very high cycle fatigue resistance of the low alloyed ... · failure in a low strength condition...

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Structural Integrity Procedia 00 (2016) 000–000 www.elsevier.com/locate/procedia

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine

P. Brandãoa, V. Infanteb, A.M. Deusc* aDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal bIDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal cCeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,

Portugal

Abstract

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991.

E-mail address: [email protected]

Procedia Structural Integrity 2 (2016) 1133–1142

Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer review under responsibility of the Scientific Committee of ECF21.10.1016/j.prostr.2016.06.145

10.1016/j.prostr.2016.06.145


ScienceDirect


2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Very High Cycle Fatigue Resistance of the Low Alloyed Steel 42CrMo4 in Medium- and

High-Strength Quenched and Tempered Condition

K.-H. Langa, *, M. Korna and T. Rohm a, b

a Karlsruhe Institute of Technology (KIT) – Institute for Applied Materials (IAM), Engelbert-Arnold-Str. 4, 76128 Karlsruhe, Germany

b University of Applied Science, Moltkestr. 30, 76133 Karlsruhe, Germany

Abstract

Low cyclical loadings can cause failure after a very high number of cycles in the so-called “Very High Cycle Fatigue” (VHCF) area. Thereby, failure initiates typically below the surface at defects like non-metallic inclusions. The appearance of VHCF failure depends on the microstructure of the material and the loading situation. E.g., a quenched and tempered steel with a given distribution of non-metallic inclusions may be insensitive to VHCF failure in a low strength condition but very sensitive in a high-strength condition. The present study investigates the influence of tempering temperature on the fatigue resistance of a low alloyed steel. Uniaxial tension-compression fatigue tests (50 Hz/1 kHz and R=-1) were performed on specimens made of 42CrMo4, which were tempered at six different temperatures to produce wide a range of ultimate strength. With the decrease in tempering temperature the sensitivity of subsurface crack initiation at inner defects increases. High tempered conditions with Rm < 1400 MPa show no failure between 106 and 109 cycles. Crack initiation almost occurs at the surface as a result of local plasticity and surface defects. The fatigue resistance at 109 cycles (Rw/9) matches to the fatigue resistance at 106

cycles (Rw/6). The low tempered conditions show a tendency of increasing life scatter and the threshold value for subsurface crack initiation increase with decreasing strength-level. The study indicated that for high-strength heat treatment conditions the difference between the fatigue strength at 106 and 109 increases with decreasing tempering temperature. A functional relationship between these two fatigue strength was found and verified experimentally. It seems that the stress intensity factor K which arises as a function of local loading conditions at inner stress-raisers depends on the yielding /hardening properties of the material around them.

* Corresponding author. Tel.: +49-721-60842605; fax: +49-721-60848044.



ScienceDirect


2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Very High Cycle Fatigue Resistance of the Low Alloyed Steel 42CrMo4 in Medium- and

High-Strength Quenched and Tempered Condition

K.-H. Langa, *, M. Korna and T. Rohm a, b

a Karlsruhe Institute of Technology (KIT) – Institute for Applied Materials (IAM), Engelbert-Arnold-Str. 4, 76128 Karlsruhe, Germany

b University of Applied Science, Moltkestr. 30, 76133 Karlsruhe, Germany

Abstract

Low cyclical loadings can cause failure after a very high number of cycles in the so-called “Very High Cycle Fatigue” (VHCF) area. Thereby, failure initiates typically below the surface at defects like non-metallic inclusions. The appearance of VHCF failure depends on the microstructure of the material and the loading situation. E.g., a quenched and tempered steel with a given distribution of non-metallic inclusions may be insensitive to VHCF failure in a low strength condition but very sensitive in a high-strength condition. The present study investigates the influence of tempering temperature on the fatigue resistance of a low alloyed steel. Uniaxial tension-compression fatigue tests (50 Hz/1 kHz and R=-1) were performed on specimens made of 42CrMo4, which were tempered at six different temperatures to produce wide a range of ultimate strength. With the decrease in tempering temperature the sensitivity of subsurface crack initiation at inner defects increases. High tempered conditions with Rm < 1400 MPa show no failure between 106 and 109 cycles. Crack initiation almost occurs at the surface as a result of local plasticity and surface defects. The fatigue resistance at 109 cycles (Rw/9) matches to the fatigue resistance at 106

cycles (Rw/6). The low tempered conditions show a tendency of increasing life scatter and the threshold value for subsurface crack initiation increase with decreasing strength-level. The study indicated that for high-strength heat treatment conditions the difference between the fatigue strength at 106 and 109 increases with decreasing tempering temperature. A functional relationship between these two fatigue strength was found and verified experimentally. It seems that the stress intensity factor K which arises as a function of local loading conditions at inner stress-raisers depends on the yielding /hardening properties of the material around them.

* Corresponding author. Tel.: +49-721-60842605; fax: +49-721-60848044.


Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the Scientific Committee of ECF21.

http://creativecommons.org/licenses/by-nc-nd/4.0/

http://creativecommons.org/licenses/by-nc-nd/4.0/

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1134 K.-H. Lang et al. / Procedia Structural Integrity 2 (2016) 1133–11422 K.-H. Lang et al. / Structural Integrity Procedia 00 (2016) 000–000

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: Heat treatment conditions; VHCF-resistance; crack initiation; VHCF-lifetime prediction; Sensitivity for VHCF-failure and local supporting effect

