Review of 20 Years Research in Fatigue of High Pressure Loaded Components

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1 82 FATIGUE 2011 Carl Hanser Verlag, München Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern. Review of 20 Years Research in Fatigue of High Pressure Loaded Components Dedicated to Professor Joachim W. Bergmann on Occasion of his 65 th Birthday Rayk Thumser, Weimar, and Wolfgang Scheibe, Stuttgart The main motivation on the research of fatigue of high pressure loaded components was the development of high pressure injection systems of Diesel engines. The common rail system was developed at ETH Zurich and allows the control of the injection pressure independently from the crankshaft speed. The worldwide 1 st common rail system [1, 2] was installed on an IFA W50 L/S on a six cylinder engine 6VD 12.5/12 for test reasons in Karl-Marx-Stadt, Germany. Unfortunately a production in series was not achieved. The first electronic common rail system in series production was built by L Orange in 1997 [3]. This paper gives an overview of the research in fatigue of high pressure loaded components. In the last 20 years the main research was carried out in Germany. This research was mainly driven by the fatigue requirements for high pressure loaded Diesel engine injection parts as common rails, injectors and pipes. The common rail system was in series production 1997 for passenger cars, Alfa Romeo JTD and later Mercedes- Benz C 220 CDI. Common rail system has also been applied for large bore Diesel Engines [4-6] as well as for airplane engines [7]. Issues of Fatigue of High Pressure Loaded Components In principle there are two methods available to raise the fatigue strength of a component. The first one is the local strengthening of the material. The second one involves reducing the local Figure 1. Equivalent van Mises stresses for a thick walled tube and a hollow sphere straining due to the external load. Due to the limitation of material strengthening the second method is more promising. For internal pressure loaded components there are some mechanical limitations present. Figure 1 shows the von Mises equivalent stresses on the inner surface of a thick walled tube [8] and a hollow sphere in dependency of the diameter ratio. For a diameter ratio larger than about three there is no more reduction of local stresses possible. Up to now the most successful procedures for the fatigue strengthening of high pressure loaded components is the autofrettage. For this an initial pressure overload is applied, see Figure 2. The first description of the autofrettage process as fatigue resistance raising procedure on cannon tubes is known from Jacob [9]. This produces a compressive residual stress field near the internal surface. The crack initiation and the crack growth behaviour are positively influenced so that the fatigue life and endurance limit is increased. Due to an initial overload one main effect has to be considered for the calculation of residual stresses. The Bauschinger Effect [10, 11] reduces the yield strength in the compressive region of the material after the previous tension loading. For the fatigue life and endurance limit the Bauschinger effect dramatically influences the calculation results [12]. Carl Hanser Verlag, München Materials Testing

2 Research Initiated and Supported by FVV (Research Association for Combustion Engines) and Supported by AiF (German Federation of Industrial Research Associations) At the end of the 80 s, the company L Orange heard something about a process called autofrettage, and L Orange was interested in evaluating the benefits of autofrettage for the fatigue resistance of autofrettaged high pressure components. The industry initiated a research project Autofrettage I [13] to investigate the behaviour of cross bored specimens with an intersection angle of 90 s made out of AISI 4140 (42CrMo4), as shown in Figure 3. It was expected that due to the autofrettage process the mean stress effect can raise endurance by circa 20 to 30 %. The experimental findings showed a crack arrest in the compressive residual stress field which lead to an enormous raise of endurance limit of the 90 cross bore (Figure 4). The prediction methods for residual stresses and crack initiation were successfully developed and verified [14-16]. The second project Autofrettage II [17] should extend the prediction methods for the crack arrest of autofrettaged components. Therefore additional sample types (45 cross bore and stepped hole) were experimentally investigated. Also, the limit number of cycles was increased from 2E6 to 1E7. The endurance limit for the 45 cross bore can be raised to a factor of 3.5 with autofrettage. Figures 5 and 6 show the arrested cracks. The prediction method for endurance limit is based on the linear elastic fracture mechanics (LEFM) using a 2D weight function for the evaluation of stress intensity factors (SIF) [18, 19]. Due to the high compressive residual stresses, the weight function itself and the threshold value for crack growth do not influence the predicted endurance limit a lot but the right prediction of the residual stresses [18, 20, 21]. A great number of high pressure loaded components, e. g. injectors, are case hardened to improve the wear resistance and for sealing surfaces. The third project Autofrettage III [24] covered the optimal combination of autofrettage and case hardening. Three sample types (90 cross bore, 45 cross bore, and stepped hole) made from AISI 4820 (18CrNiMo7-6) were