RESIDUAL STRESSES AND DISTORTION SIMULATION OF NITRIDED DISC

Laurent Barrallier1, Vincent Goret1, Patrick Vardon2, Dominique Deloison3

1MecaSurf Laboratory, Arts et Metiers ParisTech, Aix en Provence, France 2Eurocopter, Marignane, France

3EADS Innovation Works, Suresnes, France

ABSTRACT

Nitriding is a thermochemical treatment that can be used to increase fatigue life of highly loaded mechanical steel parts. The combination of hardening effect and residual stress generation allows explaining the performance treatment. Precipitation phenomena can be linked to the stress and hardening generation. In order to optimize the design of part, modeling of nitriding has been developed using a finite-element approach. The local geometry of workpiece and its influence on the nitrogen diffusion have been taken into account. Volume variation due to the precipitation has been calculated using thermodynamical calculation coupled with diffusion simulation of nitrogen and carbon. Finally, this approach has allowed the determination of the residual stress field using a micromechanic approach embedded within the finite element model. The deformations generated during nitriding have also been determined. The modeling has been applied to simple disc geometry where only one side has been nitrided. The simulation has been compared to the experiments by measurement of disc deflection and stress analysis using X-rays diffraction and material removal method in order to derive stress in iron phase and macroscopic stress respectively.

INTRODUCTION

Steel parts are generally nitrided in order to increase surface properties (wear, friction) or fatigue life. Gas nitriding is the most developed treatment for improving fatigue property of highly loaded mechanical parts such as gears or shafts (aeronautic, automotive competition�).

Improvement can be obtained through the modification of the hardness of nitrided layers (generally more than two times harder than material core), but also through the modification of the generated residual stresses [1][2][3]. In fact, tensile stresses are generally lowered by the nitriding compressive stresses, resulting in an increased number of cycles to failure. The improvement of high loaded part design process requires a good knowledge of nitriding and in particular the stress generation in order to predict:

The part fatigue life by the residual stress field knowledge, The part deformation to optimize grinding, which is the last machining operation.

Simulation of this treatment and its integration in finite element (FE) modeling can be one way to reach this approach.

Nitriding is a thermochemical treatment where nitrogen atoms diffuse in metal at temperature during a given time. In gas nitriding, atoms of nitrogen are produced by dissociation of ammonic gas. Steel grades are specially developed using chromium and aluminum as major alloying elements in addition of a small amount of other elements such as vanadium and molybdenum [4]. Steel composition was chosen in order to have nitride precipitation that is responsible of

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Advances in X-ray Analysis, Volume 52

increased hardness in the nitriding layers. Microstructure of steel nitrided layer is presented in figure 1 for 32CrMoV13 tempered french steel grade nitrided at 560°C during 120 h [5]. Compound layer with Fe2-3N and Fe4N nitrides is observed. In the diffusion layer, the transformation of base material M23C6 alloyed carbide results in the formation of M3C alloyed cementite at the ferrite grain boundaries and in the intragranular precipitation of (Cr,Fe)N alloyed nitride [6][7][8][9]. Residual stress during the treatment have been clearly linked to precipitation phenomena and volume change induced. More explanations can be found in Jegou et al. paper [10]. a)

b) c) d) e) Fig. 1: Microstructure of nitrided layer. a) Complete cross section, b) Compound layer with Fe2-3N and Fe4N nitrided, c) Alloyed cementite at grain boundary in diffusion layer (section parallel to the surface), d) Submicroscopical (Fe,Cr)N nitride precipitate in place of prior M23C6 carbide, e) Alloyed M23C6 intra and inter martensite lattes carbides in base material.

MODELING

Scale transition model

The modeling of nitriding is based on simultaneous diffusion / precipitation approach using thermodynamic database and calculations. 1D Fick equation has been solved using finite difference method in relation with precipitation or dissolution phenomena observed in nitrided layers [3]. Finally in-depth concentration of carbon and nitrogen can be calculated with the corresponding amount of precipitates formed during the treatment. Temperature and time were fixed to experimental value. This model also takes into account the value of nitrogen dissociation. With the phase mass fraction profile, it is possible to calculate at each depth the volume variation using the self-consistent scheme, which is based on mass conservation and non-diffusion of heavy elements. Using Kröner-Elsheby modeling in elastoplasticity with two mechanical

463Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52

constituents (ferrite with elastoplastic behavior and precipitates with elastic behavior), micro- and macro- residual stress state can be calculated. With this approach, it is possible to take into account volume fraction, shape, and mechanical behavior of the different phases. This modeling was implemented in FE code in order to take into account the local shape of modeled parts.

