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Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments
Available online at www.sciencedirect.com
International Journalof Fatigue
International Journal of Fatigue 30 (2008) 1279–1288
www.elsevier.com/locate/ijfatigue
Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments C.M. Sonsino a
a,*
, E. Moosbrugger
b
Fraunhofer-Institute for Structural Durability and System Reliability LBF, Darmstadt, Germany b Robert Bosch GmbH, Waiblingen, Germany Received 1 February 2007; received in revised form 27 July 2007; accepted 22 August 2007 Available online 6 September 2007
Abstract The fatigue strength behaviour of a short-glass-fibre reinforced polyamide PA66-GF35 was investigated in detail. The consideration of influencing variables like notches, fibre orientation, temperature, mean-stress and spectrum loading enable the fatigue design of high loaded plastic parts in engine compartments. A design method was developed which is based on FE calculation of the maximum local stress, the appertaining stress gradient and the highly stressed material volume. The method was verified successfully by the example of a fuel rail. 2007 Elsevier Ltd. All rights reserved. Keywords: Fatigue strength; Temperature; Notch effect; Mean-stress; Highly stressed material volume; Constant and variable amplitude loading
1. Introduction The low specific weight of plastics offers light-weight design opportunities. Therefore, the application of plastic materials in automotive engineering is increasing [1,2]. Short-glass-fibre reinforced thermoplastics are suited for cost-saving manufacturing of complex parts using injection moulding. Plastic parts are safety components when applied in brake- and fuel-feed-systems. These components must maintain their function during service life at enginecompartment-temperatures of 130 C and above without failure while withstanding cyclic loading. Therefore, they require to be designed against cyclic service loads considering material properties as well as structural shaping (stress concentration) and environment (temperature). Comprehensive knowledge of the material regarding componentrelated strength properties is essential for an appropriate and economical design. For this, the application of the local stress concept, verified in a large investigation in *
Corresponding author. Tel.: +49 06151705244; fax: +49 06151705214. E-mail address: [email protected] (C.M. Sonsino).
0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.08.017
LBF [3,4], will be demonstrated by the example of a fuel rail. 2. State of the art for designing plastic components Until now component design has exclusively used static property data such as ultimate tensile strength, yield strength, failure strain or static creep. These data are not sufficient especially when designing cyclically loaded components. Generally the step from static to cyclic loading applies data obtained with unnotched specimens (Kt = 1.0) with unrealistic results as unnotched components do not exist. The failure critical areas of components are locations with notches, i.e. stress concentrations, which must be considered properly with appropriate data. Drawing conclusions from static material properties with regard to cyclic behaviour and inferring from cyclic property data of unnotched specimens to notched conditions is not sufficient for an evaluation of the real material behaviour and resulted in the past in incorrect conclusions for metals as well as fibre-reinforced materials [5,6]. Usually, in the design of plastic parts empirical reduction
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Nomenclature D d E I Kt Kf Ls M N, N P R, R Rm Vx% e jr k, k
damage sum, diameter thickness Young’s modulus irregularity factor stress concentration factor fatigue stress concentration factor sequence length mean-stress sensitivity fatigue life under constant, variable amplitude loading probability maximum stress ratio for constant, variable amplitude loading ultimate tensile strenght highly stressed material volume elongation safety factor slope of the Woehler/Gassner curve
factors [7,8] take care of influencing parameters like notches, fibre orientation, temperature, aging, mean-stress, multiaxial stress state, loading sequence and scatter. Finite element analysis determines maximum local stresses, which are then compared with the allowable stresses based on the static tensile strength and the reduction factors. However, this procedure often leads to over-design or even to a rejection of a plastic material as a candidate material based on the suspicion that it would not satisfy the requirements. This paper presents a systematic procedure, which determines by testing of unnotched and notched specimens the influential parameters mentioned above and allows the transfer of fatigue design relevant data to the component. Thus, structural components can already be evaluated during early design phase with respect to their structural durability.
r s e l n q r
radius length, thickness strain Poisson’s ratio cycles density stress
Indexes a m el eq pl f s th x%
amplitude mean elastic equivalent plastic failure survival theoretical stress fraction
Table 1 Material data of PA66-GF35 Properties
Unit
Polyamide 66 (PA66-GF35, dry)
Ultimate tensile strength, Rm Elongation, e Youngs’s modulus, E Density, q Creep strength at 120 C, 100 h, 0.5% strain Cost/kg Cost/l pffiffiffiffiffiffiffiffiffi Plate stiffness, 3 E=q Specific strength, Rm/q
MPa % GPa g/cm3 MPa
210 3.0 11.5 1.41 16
€ € – –
3 4 20 149
3. Experimental As a typical material for highly loaded plastic components in engine compartments like intake manifolds, gears or fuel rails a Polyamide 66 with 35% (weight) of shortglass-fibres (PA66-GF35) was closely examined. Conventional material data are compiled in Table 1. Fig. 1 shows the injection moulded unnotched and notched specimens axially loaded under constant amplitude loading to derive the Woehler-lines and under random variable amplitude loading, a spectrum with a Gaussı´an amplitude distribution, Fig. 2, to obtain the Gassner-lines. The notch radii cover an observed range of geometries of plastic components. The notches were obtained during the injection moulding process. The specimens were tested dry as moulded.
Fig. 1. Specimens with different stress concentrations.
C.M. Sonsino, E. Moosbrugger / International Journal of Fatigue 30 (2008) 1279–1288
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Fig. 2. Stress-time histories and Gaussı´an cumulative amplitude distributions.