investigated. During the autofrettage process the case hardened layer cracks, and the bulk material can stop the static crack growth. If the autofrettage pressure is to high, an instable crack growth and the burst of the component will occur. The endurance limit test series showed that the combination of not carburized (base material quenched and tempered) and autofrettage leads to the highest endurance limit, see Figure 7. A simulation model of the carburizing process was developed by Diemar [25]. The prediction method for stable crack growth is based on the J-integral of Figure 3. Geometry of 90 degree crossbore specimen [13] FATIGUE 83 Figure 2. Schematic autofrettage procedure and subsequent cyclic loading the elastic plastic fracture mechanics (EPFM) and the plasticity model of Döring [26, 27]. A more detailed investigation was carried out by Linne [28]. During a long period the endurance limit design [29] could be applied to high pressure loaded components. Due to the raising pressures up to 3000 bar of injection systems of Diesel engines a fatigue life design could help to proof the requirements. The project Autofrettage IV [30] should evaluate prediction methods for constant amplitude loading (CAL), and variable amplitude loading (VAL) based on different levels [31]:

3 84 FATIGUE Figure 4. Dp-N Curve for not autofrettaged and autofrettaged 90 degree crossbore specimen, from [13, 17] Figure 5. Arrested crack on 90 degree crossbore specimen [22] Figure 7. Mean endurance limits for case hardening and autofrettage [24] 1. Nominal approach with miners rule 2. Local approach and LEFM with 3D weight function [22] 3. Local approach and EPFM with extended strip-yield model [32] 4. Local approach and explicit 3D finite element simulation [32]. The levels two and three are recommended for industrial application. The level one is only applicable when VAL test results are available. The numerical effort for level four is too large for industrial application. Common life assessments in variable amplitude loading are based on constant amplitude life curves. Such curves have been produced for R=0 and R=0.5. Furthermore, two-level tests have been performed consisting of many cycles with R>0 interrupted by one cycle with R=0. The cycle number ratio was 1:1000, exemplarily also 1: During the project a synthetic load sequence was developed with Figure 6. Arrested crack on 45 degree crossbore specimen [17, 23] the aid of the industrial working team. The standardised load sequence [33] for common-rail-applications, CORAL (COmmon RAil Load Sequence), has been designed and used in this investigation (Figures 8 and 9). Basic properties of the sequence are as follows: start-stop cycles cycles from idle to maximum pressure p max idle pressure at 14 % of p max omission level at a range of 10 % of p max total content cycles consisting of 100 identical repetitions of 300 startstop and associated intermediate cycles. The two-level tests up to the 1E7 cycles show that there is no threshold for the

4 Pressure amplitude [%] Cumulative frequency Figure 8. CORAL cumulative frequency plot damage of these small cycles, see Figure 10. At injection systems a huge number (1E9 1E10) of small cycles are present. Therefore the knowledge of half the endurance limit as omission level (mean stress corrected) has to be taken into account, which is not applicable [34] here. The current project Autofrettage V will run tests up to 1E8 cycles with the two-level tests and an extended version of CORAL. There are four different levels for prediction method under investigation and extension: 1. Nominal approach 2. Local approach and LEFM with explicit FE crack growth simulation with adaptive remeshing 3. EPFM for short and long cracks based on extended Newman (extended stripyield) model 4. EPFM for short and long cracks with explicit FE crack growth simulation with adaptive remeshing and transfer of the state variables of the plasticity model (history) [35, 36]. The crack shape development will be experimentally determined [37]. This project is expected to finish in The fatigue behaviour of internal cyclic pressurized components made from newly developed higher strength nodular cast iron like SiboDur-700 and MADI (Austempered Machinable Ductile Iron) is investigated by another research project [38]. CAL tests and VAL tests with Coral are planned. This project will also finish in From class Figure 9. CORAL rainflow matrix Low Temperature Autofrettage The austenitic stainless steel AISI 304L (X2CrNi 19 11) increases the static strength by reducing the temperature. Therefore the autofrettage pressure can be raised and higher residual stresses occur. This results in higher fatigue strength of thick walled cylinders with and without cross bores [39-43]. Due to the low tensile strength of about 550 MPa no industrial application of low temperature autofrettage is known. These investigations have also been supported by the DFG. Figure 10. CAL and VAL tests [30] To class FATIGUE 85 High Pressure Injection Tubes One project investigated the endurance of cold drawn tubes for Diesel injection systems [29, 44, 45]. A broad experimental data base has been created on the behaviour of HP-pipes made from S 460 nbk and bk+s. The pipes had an outer diameter of 6 mm, an inner diameter of 2.5 mm and a length of 150 mm. Two quality grades have been investigated (according to ISO [45]): Q with a maximum defect size of 50 μm, and O with 10 μm. For each material state two autofrettage pressures were applied.

