Fatigue strength and applications of cast aluminium alloys with different degrees of porosity

Int J Fatigue 15 No 2 (1993) pp 7 5 - 8 4

Fatigue strength and applications of cast aluminium alloys with different degrees of porosity C.M. Sonsino and J. Ziese

This paper reports on the influence of porosity on constant- and variable-amplitude fatigue of an age-hardened alloy G-AI-7Si-0.6Mg wa and a non-age-hardened alloy G-AI-11Si-Mg-Sr. Both alloys reveal a cycling hardening. The age-hardened alloy is suitable for finite fatigue life and variable-amplitude fatigue applications, but not the non-age-hardened alloy because of the flat course of its S--N curve. Despite the large differences between the static strength properties, the endurance limit properties are similar. If the degree of porosity is increased from 0 to 8, fatigue strength is reduced in the unnotched condition by about 17% for both alloys. However, in the notched condition the age-hardened alloy displays a reduction of 7% but the nonage-hardened material a drop of 20% due to its lower yield stress. The influence of the thickness of the solidified cross-section on fatigue strength in the porous condition could not be determined. Porosity can be tolerated even in safety parts, but not in highly stressed fatigue-critical areas.

Key words: cast aluminium; age hardening; porosity; constant-amplitude loading; variable-amplitude loading; mean-stress sensitivity; notch effects; damage accumulation; porosity allowance criteria The correct evaluation of the influence of casting-related porosity on the fatigue life of cast aluminium components in road and rail vehicle engineering has always been a matter of concern for design and quality assurance. This issue was investigated within the scope of a research project of the Verein Deutscher Gief~ereifachleute (Association of German Casting Experts) (VDG), Diisseldorf, which studied the agehardened alloys G-AI-7Si-0.6Mg wa, G-AI-4Cu-Ti wa and the non-age-hardened alloys G-AI-11Si-Mg-Sr, G-AI-11SiMg and G-AI-llSi-Sr frequently used for the production of fatigue-loaded components. 1 Geometric influences idealized by notched and unnotched specimens from different solidified cross-sections, as well as load-specific parameters (i.e. constant- and variable-amplitude loading with different stress ratios), were included in the investigation (Fig. 1). The alloys G-AI-7Si-0.6Mg wa and G-AI-11Si-Mg-Sr representing the aforementioned groups were used as examples to discuss the interdependence of classified gas porosity degrees in the ranges 0, 4 and 8 according to ASTM E155 and fatigue strength. How these results are used in practice is shown in automotive components such as rear suspension (with control arm, semi-trailing arm and carrier tube), front axle carrier, support bearing, wheel and steering gear.

Loading and geometry

Aluminium castings I

I Stress r a t i o :

Degree of p o r o s i t y : according to ASTM categories = 0 , = 4 , = 8

R=-I

Cast thickness 10,20,30 mm

I

I

Load- and d e s i g n - r e l a t e d parameters

Alloying and casting parameters

Fatigue tests

influence of porosity on: Constant amplitude fatigue o a Variable amplitude fatigue a

S--N c u r v e s

Material and test specimen preparation Production requirements and test specimen preparation For sampling, slab-shaped raw castings were produced with porosity degrees of 0, 4 and 8 according to ASTM guidelines 2

a n d R= 0

Axial loading: constant and variable amplitudes Stress concentration : f l a t specimens notch f a c t o r s K t = l . 0 a n d 2 . 5

o a = f (N)

fatigue-life curves

and

~a = f ( N )

Scatter of S--N curves T

, TN and a scatter of f a t i g u e - l i f e c u r v e s r~ , T/~ a

Fig. 1 O v e r v i e w of plan of investigations

0142-1123/93/020075-10 © 1993 Butterworth-Heinemann Ltd Int J Fatigue March 1993

75

T a b l e 1. H e a t t r e a t m e n t Material

Material no.

G-AI-7Si0.6Mg wa G-AI-11Si-

Annealing Quenching

Ageing

3.2371.61 12h/540 °C H20/60 °C 6h/155 °C *

--

--

--

Mg-Sr Melting of block material in gas-fired crucible furnace (contents 90 kg ) Superheating and pouring temperature: 750 °C -+ 10 °C Refining: 10 min vacuum degassing. Gassing with NH4CI to obtain desired porosity Cope and drag moulds: polyurethane bounded silica sand, grain size F 32 Heat treatment after removal of sprues and risers *Alloy not classified; except for the additional elements Mg and Sr it corresponds to material no. 3.2211 according to DIN

and wall thicknesses of 10, 20 and 30 mm similar to component cross-sections used in practice. The porosity degree was adjusted through the gas content of the melt and gassing: ie, a gas porosity with spherical, homogenously distributed pores. The heat treatments carried out during manufacturing of the castings and the different production steps are shown in Table 1. Finally, flat bar specimens with a thickness of 5 mm were taken from the centre of the relevant slabs for fatigue testing under axial load. These were then used to prepare the unnotched (Kt = 1) and notched specimens (Kt = 2.5) (Fig. 2). The influence of porosity, ie of the internal notch effect in relation to the outer notch condition on fatigue strength, was investigated with these specimens. Chemical composition, mechanical properties, microstructure and porosity