1. Introduction In recent years in the field of mechanical and plant engineering, as well as in the automotive industry, the number of durably tolerable cycles for cyclic loaded components increased. Due to high frequencies and/or long service lives high numbers of loading cycles considerably above 107 cycles may occur (Gabelli 2012, Pyttel 2011). For the design and dimensioning of cyclic loaded components currently in most material-specific regulations cyclic strength parameters are limited to a number of cycles to failure of 106 or 107 (Sonsino 2005). In the past it was shown that some metallic materials with bcc-lattice structure and interstitial dissolved impurities have no endurance limit above 106 cycles (Furuya 2011, Yang 2004, Akiniwa 2006, Sakai 2011, Bacher-Höchst 2011, Oguma 2011). For low and medium strength steels, fatigue cracks tend to initiate from the surface and there is a common relation between fatigue limit and tensile strength (Zhao 2012, Furuya 2002, Abe 2004). The study by (Zhao 2012, Bathias 2001) indicated that for many materials, the difference between the fatigue strength at 106 and 109 was larger than 30 MPa, especially for high-strength steels. The reason why the material strength has such a great influence on very-high-cycle fatigue (VHCF) behavior of materials is not completely understood (Zhao 2012). The failure, which is observed in the VHCF-regime, shows new fracture mechanisms, such as the change of crack initiation from the surface to the specimen volume. A comprehensive overview of the fracture formation and development under VHCF-loading is given in (Sakai 2011, Li 2016). Particularly in high-strength metallic materials or material states and under rotating bending is often a two-step SN-curve found (Sonsino 2007). In the classical lifetime regions (LCF = Low Cycle Fatigue, HCF = High Cycle Fatigue) to Nf ≈ 106 the crack initiation takes place at the surface. In the lifetime range between 106 and 1010 cycles crack initiation is shifted to the volume and the SN-curve forms after the classical HCF-fatigue strength plateau a second finite life fatigue strength area. It is possible that in the range of or above 1010 cycles the SN-curve changes in a second horizontal VHCF-fatigue strength plateau. In contrast, under tension and compression the SN-curve may develop only one finite life fatigue strength area ranging from 103 to 1010 cycles. In this area the stress amplitude decreases continuously although the investigated materials also shows a transition from surface crack initiation to subsurface crack initiation at lifetimes above 106 cycles. The development and importance of this behavior for different materials and loading conditions are considered fundamental in (McEviley 2008, Marines 2003, Murakami 2002, Wang 2002, Ochi 2001, Masaki 2004, Shiozawa 2002, Sohar 2008, Grad 2014). From central importance for the VHCF-behavior is to understand the mechanisms of crack initiation and subsequent crack growth. The transition to subsurface cracks is for higher strength metallic materials usually associated with the crack initiation at metallurgical inhomogeneities, such as non-metallic inclusions and the formation of so-called “Fish-Eye” features. On the fracture surface around the inclusions characteristic structures are formed which are called “Fine Granular Area (FGA)”, “Optical Dark Area (ODA)” or “Granular Bright Facet (GBF)”. The assessments of the failure critical inclusions often succeed by fracture mechanical considerations on the root of the effective area and the distance from the surface of inclusions (Murakami 2002). Different approaches for formation mechanism of FGA´s, ODA´s or GBF´s are presented and compared in (Sakai 2011, Li 2016). 2. Experimental Procedure 2.1 Material and Specimen The test material used in this investigation is the low alloyed steel 42CrMo4 (AISI 4140). The chemical composition (mass percentage) of this quenched and tempered steel is: 0.422 C, 1.062 Cr, 0.851 Mn, 0.162 Mo, 0.299 Si, 0.021 S, 0.016 P and balance Fe.

K.-H.-Lang et al. / Structural Integrity Procedia 00 (2016) 000–000 3

Fig. 1. Observed microstructure of the heat-treatment conditions 570, 450, 300, 250 , 180 and 90 (tempering temperature Tt in °C)

and GUMBEL distribution probability plot of maximum inclusion size for production quality and failure relevant /critical inclusion size.

All cylindrical smooth specimens were machined from 15 mm rolled round bar into their final shapes with a surface roughness RZ = 3.3 ± 0.67 µm (average and standard deviation). The cylindrical smooth specimens were 110 mm long, with gage section diameter of 4 mm and gage section length of 5 mm. Afterwards the specimens were austenitised at 850 °C for 20 minutes in vacuum, then oil-quenched and tempered for three hours at six different temperatures: 90 °C, 180 °C, 250 °C, 300 °C, 450 °C and 570 °C followed by furnace cooling. As a result of the respective tempering temperature different microstructures characterized by an almost uniform hardness (HV0.1) distribution of 707 ± 14 (90), 656 ± 15 (180), 626 ± 9 (250), 586 ± 9 (300), 444 ± 7 (450), 353 ± 11 (570) (average and standard deviation / tempering temperature) and a retained austenite content 3.5 Vol.-% were adjusted. Typically the hardness decreases with increasing tempering temperature and the influence of the tempering temperature on hardness after quenching can be described by the following expression (tempering master-curve): HV = 1/((1/HM) + 1,2E-7 ∙ Pt

3,4) with HM = hardness after quenching and Pt = Tt ∙ (K + lg(tt)) = HOLLOMON /JAFFE-parameter with Tt = tempering temperature, tt = tempering time and K = 17,7 – 5,8 ∙ cc (in Ma.-%). The microstructure observations with light microscopy (LOM) on color-etched sections parallel to the loading /rolling direction are shown in Fig. 1. The structural morphology is for the low tempered conditions (Tt 300 °C) tempered martensite and for the high tempered conditions typical for a quenched and tempered steel, fine dispersed cementite in a ferritic matrix. It seems that the number and size of cementite particles /carbides (non-etched particles) precipitated during tempering increased as tempering temperature increased. These changes in microstructure lead to different mechanical properties, which were determined in tensile tests with a strain rate of 3.3 ∙ 10-4 s-1. Relevant mechanical properties are listed in Tab. 1. Table 1. Applied heat treatment conditions with Tt = Tempering temperature (°C), Pt = HOLLOMON /JAFFE-Parameter and mechanical properties with Rp0.2 = (1/Rp0.2/M + 1.5E-7 ∙ Pt

3.5)-1 = 0.2% Yield strength (MPa), Rm = (1/Rm/M + 3E-8 ∙ Pt3.5)-1 = Tensile strength (MPa), A5 = 1.1 +

0.67 ∙ Pt = Fracture strain (%) and surface residual stresses σRS (MPa). Tt 570 450 300 250 180 90

(Pt) (16) (14) (11) (10) (9) (7) Rp0,2 967 1271 1505 1640 1785 (1906) Rm 1054 1378 1779 1904 2145 2212 A5 13.0 10.0 9.0 8.2 8.8 5.3 σRS -58±3 -15±8 24±22 26±16 82±23 340±12

As a result of thermally induced volume contractions and volume dilatation caused by transformation residual stresses on the specimen surfaces occurred according to the temperature profile across the specimen cross-section during quenching and cooling of oil-quenching (Liedtke 2005). Through the subsequently tempering for three hours at different temperatures every heat-treatment condition has a specific residual-stress field with a depth < 30 µm. In

0 20 40 60 80 100 120 140 160

-2

0

2

4

6

-3

8

0,05

Production quality investigation Distribution funktion

of critical inclusion size Sxz

(Oxides of the type AlCaO) Surface-Defect

450 Subsurface-Defect

450 300 250 180 90

y =

-ln (-

ln(F

) )

