material response models for sub-surface and surface rolling contact
MATERIAL RESPONSE MODELS FOR SUB-SURFACE AND SURFACE ROLLING CONTACT FATIGUE Wolfgang Nierlich1, Jürgen Gegner1,2 1
SKF GmbH, Department of Material Physics Ernst-Sachs-Strasse 5, D-97424 Schweinfurt, Germany 2
University of Siegen, Institute of Material Engineering Paul-Bonatz-Strasse 9-11, D-57068 Siegen, Germany
ABSTRACT Material mechanics theories of rolling contact loading can be reassessed by recording the alteration of characteristics measured from the edge to the core of a stressed surface via X-ray diffraction. Exceeding metallographic investigations, the developments of residual stresses and line width represent the relevant information carrier. It turned out that material changing permits a specific correlation to failure probability distributions. These relationships differ significantly for sub-surface and (near-) surface fatigue. Recent findings from certain bearing applications with higher demands on service life and reliability point to the need for applying different equivalent stress methods for modeling the material response in both types of loading: for classical subsurface overrolling fatigue that is characterized by strengthening and softening processes below the Hertzian contact area, shear stress-based hypotheses are indicated, whereas for the surface failure mode that is accompanied by embrittlement, additionally to these approaches the main normal stress-based hypothesis should be considered. Cyclic tensile stresses caused by friction can act on material-inherent crack sources. In both cases, changes of the X-ray line width, which mainly stem from plastic deformation with rearrangement of the dislocation configuration and martensite decay with carbon diffusion, serve as powerful sensor for material aging. Rig tests under controlled mixed friction conditions give an example of near-surface rolling contact fatigue. INTRODUCTION Material response models result from theoretical and experimental stressing analyses. Calculational approaches determine the pressure in Hertzian contact and the course of equivalent stresses (v. Mises stress, main shear stress, orthogonal shear stress, main normal stress) below the raceway surface and the selection of the strength hypotheses. Analyses of rolling bearings are usually based on four tools: metallography for the purpose of microstructure examinations; scanning electron microscopy and microchemical elemental analysis with the aim of material characterization on a micrometer scale; X-ray diffraction (XRD) measurements of (macro-) residual stresses, line broadening (measure of type-III micro-residual stresses), and retained austenite content directed towards loading analyses; infrared spectroscopy of used lubricants. FAILURE PROBABILITY DISTRIBUTION FUNCTION The most conspicuous reaction to stressing is bearing failure by spalling, as shown in Figs. 1 and 2. The failure probability function is a two-parameter Weibull frequency distribution: 1-182
⎡ ⎛ t ⎞m ⎤ F (t ) = 1 − R(t ) = 1 − exp ⎢− ⎜ ⎟ ⎥ , t ≥ 0 ⎣⎢ ⎝ τ ⎠ ⎦⎥
(1)
Here, F denotes the accumulated failure probability (0 ≤ F 0, F(τ) = 63.2 % holds.
Fig. 1. SEM (scanning electron microscope) micrograph, secondary electron (SE) image, of surface induced V pitting starting from an indentation on the inner ring raceway of a taper rolling bearing (left-hand side, overrolling direction from the left to the right). Fig. 2. SEM micrograph (SE image) of sub-surface induced spalling on the inner ring raceway of a deep grove ball bearing with crack formation in typical depths of 100 to 300 µm (right-hand side, overrolling direction from the left to the right). For m =1, Eq. (1) describes Rutherford's exponential law for radioactive decay (loss rate proportional to the amount present). For failure of rolling bearings, m >1 is valid: mostly, m lies between 1.1 and 2. For known m, τ is by definition determined by the following correlation: F ( L10 ) = 0.1
(2)
Here, L10 stands for the failure or survival probability of 10 and 90 %, respectively. It can be expressed in number of revolutions as follows:
⎛C ⎞ L10 = a DIN × 10 × ⎜ ⎟ ⎝P⎠
p
6
(3)
The coefficient aDIN considers the lubrication and raceway surface conditions. 1-183
Moreover, C and P denote the dynamic load rating and the dynamic equivalent bearing load, respectively expressed in kN. Information on aDIN, C, and P can be taken from the supplier's catalog. The lifetime exponent p equals 3 for ball and 10/3 for roller bearings. Since the coefficient aDIN takes values in a wide range of more than one order of magnitude, the given expressions for the failure probability can be applied to several damage mechanisms with related material response models. FAILURE MODES IN ROLLING CONTACT
It is distinguished empirically between surface initiated failures, where spalling expands from the raceway surface to some depth, and classical rolling contact fatigue spalling by cracks that break out from a certain depth. Typical examples of both cases are shown in Figs. 1 and 2, respectively. Surface rolling contact fatigue with surface induced failure is characteristic of automobile gearbox bearings. Wear debris (metallic abrasion) change the topographic structure of the raceway surfaces: a kind of statistical waviness develops. The deep groove ball bearing from Fig. 2 is free of indentations, since it stems from a test under elastohydrodynamic (EHD) lubrication conditions, and experiences sub-surface rolling contact fatigue. Figure 3 explains the difference of both material response models by distinct courses of the equivalent stress σe (according to v. Mises) below a disturbed and an undisturbed contact between raceway and rolling element.