Table 2 shows the chemical composition of the alloys G-AI7Si-0.6Mg wa and G - A I d 1Si-Mg-Sr. Table 3 shows the mechanical properties of the aforementioned alloys dependent on the solidified cross-section, the degree of porosity (P), density p and porosity 3 Vp = [p (P=0) -p(P)]/o(P=O). Density and porosity may differ even if the degree of porosity is the same. As porosity increases, tensile strength, yield point and hardness decrease; elongation after fracture, however, hardly changes. Table 4 indicates that both alloys harden cyclically when subjected to elastic-plastic cyclic stress. The microstructure 40

i

Section A--B

E ,

20

r

+o.1

-*~.~

q0

Section A--B IFretted

I

5

110

Tests were carried out mainly under axial constant-amplitude loading for the plotting of S - N curves in the finite and highcycle fatigue ranges. The majority of constant-amplitude tests were carried out under alternating load (R = - 1 ) and a small number under pulsating load (R = 0) to get an insight into mean stress sensitivity. 4 Also on a small number of notched specimens the influence of the degree of porosity on crack initiation and propagation was investigated. Some alloys were subjected to variable-amplitude loading with a Gaussian random process s having a sequence length of H0 = 5 × 10s load cycles to determine fatigue life curves. Through subsequent comparison of S - N and fatigue life curves the real damage sum was determined for future fatiguelife predictions. These tests were conducted under alternating load only. The constant-amplitude tests were carried out loadcontrolled on a 60 kN Schenck resonance fatigue-testing machine with a frequency o f f = 50 Hz. The load-controlled variable-amplitude tests were carried out on a 100 kN Schenck servohydraulic testing machine. Test frequency was f = 30 Hz. To assure a correct comparison of S - N and fatigue-life curves and to exclude testing machine influence, a few constant-amplitude tests were carried out on the servohydraulic testing machine. The constant-amplitude test results obtained on the servohydraulic machine were within the scatter range of results of the resonance fatigue-testing machine.

E v a l u a t i o n of f a t i g u e t e s t r e s u l t s

}

vw(~)

w~(~)

r

b

Fig. 2 Geometry of specimens for fatigue testing: (a) unnotched specimen (/~ = 1.0); (b) notched specimen (Kt = 2.5). Dimensions mm

76

Testing programme and facilities

Results and discussion ~Q8

a

of the alloy G-AI-Si-0.6 Mg wa consists of aluminium mixed crystals with an unmodified binary AI-Si eutectic partially changed through heat treatment and a ternary AI-Si-2Mg-Si eutectic, visible in the microsection as a light grey phase (Fig. 3). The microstructure of the cast alloy G-AI-TSi-Mg-Sr consists of aluminium mixed crystals with an AI-Si eutectic which appears to be slightly unrefined in spite of the addition of strontium (Fig. 4). Regarding porosity, it should be noted that even materials classified as having a porosity degree P = 0 are not free from pores. They have scattered/isolated micropores up to max. 0.3 mm in size. These micropores are also found adjacent to the larger pores in materials with a higher degree of porosity. With porosity degree P = 4, pore diameters up to max. 0.6 mm were found and with porosity degree P = 8, pore diameters up to max. 1.0 mm (Figs 3 and 4). Random quantitative structure analyses were carried out with plate thicknesses of 10, 20 and 30 mm and solidification times of about 200-900 s with a view to solidification conditions. Because of the different solidification times, differences were found in dendrite arm distances for the three plate thicknesses.

To describe the S - N curves with regard to their slope ks0o/o = log (N1/N2)/log(~2/¢~) within the finite fatigue life range, the knee point and endurance limit values, their scatter T = cra,(Ps = 90%)/¢,.(Ps = 10%) and the drop of fatigue strength in the high cycle range, all results were plotted on a double logarithmic graph and screened for common characteristics analogous to the concept of the standardized S - N curve. 6 This procedure was also used for the evaluation of fatigue tests with variable-amplitude loading. In this paper,

Int J Fatigue M a r c h 1993

Table 2. Chemical composition Weight % Material G-AI-7Si-0.6Mg wa G-AI-11Si-Mg-Sr

Material no.