Sxz (µm)

0,17

K.-H. Lang et al. / Procedia Structural Integrity 2 (2016) 1133–1142 11352 K.-H. Lang et al. / Structural Integrity Procedia 00 (2016) 000–000

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: Heat treatment conditions; VHCF-resistance; crack initiation; VHCF-lifetime prediction; Sensitivity for VHCF-failure and local supporting effect

1. Introduction In recent years in the field of mechanical and plant engineering, as well as in the automotive industry, the number of durably tolerable cycles for cyclic loaded components increased. Due to high frequencies and/or long service lives high numbers of loading cycles considerably above 107 cycles may occur (Gabelli 2012, Pyttel 2011). For the design and dimensioning of cyclic loaded components currently in most material-specific regulations cyclic strength parameters are limited to a number of cycles to failure of 106 or 107 (Sonsino 2005). In the past it was shown that some metallic materials with bcc-lattice structure and interstitial dissolved impurities have no endurance limit above 106 cycles (Furuya 2011, Yang 2004, Akiniwa 2006, Sakai 2011, Bacher-Höchst 2011, Oguma 2011). For low and medium strength steels, fatigue cracks tend to initiate from the surface and there is a common relation between fatigue limit and tensile strength (Zhao 2012, Furuya 2002, Abe 2004). The study by (Zhao 2012, Bathias 2001) indicated that for many materials, the difference between the fatigue strength at 106 and 109 was larger than 30 MPa, especially for high-strength steels. The reason why the material strength has such a great influence on very-high-cycle fatigue (VHCF) behavior of materials is not completely understood (Zhao 2012). The failure, which is observed in the VHCF-regime, shows new fracture mechanisms, such as the change of crack initiation from the surface to the specimen volume. A comprehensive overview of the fracture formation and development under VHCF-loading is given in (Sakai 2011, Li 2016). Particularly in high-strength metallic materials or material states and under rotating bending is often a two-step SN-curve found (Sonsino 2007). In the classical lifetime regions (LCF = Low Cycle Fatigue, HCF = High Cycle Fatigue) to Nf ≈ 106 the crack initiation takes place at the surface. In the lifetime range between 106 and 1010 cycles crack initiation is shifted to the volume and the SN-curve forms after the classical HCF-fatigue strength plateau a second finite life fatigue strength area. It is possible that in the range of or above 1010 cycles the SN-curve changes in a second horizontal VHCF-fatigue strength plateau. In contrast, under tension and compression the SN-curve may develop only one finite life fatigue strength area ranging from 103 to 1010 cycles. In this area the stress amplitude decreases continuously although the investigated materials also shows a transition from surface crack initiation to subsurface crack initiation at lifetimes above 106 cycles. The development and importance of this behavior for different materials and loading conditions are considered fundamental in (McEviley 2008, Marines 2003, Murakami 2002, Wang 2002, Ochi 2001, Masaki 2004, Shiozawa 2002, Sohar 2008, Grad 2014). From central importance for the VHCF-behavior is to understand the mechanisms of crack initiation and subsequent crack growth. The transition to subsurface cracks is for higher strength metallic materials usually associated with the crack initiation at metallurgical inhomogeneities, such as non-metallic inclusions and the formation of so-called “Fish-Eye” features. On the fracture surface around the inclusions characteristic structures are formed which are called “Fine Granular Area (FGA)”, “Optical Dark Area (ODA)” or “Granular Bright Facet (GBF)”. The assessments of the failure critical inclusions often succeed by fracture mechanical considerations on the root of the effective area and the distance from the surface of inclusions (Murakami 2002). Different approaches for formation mechanism of FGA´s, ODA´s or GBF´s are presented and compared in (Sakai 2011, Li 2016). 2. Experimental Procedure 2.1 Material and Specimen The test material used in this investigation is the low alloyed steel 42CrMo4 (AISI 4140). The chemical composition (mass percentage) of this quenched and tempered steel is: 0.422 C, 1.062 Cr, 0.851 Mn, 0.162 Mo, 0.299 Si, 0.021 S, 0.016 P and balance Fe.


Fig. 1. Observed microstructure of the heat-treatment conditions 570, 450, 300, 250 , 180 and 90 (tempering temperature Tt in °C)

and GUMBEL distribution probability plot of maximum inclusion size for production quality and failure relevant /critical inclusion size.

All cylindrical smooth specimens were machined from 15 mm rolled round bar into their final shapes with a surface roughness RZ = 3.3 ± 0.67 µm (average and standard deviation). The cylindrical smooth specimens were 110 mm long, with gage section diameter of 4 mm and gage section length of 5 mm. Afterwards the specimens were austenitised at 850 °C for 20 minutes in vacuum, then oil-quenched and tempered for three hours at six different temperatures: 90 °C, 180 °C, 250 °C, 300 °C, 450 °C and 570 °C followed by furnace cooling. As a result of the respective tempering temperature different microstructures characterized by an almost uniform hardness (HV0.1) distribution of 707 ± 14 (90), 656 ± 15 (180), 626 ± 9 (250), 586 ± 9 (300), 444 ± 7 (450), 353 ± 11 (570) (average and standard deviation / tempering temperature) and a retained austenite content 3.5 Vol.-% were adjusted. Typically the hardness decreases with increasing tempering temperature and the influence of the tempering temperature on hardness after quenching can be described by the following expression (tempering master-curve): HV = 1/((1/HM) + 1,2E-7 ∙ Pt

3,4) with HM = hardness after quenching and Pt = Tt ∙ (K + lg(tt)) = HOLLOMON /JAFFE-parameter with Tt = tempering temperature, tt = tempering time and K = 17,7 – 5,8 ∙ cc (in Ma.-%). The microstructure observations with light microscopy (LOM) on color-etched sections parallel to the loading /rolling direction are shown in Fig. 1. The structural morphology is for the low tempered conditions (Tt 300 °C) tempered martensite and for the high tempered conditions typical for a quenched and tempered steel, fine dispersed cementite in a ferritic matrix. It seems that the number and size of cementite particles /carbides (non-etched particles) precipitated during tempering increased as tempering temperature increased. These changes in microstructure lead to different mechanical properties, which were determined in tensile tests with a strain rate of 3.3 ∙ 10-4 s-1. Relevant mechanical properties are listed in Tab. 1. Table 1. Applied heat treatment conditions with Tt = Tempering temperature (°C), Pt = HOLLOMON /JAFFE-Parameter and mechanical properties with Rp0.2 = (1/Rp0.2/M + 1.5E-7 ∙ Pt

