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Fatigue behaviour of induction hardened notched components
International Journal of Fatigue 21 (1999) 611–617 www.elsevier.com/locate/ijfatigue
Fatigue behaviour of induction hardened notched components L. Bertini a, V. Fontanari a
b,*
Dip. Costruzioni Meccaniche e Nucleari, University of Pisa, Via Diotisalvi 2, 56126 Pisa, Italy b Dip. Ingegneria dei Materiali, University of Trento, Via Mesiano 77, 38050 Trento, Italy
Received 2 December 1998; received in revised form 19 February 1999; accepted 19 February 1999
Abstract In this paper the results of a numerical and experimental study concerning the effect of induction hardening on the fatigue behaviour of mechanical parts is presented. The study was performed on the UNI50CrV4 steel. Rotating bending fatigue tests were carried out in order to obtain the basic fatigue properties, while three point bending tests were carried out on notched specimens in the “as tempered” and in the “induction hardened” condition. Residual stresses produced by the induction hardening were evaluated by means of a numerical-experimental technique, making use of XRD measurements. A finite element model of the notched specimen was set up for the analysis of the stress field acting during fatigue loading; this allowed a prediction of its fatigue behaviour, which appeared to be in satisfactory agreement with experimental observations. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Bending fatigue; Induction hardening; Residual stress; Finite element modelling
1. Introduction Many mechanical parts, such as shafts, gears, springs, etc., are subjected to surface treatments, before the delivering, in order to improve fatigue and wear behaviour. The effectiveness of these treatments depends both on surface materials properties modification and on the introduction of residual stresses. Among these treatments, induction hardening is one of the most widely employed to improve component durability. It determines in the workpiece a tough core with tensile residual stresses and a hard surface layer with compressive stresses, which have proved to be very effective in extending the component fatigue life, being responsible for the delay in the initiation of cracks and, after initiation, for their closure or even arrest [1–3]. The effectiveness of residual stresses is however strictly dependent on their distribution into the component and on their evolution during service. In particular, their distribution is mainly affected by specimen geometry and by treatments parameters, whereas redistribution during
* Corresponding author. Tel.: +39-461-882430; fax: +39-461881977. E-mail address: [email protected] (V. Fontanari)
service is expected to depend principally on plastic strain experienced during the fatigue cycle [1,4–7]. In order to predict fatigue properties, these aspects have to be carefully considered. However, due to difficulties in determining residual stress fields in actual components and to the lack of actual fatigue properties of surface layers, the study and optimisation of induction hardened parts is most frequently carried out experimentally. As a consequence, the validation of a technique capable of predicting on a rational basis the fatigue behaviour of induction hardened components appears very attractive. The aim of the present paper is to study the possibility of predicting fatigue behaviour of simple structural notched components (Brugger specimens) subjected to induction hardening, on the basis of the knowledge of basic fatigue properties and of the residual stress field produced by the surface treatment. The basic characterisation of the material was obtained by carrying out rotating bending tests on an unnotched specimen in two microstructural states, aimed to represent the material of the core, unaffected by the heat treatment, and of the hardened surface layer, respectively. The residual stress analysis was conducted by using the technique proposed in [8] which, on the basis of a
0142-1123/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 9 9 ) 0 0 0 1 9 - 5
612
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Nomenclature ⌬s stress range cycles to failure Nf ⌬s1,2,3 range of principal stress in 1, 2, 3, direction ⌬seq equivalent stress range alternating equivalent stress range ⌬s∗eq sm1,2,3 static component of principal stress in 1, 2, 3, direction equivalent mean stress sm sR rupture strength
few XRD measurements, allowed us to estimate the entire stress distribution acting in the specimen. To this purpose a finite element model of the specimen was set up. This FE model was then employed for the calculation of the effective stress acting during fatigue loading by combining the residual stress field with the stresses produced by external loads. By using the basic properties of the materials, an estimate of the fatigue behaviour of a Brugger specimen was performed and the predictions proved to be in good agreement with experimental results.