Stress concentration, fibre orientation (here only the results determined with specimens with fibres in longitudinal flow direction, checked by micrographs, are presented), temperature, and stress ratio varied within the test programme. Due to large intrinsic damping the polymer heats up during cyclic loading depending on load frequency and level. This self-heating can diminish the fatigue life. Therefore, a loading frequency must be low enough to ensure that specimen temperature does not exceed a given limit, here 35 C. Otherwise the temperature will rapidly rise until the specimen fails. Fig. 3 shows the effect of loading frequency on self-heating of unnotched specimens and the cycles to failure. Increasing the frequency from 4 to 5 s1 at R = 1 resulting in an increase of self-heating from 30 to 72 C and changing the frequency from 5 to 8 s1at R = 0 resulting in an increase in heating from 30 to 90 C reduces the fatigue life by at least a factor of 10. But at lower load levels where less
Fig. 3. Influence of loading frequency on the fatigue life of short-fibre reinforced polyamide.
energy is induced larger frequencies, 6 and 8 s1, Fig. 3, show no detrimental self-heating. For notched specimens higher frequencies can be allowed as the maximum stressed material volume is much smaller compared to unnotched specimens. The heat can dissipate easily to the neighbouring less stressed and less warm volume. However, in practice the described heating effect of the load frequency should not be overestimated. To investigate material properties failures must be generated during the tests by high loads. But as the loads in service must be much less than during tests, because of safety considerations, much higher frequencies than in tests can be allowed without heating effects. Specimens with various stress concentrations allow the evaluation of the notch sensitivity on fatigue strength. The Woehler-lines for fully reversed loading (R = 1) presented in Fig. 4 in the nominal stress system (ra,n = Fa/An) show a distinct drop of fatigue strength with increasing notch factor, i.e. increasing notch severity. As distinguished from the behaviour of metals whose S–N curves run significantly steeper with increasing stress concentration, notch severity slightly affects the slope of the S–N curves of PA66-GF35. Furthermore, Fig. 4 reveals that contrary to steels and light metal alloys the S–N curves of short-fibre reinforced plastics do not change slope within the investigated cycle range up to 108. In particular no shallowing of the slope in the high-cycle regime can be found in contrast to metals [9]. Fig. 5 shows Woehler-lines resulting from tests at room temperature (RT = 21 to 23 C), 80 and 130 C. High temperatures reduce the fatigue strength considerably. Thereby, the slopes of the Woehler-lines remain nearly constant. A characteristic of polymers is that the notch influence almost vanishes at high temperatures (Fig. 6). Due to the softening of the material with increased temperature the notch sensitivity is reduced. The distance between Woehler-lines of notched and unnotched specimens is
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Fig. 4. Influence of notches on the fatigue strength of short-fibre reinforced polyamide.
100
RT
MPa
Material: PA66-GF35
Nominal stress amplitude σ an
80 60
80° C
k: 13.2
40
20
130° C
19.0
19.5 Specimen: Loading:i
flat, K t =1.0 in fibre orientation, axial R= -1, f=0.5-2.0 s-1 Environment:air
Ps= 50%
10 10 3
10 4
10 5
10 6
10 7
8
10
Cycles to failure N f
Fig. 5. Influence of temperature on the fatigue strength of short-fibre reinforced polyamide.
100
MPa
Probe: Flachprobe PA66 —G F35 Belastung: Axial, R = -1 Umgebung: 130°C
80
Material: Ps = 50%
Nominal stress amplitude σan
60
Pü= 50[% ]
Specimen:f
lat
Loading:i
n fibreo rientation, K t
axial, R = -1, f =1-18 s-1
1,0 Environment: 4,7 air, 130°C 9,8
40
k: 19.5 20.3 16.6
Kt
20
1.0 4.7 9.8 10
10
3
10
4
10
5
10
6
10
7
Cycles to failure Nf
Fig. 6. Influence of notches on fatigue strength under elevated temperature.
10
8
C.M. Sonsino, E. Moosbrugger / International Journal of Fatigue 30 (2008) 1279–1288
significantly smaller at 130 C than at room temperature, compare Figs. 5 and 6. An increase of the stress concentration does not lead to a further reduction of fatigue strength. Fig. 7 shows the influence of different stress ratios R on fatigue strength in interaction with different stress concentrations. Tensile mean-stresses diminish the endurable stress amplitude as shown in Fig. 8. However, this decrease is not caused by the mean-stress sensitivity M¼
ran ðR ¼ 1Þ 1 ran ðR ¼ 0Þ
ð1Þ
of the material alone, but to some extent also by cyclic creep [10]. This decrease is less in the presence of notches because of stress gradients which diminish the cyclic creep. The results of variable amplitude loading with the Gaussı´an random load sequence, Fig. 2, when plotted with maximum spectrum stress amplitude show longer fatigue lives than constant amplitude fatigue loading, as expected (Fig. 9). For the same maximum amplitude variable
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amplituded loading always results in a significantly higher fatigue life than constant amplitude loading, due to the less damaging contribution of the smaller amplitudes of the spectrum [11]. The consideration of this fact enables the design of light-weight components through thinner crosssections [11], because for a requested fatigue life under variable amplitude loading much higher stresses can be allowed than under constant amplitude loading. The results of the Gassner-tests serve to determine the real damage sums Dreal ¼
N exp ; N cal ðDth ¼ 1:0Þ
ð2Þ
which are necessary for fatigue life calculations. As the Woehler-lines of the investigated polyamide do not have a knee-point, the elementary Palmgren–Miner rule is applied: Xn D¼ 6 1:0: ð3Þ N i The real damage sums were determined for all test series inclusively for the fuel rail between 0.1 and 10, which is also typical for composite materials [12] (Fig. 10). It can be
Fig. 7. Woehler-lines of short-glass-fibre reinforced polyamide under different stress ratios.
Fig. 8. Relation between mean-stress and stress amplitude.
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Fig. 9. Woehler- and Gassner-lines of short-fibre reinforced polyamide.
observed that a calculation with Dth = 1.0 renders a conservative assumption for fully reversed loading. However for pulsating loading an unsafe estimate is rendered, probably because of cyclic creep under pulsating pressure which is not considered by the linear damage accumulation. With Dreal = 0.5 all results for R = 1 and with Dreal = 0.1 all results for R = 0 are covered. 4. Transmission of specimen test results to components
Fig. 10. Comparison of experimental and calculated fatigue lives.
The transferability of the data obtained with specimens will be demonstrated for a fuel rail, Fig. 11, made of PA66GF35, which substituted a steel variant because of significant weight and cost advantages. The critical locations are the sharp notches, Fig. 12, in the connection with the pressure controller. Pulsating internal pressure (R = 0) up to Dpmax = 3.5 bar is the essential loading of this component at maximum service temperature of 130 C. However, to produce fatigue failures during tests much higher pressures with a pulsating frequency of 5 to 10 s1 were applied. In Fig. 13 the results obtained under constant and variable amplitude loading under RT and 130 C are compiled.
