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Correlation between residual stress and plastic strain amplitude during low cycle fatigue of mechanically surface treated austenitic stainless steel AISI 304 and ferritic–pearlitic steel SAE 1045
Materials Science and Engineering A 491 (2008) 297–303
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Correlation between residual stress and plastic strain amplitude during low cycle fatigue of mechanically surface treated austenitic stainless steel AISI 304 and ferritic–pearlitic steel SAE 1045 I. Nikitin ∗ , M. Besel Institute of Materials Engineering, University of Kassel, 34125 Kassel, Hessen, Germany
a r t i c l e
i n f o
Article history: Received 29 June 2007 Received in revised form 30 January 2008 Accepted 25 March 2008 Keywords: Deep rolling Residual stress relaxation Fatigue Strain ageing AISI 304 SAE 1045
a b s t r a c t Mechanical surface treatments such as deep rolling are known to affect the near-surface microstructure and induce, e.g. residual stresses and/or increase the surface hardness. It is well known that, e.g. compressive residual stress states usually increase the lifetime under fatigue loading. The stress relaxation behaviour and the stability of the residual stress during fatigue loading depend on the mechanical surface treatment method. In this paper three different surface treatments are used and their effects on the low cycle fatigue behaviour of austenitic stainless steel (AISI 304) and ferritic–pearlitic steel (SAE 1045) are investigated. X-ray diffraction is applied for the non-destructive evaluation of the stress state and the microstructure. It is found that consecutive deep rolling & annealing as well as high temperature deep rolling produce more stable near-surface stress states than conventional deep rolling at room temperature. The plastic strain amplitudes during fatigue loading are measured and it is shown that they correlate well with the induced residual stress and its relaxation, respectively. Furthermore, Coffin–Manson plots are presented which clearly show the correlation between the plastic strain amplitude and the fatigue lifetime. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Mechanical surface treatments, for example deep rolling, shot peening, hammering and roll burnishing induce several beneficial effects into metallic surface. Most mechanical surface treatments enhance the mechanical properties and they are mainly used to improve fatigue properties of metallic materials [1,2]. Normally the most obvious effect of these mechanical surface treatments is the reduction of the surface roughness. As a common matter of fact surface roughness can cause local stress concentration and therefore shorten the time to crack initiation. Thus a reduction of the surface roughness normally increases the lifetime. Further on the relatively high work hardening state and the residual stress state due to the surface treatment are responsible for the lowering of the plastic strain amplitude during fatigue loading. In addition, compressive residual stresses may suppress or even stop crack propagation. This results in an enhancement of the lifetime to failure. But the near-surface compressive residual stress state and the work hardening state are unstable during fatigue. Especially in the case of low cycle fatigue plastic deformation occurs in each cycle. There-
∗ Corresponding author. Tel.: +49 9412022047; fax: +49 941202942047. E-mail address: Ivan.Nikitin@infineon.com (I. Nikitin). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.03.034
fore, as shown in a previous study [3,7], the residual stress state relaxes continuously with increasing number of cycles. The relaxation of the residual stress as well as of the work hardening lead to an increase of the plastic strain amplitude and decrease of numbers of load cycles to failure. The resistance of the microstructure to local plastic flow has a strong influence on the residual stress stability and thus on the fatigue behaviour of mechanically surface treated steels [3]. The relaxation behaviour and the stability of the residual stress depend on the mechanical surface treatment method. The effects of dynamic and/or static strain ageing in combination with mechanical surface treatments result in more stable near-surface stress states and microstructures than that of conventional mechanical surface treatment. This strain ageing effect is used in warm peening [4,5], high temperature deep rolling [6], consecutive heat treatment after mechanical surface treatment [7] and so-called warm stress double shot peening [8,9]. The resistance to local plastic flow is increased due to solute atoms or fine precipitations which impede the migration of dislocations. This leads to a higher stability of the residual stress state especially during low cycle fatigue. As mentioned above plastic deformation, i.e. plastic strain occurs in each load cycle in the regime of low cycle fatigue. The amplitude of this plastic strain is determined as half of the hysteresis curve opening during one cycle. This plastic strain amplitude
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describes the degree of damage for metallic materials and can be correlated to the total lifetime by the so-called Coffin–Manson law [10,11]. The Coffin–Manson relation has been observed for many different metallic materials and for many different surface treatment methods [12]. Surface treatment frequently reduces the plastic strain amplitude of many metallic materials [6,13,14]. The correlation between the plastic strain amplitude under low cycle fatigue and the residual stress for a deep rolled material state was already investigated in Ref. [7]. As long as the residual stress measurements are carried out only for the surface of the material, i.e. no depth profile is measured, this correlation works as a nondestructive characterization of the cyclic deformation behaviour of mechanically surface treated metallic materials. Also, this present study applies Coffin–Manson plots to link the correlation between residual stress states and plastic strain amplitudes to the number of load cycles to failure under low cycle fatigue loading. Fig. 1. Coffin–Manson law for SAE 1045.
2. Experimental procedures The investigated materials were hot rolled cylindrical bars (14 mm diameter) of AISI 304 austenitic stainless steel and SAE 1045 ferritic–pearlitic steel. The microstructure of AISI 304 was fully austenitic with an average grain size of 70 m. Prior to fatigue testing the SAE 1045 steel was stress relieved at 650 ◦ C for 90 min and furnace cooled. The grain size of ferrite and pearlite grains in SAE 1045 was about 10 m and 20 m, respectively. A deep rolling force of 0.5 kN and 1 kN was applied for both materials. The heating of the specimens during deep rolling was carried out by an induction furnace. An annealing after deep rolling was carried out in salt-bath furnace. Fatigue experiments were performed under load control in tension–compression on a standard servohydraulic testing machine with a load ratio R = −1 and a frequency of 5 Hz. For the austenitic steel (AISI 304) stress levels between 280 MPa and 450 MPa are investigated. The stress levels of the ferritic–pearlitic steel (SAE 1045) are in the range of 280–600 MPa. Deformation is measured with a capacitive displacement transducer. Based on this deformation the strain during each load cycle is determined. The plastic strain amplitude is the half opening of the hysteresis curve during each cycle of the cyclic fatigue test. The exact calculation method of the plastic strain amplitude from stress strain curves and hysteresis curves, respectively, is given in Ref. [15]. For residual stress measurements the fatigue tests were interrupted after the compressive load at a defined number of load cycles. Residual stress measurements were performed by a standard X-ray diffraction device according to the sin2 -method, using Cr-K␣radiation, the {2 2 0}-Bragg peak of the austenite phase for AISI 304 (interference of 2 = 128.5◦ , measured between 126◦ and 132◦ , -tipping ± 60◦ ), and {2 1 1}-Bragg peak of the ferrite phase for SAE 1045 (interference of 2 = 156.1◦ , measured between 153.6◦ and 158.6◦ , -tipping ± 60◦ ). Subsequently, fatigue tests were continued with the same samples. Finally depth profiles were obtained by successive electrolytical removal of material. A correction of the measured stress state to compensate the effect of the electrolytic removal of the material was not carried out.