3.5)-1 = 0.2% Yield strength (MPa), Rm = (1/Rm/M + 3E-8 ∙ Pt3.5)-1 = Tensile strength (MPa), A5 = 1.1 +

0.67 ∙ Pt = Fracture strain (%) and surface residual stresses σRS (MPa). Tt 570 450 300 250 180 90

(Pt) (16) (14) (11) (10) (9) (7) Rp0,2 967 1271 1505 1640 1785 (1906) Rm 1054 1378 1779 1904 2145 2212 A5 13.0 10.0 9.0 8.2 8.8 5.3 σRS -58±3 -15±8 24±22 26±16 82±23 340±12

As a result of thermally induced volume contractions and volume dilatation caused by transformation residual stresses on the specimen surfaces occurred according to the temperature profile across the specimen cross-section during quenching and cooling of oil-quenching (Liedtke 2005). Through the subsequently tempering for three hours at different temperatures every heat-treatment condition has a specific residual-stress field with a depth < 30 µm. In

0 20 40 60 80 100 120 140 160

-2

0

2

4

6

-3

8

0,05

Production quality investigation Distribution funktion

of critical inclusion size Sxz

(Oxides of the type AlCaO) Surface-Defect

450 Subsurface-Defect

450 300 250 180 90

y =

-ln (-

ln(F

) )

Sxz (µm)

0,17


addition, the residual stress σRS, after the heat treatment, on the surface of the specimen was measured by the sin²ψ-method along the axis of the specimen using x-ray diffraction pattern of the α-Fe {211} crystal plane obtained by Cr-Kαradiation. The estimated residual stresses (σRS) at the surface are also listed in (Tabel 1). The high tempered conditions are largely macro residual stress-free (Tt = 570 °C) or exhibit low comprehensive residual stresses (Tt = 450 °C) at the surface. The low tempered conditions (Tt = 300, 250, 180 and 90°C) processes tensile residual stresses up to 340 MPa (Tt = 90 °C) at the surface. According to the current state of knowledge usually non-metallic inclusions, their type, size and distance from the surface, are responsible for the failure of high-strength steels in the VHCF-regime (Grad 2014, Murakami 1989). For this reason sections parallel to the gauge length were prepared to determine the nature and content of non-metallic inclusions, according to (DIN 10247). The by LOM/EDX detected inclusions were oxides (AlCaO, SiO), sulfides (MnS) and nitrides (TiN). In an inspection area of SiA = 207 mm², the width Pw and length Pl 3 µm of all inclusions were classified and the maximum inclusion size were measured (Pw, Pl). The medium content Kn is 26/mm² (Oxides), 1.6/mm² (Sulfides) 0.52/mm² (Nitrides) and the maximum width Pw,max of the respective inclusion type is 23 µm (Oxides), 6.7 (Sulfides) and 7.8 µm (Nitrides). Furthermore, the maximum inclusion size in a certain volume V (mm³) was estimated by using the statistics of extreme values (SEV) method (Anderson 2000, Li 2013). Cross-sections were polished up to 0.25 µm diamond grain size to obtain a high-quality contrast of the non-metallic inclusions in the surrounding steel-matrix. An inspection area of SiA = 207 mm² were scanned by an optical light microscope. Afterwards the maximum inclusion size √Sxz,max of 200 standard inspection areas of S0 = 1.035 mm² were identified and measured by using the image analysis software ANALYSIS. The detected inclusions were oxides with maximum sizes √Sxz,max of 2.75 to 34.64 µm, which can be characterized by GUMBEL extreme value distribution, as it is shown in Fig. 1 (left). The maximum inclusion size in a certain volume XV with the return period T = V/V0 = V/(SiA·h) can be estimated with the following expression (Murakami 1989, Anderson 2000): XV = λ – δ ∙ ln(-ln(1-1/T)). The thickness is defined as the average inclusion size (8.21µm). With a high stressed volume V = 62.85 mm³, location parameter = 6.09 µm and scale parameter δ = 3.74 µm (estimated by using the method of least squares) is the predicted maximum inclusion size X63 = 44.07 µm. 2.2 Testing equipment and procedure

The fatigue tests to determine the cyclic resistance up to the VHCF-regime were carried out stress controlled at a stress ratio R = -1 for 50 Hz /Nl = 107 and 1000 Hz /Nl = 109 at room temperature. The 50 Hz tests conducted to catch up with the LCF/HCF-regime and to determine a possible influence of the test frequency on the fatigue strength. For these experiments a standard SCHENK servo hydraulic testing machine was used. To realize fatigue tests in the VHCF-regime a self-developed resonance testing machine was used. Initial damage could be detected on a drop in resonance frequency and an increase in the non-linearity parameter by (Kumar 2010) due to the stiffness reduction (crack-induced). The surface temperature of the specimen could be used in addition to detect damage, because the temperature increases very strongly just before fracture. Using a combination of tracing the frequency and the surface temperature the experiments could be terminated just before fracture. To reduce the influence of self-heating the specimens are cooled by compressed air when temperature increases more than 10 K. 3. Experimental Results and Discussions

3.1. Influence of tempering condition on the VHCF-resistance Results of fatigue tests under axial loading for the different tempering conditions 570 and 90 were shown as S-N diagram in Fig. 3. The fatigue limits for 106 (Rw/6/50kHz, Rw/6/1kHz) and 109 cycles and fracture probability lines were determined by a modified arcsin√P- and staircase-method respectively (Dengel 1989).


Fig. 2. S-N diagrams for the heat-treatment condition 570 (left) and 90 (right)

with fracture probability lines Pf = 10 %, 50 % and 90 and normalized S-N diagrams for the respective heat-treatment condition.