Fig. 11. Fuel rail.
C.M. Sonsino, E. Moosbrugger / International Journal of Fatigue 30 (2008) 1279–1288
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direct assessment using the Woehler- as well as the Gassner-lines (as presented in Figs. 4–9 in the nominal system) is not possible. For this, local fatigue life curves are necessary which must also consider local material properties such as surface state, fibre orientation, stress gradients and last but not least the local multiaxial stress state. Beyond this the failure criteria (in the present case total failure) must be the same for component and specimen. The fatigue life curves can be transformed from the nominal into the local system, Fig. 14, linear-elastically by ra;loc ¼ ra;1;max ¼ K t ran :
Fig. 12. Critical areas of the connection with the pressure controller.
5. Methodology As the fatigue critical locations are notches to which neither a notch factor nor a nominal stress can be allocated, a
ð4Þ
The use of the curves transformed into the maximum local principal stress also requires the determination of the local principal stresses as equivalent stresses in the critical areas of the connection. As the fibre directions in the notches of the specimens and of the connection correspond to each other, checked by micrographs, an anisotropy [13] needs not to be considered. Furthermore, as the material has a low ductility, revealed by low elongation values at room and higher temperatures, the principal stress hypothesis [14] can be applied in this case. Otherwise, a multiaxial
Fig. 13. Fatigue behaviour of fuel rails of short-fibre reinforced plastics.
1000 Ps=50%
MPa
Stress amplitude σa
Notchf actorK t : Local syst em
9.8 *K t
100 Nominal syst em
Influenceo f stress gradients (support effect) 1.0
9.8
10
Loadingm ode: axial, R=-1, in fibre direction, T=RT
102
103
104
105 Cyclest of ailure N f
(r=0.2mm)
106
107
108
Fig. 14. S–N-curves of a short-fibre reinforced polyamide in the nominal and local stress system.
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hypothesis considering anisotropy, like the Tsai-Wu or Tsai-Hill-criterion [15–17] should be used. Thus, this transformation alone is not sufficient for the assessment of the component. It is necessary to also account for the effect of stress gradients on the bearable local stress [18]. If the local stresses are plotted as a function of the stress concentration factor, Fig. 15, an increase of the bearable local stresses is observed the higher the stress concentration becomes. This fact is called the macro-support effect and is caused by stress gradients as defined by [18] v ¼
1 dr1 : r1;max dx
ð5Þ
The consideration of the material dependent influence on the bearable stress leads to higher local permissible stresses than those obtained with unnotched specimens and opens up light-weight design options. However, this effect is not controlled by the stress gradients alone, it is also determined by the highly stressed (strained) material volume which results from the gradients [19–22]. Fig. 16 displays for two simple geometries how the maximum
stressed material volume, defined as the volume in which the maximum local stress drops from 100% to a given value, i.e 90% or 80%, can be calculated approximately. This concept [19] was verified for metallic components [20–22] with good success using the volume fraction V90. For short-fibre reinforced specimens and components, the FE modelling with the volume V80 proved to be more practical than V90. From the Woehler-lines of unnotched and notched specimens, according to this procedure, a set of stress-volume lines for constant fatigue lives gives the basis for the assessment of the durability of the component (Fig. 17). The sharper a notch, the steeper are the stress gradients and the smaller the highly stressed material volume. As the probability of failure decreases with smaller material volume, the bearable local equivalent stress is higher than for bigger material volumes, Fig. 17, as for axially loaded unnotched specimens with a homogeneous stress distribution. The allocation of the calculated maximum local equivalent stress amplitude and maximum stressed volume of the critical area of the component into this diagram cross at the
Fig. 15. Nominal and local stress amplitude of a short-fibre reinforced polyamide as a function of the stress concentration.
Fig. 16. Determination of highly stressed material volumes V90 or V80 on simple geometries.
C.M. Sonsino, E. Moosbrugger / International Journal of Fatigue 30 (2008) 1279–1288
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Fig. 17. Relation between maximum stressed material volume and local equivalent stress.
fatigue life to be expected. For component design, the allowable stresses or fatigue lives are obtained by reducing the values with the probability of survival of Ps = 50% with safety factors [21–24], which depend on the scatter of fatigue data, manufacturing and on the required probability of failure of the component. 6. Application The verification of the design methodology described will be carried out on the basis of Ps = 50% – data obtained with specimens and components. The FE-model of the critical area of the fuel rail, Fig. 12, is shown in Fig. 18. The local maximum principal stress, the appertaining stress gradients along the surface as well as the thickness for determining the maximum stressed material volume V80 are calculated linear-elastically. In Table 2 calculated and experimental results for a constant amplitude fatigue life of Nr = 1 · 106 cycles with a probability of survival of Ps = 50% are compared. According to the presented methodology the maximum local stress
Table 2 Comparison of calculated and experimental maximum local stresses in the critical area and internal pressures of the fuel rail for a constant amplitude fatigue life Nf = 1 · 106 cycles (Ps = 50%) T
RT
130 C
Nf (Ps = 50%)
r1,max in MPa (FE) V80 in mm3 Dpmax in bar (FE) r1,max in MPa (exp) Dpmax in bar (exp)
641 0.002 13.2 646 13.3
392 0.002 8.1 460 9.5
1 · 106
determined by FE is almost equal to the stress obtained from the experiments for room temperature, but for 130 C the numerical values of local principal stress and pressure are on the conservative side. In both cases the ultimate tensile strength Rm = 210 MPa (for room temperature) is exceeded significantly. This proves that the use of quasi-static material properties is obviously not appropriate for fatigue design. The behaviour of the fuel rail under variable amplitude pulsating loading is important with regard to service. In Table 3 mean fatigue lives obtained under the Gaussı´an spectrum, Fig. 2, at room temperature and 130 C, respectively, are compared with the calculated values for a maximum internal pressure of Dpmax = 18 bar (N.B.: in service the maximum pressure is Dpmax = 3.5 bar). With the knowledge obtained from the cumulative test series the fatigue lives are calculated according to the elementary Palmgren–Miner rule (Woehler-line without knee-point) Table 3 Calculated and experimental fatigue lives for Gaussı´an spectrum loading (R ¼ 0; Ls ¼ 5 104 ) with Dpmax = 18 bar
Fig. 18. FE-model of the critical area.