2. Experimental characterisation 2.1. Materials and testing procedure The study was carried out on the UNI50CrV4 steel, which is typically used for the production of mechanical parts such as gears. The induction hardening treatment is usually applied to these components in order to improve their resistance to pitting. The nominal chemical composition of the material is reported in Table 1. The material was studied in two different heat treatment conditions: “As Tempered” (AT) and “As quenched and stress relieved” (AQ). In addition, the induction hardening (IH) surface treatment was applied to notched (Brugger) specimens, machined from bars in the AT microstructural state. The AQ microstructure was produced by carefully selecting the treatment parameters [9] in order to reproduce, in plain specimens, a martensitic microstructure with mechanical properties similar to those of the surface layer produced by the IH treat-
ment. Relevant data on the heat treatments are reported in Table 2. The values of hardness for the three different material conditions and the results of tensile tests on AT and AQ materials are summarised in Table 3, whereas the tensile curves for AT and AQ material are compared in Fig. 1, showing for the latter material a remarkable increase in tensile strength, accompanied by a strong reduction of ductility. The basic fatigue characterisation of the AT and AQ materials was performed by means of rotating bending tests using the specimen shown in Fig. 2. The tests were carried out on a Schenk testing machine at a frequency of 30 Hz and were terminated by the complete fracture of the specimen. In addition Three Point Bending (TPB) fatigue tests were performed on Brugger specimen (Fig. 3). This type of specimen is aimed to simulate the stress and strain field typical of gear teeth root. The theoretical stress concentration factor, Kt is equal to 1.56. Some of these specimens were subjected to the surface induction hardening treatment, which was carried out in an industrial plant, by using a specific induction tool and a multi-frequency magnetic field, in order to obtain an optimised profile of the hardened layer in dependence of the notch geometry. The TPB tests were carried out on a Instron hydraulic testing machine, with a stress ratio of R=0.05, a frequency of 30 Hz and a bending span of 60 mm. The tests were interrupted after a detectable increase of the maximum bending deflection (ca. 15%). Both the rotating bending specimens and the Brugger specimens were machined to the same surface roughness (Ra=4.5–5 µm), in order to avoid the use of empirical coefficients for accounting for surface finishing. Following the standard procedure, the Wo¨hler curves were determined for both rotating bending and TPB on the basis of 25–30 tests. In particular, the staircase method [10,11] was employed to derive the fatigue limit, whereas in the finite life region the 50% survival probability curve was obtained by least square fitting the following relationship: ⌬s⫽C·N−1/K . f
(1)
The 10% and 90% survival probability curves were then determined from the estimated regression variance, by assuming a uniform scatter for the whole fatigue curve.
Table 1 Chemical composition of the UNI50CrV4 steel C
Si(max)
Mn
P(max)
S(max)
Cr
0.47/0.55
0.4
0.7/1.1
0.035
0.035
0.9/1.2
Mo
Ni
V
–
–
0.1/0.25
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
613
Table 2 Heat treatment parameters AT
AQ
Austenitization Quenching (oil) Tempering
860°C 80°C 550°C/2 h
IH
Austenitization Quenching (oil) Stress relieving
890°C 80°C 200°C/6 h
Surface austenitization 870°C quenching 80°C Minimum hardened depth 0.8 mm
Table 3 Mechanical properties produced by the heat treatments
HV10 sy0.1 (MPa) UTS (MPa)
AT
AQ
IH
340 800 1200
650 – 1950
680 (surface) – –
Fig. 3.
Fig. 1.
Fig. 2.
330 (core) – –
Brugger specimen for TPB tests.
Tensile stress strain curves.
Rotating bending fatigue specimen (dimensions in mm).
2.2. Characterization of the induction hardened layer On the basis of the microstructural analysis and of the microhardness profiles a martensitic layer having a uniform depth on the specimen wing (ca. 1.3 mm) and a minimum depth at the notch root (ca. 0.7–0.8 mm) was observed. The transition between this layer and the unaffected core occurs over a very narrow region where the effect of high temperature tempering of the initial microstructure can be detected. An example of the hardened profile is shown in Fig. 4. Residual stress profiles were measured by means of
Fig. 4.
Typical profile of the induction hardened layer.
the XRD technique at the notch root and on the specimen wing at half width. The surface layer was progressively removed by electrolitically polishing in order to obtain the stress distribution through the depth. The relaxation and redistribution of residual stress due to surface removal were taken in account by an approximate formula [12]. Measures were conducted up to a depth
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in the surface layer between the martensitic microstructure and the compressive stresses. This aspect and the observed equibiaxiality of the stress field can be considered as a confirmation of the fact that the residual stress field is mainly due to the volume expansion associated with the martensitic transformation [1,2]. 2.3. Results of the fatigue tests Fig. 5.
Schematic drawing of the stress components measured.
greater than the hardened layer (1.1 mm at the notch root and 1.5 mm on the specimen wing). With reference to the scheme of Fig. 5, both the sx (longitudinal) and sz (transversal) stress components were measured on the specimen wing, whereas at notch root it was possible to determine only the sz. As expected [2,3], the two stress components presented comparable values in the wing, so that the stress field can be considered rather equibiaxial. The differences between the sz component at the notch root and on the specimen wing were also found to be rather small (less than 10%). As an example, in Fig. 6, the microhardness and the residual stress profiles determined at notch root are reported. As expected, the residual stress distribution presents a deep compressive peak in the hardened layer, a sharp gradient in the region of transition between the hardened layer and the unaffected core and tensile values below the hardened layer. The microhardness profile is also in agreement with the microstructure variations. The surface layer is constituted by very hard martensite with uniform microstructure, whereas the core maintains the initial tempered martensite microstructure. The high temperature tempering in the region of step transition determines the slightly lower microhardness values with respect to those of the unaffected core. By considering the microhardness and the residual stress profiles a direct correspondence can be observed
Fig. 6. Microhardness and residual stress profiles measured at notch root.