Cu

Si

Mg

Ti

Fe

Sr

3.2371.61 *

---

6.7-7.1 10.6-11.0

0.60-0.69 0.12-0.17

0.16-0.20 0.15-0.17

0.08-0.10 0.06-0.08

-470-570 ppm

• Alloy not classified; except for Mg and Sr it corresponds to material no. 3.2211 of Honsel-Werke AG

Table 3. Conventional material properties S Material

(mm)

P

p

A S T M E 155 (g cm -3)

Vp

Rm

Rpo.2

A

HB

(%)

(MPa)

(MPa)

(%)

5/250

10

0

2.67

0

319

242

4.0

111

20

0 4 8

2.67 2.57 2.44

0 3.7 8.6

288 280 270

252 253 235

1.4 1.3 1.6

104 102 101

0 8

2.67 2.59

0 3.0

131 130

86 78

2.4 3.2

53 49

G-AI-7Si-0.6Mg wa

G-AI- 11Si-Mg-S r 20

Source: HonseI-WerkeAG (DIN 50125)

Table 4. Material data from monotonic and cyclic stress-strain curves

Material G-AI-7Si-0.6Mg wa G-AI-11Si-Mg-Sr

Rpo.2, monotonic Rpo.2, cyclic

E

(MPa)

(MPa)

(GPa)

286 96

302 107

74 77

Solidified cross-section s = 20 mm, degree of porosity P ~ 0 Data obtained with small specimens 3.6 mm x 4.5 mm x 10mm

the maximum value of the sequence Oran is used for plotting the results. The data are shown in Tables 5 and 6. Some S - N and fatigue-life curves are shown in Figs 5 and 6. When the fatigue test results were plotted, nominal stress amplitude was entered on the stress axis and the number of cycles to rupture on the cycle axis. Local stress in the notch root can be calculated with the help of the relation Cra local = /it or,, for elastic stress and with cyclic stress-strain curves for elastic-plastic stress according to a modified Neuber rule. 7's Through the determination of the number of cycles to crack initiation for the first technical crack with a depth of about 0.5 mm, it is possible to estimate the relationship between the number of cycles to crack and rupture.

Evaluation of variable-amplitude tests for fatigue-life predictions For the investigated alloys, the corresponding S - N and fatigue-life curves under the random-load sequence with Gaussian distribution are already determined for different degrees of porosity and notch types (Fig. 5). 1 The corresponding damage sum can be computed by comparing the S - N

Int J Fatigue March 1993

and fatigue-life curves. These data can then be used by the designer for fatigue-life estimations of components manufactured from the same alloys. In this paper, damage accumulation is determined by means of the modified Palmgren-Miner linear damage-accumulation hypothesis. 9-11 The drop in endurance limit due to its excedance under variable-amplitude loading is taken into account through a hypothetical extension of the S - N curve starting at the knee point with a slope of k' = 2 k - 2 . These calculations are carried out on the basis of nominal stress. On notched specimens, however, the consideration of local notch stress does not offer any advantages. 12 In the range upwards of 107 load cycles with a nominal stress amplitude of about 100 MPa and a notch factor K, = 2.5, local stress is below the cyclic 0.2% yield strength. The structural yield strength in the notch root, however, is higher owing to the supporting effect of stress gradients. 8 This is why these investigations do not show any marked differences with regard to damage sum and fatigue strength data for notched and unnotched specimens. Real damage sums for the alloy G-AI-7Si-0.6Mg wa lie between 0.5 and 1.0 irrespective of the degree of porosity. The damage sums here correspond to the damage sums determined on forged aluminium wheels under random loads. 13 These results confirm that the described damage accumulation law using the allowable damage sum D~ = 0.5 can be applied for fatigue life estimation. Figure 5 also shows the fatigue strength ratios, TM which give the exceedance of the endurance limit at 5×10 6 cycles by the maximum nominal stress of the variable amplitude test (V = &,,/era, ). The ratios are between 2.6 and 2.8 owing to the large difference between yield strength and endurance limit. This difference also determines the gradient of the S - N curve in the finite fatigue life range. With the alloy G-AI-11Si-Mg-Sr, however, there

77

-

e

O D.

O P •

g

*4 D IL

't W O

] mm

I mm

a)

Fig. 3 Distribution of pores ( G - A I - S i - 0 . 6 M g w a ) : (a) p o r o s i t y P = 0, d e n s i t y p = 2.67 g crn 3; (b) P = 4, p = 2.57 g c m -3; (c) P = 8; p = 2.44 g c m

3

Fig. 4 Distribution of pores (G-AI-11Si-Mg-Sr): (a) P = 0, p = 2.67 g cm-3; (b) P = 8, p --- 2.59 g cm -3

is very little difference between yield strength and endurance limit. Consequently, the S - N curves for this alloy are very flat (Fig. 6). For this reason, this alloy is more suitable for components subjected to loads in the endurance limit range. For components subjected to stochastic loads, this material should only be used if the structural yield strength of the component is not exceeded. Mean stress sensitivity, notch factor and porosity

The mean stress sensitivity and fatigue notch factor shown in Fig. 7 are applicable to the endurance limit range only. Figure 7 contains only the values for the alloy G-AI-7Si0.6Mg wa. Because of the differences in density and porosity, the values for the other alloy (see Table 3) were not plotted on the same graph. However, all values are discussed jointly in the following.