FE model

The main objective is to have a good description of the needed multiscale approach. Residual stress generation is due to precipitation phenomena that occur at nanometric scale. Using self-consistent approach it is possible to reach the grains scale (about micrometric scale). With the FE software used, the scale of part can be correctly described with a good mesh. Model implementation was performed in Abaqus� FE software using Anaqus� subroutines (UMAT,

UEXPAN) and PYTHON script. Flow chart is given at figure 2.a. UEXPAN subroutine is chosen to calculate volume change in each cell using the amount of phase and the local chemical composition. UMAT is used to perform the self-consistent calculation to determine plastic deformation of ferrite and elastic properties in each cell. Finally micro (in the ferrite and precipitate constituents) and macro residual stresses can be calculated. In fact, 1D simulation is used to calculate in-depth carbon and nitrogen composition profiles which are transposed on the mesh of FE model. With PYTHON script it was possible to perform a convergence test in order to minimize the difference between the local stress in ferrite calculated using micro-macro model and FE model by increasing volume loading as shown figure 2.b.

a) b)

Fig. 2: a) Flow chart of modeling, b) Test on the constitutive law of ferrite.

With FE modeling 3D residual stress tensor can be calculated close to the edge of one face nitrided thin disc for example. Figure 3.a shows the mesh used for this calculation. Regular meshing was used with a refinement close to the surface. Cell size cannot be chosen smaller than the grain size (20 µm) to make sense. Calculation was performed using 2D axisymmetric description of disc. For this type of application the number of degree of freedom is about 70 000 and the calculus time is about 24 hours using a rather old computer (Compaq Dec-Alpha). Figure 3.b gives macroscopical stress state along a line parallel to the sample surface at 20 µm below the

surface (C line). It clearly shows that it is a biaxial stress state far to the edge (11=22,

464Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52

33=12=0). Close to the edge, stress state changes from 2D to 3D with 33 and 12 components. At the edge, limit condition 11=0 is verified. Edge effect is observed at more than 4 mm from the lateral border of the disc. This type of result can be very interesting for real parts where small unnitrided holes were machined (after nitriding) for example. In this case von Mises stress varies from 550 MPa far to the edge to 350 MPa at the edge, this variation will affect local fatigue life of material.

a) b)

Fig. 3: a) Mesh and coordinates used for FE modeling, b) Border effect on macroscopic residual stresses.

EXPERIMENTAL

Deflection method

Macroscopic residual stress generated by nitriding treatment has been determined using a deflection method based on the removal of material and the measure of curvature radius. To perform this approach we assume that stress state is axisymmetric and the stress gradient negligible in the removal depth. Specimens used are 200 mm diameter by 5.9 mm thickness thin discs from 32CrMoV13 french grade steel. Only one face of the disc has been gas nitrided at 560°C during 120 h, the others faces have been protected by a copper coating. Material removal was performed using chemical machining and the removal step was varied from 100 µm to

150 µm. For each depth analysed, material removal was performed on a different disc and

measurement was performed using a 3D device. The disc radius was determined with least square method for 220 measured points by sphere fitting.

X-ray diffraction

Residual stress in ferrite has been determined using X-ray diffraction method with Siemens D500 device. Table 1 gives the parameters used for this calculation performed with sin2

method, in-depth at the center on the disc. Material removal was performed using chemical machining. Due to the size of the disc, stress relieve is negligible. Multiphase aspect of nitrided layers and

3

21

465Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52

axisymmetry of stress tensor implicate that only 11-33 stress can be calculated in ferrite. Stress state in another phase cannot be reached with laboratory X-ray diffraction device due to the small amount of the volume fraction (<5 %).

Parameters Diffracting

planes Radiation

Irradiate area angles

½ S2hkl

(TPa-1) Time Mounting

Peak fitting

Iron {211} Cr-K 3 mm 9 from -41.4°

to 45° 5.061 30 s by

peak Pseudo-voigt 2

Tab. 1: X-ray diffraction parameters used to determine residual stress profile in nitrided disc.