Fig. 3. Von Mises equivalent stress as a function of the distance from the Hertzian contact (rolling element on a smaller scale). 2a denotes the width of the concerning contact ellipse. According to the maximum distortion energy hypothesis, residual stresses are formed when σe>Rp holds; Rp denotes the yield point.
The profile of the equivalent stress below the undisturbed Hertzian macro contact reaches its maximum, σ emax , in a depth of z0=0.71·a, where a is the small seminaxis of the contact area. Due to overrolling of many Hertzian micro contacts in the disturbed contact, the statistical waviness shifts the equivalent stress maximum to the outermost edge zone and increases its magnitude: the result is surface distress with significantly reduced lifetime.
1-184
XRD VALIDATION OF THE MATERIAL RESPONSE MODELS
In particular cases, the courses of the equivalent stresses illustrated in Fig. 3 can be confirmed by residual stress analyses by means of XRD measurements using the sin2ψ technique (1). Formation of compressive residual stresses below the raceway surface reveals that regions, where the v. Mises equivalent stress exceeds the yield point of the material. The example of surface rolling contact fatigue in Fig. 4 shows the inner ring raceway of a deep grove ball bearing that is densely covered with indentations due to heavy lubricant contamination.
Fig. 4. SEM micrograph (SE image) of the inner ring raceway of a ball bearing from a gearbox test with heavily contaminated lubricant.
The Hertzian micro contacts, which arise by overrolling of these indentations, provide the residual stress profile of Fig. 5 with the maximum of compressive residual stresses in a depth of around 20 µm. Incidentally, this is an example of material ratcheting.
Fig. 5. Residual stress profile below the inner ring raceway of the bearing from Fig. 4.
From the build-up of compressive residual stresses with a maximum in the depth of around 150 µm in Fig. 6, a Hertzian pressure p0 of 3300 MPa at the inner ring contact 1-185
of a gearbox main shaft bearing can be derived. Here, the competing sub-surface fatigue model appears but with much lower failure probability. The reduction of the full width at half maximum (FWHM) of the martensite {211} diffraction line at the end of a steady state stage increases with rising number of revolutions and serves as a basis for the estimation of material aging. Usually, the decrease of the normalized line broadening, b/B, is determined, where b and B denote the FWHM values in the stressed zones and the unstressed region (core), respectively. The corresponding XRD characteristics for the example in Fig. 6 equal b/B ≥ 0.85 for the raceway surface (low uncertainty due to small FWHM pre-reduction by the finishing process) and b/B = 0.75 for the maximum in the depth.
Fig. 6. Depth profiles of residual stresses and {211} α(')-Fe line width below the inner ring raceway of a deep groove ball bearing. TIME-DEPENDENT ALTERATION OF XRD MATERIAL PARAMETERS
Material ratcheting occurs in the upper fatigue strength range and does not develop a steady state in the loaded volume elements even for short times. In the lower fatigue strength range, the XRD material parameters obey a time-dependent alteration scheme proposed by Voskamp (2). Here, a steady state is followed by material softening that is expressed in a decrease of the normalized characteristic line width, b/B. Figures 7 and 8 illustrate this process for the surface and sub-surface failure mode (3, 4). This data stems from rig tests with taper roller and deep groove ball bearings, respectively, and can thus be correlated with statistical parameters of the failure probability distribution, e.g. bearing life related to 10 % failure percentage, L10. For subsurface initiated failure of the ball bearings, L10 falls in the range of advanced material aging that is determined by b/B ≈ 0.64 in the depth of maximum FWHM change below the raceway. The L10 life of the taper roller bearings, in contrast, is correlated with b/B ≈ 0.86, where b is measured on the raceway surface. The calibration diagrams of the XRD lifetime equivalent, b/B, in Figs. 7 and 8 considerably contribute to the estimation of material aging of rolling bearings from field (tests). The method is described as material response analysis, MRA (1, 3, 5).