residual stress state prevents the crack propagation in metallic materials. All these effects have a strong influence on the fatigue life of surface treated metallic materials. The amount of the accumulated plastic strain during fatigue reflects the damage state of the material. This accumulated plastic strain is a measure for the energy accommodated by the material. In general it may include self-heating of the specimen, the work hardening and residual stress change during fatigue, crack initiation, crack opening, crack closing and also crack propagation. For both investigated steels conventional deep rolling at room temperature decreases strongly the amount of plastic strain. A higher decrease in the plastic strain and consequently a higher lifetime compared to the conventionally deep rolled condition is achieved using consecutive heat treatment after deep rolling. The lowest plastic strain and therefore highest fatigue lifetime for a specific stress level in low cycle fatigue was observed for high temperature deep rolling condition for both investigated steels [3,13,14]. Nevertheless in the regime of low cycle fatigue the stability of the residual stress states and of the work hardening states are the key factors dominating the plastic strain amplitude and according to this the lifetime. This statement holds especially in the present case of the two relatively “soft” austenitic and ferritic–pearlitic steels because as a common matter of fact residual stress and work hardening states are less stable in soft materials than in “hard” materials. Figs. 1 and 2 show the Coffin–Manson plots for all investigated surface treatment conditions for ferritic–pearlitic (Fig. 1) and austenitic (Fig. 2) steel. It is important to keep in mind that measuring values showing the same plastic strain amplitude and measuring values with the same lifetime belong to experiments
3. Results and discussion The investigated surface treatments show clearly differences in the fatigue behaviour of both investigated steels. Firstly the deep rolling decreases the amount of the plastic strain amplitude [1,3,6,7,12–14]. For ferritic–pearlitic steel also the beginning of detected plastic deformation is switched to the higher number of cycles [7,14]. Secondly the lower roughness of the surface increase fatigue time for crack initiation. In addition a high compressive
Fig. 2. Coffin–Manson law for AISI 304.
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Fig. 3. Residual stress relaxation depth profile of deep rolled AISI 304 (a) and correlation of residual stresses in different depths with the plastic strain amplitude (b) ( a = 350 MPa, RT).
with different stress amplitudes. This means that for a specific number of load cycles all surface treated specimens experienced a higher fatigue stress level than the corresponding untreated specimen. According to this in all experiments with the same stress amplitude the surface treated specimens showed a higher lifetime than the untreated specimens. For both investigated steels normally the cracks that lead to failure start from the surface. Typically one dominant crack was found to cause failure. But high temperature deep rolled SAE 1045 showed a different behaviour for lifetimes higher than 106 load cycles. Under these conditions the cracks start in the regions of tensile residual stress without visible initial defects. Also, only for this cases failure due to multiple crack propagation was observed [14]. In both figures high temperature deep rolling results in a strong decrease of the plastic strain amplitude for a specific fatigue lifetime compared to the untreated condition. For lifetimes over 10,000 cycles the plastic strain amplitude for the deep rolled state is higher than for the untreated condition. The high stress amplitudes in the lifetime region below 10,000 cycles generate high plastic flow with measurable sample heating. Under these conditions the residual stress and work hardening state are not stable and the positive effects of deep rolling on the fatigue lifetime is smaller. But compared to the untreated specimens the high initial amount of work hardening still decreases the plastic flow for comparable lifetime to failure. In contrast, for the higher lifetimes the residual stress and also work hardening are more stable. The deep rolled condition can resist higher plastic strain amplitudes and achieve sufficient longer fatigue life for comparable plastic strain amplitudes, although for comparable plastic strain amplitudes the stress level is much higher than that of the untreated specimens. In general it is found for both materials that for stress controlled fatigue experiments with the same stress level all investigated surface treatments result always in higher fatigue lifetime and lower plastic strain amplitudes. Due to the lower stress level the residual stress state and the work hardening state are more stable for higher lifetimes. Therefore it is found that the relative increase of lifetime due to surface treatment is higher for specimens with a longer lifetime (lower stress amplitude level respectively). The high temperature deep rolling condition shows the highest shift in the Coffin–Manson plot. This shift is a result of completely different plastic deformation mechanisms during fatigue loading. Beside the “normal” deep rolling effects like residual stress and work hardening the small carbides and also dynamical strain ageing result in a very strong additional decrease of the plastic deformation. In the stress controlled fatigue tests this effect induces a strong increase of the fatigue lifetime [6,14]. In the Coffin–Manson plot this effect can be seen in the strong shifting to lower plastic
strains for comparable lifetimes to failure. The high temperature deep rolling results in superior fatigue properties under stress controlled test condition compared to all other investigated surface treatments. But in contrast to that under strain controlled or plastic strain controlled test conditions there will be strong lowering of the fatigue lifetime for the high temperature deep rolling state. The Coffin–Manson plots show that the plastic deformation experienced during high temperature deep rolling and also during the consecutive treatment (deep rolling & heat treatment) decreases the maximum possible plastic strain amplitude and therefore will decrease the lifetime to failure in strain controlled or plastic strain controlled tests. The investigated mechanical surface treatments produce changes in the microstructures (residual stress, work hardening) of different stability. As a result the residual stress relaxation rate during fatigue is strongly dependent on the surface treatment method. Also, the rate of change of the plastic strain amplitude depends on the kind of surface treatment. The Coffin–Manson law remains applicable for all investigated surface treatments. Generally, surface treatments reduce the plastic strain amplitude (for the same stress levels) and consequently extend the fatigue life. Obviously, a hard microstructure (i.e. with a high yield strength) results in a stable residual stress state, lower plastic strain amplitude and therefore in a longer fatigue lifetime. In this study three surface treatment methods inducing three different residual stress and work hardening states were chosen to investigate the correlation between residual stress and (cyclic) plastic strain amplitude. The applied methods are room temperature deep rolling, deep rolling & annealing and deep rolling at elevated temperature. Previous studies show that for AISI 304 the best fatigue improvement due to the mechanical surface treatment is achieved by deep rolling at 550 ◦ C, second best by deep rolling & annealing (15 min at 500 ◦ C), and the least benefit is gained by conventional deep rolling [3,14]. For SAE 1045 the best fatigue improvement is obtained by deep rolling at 350 ◦ C followed by deep rolling & annealing (1 min at 325 ◦ C) and least improvement from conventional deep rolling. For both investigated steels the highest stability of the residual stress and the work hardening state is achieved by deep rolling at elevated temperatures. This is due the combination of deep rolling and dynamical strain ageing [6,7,13] and results, as mentioned above, in the lowest plastic strain amplitude and the highest fatigue life (for equivalent stress levels). As already discussed before for both investigated steels – independent of the surface treatment – a higher plastic strain amplitude leads to a lower lifetime. It is clearly shown, that the slope and the location of the Coffin–Manson curves (Figs. 1 and 2) are affected