5 86 FATIGUE Figure 11. Endurance limits of cold drawn tubes for Diesel injection systems (90 %, 50 %, 10 % and 1 ppm failure Probability) [29] Figure 12. Investigated Common Rail sample [22] Additionally, non-autofrettaged pipes were also investigated. In total about 340 pipes have been tested in the endurance regime using the Logit method [46-48]. The mean endurance limit Δp E, the 10 and 90 per cent pressures and allowable pressures Δp E (1ppm) are given in Figure 11. The autofrettage increases the mean endurance limit. The more positive effect is the reducing of the scatter. This reduces the safety factor for 1 ppm failure probability (series production). Consequently the allowable 1 ppm pressures will increase at least to the double value of not autofrettaged variants. The prediction method for endurance is based on Dörings plasticity model [26, 27] and EPFM for crack arrest. Other Research Results Vetter, Mischorr, and Lambrecht [49, 50] as well as Mischorr [51] investigated experimentally the fatigue behaviour of components made from high alloy chrome-nickel steels such as X5 CrNi MoCu 218 and X5 CrNiMo 165 under cyclic pressure loading. For thick walled tubes there was an influence of the specimen orientation on the endurance limit discoverable. For thick walled tubes with cross bores this was not observed. Thumser, Bergmann and Vormwald [12, 20, 52] developed an easy method for predicting the residual stresses due to autofrettage including the Bauschinger Effect. This method is based on the idea of the Bauschinger effect factor (BEF) [53, 54] for axisymmetric problems. The calculation is separated in two independent calculation steps, one for loading and one for unloading the autofrettage pressure. With good accuracy the loading calculation can be carried out with a multilinear kinematic or isotropic plasticity model. The reached plastic equivalent strain is exported and read as pseudo-temperature for the unloading step. The material parameters can be set as dependent on temperature (pseudo) to include the Bauschinger effect. The residual stresses are calculated as superposition of loading and unloading stresses. Comparisons show the huge influence of the Bauschinger effect on the predicted endurance limits. Nowadays this method is known as variable material property (VMP) method [55-57]. Greuling [21] extended the methods developed in project Autofrettage II [17] by using different 2D weight functions showing no large impact on the endurance limit prediction. For the 90 cross boring alternatively it was investigated the 3D weigth function of Oore and Burns [58, 59] for the calculation of SIF s based on fractographic crack shapes at the endurance limit. The question of re-autofrettage was investigated by Parker [60] and Jahed, Moghadam and Shambooli [61] by numerical calculation for a Q&T steel AISI 4340 for a thick walled tube: There is no benefit of applying two times the same autofrettage pressure. The sequence low/high pressure produces nearly the same residual stress field as applying a high pressure once. The sequence high/low pressure can increase the compressive residual stresses up to 20 %. Spickenreuther [62] studied different fatigue prediction methods for casehardened Diesel injection nozzles, focusing on surface finish, mean stress influence, local hardness, and notch sharpness. Eleven fatigue test series were carried out. Unfortunatelly the scatters of the experimental endurance limits are so huge that the influences are not separable.

6 FATIGUE Carl Hanser Verlag, München Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern. Figure 13. Experimental and predicted lifes for common rail sample under CORAL VAL [22] Leutwein [63] performed an investigation of the benefit of autofrettage for pumps made of spheroidal cast iron. This was carried out for different materials, EN-GJS , EN-GJS and EN-GJS The autofrettage has only a low benefit of about 30 % in increasing the endurance limit. A crack arrest for the autofrettaged specimens could not be observed. The prediction method for crack initiation shows good agreement with experimental results. Lechmann et al. [64, 65] developed a model for endurance limit prediction for components with compressive residual stresses, especially due to autofrettage. The residual stresses were predicted by a plasticity model from Armstrong, Frederic, Lemaitre, and Chaboche [66, 67]. The numerical crack growth simulation was performed with a 3D model using crack growth procedure of Lin and Smith [68-70], which allows remeshing a plane crack surface. The procedure is validated