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Figs. 7, 8. Calibration diagrams for the surface and the sub-surface failure mode. STRENGTH (STRESS) HYPOTHESES FOR ROLLING CONTACT
In the previous sections, the strength hypothesis of maximum distortion energy is implicitly presumed. According to v. Mises, the fictitious equivalent stress for the multiaxial stress state is calculated as follows: σ deh = e
[
1 ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 2
]
(4)
The main normal stresses are, by convention, arranged according to σ1 ≥ σ2 ≥ σ3. Approximately, the criterion of Eq. (4) can also be interpreted by the hypothesis of maximum shear stress. From this approach, the Tresca equivalent stress is derived as follows: τ max =
σ1 − σ 3 2
⇒ σ ssh e = 2 ⋅ τ max = σ1 − σ 3
(5)
The high hydrostatic pressure in the contact area supports this hypothesis. Measured residual stress depth profiles also clearly point to the equivalent stress courses in accordance with the distortion energy. Influence of Friction
An analysis of the influence of friction in rolling-sliding contact shows that this effect presents another possibility to shift the maximum equivalent stress to the surface (6). Moreover, depending upon the value of the friction coefficient, additional sliding movements create tangential stresses. The resulting shift of the equivalent stress depth profile is illustrated in Fig. 9 on the example of the maximum shear stress. The connection to the Tresca equivalent stress is given in Eq. (5). An example is given in Figs. 10 and 11. This rolling bearing rig test is performed with controlled sliding friction portion of around 5 W/mm2 contact area-related power loss. 1-187
Fig. 9. Influence of friction in a rolling-sliding contact on the distance curve of the maximum shear stress.
The measured distance curves of residual stresses and line width below the outer ring raceway after 5·106 revolutions are presented in Fig. 10. The reduction of the normalized line width on the raceway surface equals b/B ≥ 0.78. A moderate build-up of compressive residual stresses ranges up to a depth of around 60 µm.
Fig. 10. Depth profiles of residual stresses and XRD line broadening below the outer ring raceway in the load zone of a cylindrical roller bearing.
The SEM image in Fig. 11 reveals incipient raceway damage. Thus, a surface induced failure is also confirmed in the case of mixed friction (boundary lubrication). The contact area-related power loss triggers tribochemical reactions at material inherent crack sources. Therefore, it provides additional causes of surface induced failure. The rolling bearing rig test under controlled sliding friction results in the formation of compressive residual stresses as shown in Fig. 10. A build-up of residual stresses in the near-surface region below raceways of negligible statistical waviness has repeat1-188
edly been measured on field returns and successfully interpreted as a result of threedimensional vibrations. In most cases, monotonically decreasing distance curves appear, occasionally up to the depth of the maximum of the equivalent stress for the nominal Hertzian pressure.
Fig. 11. SEM micrograph (SE mode) of surface cracking and material removal on the outer ring raceway (load zone) of the rig test bearing from Fig. 10.
According to the maximum shear stress distribution of Fig. 9, monotonically decreasing residual stress profiles are only possible for friction coefficients μ > 0.25. This assumption superficially conflicts with experimentally measured friction coefficients, which are noticeably lower. However, partitioning of the nominal Hertzian contact area into several real contact regions with distinct friction coefficients points out an explanation approach: the measured macroscopic friction coefficient is then a result of averaging based on the Voigt, Reuss or combined rule-of-mixtures. Repeatedly interactions of real contact regions lead to the results of the XRD analyses. This way, nearsurface tensile stresses given by Wuttke for the Hertzian contact with friction can be considered (7), particularly for additional loading by machine vibrations. Formally, a near-surface tensile stress of around 0.5·p0 acts for a friction coefficient μ = 0.3 at the runout of a Hertzian contact (opposite side to the sliding direction). Mixed Fracture Behavior
Precise observations and targeted search through the last two decades have led to the sporadic detection of brittle fracture-like material breaking at raceway surfaces. Structureless separating faces are found that are orientated perpendicular to the surface around inclusions in a depth of about 30 µm. Intercrystalline fractures along former austenite grain boundaries occur. Also, breaking with massive and block martensite structures in the separating faces is detected. These rather rare observations are restricted to small regions of less than 0.1 mm in size, what can be explained by fast transformation of such initially unpassivated areas due to tribochemical reactions. In the scanning electron microscope, material breaking along martensite grain boundaries is detected in connection with carbide films in the outermost edge zones below raceways in metallographic microsections. This finding suggests increasing embrittle-
1-189
ment during rolling contact stressing. The effect on the fracture strength and the idea of the following novel model for surface initiated failure are illustrated in Fig. 12:
Fig. 12. Schematic representation of the surface embrittlement model.