In case of high tempered condition (570) no fatigue resistance drop can be observed between 3∙106 and 109 cycles, but a reduced fatigue limit for a testing frequency of 1 kHz. On the other hand shows the low tempered condition (90) a fatigue resistance drop of 36 %/decade in the range of 106 and 109 cycles. Based on the examination of fracture surface of every failed specimen by scanning electron microscope (SEM) the fatigue failure is classified into surface (open symbols) and interior inclusion-induced fracture with fish-eye formation (solid and half solid symbols). The crack initiation side is divided in the following groups: surface, surface defect (in contact with the surface or in a depth tI< 100µm), Volume with and without ODA formation (t > 100µm). As it is presented in the normalized S-N diagrams the ODA-formation determine the lifetime in the VHCF-regime (N > 107). The normalized S-N diagrams for both heat treatment conditions are fitted to the fatigue data for surface-induced failure by the standard linear regression method is shown by the black (50 Hz) and red (1 kHz) line. Based on the results of the 10 % and 90 % fracture probability lines, the scatter ranges Tσ = σ90%/σ10% and TN = N90%/N10% are also labeled. It can be seen in Fig. 3, that the scatter range of fatigue limit for surface induced failure and for number of cycles to failure increases with decreasing tempering temperature in the HCF-regime typically. It seems that the heat-treatment condition 90 has a fatigue limit for inner crack initiation at 109 cycles, but a further drop in fatigue strength at higher cycles could not excluded. Generally the high tempering conditions (570 , 450) show no difference between the fatigue strength at 106 and 109 cycles and a linear relationship involving tensile strength (or hardness) and the respective fatigue limit, as shown in Fig. 3. As expected the fatigue limit for surface induced failure increases with decreasing tempering temperature (Fig. 3). The relation between tensile strength and fatigue strength for surface initiated failure (Rw/O) could be estimated by a modified quadratic equation (solid blue (1 kHz) thin and black (50 Hz) thin line, Fig. 3), according to (Pan 2014): Rw/O = FO ∙ Fm ∙ Rw0 with Rw0 = (0.67 - 31.5 ∙ Rm/E) ∙ Rm and E = 210318 MPa, Rm is the respective tensile strength in MPa. Based on (fkm 2003), the influence of surface roughness and residual stresses on the fatigue strength can be taken into account by the two parameters FO (RZ) and Fm (σRS). However, it must be said that the parameter Fm overestimates the influence of surface residual stresses caused by the heat treatment. In our case it is sufficient to take the surface roughness for an accuracy of less than 5 % into account. A reason could be the low depth of the acting residual stresses. Also can be seen in Fig. 3 (left), the testing frequency has a non-negligible influence on the fatigue strength of surface induced fracture. Compared to the 50 Hz – tests, the fatigue strength for 1 kHz is less. It is believed that the reduced fatigue strength is caused by a local self-heating process at micro-notches (roughness or brush-marks) on the specimen surface. It seems, that a macroscopic self-heating of less than 10 K in combination with a roughness of Rz = 3.3 µm is critical for surface induced failure. This thermal influence reduces the critical shear-stress for dislocation movements and thus the formation of persistent slip bands. The low tempering conditions (300, 250, 180 and 90) show a marked difference in their surface and volume resistance of up to 32 %. This comparison indicates a different VHCF-sensitivity with a critical tensile strength of 1400 MPa of the chosen tempering conditions. It seems that the difference between Rw/1E6 and Rw/1E9 increases with decreasing tempering temperatures and could be described for the investigated heat treatment condition by a linear relationship Rw/1E9 = (1-Z*) · Rw/O. The respective fatigue

10-1103 105 107 109 1011

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--

--

63

339

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216

k = 790

408

57016

109

Failure 50 Hz Failure 1kHz Run Out

339 V0 = r20 l0 in (mm³)

456 R50%w/6/50Hz in (MPa)

408 R50%w/6/1kHz in (MPa)

456

0,25

/

2 (M

Pa)

Nf 107

10

10-1 103 105 107 109 1011

1200

300

400

500

600

700

800

900

-

-

-

-

-

-

-

236

236

631/5

3/7

2/2

2/3

0/5

1/4

561

k = 5 / k* = 25

Failure 50 Hz Failure 1 kHz Run Out

236 V0 = r20 l0 in (mm³)

641 R50%w/6/50Hz in (MPa)


0/5 Run Out /Test

641

10

90

109

907

/

2 (M

Pa)

Nf 0,25 10710-1 101 103 105 107 109 1011

0,7

0,8

0,9

1

1,1

1,2

1,3

1,4

1,5

kO = 10/7

T = 1,02

Regression line 50 Hz mit /2Rw/6 = 3,8 NB

-0,1

1 kHz OA /50 Hz OA /1 kHz

mit R50%w/6/50Hz

mit R50%w/6/1kHz0,7

57016

/

2Rw

/6 (M

Pa)

Nf

0,25

TN = 3,57

100 103 106 109

0,5

0,75

1

1,25

1,5

11

14

17

18 24

1921

27

31

2228

30

25 26

20

23

2932

15

kO = 9,4(6) /8,7(5)

T = 1,14

Regression line 50 Hz mit /2Rw/6 = 4NB

-0,11


mit R50%w/6/50Hz

mit R50%w/6/1kHz

DoK /N 1 kHz VoA 1 kHz VoA/ODA 1 kHz

907

/

2Rw

/6 (M

Pa)

Nf

0,25

TN = 4,44

1011


addition, the residual stress σRS, after the heat treatment, on the surface of the specimen was measured by the sin²ψ-method along the axis of the specimen using x-ray diffraction pattern of the α-Fe {211} crystal plane obtained by Cr-Kαradiation. The estimated residual stresses (σRS) at the surface are also listed in (Tabel 1). The high tempered conditions are largely macro residual stress-free (Tt = 570 °C) or exhibit low comprehensive residual stresses (Tt = 450 °C) at the surface. The low tempered conditions (Tt = 300, 250, 180 and 90°C) processes tensile residual stresses up to 340 MPa (Tt = 90 °C) at the surface. According to the current state of knowledge usually non-metallic inclusions, their type, size and distance from the surface, are responsible for the failure of high-strength steels in the VHCF-regime (Grad 2014, Murakami 1989). For this reason sections parallel to the gauge length were prepared to determine the nature and content of non-metallic inclusions, according to (DIN 10247). The by LOM/EDX detected inclusions were oxides (AlCaO, SiO), sulfides (MnS) and nitrides (TiN). In an inspection area of SiA = 207 mm², the width Pw and length Pl 3 µm of all inclusions were classified and the maximum inclusion size were measured (Pw, Pl). The medium content Kn is 26/mm² (Oxides), 1.6/mm² (Sulfides) 0.52/mm² (Nitrides) and the maximum width Pw,max of the respective inclusion type is 23 µm (Oxides), 6.7 (Sulfides) and 7.8 µm (Nitrides). Furthermore, the maximum inclusion size in a certain volume V (mm³) was estimated by using the statistics of extreme values (SEV) method (Anderson 2000, Li 2013). Cross-sections were polished up to 0.25 µm diamond grain size to obtain a high-quality contrast of the non-metallic inclusions in the surrounding steel-matrix. An inspection area of SiA = 207 mm² were scanned by an optical light microscope. Afterwards the maximum inclusion size √Sxz,max of 200 standard inspection areas of S0 = 1.035 mm² were identified and measured by using the image analysis software ANALYSIS. The detected inclusions were oxides with maximum sizes √Sxz,max of 2.75 to 34.64 µm, which can be characterized by GUMBEL extreme value distribution, as it is shown in Fig. 1 (left). The maximum inclusion size in a certain volume XV with the return period T = V/V0 = V/(SiA·h) can be estimated with the following expression (Murakami 1989, Anderson 2000): XV = λ – δ ∙ ln(-ln(1-1/T)). The thickness is defined as the average inclusion size (8.21µm). With a high stressed volume V = 62.85 mm³, location parameter = 6.09 µm and scale parameter δ = 3.74 µm (estimated by using the method of least squares) is the predicted maximum inclusion size X63 = 44.07 µm. 2.2 Testing equipment and procedure