78

The mean stress sensitivity of the alloy G-AI-7Si-0.6Mg wa is between M = 0.42 and 0.49. The mean stress sensitivity of the material G-AI-11Si-Mg-Sr is somewhat lower and lies between M = 0.37 and 0.43. Figure 7 shows that mean stress sensitivity drops as density decreases and porosity increases. However, because toughness decreased as porosity increased, a decrease in mean stress sensitivity was not expected. As expected, the fatigue notch factor for the material G-A1-7Si-0.6Mg decreases as porosity increases (Fig. 7). It may be concluded that the material's sensitivity to exterior, mechanically induced notches decreases as porosity (internal notches) increases. E n d u r a n c e l i m i t and p o r o s i t y

The S - N curves for both alloys in notched and unnotched condition are compared in Figs 8 and 9. With the cast alloy G-AI-7Si-0.6Mg wa in unnotched

Int J Fatigue M a r c h 1993

T a b l e 5. D a t a f r o m S - N

a n d f a t i g u e - l i f e curves

(a) constant-amplitude loading

(3. 200[ a

Material

Notch R= Slope Knee point factor, K.t O'mln/ O'rnax k5oo/= Nk %*

io

E

I I 10 0t-

G-AI-7Si-0.6Mg wa 1.0 2.5

4.0 4.8 4.0

1 x 106 2 x 106

23 17 23

G-Al-11Si-Mg-Sr

-1 0 -1

16.0 16.0 16.0

5 x 106 1 × 107

9 9 9

1.0 2.5

Notch factor Kt

Stress ratio e =

~min/~rmax

I°adi~

2°°|b-

----"----~l

T-1"I 25 - ." " ~'J~ "~

~

"

lO~'(pl

g

7 - - ' r - r ~ { J ' s,

r~.k=7 ~7~,~'-~ T = 1:1.25 t ~ ~ . ~ "~'/.~~ v a r i a b l e v : ~ ~ amplitude ~ . -~ = • loading 501- C o n s t a n t : a m p l i t u d e ~ ' ~ - ' ~ - ~ . i ~-L~ ,1:1"40 1

100 |

[

E t~

I

25 104

E Z

k

" ~ ' ~ " "~ L

,oading

I

i ,JliJHI

~ ~,~I

t i l=JlHl--i

2

2

2

5 105

5 106

C y c l e s to r u p t u r e

5 107

i ,llllll

2

5

NR, NR

Slope

ksoo/o

1.0 G-AI-7Si-0.6Mg wa

"~'~ ~_'~" ~ ~

k=7 I ~ ' ~ ~ "//~ T = 1:1.25 ~ ~ Variable~ v = 2.65 ~ .~.lamnlitude - -•' ~ T= 1:1.401 Ioadin

Fig. 5 S-N and fatigue-life curves for the alloy G-AI-7Si-0.6Mg wa ( P = 0 , s = 2 0 m m ) . Loading mode: axial; R, R = - I , f = 5 0 / 3 0 H z . Flat specimen, d = 5 m m . (a) K,= 1.0; (b) Kt = 2.5

(b) variable-amplitude loading Material

~

sol

~n

Scatter: 7",= ~(P,=90%)/cr(P,=IO%) = 1:1.25 at N=10 s cycles and 1:1.40 after the knee point *Drop of fatigue strength a decade after the knee point

~

~-.~r" ~ " ~

| Constant-amplitude~'~--_~.- ~

OrO

-1 0 -1

=1:1.25 ,~ T",.,~ k-4

r-

- 1

7.0

2.5 Scatter: T~ = ~(Ps=90%)/&(P,=IO%) = 1:1.25

condition, the endurance limit decreases by 11% and 17% respectively when the degree of porosity is increased from P = 0 to 4 and P = 8. As expected, this decrease is distinctly lower in the notched condition. With P = 4 there is hardly any decrease and with P = 8 there is a drop of 7%. Therefore it may be concluded that in the presence of external notches,

T a b l e 6. E n d u r a b l e n o m i n a l stress a m p l i t u d e s Material

G-AI- 1 1 S i - M g - S r

S (mm)

P

Kt

R

~a.*

20

8

2.5

-1

33

B

0

35

m

- 1

48

m

-1

41

1.0

0

2.5

0

40

m

- 1

57

m

2.5

- 1

38

--

1.0

- 1

54

--

2.5

- 1

38

1.0

- 1

54

--

2.5

-1

41

109

0

41

--

- 1

59

156

-1

41

113

44

--

6.5

172

1.0

G-AI-7Si-0.6Mg wa

30

20

8

8

4

1.0

0

2.5 1.0

0 -1

10

0

&..*

1.0

0 -1

43 73

*Constant (or,,) and variable (&,,) amplitude Ioadings with Ps = 50% at N= 5 x 106 cycles

Int J F a t i g u e M a r c h 1993

79

200

I001- a

k = 16

//-" ....