Results of rotating bending fatigue tests are reported in Fig. 7. AT material shows a fatigue limit (475 MPa) lower than that of the AQ material (507 MPa), whereas it exhibits a higher fatigue strength in the finite life region. The small difference in the fatigue limit (nearly 10%) between the two materials, in the presence of a much higher difference (nearly 60%) in the monotonic tensile strength, can be explained by considering the higher sensitivity of the AQ material to surface roughness (Ra=4.5–5 µm) [11,13]. Such higher sensitivity is probably an indication that the propagation of the small cracks whose initiation is favoured by surface roughness is easier in the AQ than in the AT microstructure, with a lower probability for such cracks to be stopped by microstructural barriers or other obstacles in early propagation stages. The results of TPB tests conducted on AT and IH materials are compared in Fig. 8. As can be observed the induction hardening determines a strong increase in the fatigue resistance (about 50% increase in endurance limit). Based on the results of rotating bending tests, this difference could not be explained by considering the microstructural differences only and appeared to be mainly due to the influence of the residual stress field produced by the IH treatment. For the AT material the crack initiation site was located at the notch root, in the corner of the wing. After initiation, the crack propagates as a corner crack, as shown in Fig. 9(a), and reached a few mm in length before the end of the test. For IH material the failure
Fig. 7.
Rotating bending fatigue curves for AQ and AT materials.
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Fig. 8.
615
TPB fatigue curves for IH and AT materials.
site was located on the wing immediately before the notch fillet. After test stop, based on compliance increase, the crack usually spread all over the wing width, with a front nearly parallel to the wing surface and a depth of a few mm (Fig. 9(b)). Unfortunately, due to the extremely fine microstructure, the appearance of the crack surface did not allow us to clearly indicate the initiation site, which could be located either on the surface or at the interface between the IH and the core material.
3. Numerical modelling 3.1. Residual stress analysis The analysis of residual stress distribution was conducted by the technique presented in [8], which is based on assuming that the residual stress field is due to the presence in the body of a hydrostatic initial strain distribution (ISD). This is consistent with the experimental evidence that residual stresses are generated by the volume change due to martensitic transformation. In the present case on the basis of the experimental evidence, it appeared reasonable to assume the ISD varied with normal distance from the IH treated surfaces only. In
Fig. 9.
Fig. 10.
F.E. mesh adopted for the analysis.
order to account for local variability of the IH penetration, as occurring for instance at the notch root, such distance was normalised over the total thickness of the hardened region. Assuming a parametric representation of ISD (in this case a piecewise linear curve was employed) it is possible to derive, by the finite element method (FEM), the influence coefficients giving the contribution of each single parameter to the value of residual stress in specified points. Applying linear superposition and equating to the measured residual stress values, an overdetermined linear system is obtained, having the ISD parameters as unknowns. By solving this system (e.g. by the normal equation method) the ISD can be determined. Imposing this ISD as a loading condition for the FEM model, an estimate of the complete (3D) residual stress field can be achieved. The FE model developed for the calculation is reported in Fig. 10. It was set up by using the Ansys 5.3 code. In order to take advantage of the symmetry, only a quarter of the Brugger specimen was modelled, by
Fracture surfaces: (a) AT material, (b) IH material.
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L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
using eight nodes brick elements. The mesh in the surface region was particularly refined with the purpose of better reproducing the shape and the characteristics of the hardened layer, as detected and measured by metallographic analysis. It is worth noting that due to geometry effects, the hydrostatic ISD produces a stress field which is not hydrostatic but fully triaxial. The comparison between the XRD measurements and predictions obtained by the outlined procedure is reported in Fig. 11, showing a satisfactory agreement (the difference is always within few percent, below the uncertainties of the experimental technique). In the same figure the ISD is also plotted. It is interesting to observe that it assumes, in the IH zone, a mean value of about 2100 µm/m which is quite reasonable from a physical point of view, being a fraction of the volume expansion (⬇4%) due to the phase transformation. Even if further confirmation would surely be required to assess the accuracy of the calculated 3D residual stress field, it appeared reasonable to use it as a basis, in order to predict the fatigue behaviour of the IH Brugger specimen. 3.2. Modelling of the fatigue behaviour For the prediction of the fatigue behaviour for both AT and IH Brugger specimens, taking into account the type of external loading and the substantial invariability of the principal stress directions during fatigue cycle, the Sines approach was employed in order to account for multiaxiality:
冑
⌬seq⫽ (⌬s1−⌬s2)2+(⌬s2−⌬s3)2+(⌬s3−⌬s1)2,
(2)
sm⫽sm1⫹sm2⫹sm3. Moreover, the Gerber criterion [11] was used to account for the mean stress effect:
Fig. 11. Comparison between the experimental and numerical residual stress profiles.
