whereas the cyclic strength of material extracted from
actually cast components may be significantly lower.
Material defects act as starting places for fatigue cracks
and deteriorate the fatigue behaviour of the cast. Early
fatigue investigations already showed that porosity acts as
main crack initiation place in cast magnesium [5,6].
Studying fatigue properties of AM50 alloy samples obtained
from different places of prototype control arms and wheels
showed that fatigue performance was significantly affected
International Journal of Fatigue 27 (2005) 1076–1088
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H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1077
by the shrink and gas porosity at the extraction place [7].
Porosity as the source of fatigue cracks has been found in
several investigations of AZ91, AM50 and AM60 [8–16].
Besides porosity, oxides [17] and Manganese-particle-
enriched regions [18] may act as preferential sources of
fatigue cracks in cast magnesium. Fatigue lifetimes are
influenced by the size of the material defect, i.e. the larger
the defect the shorter the fatigue lifetime [7,8,15,17]. The
lower the cyclic load, the greater the influence of defects on
fatigue properties. Cycling AZ91 T4 at strain amplitude
10K3, for example, led to lifetimes between 103 and
5!105 cycles, depending on the defect size in the sample
[17]. Thus, the fatigue properties of magnesium alloys are
strongly influenced by the quality of the cast. Meaningful
comparison of the cyclic properties of cast magnesium and
aluminium requires testing both materials in conditions
comparable to the intended technical application.
In a previous work [19], the fatigue properties at room
temperature of high-pressure die-cast magnesium alloys
AZ91 hp, AS21 hp, AE42 hp and AM60 hp have been
compared to the aluminium alloy AlSi9Cu3, which is most
frequently used in high-pressure die-casting in Germany.
The materials were produced under conditions comparable
to the casting of actual components. Porosity, which is
inevitable in high-pressure die-casting, was most important
for crack initiation and fatigue lifetime, and cracks, nearly,
exclusively started at these material defects. All alloys
showed an endurance limit in ambient air with maximum
cycles to failure of about 2!107. Fracture mechanics
principles were applied considering porosity as initial
cracks. Failed specimens and runnouts were evaluated to
determine the so-called ‘critical stress intensity factor’, Kcrit,
which determines the maximum stress amplitude a material
can sustain without fatigue failure in presence of porosity.
This parameter was used to link the fracture probability with
the distribution of defects in the cast materials.
Considering porosity as initial cracks is a well estab-
lished method to model the fatigue behaviour of cast
aluminium alloys, and fatigue lifetime may be considered as
numbers of cycles necessary to propagate the crack to
fracture [20–23]. Investigations on 319 T7 aluminium
verified [24,25] that the crack initiation period at porosity
is negligible and cracks may initiate even at stresses below
the endurance limit. The larger the casting defect the shorter
the crack extension period. Thus the observed fatigue
lifetimes are inversely correlated to the size of the defect in
constant amplitude [20–23] as well as in variable amplitude
Table 1
Chemical compositions (in wt%)
Al Zn Mn Si
AlSi9Cu3 Rem 1.2 0.1–0.4 8–11
AZ91 hp 8.90 0.79 0.21 0.01
AS21 hp 2.20 !0.01 0.16 0.98
AE42 hp 3.90 0.004 0.37 0.007
tests [26,27]. Recently, fracture mechanics concept has been
similarly applied to predict lifetimes of cast magnesium
AZ91 by integrating growth rates of cracks initiating at
porosity [15].
In the present investigation, the fatigue properties of
high-pressure die-cast magnesium alloys AZ91 hp, AS21 hp
and AE42 hp are studied at elevated temperatures, and the
aluminium alloy AlSi9Cu3 serves for comparison. Fatigue
lifetime and crack growth experiments are performed and
the obtained results are compared to the fatigue perform-
ance at room temperature. The aluminium alloy is tested at
150 8C. The magnesium alloys are cycled at the lower
temperature of 125 8C due to their inferior creep resistance.
However, this temperature is meaningful for several
practical applications, in gearbox housings for example,
where one of the alloys (AZ91) is actually used [28]. Mainly
high cycle fatigue properties and near threshold fatigue
crack growth behaviour are investigated. The endurance
limit is determined at 109 cycles, and maximum fatigue
crack growth rates of 10K12 m/cycle are used to characterise
threshold stress intensity. The experiments are performed
using the ultrasonic fatigue testing method working at cyclic
frequency 20 kHz. Previous experiments, though at room
temperature, have shown that similar lifetimes are measured
cycling at 20 and 50 Hz [19] and no pronounced effect of
cyclic frequency on fatigue performance of these alloys may
be expected therefore. Fracture surface studies and fracture
mechanics considerations serve to evaluate the influence of
porosity on fatigue properties.
2. Materials and procedure
2.1. Materials
Fatigue properties of the aluminium alloy AlSi9Cu3 and
the magnesium alloys AZ91 hp, AS21 hp and AE42 hp are
investigated. The materials are produced by high-pressure
die-casting at a solidification pressure of 60 MPa (AZ91
hp), 53 MPa (AE42 hp, AlSi9Cu3) and 30 MPa (AS21 hp),
respectively. Table 1 shows the chemical compositions of
the investigated alloys, and Table 2 summarises their
static strength properties at ambient and elevated
temperatures [29].
The materials are cast in bars with stepwise varying
thickness. Specimens used in constant amplitude fatigue
lifetime investigations (S–N tests) are shown in Fig. 1(a).
Ce Fe Cu Ni Mg
1.0 2.0–3.5 0.1–0.5
0.003 0.001 0.001 Rem
!0.01 !0.002 !0.001 Rem
0.94 0.0003 0.0003 0.001 Rem
Table 2
Ultimate tensile strength (Rm), yield stress (Rp0.2) and fracture strain (A5) at ambient and elevated temperatures
Rm (MPa) Rp0.2 (MPa) A5 (%)
AlSi9Cu3 216 (20 8C), 198 (150 8C) 134 (20 8C), 123 (150 8C) 1.0 (20 8C), 1.1 (150 8C)
AZ91 hp 190 (20 8C), 165 (125 8C) 118 (20 8C), 93 (125 8C) 3.6 (20 8C), 12.7 (125 8C)
AS21 hp 131 (20 8C), 103 (125 8C) 84 (20 8C), 65 (125 8C) 2.1 (20 8C), 4.2 (125 8C)
AE42 hp 184 (20 8C), 146 (125 8C) 101 (20 8C), 82 (125 8C) 5.0 (20 8C), 18.8 (125 8C)
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881078
These specimens are obtained from the bar at a thickness of
7.5 mm and 1.25 mm was removed from both sides to obtain
the final specimen thickness of 5 mm. Edges in the centres
of the specimens were rounded (radius 0.5 mm) and the
surfaces were polished parallel to the specimen axis prior to
the measurements with abrasive paper of grade 1000.