The contribution of brittle fracture is best described by the strength hypothesis of maximum normal stress. Whereas the v. Mises equivalent stress hypothesis according to Eq. (4) is valid for broad regions of the Hertzian contact, the following expression with a friction-dependent parameter κ > 0 thus characterizes the runout more suitably: σ ensh = σ1 = κ (μ ) ⋅ p 0
(6)
The equivalent normal stress scatters due to varying friction conditions. This strength hypothesis is supported by diminishing surface residual stresses in many cases of mixed friction. With increasing embrittlement, the failure initiation shifts towards the surface. The damage mechanism of two camshafts from stationary diesel engines after 5300 and 11800 h of operation at 750 rpm serves as an example of the discussed combined strength hypothesis. Figure 13 summarizes the distance curves of residual stress and line width below the cam race track of a camshaft after 5300 h running time:
Fig. 13. Residual stress and line broadening depth profiles below a cam race track of a camshaft after 5300 h of operation at a rotational speed of 750 rpm.
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According to the line width reduction, most pronounced material aging occurs in an edge zone of less than 20 µm in depth. The relative residual stress minimum in a surface distance of 60 µm is real as it also emerges in the XRD line broadening profile. At areas with gray staining on the cam race tracks of the camshaft with 11800 h running time, axially orientated surface cracks and austenite grain boundary breaking are shown in the SEM micrographs (SE images) of Figs. 14 to 17.
Figs. 14, 15. SEM micrographs (overview and detail) of surface cracks on a cam race track of the camshaft with 11800 h of operation at 750 rpm.
Some plate carbides, which are analyzed in the stains of the gray staining, contain less chromium than the matrix (martensitically induction hardened rolling bearing steel SAE 52100, German denotation 100Cr6). Obviously, these precipitations are formed during operation of the camshaft.
Figs. 16, 17. SEM micrographs of γ grain boundary fractures on a cam race track of the camshaft with 11800 h running time at 750 rpm (detail on the right). SUMMARY AND CONCLUSIONS
Rolling bearings are subjected to a limited lifetime with a Weibull failure probability distribution. Depending on loading and application, the failure causes can be detected on the surface or in a certain depth below the raceway. Spatially resolved X-ray diffraction measurements of the residual stresses and the line widths reveal type and position of stressing as well as the degree of material aging. A 1-191
differentiation between the surface and the sub-surface fatigue model proves itself in practice. Provided the same material aging exists for both models, the surface fatigue model results in a considerably higher failure probability. Apart from contamination of the lubricant, friction also shifts the equivalent stress profile to the surface and leads to cracking and material removal there, as shown in an example. Mixed fracture behavior on raceway surfaces is a consequence of with material aging increasing embrittlement. Thus, for the consideration of tensile stresses, which occur in mixed friction, the modification of the strength hypothesis to the normal stress hypothesis is proposed. REFERENCES
1. Nierlich W, Gegner J: 'Material response analysis of rolling bearings using X-ray diffraction measurements'. 4th Int Congr Materials Week, Munich, Werkstoffwoche-Partnerschaft, CD-ROM ISBN 3-88355-302-6, 2001. 2. Voskamp A P: Microstructural changes during rolling contact fatigue − metal fatigue in the subsurface region of deep groove ball bearing inner rings. Thesis, Delft, Delft University of Technology, 1996. 3. Nierlich W, Voskamp A P, Hengerer F: 'Röntgenographische Werkstoffbeanspruchungsanalyse zur Beurteilung der Ausfallwahrscheinlichkeit von Wälzlagern'. Düsseldorf, VDI-Verlag, VDI-Berichte 1998 (1380) 113-29. 4. Voskamp A P: 'Ermüdung und Werkstoffverhalten im Wälzkontakt'. HTM 1998 53 (1) 25-30. 5. Gegner J: 'Material response analysis and its application to rig tests for the surface failure (Nierlich damage mode) of rolling bearings'. Mater. Sci. and Eng. Technol. 2006 37 (3) 249-59. 6. Broszeit E, Heß F J, Kloos K H: 'Werkstoffanstrengung bei oszillierender Gleitbewegung'. Z. Werkstofftech. 1977 8 (12) 425-32. 7. Wuttke W: Tribophysik − Reibung und Verschleiß von Metallen. München, Hanser Verlag, 1987.