on an autofrettaged common rail part made from forging steel 38MnVS6. There is a good agreement of the predicted endurance limit with the experimental result. Thumser [22] used an engineering approach for the calculation procedures for crack growth calculation. This includes the calculation of autofrettage stress, the stress intensity, the crack opening, and closing behaviour of the crack growth. The residual stress calculation module for autofrettage is based on the superposition of autofrettage load as well as the discharge and makes it possible to consider the Bauschinger effect. Stress intensities are identified with a 3D weight function [58, 59], which was already used by Greuling [21]. The crack opening and closing effects are reproduced with approximation equations, e.g. [71]. The phrasing of the Paris- Erdogan [72] relationship for effective stress intensity factor was used for the crack growth relationship. The threshold of the stress intensity has little influence on the prediction of crack arrest endurance limit of autofretted cross bores as the crack opening force is very close to the maximum pressure. In total 14 test series of cross borings (e.g. from projects Autofrettage I-IV [13, 17, 24, 30]) were carried out for the verification of the calculation procedure for the threshold of the inner pressure experiments. Figure 12 shows the FE-model of the investigated common rail sample. The prediction and experimental results for CORAL VAL are in good accordance, Figure 13. The model shows a suitable prediction quality for mean value with low dispersion. This demonstrates the performance of the proposed life prediction method. There are still other fields of high pressure applications than high pressure Diesel injection systems, e.g. highpressure food preservation [73-76], waterjet cutting [77-79], and LDPE production [80, 81]. A lot of research has Figure 14. Experimental and predicted endurance limit for samples with bore intersections [22] been done in the field of cannon tubes, e.g. [53, 82-88]. Due to the explosion, the gas pressure can reach up to 700 MPa. Theautofrettage process is used to extend the fatigue life. The main advantage of the autofrettage is the reduction of the scatter and reducing the influence of surface roughness for high pressure tubes. For bore intersections (crossboring) the intersection quality is of lower interest because of the small influence of the crack initiation. Based on the results in [22] the endurance limit values are plotted in Figure 14. Based on the experience from the service at MFPA Weimar, it seems that the notch sharpness is not influencing the endurance of autofrettaged crossbores. The material itself and the autofrettage pressure determine the mean endurance limit. However, the specimen geometry is determined by the burst pressure and thus limits the maximum autofrettage pressure. For a rough approximation of burst pressure the formula of Faupel [89] is recommended for application on tubes and also for outer geometries. Outlook Plenty of knowledge of fatigue of high pressure components has been discovered. However many areas require further research. One main problem is measuring the residual stresses due to autofrettage.

7 88 FATIGUE 2011 Carl Hanser Verlag, München Nicht zur Verwendung in Intranet- und Internet-Angeboten sowie elektronischen Verteilern. Up to now there is no experimental procedure available, which allows verifying the residual stress calculation. X-ray and other [90] measurements require a certain measurement diameter (~0.5 mm) and often accessible surface. This normally requires cutting the sample open and changes the residual stress state [24]. Also for quality control reasons in production in series the application of autofrettage cannot be controlled nor the corresponding level of autofrettage by non-destructive testing methods (NDT). Another unsolved problem is the influence of the frequency of pressure loading. The fluid has to penetrate the crack. There must be a frequency where the cyclic penetration of the crack is no more possible. The cyclic loading on the crack face is thus reduced. On test rigs normally lower frequencies than the real application on Diesel injection systems are performed. The strain rising effect due to the lower test frequency is not known. The impact assessment is up to now not possible. For some special applications (heavy fuel oil) of injection systems the operation temperature is between 130 C and 190 C. For case-hardened steels this is close to the tempering temperature. As well as for autofrettaged components it