冉 冊
⌬seq sm 2 ⫽1⫺ . ⌬s∗eq sR
(3)
Fatigue behaviour was assumed to be independent from compressive mean stress, as usual for this type of material [11,13]. This was thought to be a reasonable hypothesis in view of the lack of specific results. The analysis of stress/strain distribution due to external loading was conducted by the model reported in Fig. 10. As results indicated that yield strength could be exceeded at the notch root, at least for higher loads, an elasto–plastic analysis based on the kinematic hardening model was conducted. Taking into account the limited extent of plastic deformation, the monotonic true stress and true strain curves were employed. The fatigue curves obtained from rotating bending tests conducted on AQ and AT materials were assumed as reference curves for the hardened surface layer and for the core material of Brugger IH specimens, respectively. The same assumption was made for monotonic properties. The influence of size and surface roughness was not considered, as Brugger and cylindrical specimens were nearly equivalent from these points of view. Notch sensitivity was accounted for by using the approach proposed by Neuber [13], obtaining a value of q=0.90 for the AT material and a value of 0.95 for the IH material. Nearly the same values of q can be obtained by considering the diagram reported in [11]. Fatigue lives corresponding to 90%, 50%, 10% of survival probability were determined on the basis of the scatter band of the rotating bending curves. The resulting curves are compared with the experimental ones in Fig. 12 for AT Brugger specimens, showing a fairly good agreement, which appeared to indicate a satisfactory reproduction of basic material behaviour and of notch effects. In this case failure was predicted to occur at the notch root on the wing corner, in agreement with experimental observations. As regards IH treated specimens, a residual stress field
Fig. 12. Comparison between experimental and numerical fatigue curves determined on a notched specimen for AT material.
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Fig. 13. Comparison between experimental and numerical fatigue curves determined on a notched specimen for IH material.
was firstly applied to the model, followed by external loading. This allowed us to estimate the actual stress cycles experienced by different material zones. The predictions are compared with experimental results in Fig. 13. Once again a quite satisfactory agreement was obtained, which appears encouraging towards the development of tools for a rational prediction of fatigue behaviour of surface treated components. Also in this case, the crack was predicted to nucleate at the notch root. The surface was indicated as the most critical site but the stresses in the subsurface region were estimated to be also very close to the local strength, so that a nucleation of fatigue cracks in this zone must also be considered possible. The analysis was conducted implicitly assuming that the fatigue life of a specimen is dominated by the initiation and early propagation stage, which are both controlled by the local stress state at the notch root, rather than by the macroscopic crack propagation stage. This appeared reasonable, based both on experimental observation and on reduced specimen size, and was substantially confirmed by the rather good agreement of prediction with experimental data. However, for the application to actual structures, the propagation stage should be carefully considered, also including the effects of residual stresses, for instance with the techniques proposed in [14,15].
4. Conclusion An experimental and numerical investigation of the fatigue behaviour of induction hardened components was presented. From the results reported and discussed, the following conclusions can be drawn: 1. the induction hardening treatment confirmed its efficiency in giving a remarkable improvement of
617
fatigue performances; in this case an increase of the fatigue limit by about 50% was observed for notched components; 2. such improvement of fatigue behaviour appears to be mainly produced by the residual stress field which is strongly compressive in the martensitic surface layer; 3. the fatigue properties of the surface layer, estimated by performing a specific heat treatment on plain specimens, did not appear to be significantly different from those of the core material for the present case, probably due to surface roughness effects; 4. the proposed procedure, based on a full-field estimate of the residual stress field and on the characterisation of basic fatigue properties of material in different metallurgical states, proved its capability of satisfactorily predicting the fatigue endurance of notched surface induction hardened components, both as regards finite life and fatigue limits.