Rm/Rpo.2

a R = - i ~,,,,.~ T= 1:1.LI0

/

p C ro

"~""~'~~ " ~ _ /288•252 R = 0 ~,,,,~ " ' - ~ --~ ~ - . ~ / 2 8 0 / 253

100

I0

- - ~ ~ - - ~

so "~

I

L

I

~_ 200 b

E

E r~

100 O) L 4.o m

r-----__ -

50 25

Z

lO 4

-

k=16

. . . . . . .

"------" - ~ . I

i

I

2

lllll[

I

5 105

2

I

l

llllll

l

2

L

T= 1:1.40 p

~__. . . . .

5 106

25

I

l

Itllll

I

2

I

l

I II

R-

|

1o%

5 107

1 ~ - - ~...._._.__

l z

I

/131/86

130/78

---------::

251

I

5

L

Rm/Rpo.2

100~-b

.I . . I. . .I . I.

104

2

,

5 105

Cycles to rupture, N R

........

2

p

: : ,

5 106

.i . . l. . .I . .JllJl]

2

,

5 107

7 ~. ~ ]

i

i

2

i i iii

5

Cycles to rupture, NR

Fig. 6 S-N curves for the alloy G-AI-11Si-Mg-Sr ( P = 0 , s=20mm). Loading mode: axial; R = - I , f = 5 0 H z . Flat specimen, d = 5 mm. (a) Kt = 1.0; (b) Kt = 2.5

Fig. 8 Comparison of S-N curves for: (a) G-AI-7Si-0.6 wa, s = 20 m m ; (b) G-AI-11Si-Mg-Sr, s = 20 mm. Loading mode: axial, f = 50 Hz. Flat specimen: d = 5 m m ; K, = 1.0

I .60

200

C 1.55 o

Rm/Rp 0.2 288•252 (P=0)

c

2801253 [P=4)

1.50 lOO -

c-

"<-

,,~

a

270•235

co 1.45 m 1.40

roe

~

I .35

3.70 i

t

Porosity in %

I

i

l

8.60

131/86 (P=0)

b

""~'~

5o

m

t I

130/87

0.50

oE Z

>:

25

104 0.45

i

2

i

iJllld

5

L

105

2

,

I,liliJ

5

I

106

2

J

tlIJlll

5

=

107

2

I

==,,*,

5

Cycles to rupture, N R

-~~PI f l ] ~ 4 P

4)

Fig. 9 Comparison of S-N curves for: (a) G-AI-7Si-0.6Mg wa: (b) G-AI-11Si-Mg-Sr. Loading mode: axial, f = 5 0 H z . Flat specimen: d=5mm, s=20mm. Kt=2.5

(P 8)

0.40 ¢-

0.35 2.70

0 i

3.70 Porosity in % L

I

2.60

I

i

I

2.50

8.60 I I

2.40

Density ( g c m -3) Fig. 7 Density and: (a) fatigue notch factor Kf = ~.n(K,=l)/(Ta, (K,>I); (b) mean stress sensitivity M = (Ta,(R= - 1 ) / Cr.n(R = 0) - 1. Alloy: G-AI-7Si-0.6Mg; NG = 5 X 10% S = 20 mm. R = (a) - 1 , (b) - 1 / 0 ; Kt = (a) 1.0/2.5, (b) 1.0

pores have hardly any influence on the fatigue strength of axially stressed components. In the unnotched condition and with a degree of porosity P = 8, the endurance limit of the alloy G-AI-11Si-Mg-Sr dropped by 16% similar to the aforementioned material. In the notched condition, however, there was an unexpected decrease of 20%. This difference between the alloys G-AI7Si-0.6Mg wa and G-AI-11Si-Mg-Sr can be explained by allocating a fatigue notch factor to the pores and by considering the yield strength of the non-porous condition.l Regarding the fatigue notch factor, the microstructural analyses reveal relatively round and homogeneously distributed pores. According to Ref 15, a maximum notch factor of/it, pore = 3 may be allocated to the pores under these geometric conditions and on the basis of the slab model.