Fatigue crack growth tests were performed using single
edge notched specimens as shown in Fig. 1(b). These
specimens were obtained from the bar at a thickness of
15 mm. A notch was introduced by spark erosion and served
to obtain a defined place for crack initiation.
2.2. Fatigue testing method
The ultrasonic fatigue testing method has been used to
perform fatigue lifetime and fracture mechanics
investigations at load ratio RZK1. Specimens are excited
to resonance vibrations at a frequency of approximately
20 kHz, which leads to maximum vibration amplitudes at
both specimen’s ends and maximum strain amplitudes in
54
14
108
R 60
7
5
43
15
86
15
R 60
3
Notch1
(a)
(b)
Fig. 1. Specimen shapes used in (a) S–N tes
the specimen’s centre, i.e. at the place of the vibration node.
Strain gauges are used to measure the cyclic strain and to
calibrate the experiments. At one specimen’s end a vibration
gauge serves to measure the vibration (displacement)
amplitude, which is used to control the experiment. The
displacement amplitude of the specimen is kept constant at
the pre-selected magnitude with high accuracy (typically
within G1%). Specimens are not cycled continuously but
in a sequence of pulses of 25 ms each (approximately
500 cycles) and pauses of adequate length (25–250 ms),
since continuous cycling would increase specimen
temperature due to internal friction. Stress amplitudes are
calculated using the measured strain amplitudes and the
Youngs’ moduli of the materials, i.e. 45 GPa at 20 8C and
41 GPa at 125 8C for the magnesium alloys [29] and 77 GPa
at 20 8C and 71 GPa at 150 8C for AlSi9Cu3.
S–N experiments at elevated temperatures are per-
formed, in principle, in a similar manner to the
experiments in ambient air described previously [19].
The main experimental difference is that heated air
14
15
15
ts and (b) fatigue crack growth tests.
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1079
provided by a hot air fan flows against the specimens.
Specimen surface temperatures are controlled either with
thermocouples or with temperature-dependent current
sources and are kept constant at 150 8C (aluminium
alloy) and 125 8C (magnesium alloys), respectively.
Previously obtained S–N data of the alloys measured in
ambient air of 18–22 8C and 40–60% relative humidity
are shown for comparison.
Specimens were loaded until failure or at least
109 cycles, if they did not fail (runnouts). At high cyclic
stresses, where all tested specimens failed, power law
functions of cyclic stress, s and cycles to failure, N are used
to approximate data (Eq. (1)):
skN Z const (1)
A log normal distribution of cycles to failure is assumed
to calculate 50% probability for failure. To evaluate the
endurance limit at 109 cycles, a procedure recommended by
Maenning [30] is used. If i is the number of specimens failed
below 109 cycles and n is the number of specimens tested at
this stress level, the probability for failure, PF(s) is
calculated using Eq. (2):
PFðsÞ Zð3i K1Þ
3n C1
�������� (2)
The Probit function serves to approximate the probabil-
ities for failure. The mean endurance limits at 109 cycles
(50% fracture probability below 109 cycles) and their
standard deviations are evaluated. Twenty-five specimens
or more are used in each testing series to obtain statistically
meaningful data.
Fatigue crack growth at elevated temperatures is studied
by introducing the single edge notched specimens in warm
airflow. Crack growth rates, Da/DN at certain cyclic stress
intensity amplitude, Kmax are measured by decreasing and
increasing the stress intensity in 5–7% steps in successive
experiments. Crack growth rates are determined as mean
growth rates over crack length increments of 0.15–0.20 mm.
Video equipment and magnification lenses serve to
determine crack length on the specimen’s surface with a
resolution of approximately 7 mm. If no crack growth
is detected, cycling the specimen with at least 2!107 cycles serves to determine threshold stress intensity.
With the optical resolution, the maximum growth rate of
3.5!10K13 m/cycle is used to characterise threshold.
Previously performed fatigue crack growth experiments in
ambient air (18–22 8C, 40–60% relative humidity) and in a
vacuum (pressure ranges from 10K3 to 5!10K3 Pa) are
included for comparison [31]. In ambient air, cycling the
specimen for 2!107 cycles served to determine threshold
stress intensity, similar to the experiments in warm air. In
vacuum, the threshold is determined loading the specimens
with 108 cycles to account for the lower optical resolution
using a vacuum chamber [31]. Details of ultrasonic fatigue
and fatigue crack growth experiments, determination of
cyclic stress intensity and the evaluation of data are
described elsewhere [32].
2.3. Evaluation of porosity
In the investigated alloys, nearly all fatigue cracks
initiate at porosity (voids and shrinkage) [19]. To determine
the size of material affected by porosity at the crack
initiating place, fracture surfaces were examined using
scanning electron microscopy (SEM). The projected area of
the defect in specimen’s length direction (i.e. the direction
of principal stress), termed ‘defect area’ is evaluated. Defect
areas are evaluated for two purposes. It may be assumed that
fatigue cracks initiate at one of the largest material defects
in the stressed volumes of the specimen. Thus, the
distribution of defect areas reflects the distribution of the
largest material defects of the alloy, which characterises
the quality of the cast and is most important for the fatigue
properties of the material.
Considering porosity as an initial crack, fracture surface
studies are used for fracture mechanics considerations.
Murakami et al. [33] have shown that the stress intensity
factor of a flaw is influenced by its shape by less than 10%
and may be calculated considering solely the applied stress,
the projected area of the flaw and its location. Assuming the
area affected by porosity (Defect Area) as an initial crack,
the stress intensity amplitude, Kmax is calculated for RZK1
loading with Eq. (3)
Kmax Z smaxa
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDefect Area
pq
(3)
where smax is the cyclic stress amplitude, aZ0.65 for
surface defects (and for defects close to the surface [19]) and
aZ0.50, if the crack originates from internal porosity. If
specimens failed, the stress intensity was sufficient to
prolong the fatigue crack from the initial defect to rupture,
whereas runnouts either contained too small porosity or
were stressed at too low stress amplitudes. To include
runnouts in the analysis, these specimens were fractured at
higher stress amplitudes after low amplitude cycling.
Fatigue data produced with runnouts at the high stress are
not included in the diagrams or in the evaluations of the
endurance limits due to possible coaxing effects, and high
stress cycling of runnouts solely served to produce the
fracture surfaces.