References [1] Thelning KE. Steel and its heat treatments. London: Butterworths, 1984. [2] Bello` JM, Fernandez BJ, Lopez V, Ruiz J. Tensiones internas inducidas por temple superficial con laser del acero 50 CrV4. Efecto en el comportamiento frente a la fatiga. Rev Metal Madrid 1992;28(1):3–13. [3] Melander M. Theoretical and experimental study of stationary and progressive induction hardening. Journal of Heat Treating 1985;4(2):145–65. [4] Landgraf RW, Chernenkoff RA. Residual stress effects on fatigue of surface processed steels. ASTM STP 1988;1004:1–12. [5] Dong-Hui X, Zhen-Bang K. A study on the distribution of residual stress due to surface induction hardening. Journal of Engineering Materials and Technology 1996;118:571–5. [6] Kewei X, Naisai H, Huijiu Z. Prediction of notch fatigue limits in a compressive residual stress field. Engineering Fracture Mechanics 1996;54(2):171–6. [7] Kewei X, Jiaven H, Huijiu Z. Effect of residual stress on fatigue behaviour of notches. Fatigue 1994;16(7):337–43. [8] Beghini M, Bertini L. Residual stress modelling by experimental measurements and finite elements analysis. Journal of Strain Analysis 1990;25(2):103–8. [9] Atlas zur Wa¨rmebehandlung der Sta¨hle. Band 4. Du¨sseldorf: Verlag Stahleisen mbh, 1976. [10] Buxbaum O. Betriebfestigkeit, Sichere und wirtschaftliche Bemessung schwingbruchgefaehrdeter Bauteile, 2nd ed. Dusseldorf: Stahleisen mbH, 1992. [11] Collins JA. Failure of materials in mechanical design, 2nd ed. New York: John Wiley and Sons, 1993. [12] Moore MG. SAE Trans 1958;66:340. [13] Dieter GE. Mechanical metallurgy. New York: McGraw-Hill, 1986. [14] Beghini M, Bertini L. Analytical and numerical evaluation of residual stress effects on fatigue crack propagation. In: Computer and experiments in stress analysis. Berlin: Springer Verlag, 1989:187–97. [15] Beghini M, Bertini L, Fontanari V. Fatigue life evaluation by weight functions for orthotropic bridge decks. Theoretical and Applied Fracture Mechanics 1997;28:41–50.
Fatigue behaviour of induction hardened notched components L. Bertini a, V. Fontanari a
b,*
Dip. Costruzioni Meccaniche e Nucleari, University of Pisa, Via Diotisalvi 2, 56126 Pisa, Italy b Dip. Ingegneria dei Materiali, University of Trento, Via Mesiano 77, 38050 Trento, Italy
Received 2 December 1998; received in revised form 19 February 1999; accepted 19 February 1999
Abstract In this paper the results of a numerical and experimental study concerning the effect of induction hardening on the fatigue behaviour of mechanical parts is presented. The study was performed on the UNI50CrV4 steel. Rotating bending fatigue tests were carried out in order to obtain the basic fatigue properties, while three point bending tests were carried out on notched specimens in the “as tempered” and in the “induction hardened” condition. Residual stresses produced by the induction hardening were evaluated by means of a numerical-experimental technique, making use of XRD measurements. A finite element model of the notched specimen was set up for the analysis of the stress field acting during fatigue loading; this allowed a prediction of its fatigue behaviour, which appeared to be in satisfactory agreement with experimental observations. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Bending fatigue; Induction hardening; Residual stress; Finite element modelling
1. Introduction Many mechanical parts, such as shafts, gears, springs, etc., are subjected to surface treatments, before the delivering, in order to improve fatigue and wear behaviour. The effectiveness of these treatments depends both on surface materials properties modification and on the introduction of residual stresses. Among these treatments, induction hardening is one of the most widely employed to improve component durability. It determines in the workpiece a tough core with tensile residual stresses and a hard surface layer with compressive stresses, which have proved to be very effective in extending the component fatigue life, being responsible for the delay in the initiation of cracks and, after initiation, for their closure or even arrest [1–3]. The effectiveness of residual stresses is however strictly dependent on their distribution into the component and on their evolution during service. In particular, their distribution is mainly affected by specimen geometry and by treatments parameters, whereas redistribution during
* Corresponding author. Tel.: +39-461-882430; fax: +39-461881977. E-mail address: [email protected] (V. Fontanari)
service is expected to depend principally on plastic strain experienced during the fatigue cycle [1,4–7]. In order to predict fatigue properties, these aspects have to be carefully considered. However, due to difficulties in determining residual stress fields in actual components and to the lack of actual fatigue properties of surface layers, the study and optimisation of induction hardened parts is most frequently carried out experimentally. As a consequence, the validation of a technique capable of predicting on a rational basis the fatigue behaviour of induction hardened components appears very attractive. The aim of the present paper is to study the possibility of predicting fatigue behaviour of simple structural notched components (Brugger specimens) subjected to induction hardening, on the basis of the knowledge of basic fatigue properties and of the residual stress field produced by the surface treatment. The basic characterisation of the material was obtained by carrying out rotating bending tests on an unnotched specimen in two microstructural states, aimed to represent the material of the core, unaffected by the heat treatment, and of the hardened surface layer, respectively. The residual stress analysis was conducted by using the technique proposed in [8] which, on the basis of a
0142-1123/99/$ - see front matter. 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 9 9 ) 0 0 0 1 9 - 5
612
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Nomenclature ⌬s stress range cycles to failure Nf ⌬s1,2,3 range of principal stress in 1, 2, 3, direction ⌬seq equivalent stress range alternating equivalent stress range ⌬s∗eq sm1,2,3 static component of principal stress in 1, 2, 3, direction equivalent mean stress sm sR rupture strength
few XRD measurements, allowed us to estimate the entire stress distribution acting in the specimen. To this purpose a finite element model of the specimen was set up. This FE model was then employed for the calculation of the effective stress acting during fatigue loading by combining the residual stress field with the stresses produced by external loads. By using the basic properties of the materials, an estimate of the fatigue behaviour of a Brugger specimen was performed and the predictions proved to be in good agreement with experimental results.