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by the surface treatments. The fitting curves of the three different surface treatments are nearly parallel (except untreated condition) especially that one of the high temperature deep rolled states has the same exponent (slope) as that one of the deep rolled & annealed states. In general the graph of the high temperature deep rolling shows lower plastic strain amplitudes than the conventional deep rolling and also untreated condition (same stress amplitudes). This is mainly due to the significantly higher stability of the induced residual stress and work hardening states. This effect was observed for both investigated steels and for all investigated stress amplitudes and temperatures up to 600 ◦ C [3]. Fig. 3a shows the residual stress versus the depth for different numbers of load cycles ( a = 350 MPa). As a common matter of fact the relaxation of the residual stress increases with the number of cycles. Fig. 3b shows exemplarily the residual stress relaxation against the number of cycles for deep rolled AISI 304 and a stress amplitude of 350 MPa. The compressive residual stress profiles relax continuously with increasing number of cycles in all investigated depths up to 0.5 mm (see Fig. 3a). The residual stress relaxation rate of the surface layer (depth 0.00 mm) is a little bit higher than that of the subsurface regions. Fig. 4a shows a very clear correlation between the plastic strain amplitude and the residual stress for the deep rolled state. The increase of the plastic strain amplitude attends the decrease of the surface compressive residual stress (Figs. 4 and 5 Figs. 4a and 5a). This correlation is strongly linear for the deep rolled condition (Fig. 5a). The slope and the shape of these correlation curves are independent of the stress amplitude for all investigated conditions. On the other hand, the microstructures stabilized by strain ageing show a non-linear correlation between the plastic strain amplitude and the compressive residual stress. The correlation is described by two lines with different slopes. For deep rolling & annealing (500 ◦ C, 15 min) the residual stress remains relatively stable up to a plastic strain amplitude of about 0.7‰. Below this level of plastic strain amplitude no residual stress relaxation was found. Thereafter, the residual stress relaxation rate increases strongly with increasing plastic strain amplitude. For high temperature deep rolling (550 ◦ C) the relaxation rate increases strongly beyond a plastic strain amplitude of about 0.4‰ which is comparably lower than that for the deep rolled and annealed state. This is consistent with the findings in Figs. 1 and 2. In comparison with the other surface treated states the straight line of the high temperature deep rolled state is clearly shifted to lower plastic strain amplitudes for equivalent fatigue lifetimes. To explain the different residual stress relaxation behaviour of the investigated surface treatments it is necessary to draw a distinction between the hard cold worked surface and the relatively soft core of the specimens. According to the Masing-Model [15], the soft core material completely accommodates the plastic strain up to the elastic strain barrier of the much harder surface. The measured plastic strain amplitude is a kind of resultant of the hard surface and the soft core. Therefore, the change in the plastic strain amplitude is not always caused by plastic flow (dislocation movement) in the near (hard) surface regions. This idea of different layers is also applied in the multi-layer-model that is used for the description of the deformation behaviour of shot peened steel AISI 4140 [16]. Already after the first cycle the level of the plastic strain amplitude in the austenitic stainless steel is relatively high (see Fig. 4). This increase of the plastic strain amplitude is caused by the simultaneous moving of free dislocations in one direction in different grains. A migration of dislocations in the near-surface region may cause the relaxation of the compressive residual stress. But according to the Masing-Model, the plastic strain is easier stored in the relatively soft core, and therefore the plastic flow (migration of dislocations) and, i.e. the residual stress relaxation should also start
in the soft core. The relatively high compressive residual stress at the surface requires a balancing tensile stress below the surface in the relatively soft core [7]. Furthermore, the plastic flow in this region with high tensile residual stress (soft core) results in a change of the surface compressive residual stress. In contrast to the soft core, the relatively hard surface regions have lower plastic flow (less dislocation movement). Consequently the FWHM-value, i.e. the work hardening state of the surface shows no or only little changes compared to the high residual stress relaxation (see Fig. 4). Conventional deep rolling leads to strain hardening through the hindrance of the dislocation movement caused mainly by dislocation/dislocation intersection. A relatively high dislocation density is necessary to produce this effect. In the region with high tensile residual stress the dislocation density is clearly lower than that of the near top surface regions with high compressive residual stress state [6,12]. Therefore the tensile residual stress of the soft core could easier be relaxed even at low plastic strain amplitudes (Fig. 5a). This effect can be seen also by hardness measurement. The hard surface layer of deep rolled condition becomes softer. In contrast to this, the originally undeformed soft core shows an increase of the hardness during fatigue [3]. The higher the stress amplitude is, the higher is the hardness increase in the core, and the higher is the hardness decrease of the surface. In contrast, the static strain ageing caused by deep rolling & annealing reduces the migration of dislocations by interstitial solute atoms [15]. Generally, dislocations are surrounded by an elastic stress field consisting of regions of tensile stress and regions of compression stress. The solute interstitial atoms like carbon or nitrogen can easily fill the interlattice positions in the tensile stress field near the dislocation. So the density of interstitial atoms becomes higher near dislocations. This constrains the migration of dislocations, they are “pinned”. This reduced migration of dislocations causes higher hardness and yield stress, i.e. a lower (or even no) plastic flow for a given stress state. Therefore the residual stress state remains stable up to a plastic strain amplitude of 0.7‰ (Fig. 5a). This plastic strain could be realised only by plastic flow (i.e. migration and creation of new dislocations) in the soft core region far distant from the tensile stress maximum. The residual stress level relaxes only when the plastic strain amplitude increases and plastic flow occurs near the tensile stress region. When this plastic flow in the annealed state starts, then the relaxation rate increases strongly. This relaxation rate increase takes place, when the dislocations become free from the interstitial solute atoms. The high temperature deep rolled state represents a mix of the states described above. The hardening is caused by dynamical strain ageing and carbide precipitations [6]. In contrast to the annealed state there is an observable amount of unpinned dislocations which lead to a lower yield stress. Therefore the residual stress relaxation occurs even at low plastic strain amplitudes. Up to the plastic strain amplitude of about 0.4‰ (Fig. 5a) the pinned dislocations become free and an additional migration of dislocations starts so that the relaxation rate increases clearly. Figs. 4–7 shows the full width at half maximum (FWHM) values in addition to the residual stress and the plastic strain amplitudes. The FWHM values for AISI 304 (Figs. 4 and 5 Figs. 4b and 5b) remain stable up to some critical plastic strain amplitudes before they decrease. This behaviour is observed for all surface conditions and stress amplitudes. Thereafter, the FWHM values decrease continuously with increasing plastic strain amplitude (Fig. 5b). The comparison of the Fig. 5a and b shows that for the deep rolled & annealed state the residual stress relaxation and the change of the FWHM values start at the same plastic strain amplitude of about 0.7‰. As mentioned above for the residual stress relaxation this point was explained with the breaking away of the dislocations from the Cottrell clouds and/or small carbides. It might be reason-
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Fig. 4. Correlation of residual stress relaxation (a) and FWHM change (b) of deep rolled AISI 304 with the plastic strain amplitude ( a = 340 MPa, RT).