Calculating the stress intensity factors for failed speci-
mens and runnouts serves to quantify the lowest stress
intensity factor necessary for fracture and the highest stress
intensity where no failure occurred. The range between
these two values is termed critical stress intensity amplitude,
Kcrit [19] and characterises the range where specimens may
fail whereas others do not. The surfaces of some AlSi9Cu3
and AZ91 hp specimens which were cycled in warm air and
did not fail within 109 cycles were examined in the SEM
using a rotating stage. This served to investigate non-
propagating cracks in runnout specimens.
104 105 106 107 108 10940
50
60
80
100
Ambient Air, 20 ˚CWarm Air, 150 ˚C
Number of Cycles
Stre
ss A
mpl
itude
(M
Pa)
150(a)
120
104 105 106 107 108 109
20
30
40
50
60
80
100
Ambient Air, 20 ˚CWarm Air, 125 ˚C
Number of Cycles
Stre
ss A
mpl
itude
(M
Pa)
(b)
104 105 106 107 108 109
20
30
40
50
60
80
100
Ambient Air, 20 ˚CWarm Air, 125 ˚C
Number of Cycles
Stre
ss A
mpl
itude
(M
Pa)
(c) (d)
104 105 106 107 108 109
20
30
40
50
60
80
100
Ambient Air, 20 ˚CWarm Air, 125 ˚C
Number of Cycles
Stre
ss A
mpl
itude
(M
Pa)
Fig. 2. S–N data of (a) AlSi9Cu3, (b) AZ91 hp, (c) AS21 hp and (d) AE42 hp at ambient (open circles, dashed lines) and elevated temperatures (closed circles,
solid lines).
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881080
3. Results
Table 3
Mean endurance limits (50% fracture probability at 109 cycles) and
standard deviation in warm air (150 8C for AlSi9Cu3, 125 8C for AZ91 hp,
AS21 hp and AE42 hp) and in ambient air (20 8C)
Mean endurance limitG
standard deviation, warm
air (MPa)
Mean endurance limitG
standard deviation, ambient
air (MPa)
AlSi9Cu3 61G12 75G14
AZ91 hp 41G6 45G7
AS21 hp 27G5 38G8
AE42 hp 35G5 42G9
3.1. S–N data
The results of constant amplitude lifetime investigations
are presented in Fig. 2. Fatigue data measured at elevated
temperatures are shown with closed circles, and previously
measured data at ambient temperature [19] are included with
open circles. Specimens which did not fail within minimum
109 cycles (runnouts) are marked with arrows. Two straight
lines in the double logarithmic diagrams are used to
characterise 50% fracture probability at elevated tempera-
tures (solid lines) and at ambient temperature (dashed lines).
Below 106–107 cycles, lines with constant slope indicate
increasing mean lifetimes with decreasing cyclic stresses.
The exponents k (Eq. (1)) are in the range from 6 to 8 for all
four materials at both temperatures. Above approximately
2!107 cycles, failures are rare, and data are approximated
with lines parallel to the abscissa. No AlSi9Cu3 specimen
(Fig. 2(a)), one AZ91 hp specimen cycled in ambient
air (Fig. 2(b)), two AS21 hp specimens cycled in warm air
(Fig. 2(c)) and one AE42 hp specimen cycled in warm
air (Fig. 2(d)) failed at numbers of cycles greater than
2!107.
Table 3 summarises the mean endurance limits and their
standard deviation in warm and ambient air. Mean
endurance limits decrease as the testing temperature
increases. In AlSi9Cu3, the mean endurance limit at
150 8C is approximately 80% of the cyclic stress measured
at 20 8C. The mean endurance limit of the magnesium alloys
at 125 8C is approximately 90% (AZ91 hp), 70% (AS21 hp)
and 85% (AE42 hp) of the respective stresses found in
ambient air. Standard deviations of the mean endurance
80
100
AlSi9Cu3
AZ91 hp
)
(a)
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1081
limits of all materials are about 15–20% of the respective
mean values in both environments. Specimens may fail in
ambient air at stresses where others survived in warm air.
The pronounced scatter in the cyclic properties is caused by
material defects.
0
20
40
60
< 0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5
AS21 hp
AE42 hp
Rel
ativ
e Fr
eque
ncy
(%
Defect Area (mm2)
Equivalent Diameter (mm)
< 0.8 0.8-1.1 1.1-1.4 1.4-1.6 1.6-1.8
AlSi9Cu3AZ91 hpAS21 hpAE42 hp
Prob
abili
ty o
f O
ccur
renc
e
0.01
0.05
0.20
0.50
0.80
0.95
0.99
(b)
3.2. Fatigue crack initiation
Porosity plays a most important role for crack initiation
and fatigue performance in the investigated alloys. Fatigue
cracks in 105 of the 107 specimens fractured in warm air
initiated at this kind of material defect. Large areas with
porosity may lead to drastically reduced lifetimes. In
AlSi9Cu3, one specimen cycled at 85 MPa failed after
1.0!104 cycles, whereas the other specimens stressed at
this amplitude survived at least 5.7!104 cycles (Fig. 2(a)).
Fatigue crack initiation area of this specimen is shown in
Fig. 3. Close to the surface, voids created by gas porosity
surrounded by dendrites and shrinkage porosity are visible.
The defect area of this specimen is approximately 2.5 mm2,
which is the largest defect area found on fracture surfaces of
all specimens. The damaging influence of this defect on the
fatigue behaviour is caused by its large size and the location
close to the specimen surface.
Defect areas at the crack initiation places of all specimens
have been evaluated, and the size distributions are shown in
Fig. 4. In Fig. 4(a), defect areas are classified in a histogram
and Fig. 4(b) shows a probability diagram. The defect areas
found on fracture surfaces of specimens ruptured in ambient
air [19] are included to enlarge the statistical basis. The
arithmetical mean and the maximum defect areas and
the equivalent diameters, i.e. the diameter of a circle with the
same area, are shown in Table 4. Defect areas range from
0.017 to 2.5 mm2, and defects greater than 1 mm2 could be
detected in each material. AE42 hp contains, on average, the
smallest defects. Defect areas in AS21 hp are, on average,
approximately a factor of 1.7 larger than in AE42 hp.
Fig. 3. Porosity visible on the fracture surface of AlSi9Cu3 specimen
which was cycled at 85 MPa in warm air of 150 8C and failed after
1.0!104 cycles.