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SKF GmbH, Department of Material Physics Ernst-Sachs-Strasse 5, D-97424 Schweinfurt, Germany 2
University of Siegen, Institute of Material Engineering Paul-Bonatz-Strasse 9-11, D-57068 Siegen, Germany
ABSTRACT Material mechanics theories of rolling contact loading can be reassessed by recording the alteration of characteristics measured from the edge to the core of a stressed surface via X-ray diffraction. Exceeding metallographic investigations, the developments of residual stresses and line width represent the relevant information carrier. It turned out that material changing permits a specific correlation to failure probability distributions. These relationships differ significantly for sub-surface and (near-) surface fatigue. Recent findings from certain bearing applications with higher demands on service life and reliability point to the need for applying different equivalent stress methods for modeling the material response in both types of loading: for classical subsurface overrolling fatigue that is characterized by strengthening and softening processes below the Hertzian contact area, shear stress-based hypotheses are indicated, whereas for the surface failure mode that is accompanied by embrittlement, additionally to these approaches the main normal stress-based hypothesis should be considered. Cyclic tensile stresses caused by friction can act on material-inherent crack sources. In both cases, changes of the X-ray line width, which mainly stem from plastic deformation with rearrangement of the dislocation configuration and martensite decay with carbon diffusion, serve as powerful sensor for material aging. Rig tests under controlled mixed friction conditions give an example of near-surface rolling contact fatigue. INTRODUCTION Material response models result from theoretical and experimental stressing analyses. Calculational approaches determine the pressure in Hertzian contact and the course of equivalent stresses (v. Mises stress, main shear stress, orthogonal shear stress, main normal stress) below the raceway surface and the selection of the strength hypotheses. Analyses of rolling bearings are usually based on four tools: metallography for the purpose of microstructure examinations; scanning electron microscopy and microchemical elemental analysis with the aim of material characterization on a micrometer scale; X-ray diffraction (XRD) measurements of (macro-) residual stresses, line broadening (measure of type-III micro-residual stresses), and retained austenite content directed towards loading analyses; infrared spectroscopy of used lubricants. FAILURE PROBABILITY DISTRIBUTION FUNCTION The most conspicuous reaction to stressing is bearing failure by spalling, as shown in Figs. 1 and 2. The failure probability function is a two-parameter Weibull frequency distribution: 1-182
⎡ ⎛ t ⎞m ⎤ F (t ) = 1 − R(t ) = 1 − exp ⎢− ⎜ ⎟ ⎥ , t ≥ 0 ⎣⎢ ⎝ τ ⎠ ⎦⎥
(1)
Here, F denotes the accumulated failure probability (0 ≤ F 0, F(τ) = 63.2 % holds.
Fig. 1. SEM (scanning electron microscope) micrograph, secondary electron (SE) image, of surface induced V pitting starting from an indentation on the inner ring raceway of a taper rolling bearing (left-hand side, overrolling direction from the left to the right). Fig. 2. SEM micrograph (SE image) of sub-surface induced spalling on the inner ring raceway of a deep grove ball bearing with crack formation in typical depths of 100 to 300 µm (right-hand side, overrolling direction from the left to the right). For m =1, Eq. (1) describes Rutherford's exponential law for radioactive decay (loss rate proportional to the amount present). For failure of rolling bearings, m >1 is valid: mostly, m lies between 1.1 and 2. For known m, τ is by definition determined by the following correlation: F ( L10 ) = 0.1
(2)
Here, L10 stands for the failure or survival probability of 10 and 90 %, respectively. It can be expressed in number of revolutions as follows:
⎛C ⎞ L10 = a DIN × 10 × ⎜ ⎟ ⎝P⎠
p
6
(3)
The coefficient aDIN considers the lubrication and raceway surface conditions. 1-183
Moreover, C and P denote the dynamic load rating and the dynamic equivalent bearing load, respectively expressed in kN. Information on aDIN, C, and P can be taken from the supplier's catalog. The lifetime exponent p equals 3 for ball and 10/3 for roller bearings. Since the coefficient aDIN takes values in a wide range of more than one order of magnitude, the given expressions for the failure probability can be applied to several damage mechanisms with related material response models. FAILURE MODES IN ROLLING CONTACT
It is distinguished empirically between surface initiated failures, where spalling expands from the raceway surface to some depth, and classical rolling contact fatigue spalling by cracks that break out from a certain depth. Typical examples of both cases are shown in Figs. 1 and 2, respectively. Surface rolling contact fatigue with surface induced failure is characteristic of automobile gearbox bearings. Wear debris (metallic abrasion) change the topographic structure of the raceway surfaces: a kind of statistical waviness develops. The deep groove ball bearing from Fig. 2 is free of indentations, since it stems from a test under elastohydrodynamic (EHD) lubrication conditions, and experiences sub-surface rolling contact fatigue. Figure 3 explains the difference of both material response models by distinct courses of the equivalent stress σe (according to v. Mises) below a disturbed and an undisturbed contact between raceway and rolling element.