2. Experimental characterisation 2.1. Materials and testing procedure The study was carried out on the UNI50CrV4 steel, which is typically used for the production of mechanical parts such as gears. The induction hardening treatment is usually applied to these components in order to improve their resistance to pitting. The nominal chemical composition of the material is reported in Table 1. The material was studied in two different heat treatment conditions: “As Tempered” (AT) and “As quenched and stress relieved” (AQ). In addition, the induction hardening (IH) surface treatment was applied to notched (Brugger) specimens, machined from bars in the AT microstructural state. The AQ microstructure was produced by carefully selecting the treatment parameters [9] in order to reproduce, in plain specimens, a martensitic microstructure with mechanical properties similar to those of the surface layer produced by the IH treat-
ment. Relevant data on the heat treatments are reported in Table 2. The values of hardness for the three different material conditions and the results of tensile tests on AT and AQ materials are summarised in Table 3, whereas the tensile curves for AT and AQ material are compared in Fig. 1, showing for the latter material a remarkable increase in tensile strength, accompanied by a strong reduction of ductility. The basic fatigue characterisation of the AT and AQ materials was performed by means of rotating bending tests using the specimen shown in Fig. 2. The tests were carried out on a Schenk testing machine at a frequency of 30 Hz and were terminated by the complete fracture of the specimen. In addition Three Point Bending (TPB) fatigue tests were performed on Brugger specimen (Fig. 3). This type of specimen is aimed to simulate the stress and strain field typical of gear teeth root. The theoretical stress concentration factor, Kt is equal to 1.56. Some of these specimens were subjected to the surface induction hardening treatment, which was carried out in an industrial plant, by using a specific induction tool and a multi-frequency magnetic field, in order to obtain an optimised profile of the hardened layer in dependence of the notch geometry. The TPB tests were carried out on a Instron hydraulic testing machine, with a stress ratio of R=0.05, a frequency of 30 Hz and a bending span of 60 mm. The tests were interrupted after a detectable increase of the maximum bending deflection (ca. 15%). Both the rotating bending specimens and the Brugger specimens were machined to the same surface roughness (Ra=4.5–5 µm), in order to avoid the use of empirical coefficients for accounting for surface finishing. Following the standard procedure, the Wo¨hler curves were determined for both rotating bending and TPB on the basis of 25–30 tests. In particular, the staircase method [10,11] was employed to derive the fatigue limit, whereas in the finite life region the 50% survival probability curve was obtained by least square fitting the following relationship: ⌬s⫽C·N−1/K . f
(1)
The 10% and 90% survival probability curves were then determined from the estimated regression variance, by assuming a uniform scatter for the whole fatigue curve.
Table 1 Chemical composition of the UNI50CrV4 steel C
Si(max)
Mn
P(max)
S(max)
Cr
0.47/0.55
0.4
0.7/1.1
0.035
0.035
0.9/1.2
Mo
Ni
V
–
–
0.1/0.25
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
613
Table 2 Heat treatment parameters AT
AQ
Austenitization Quenching (oil) Tempering
860°C 80°C 550°C/2 h
IH
Austenitization Quenching (oil) Stress relieving
890°C 80°C 200°C/6 h
Surface austenitization 870°C quenching 80°C Minimum hardened depth 0.8 mm
Table 3 Mechanical properties produced by the heat treatments
HV10 sy0.1 (MPa) UTS (MPa)
AT
AQ
IH
340 800 1200
650 – 1950
680 (surface) – –
Fig. 3.
Fig. 1.
Fig. 2.
330 (core) – –
Brugger specimen for TPB tests.
Tensile stress strain curves.
Rotating bending fatigue specimen (dimensions in mm).
2.2. Characterization of the induction hardened layer On the basis of the microstructural analysis and of the microhardness profiles a martensitic layer having a uniform depth on the specimen wing (ca. 1.3 mm) and a minimum depth at the notch root (ca. 0.7–0.8 mm) was observed. The transition between this layer and the unaffected core occurs over a very narrow region where the effect of high temperature tempering of the initial microstructure can be detected. An example of the hardened profile is shown in Fig. 4. Residual stress profiles were measured by means of
Fig. 4.
Typical profile of the induction hardened layer.
the XRD technique at the notch root and on the specimen wing at half width. The surface layer was progressively removed by electrolitically polishing in order to obtain the stress distribution through the depth. The relaxation and redistribution of residual stress due to surface removal were taken in account by an approximate formula [12]. Measures were conducted up to a depth
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L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
in the surface layer between the martensitic microstructure and the compressive stresses. This aspect and the observed equibiaxiality of the stress field can be considered as a confirmation of the fact that the residual stress field is mainly due to the volume expansion associated with the martensitic transformation [1,2]. 2.3. Results of the fatigue tests Fig. 5.