Defect Area (mm2)
0.050.02 0.50.20.1 1 2
Equivalent Diameter (mm)
0.250.16 0.80.50.35 1.1 1.6
Fig. 4. Size distribution of defect areas at the crack initiation location and
equivalent diameters presented (a) in a histogram and (b) in a probability
plot. In (b), the abscissa indicates the size of defect areas and the ordinate
shows the probability that specimens contain porosity larger than this size.
The sizes of large defects in AZ91 hp are comparable to
large defects in AS21 hp, whereas the mean size is smaller.
Mean and maximum sizes of defect areas in AlSi9Cu3 are
larger than in the magnesium alloys.
Surface studies of runnout specimens in the SEM
served to find fatigue cracks, which did not grow until
fracture within 109 cycles (non-propagating cracks). The
upper parts of Figs. 5 and 6 show non-propagating cracks
Table 4
Arithmetical mean and maximum size of defect areas and respective
equivalent diameters at the crack initiation sites
Mean
defect
area
(mm2)
Equivalent
diameter of the
mean defect
area (mm)
Largest
defect
area
(mm2)
Equivalent
diameter of the
largest defect
area (mm)
AlSi9Cu3 0.63 0.89 2.50 1.78
AZ91 hp 0.30 0.61 1.43 1.35
AS21 hp 0.42 0.74 1.47 1.37
AE42 hp 0.25 0.56 1.42 1.34
Fig. 6. Non-propagating fatigue crack in AZ91 hp: the fatigue crack (upper
figure) was visible on the specimen’s surface after cycling at 38 MPa for
1.51!109 cycles. Then the specimen was ruptured at 64 MPa in 1.30!
105 cycles to produce the fracture surface (lower figure). Fatigue crack and
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881082
found on the surface of an AlSi9Cu3 specimen (Fig. 5)
and on the surface of an AZ91 hp specimen (Fig. 6),
respectively. The AlSi9Cu3 specimen was loaded with
1.05!109 cycles at 47.5 MPa, which is 78% of the mean
endurance limit of this material in warm air. The AZ91 hp
specimen was cycled at 38 MPa (90% of the mean
endurance limit) for 1.51!109 cycles. Several SEM
pictures of the specimens’ surfaces at different magnifi-
cations were taken to exactly locate the indicated crack
tips. Afterwards, the specimens were removed from the
SEM and fractured at higher cyclic stresses. This served
to produce the fracture surfaces, which are shown at the
same magnification in the lower part of Figs. 5 and 6. Gas
porosity is the origin of both fatigue cracks. Crack length
on the surfaces are 1.0 mm (AlSi9Cu3) and 1.6 mm
Fig. 5. Non-propagating fatigue crack in AlSi9Cu3: the fatigue crack (upper
figure) was visible on the specimen’s surface after cycling at 47.5 MPa for
1.05!109 cycles. Then the specimen was ruptured at 85 MPa in 1.15!105 cycles to produce the fracture surface (lower figure). Fatigue crack and
fracture surface are at the same magnification, indicated on the upper figure.
fracture surface are at the same magnification, indicated on the upper figure.
(AZ91 hp). These crack lengths are considerably larger
than the respective sizes of the crack initiating porosity.
The longest cracks observed on surfaces of runnout
AlSi9Cu3 specimens were 1.2 mm and were found on two
specimens cycled at 47.5 and 57 MPa, respectively. The
longest surface cracks of runnout AZ91 hp specimens
were 1.6 mm (Fig. 6) and 1.2 mm after cycling at 38 MPa.
3.3. Critical stress intensity amplitude
Assuming the area affected by porosity as the initial crack
and using Eq. (3), the stress intensity amplitudes of all
specimens were evaluated. Runnout specimens were frac-
tured at high stresses to locate defects, which were too small
to cause failure at the low loads. Stress intensity amplitudes
of fractured specimens and runnouts are shown in Fig. 7 with
closed and open circles, respectively. Shaded areas indicate
the ranges of the critical stress intensity factors, i.e. stress
intensity amplitudes, which caused failure of some speci-
mens and no failure of others. Table 5 summarizes the
critical stress intensity factors at elevated temperature.
Additionally, previously determined critical stress intensity
factors in ambient air are shown. Mean values of the critical
stress intensity factors in warm air are approximately 90%
(AlSi9Cu3, AZ91 hp) or 80% (AS21 hp, AE42 hp) of the
respective values found in ambient air. The ranges of
0.5 0.7 1 2 3 4 5
Kmax (MPam1/2)
No Failure
AlSi9Cu3
Failure
0.5 0.7 1 2 3
No Failure
AZ91 hp
Failure
Kmax (MPam1/2)
0.3 0.5 0.7 1 2 3
No Failure
AS21 hp
Failure
Kmax (MPam1/2)
0.3
0.3
0.5 0.7 1 2 3
AE42 hp
No Failure Failure
Kmax (MPam1/2)
Fig. 7. Stress intensities of broken specimens (solid circles) and runnouts (open circles) assuming the defect area as crack. The shaded region indicates the
critical stress intensity range where failures as well as runnouts occurred.
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1083
the critical stress intensity amplitudes in warm air are
typically twice as large as in ambient air.
The fraction of fatigue cracks initiating at material
defects at the surface is also shown in Table 5. In AlSi9Cu3,
about 1/3 of the fatigue cracks initiated at surface porosity
and 2/3 at internal defects in warm as well as ambient air.
Crack initiation in the magnesium alloys in ambient air is
preferentially at the surface, and 10% or less initiate from
the interior. In warm air, this preference for surface crack
initiation is less pronounced, and fatal fatigue cracks in
approximately 25% (AZ91 hp, AE42 hp) or more (AS21 hp)
of the fractured specimens initiated at internal porosity.
3.4. Fatigue crack growth and threshold data
In Fig. 8, the results of fatigue crack growth tests in warm
air of 150 8C (AlSi9Cu3, Fig. 8(a)) and 125 8C (AZ91 hp,
Fig. 8(b) and AS21 hp, Fig. 8(c)) are shown. For
comparison, previously measured data in ambient air
(open circles) and in a vacuum (triangles) are included
[31]. Arrows indicate that no crack growth was observed
within the optical resolution of crack length measurement
cycling the specimens for 2!107 cycles (warm air and
ambient air) or 108 cycles (vacuum). These measurements
indicate threshold stress intensities with limiting growth
Table 5
Critical stress intensity amplitudes and frequency of crack initiation at the surfac
Critical stress intensity
amplitude in warm air,
Kcrit (MPam1/2)
Fraction of cracks
starting at the surfa
warm air
AlSi9Cu3 1.4–1.8 0.37
AZ91 hp 0.85–1.05 0.72
AS21 hp 0.55–0.75 0.56
AE42 hp 0.7–0.9 0.76
rates of 3.5!10K13 m/cycle. Table 6 summarises the
threshold stress intensity amplitudes at load ratio RZK1
in the three environments.