Fig. 3. Von Mises equivalent stress as a function of the distance from the Hertzian contact (rolling element on a smaller scale). 2a denotes the width of the concerning contact ellipse. According to the maximum distortion energy hypothesis, residual stresses are formed when σe>Rp holds; Rp denotes the yield point.
The profile of the equivalent stress below the undisturbed Hertzian macro contact reaches its maximum, σ emax , in a depth of z0=0.71·a, where a is the small seminaxis of the contact area. Due to overrolling of many Hertzian micro contacts in the disturbed contact, the statistical waviness shifts the equivalent stress maximum to the outermost edge zone and increases its magnitude: the result is surface distress with significantly reduced lifetime.
1-184
XRD VALIDATION OF THE MATERIAL RESPONSE MODELS
In particular cases, the courses of the equivalent stresses illustrated in Fig. 3 can be confirmed by residual stress analyses by means of XRD measurements using the sin2ψ technique (1). Formation of compressive residual stresses below the raceway surface reveals that regions, where the v. Mises equivalent stress exceeds the yield point of the material. The example of surface rolling contact fatigue in Fig. 4 shows the inner ring raceway of a deep grove ball bearing that is densely covered with indentations due to heavy lubricant contamination.
Fig. 4. SEM micrograph (SE image) of the inner ring raceway of a ball bearing from a gearbox test with heavily contaminated lubricant.
The Hertzian micro contacts, which arise by overrolling of these indentations, provide the residual stress profile of Fig. 5 with the maximum of compressive residual stresses in a depth of around 20 µm. Incidentally, this is an example of material ratcheting.
Fig. 5. Residual stress profile below the inner ring raceway of the bearing from Fig. 4.
From the build-up of compressive residual stresses with a maximum in the depth of around 150 µm in Fig. 6, a Hertzian pressure p0 of 3300 MPa at the inner ring contact 1-185
of a gearbox main shaft bearing can be derived. Here, the competing sub-surface fatigue model appears but with much lower failure probability. The reduction of the full width at half maximum (FWHM) of the martensite {211} diffraction line at the end of a steady state stage increases with rising number of revolutions and serves as a basis for the estimation of material aging. Usually, the decrease of the normalized line broadening, b/B, is determined, where b and B denote the FWHM values in the stressed zones and the unstressed region (core), respectively. The corresponding XRD characteristics for the example in Fig. 6 equal b/B ≥ 0.85 for the raceway surface (low uncertainty due to small FWHM pre-reduction by the finishing process) and b/B = 0.75 for the maximum in the depth.
Fig. 6. Depth profiles of residual stresses and {211} α(')-Fe line width below the inner ring raceway of a deep groove ball bearing. TIME-DEPENDENT ALTERATION OF XRD MATERIAL PARAMETERS
Material ratcheting occurs in the upper fatigue strength range and does not develop a steady state in the loaded volume elements even for short times. In the lower fatigue strength range, the XRD material parameters obey a time-dependent alteration scheme proposed by Voskamp (2). Here, a steady state is followed by material softening that is expressed in a decrease of the normalized characteristic line width, b/B. Figures 7 and 8 illustrate this process for the surface and sub-surface failure mode (3, 4). This data stems from rig tests with taper roller and deep groove ball bearings, respectively, and can thus be correlated with statistical parameters of the failure probability distribution, e.g. bearing life related to 10 % failure percentage, L10. For subsurface initiated failure of the ball bearings, L10 falls in the range of advanced material aging that is determined by b/B ≈ 0.64 in the depth of maximum FWHM change below the raceway. The L10 life of the taper roller bearings, in contrast, is correlated with b/B ≈ 0.86, where b is measured on the raceway surface. The calibration diagrams of the XRD lifetime equivalent, b/B, in Figs. 7 and 8 considerably contribute to the estimation of material aging of rolling bearings from field (tests). The method is described as material response analysis, MRA (1, 3, 5).