The fatigue tests to determine the cyclic resistance up to the VHCF-regime were carried out stress controlled at a stress ratio R = -1 for 50 Hz /Nl = 107 and 1000 Hz /Nl = 109 at room temperature. The 50 Hz tests conducted to catch up with the LCF/HCF-regime and to determine a possible influence of the test frequency on the fatigue strength. For these experiments a standard SCHENK servo hydraulic testing machine was used. To realize fatigue tests in the VHCF-regime a self-developed resonance testing machine was used. Initial damage could be detected on a drop in resonance frequency and an increase in the non-linearity parameter by (Kumar 2010) due to the stiffness reduction (crack-induced). The surface temperature of the specimen could be used in addition to detect damage, because the temperature increases very strongly just before fracture. Using a combination of tracing the frequency and the surface temperature the experiments could be terminated just before fracture. To reduce the influence of self-heating the specimens are cooled by compressed air when temperature increases more than 10 K. 3. Experimental Results and Discussions

3.1. Influence of tempering condition on the VHCF-resistance Results of fatigue tests under axial loading for the different tempering conditions 570 and 90 were shown as S-N diagram in Fig. 3. The fatigue limits for 106 (Rw/6/50kHz, Rw/6/1kHz) and 109 cycles and fracture probability lines were determined by a modified arcsin√P- and staircase-method respectively (Dengel 1989).


Fig. 2. S-N diagrams for the heat-treatment condition 570 (left) and 90 (right)

with fracture probability lines Pf = 10 %, 50 % and 90 and normalized S-N diagrams for the respective heat-treatment condition.

In case of high tempered condition (570) no fatigue resistance drop can be observed between 3∙106 and 109 cycles, but a reduced fatigue limit for a testing frequency of 1 kHz. On the other hand shows the low tempered condition (90) a fatigue resistance drop of 36 %/decade in the range of 106 and 109 cycles. Based on the examination of fracture surface of every failed specimen by scanning electron microscope (SEM) the fatigue failure is classified into surface (open symbols) and interior inclusion-induced fracture with fish-eye formation (solid and half solid symbols). The crack initiation side is divided in the following groups: surface, surface defect (in contact with the surface or in a depth tI< 100µm), Volume with and without ODA formation (t > 100µm). As it is presented in the normalized S-N diagrams the ODA-formation determine the lifetime in the VHCF-regime (N > 107). The normalized S-N diagrams for both heat treatment conditions are fitted to the fatigue data for surface-induced failure by the standard linear regression method is shown by the black (50 Hz) and red (1 kHz) line. Based on the results of the 10 % and 90 % fracture probability lines, the scatter ranges Tσ = σ90%/σ10% and TN = N90%/N10% are also labeled. It can be seen in Fig. 3, that the scatter range of fatigue limit for surface induced failure and for number of cycles to failure increases with decreasing tempering temperature in the HCF-regime typically. It seems that the heat-treatment condition 90 has a fatigue limit for inner crack initiation at 109 cycles, but a further drop in fatigue strength at higher cycles could not excluded. Generally the high tempering conditions (570 , 450) show no difference between the fatigue strength at 106 and 109 cycles and a linear relationship involving tensile strength (or hardness) and the respective fatigue limit, as shown in Fig. 3. As expected the fatigue limit for surface induced failure increases with decreasing tempering temperature (Fig. 3). The relation between tensile strength and fatigue strength for surface initiated failure (Rw/O) could be estimated by a modified quadratic equation (solid blue (1 kHz) thin and black (50 Hz) thin line, Fig. 3), according to (Pan 2014): Rw/O = FO ∙ Fm ∙ Rw0 with Rw0 = (0.67 - 31.5 ∙ Rm/E) ∙ Rm and E = 210318 MPa, Rm is the respective tensile strength in MPa. Based on (fkm 2003), the influence of surface roughness and residual stresses on the fatigue strength can be taken into account by the two parameters FO (RZ) and Fm (σRS). However, it must be said that the parameter Fm overestimates the influence of surface residual stresses caused by the heat treatment. In our case it is sufficient to take the surface roughness for an accuracy of less than 5 % into account. A reason could be the low depth of the acting residual stresses. Also can be seen in Fig. 3 (left), the testing frequency has a non-negligible influence on the fatigue strength of surface induced fracture. Compared to the 50 Hz – tests, the fatigue strength for 1 kHz is less. It is believed that the reduced fatigue strength is caused by a local self-heating process at micro-notches (roughness or brush-marks) on the specimen surface. It seems, that a macroscopic self-heating of less than 10 K in combination with a roughness of Rz = 3.3 µm is critical for surface induced failure. This thermal influence reduces the critical shear-stress for dislocation movements and thus the formation of persistent slip bands. The low tempering conditions (300, 250, 180 and 90) show a marked difference in their surface and volume resistance of up to 32 %. This comparison indicates a different VHCF-sensitivity with a critical tensile strength of 1400 MPa of the chosen tempering conditions. It seems that the difference between Rw/1E6 and Rw/1E9 increases with decreasing tempering temperatures and could be described for the investigated heat treatment condition by a linear relationship Rw/1E9 = (1-Z*) · Rw/O. The respective fatigue