Increasing testing temperature leads to increased fatigue
crack propagation rates and reduced threshold stress
intensities in all three materials. Compared with ambient
air, crack growth data measured in warm air are shifted
towards lower stress intensity amplitudes. Threshold stress
intensities at elevated temperatures are approximately 80%
of the respective values found in ambient air. Minimum
growth rates of propagating cracks in warm and ambient air
are about 10K11 m/cycle (AlSi9Cu3), 10K10 m/cycle (AZ91
hp) and 3!10K11 m/cycle (AS21 hp) and lower growth
rates result from experiments, in which a crack propagated
first and stopped afterwards, although stress intensity
amplitude was kept constant. In vacuum, threshold
behaviour in the magnesium alloys is not so distinct as in
ambient or warm air, and cycling close to the threshold
could produce mean fatigue crack propagation rates in the
regime of 10K12–10K11 m/cycle.
Fatigue fracture surface of AS21 hp after near threshold
cycling at 20 and 125 8C is shown in Fig. 9. The specimen
was initially cycled in ambient air at constant stress intensity
amplitude of 1.6 MPam1/2. Then the experiment continued
in warm air at the same stress intensity. Fig. 9 shows the area
e in warm air and in ambient air, respectively
ce,
Critical stress intensity
amplitude in ambient air,
Kcrit (MPam1/2)
Fraction of cracks
starting at the surface,
ambient air
1.75–1.95 0.33
1.0–1.1 0.92
0.7–0.8 0.96
0.9–1.1 0.90
10-13
10-12
10-11
10-10
10-9
10-8
10-7
1 2 3 4 5 6 7 8
Fatig
ue C
rack
Gro
wth
Rat
e (m
/ C
ycle
)
Kmax (MPam1/2)
10-13
10-12
10-11
10-10
10-9
10-8
10-7
0.8 1 2 3 4 5 6
Fatig
ue C
rack
Gro
wth
Rat
e (m
/ C
ycle
)
Kmax (MPam1/2)
10-13
10-12
10-11
10-10
10-9
10-8
10-7
0.8 1 2 3 4 5 6
Fatig
ue C
rack
Gro
wth
Rat
e (m
/ C
ycle
)
Kmax (MPam1/2)
(a) (b)
(c)
Fig. 8. Fatigue crack growth data of (a) AlSi9Cu3, (b) AZ91 hp and (c) AS21 hp in warm air (closed circles), ambient air (open circles) and in vacuum
(triangles).
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881084
on the fracture surface, where the environment has been
changed from low temperature (left side of the figure) to
elevated temperature (right side of the figure). Crack growth
is transcrystalline, relatively flat and shows no apparent
differences after cycling in both environments. The fracture
surfaces of the other testing materials were also similar after
cycling in ambient and warm air. Shrinkage porosity and
dendrites are visible in the upper section of Fig. 9. Porosity
is visible on several areas of the fracture surfaces and is
probably the main reason for the pronounced scatter of
fatigue crack growth data.
Table 6
Threshold stress intensities at RZK1 determined in warm air (150 8C for AlSi9C
Threshold stress intensity amplitude
in warm air, Kmax,th (MPam1/2)
Threshold s
in ambient a
AlSi9Cu3 1.95–2.2 2.45–2.7
AZ91 hp 1.05–1.2 1.30–1.55
AS21 hp 0.95–1.15 1.25–1.45
4. Discussion
Increasing the testing temperature deteriorated the
fatigue properties of high-pressure die-cast magnesium
alloys. S–N fatigue tests in warm airflow (125 8C) delivered
endurance limits at 109 cycles, which were 70–90% of
the respective stresses found in ambient air (20 8C), and
threshold stress intensities decreased to approximately 80%
of the values found at the low temperature. Loss of cyclic
strengths is within ranges comparable to the decrease of
static strengths, since tensile strengths at elevated
u3, 125 8C for AZ91 hp and AS21 hp), ambient air (20 8C) and in vacuum
tress intensity amplitude
ir, Kmax,th (MPam1/2)
Threshold stress intensity amplitude
in vacuum, Kmax,th (MPam1/2)
3.3–3.4
2.1–2.3
2.3–2.7
Fig. 9. Fatigue fracture surface of AS21 hp produced in ambient and warm
air. The picture shows the area where the temperature was increased from
20 8C (left side of the figure) to 125 8C (right side of the figure). Crack
growth direction is from left to right.
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1085
temperature are 80–85% and yield strengths are about 80%
of the respective stresses found at ambient temperatures.
Within the investigated magnesium alloys, AZ91 hp showed
better cyclic properties in warm air than AE42 hp, and AS21
hp exhibited the lowest cyclic strength, which is the same
ranking as in ambient air environment.
AlSi9Cu3 is a typical aluminium alloy used in high-
pressure die-casting, and cyclic properties of the magnesium
alloys may be compared with this material. Testing the
aluminium alloy at 150 8C, fatigue limit and threshold stress
intensity were about 80% of the respective values
determined in ambient air. Deterioration of fatigue proper-
ties of the magnesium alloys by increasing the temperature
to 125 8C is comparable to the loss of cyclic strength of the
aluminium alloy by increasing the temperature to 150 8C.
The mean fatigue limit of AZ91 hp at 125 8C is about 65%
of the stress amplitude determined for AlSi9Cu3 at 150 8C,
and threshold stress intensity is about 55% of the respective
value of the aluminium alloy. The fatigue limits of the
magnesium alloys at 20 and 125 8C are 40–45% of their
respective yield stresses and 25–30% of the tensile
strengths, whereas the fatigue limits of AlSi9Cu3 at low
and elevated temperatures are 50–55% of its yield strength
and 30–35% of the tensile strength.
Increase of temperature leads to greater cyclic plasticity
involved with fatigue cycling [11], greater accumulated
fatigue damage and thus lower cyclic strength of
magnesium alloys [34,35]. Several aspects of the fatigue
process at elevated and room temperature are, however,
comparable. Fatigue cracks start, nearly, exclusively (more
than 98%) at porosity in both environments. No obvious
temperature influence on crack path and fracture surface
appearance can be observed. Initial crack growth at porosity
and crack propagation at near threshold stress intensities is
mainly inside the (a-Mg) grains and tends to avoid
interdendritic regions [19,31], which is consistent with
the observations of Horstemeyer et al. [13] who found such
crack paths cycling AM60-B and AZ91-T4 [17] at low
stress intensity amplitudes. In contrast, at high cyclic
stresses [36], at high temperatures of 250 8C [34] or stress
intensities distinctly above threshold [13,17] cracks mainly
initiate and propagate in the interdendritic region. The
shapes of the S–N curves measured in warm air resemble the
respective curves determined in ambient air environment,
and increasing the testing temperature shifts the S–N curves
towards lower cyclic stresses. In both environments, an
endurance limit is found and cycles to failure above
2!107 cycles are rare.