able that the annihilation and the migration of dislocations start at the same plastic strain amplitude. Fig. 6a and b show a clear correlation between the plastic strain amplitude and the residual stress state/FWHM value for room temperature deep rolled SAE 1045. Due to limitations in the resolution of the displacement transducer in the first tens of cycles the amount of the plastic strain amplitude cannot be measured. In the beginning plastic activity occurs only in a few randomly distributed grains. As mentioned above, interstitial solute atoms like carbon lead to the suppression of dislocation migration. After several tens of load
cycles the cumulated local damage results in local stress fields that facilitate the breakaway of the dislocations from solute atoms. This is similar to the effects of distinct yield stress observed for ferritic steels. Thereafter, a kind of collective plastic flow occurs leading to a macroscopic plastic deformation that can be measured with the used equipment. Regardless of the missing macroscopic plastic strain, the level of the residual stress relaxes from the first cycle on. This relaxation can be explained by local plasticity. Local plastic flow in several areas and various directions results in the relaxation of residual stress. But as long as there is no common direction of the
Fig. 5. Residual stress dependence on plastic strain amplitude (a) and FWHM dependence on plastic strain amplitude (b) (AISI 304, for different a , RT and different surface treatments).
Fig. 6. Correlation of residual stress relaxation (a) and FWHM change of deep rolled SAE1045 with plastic strain amplitude (b) ( a = 340 MPa, RT).
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Fig. 7. Residual stress dependence on plastic strain amplitude (a) and FWHM dependence on plastic strain amplitude (b) (SAE 1045, for different surface treatments).
Fig. 8. Correlation between residual stress/FWHM and cyclic life (deep rolled state of AISI 304 and SAE 1045).
plastic flow, and the number of plastic active areas is low, there is no detectable macroscopic plastic strain. Therefore the effect of this local plastic flow cannot be measured with the used deformation measuring device. As shown in Fig. 7 a high plastic strain amplitude leads to a lower level of the residual stress and lower FWHM values. While the different surface treatment methods result in different residual stress states (Fig. 7a), the FWHM values are nearly independent of the surface treatment methods (Fig. 7b). After a plastic strain amplitude of about 0.05‰ the FWHM values are for all investigated surface treatments almost identical and beyond a plastic strain amplitude of about 0.5‰ the FWHM values relax more strongly. In spite of the clear correlation between the residual stress and the plastic strain amplitude for the conventionally deep rolled condition it is nearly impossible to predict the lifetime to failure accurately. The correlation between the residual stress state at half of lifetime to failure (Nf /2) and the number of cycles to failure for conventional deep rolled AISI 304 as well as SAE 1045 is relatively bad (Fig. 8). The correlation of the lifetime with the FWHM value is slightly better. Anyway, residual stress measurements describe the cyclic softening of the investigated materials quite well and can be used to evaluate the degree of damage in the investigated metals under fatigue loading. 4. Conclusions Based on the investigations of the correlation between residual stress and plastic strain amplitude for mechanical surface treated
AISI 304 and SAE 1045, the following conclusions are made: 1. The cyclic softening of the investigated materials leads to residual stress relaxation as well as a decrease of FWHM values. 2. The residual stress can be correlated to the plastic strain amplitude. The dependency is linear for all surface treated SAE 1045 and for conventionally deep rolled AISI 304. However, a nonlinear dependency was found for the high temperature deep rolled and deep rolled & annealed condition for AISI 304. 3. The relaxation of FWHM values of AISI 304 starts beyond some critical level of strain amplitude and is strongly dependent on the surface treatment. 4. The relaxation of FWHM value of SAE 1045 is independent of the surface treatment state. 5. The correlation between cyclic lifetime to failure and residual stress for conventional deep rolled AISI 304 as well as SAE 1045 is not pronounced. The correlation to the FWHM value shows slightly better results.
Acknowledgements The authors would like to express sincere thanks to Prof. B. Scholtes for experimental patronage and fruitful scientifically discussion. Thanks to the German Science Foundation (DFG) for financial support of the Emmy-Noether-group in Kassel, led by Dr. I. Altenberger, under contract number Al 558/1-2 and Al 558/1-3 and also Dr. I. Altenberger for scientifically discussion.
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References [1] L. Wagner, Mater. Sci. Eng. A 263 (1999) 210. [2] R.K. Nalla, I. Altenberger, U. Noster, G.Y. Lui, B. Scholtes, R.O. Ritche, Mater. Sci. Eng. A 355 (2003) 216. ¨ [3] I. Nikitin, Zur Verbesserung des Ermudungsverhaltens des austenitischen Stahls X5CrNi18-10 im Temperaturbereich 25–600 ◦ C durch mechanische Randschichtverfestigungsverfahren, Dissertation, Kassel, 2007. ¨ [4] M. Schilling-Praetzel, Dissertation, Einfluss der Werkstucktemperatur beim Kugelstrahlen auf die Schwingfestigkeit von Drehstabfedern, Aachen, 1995. [5] A. Wick, Dissertation, Randschichtzustand und Schwingfestigkeit von 42CrMo4 ¨ nach Kugelstrahlen unter Vorspannung und bei erhohter Temperatur, Univer¨ Karlsruhe, Band 2/99, Herausgeber, D. Lohe, ¨ ¨ ¨ sitat H. Muller, O. Vohringer, 1999. [6] I. Nikitin, I. Altenberger, B. Scholtes, ICSP 9, Paris 2005, A26.