T
RT
130 C
Dpmax in bar
Nf (FE, Ps = 50%) Dreal r1,max (FE) in MPa V80 in mm3 Nf (exp) Ps = 50% r1,max (exp) in MPa
1.42 · 107 0.5 837 0.002 1.41 · 107 837
1.10 · 105 1.0 837 0.002 3.60 · 105 837
18
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with the particular real damage sums. Again, the estimate for 130 C is on the conservative side. The calculations as well as the experimental results at Dpmax = 18 bar contain a high safety factor jr 5 and prove that for the service pressure of Dpmax = 3.5 bar a reliable durability of the fuel rail can be expected, as already verified by the service use of the components over more than 10 years without any failures. 7. Outlook The developed design procedure with local fatigue data considering surface state, fibre orientation, stress concentration, stress gradients, highly stressed material volume and multiaxiality is appropriate to reliably estimate the fatigue life of high loaded plastic parts installed in engine compartments. It has been clearly shown that with static properties like ultimate tensile stress, the analysed design would be rejected or a much thicker component would be proposed as obtained by a fatigue and notch effect based design. Investigations on other plastic materials with different matrix materials, fibres and fibre contents, should enlarge the database now available for PA66-GF35. Missing knowledge regarding the ability to withstand fuel environment and local multiaxial stresses with changing principal stress directions opens a broad field of future investigations. References [1] Plastics in automobile industry 2004. In: VDI-Report No. 4260; 2004. [2] Vollrath K. Polymer versus Steel and Glass. Automobile-Development 2004;5:50–2. [3] Moosbrugger E, Wieland R, Gumnior P, Gerharz J. Betriebsfeste Auslegung hochbelasteter Kunststoffbauteile im Motorraum (Design and dimensioning of highly loaded plastic parts in engine compartments). Materialpru¨fung 2005;47:445–9. [4] Gumnior P, Gerharz JJ, Sonsino CM, Hanselka H. Entwicklung eines Bemessungskonzeptes zur betriebsfesten Auslegung von Bauteilen aus kurzfaserversta¨rktem Polyamid [Development of a methodology for structural durability design of components from short-fibre reinforced polyamide]. LBF-Report No. 182141. Darmstadt, Germany: Fraunhofer-Institute for Structural Durability and System Reliability LBF; 2002 [partially published in this paper]. [5] Sonsino CM. Material selection for impact and cyclically loaded metal components. In: DVM-Report No. 127; 2000. p. 21–38. [6] Huth H, Mattheij P, Gerharz JJ. Effect of notches and impact damage on structural durability of composite materials. In: DVM-Report No. 127; 2000. p. 39–50. [7] Ehrenstein GW. Designing with polymers. Munich/Vienna: Carl Hanser Publishing; 1995.
[8] Erhard G. Designing with polymers. Munich/Vienna: Carl Hanser Publishing; 1999. [9] Sonsino CM. Endurance limit – a fiction. Konstruktion 2005;4:87–92. [10] Mallick PK, Zhou Y. Effect of mean-stress on the stress-controlled fatigue of a short e-glass fiber reinforced polyamide-6,6. Int J Fatigue 2004;26:941–6. [11] Sonsino CM. Principles of variable amplitude fatigue design and testing. Fatigue testing and analysis under variable amplitude loading conditions. In: McKeighan PC, Ranganathan N, editors. ASTM STP 1439. West Conshohocken, PA: ASTM International; 2005. p. 3–23. [12] Mattheij P. Application of Miner’s linear damage accumulation hypothesis on composite materials. Conference on plastics, 11 and 12 November 1992. Wu¨rzburg/Germany: Su¨ddeutsches Kunststoffzentrum. [13] Bernasconi A, Davoli P, Basile A, Filippi A. Effect of fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide-6. Int J Fatigue 2007;29(2):199–208. [14] Sonsino CM, Grubisic V. Multiaxial fatigue behaviour of sintered steels under combined in- and out-of-phase bending and torsion. Zeitschrift Werkstofftechnik 1987;18:148–57. [15] Gerharz JJ, Gumnior P, Sonsino CM, Bu¨ter A, Hanselka H. Einfluss mehrachsiger Belastungszusta¨nde mit konstanten und vera¨nderlichen Hauptspannungsrichtungen auf die Schwingfestigkeit von kurzfaserversta¨rktem Polyamid [Influence of multiaxial stress states with constant and varying principal stress directions on the fatigue strength of short glass-fibre reinforced polyamide]. LBF-Report No. 186449. Darmstadt/Germany: Fraunhofer-Institute for Structural Durability and System Reliability LBF; 2005 [partially published in this paper]. [16] Bolender K, Bu¨ter A, Sonsino CM. Fatigue behaviour of short fibre reinforced polyamide under multiaxial loading. In: 12th European conference on composite materials ECCM, Biarritz, France; 29.08– 01.09.2006. [17] De Monte M, Moosbrugger E, Bolender K, Quaresimin M. Fatigue failure assessment of short glass fibre reinforced polyamides 6.6 under multiaxial loading. Associazione Italiana per l’Analisi delle Sollecitazioni (AIAS), XXXV Convegno Nazionale, Universita` Politecnica delle Marche; 13–16.09.2006. [18] Siebel E, Stieler M. Spannungsverteilung, schwingende Beanspruchung [Stress distribution, cyclic loading].VDI-Z 97, 5; 1955. p. 121– 6. [19] Kuguel R. A relation between theoretical stress concentration factor and fatigue notch factor deducted from the concept of highly stressed volume. ASTM STP Proc 1961;61:732–48. [20] Sonsino CM. Evaluating the fatigue behaviour of components with consideration of local stresses. Konstruktion 1993;45:25–33. [21] Sonsino CM, Kaufmann H, Grubisic V. Transferability of material data for the example of a randomly fatigue loaded stub axle. SAE transactions section 5. J Mater Manuf 1997;106:649–70. [22] Sonsino CM. Fatigue design concepts for PM parts and required material data – an overview. Princeton: Metal Powder Industries Federation (MPIF); 2003. [23] Sonsino CM, Dieterich K. Fatigue design with cast magnesium alloys under constant and variable amplitude loading. Int J Fatigue 2006;28:183–93. [24] Haibach E. Betriebsfestigkeit – Verfahren und Daten zur Berechnung [Structural durability – methods and data for calculation]. 2nd ed. Du¨sseldorf: Springer-Verlag; 2003.