Fatigue cracks were found on the surfaces of some
specimens, which were cycled with minimum 109 cycles
and did not fail. These cracks may be assumed as
non-propagating cracks, since possible mean growth
rates to reach 1 mm within 109 cycles would correspond
to 10K12 m/cycle, which is below technical significance, at
least in automotive applications. Comparable maximum
lengths of non-propagating cracks are observed by Caton
[24] who found crack length greater than 1 mm in 319 T7
aluminium specimens, which did not fail within 108 cycles.
In the magnesium alloy AZ91D, decreasing growth rates
with increasing crack length and non-propagating fatigue
crack are documented for cycling notched specimens at low
stress amplitudes [37]. Stop of crack growth of fatigue
cracks initiating at porosity may be explained by increasing
crack opening stress intensity with increasing crack length
[38], which eventually causes too low effective stress
intensity ranges to further propagate the crack.
The endurance limit behaviour of the investigated
materials is caused by porosity and the phenomenon of
non-propagating cracks and is not an inherent property of
the alloys. Testing AZ91 hp produced by gravity die-casting
[8] and Vacural die-casting [19] and evaluating solely
defect-free samples, considerably higher cyclic strength,
monotonic increase of lifetimes with decreasing cyclic
stresses and no endurance limit below 109 cycles was found.
Similarly, cast aluminium alloys frequently do not show a
fatigue limit [4]. Thus, the endurance limit stress of the
investigated alloys may be ascribed to the distribution of
porosity and the capability of the microstructure to stop
crack propagation. At low stress intensities, particles in the
interdendritic region and grain boundaries may serve as
barriers and decelerate fatigue crack propagation rates [17].
The critical stress intensity amplitude, Kcrit may be used
as measure for the sensitivity of the microstructure to
defects, i.e. the greater Kcrit, the higher cyclic stresses are
necessary to propagate a crack initiating at porosity to
rupture. Specimens can sustain cyclic stresses without
fatigue failure if the cyclic stress intensity determined for its
most damaging porosity is lower than Kcrit. Considering
the distribution of porosity and the preference for
crack initiation at the surface or in the interior, the
probability for failure at certain stress amplitude may be
linked to the distribution of porosity in a material [19].
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881086
Comparing the magnesium alloys, mean value of Kcrit of
AZ91 hp in warm air is about a factor 1.45 higher than Kcrit
of AS21 hp. The mean endurance limit of AZ91 hp is a
factor 1.52 higher than the mean endurance limit of AS21
hp. Thus, the lower fatigue strength of AS21 hp is mainly
caused by its greater defect sensitivity and to a far lesser
extent by the greater mean defect size. On the other hand,
mean defect size in AE42 hp is smaller than in AZ91 hp.
Mean value of Kcrit of AZ91 hp is, however, about a factor
1.2 higher than Kcrit of AE42 hp, and consequently its mean
fatigue limit is a factor 1.17 higher. Within comparable
microstructures, the growth rates of small fatigue cracks
increase as the yield strengths decrease [23]. This may be
the reason for the correlation of Kcrit with the yield strength
of the magnesium alloys, i.e. the higher the yield stress, the
higher the critical stress intensity. Kcrit is lower than the
threshold stress intensity of long cracks since short cracks
grow at cyclic stress intensities below the long crack
threshold [39]. Effective threshold stress intensities of AZ91
are found at 0.7 MPam1/2 [40,41] and 0.55 MPam1/2 [15],
and Kcrit is larger than this value.
The greatest effect of testing temperature on the fatigue
performance was found in endurance tests of AS21 hp,
where the mean endurance limit at 125 8C is 71% of the
stress found at 20 8C. A more pronounced influence of
testing environment is observed comparing crack propa-
gation properties in ambient air and vacuum. Threshold
stress intensity of AZ91 hp in vacuum is a factor 1.55 higher
than in ambient air, and a factor 1.85 higher threshold value
in vacuum is found for AS21 hp. The deleterious influence
of ambient air on fatigue damage in magnesium alloys is
caused by air humidity, which accelerates crack growth and
reduces the plasticity at the crack tip [42–45]. Chemical
processes on the newly created surfaces are especially
pronounced for near threshold cycling and slowly growing
fatigue cracks [31]. Fatigue cracks form more rapidly and
short cracks propagate faster if cycled in humid environ-
ment instead of in a vacuum [16]. In aluminium alloys, air
humidity has a similar deleterious effect on fatigue crack
growth [46–48]. However, compared with other aluminium
alloys [49,50], the influence of atmospheric moisture on
near threshold fatigue crack growth in AlSi9Cu3 is
relatively small, and threshold stress intensity in vacuum
is only a factor 1.3 higher than in ambient air.
In the absence of environmental effects, crack initiation
location would be expected at the defect with the greatest
value of a(Defect Area)1/4, according to Eq. (3). However,
fatigue cracks which initiate at surface defects grow under
the influence of atmospheric moisture, whereas initial crack
growth of internal cracks is in vacuum. In AlSi9Cu3, the
deleterious influence of atmospheric moisture is relatively
weak. Fatigue cracks preferentially initiate inside the
specimen due to the greater probability that large defects
are located in the interior of the stressed volume than at
the surface. In the magnesium alloys, the stronger
environmental effect causes preferential crack initiation at
surface defects. In ambient air, crack initiation is almost
exclusively (90% or more) at surface defects and the range
of the critical stress intensity is narrow (Table 5). At
elevated temperature, fatigue loading involves greater
cyclic plasticity, which makes initiation of fatal cracks at
(large) internal defects more probable. Minimum stress
intensities necessary to propagate small cracks to fracture at
125 8C are probably different in inert environment and air.
The greater variation of the crack initiation location is
probably one reason for the wider range of the critical stress
intensity at 125 compared with 20 8C.
5. Conclusions
The fatigue properties of the magnesium alloys AZ91 hp,
AS21 hp and AE42 hp and of the aluminium alloy AlSi9Cu3
produced by high-pressure die-casting have been investi-
gated in warm air. Experiments in ambient air served for
comparison, and the following conclusions may be drawn.
1.