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[7] I. Altenberger, in: B. Scholtes (Ed.), Mikrostrukturelle Untersuchungen Mechanisch Randschichtverfestigter Bereiche Schwingend Beanspruchter Met¨ Bibliothek, Kassel, 2000. allischer Werkstoffe, Universitat [8] A. Tange, K. Ando, Mater. Sci. Technol. 18 (6) (2002) 642. [9] H. Ishigami, K. Matsui, Y. Lin, K. Ando, Fatigue Fract. Eng. Mater. Struct. 23 (11) (2000) 959. [10] L.F. Coffin, Trans. ASME 76 (1954) 931. [11] S.S. Manson, NACA TN-2933, 1953. [12] I. Nikitin, B. Scholtes, H.J. Maier, I. Altenberger, Scripta Mater. 50 (2004) 1345. [13] I. Nikitin, I. Altenberger, B. Scholtes, 11th Int. Conf on Fracture Turin, 2005, CD-Rom. [14] I. Altenberger, I. Nikitin, B. Scholtes, ICSP 9, Paris, 2005, A113. [15] H.-J. Christ, Wechselverformung von Metallen, Springer–Verlag, Berlin, 1991, p. 275. [16] V. Schulze, O. Vohringer, E. Macherauch, Z. Metall. 89 (10) (1998) 719.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Correlation between residual stress and plastic strain amplitude during low cycle fatigue of mechanically surface treated austenitic stainless steel AISI 304 and ferritic–pearlitic steel SAE 1045 I. Nikitin ∗ , M. Besel Institute of Materials Engineering, University of Kassel, 34125 Kassel, Hessen, Germany
a r t i c l e
i n f o
Article history: Received 29 June 2007 Received in revised form 30 January 2008 Accepted 25 March 2008 Keywords: Deep rolling Residual stress relaxation Fatigue Strain ageing AISI 304 SAE 1045
a b s t r a c t Mechanical surface treatments such as deep rolling are known to affect the near-surface microstructure and induce, e.g. residual stresses and/or increase the surface hardness. It is well known that, e.g. compressive residual stress states usually increase the lifetime under fatigue loading. The stress relaxation behaviour and the stability of the residual stress during fatigue loading depend on the mechanical surface treatment method. In this paper three different surface treatments are used and their effects on the low cycle fatigue behaviour of austenitic stainless steel (AISI 304) and ferritic–pearlitic steel (SAE 1045) are investigated. X-ray diffraction is applied for the non-destructive evaluation of the stress state and the microstructure. It is found that consecutive deep rolling & annealing as well as high temperature deep rolling produce more stable near-surface stress states than conventional deep rolling at room temperature. The plastic strain amplitudes during fatigue loading are measured and it is shown that they correlate well with the induced residual stress and its relaxation, respectively. Furthermore, Coffin–Manson plots are presented which clearly show the correlation between the plastic strain amplitude and the fatigue lifetime. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Mechanical surface treatments, for example deep rolling, shot peening, hammering and roll burnishing induce several beneficial effects into metallic surface. Most mechanical surface treatments enhance the mechanical properties and they are mainly used to improve fatigue properties of metallic materials [1,2]. Normally the most obvious effect of these mechanical surface treatments is the reduction of the surface roughness. As a common matter of fact surface roughness can cause local stress concentration and therefore shorten the time to crack initiation. Thus a reduction of the surface roughness normally increases the lifetime. Further on the relatively high work hardening state and the residual stress state due to the surface treatment are responsible for the lowering of the plastic strain amplitude during fatigue loading. In addition, compressive residual stresses may suppress or even stop crack propagation. This results in an enhancement of the lifetime to failure. But the near-surface compressive residual stress state and the work hardening state are unstable during fatigue. Especially in the case of low cycle fatigue plastic deformation occurs in each cycle. There-
∗ Corresponding author. Tel.: +49 9412022047; fax: +49 941202942047. E-mail address: Ivan.Nikitin@infineon.com (I. Nikitin). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.03.034
fore, as shown in a previous study [3,7], the residual stress state relaxes continuously with increasing number of cycles. The relaxation of the residual stress as well as of the work hardening lead to an increase of the plastic strain amplitude and decrease of numbers of load cycles to failure. The resistance of the microstructure to local plastic flow has a strong influence on the residual stress stability and thus on the fatigue behaviour of mechanically surface treated steels [3]. The relaxation behaviour and the stability of the residual stress depend on the mechanical surface treatment method. The effects of dynamic and/or static strain ageing in combination with mechanical surface treatments result in more stable near-surface stress states and microstructures than that of conventional mechanical surface treatment. This strain ageing effect is used in warm peening [4,5], high temperature deep rolling [6], consecutive heat treatment after mechanical surface treatment [7] and so-called warm stress double shot peening [8,9]. The resistance to local plastic flow is increased due to solute atoms or fine precipitations which impede the migration of dislocations. This leads to a higher stability of the residual stress state especially during low cycle fatigue. As mentioned above plastic deformation, i.e. plastic strain occurs in each load cycle in the regime of low cycle fatigue. The amplitude of this plastic strain is determined as half of the hysteresis curve opening during one cycle. This plastic strain amplitude
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describes the degree of damage for metallic materials and can be correlated to the total lifetime by the so-called Coffin–Manson law [10,11]. The Coffin–Manson relation has been observed for many different metallic materials and for many different surface treatment methods [12]. Surface treatment frequently reduces the plastic strain amplitude of many metallic materials [6,13,14]. The correlation between the plastic strain amplitude under low cycle fatigue and the residual stress for a deep rolled material state was already investigated in Ref. [7]. As long as the residual stress measurements are carried out only for the surface of the material, i.e. no depth profile is measured, this correlation works as a nondestructive characterization of the cyclic deformation behaviour of mechanically surface treated metallic materials. Also, this present study applies Coffin–Manson plots to link the correlation between residual stress states and plastic strain amplitudes to the number of load cycles to failure under low cycle fatigue loading. Fig. 1. Coffin–Manson law for SAE 1045.