International Journalof Fatigue
International Journal of Fatigue 30 (2008) 1279–1288
www.elsevier.com/locate/ijfatigue
Fatigue design of highly loaded short-glass-fibre reinforced polyamide parts in engine compartments C.M. Sonsino a
a,*
, E. Moosbrugger
b
Fraunhofer-Institute for Structural Durability and System Reliability LBF, Darmstadt, Germany b Robert Bosch GmbH, Waiblingen, Germany Received 1 February 2007; received in revised form 27 July 2007; accepted 22 August 2007 Available online 6 September 2007
Abstract The fatigue strength behaviour of a short-glass-fibre reinforced polyamide PA66-GF35 was investigated in detail. The consideration of influencing variables like notches, fibre orientation, temperature, mean-stress and spectrum loading enable the fatigue design of high loaded plastic parts in engine compartments. A design method was developed which is based on FE calculation of the maximum local stress, the appertaining stress gradient and the highly stressed material volume. The method was verified successfully by the example of a fuel rail. 2007 Elsevier Ltd. All rights reserved. Keywords: Fatigue strength; Temperature; Notch effect; Mean-stress; Highly stressed material volume; Constant and variable amplitude loading
1. Introduction The low specific weight of plastics offers light-weight design opportunities. Therefore, the application of plastic materials in automotive engineering is increasing [1,2]. Short-glass-fibre reinforced thermoplastics are suited for cost-saving manufacturing of complex parts using injection moulding. Plastic parts are safety components when applied in brake- and fuel-feed-systems. These components must maintain their function during service life at enginecompartment-temperatures of 130 C and above without failure while withstanding cyclic loading. Therefore, they require to be designed against cyclic service loads considering material properties as well as structural shaping (stress concentration) and environment (temperature). Comprehensive knowledge of the material regarding componentrelated strength properties is essential for an appropriate and economical design. For this, the application of the local stress concept, verified in a large investigation in *
Corresponding author. Tel.: +49 06151705244; fax: +49 06151705214. E-mail address: [email protected] (C.M. Sonsino).
0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.08.017
LBF [3,4], will be demonstrated by the example of a fuel rail. 2. State of the art for designing plastic components Until now component design has exclusively used static property data such as ultimate tensile strength, yield strength, failure strain or static creep. These data are not sufficient especially when designing cyclically loaded components. Generally the step from static to cyclic loading applies data obtained with unnotched specimens (Kt = 1.0) with unrealistic results as unnotched components do not exist. The failure critical areas of components are locations with notches, i.e. stress concentrations, which must be considered properly with appropriate data. Drawing conclusions from static material properties with regard to cyclic behaviour and inferring from cyclic property data of unnotched specimens to notched conditions is not sufficient for an evaluation of the real material behaviour and resulted in the past in incorrect conclusions for metals as well as fibre-reinforced materials [5,6]. Usually, in the design of plastic parts empirical reduction
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C.M. Sonsino, E. Moosbrugger / International Journal of Fatigue 30 (2008) 1279–1288
Nomenclature D d E I Kt Kf Ls M N, N P R, R Rm Vx% e jr k, k
damage sum, diameter thickness Young’s modulus irregularity factor stress concentration factor fatigue stress concentration factor sequence length mean-stress sensitivity fatigue life under constant, variable amplitude loading probability maximum stress ratio for constant, variable amplitude loading ultimate tensile strenght highly stressed material volume elongation safety factor slope of the Woehler/Gassner curve
factors [7,8] take care of influencing parameters like notches, fibre orientation, temperature, aging, mean-stress, multiaxial stress state, loading sequence and scatter. Finite element analysis determines maximum local stresses, which are then compared with the allowable stresses based on the static tensile strength and the reduction factors. However, this procedure often leads to over-design or even to a rejection of a plastic material as a candidate material based on the suspicion that it would not satisfy the requirements. This paper presents a systematic procedure, which determines by testing of unnotched and notched specimens the influential parameters mentioned above and allows the transfer of fatigue design relevant data to the component. Thus, structural components can already be evaluated during early design phase with respect to their structural durability.
r s e l n q r
radius length, thickness strain Poisson’s ratio cycles density stress
Indexes a m el eq pl f s th x%
amplitude mean elastic equivalent plastic failure survival theoretical stress fraction
Table 1 Material data of PA66-GF35 Properties
Unit
Polyamide 66 (PA66-GF35, dry)
Ultimate tensile strength, Rm Elongation, e Youngs’s modulus, E Density, q Creep strength at 120 C, 100 h, 0.5% strain Cost/kg Cost/l pffiffiffiffiffiffiffiffiffi Plate stiffness, 3 E=q Specific strength, Rm/q
MPa % GPa g/cm3 MPa
210 3.0 11.5 1.41 16
€ € – –
3 4 20 149
3. Experimental As a typical material for highly loaded plastic components in engine compartments like intake manifolds, gears or fuel rails a Polyamide 66 with 35% (weight) of shortglass-fibres (PA66-GF35) was closely examined. Conventional material data are compiled in Table 1. Fig. 1 shows the injection moulded unnotched and notched specimens axially loaded under constant amplitude loading to derive the Woehler-lines and under random variable amplitude loading, a spectrum with a Gaussı´an amplitude distribution, Fig. 2, to obtain the Gassner-lines. The notch radii cover an observed range of geometries of plastic components. The notches were obtained during the injection moulding process. The specimens were tested dry as moulded.
Fig. 1. Specimens with different stress concentrations.
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Fig. 2. Stress-time histories and Gaussı´an cumulative amplitude distributions.