Increasing testing temperature to 125 8C decreases theendurance limits of the magnesium alloys at 109 cycles
to 70–90% of the stress amplitudes determined at room
temperature, and the threshold stress intensities are about
80% of the respective values at 20 8C. Loss of fatigue
strength of the aluminium alloy is in comparable ranges
by increasing the temperature to 150 8C. Shapes of the
S–N curves are similar at low and elevated temperatures
and the curves are shifted towards lower cyclic stresses.
Fatigue crack growth curves are shifted towards lower
cyclic stress intensities.
2.
The magnesium alloy AZ91 hp reaches about 2/3 of theendurance limit stress of AlSi9Cu3 and threshold stress
intensities at low and elevated temperature are about
55% of the respective values of the aluminium alloy.
AZ91 hp shows better cyclic properties than AE42 hp at
room and elevated temperatures, and the lowest cyclic
strength was found for AS21 hp, which corresponds to
the ranking of the static strength properties of these
alloys.
3.
Fatigue crack initiation is, nearly, exclusively (greater98%) at porosity in warm and ambient air and fatigue
crack propagation is mainly transgranular. Fatigue
cracks initiate at porosity even at stresses below the
endurance limit. The longest cracks found on surfaces of
specimens which survived 109 cycles were 1.0–1.6 mm.
The endurance limit is related to a non-propagating
condition of cracks rather than a non-initiating condition.
4.
Considering the area affected by porosity as initial crack,failed and runnout specimens are used to determine the
critical stress intensity amplitude, Kcrit. Materials can
sustain cyclic stresses without fatigue failure if the cyclic
stress intensity determined for their most damaging
porosity is lower than Kcrit. The critical stress intensity
amplitude is smaller than the threshold stress intensity of
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–1088 1087
long cracks and larger than the effective threshold stress
intensity and can be used to quantify the sensitivity of a
material to defects.
Acknowledgements
Investigations were financed by the AUDI AG, Ingol-
stadt, which is gratefully acknowledged.
References
[1] Aghion E, Eliezer D, editors. Proceedings of the first Israeli
international conference on magnesium science and technology,
Dead Sea, Israel. Israel: Magnesium Research Institute; 1997.
[2] Mordike BL, Kainer KU, editors. Magnesium alloys and their
applications. Wolfsburg, Germany: Werkstoff-Info GmbH Frankfurt;
1998.
[3] Kainer KU, editor. Magnesium alloys and their applications.
Weinheim, Germany: Wiley–VCH Verlag GmbH; 2004.
[4] Henry SD, Davidson GM, Lampman SR, Reidenbach F, Boring RL,
Scott WW, editors. Fatigue data book: light structural alloys. New
Jersy: ASM International; 1995.
[5] Bhambri AK, Kattamis TZ. Cast microstructure and fatigue behavior
of a grain-refined Mg–Zn–Zr alloy. Met Trans 1971;2:1869–74.
[6] Chaudhuri SK, Nair K. Influence of microshrinkage on mechanical
properties of a magnesium–zinc–zirkonium–rare earth alloy. Mater
Sci Eng 1979;37:159–64.
[7] Donlon WT, Paige C, Morris CJ, Allison JE. The effects of casting
defects and microstructure on the mechanical properties of die cast
AM50 magnesium and 356 aluminum. Proceedings of the aluminum
and magnesium for automotive applications, Cleveland, Ohio, USA.
USA: Minerals, Metals and Materials Society/AIME; 1996, p. 17–27.
[8] Mayer H, Lipowsky H, Papakyriacou M, Rosch R, Stich A, Stanzl-
Tschegg S. Application of ultrasound for fatigue testing of lightweight
alloys. Fatigue Fract Eng Mater Struct 1999;22:591–9.
[9] Rodrigo D, Murray M, Mao H, Brevick J, Mobley C, Chandrasekar V,
et al. Effects of section size and microstructural features on the
mechanical properties of die cast AZ91D and AM60B magnesium
alloy test bars. SAE Trans: J Mater Manufact 1999;108:785–9.
[10] Liu Z, Wang Z, Wang Y, Liu Z. Cyclic deformation behaviour of high
pressure die casting alloy AM50. J Mater Sci Lett 1999;18:1567–9.
[11] Eisenmeier G, Holzwarth B, Hoppel HW, Mugrabi H. Cyclic
deformation and fatigue behaviour of the magnesium alloy AZ91.
Mater Sci Eng 2001;A319–321:578–82.
[12] Potzies C. PhD Dissertation: Zum Ermudungsverhalten der Mag-
nesium-Gusslegierung G-MgAl9Zn1 (AZ91). Berlin, TU Berlin:
Verkehrs- und Maschinensysteme; 2001.
[13] Horstemeyer MF, Yang N, Gall K, McDowell D, Fan J, Gullett P.
High cycle fatigue mechanisms in a cast AM60B magnesium alloy.
Fatigue Fract Eng Mater Struct 2002;25:1045–56.
[14] Renner F, Zenner H. Fatigue strength of die-cast magnesium
components. Fatigue Fract Eng Mater Struct 2002;25:1157–68.
[15] Sajuri ZB, Umehara T, Miyashita Y, Mutoh Y. Fatigue-life prediction
of magnesium alloys for structural applications. Adv Eng Mater 2003;
5(12):910–6.
[16] Gall K, Biallas G, Maier HJ, Gullet P, Horstemeyer MF,
McDowell DL, et al. In-situ observations of high cycle fatigue
mechanisms in cast AM60B magnesium in vacuum and water vapor
environments. Int J Fatigue 2004;26(1):59–70.
[17] Horstemeyer MF, Yang N, Gall K, McDowell DL, Fan J, Gullett PM.
High cycle fatigue of a die cast AZ91-T4 magnesium alloy. Acta
Mater 2004;52(5):1327–36.
[18] Mayer H, Papakyriacou M, Stanzl-Tschegg S, Tschegg E, Zettl B,
Lipowsky H, et al. Korrosionsermudung verschiedener Aluminium-
und Magnesium-Gublegierungen. Materials and Corrosion 1999;50:
81–9.
[19] Mayer H, Papakyriacou M, Zettl B, Stanzl-Tschegg SE. Influence of
porosity on the fatigue limit of die cast magnesium and aluminium
alloys. Int J Fatigue 2003;25(3):245–56.
[20] Couper MJ, Neeson AE, Griffith JR. Casting defects and the fatigue
behavior of an aluminium casting alloy. Fatigue Fract Eng Mater
Struct 1990;13(3):213–27.