is not known how stable the residual stresses under cyclic internal pressure loading and higher temperatures are. References 1 IMC- Exponat: latestversion=true&workshop=-1&format =HTML&fileTypeVersionId=-1&aFileName =&URLID= Common-Rail-Einspritzung: https:// secure.wikimedia.org/wikipedia/de/wiki/ Common-Rail-Einspritzung 3 R. W. Jorach, W. Scheibe, R. Prillwitz, H. Ressel, and L. Bakaj: The upcoming generation of common rail injection systems for large bore engines from L Orange GmbH, ICE Vol. 39 (2002): Design, Application, Performance and Emissions Of Modern Internal Combustion Engine Systems and Components, pp D. Woodyard: Pounder s Marine Diesel Engines and Gas Turbines, 8 th Edition Butterworth-Heinemann, Oxford (2004) 5 W. Rainer, H. Doppler, O. Altmann: Schweröl Common Rail Einspritzsysteme für Großmotoren, MTZ 61 (2000), No. 12, p W. Rainer, H. Doppler, H. Ressel, W. Scheibe: Common Rail Applications for Medium Speed Engines The Answer from the Fuel Injection System Supplier on the Customers Demands, CIMAC Central Secretariat c/o VDMA e.v. (2008), pp Thielert Centurion 4.0 Flugmotor Technische Daten 8 G. Lamé, B. P. E. Clapeyron: Mémoire sur l équilibre intérieur des corps solides homogènes, Paris (1833), http//www.thielert.com 9 L. Jacob: Résistance et construction des bouches à feu, Memorial de L artillerie Nacale (1909), Paris, Doin, p J. Bauschinger: Über die Veränderung der Elastizitätgrenze und der Festigkeit des Eisens und Stahls durch Strecken, Quetschen, Erwärmen, Abkühlen und durch oftmals wiederholte Belastung, Mitteilungen des mechanischen technischen Labors der Technischen Hochschule München (1886), p R. P. Skelton, H. J. Maier, H. Christ: The Bauschinger effect, Masing model and the Ramberg-Osgood relation for cyclic deformation in metals, Materials Science and Engineering A 238 (1997), No. 2, pp R. Thumser, J. W. Bergmann, M. Vormwald: Residual stress fields and fatigue analysis of autofrettaged parts, International Journal of Pressure Vessels and Piping 79 (2001), No. 2, pp T. Seeger, M. Schön, J. W. Bergmann, M. Vormwald: Autofrettage I: Vorhaben Nr. 478, Dauerfestigkeitssteigerung durch Autofrettage, Abschlußbericht, Forschungsberichte Verbrennungskraftmaschinen, Heft 550, FVV Frankfurt (1993) 14 M. Schön, V. B. Köttgen, T. Seeger: A numerical procedure to calculate residual stresses and fatigue life of pressurized components after autofrettage, Proc. of the Third Int. Conf. on Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials, (1993), pp T. Seeger, M. Schön, V. B. Köttgen, J. W. Bergmann, M. Vormwald: Steigerung der Schwingfestigkeit druckführender Bauteile durch Autofrettage, Moderne Fertigungstechnologien zur Lebensdauersteigerung 117 (1991), pp M. Schön: Eigenspannungs- und Dauerfestigkeitsberechnungen autofrettierter innendruckbeanspruchter Bauteile, Dissertation, TH Darmstadt, Institut für Stahlbau und Werkstoffmechanik (1995) 17 T. Seeger, S. Greuling, J. W. Bergmann, Autofrettage II: Vorhaben Nr. 671, Dauerfestigkeitssteigerung durch Autofrettage II, Abschlußbericht, Heft 704, FVV, Frankfurt (2001) 18 S. Greuling, T. Seeger: A model for endurance limit calculation of autofrettaged pressurized components considering crack arrest, Proc. of the 8 th International Conference on Fatigue, Vol. 2, Stockholm, Sweden (2002), pp S. Greuling, J. W. Bergmann, R. Thumser: Ein Konzept zur Dauerfestigkeitssteigerung autofrettierter Bauteile unter Innendruck, Materialwissenschaften und Werkstofftechnik 32 (2001), No. 4, pp R. Thumser, J. W. Bergmann, M. Vormwald: Residual stress fields and fatigue analysis of autofrettaged parts, International Journal of Pressure Vessels and Piping 79 (2002), No. 2, pp S. Greuling: Dauerfestigkeitsberechnung autofrettierter innendruckbelasteter Bauteile mit Bohrungskreuzungen unter Berücksichtigung stehen bleibender Risse, Dissertation, TH Darmstadt, Institut für Stahlbau und Werkstoffmechanik (2005) 22 R. Thumser: Simulation des Rissfortschritts in autofrettierten und nicht autofrettierten Bohrungsverschneidungen auf der Grundlage der linear-elastischen Bruchmechanik, Dissertation, Bauhaus Universität Weimar, Fakultät Bauingenieurwesen (2009) 23 J. W. Bergmann, Personal Communication (2000) 24 A. Diemar, K. Linne, J. W. Bergmann, M. Vormwald: Einsatzhärten und Autofrettage, Vorhaben Nr. 784, Dauerfestigkeitssteigerung einsatzgehärteter Hochdruckbauteile durch Autofrettage, Abschlußbericht, Heft 783 FVV, Frankfurt (2004) 25 A. Diemar: Simulation des Einsatzhärtens und Abschätzung der Dauerfestigkeit einsatzgehärteter Bauteile, Dissertation, Bauhaus-Universität