10-1103 105 107 109 1011

1250

300

350

400

450

500

550

600

650

---

- -

--

--

63

339

-

216

k = 790

408

57016

109

Failure 50 Hz Failure 1kHz Run Out

339 V0 = r20 l0 in (mm³)

456 R50%w/6/50Hz in (MPa)


456

0,25

/

2 (M

Pa)

Nf 107

10

10-1 103 105 107 109 1011

1200

300

400

500

600

700

800

900

-

-

-

-

-

-

-

236

236

631/5

3/7

2/2

2/3

0/5

1/4

561

k = 5 / k* = 25

Failure 50 Hz Failure 1 kHz Run Out

236 V0 = r20 l0 in (mm³)

641 R50%w/6/50Hz in (MPa)


0/5 Run Out /Test

641

10

90

109

907

/

2 (M

Pa)

Nf 0,25 10710-1 101 103 105 107 109 1011

0,7

0,8

0,9

1

1,1

1,2

1,3

1,4

1,5

kO = 10/7

T = 1,02

Regression line 50 Hz mit /2Rw/6 = 3,8 NB

-0,1


mit R50%w/6/50Hz

mit R50%w/6/1kHz0,7

57016

/

2Rw

/6 (M

Pa)

Nf

0,25

TN = 3,57

100 103 106 109

0,5

0,75

1

1,25

1,5

11

14

17

18 24

1921

27

31

2228

30

25 26

20

23

2932

15

kO = 9,4(6) /8,7(5)

T = 1,14

Regression line 50 Hz mit /2Rw/6 = 4NB

-0,11


mit R50%w/6/50Hz

mit R50%w/6/1kHz

DoK /N 1 kHz VoA 1 kHz VoA/ODA 1 kHz

907

/

2Rw

/6 (M

Pa)

Nf

0,25

TN = 4,44

1011


0 500 1000 1500 2000 2500 30000

100

200

300

400

500

600

700

63216

339

63

216

Fatigue Limit Rw/O 50 Hz für PB = 50 %

1 kHz 1 kHz Exponential-Approach

50 Hz Exponential-Approach

1 kHz Parabol-Approach

339 Testing Volume V0 in (mm³)

1

50

Rw

/O (M

Pa)

Rm (MPa) 0 500 1000 1500 2000 2500 30000

100

200

300

400

500

600

700

0

0

-81-119

-1270

0

-47-160 -176

-207

-123

7

1

9 8

Fatigue Resistance Rw/O

/surface für N = 106 /50Hz

für N = 106 /1 kHz Fatigue Resistance Rw/V

/subsurface für N = 109 6 Cycles in (log(N))0,05 Test frequency in (kHz)-123 Fatigue Resistance Drop in (MPa)

0,05

Rw

/N (M

Pa)

Rm (MPa)

6

strength reduction factor Z* and the absolute deviation between Rw/O and Rw/1E9 are listed in Tab. 2 and labeled in Fig. 3 (left). Table 2. Absolute deviation ΔR50 (50 Hz), ΔR1 (1 kHz) between Rw/1E6 and Rw/1E9 and fatigue strength reduction factor Z50

* (50 Hz), Z50* (1 kHz).

Tt 570 450 300 250 180 90 ΔR50 0 0 123 160 176 207 Z50* 0 0 0.21 0.26 0.28 0.32 ΔR1 0 0 47 81 119 127 Z1* 0 0 0.09 0.15 0.21 0.23

Fig. 3. Relationship between tensile strength and fatigue strength at 106 and 109 cycles with black lines = 50 Hz and blue lines = 1 kHz (left) and prediction areas of threshold stress and number of cycles to failure (right).

The linear relations between fatigue limit and tensile strength for the high tempering conditions is related to surface fatigue crack initiation mechanisms, while for low tempering conditions, a fracture process given by an internal fatigue crack initiation defines the relationship between fatigue limit and material strength (Pang 2014). As a failure criterion for the failure in the VHCF regime the stress intensity factor (SIF) at inclusions was chosen. Thus we are able to calculate the SIF at the edge of interior inclusion and ODA (Fig. 4) with the following equation (Murakami 1989): Kmax = f ∙ Δσ/2 ∙ π0,5 ∙ Sxz

0,25 with Δσ/2 = nominal stress in the gauge section in MPa, Sxz = inclusion area in µm and f = location parameter (fV = 0.5 for subsurface defects and fO = 0.65 for surface defects). The threshold value for crack initiation at inner and surface inclusions is also given by (Murakami 1989): ΔKth = i ∙ (HV+120) ∙ Sxz

1/6 with iV = 2.77 ∙ 10-3 for subsurface defects, iO = 3.3 ∙ 10-3 for surface defects and Sxz = inclusion area in m.

Fig. 4. Calculation of SIF for inclusion (550 MPa) and Inclusion + ODA (513 MPa).

Energy dispersive X-ray spectroscopy shows that the crack initiating particles in the investigated heat-treatment conditions of the low alloyed steel 42CrMo4 are nonmetallic inclusions of type AlCaO. The square root of the


inclusion surface area, √Sxz is used to characterize the size of inclusions. Fig. 1 (right) shows in the probability diagram of extreme value the inclusion size of fracture origin obtained from the fracture surface of all heat treatment conditions which fatigue test was carried out. The comparison with the detected inclusion size by the purity-analysis shows that a still greater √Sxz can be detected from the fracture surface of fatigue test specimen. The inclusion sizes were 47 – 82 µm (450), 142 – 20 µm (300), 95 – 22 µm (250), 96 – 16 µm (180) and 102 – 30 µm (90). Fig. 5 (left) shows the equivalent inclusion size as a function of lifetime separated in each heat treatment condition (characterized by regression lines). The typically size-effect, decreasing inclusion size with increasing fatigue life could be observed for all heat-treatment conditions. It seems that there is a relation between the critical inclusion size for failure and heat treatment condition. In the HCF regime (Nf < 107) the critical inclusion size for low tempered heat treatment conditions is smaller than for the high tempered heat treatment conditions. In the VHCF-regime, the conditions are reversed for inclusions with ODA-formation (blue symbols). A possible cause for this observation could be that for inclusions without ODA formation the long crack threshold for crack initiation and for inclusions with ODA formation the short crack threshold is dominant. Because the long crack threshold increases with increasing tempering temperature and short crack threshold decreases. So the high tempered heat treatment condition need for crack initiation in the HCF-regime a much higher stress intensity factor at the border of inclusion as the low tempered conditions. Same ratio can be observed for the relationship between the maximum stress intensity factor for the inclusions and fatigue life (Fig.5). But it can be also seen in Fig. 5, that the stress intensity factor for the ODA-size is not constant and show a decreasing behavior for increasing number of cycles to failure.