[21] Ting JC, Lawrence FV. Modeling the long-life fatigue behaviour of a
cast aluminium alloy. Fatigue Fract Eng Mater Struct 1993;16(6):
631–47.
[22] Skallerud B, Iveland T, Harkegard G. Fatigue life assessment of
aluminium alloys with casting defects. Eng Fract Mech 1993;44(6):
857–74.
[23] Caton MJ, Jones JW, Allison JE. Use of small fatigue crack growth
analysis in predicting the S–N response of cast aluminium alloys. In:
Newman JC, Piascik RS, editors. Fatigue crack growth thresholds,
endurance limits, and design, ASTM STP 1372. West Conshohocken,
PA: ASTM; 2000, p. 285–303.
[24] Caton MJ. PhD Dissertation: predicting fatigue properties of cast
aluminium by characterizing small-crack propagation behavior. Ann
Arbor, MI: University of Michigan; 2001.
[25] Caton MJ, Jones JW, Mayer H, Stanzl-Tschegg S, Allison JE.
Demonstration of an endurance limit in cast 319 aluminum. Metall
Mater Trans A 2003;34A:33–41.
[26] Stanzl-Tschegg SE, Mayer HR, Tschegg EK, Beste A. In-service
loading of AlSi11 aluminium cast alloy in the very high cycle regime.
Int J Fatigue 1993;15(4):311–6.
[27] Dabayeh AA, Xu RX, DU BP, Topper TH. Fatigue of cast aluminium
alloy under constant and variable-amplitude loading. Int J Fatigue
1996;18(2):95–104.
[28] Schumann S, Friedrich F. The use of magnesium in cars—today and in
future. Proceedings of the magnesium alloys and their applications.
Wolfsburg, Germany: Werkstoff-Info GmbH Frankfurt; 1998, p. 3–13.
[29] Schindelbacher G, Rosch R. Mechanical properties of magnesium die
casting alloys at elevated temperatures and microstructure depen-
dence of wall thickness. In: Mordike BL, Kainer KU, editors.
Magnesium alloys and their application. Frankfurt: Werkstoff-
Informationsgesellschaft; 1998, p. 247–52.
[30] Maenning WW. Planning and evaluation of fatigue tests. In:
Lampman SR, Davidson GM, Reidenbach F, et al, editors. ASM
Handbook Fatigue and Fracture, vol. 19. Materials Park, OH: ASM
International; 1997. p. 303–13.
[31] Papakyriacou M, Mayer H, Fuchs U, Stanzl-Tschegg SE, Wei RP.
Influence of atmospheric moisture on slow fatigue crack growth at
ultrasonic frequency in aluminium and magnesium alloys. Fatigue
Fract Eng Mater Struct 2002;25(8/9):795–804.
[32] Mayer H. Fatigue crack growth and threshold measurements at very
high frequencies. Int Mater Rev 1999;44(1):1–36.
[33] Murakami Y, Endo M. The area parameter model for small defects
and nonmetallic inclusions in fatigue strength: experimental evi-
dences and applications. Proceedings of the theoretical concepts and
numerical analysis of fatigue, Birmingham, UK. Cradley Heath,
Warley, UK: Engineering Materials Advisory Services Ltd; 1992.
[34] May MJ, Honeycombe RWK. The effect of temperature on the fatigue
behaviour of magnesium and some magnesium alloys. J Inst Metals
1963;92:41–9.
[35] Ogarevic VV, Stephens RI. Fatigue of magnesium alloys. Annu Rev
Mater Sci 1990;20:141–77.
[36] Wang X, Fan J. SEM online investigation of fatigue crack initiation
and propagation in cast aluminium alloy. J Mater Sci 2004;39:
2617–20.
[37] Venkateswaran P, Raman SGS, Pathak SD, Miyashita Y, Mutoh Y.
Fatigue crack growth behaviour of a die-cast magnesium alloy
AZ91D. Mater Lett 2004;58:2525–9.
H. Mayer et al. / International Journal of Fatigue 27 (2005) 1076–10881088
[38] Ishihara S, McEvily AJ. Analysis of short fatigue crack growth in
aluminum alloys. Int J Fatigue 2002;24:1169–74.
[39] Pearson S. Initiation of fatigue cracks in commercial aluminium alloys
and the subsequent propagation of very short cracks. Eng Fract Mech
1975;7:235–47.
[40] Goodenberger DL, Stephens RI. Fatigue of AZ91E-T6 cast mag-
nesium alloy. J Eng Mater Technol 1993;115:391–7.
[41] Jung HC, Yim CD, Park WW, Lee CS, Shin KS. Fatigue crack
propagation behavior of AZ91D magnesium alloy. Mater Sci Forum
2003;419–422:75–80.
[42] Grinberg NM. The effect of vacuum on fatigue crack growth. Int
J Fatigue 1982;4(2):83–95.
[43] Serdyuk VA, Grindberg NM. The plastic zone and growth of fatigue
cracks in magnesium MA12 alloy at room and low temperatures. Int
J Fatigue 1983;5(2):79–85.
[44] Kobayashi Y, Shibusawa T, Ishikawa K. Environmental effect of
fatigue crack propagation of magnesium alloy. Mater Sci Eng 1997;
A234–236:220–2.
[45] Kobayashi Y, Takano T, Ishikawa K. Effect of oxygen and hydrogen
on fatigue crack propagation of AZ91 and AM60 alloys. Proceedings
of the seventh international fatigue conference, Bejing. Cradley
Heath, UK: EMAS; 1999.
[46] Bradshaw FJ, Wheeler C. The influence of gaseous environment and
fatigue frequency on the growth of fatigue cracks in some aluminium
alloys. Int J Fract Mech 1969;5(4):255–68.
[47] Wei RP. Some aspects of environment-enhanced fatigue-crack
growth. Eng Fract Mech 1970;1:633–51.
[48] Davidson DL, Lankford J. The effect of water vapor on fatigue crack
tip mechanics in 7075-T651 aluminium alloy. Fatigue Fract Eng
Mater Struct 1983;6(3):241–56.
[49] Holper B, Mayer H, Vasudevan AK, Stanzl-Tschegg SE. Near
threshold fatigue crack growth in aluminium alloys at low and
ultrasonic frequency: influences of specimen thickness, strain rate,
slip behaviour and air humidity. Int J Fatigue 2003;25(5):
397–411.
[50] Holper B, Mayer H, Vasudevan AK, Stanzl-Tschegg SE. Near
threshold fatigue crack growth at positive load ratio in aluminium
alloys at low and ultrasonic frequency: influences of strain
rate, slip behaviour and air humidity. Int J Fatigue 2004;26(1):
27–38.