1-186
Figs. 7, 8. Calibration diagrams for the surface and the sub-surface failure mode. STRENGTH (STRESS) HYPOTHESES FOR ROLLING CONTACT
In the previous sections, the strength hypothesis of maximum distortion energy is implicitly presumed. According to v. Mises, the fictitious equivalent stress for the multiaxial stress state is calculated as follows: σ deh = e
[
1 ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + (σ 3 − σ 1 ) 2 2
]
(4)
The main normal stresses are, by convention, arranged according to σ1 ≥ σ2 ≥ σ3. Approximately, the criterion of Eq. (4) can also be interpreted by the hypothesis of maximum shear stress. From this approach, the Tresca equivalent stress is derived as follows: τ max =
σ1 − σ 3 2
⇒ σ ssh e = 2 ⋅ τ max = σ1 − σ 3
(5)
The high hydrostatic pressure in the contact area supports this hypothesis. Measured residual stress depth profiles also clearly point to the equivalent stress courses in accordance with the distortion energy. Influence of Friction
An analysis of the influence of friction in rolling-sliding contact shows that this effect presents another possibility to shift the maximum equivalent stress to the surface (6). Moreover, depending upon the value of the friction coefficient, additional sliding movements create tangential stresses. The resulting shift of the equivalent stress depth profile is illustrated in Fig. 9 on the example of the maximum shear stress. The connection to the Tresca equivalent stress is given in Eq. (5). An example is given in Figs. 10 and 11. This rolling bearing rig test is performed with controlled sliding friction portion of around 5 W/mm2 contact area-related power loss. 1-187
Fig. 9. Influence of friction in a rolling-sliding contact on the distance curve of the maximum shear stress.
The measured distance curves of residual stresses and line width below the outer ring raceway after 5·106 revolutions are presented in Fig. 10. The reduction of the normalized line width on the raceway surface equals b/B ≥ 0.78. A moderate build-up of compressive residual stresses ranges up to a depth of around 60 µm.
Fig. 10. Depth profiles of residual stresses and XRD line broadening below the outer ring raceway in the load zone of a cylindrical roller bearing.
The SEM image in Fig. 11 reveals incipient raceway damage. Thus, a surface induced failure is also confirmed in the case of mixed friction (boundary lubrication). The contact area-related power loss triggers tribochemical reactions at material inherent crack sources. Therefore, it provides additional causes of surface induced failure. The rolling bearing rig test under controlled sliding friction results in the formation of compressive residual stresses as shown in Fig. 10. A build-up of residual stresses in the near-surface region below raceways of negligible statistical waviness has repeat1-188
edly been measured on field returns and successfully interpreted as a result of threedimensional vibrations. In most cases, monotonically decreasing distance curves appear, occasionally up to the depth of the maximum of the equivalent stress for the nominal Hertzian pressure.
Fig. 11. SEM micrograph (SE mode) of surface cracking and material removal on the outer ring raceway (load zone) of the rig test bearing from Fig. 10.
According to the maximum shear stress distribution of Fig. 9, monotonically decreasing residual stress profiles are only possible for friction coefficients μ > 0.25. This assumption superficially conflicts with experimentally measured friction coefficients, which are noticeably lower. However, partitioning of the nominal Hertzian contact area into several real contact regions with distinct friction coefficients points out an explanation approach: the measured macroscopic friction coefficient is then a result of averaging based on the Voigt, Reuss or combined rule-of-mixtures. Repeatedly interactions of real contact regions lead to the results of the XRD analyses. This way, nearsurface tensile stresses given by Wuttke for the Hertzian contact with friction can be considered (7), particularly for additional loading by machine vibrations. Formally, a near-surface tensile stress of around 0.5·p0 acts for a friction coefficient μ = 0.3 at the runout of a Hertzian contact (opposite side to the sliding direction). Mixed Fracture Behavior
Precise observations and targeted search through the last two decades have led to the sporadic detection of brittle fracture-like material breaking at raceway surfaces. Structureless separating faces are found that are orientated perpendicular to the surface around inclusions in a depth of about 30 µm. Intercrystalline fractures along former austenite grain boundaries occur. Also, breaking with massive and block martensite structures in the separating faces is detected. These rather rare observations are restricted to small regions of less than 0.1 mm in size, what can be explained by fast transformation of such initially unpassivated areas due to tribochemical reactions. In the scanning electron microscope, material breaking along martensite grain boundaries is detected in connection with carbide films in the outermost edge zones below raceways in metallographic microsections. This finding suggests increasing embrittle-
1-189
ment during rolling contact stressing. The effect on the fracture strength and the idea of the following novel model for surface initiated failure are illustrated in Fig. 12:
Fig. 12. Schematic representation of the surface embrittlement model.