80

In the unnotched specimens, stress distribution in the non-porous condition is homogeneous. In the porous condition, stress distribution is increased uniformly through the pores. As the loaded porous material volume is the same for both alloys, the reduction in fatigue strength is comparable. In the notched condition, however, an inhomogeneous stress distribution is already created by the external notch. Whereas notch root stress is far below 0.2% yield strength for the non-porous age-hardened alloy, the outer notch of the non-age-hardened alloy already starts yielding, but only in the vicinity of the surface area of the outer notch. In the porous condition, there is a further increase in local notch root stress for the age-hardened alloy. But, because of the high 0.2% yield strength there is little plastic deformation in the vicinity of the surface area. However, with the non-agehardened alloy in the porous condition, the plastically deformed area is much higher because of the low 0.2% yield strength and comparable to the maximum stressed volume of the unnotched porous specimen. Therefore, for the agehardened alloy, the drop in endurance limit is far lower than for the non-hardened alloy in the notched condition. These results were obtained under axial loading. For the alloy G-A1-7Si-0.6Mg wa in the unnotched but porous condition, the drop in endurance limit under bending is

Int J Fatigue

March

1993

80

a

70 60

Kt=l.0

e-

50

OPt0 OP:4 ®P=8

40 E

,~ LU

~7t

®~

Kt=2. 5

30

6°lb

1696

11o

'°f

3o

0

Kt

20g I

10

1.0

K t = 2.5 I

20

30

Solidified cross-section, s (ram) Fig. 10 Influence of solidified cross-section, porosity and notch factor on the endurance limit at NG = 5 x I 0 e cycles: (a) GAI-7Si-0.6Mg w a ; (b) G-AI-IISi-Mg-Sr. Loading m o d e : axial,

R=-I

Fig. 12 Front axle carrier; GK-AI-(Sr)Si-Mg w a

Mechanical properties and endurance limit expected to be markedly lower than under axial load compared with the non-porous condition. This might be because the stress gradients limit the size of the maximum stressed material volume as in the case of the notched condition. For the alloy G-Al-11Si-Mg-Sr in notched and unnotched conditions subjected to bending, however, the porosity should result in the aforementioned endurance limit reduction compared with the non-porous condition. Because of the supporting effect under bending, the fatigue strength values for the materials investigated may be higher than under axial load. The fatigue strength results obtained from the alloy G-AI-TSi-0.6Mg wa show that in the evaluation of fatigue critical areas of components, ie, areas with high stress concentration or notches, the influence of porosity is not as serious as determined with unnotched specimens.

The relationship between the 0.2% yield strength and the shape of the S - N curves in the finite life range (F/igs 5, 6, 8 and 9) has already been pointed out. It is remakkable that the endurance limit in the notched and unnotched non-porous condition is comparable in spite of the different tensile strength and 0.2% yield strength values (Figs 8 and 9). It follows that tensile strength alone does not influence the endurance limit. Regarding applications exclusively in the endurance limit range, preference may be given to the non-age-hardened alloy G-Al-IISi-Mg-Sr because in contrast to the age-hardened alloy G-AI-7Si-0.6Mg wa, the costs for heat treatment can be saved.

Influence of solidified cross-section in conjunction with porosity

Application of the results to component behaviour

Figure 10 shows the influence of material, porosity and solidified cross-section on the endurance limit. In the non-porous and unnotched condition, the endurance limit decreases as the solidified cross-section increases. As the melt cooling time also increases between 200 and 900 s, the spaces between the dendrite arms increase which explains the drop in fatigue strength. 16 In the presence of pores or design notches, this influence is suppressed.

If the modified Palmgren-Miner Rule is applied for fatiguelife prediction of components made of age-hardened alloys and subjected to stochastic loading, a damage sum of D = 0.5-1.0 may be taken as a basis. A greater scatter of damage sum, as may be the case with other materials, 17'18 need not be taken into account. Practical experience with

Fig. 11 A l u m i n i u m c o m p o n e n t s in Z1 rear suspension

Int J Fatigue March 1993

Fig. 13 A l u m i n i u m front axle carrier divided into zones for evaluation of porosity

81

necessary to lower unsprung mass and total vehicle weight. Chassis safety parts, however, are hardly ever made of cast aluminium. The material properties of forged components are well known; they can be influenced to a large extent and produced within acceptable scatter limits. The properties of cast aluminium parts depend on the quality of the basic material, mould design and component design. The component must withstand not only the stress under normal driving conditions but also misuse without primary fracture. The stress to which aluminium components are subjected to is known as a result of extensive measurements. Thus the specific characteristics of the entire component can be determined. 19

Chassis components Fig. 14 Rack and pinion steering gear housing with casting defects (shrinkage holes)

cast aluminium wheels and the results of this study serve as proof. Because of its high tensile strength and 0.2% yield strength and the consequently steeper S - N curve, the age-hardened alloy G-A1-7Si-0.6Mg wa is superior to the non-age-hardened alloy G-AI-11Si-Mg-Sr with its flatter S - N curve in the finite fatigue-life and variable-amplitude fatigue strength ranges. In the endurance limit range, the two alloys are equal in the non-porous condition. Therefore it is quite possible to use the non-age-hardened alloy for applications exclusively in the endurance limit range. With a component made of the age-hardened alloy G-A1-7Si-0.6Mg wa, porosity (P < 8) in the critical area with inhomogeneous stress distribution is not as serious as with homogeneous stress distribution or with the non-agehardened alloy G-AI-11Si-Mg-Sr. However, in critical areas of safety components like wheels and swivel bearings, porosity should be kept to a minimum because it is not always possible to avoid overloading in such areas under service conditions.