Schematic drawing of the stress components measured.
greater than the hardened layer (1.1 mm at the notch root and 1.5 mm on the specimen wing). With reference to the scheme of Fig. 5, both the sx (longitudinal) and sz (transversal) stress components were measured on the specimen wing, whereas at notch root it was possible to determine only the sz. As expected [2,3], the two stress components presented comparable values in the wing, so that the stress field can be considered rather equibiaxial. The differences between the sz component at the notch root and on the specimen wing were also found to be rather small (less than 10%). As an example, in Fig. 6, the microhardness and the residual stress profiles determined at notch root are reported. As expected, the residual stress distribution presents a deep compressive peak in the hardened layer, a sharp gradient in the region of transition between the hardened layer and the unaffected core and tensile values below the hardened layer. The microhardness profile is also in agreement with the microstructure variations. The surface layer is constituted by very hard martensite with uniform microstructure, whereas the core maintains the initial tempered martensite microstructure. The high temperature tempering in the region of step transition determines the slightly lower microhardness values with respect to those of the unaffected core. By considering the microhardness and the residual stress profiles a direct correspondence can be observed
Fig. 6. Microhardness and residual stress profiles measured at notch root.
Results of rotating bending fatigue tests are reported in Fig. 7. AT material shows a fatigue limit (475 MPa) lower than that of the AQ material (507 MPa), whereas it exhibits a higher fatigue strength in the finite life region. The small difference in the fatigue limit (nearly 10%) between the two materials, in the presence of a much higher difference (nearly 60%) in the monotonic tensile strength, can be explained by considering the higher sensitivity of the AQ material to surface roughness (Ra=4.5–5 µm) [11,13]. Such higher sensitivity is probably an indication that the propagation of the small cracks whose initiation is favoured by surface roughness is easier in the AQ than in the AT microstructure, with a lower probability for such cracks to be stopped by microstructural barriers or other obstacles in early propagation stages. The results of TPB tests conducted on AT and IH materials are compared in Fig. 8. As can be observed the induction hardening determines a strong increase in the fatigue resistance (about 50% increase in endurance limit). Based on the results of rotating bending tests, this difference could not be explained by considering the microstructural differences only and appeared to be mainly due to the influence of the residual stress field produced by the IH treatment. For the AT material the crack initiation site was located at the notch root, in the corner of the wing. After initiation, the crack propagates as a corner crack, as shown in Fig. 9(a), and reached a few mm in length before the end of the test. For IH material the failure
Fig. 7.
Rotating bending fatigue curves for AQ and AT materials.
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Fig. 8.
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TPB fatigue curves for IH and AT materials.
site was located on the wing immediately before the notch fillet. After test stop, based on compliance increase, the crack usually spread all over the wing width, with a front nearly parallel to the wing surface and a depth of a few mm (Fig. 9(b)). Unfortunately, due to the extremely fine microstructure, the appearance of the crack surface did not allow us to clearly indicate the initiation site, which could be located either on the surface or at the interface between the IH and the core material.
3. Numerical modelling 3.1. Residual stress analysis The analysis of residual stress distribution was conducted by the technique presented in [8], which is based on assuming that the residual stress field is due to the presence in the body of a hydrostatic initial strain distribution (ISD). This is consistent with the experimental evidence that residual stresses are generated by the volume change due to martensitic transformation. In the present case on the basis of the experimental evidence, it appeared reasonable to assume the ISD varied with normal distance from the IH treated surfaces only. In
Fig. 9.
Fig. 10.
F.E. mesh adopted for the analysis.
order to account for local variability of the IH penetration, as occurring for instance at the notch root, such distance was normalised over the total thickness of the hardened region. Assuming a parametric representation of ISD (in this case a piecewise linear curve was employed) it is possible to derive, by the finite element method (FEM), the influence coefficients giving the contribution of each single parameter to the value of residual stress in specified points. Applying linear superposition and equating to the measured residual stress values, an overdetermined linear system is obtained, having the ISD parameters as unknowns. By solving this system (e.g. by the normal equation method) the ISD can be determined. Imposing this ISD as a loading condition for the FEM model, an estimate of the complete (3D) residual stress field can be achieved. The FE model developed for the calculation is reported in Fig. 10. It was set up by using the Ansys 5.3 code. In order to take advantage of the symmetry, only a quarter of the Brugger specimen was modelled, by
Fracture surfaces: (a) AT material, (b) IH material.