2. Experimental procedures The investigated materials were hot rolled cylindrical bars (14 mm diameter) of AISI 304 austenitic stainless steel and SAE 1045 ferritic–pearlitic steel. The microstructure of AISI 304 was fully austenitic with an average grain size of 70 m. Prior to fatigue testing the SAE 1045 steel was stress relieved at 650 ◦ C for 90 min and furnace cooled. The grain size of ferrite and pearlite grains in SAE 1045 was about 10 m and 20 m, respectively. A deep rolling force of 0.5 kN and 1 kN was applied for both materials. The heating of the specimens during deep rolling was carried out by an induction furnace. An annealing after deep rolling was carried out in salt-bath furnace. Fatigue experiments were performed under load control in tension–compression on a standard servohydraulic testing machine with a load ratio R = −1 and a frequency of 5 Hz. For the austenitic steel (AISI 304) stress levels between 280 MPa and 450 MPa are investigated. The stress levels of the ferritic–pearlitic steel (SAE 1045) are in the range of 280–600 MPa. Deformation is measured with a capacitive displacement transducer. Based on this deformation the strain during each load cycle is determined. The plastic strain amplitude is the half opening of the hysteresis curve during each cycle of the cyclic fatigue test. The exact calculation method of the plastic strain amplitude from stress strain curves and hysteresis curves, respectively, is given in Ref. [15]. For residual stress measurements the fatigue tests were interrupted after the compressive load at a defined number of load cycles. Residual stress measurements were performed by a standard X-ray diffraction device according to the sin2 -method, using Cr-K␣radiation, the {2 2 0}-Bragg peak of the austenite phase for AISI 304 (interference of 2 = 128.5◦ , measured between 126◦ and 132◦ , -tipping ± 60◦ ), and {2 1 1}-Bragg peak of the ferrite phase for SAE 1045 (interference of 2 = 156.1◦ , measured between 153.6◦ and 158.6◦ , -tipping ± 60◦ ). Subsequently, fatigue tests were continued with the same samples. Finally depth profiles were obtained by successive electrolytical removal of material. A correction of the measured stress state to compensate the effect of the electrolytic removal of the material was not carried out.
residual stress state prevents the crack propagation in metallic materials. All these effects have a strong influence on the fatigue life of surface treated metallic materials. The amount of the accumulated plastic strain during fatigue reflects the damage state of the material. This accumulated plastic strain is a measure for the energy accommodated by the material. In general it may include self-heating of the specimen, the work hardening and residual stress change during fatigue, crack initiation, crack opening, crack closing and also crack propagation. For both investigated steels conventional deep rolling at room temperature decreases strongly the amount of plastic strain. A higher decrease in the plastic strain and consequently a higher lifetime compared to the conventionally deep rolled condition is achieved using consecutive heat treatment after deep rolling. The lowest plastic strain and therefore highest fatigue lifetime for a specific stress level in low cycle fatigue was observed for high temperature deep rolling condition for both investigated steels [3,13,14]. Nevertheless in the regime of low cycle fatigue the stability of the residual stress states and of the work hardening states are the key factors dominating the plastic strain amplitude and according to this the lifetime. This statement holds especially in the present case of the two relatively “soft” austenitic and ferritic–pearlitic steels because as a common matter of fact residual stress and work hardening states are less stable in soft materials than in “hard” materials. Figs. 1 and 2 show the Coffin–Manson plots for all investigated surface treatment conditions for ferritic–pearlitic (Fig. 1) and austenitic (Fig. 2) steel. It is important to keep in mind that measuring values showing the same plastic strain amplitude and measuring values with the same lifetime belong to experiments
3. Results and discussion The investigated surface treatments show clearly differences in the fatigue behaviour of both investigated steels. Firstly the deep rolling decreases the amount of the plastic strain amplitude [1,3,6,7,12–14]. For ferritic–pearlitic steel also the beginning of detected plastic deformation is switched to the higher number of cycles [7,14]. Secondly the lower roughness of the surface increase fatigue time for crack initiation. In addition a high compressive
Fig. 2. Coffin–Manson law for AISI 304.
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Fig. 3. Residual stress relaxation depth profile of deep rolled AISI 304 (a) and correlation of residual stresses in different depths with the plastic strain amplitude (b) ( a = 350 MPa, RT).
with different stress amplitudes. This means that for a specific number of load cycles all surface treated specimens experienced a higher fatigue stress level than the corresponding untreated specimen. According to this in all experiments with the same stress amplitude the surface treated specimens showed a higher lifetime than the untreated specimens. For both investigated steels normally the cracks that lead to failure start from the surface. Typically one dominant crack was found to cause failure. But high temperature deep rolled SAE 1045 showed a different behaviour for lifetimes higher than 106 load cycles. Under these conditions the cracks start in the regions of tensile residual stress without visible initial defects. Also, only for this cases failure due to multiple crack propagation was observed [14]. In both figures high temperature deep rolling results in a strong decrease of the plastic strain amplitude for a specific fatigue lifetime compared to the untreated condition. For lifetimes over 10,000 cycles the plastic strain amplitude for the deep rolled state is higher than for the untreated condition. The high stress amplitudes in the lifetime region below 10,000 cycles generate high plastic flow with measurable sample heating. Under these conditions the residual stress and work hardening state are not stable and the positive effects of deep rolling on the fatigue lifetime is smaller. But compared to the untreated specimens the high initial amount of work hardening still decreases the plastic flow for comparable lifetime to failure. In contrast, for the higher lifetimes the residual stress and also work hardening are more stable. The deep rolled condition can resist higher plastic strain amplitudes and achieve sufficient longer fatigue life for comparable plastic strain amplitudes, although for comparable plastic strain amplitudes the stress level is much higher than that of the untreated specimens. In general it is found for both materials that for stress controlled fatigue experiments with the same stress level all investigated surface treatments result always in higher fatigue lifetime and lower plastic strain amplitudes. Due to the lower stress level the residual stress state and the work hardening state are more stable for higher lifetimes. Therefore it is found that the relative increase of lifetime due to surface treatment is higher for specimens with a longer lifetime (lower stress amplitude level respectively). The high temperature deep rolling condition shows the highest shift in the Coffin–Manson plot. This shift is a result of completely different plastic deformation mechanisms during fatigue loading. Beside the “normal” deep rolling effects like residual stress and work hardening the small carbides and also dynamical strain ageing result in a very strong additional decrease of the plastic deformation. In the stress controlled fatigue tests this effect induces a strong increase of the fatigue lifetime [6,14]. In the Coffin–Manson plot this effect can be seen in the strong shifting to lower plastic