Weimar, Fakultät Bauingenieurwesen (2007) 26 R. Döring, J. Hoffmeyer, T. Seeger, M. Vormwald: A plasticity model for calculating stress-strain sequences under multiaxial non-proportional cyclic loading, Computational Materials Science 28 (2003), No. 3, pp R. Döring: Zum Deformations- und Schädigungsverhalten metallischer Werkstoffe unter mehrachsig nichtproportionalen zyklischen Beanspruchungen, Dissertation, TU Darmstadt, Institut für Stahlbau und Werkstoffmechanik (2005) 28 K. Linne: Untersuchungen des Anriss- und Rissfortschrittverhaltens von Bauteilen aus Gradientenwerkstoffen nach statischen Überlasten, Dissertation, TU Darmstadt, Institut für Stahlbau und Werkstoffmechanik (2008) 29 E. Herz, R. Thumser, M. Vormwald, J. W. Bergmann: Endurance limit design of high pressure diesel injection pipes for low failure probability, Fatigue Design 2005, Senlis, p R. Thumser, E. Herz, O. Hertel, J. W. Bergmann, M. Vormwald: Betriebsfestigkeit Hochdruckbauteile, Vorhaben Nr. 880, Betriebsfestigkeit gekerbter Hochdruckbauteile ohne und mit Autofrettage, Abschlussbericht, FVV, Frankfurt (2009) 31 E. Herz, O. Hertel, M. Vormwald, R. Thumser, J. W. Bergmann: Fatigue life of high pressure diesel injection components under variable amplitude loading, Proc. of the 2 nd Int. Conf. on Material and Component Performance under Variable Amplitude Loading, Vol. 2 (2009), pp

8 Abstract Übersicht über 20 Jahre Forschung zur Ermüdung von Hochdruckkomponenten Prof. Joachim W. Bergmann zum 65. Geburtstag gewidmet. Der vorliegende Beitrag vermittelt einen Überblick zur Forschung auf dem Gebiet der Ermüdung von Hochdruckkomponenten. In den vergangenen 20 Jahren wurde der Hauptteil der Forschung hierzu in Deutschland durchgeführt. Diese Arbeiten wurden maßgeblich von den Festigkeitsanforderungen an hochdruckbelasteten Einspritzkomponenten in Dieselmotoren getrieben, wie beispielsweise Common Rails, Einspritzdüsen und Leitungen. 32 E. Herz, O. Hertel, M. Vormwald: Numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes, Engineering Fracture Mechanics, im Druck /j.enfracmech P. Heuler, H. Klätschke: Generation and use of standardized load spectra and loadtime histories, Proc. of the International Conf. on Fatigue 2003, Sevilla (2003), International Journal of Fatigue, Vol. 27, Issue 8, August 2005, pp P. Heuler, T. Seeger: A criterion for omission of variable amplitude loading histories, International Journal of Fatigue 8 (1986), No. 4, pp P. Zerres, M. Vormwald: Numerical simulation of crack growth under cyclic loading with a focus on elastic-plastic material behaviour, Proc. of the 18 th European Conference on Fracture, DVM, Berlin (2010), 36 P. Zerres: Numerische Simulation des Ermüdungsrissfortschrittes in metallischen Strukturen unter Berücksichtigung zyklischer Plastizitätseffekte, Dissertation, TU Darmstadt, Institut für Stahlbau und Werkstoffmechanik (2010) 37 R. Thumser, M. Schickert, S. Kleemann, J. Winge, U. Gerth: Crack growth measurements in notches under cyclic internal pressure loading, Proc. of the 18 th European Conference on Fracture, DVM, Dresden (2010) 38 S. Schönborn, H. Hanselka: Drucksteigerung bei zyklisch innendruckbeanspruchten Bauteilen durch Verwendung von neu entwickelten höherfesten Gusswerkstoffen Zwischenbericht über das Vorhaben Nr. 941 (AIF-Nr N/1), Informationstagung Motoren, Bad Neuenahr, Heft R545 (2009) 39 H. Mughrabi, B. Donth, G. Vetter: Lowtemperature autofrettage: An improved technique to enhance the fatigue resistance of thick walled tubes against pulsating internal pressure, Fatigue Fract. Engng. Mater. Struct. 20 (1997), pp H. Mughrabi, B. Donth, H. Feng: Optimal residual stresses introduced in thickwalled tubes by low temperature autofrettage: Enhancement of fatigue resistance against internal pressure, Proc. of the 5 th International Conference of Residual Stresses, Linkoping, Schweden (1997), pp H. Feng, H. Mughrabi, B. Donth: Finiteelement modelling of low-temperature autofrettage of thick-walled tubes of Austenitic stainless steel AISI 304L: Part I, Smooth thick walled tubes, Modelling Simul. Mater. Sci. Eng. 6 (1998), pp H. Feng, B. Donth, H. Mughrabi: Finiteelement modelling of low-temperature autofrettage of thick-walled tubes of Austenitic stainless steel AISI 304L: Part II, Thick walled tube with cross-bore, Modelling Simul. Mater. Sci. Eng. 6 (1998), pp B. Dhonth: Tieftemperatur-Autofrettage und Ermüdungsverhalten dickwandiger Rohr aus dem metastabilen austenitischen Stahl X2CrNi bei schwellendem Innendruck, Dissertation, Universität Erlangen-Nürnberg (1996) 44 E. Herz, R. Thumser, M. Vormwald, J. W. Bergmann: Endurance limit of auofrettaged Diesel-engine injection tubes with defects, Engineering Fracture Mechanics 73 (2005), No. 1, pp ISO 8535: Compression-Ignition Engines Steel Tubes for High-Pressure Fuel Injection Pipes Part 1: Requirements for Seamless Cold-Drawn Single-Wall Tubes (1996) 46 J. Berkson: A statistically precise and relatively simple method of estimating the bioassay with quantal response, based on the logistic function, Journal of the American Statistical Association 48 (1953), No. 263, pp N. Balakrishnan: Handbook of the Logistic Distribution, Dekker, New York (1992) 48 N. Balakrishnan: Maximum likelihood estimation based on complete and type II censored samples, Journal of the American Statistical Association, Vol. 26 (1990) 2, pp G. Vetter, D. Lambrecht, G. Mischorr: Zur Ermüdung dickwandiger Rohre aus weichmartensitischen und halbaustenitischen Chrom-Nickel-Stählen durch schwellenden Innendruck, 3R International 31 (1992), pp FATIGUE G. Vetter, D. Lambrecht, G. Mischorr: Fatigue of thick-walled pipes from soft martensitic and semi-austenitic Chromium Nickel steels under pulsating internal pressure, Chem. Eng. Technol. 15 (1992), pp G. Mischorr: Zur Ermüdung dickwandiger Rohre aus weichmartensitischen und halbaustenitischen Chrom-Nickel Stählen durch schwellenden Innendruck, Friedrich Alexander Universität Erlangen-Nürnberg (1990) 52 R. Thumser, J. W. Bergmann, M. Vormwald: Design of autofrettaged diesel injection components based on fracture mechanics: Pressure Vessel and Piping Design an Analysis, ASME (2001), pp M. Perl, J. Perry: The beneficial contribution of realisitc autofrettage to the loadcarrying capacity of thick-walled spherical pressure vessels, Journal of Pressure Vessel Technology 132 (2010), No. 1, pp H. Jahed, R. Sethuraman, R. N. Dubey: A varaible property approach for solving elastic-plastic problems, International Journal of Pressure Vessels and Piping 71 (1997), pp H. Jahed, B. Farshi, M. Hosseini: Fatigue life prediction of autofrettage tubes using actual material behaviour, International Journal of Pressure Vessels and Piping 83 (2006), No. 10, pp M. Maleki, G. Farrahi, B. Haghpanah Jahromi, E. Hosseinian: Residual stress analysis of autofrettaged thick-walled spherical pressure vessel, International Journal of Pressure Vessels and Piping 87 (2010), No. 7, pp G. Farrahi, S. Faghidian, D. Smith: Reconstruction of residual stresses in autofrettaged thick-walled tubes from limited measurements, International Journal of Pressure Vessels and Piping 86 (2009), No. 11, pp M. Oore, D. J. Burns: Estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields, Proc. of the 4 th International Conf. on Pressure Vessel Technology (1980), Vol. 1, pp M. Oore, D. J. Burns, Estimation of stress intensity factors for embedded irregular cracks subjected to arbitrary normal stress fields, Journal of Pressure Vessel Technology 102 (1980), pp A. P. Parker: A re-autofrettage procedure for mitigation of Bauschinger effect in thick cylinders, Journal of Pressure Vessel Technology 126 (2004), No. 4, pp H. Jahed, B. A. Moghadam, M. 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9 90 FATIGUE belasteter Bauteile aus Kugelgraphitguss, Dissertation, TU Ilmenau, Fakultät für Maschinenbau (2008) 64 M. Lechmann: Entwicklung eines schwingbruchmechanischen Auslegungskonzeptes für innendruckbeanspruchte Bauteile mit ausgeprägten Druckeigenspannungsfeldern, Universität Stuttgart, Fakultät Maschinenbau (2007) 65 M. Lechmann, E. Roos, M. Höchst, A. Scheffold: Kennwerte zur Schwingbruchmechanischen Auslegung von Bauteilen mit Ausgeprägten Druckeigenspannungsfeldern, Proc. of the Conference DVM Tag 2006: Werkstoffkennwerte: Basis für Bauteilauslegung und Simulation, DVM, Berlin (2006) 66 P. J. Armstrong, C. O. Frederick: A Mathematical Representation of the Multiaxial Bauschinger Effect, CEGB Report, RD/B/ N731, Berkeley Nuclear Laboratories (1966) 67 J. Lemaitre, J. Chaboche: Mechanics of Solid Materials, Cambridge University Press, Cambridge, UK (1990) 68 X. Lin, B. Sci, M. Sci: Numerical Simulation of Fatigue Crack Growth, Ph.D. Thesis, The University of Sheffield, UK (1994) 69 X. B. Lin, R. A. Smith: Stress intensity factors for semi-elliptical internal surface cracks in autofrettaged thick-walled cyclinders, Journal of Strain Analysis 32 (1997), No. 5, pp X. Lin, R. Smith: Direct simulation of fatigue crack growth for arbitrary-shaped defects in pressure vessels Proceedings of the Institution of Mechanical Engineers Part C, Journal of Mechanical Engineering Science 213 (1998), No. 2, pp F. K. Ibrahim, J. C. Thompson, T. H. Topper: A study of the effect of mechanical variables on fatigue crack closure and propagation, International Journal of Fatigue 8 (1986), No. 3, pp P. C. Paris, F. Erdogan: A critical analysis of crack propagation laws, Journal of Basic Engineering 85 (1960), pp D. Knorr: High pressure processing for preservation, modification and transformation of foods, High Pressure Research 22 (2002), No. 3, pp J. C. Cheftel: Review: High-pressure, microbial inactivation and food preservation, Food Science and Technology International 1 (1995), No. 2, pp R. Hayashi: High pressure in food processing and preservation: Principle, application and development, High Pressure Research 7 (1991), No. 1, pp J. M. Alegre, P. Bravo, M. Preciado: Fatigue behaviour of an autofrettaged high-pressure vessel for the food industry, Engineering Failure Analysis 14 (2007), No. 2, pp A. M. Hoogstrate, T. Susuzlu, B. Karpuschewski: High performance cutting with abrasive waterjets beyond 400 MPa, CIRP Annals Manufacturing Technology 55 (2006), No. 1, pp T. Susuzlu, A. M. Hoogstrate, B. Karpuschewski: Effectiveness of ultra-high pressure waterjets up to 700 MPa, Proc. of the 17 th International Conference on Water Jetting: Advances and Future Needs, Mainz (2004), pp F. H. Trieb, J. Schedelmaier, M. Poelzl: Developments on optimized Autofrettage of high pressure components for waterjet cutting pumps, Proc. of the 17 th International Conference on Water Jetting: Advances and Future Needs, (2004), pp E. Giacomelli, P. Battagli, N. Campo, F. Graziani: Autofrettaging procedure on LDPE hyper-compressor components, ASME Pressure Vessels and Piping Conference, New York (2006), pp G. Groos, B. Glaser, F. Raue, S. Kaiser: Integrity evaluation of new designed T-pieces for LDPE-reactors, PVP-Vol. 406 High Pressure Technology_2000 ASME 2000 (2000), pp D. P. Kendall: A short history of high pressure technology from Bridgman to Division 3, Journal of Pressure Vessel Technology 122 (2000), No. 3, pp J. H. Underwood, E. Troiano: Critical fracture processes in army cannons: A review, Journal of Pressure Vessel Technology 125 (2003), pp W. Shim, J. Kim, Y. Lee, K. Cha, S. Hong: A study on hydraulic autofrettage of thickwalled cylinders incorporating Bauschinger effect, Experimental Mechanics 50 (2010), No. 5, pp A. P. Parker, G. P. O Hara, J. H. Underwood: Hydraulic versus swage autofrettage and implications of the Bauschinger effect, Journal of Pressure Vessel Technology 125 (2003), No. 3, pp J. Perry, J. Aboudi: Elasto-plastic stresses in thick walled cylinders, Journal of Pressure Vessel Technology 125 (2003), pp P. Livieri, P. Lazzarin: Autofrettaged cylindrical vessels and Bauschinger effect: An analytical frame for evaluating residual stress distributions, Journal of Pressure Vessel Technology 124 (2002), No. 1, pp C. Levy, M. Perl, S. Kotagiri: The Bauschinger effect s influence on the SIF s of multiple longitudinal coplanar cracks in autofrettaged pressurized cylinders, Engineering Fracture Mechanics 73 (2006), No. 13, pp J. H. Faupel: Yield and bursting of heavywall cylinders, Trans ASME (American Society of Mechanical Engineers), Vol. 78, 5 (1956), pp L. Pintschovius, E. Macherauch, B. Scholtes: Determination of residual stresses in autofrettaged steel tubes by Neutron and X-ray diffraction, Materials Science and Engineering 84 (1986), pp The Authors of This Contribution Dr.-Ing. Rayk Thumser, born in 1975, studied Civil Engineering at the Bauhaus-Universität Weimar. Since 1999 he is working as a research assistant at the Components, Constructions & Materials department at the Materialforschungs- und -Prüfanstalt an der Bauhaus-Universität Weimar (MFPA). His main scientific interest is in the field of fatigue and fracture under cyclic internal pressure loading. In 2009 he made his conferral as a doctorate. Since 2004 he is the Manager of the Department Materials and Components at the MFPA. Dr.-Ing. Wolfgang Scheibe, born in 1949, studied Manufacturing Technology and Machine Tools at the Technische Universität Dresden. He received his doctorate there in Up until 1978 he was the CTO for VEB Dresdener Einspritzgeräte (until 1972 L Orange-Einspritzgeräte KG). He was employed by L Orange GmbH in Stuttgart since 1979 as research engineer for future projects, as head of the testing department for storage injection as well as head of special projects. Since 1989 he is accompaning the FVV working group Autofrettage. You will find the article and additional material by entering the document number MP on our website at

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