Stress concentration, fibre orientation (here only the results determined with specimens with fibres in longitudinal flow direction, checked by micrographs, are presented), temperature, and stress ratio varied within the test programme. Due to large intrinsic damping the polymer heats up during cyclic loading depending on load frequency and level. This self-heating can diminish the fatigue life. Therefore, a loading frequency must be low enough to ensure that specimen temperature does not exceed a given limit, here 35 C. Otherwise the temperature will rapidly rise until the specimen fails. Fig. 3 shows the effect of loading frequency on self-heating of unnotched specimens and the cycles to failure. Increasing the frequency from 4 to 5 s1 at R = 1 resulting in an increase of self-heating from 30 to 72 C and changing the frequency from 5 to 8 s1at R = 0 resulting in an increase in heating from 30 to 90 C reduces the fatigue life by at least a factor of 10. But at lower load levels where less
Fig. 3. Influence of loading frequency on the fatigue life of short-fibre reinforced polyamide.
energy is induced larger frequencies, 6 and 8 s1, Fig. 3, show no detrimental self-heating. For notched specimens higher frequencies can be allowed as the maximum stressed material volume is much smaller compared to unnotched specimens. The heat can dissipate easily to the neighbouring less stressed and less warm volume. However, in practice the described heating effect of the load frequency should not be overestimated. To investigate material properties failures must be generated during the tests by high loads. But as the loads in service must be much less than during tests, because of safety considerations, much higher frequencies than in tests can be allowed without heating effects. Specimens with various stress concentrations allow the evaluation of the notch sensitivity on fatigue strength. The Woehler-lines for fully reversed loading (R = 1) presented in Fig. 4 in the nominal stress system (ra,n = Fa/An) show a distinct drop of fatigue strength with increasing notch factor, i.e. increasing notch severity. As distinguished from the behaviour of metals whose S–N curves run significantly steeper with increasing stress concentration, notch severity slightly affects the slope of the S–N curves of PA66-GF35. Furthermore, Fig. 4 reveals that contrary to steels and light metal alloys the S–N curves of short-fibre reinforced plastics do not change slope within the investigated cycle range up to 108. In particular no shallowing of the slope in the high-cycle regime can be found in contrast to metals [9]. Fig. 5 shows Woehler-lines resulting from tests at room temperature (RT = 21 to 23 C), 80 and 130 C. High temperatures reduce the fatigue strength considerably. Thereby, the slopes of the Woehler-lines remain nearly constant. A characteristic of polymers is that the notch influence almost vanishes at high temperatures (Fig. 6). Due to the softening of the material with increased temperature the notch sensitivity is reduced. The distance between Woehler-lines of notched and unnotched specimens is
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Fig. 4. Influence of notches on the fatigue strength of short-fibre reinforced polyamide.
100
RT
MPa
Material: PA66-GF35
Nominal stress amplitude σ an
80 60
80° C
k: 13.2
40
20
130° C
19.0
19.5 Specimen: Loading:i
flat, K t =1.0 in fibre orientation, axial R= -1, f=0.5-2.0 s-1 Environment:air
Ps= 50%
10 10 3
10 4
10 5
10 6
10 7
8
10
Cycles to failure N f
Fig. 5. Influence of temperature on the fatigue strength of short-fibre reinforced polyamide.
100
MPa
Probe: Flachprobe PA66 —G F35 Belastung: Axial, R = -1 Umgebung: 130°C
80
Material: Ps = 50%
Nominal stress amplitude σan
60
Pü= 50[% ]
Specimen:f
lat
Loading:i
n fibreo rientation, K t
axial, R = -1, f =1-18 s-1
1,0 Environment: 4,7 air, 130°C 9,8
40
k: 19.5 20.3 16.6
Kt
20
1.0 4.7 9.8 10
10
3
10
4
10
5
10
6
10
7
Cycles to failure Nf
Fig. 6. Influence of notches on fatigue strength under elevated temperature.
10
8
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significantly smaller at 130 C than at room temperature, compare Figs. 5 and 6. An increase of the stress concentration does not lead to a further reduction of fatigue strength. Fig. 7 shows the influence of different stress ratios R on fatigue strength in interaction with different stress concentrations. Tensile mean-stresses diminish the endurable stress amplitude as shown in Fig. 8. However, this decrease is not caused by the mean-stress sensitivity M¼
ran ðR ¼ 1Þ 1 ran ðR ¼ 0Þ
ð1Þ
of the material alone, but to some extent also by cyclic creep [10]. This decrease is less in the presence of notches because of stress gradients which diminish the cyclic creep. The results of variable amplitude loading with the Gaussı´an random load sequence, Fig. 2, when plotted with maximum spectrum stress amplitude show longer fatigue lives than constant amplitude fatigue loading, as expected (Fig. 9). For the same maximum amplitude variable
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amplituded loading always results in a significantly higher fatigue life than constant amplitude loading, due to the less damaging contribution of the smaller amplitudes of the spectrum [11]. The consideration of this fact enables the design of light-weight components through thinner crosssections [11], because for a requested fatigue life under variable amplitude loading much higher stresses can be allowed than under constant amplitude loading. The results of the Gassner-tests serve to determine the real damage sums Dreal ¼
N exp ; N cal ðDth ¼ 1:0Þ
ð2Þ
which are necessary for fatigue life calculations. As the Woehler-lines of the investigated polyamide do not have a knee-point, the elementary Palmgren–Miner rule is applied: Xn D¼ 6 1:0: ð3Þ N i The real damage sums were determined for all test series inclusively for the fuel rail between 0.1 and 10, which is also typical for composite materials [12] (Fig. 10). It can be
Fig. 7. Woehler-lines of short-glass-fibre reinforced polyamide under different stress ratios.
Fig. 8. Relation between mean-stress and stress amplitude.
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Fig. 9. Woehler- and Gassner-lines of short-fibre reinforced polyamide.
observed that a calculation with Dth = 1.0 renders a conservative assumption for fully reversed loading. However for pulsating loading an unsafe estimate is rendered, probably because of cyclic creep under pulsating pressure which is not considered by the linear damage accumulation. With Dreal = 0.5 all results for R = 1 and with Dreal = 0.1 all results for R = 0 are covered. 4. Transmission of specimen test results to components
Fig. 10. Comparison of experimental and calculated fatigue lives.
The transferability of the data obtained with specimens will be demonstrated for a fuel rail, Fig. 11, made of PA66GF35, which substituted a steel variant because of significant weight and cost advantages. The critical locations are the sharp notches, Fig. 12, in the connection with the pressure controller. Pulsating internal pressure (R = 0) up to Dpmax = 3.5 bar is the essential loading of this component at maximum service temperature of 130 C. However, to produce fatigue failures during tests much higher pressures with a pulsating frequency of 5 to 10 s1 were applied. In Fig. 13 the results obtained under constant and variable amplitude loading under RT and 130 C are compiled.