RESULTS AND DISCUSSION

FE modeling is performed using the same approach and parameters used previously. The thin disc calculated curvature is compared to the one measured from non-chemically machined disc. A good agreement is found about 3 m radius. Figure 4.a shows the evolution of measured curvature radius as function of material removal. When the whole nitrided layer (i.e. the source of residual stress) is removed at approximately 0.8 mm below the top surface, the evolution of radius stopped corresponding to a flat thin disc (8 m radius due to the measurement error). Using deflexion method, macroscopic stress can be calculated and plotted in figure 4.b. Nitriding depth is found about 1 mm as shown in optical micrograph. FE calculation is also plotted on the same graph. A good agreement is found for the value of maximum compressive residual stress ( 700 MPa). Stress close to the surface and affected depth are not well calculated probably due to diffusion/precipitation approximation made in 1D modeling. Improvement of this part will be performed.

a) b) Fig. 4: a) Curvature radius vs. matter removal, comparison with FE modeling (@ the surface), b)

Macroscopic stress using deflection method and FE modeling.

466Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52

Calculated residual stress in ferrite (local) using FE method can be compared to X-ray diffraction determination. In fact, due to the multiphase system only 11

33

in the ferrite ( superscript for ferrite) can be evaluated using X-ray diffraction and compared to FE calculus. Only � 33 macro-stress (hat for macro) can be equal to none in depth (non lateral gradient assumption). Figure 5.a shows ferrite residual stress profile. Level of maximum compressive stress is in good agreement between measure and modeling. Volume fraction of precipitation is about 5-10 % in the nitrided layer, with these values maximum of compressive stresses can be estimated equal to 5-10 times compressive macro stress. For the same previous reasons the stress close to the surface and the affected depth are different. In figure 5.b is possible to have an idea of the difference between macro (FE calculated) and micro (in ferrite X-ray determined) stress state. The maximum of compressive stress is approximately twice more important for macroscopic stress than microscopic stress.

Fig. 5: Residual stress in ferrite ( 11-33) determined using X-ray diffraction and calculated with FE modeling, c) Comparison of micro (in ferrite) and macro residual stress.

CONCLUSION

Using physical approach of nitriding, it is possible to model this thermochemical treatment by using multiscale approach based on self-consistent scheme and finite element modeling. Residual stress generated by nitriding can be calculated considering macro or micro scales. Simulation results have been compared to experiment using deflection method for macro-stress determination and X-ray diffraction for micro-stress determination. With this approach distortion and residual stress of simple part (thin disc) have been calculated. This result is enough important to underline it because macro-stress is directly responsible of part distortion. Generally stress analysis used X-ray diffraction technique to evaluate stress profile of treated part. In the case of nitriding treatment X-ray stress (micro) are not equal to macro stress. For fatigue life this aspect

467Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52

is really important. This consideration can be extended for another surface treatment with multiphase materials.

ACKNOWNLEDGEMENT

The first author wishes to thank EADS Innovation Works, Suresnes and Eurocopter, Marignane for supporting this work and PhD thesis of Vincent.

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[5] V. Goret � Modélisation de la nitruration : prise en compte de la géométrie des pièces

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[6] J.-N. Locquet � Caractérisation métallurgique et mécanique des couches nitrurées, relation

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[8] J.-N. Locquet, L. Barrallier � X-ray end SEM investigations of precipitates in nitrided layers. Application to chromium-alloyed steels. ECRS 4, Cluny, France, June 1996.

[9] C. Ginter, L. Torchane, J. Dulcy, M. Gantois, A. Malchère, C. Esnouf, T. Turpin � A new approach to hardening mechanisms in the diffusion layer of gas nitrided alpha-alloyed steels. Effects of chromium and aluminium: experimental and simulation studies. La metallurgia italiana, 7-8, pp.29-35, 2006.

[10] S. Jegou, R. Kubler, L. Barrallier, F. Roch � Phase tranformation involving residual stresses during gaz nitrided of steel. ICRS 8, Denver, USA, Aug. 2008.

468Copyright ©JCPDS-International Centre for Diffraction Data 2009 ISSN 1097-0002Advances in X-ray Analysis, Volume 52