strains for comparable lifetimes to failure. The high temperature deep rolling results in superior fatigue properties under stress controlled test condition compared to all other investigated surface treatments. But in contrast to that under strain controlled or plastic strain controlled test conditions there will be strong lowering of the fatigue lifetime for the high temperature deep rolling state. The Coffin–Manson plots show that the plastic deformation experienced during high temperature deep rolling and also during the consecutive treatment (deep rolling & heat treatment) decreases the maximum possible plastic strain amplitude and therefore will decrease the lifetime to failure in strain controlled or plastic strain controlled tests. The investigated mechanical surface treatments produce changes in the microstructures (residual stress, work hardening) of different stability. As a result the residual stress relaxation rate during fatigue is strongly dependent on the surface treatment method. Also, the rate of change of the plastic strain amplitude depends on the kind of surface treatment. The Coffin–Manson law remains applicable for all investigated surface treatments. Generally, surface treatments reduce the plastic strain amplitude (for the same stress levels) and consequently extend the fatigue life. Obviously, a hard microstructure (i.e. with a high yield strength) results in a stable residual stress state, lower plastic strain amplitude and therefore in a longer fatigue lifetime. In this study three surface treatment methods inducing three different residual stress and work hardening states were chosen to investigate the correlation between residual stress and (cyclic) plastic strain amplitude. The applied methods are room temperature deep rolling, deep rolling & annealing and deep rolling at elevated temperature. Previous studies show that for AISI 304 the best fatigue improvement due to the mechanical surface treatment is achieved by deep rolling at 550 ◦ C, second best by deep rolling & annealing (15 min at 500 ◦ C), and the least benefit is gained by conventional deep rolling [3,14]. For SAE 1045 the best fatigue improvement is obtained by deep rolling at 350 ◦ C followed by deep rolling & annealing (1 min at 325 ◦ C) and least improvement from conventional deep rolling. For both investigated steels the highest stability of the residual stress and the work hardening state is achieved by deep rolling at elevated temperatures. This is due the combination of deep rolling and dynamical strain ageing [6,7,13] and results, as mentioned above, in the lowest plastic strain amplitude and the highest fatigue life (for equivalent stress levels). As already discussed before for both investigated steels – independent of the surface treatment – a higher plastic strain amplitude leads to a lower lifetime. It is clearly shown, that the slope and the location of the Coffin–Manson curves (Figs. 1 and 2) are affected
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by the surface treatments. The fitting curves of the three different surface treatments are nearly parallel (except untreated condition) especially that one of the high temperature deep rolled states has the same exponent (slope) as that one of the deep rolled & annealed states. In general the graph of the high temperature deep rolling shows lower plastic strain amplitudes than the conventional deep rolling and also untreated condition (same stress amplitudes). This is mainly due to the significantly higher stability of the induced residual stress and work hardening states. This effect was observed for both investigated steels and for all investigated stress amplitudes and temperatures up to 600 ◦ C [3]. Fig. 3a shows the residual stress versus the depth for different numbers of load cycles ( a = 350 MPa). As a common matter of fact the relaxation of the residual stress increases with the number of cycles. Fig. 3b shows exemplarily the residual stress relaxation against the number of cycles for deep rolled AISI 304 and a stress amplitude of 350 MPa. The compressive residual stress profiles relax continuously with increasing number of cycles in all investigated depths up to 0.5 mm (see Fig. 3a). The residual stress relaxation rate of the surface layer (depth 0.00 mm) is a little bit higher than that of the subsurface regions. Fig. 4a shows a very clear correlation between the plastic strain amplitude and the residual stress for the deep rolled state. The increase of the plastic strain amplitude attends the decrease of the surface compressive residual stress (Figs. 4 and 5 Figs. 4a and 5a). This correlation is strongly linear for the deep rolled condition (Fig. 5a). The slope and the shape of these correlation curves are independent of the stress amplitude for all investigated conditions. On the other hand, the microstructures stabilized by strain ageing show a non-linear correlation between the plastic strain amplitude and the compressive residual stress. The correlation is described by two lines with different slopes. For deep rolling & annealing (500 ◦ C, 15 min) the residual stress remains relatively stable up to a plastic strain amplitude of about 0.7‰. Below this level of plastic strain amplitude no residual stress relaxation was found. Thereafter, the residual stress relaxation rate increases strongly with increasing plastic strain amplitude. For high temperature deep rolling (550 ◦ C) the relaxation rate increases strongly beyond a plastic strain amplitude of about 0.4‰ which is comparably lower than that for the deep rolled and annealed state. This is consistent with the findings in Figs. 1 and 2. In comparison with the other surface treated states the straight line of the high temperature deep rolled state is clearly shifted to lower plastic strain amplitudes for equivalent fatigue lifetimes. To explain the different residual stress relaxation behaviour of the investigated surface treatments it is necessary to draw a distinction between the hard cold worked surface and the relatively soft core of the specimens. According to the Masing-Model [15], the soft core material completely accommodates the plastic strain up to the elastic strain barrier of the much harder surface. The measured plastic strain amplitude is a kind of resultant of the hard surface and the soft core. Therefore, the change in the plastic strain amplitude is not always caused by plastic flow (dislocation movement) in the near (hard) surface regions. This idea of different layers is also applied in the multi-layer-model that is used for the description of the deformation behaviour of shot peened steel AISI 4140 [16]. Already after the first cycle the level of the plastic strain amplitude in the austenitic stainless steel is relatively high (see Fig. 4). This increase of the plastic strain amplitude is caused by the simultaneous moving of free dislocations in one direction in different grains. A migration of dislocations in the near-surface region may cause the relaxation of the compressive residual stress. But according to the Masing-Model, the plastic strain is easier stored in the relatively soft core, and therefore the plastic flow (migration of dislocations) and, i.e. the residual stress relaxation should also start