Fig. 5. Size effect of the critical inclusion size and maximum stress intensity factor for √Sxz (left)

and normalized SIF for inclusion and ODA-size and ODA-growth curves (right).

The blue symbols in Fig. 5 indicated the inclusions which show on the fracture surface an ODA-formation. Fig. 5 (right) shows the relation between SIF of the failure-initiating inclusions (hollow symbols) / the ODA-edge (solid symbols) and number of cycles to failure Nf normalized to the threshold value for short crack growth. For all critical tempering conditions Kmax,I decrease with increasing lifetime. It is crucial that on the one hand all inclusions with a ratio of Kmax,I / Kth > 1 formed no ODA. On the other hand also inclusions with a smaller ratio may play an important role for failure initiation at inner inclusions. The formation of an ODA can cause locally a critical ratio Kmax,I / Kth> 1 even if the SIF of the inclusion is below the threshold value. Fig. 5 (right) also shows the dependence of the ODA growth on the fatigue life. The observed increasing of the ODA size with increasing lifetime is typically for steels in the VHCF-regime and can be approximate by the shown power law approach. A clear influence of the heat treatment conditions on the ODA size could not be identified. For the calculation of the threshold stress for crack initiation (endurance limit) at inner defects all stress intensity factors are normalized on the fatigue crack threshold for long cracks and the inclusions size on the microstructure length according to (Fujimoto 2001) (Fig. 6 (left)). With the determined relationship between the normalized stress intensity factors and inclusion sizes the threshold stress could be calculated as a function of tempering temperature and testing frequency as it is shown in Fig. 3 (right). The

10-1 102 105 108 1011

0

40

80

120

160

200

1410

9

Equivalent crack length 45014

(subsurface defect) Surface defekt 30011

25010

1809

907

with ODA-formation 14 Tempering paramter PA

Sxz

(µm

)

Nf

0,25

7

11

10-1 102 105 108 1011

0

2

4

6

8

10

21

10

10/11

7

SIF Sxz) /45014

30011

25010

1809

907

SIF SODA/E) /907

14 Tempering Parameter PA14

11

9

Nf

0,25

Km

ax (M

Pam

)

10-1 102 105 108 1011

0

30

60

90

120

150 Equivalent ODA-size

30011

25010

1809

907

ODA-growth curve VoA/907

DON/907

9

7

11

10

9

Nf

0,25

7

7

SO

DA (µ

m)

10-1 102 105 108 1011

0,0

0,5

1,0

1,5

2,0 Tolerance Range 10% SIF Sxz) /45014

SIF für SODA/E) /30011

25010

1809

907

Nf

0,25

max

/K

th/k


100 105 1010 1015 1020

100

105

1010

1015

1020

2

Nf/0

Nf/E

Tolerance range 1dGO DoK 45014 VoA 45014

Sxz

30011

25010

1809

907

907 SODA/E

2 dGO

2

0 200 400 600 800 10000

200

400

600

800

1000

2

ODA-formation

- 20%

Tolerance range 10 % 1 kHz

VoA 45014

DoK 45014

30011

25010

1809

907

Rxz

(MPa

)

/2 (MPa)

+ 20%

10-4 10-2 100 102 104

0,5

1

1,5

2

2,5

3

0,3

2

Relative crack growth resistance [Fuj01]

[Mur89] rSIF 45014

Sxz

30011

25010

1809

907

rSIF 907

SODA/E

7 Pt

Sxz /4Y21r0

K

xz /

th

/l

14V/O

7V/O

testing frequency dominates the fatigue limit or surface initiated fracture. The location of inclusions (surface or subsurface) could be taken into account with the geometry factors YO = 0.9 (surface) and YV = 0.7 (subsurface). The two parameters are approximated from the different calculations for the stress intensity factor according to (Murakami 1989). A linear relationship could be observed (Fig. 5 (left)). The fatigue limit areas describes the threshold stress for crack initiation as a function tempering temperature, inclusion size and inclusion position (fO = surface, fV = subsurface). Also the critical inclusion size for the first decrease of fatigue resistance is labeled in Fig. 3 (red line). As it is shown in Fig. 6 the predicted fatigue limit approach Δσth = (Sxz

0,25 /(4Y2r0fπ0.5)) · ΔKth,l has an accuracy less than 10 %. For a more conservative approach of the threshold stress the usage of √SODA/E is necessary. As a result of the observed size effect the number of cycles to failure could be calculated by the approach of (Akiniwa 2006). The determined parameter m and C are listed for several heat treatment conditions in Tab. 3 and the influence of tempering temperature is illustrated in Fig. 3 (right). Table 3. Parameters m and C for the predicted approach according to (Akiniwa 2006).

Tt 570 450 300 250 180 90 Pt (16) (14) (11) (10) (9) (7) m - 5.45 7.14 11.33 11.46 12.41 C - 6.92E-15 1.49E-16 4.25E-19 2E-19 8.73E-20

Fig. 6. Normalized crack growth resistance curve (left) and accuracy of the predicted predictions for threshold stress and lifetime (right)

4. Conclusion

Based on the experimental results for the fatigue strength at 107 and 109 cycles of different heat-treatment conditions of the steel 42CrMo4, expressions of the fatigue strength and number of cycles to failure were proposed to predict the S-N diagram in the VHCF-regime for critical heat-treatment conditions (Rm/c > 1400 MPa). The combination of the predictions accords well with the experimental results and there is a possibility to predict the life scatter in the VHCF-regime (see fig. 7). On the other hand the present results lead to a differentiated conception on the sensitivity for failure in the VHCF-regime. The occurrence of VHCF-failure depends on the loading situation which is induced in the surroundings of an inclusion. This loading situation is controlled by the arising local stress state and the yielding characteristics of the matrix nearby the inclusion. Maybe there is a relation between the ODA-size and plastic zone around the inclusions. As current work in the research project a VHCF-sensitivity model will be proposed which assesses the VHCF sensitivity of different microstructural conditions of steels. The model will base on the presented results and will give an explanation to the observation that the inclusion size is decreasing with increasing life time and for the ODA-formation as a function of tempering temperature.


5. Acknowledgements

The authors would like to thank the German Research Foundation (DFG) for the financial support.

6. References

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very high cycle fatigue resistance of the low alloyed ... · failure in a low strength condition...

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