A p p l i c a t i o n s in a u t o m o b i l e

production

Cast aluminium has long been used for engine or transmission casings, cylinder heads, etc. Cast chassis components are

On the rear suspension of the BMW Z1, the semi-trailing arm and upper control arm, the wheel, the transmission and differential adaptor of the carrier tube are made of cast aluminium (Fig. 11).

Front axle carrier The front axle carrier of the 3-series four-wheel drive (Fig. 12) is made of GK-AI-gSi-Mg(Sr) wa and requires high fatigue strength and adequate ductility. The microstructure must be free from pores to prevent setting and prestressing losses. Through the determination of reference samples, the front axle carrier is divided into several zones (Fig. 13). In this way, quality requirements are clearly defined for both the manufacturer and the customer.

Steering gear Steering gear components (Fig. 14) made of GD-AI-6Si-4Cu are among the most important safety parts of a car. The rack and pinion steering gear is subject to very high stresses in the transition area steering shaft mount/rack and pinion guide (section A-A). Consequently, defects are not allowed in this area. The casting is designed in such a way that pores accumulate in those areas of the steering shaft mount which are subsequently drilled out. The mounting flange is not highly stressed and shrinkage holes are permissible up to a certain size and arrangement.

Fig. 15 (a) Brake master cylinder: GK-AI-7Si-Mg wa; semi-sold moulding, leak-proof, hard anodized cylinder housing. (b) Globular microstructure 82

Int J Fatigue March 1993

~Front~strut

Fig. 16 Strut support bearing in GD-AI-10Si-Mg wa: fairly pore-free; heat-treatable; rolled-in alloy flange (ball bearing mounting)

Table 7. Allowable shrinkage distribution in an aluminium cast disc wheeV ° tub

Area Vheel disc

tim flange

Hub Wheel disc Rim flange Bead seat Hump Rim well

Size Frequency(mm) 0 =1% =3% -=3% =3% ~5%

-=0 41 ~<2 ~<2 ~<2 ~<2

Number Size of of areas areas* (cm 2) 0 3 5 5 5 8

2.5 2.5 2.5 2.5 2.5 2.5

lead seat

*These areas with defects are allowed, if their distances along the circumference are />5 cm

-lump

through heat treatment and high ductility can fulfil these requirements.

Passenger car wheels tim well Fig. 17 Aluminium cast disc wheel. See Table 7 for allowable

shrinkage distribution

Brake master cylinder housing The brake master cylinder housing (GK-AI-7Si-Mg wa) must be absolutely leak-proof (high pressure > 350 bar) and wearresistant on the inner side. The component is produced by the SSM method (semi-solid moulding) and the cylinder housing is hard anodized (Fig. 15).

Support bearing The support bearing of the front strut (GD-AI-10Si-Mg wa) has to carry the wheel load (Fig. 16). The bearing flange is pressure diecast and the ball bearing is rolled in cold. Only a fairly pore-free microstructure with high fatigue strength

Int J Fatigue March 1993

Passenger car wheels belong also to safety parts which must never fail. Therefore, the production of cast aluminium wheels, eg from G-A1-7Si-0.6Mg wa, is permanently controlled by X-rays. Based on the knowledge of local stresses due to service loading, aluminium wheels are divided into different areas with different size of porosity and shrinkages. The most critical area is the hub where porosities or shrinkages are not allowed (Fig. 17 and Table 7). 20

Summary The results show that in spite of the large difference between the static strength properties of age-hardened and non-agehardened alloys, the endurance limit values are similar. Apart from applications in the endurance limit range, the agehardened alloy is suitable also in the finite fatigue life and variable-amplitude fatigue strength range because of its steep S - N curve. The non-age-hardened alloy is more suitable for

83

applications in the endurance limit range. All alloys investigated reveal cyclic hardening when the yield point is exceeded repeatedly. The degree of porosity influences fatigue strength in different ways. If the degree of porosity is increased from about 0 to 8, fatigue strength in the unnotched condition is reduced by about 17% for both alloy groups. In the notched condition, the age-hardened alloy displays a 7% drop in fatigue strength. For the non-hardened alloy, fatigue strength drops by 20% because of the lower yield point in the notched condition. There is no evidence that the size of the solidified cross-section has any influence on fatigue strength in the porous condition. Even in safety parts porosity can be tolerated. But it must be avoided in critical areas.

9.

Palmgren, A. 'Die Lebensdauer yon Kugellagern' VD/-Z 8 14 (1924) pp 339-341

10.

Miner, M.A. 'Cumulative damage in fatigue' JApp/Mech 12 3 (1945) pp A159-A164

11.