in the soft core. The relatively high compressive residual stress at the surface requires a balancing tensile stress below the surface in the relatively soft core [7]. Furthermore, the plastic flow in this region with high tensile residual stress (soft core) results in a change of the surface compressive residual stress. In contrast to the soft core, the relatively hard surface regions have lower plastic flow (less dislocation movement). Consequently the FWHM-value, i.e. the work hardening state of the surface shows no or only little changes compared to the high residual stress relaxation (see Fig. 4). Conventional deep rolling leads to strain hardening through the hindrance of the dislocation movement caused mainly by dislocation/dislocation intersection. A relatively high dislocation density is necessary to produce this effect. In the region with high tensile residual stress the dislocation density is clearly lower than that of the near top surface regions with high compressive residual stress state [6,12]. Therefore the tensile residual stress of the soft core could easier be relaxed even at low plastic strain amplitudes (Fig. 5a). This effect can be seen also by hardness measurement. The hard surface layer of deep rolled condition becomes softer. In contrast to this, the originally undeformed soft core shows an increase of the hardness during fatigue [3]. The higher the stress amplitude is, the higher is the hardness increase in the core, and the higher is the hardness decrease of the surface. In contrast, the static strain ageing caused by deep rolling & annealing reduces the migration of dislocations by interstitial solute atoms [15]. Generally, dislocations are surrounded by an elastic stress field consisting of regions of tensile stress and regions of compression stress. The solute interstitial atoms like carbon or nitrogen can easily fill the interlattice positions in the tensile stress field near the dislocation. So the density of interstitial atoms becomes higher near dislocations. This constrains the migration of dislocations, they are “pinned”. This reduced migration of dislocations causes higher hardness and yield stress, i.e. a lower (or even no) plastic flow for a given stress state. Therefore the residual stress state remains stable up to a plastic strain amplitude of 0.7‰ (Fig. 5a). This plastic strain could be realised only by plastic flow (i.e. migration and creation of new dislocations) in the soft core region far distant from the tensile stress maximum. The residual stress level relaxes only when the plastic strain amplitude increases and plastic flow occurs near the tensile stress region. When this plastic flow in the annealed state starts, then the relaxation rate increases strongly. This relaxation rate increase takes place, when the dislocations become free from the interstitial solute atoms. The high temperature deep rolled state represents a mix of the states described above. The hardening is caused by dynamical strain ageing and carbide precipitations [6]. In contrast to the annealed state there is an observable amount of unpinned dislocations which lead to a lower yield stress. Therefore the residual stress relaxation occurs even at low plastic strain amplitudes. Up to the plastic strain amplitude of about 0.4‰ (Fig. 5a) the pinned dislocations become free and an additional migration of dislocations starts so that the relaxation rate increases clearly. Figs. 4–7 shows the full width at half maximum (FWHM) values in addition to the residual stress and the plastic strain amplitudes. The FWHM values for AISI 304 (Figs. 4 and 5 Figs. 4b and 5b) remain stable up to some critical plastic strain amplitudes before they decrease. This behaviour is observed for all surface conditions and stress amplitudes. Thereafter, the FWHM values decrease continuously with increasing plastic strain amplitude (Fig. 5b). The comparison of the Fig. 5a and b shows that for the deep rolled & annealed state the residual stress relaxation and the change of the FWHM values start at the same plastic strain amplitude of about 0.7‰. As mentioned above for the residual stress relaxation this point was explained with the breaking away of the dislocations from the Cottrell clouds and/or small carbides. It might be reason-
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Fig. 4. Correlation of residual stress relaxation (a) and FWHM change (b) of deep rolled AISI 304 with the plastic strain amplitude ( a = 340 MPa, RT).
able that the annihilation and the migration of dislocations start at the same plastic strain amplitude. Fig. 6a and b show a clear correlation between the plastic strain amplitude and the residual stress state/FWHM value for room temperature deep rolled SAE 1045. Due to limitations in the resolution of the displacement transducer in the first tens of cycles the amount of the plastic strain amplitude cannot be measured. In the beginning plastic activity occurs only in a few randomly distributed grains. As mentioned above, interstitial solute atoms like carbon lead to the suppression of dislocation migration. After several tens of load
cycles the cumulated local damage results in local stress fields that facilitate the breakaway of the dislocations from solute atoms. This is similar to the effects of distinct yield stress observed for ferritic steels. Thereafter, a kind of collective plastic flow occurs leading to a macroscopic plastic deformation that can be measured with the used equipment. Regardless of the missing macroscopic plastic strain, the level of the residual stress relaxes from the first cycle on. This relaxation can be explained by local plasticity. Local plastic flow in several areas and various directions results in the relaxation of residual stress. But as long as there is no common direction of the
Fig. 5. Residual stress dependence on plastic strain amplitude (a) and FWHM dependence on plastic strain amplitude (b) (AISI 304, for different a , RT and different surface treatments).
Fig. 6. Correlation of residual stress relaxation (a) and FWHM change of deep rolled SAE1045 with plastic strain amplitude (b) ( a = 340 MPa, RT).
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Fig. 7. Residual stress dependence on plastic strain amplitude (a) and FWHM dependence on plastic strain amplitude (b) (SAE 1045, for different surface treatments).
Fig. 8. Correlation between residual stress/FWHM and cyclic life (deep rolled state of AISI 304 and SAE 1045).
plastic flow, and the number of plastic active areas is low, there is no detectable macroscopic plastic strain. Therefore the effect of this local plastic flow cannot be measured with the used deformation measuring device. As shown in Fig. 7 a high plastic strain amplitude leads to a lower level of the residual stress and lower FWHM values. While the different surface treatment methods result in different residual stress states (Fig. 7a), the FWHM values are nearly independent of the surface treatment methods (Fig. 7b). After a plastic strain amplitude of about 0.05‰ the FWHM values are for all investigated surface treatments almost identical and beyond a plastic strain amplitude of about 0.5‰ the FWHM values relax more strongly. In spite of the clear correlation between the residual stress and the plastic strain amplitude for the conventionally deep rolled condition it is nearly impossible to predict the lifetime to failure accurately. The correlation between the residual stress state at half of lifetime to failure (Nf /2) and the number of cycles to failure for conventional deep rolled AISI 304 as well as SAE 1045 is relatively bad (Fig. 8). The correlation of the lifetime with the FWHM value is slightly better. Anyway, residual stress measurements describe the cyclic softening of the investigated materials quite well and can be used to evaluate the degree of damage in the investigated metals under fatigue loading. 4. Conclusions Based on the investigations of the correlation between residual stress and plastic strain amplitude for mechanical surface treated
AISI 304 and SAE 1045, the following conclusions are made: 1. The cyclic softening of the investigated materials leads to residual stress relaxation as well as a decrease of FWHM values. 2. The residual stress can be correlated to the plastic strain amplitude. The dependency is linear for all surface treated SAE 1045 and for conventionally deep rolled AISI 304. However, a nonlinear dependency was found for the high temperature deep rolled and deep rolled & annealed condition for AISI 304. 3. The relaxation of FWHM values of AISI 304 starts beyond some critical level of strain amplitude and is strongly dependent on the surface treatment. 4. The relaxation of FWHM value of SAE 1045 is independent of the surface treatment state. 5. The correlation between cyclic lifetime to failure and residual stress for conventional deep rolled AISI 304 as well as SAE 1045 is not pronounced. The correlation to the FWHM value shows slightly better results.
Acknowledgements The authors would like to express sincere thanks to Prof. B. Scholtes for experimental patronage and fruitful scientifically discussion. Thanks to the German Science Foundation (DFG) for financial support of the Emmy-Noether-group in Kassel, led by Dr. I. Altenberger, under contract number Al 558/1-2 and Al 558/1-3 and also Dr. I. Altenberger for scientifically discussion.
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