Fig. 11. Fuel rail.
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direct assessment using the Woehler- as well as the Gassner-lines (as presented in Figs. 4–9 in the nominal system) is not possible. For this, local fatigue life curves are necessary which must also consider local material properties such as surface state, fibre orientation, stress gradients and last but not least the local multiaxial stress state. Beyond this the failure criteria (in the present case total failure) must be the same for component and specimen. The fatigue life curves can be transformed from the nominal into the local system, Fig. 14, linear-elastically by ra;loc ¼ ra;1;max ¼ K t ran :
Fig. 12. Critical areas of the connection with the pressure controller.
5. Methodology As the fatigue critical locations are notches to which neither a notch factor nor a nominal stress can be allocated, a
ð4Þ
The use of the curves transformed into the maximum local principal stress also requires the determination of the local principal stresses as equivalent stresses in the critical areas of the connection. As the fibre directions in the notches of the specimens and of the connection correspond to each other, checked by micrographs, an anisotropy [13] needs not to be considered. Furthermore, as the material has a low ductility, revealed by low elongation values at room and higher temperatures, the principal stress hypothesis [14] can be applied in this case. Otherwise, a multiaxial
Fig. 13. Fatigue behaviour of fuel rails of short-fibre reinforced plastics.
1000 Ps=50%
MPa
Stress amplitude σa
Notchf actorK t : Local syst em
9.8 *K t
100 Nominal syst em
Influenceo f stress gradients (support effect) 1.0
9.8
10
Loadingm ode: axial, R=-1, in fibre direction, T=RT
102
103
104
105 Cyclest of ailure N f
(r=0.2mm)
106
107
108
Fig. 14. S–N-curves of a short-fibre reinforced polyamide in the nominal and local stress system.
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hypothesis considering anisotropy, like the Tsai-Wu or Tsai-Hill-criterion [15–17] should be used. Thus, this transformation alone is not sufficient for the assessment of the component. It is necessary to also account for the effect of stress gradients on the bearable local stress [18]. If the local stresses are plotted as a function of the stress concentration factor, Fig. 15, an increase of the bearable local stresses is observed the higher the stress concentration becomes. This fact is called the macro-support effect and is caused by stress gradients as defined by [18] v ¼
1 dr1 : r1;max dx
ð5Þ
The consideration of the material dependent influence on the bearable stress leads to higher local permissible stresses than those obtained with unnotched specimens and opens up light-weight design options. However, this effect is not controlled by the stress gradients alone, it is also determined by the highly stressed (strained) material volume which results from the gradients [19–22]. Fig. 16 displays for two simple geometries how the maximum
stressed material volume, defined as the volume in which the maximum local stress drops from 100% to a given value, i.e 90% or 80%, can be calculated approximately. This concept [19] was verified for metallic components [20–22] with good success using the volume fraction V90. For short-fibre reinforced specimens and components, the FE modelling with the volume V80 proved to be more practical than V90. From the Woehler-lines of unnotched and notched specimens, according to this procedure, a set of stress-volume lines for constant fatigue lives gives the basis for the assessment of the durability of the component (Fig. 17). The sharper a notch, the steeper are the stress gradients and the smaller the highly stressed material volume. As the probability of failure decreases with smaller material volume, the bearable local equivalent stress is higher than for bigger material volumes, Fig. 17, as for axially loaded unnotched specimens with a homogeneous stress distribution. The allocation of the calculated maximum local equivalent stress amplitude and maximum stressed volume of the critical area of the component into this diagram cross at the
Fig. 15. Nominal and local stress amplitude of a short-fibre reinforced polyamide as a function of the stress concentration.
Fig. 16. Determination of highly stressed material volumes V90 or V80 on simple geometries.
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Fig. 17. Relation between maximum stressed material volume and local equivalent stress.
fatigue life to be expected. For component design, the allowable stresses or fatigue lives are obtained by reducing the values with the probability of survival of Ps = 50% with safety factors [21–24], which depend on the scatter of fatigue data, manufacturing and on the required probability of failure of the component. 6. Application The verification of the design methodology described will be carried out on the basis of Ps = 50% – data obtained with specimens and components. The FE-model of the critical area of the fuel rail, Fig. 12, is shown in Fig. 18. The local maximum principal stress, the appertaining stress gradients along the surface as well as the thickness for determining the maximum stressed material volume V80 are calculated linear-elastically. In Table 2 calculated and experimental results for a constant amplitude fatigue life of Nr = 1 · 106 cycles with a probability of survival of Ps = 50% are compared. According to the presented methodology the maximum local stress
Table 2 Comparison of calculated and experimental maximum local stresses in the critical area and internal pressures of the fuel rail for a constant amplitude fatigue life Nf = 1 · 106 cycles (Ps = 50%) T
RT
130 C
Nf (Ps = 50%)
r1,max in MPa (FE) V80 in mm3 Dpmax in bar (FE) r1,max in MPa (exp) Dpmax in bar (exp)
641 0.002 13.2 646 13.3
392 0.002 8.1 460 9.5
1 · 106
determined by FE is almost equal to the stress obtained from the experiments for room temperature, but for 130 C the numerical values of local principal stress and pressure are on the conservative side. In both cases the ultimate tensile strength Rm = 210 MPa (for room temperature) is exceeded significantly. This proves that the use of quasi-static material properties is obviously not appropriate for fatigue design. The behaviour of the fuel rail under variable amplitude pulsating loading is important with regard to service. In Table 3 mean fatigue lives obtained under the Gaussı´an spectrum, Fig. 2, at room temperature and 130 C, respectively, are compared with the calculated values for a maximum internal pressure of Dpmax = 18 bar (N.B.: in service the maximum pressure is Dpmax = 3.5 bar). With the knowledge obtained from the cumulative test series the fatigue lives are calculated according to the elementary Palmgren–Miner rule (Woehler-line without knee-point) Table 3 Calculated and experimental fatigue lives for Gaussı´an spectrum loading (R ¼ 0; Ls ¼ 5 104 ) with Dpmax = 18 bar
Fig. 18. FE-model of the critical area.