The contribution of brittle fracture is best described by the strength hypothesis of maximum normal stress. Whereas the v. Mises equivalent stress hypothesis according to Eq. (4) is valid for broad regions of the Hertzian contact, the following expression with a friction-dependent parameter κ > 0 thus characterizes the runout more suitably: σ ensh = σ1 = κ (μ ) ⋅ p 0
(6)
The equivalent normal stress scatters due to varying friction conditions. This strength hypothesis is supported by diminishing surface residual stresses in many cases of mixed friction. With increasing embrittlement, the failure initiation shifts towards the surface. The damage mechanism of two camshafts from stationary diesel engines after 5300 and 11800 h of operation at 750 rpm serves as an example of the discussed combined strength hypothesis. Figure 13 summarizes the distance curves of residual stress and line width below the cam race track of a camshaft after 5300 h running time:
Fig. 13. Residual stress and line broadening depth profiles below a cam race track of a camshaft after 5300 h of operation at a rotational speed of 750 rpm.
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According to the line width reduction, most pronounced material aging occurs in an edge zone of less than 20 µm in depth. The relative residual stress minimum in a surface distance of 60 µm is real as it also emerges in the XRD line broadening profile. At areas with gray staining on the cam race tracks of the camshaft with 11800 h running time, axially orientated surface cracks and austenite grain boundary breaking are shown in the SEM micrographs (SE images) of Figs. 14 to 17.
Figs. 14, 15. SEM micrographs (overview and detail) of surface cracks on a cam race track of the camshaft with 11800 h of operation at 750 rpm.
Some plate carbides, which are analyzed in the stains of the gray staining, contain less chromium than the matrix (martensitically induction hardened rolling bearing steel SAE 52100, German denotation 100Cr6). Obviously, these precipitations are formed during operation of the camshaft.
Figs. 16, 17. SEM micrographs of γ grain boundary fractures on a cam race track of the camshaft with 11800 h running time at 750 rpm (detail on the right). SUMMARY AND CONCLUSIONS
Rolling bearings are subjected to a limited lifetime with a Weibull failure probability distribution. Depending on loading and application, the failure causes can be detected on the surface or in a certain depth below the raceway. Spatially resolved X-ray diffraction measurements of the residual stresses and the line widths reveal type and position of stressing as well as the degree of material aging. A 1-191
differentiation between the surface and the sub-surface fatigue model proves itself in practice. Provided the same material aging exists for both models, the surface fatigue model results in a considerably higher failure probability. Apart from contamination of the lubricant, friction also shifts the equivalent stress profile to the surface and leads to cracking and material removal there, as shown in an example. Mixed fracture behavior on raceway surfaces is a consequence of with material aging increasing embrittlement. Thus, for the consideration of tensile stresses, which occur in mixed friction, the modification of the strength hypothesis to the normal stress hypothesis is proposed. REFERENCES
1. Nierlich W, Gegner J: 'Material response analysis of rolling bearings using X-ray diffraction measurements'. 4th Int Congr Materials Week, Munich, Werkstoffwoche-Partnerschaft, CD-ROM ISBN 3-88355-302-6, 2001. 2. Voskamp A P: Microstructural changes during rolling contact fatigue − metal fatigue in the subsurface region of deep groove ball bearing inner rings. Thesis, Delft, Delft University of Technology, 1996. 3. Nierlich W, Voskamp A P, Hengerer F: 'Röntgenographische Werkstoffbeanspruchungsanalyse zur Beurteilung der Ausfallwahrscheinlichkeit von Wälzlagern'. Düsseldorf, VDI-Verlag, VDI-Berichte 1998 (1380) 113-29. 4. Voskamp A P: 'Ermüdung und Werkstoffverhalten im Wälzkontakt'. HTM 1998 53 (1) 25-30. 5. Gegner J: 'Material response analysis and its application to rig tests for the surface failure (Nierlich damage mode) of rolling bearings'. Mater. Sci. and Eng. Technol. 2006 37 (3) 249-59. 6. Broszeit E, Heß F J, Kloos K H: 'Werkstoffanstrengung bei oszillierender Gleitbewegung'. Z. Werkstofftech. 1977 8 (12) 425-32. 7. Wuttke W: Tribophysik − Reibung und Verschleiß von Metallen. München, Hanser Verlag, 1987.
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