Haibach, E. 'Modifizierte lineare Schadensakkumulationshypothese zur Ber0cksichtigung des Dauerfestigkeitsabfalls mit fortschreitender Sch~idigung' Technische Mitteilungen TM-No. 50/70 (Fraunhofer-lnstitut fur Betriebsfestigkeit (LBF), Darmstadt, 1970)

12.

Buxbaum, O. etal'Vergleich der Lebensdauervorhersage nach dem Kerbgrundkonzept und dem Nennspannungskonzept' Bericht Nr. FB-169 (Fraunhofer-lnstitut fur Betriebsfestigkeit (LBF), Darmstadt, 1983)

13.

Grubisic, V. and Lowak, H. 'Possibility to determine aluminium wheels fatigue life by local strain concept' SAE Paper No. 880698{Society of Automotive Engineers, 1988)

14.

Gal~ner,E. and Kreutz, P. Bedeutung des Programmbelastungs-Versuchs a/s einfachste Form der Simulation zufallsartiger Beanspruchungen (Selbstverlag, Darmstadt 1981)

References Sonsino, C.M. and Dieterich, K. 'Einflu~ der Porosit~it auf das Schwingfestigkeitsverhalten von AluminiumGuBwerkstoffen' Bericht Nr FB-188 (Fraunhofer-lnstitut for Betriebsfestigkeit (LBF), Darmstadt, 1990)

15,

Peterson, R.E. Stress Concentration Design Factors (John Wiley & Sons Inc, New York, 1953)

16.

Standard Reference Radiographs for /nspection of A/uminium and Magnesium Castings, ASTM E 155-79 (American Society for Testing and Materials, 1979)

17.

Arbenz, H. 'Qualit~tsbeschreibung von Aluminium-GuBst0cken anhand yon Gef0gemerkmalen' Gie/~erei 66 19 (1979) pp 702-711

18.

Ostermann, H. and Grubisic, V. 'Einflul~ des Werkstoffes auf die ertragbare Schwingbeanspruchung' in W. Dahl (ed) Verhalten yon Stah/ bei schwingender Beanspruchung, Kontaktstudium Werkstoffkunde Eisen und Stahl ///(Verlag Stahleisen, D0sseldorf, 1979) pp 243-260

19.

5.

Fischer, R., K6bler, H.G. and Wendt, U. 'Synthese zufallsartiger Lastfolgen zur Anwendung bei Betriebsfestigkeitsversuchen' Fortschritt-Bericht VDI-Z (1979) 5 40

20.

6.

Haibach, E. and Matschke, C. 'The concept of uniform scatter bands for analyzing S-N curves of unnotched and notched specimens in structural steel' in ASTM STP 770 (American Society for Testing and Materials, 1982) pp 549-571

Honma, U. and Kitaoks, S. 'Fatigue strength and mechanical properties of aluminium alloy castings of different structural fineness' A/uminium 60 12 (1984) pp 917-920 Buxbaum, O. Betriebsfestigkeit--Sichere und wirtschaft/iche Bemessung schwingbruchgef~hrdeter Bautei/e (Verlag Stahleisen mbH, D0sseldorf, 1992) Sch0tz, W. 'Lebensdauervorhersage schwingend beanspruchter Bauteile' WerkstoffermSdung und Bauteilfestigkeit, Vortr~ge des DVM-Ko//oquiums, Berlin, 1980 (Deutscher Verband fur Materialpr0fung e.V., Berlin, 1980) pp 341-405 Gruber, S., GOnther, B. and Knall, G. 'Betriebsfestigkeit yon hochbeanspruchten Kraftfahrzeug-Bauteilen aus Aluminiumguf~' Seminar in Meschede Aluminium-Formguf3teile mit innovativer Technologie (1990) Wimmer, A. and Lipowsky, Hj. 'Sch~/den an Fertigungskerben--0bersicht' Kerben und Betriebsfestigkeit. 15. Vortragsveranstaltung des DVM-Arbeitskreises Betriebsfestigkeit, Ingolstadt, 18-19 October 1989 (Deutscher Verband for Materialforschung und-pr0fung, Berlin, 1989) pp 133-161

7.

Neuber, H. '0ber die BerOcksichtigung der Spannungskonzentration bei Festigkeitsberechnungen' Konstruktion 20 7 (1968) pp 245-250

1.

2.

3.

4.

8.

84

Sonsino, C.M. 'Einfluf~ yon Kaltverformungen bis 5% auf das Kurzzeitschwingfestigkeitsverhalten metallischer Werkstoffe' Bericht Nr FB-161 (Fraunhofer-lnstitut for Betriebsfestigkeit (LBF), Damstadt, 1982)

Authors

C.M. Sonsino is with the Fraunhofer-Institut fiir Betriebsfestigkeit (LBF), Darmstadt, FRG. J. Ziese is with Bayerische Motoren Werke AG (BMW), Munich, FRG. Received 10 February 1992; revised 6 August 1992.

Int J F a t i g u e M a r c h 1993