T
RT
130 C
Dpmax in bar
Nf (FE, Ps = 50%) Dreal r1,max (FE) in MPa V80 in mm3 Nf (exp) Ps = 50% r1,max (exp) in MPa
1.42 · 107 0.5 837 0.002 1.41 · 107 837
1.10 · 105 1.0 837 0.002 3.60 · 105 837
18
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with the particular real damage sums. Again, the estimate for 130 C is on the conservative side. The calculations as well as the experimental results at Dpmax = 18 bar contain a high safety factor jr 5 and prove that for the service pressure of Dpmax = 3.5 bar a reliable durability of the fuel rail can be expected, as already verified by the service use of the components over more than 10 years without any failures. 7. Outlook The developed design procedure with local fatigue data considering surface state, fibre orientation, stress concentration, stress gradients, highly stressed material volume and multiaxiality is appropriate to reliably estimate the fatigue life of high loaded plastic parts installed in engine compartments. It has been clearly shown that with static properties like ultimate tensile stress, the analysed design would be rejected or a much thicker component would be proposed as obtained by a fatigue and notch effect based design. Investigations on other plastic materials with different matrix materials, fibres and fibre contents, should enlarge the database now available for PA66-GF35. Missing knowledge regarding the ability to withstand fuel environment and local multiaxial stresses with changing principal stress directions opens a broad field of future investigations. References [1] Plastics in automobile industry 2004. In: VDI-Report No. 4260; 2004. [2] Vollrath K. Polymer versus Steel and Glass. Automobile-Development 2004;5:50–2. [3] Moosbrugger E, Wieland R, Gumnior P, Gerharz J. Betriebsfeste Auslegung hochbelasteter Kunststoffbauteile im Motorraum (Design and dimensioning of highly loaded plastic parts in engine compartments). Materialpru¨fung 2005;47:445–9. [4] Gumnior P, Gerharz JJ, Sonsino CM, Hanselka H. Entwicklung eines Bemessungskonzeptes zur betriebsfesten Auslegung von Bauteilen aus kurzfaserversta¨rktem Polyamid [Development of a methodology for structural durability design of components from short-fibre reinforced polyamide]. LBF-Report No. 182141. Darmstadt, Germany: Fraunhofer-Institute for Structural Durability and System Reliability LBF; 2002 [partially published in this paper]. [5] Sonsino CM. Material selection for impact and cyclically loaded metal components. In: DVM-Report No. 127; 2000. p. 21–38. [6] Huth H, Mattheij P, Gerharz JJ. Effect of notches and impact damage on structural durability of composite materials. In: DVM-Report No. 127; 2000. p. 39–50. [7] Ehrenstein GW. Designing with polymers. Munich/Vienna: Carl Hanser Publishing; 1995.
[8] Erhard G. Designing with polymers. Munich/Vienna: Carl Hanser Publishing; 1999. [9] Sonsino CM. Endurance limit – a fiction. Konstruktion 2005;4:87–92. [10] Mallick PK, Zhou Y. Effect of mean-stress on the stress-controlled fatigue of a short e-glass fiber reinforced polyamide-6,6. Int J Fatigue 2004;26:941–6. [11] Sonsino CM. Principles of variable amplitude fatigue design and testing. Fatigue testing and analysis under variable amplitude loading conditions. In: McKeighan PC, Ranganathan N, editors. ASTM STP 1439. West Conshohocken, PA: ASTM International; 2005. p. 3–23. [12] Mattheij P. Application of Miner’s linear damage accumulation hypothesis on composite materials. Conference on plastics, 11 and 12 November 1992. Wu¨rzburg/Germany: Su¨ddeutsches Kunststoffzentrum. [13] Bernasconi A, Davoli P, Basile A, Filippi A. Effect of fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide-6. Int J Fatigue 2007;29(2):199–208. [14] Sonsino CM, Grubisic V. Multiaxial fatigue behaviour of sintered steels under combined in- and out-of-phase bending and torsion. Zeitschrift Werkstofftechnik 1987;18:148–57. [15] Gerharz JJ, Gumnior P, Sonsino CM, Bu¨ter A, Hanselka H. Einfluss mehrachsiger Belastungszusta¨nde mit konstanten und vera¨nderlichen Hauptspannungsrichtungen auf die Schwingfestigkeit von kurzfaserversta¨rktem Polyamid [Influence of multiaxial stress states with constant and varying principal stress directions on the fatigue strength of short glass-fibre reinforced polyamide]. LBF-Report No. 186449. Darmstadt/Germany: Fraunhofer-Institute for Structural Durability and System Reliability LBF; 2005 [partially published in this paper]. [16] Bolender K, Bu¨ter A, Sonsino CM. Fatigue behaviour of short fibre reinforced polyamide under multiaxial loading. In: 12th European conference on composite materials ECCM, Biarritz, France; 29.08– 01.09.2006. [17] De Monte M, Moosbrugger E, Bolender K, Quaresimin M. Fatigue failure assessment of short glass fibre reinforced polyamides 6.6 under multiaxial loading. Associazione Italiana per l’Analisi delle Sollecitazioni (AIAS), XXXV Convegno Nazionale, Universita` Politecnica delle Marche; 13–16.09.2006. [18] Siebel E, Stieler M. Spannungsverteilung, schwingende Beanspruchung [Stress distribution, cyclic loading].VDI-Z 97, 5; 1955. p. 121– 6. [19] Kuguel R. A relation between theoretical stress concentration factor and fatigue notch factor deducted from the concept of highly stressed volume. ASTM STP Proc 1961;61:732–48. [20] Sonsino CM. Evaluating the fatigue behaviour of components with consideration of local stresses. Konstruktion 1993;45:25–33. [21] Sonsino CM, Kaufmann H, Grubisic V. Transferability of material data for the example of a randomly fatigue loaded stub axle. SAE transactions section 5. J Mater Manuf 1997;106:649–70. [22] Sonsino CM. Fatigue design concepts for PM parts and required material data – an overview. Princeton: Metal Powder Industries Federation (MPIF); 2003. [23] Sonsino CM, Dieterich K. Fatigue design with cast magnesium alloys under constant and variable amplitude loading. Int J Fatigue 2006;28:183–93. [24] Haibach E. Betriebsfestigkeit – Verfahren und Daten zur Berechnung [Structural durability – methods and data for calculation]. 2nd ed. Du¨sseldorf: Springer-Verlag; 2003.