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using eight nodes brick elements. The mesh in the surface region was particularly refined with the purpose of better reproducing the shape and the characteristics of the hardened layer, as detected and measured by metallographic analysis. It is worth noting that due to geometry effects, the hydrostatic ISD produces a stress field which is not hydrostatic but fully triaxial. The comparison between the XRD measurements and predictions obtained by the outlined procedure is reported in Fig. 11, showing a satisfactory agreement (the difference is always within few percent, below the uncertainties of the experimental technique). In the same figure the ISD is also plotted. It is interesting to observe that it assumes, in the IH zone, a mean value of about 2100 µm/m which is quite reasonable from a physical point of view, being a fraction of the volume expansion (⬇4%) due to the phase transformation. Even if further confirmation would surely be required to assess the accuracy of the calculated 3D residual stress field, it appeared reasonable to use it as a basis, in order to predict the fatigue behaviour of the IH Brugger specimen. 3.2. Modelling of the fatigue behaviour For the prediction of the fatigue behaviour for both AT and IH Brugger specimens, taking into account the type of external loading and the substantial invariability of the principal stress directions during fatigue cycle, the Sines approach was employed in order to account for multiaxiality:
冑
⌬seq⫽ (⌬s1−⌬s2)2+(⌬s2−⌬s3)2+(⌬s3−⌬s1)2,
(2)
sm⫽sm1⫹sm2⫹sm3. Moreover, the Gerber criterion [11] was used to account for the mean stress effect:
Fig. 11. Comparison between the experimental and numerical residual stress profiles.
冉 冊
⌬seq sm 2 ⫽1⫺ . ⌬s∗eq sR
(3)
Fatigue behaviour was assumed to be independent from compressive mean stress, as usual for this type of material [11,13]. This was thought to be a reasonable hypothesis in view of the lack of specific results. The analysis of stress/strain distribution due to external loading was conducted by the model reported in Fig. 10. As results indicated that yield strength could be exceeded at the notch root, at least for higher loads, an elasto–plastic analysis based on the kinematic hardening model was conducted. Taking into account the limited extent of plastic deformation, the monotonic true stress and true strain curves were employed. The fatigue curves obtained from rotating bending tests conducted on AQ and AT materials were assumed as reference curves for the hardened surface layer and for the core material of Brugger IH specimens, respectively. The same assumption was made for monotonic properties. The influence of size and surface roughness was not considered, as Brugger and cylindrical specimens were nearly equivalent from these points of view. Notch sensitivity was accounted for by using the approach proposed by Neuber [13], obtaining a value of q=0.90 for the AT material and a value of 0.95 for the IH material. Nearly the same values of q can be obtained by considering the diagram reported in [11]. Fatigue lives corresponding to 90%, 50%, 10% of survival probability were determined on the basis of the scatter band of the rotating bending curves. The resulting curves are compared with the experimental ones in Fig. 12 for AT Brugger specimens, showing a fairly good agreement, which appeared to indicate a satisfactory reproduction of basic material behaviour and of notch effects. In this case failure was predicted to occur at the notch root on the wing corner, in agreement with experimental observations. As regards IH treated specimens, a residual stress field
Fig. 12. Comparison between experimental and numerical fatigue curves determined on a notched specimen for AT material.
L. Bertini, V. Fontanari / International Journal of Fatigue 21 (1999) 611–617
Fig. 13. Comparison between experimental and numerical fatigue curves determined on a notched specimen for IH material.
was firstly applied to the model, followed by external loading. This allowed us to estimate the actual stress cycles experienced by different material zones. The predictions are compared with experimental results in Fig. 13. Once again a quite satisfactory agreement was obtained, which appears encouraging towards the development of tools for a rational prediction of fatigue behaviour of surface treated components. Also in this case, the crack was predicted to nucleate at the notch root. The surface was indicated as the most critical site but the stresses in the subsurface region were estimated to be also very close to the local strength, so that a nucleation of fatigue cracks in this zone must also be considered possible. The analysis was conducted implicitly assuming that the fatigue life of a specimen is dominated by the initiation and early propagation stage, which are both controlled by the local stress state at the notch root, rather than by the macroscopic crack propagation stage. This appeared reasonable, based both on experimental observation and on reduced specimen size, and was substantially confirmed by the rather good agreement of prediction with experimental data. However, for the application to actual structures, the propagation stage should be carefully considered, also including the effects of residual stresses, for instance with the techniques proposed in [14,15].
4. Conclusion An experimental and numerical investigation of the fatigue behaviour of induction hardened components was presented. From the results reported and discussed, the following conclusions can be drawn: 1. the induction hardening treatment confirmed its efficiency in giving a remarkable improvement of
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fatigue performances; in this case an increase of the fatigue limit by about 50% was observed for notched components; 2. such improvement of fatigue behaviour appears to be mainly produced by the residual stress field which is strongly compressive in the martensitic surface layer; 3. the fatigue properties of the surface layer, estimated by performing a specific heat treatment on plain specimens, did not appear to be significantly different from those of the core material for the present case, probably due to surface roughness effects; 4. the proposed procedure, based on a full-field estimate of the residual stress field and on the characterisation of basic fatigue properties of material in different metallurgical states, proved its capability of satisfactorily predicting the fatigue endurance of notched surface induction hardened components, both as regards finite life and fatigue limits.
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