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MODELISATION OF THE THERMOMECHANICAL BEHAVIOUR OF A 12Cr-0.1C PTA COATINGK.NECIB ; M.A. Belouchrani ; A. BRITAH
Laboratoire Gיnie des Matיriaux,
Bp 17, Bordj-El-Bahri - Algיrie,
Tיl. : (2132) 86.34.69 / (2132) 42.67.53
Fax : (2132) 86.32.04
The purpose of this work is, firstly, to evaluate by x-rays and neutronic diffractions the residual stresses in the coating and its substrate after thermal fatigue cycling in the range (500-20°C) comparatively with those evaluated at the initial state. Secondly, the cyclic mechanical behaviour of the coating material in the range (20-500°C) is described according to the selected viscoplastic behaviour law which parameters were identified by means of a systematic numerical procedure (a computer program of simulation and identification). A correlation between the residual stresses values and the stress levels reached during the mechanical tests is established according to the microstructure of the coating material.
Keywords : Plasma Semi-Transferred Process - Stainless Steel Coating - Residual Stresses - X Rays and Neutronic Diffractions - Cyclic Mechanical Behaviour - Viscoplastic Model.
The deterioration of the rolling mill cylinders can be attributed to many factors : mechanical contacts, corrosion, abrasion and also thermal cycling. To protect the surface of these tools against the different modes of degradation, the use of coatings materials is required. Generally, materials such as stainless steels, nickel or cobalt base alloys, are used for their sufficient mechanical strength especially, at high temperature.
The principal techniques for the deposition of surface coatings are combustion flame, arc wire, high velocity combustion and plasma spraying . Among them the Plasma semi-Transferred Arc (PTA) process is nowadays developing as it generally implies low operating costs associated with an improved efficiency, a low porosity rate and a low dilution percentage of the substrate . However, this depositioning process can induce the presence of an important residual stresses field which can play an important part in the thermal fatigue behaviour. Therefore the evaluation of these residual stresses is of fundamental interest for the assessment of the coating process.
In this work we have focused our attention, firstly, on the evaluation by x-rays and neutronic diffractions of the residual stresses in the coating and its substrate after thermal fatigue cycling in the range (500-20°C) comparatively with those evaluated at the initial state. Secondly, the cyclic mechanical behaviour of the coating material is studied in the range (20-500°C) according to the selected viscoplastic behaviour law which parameters were identified by means of a systematic numerical procedure.
The material investigated in this work is a martensitic stainless steel coating, (named Z10C12 according to the french standard ; AISI 408 according to the American standard), deposited by a PTA process on a ferritic steel. Its chemical composition is reported in Table 1. According to this composition the coating could be classified as belonging to the class II of the "Super12%Cr Steels" .
|Table 1: Chemical composition of the ZI0C12 stainless steel coating (%wt)|
The physical metallurgy of the 12Cr type alloys have been reviewed . However, for most of these studies, the alloys have been thermally treated beforehand (austinizing at 1100°C for 1h followed by air cooling to room temperature and tempering at 500°C) [5-6].
The existence of a microstructural transformation from a martensite to a ferrite substructure has been established; this evolution was confirmed by the changes observed in hardness from 500Hv before tempering, to about 360Hv after tempering at 500°C [7-8].
These authors concluded that the decrease in hardness according to the tempering time or temperature could be due to a combination of precipitate coarsening and cell rearrangement of the lath structure. In the present investigation, the martensite stainless steel coating was not tempered before the tests.
Thermal Fatigue Tests Experimental Tests Numerical Simulation
A cylinder of 25CD4 steel coated with 2mm thickness of the Z10C12 alloy is chosen in order to simulate rolling mill cylinders. The cylinder is high frequency heated with a “pancake” inductor type and cooled with a compressed air system on its surface and a lengthwise water circulation inside of it ; its rotation rate is 1.1 R.P.M. An experimental temperature map has been constructed using an infra-red pyrometer for surface measurements and thermocouples for thickness temperature measurements (fig.1). The temperature measurement values are established to agree the industry measurements.
Fig 1: View of the thermal fatigue simulator.
For this study, two codes were used : the first one (ZיBuLoN) is a Finite Elements code with a number of plastic and viscoplastic constitutive equations  ; the second one is SiDoLo . The two codes are linked by means of a numerical interface. The stationary temperature map is known in some points on the surface of the cylinder (simulator) and inside of it. The identification problem is formulated by comparison between these data and the temperature and the temperature predicted in the same location by a thermal finite element calculation. The thermal exchanges between the component and water or air involve convection heat transfer coefficients hi ; these coefficients would be identified by the numerical optimisation, after their reading and transferring by the numerical interface; the same procedure is used for the induced heat parameter qvi (fig.2). Then, the anisothermal mechanical behaviour of the structure is calculated using the thermal optimised loading of the cylinder and the viscoplastic behaviour law; the parameter values are linearly interpolated as a function of the temperature.
Fig 2: Application zones of thermal flow.
Neutron Diffraction Analysis
Neutron diffraction experiments were carried out on the 3T1 powder diffractometer of the Orphיe reactor at the Lיon Brillouin Laboratory (CEN-Saclay ; France). The reflection (200) was examined with an incident neutrons of 1.98ֵ wavelength selected from the (111) plane of copper monochromator. A gauge volume of 20 cubic millimeters was achieved using vertical slits of 1x20mm2 in the incident and diffracted beam . The sample under consideration was a 25CD4 steel cylinder, with a diameter of 76mm, coated with 2mm thickness of Z10C12 alloy. The deposition has been carried out in a one layer process along helicoidal beads (fig.3). In order to obtain results average over the whole sample circumference, the sample was made to rotate around its longitudinal axis (fig.4).
Fig 3. Schematically view of the rolling simulator with the stresses directions.
|Fig 4. Sample and mounting set-up for neutron diffraction strain measurements.|
Diffraction peaks were measured in three different positions along the sample radius : one in the coating (R=39mm), at the interface between the coating and the substrate (R=38mm) and one in the substrate (R=37mm). At each location Bragg peaks were scanned at five different y values, corresponding to sin2 y = 0.002, 0.05, 0.15, 0.29, 0.46. The unstressed lattice plane spacings were measured from a powder grinded from the coating and its substrate .
Using the “sin2y method”, with the appropriate Young’s moduli and Poisson’s ratios , the radial and tangential stresses were then calculated.
X- ray Measurements
In order to check the validity of the results obtained by neutron diffraction experiments, a set of X- ray measurements have been performed with a similar sample to the previous one. The equipment used for the measurements of residual stresses was an X-ray stresses analyser available at IRSID (Firminy; France).
The diffraction profile of the (211) planes was obtained by Cr-Ka radiation. The residual stresses were determined by the “sin2y method”, examining nine ytilts, evenly distributed between -36° and +39°.
As the measurements position could be affected along the deposition beads, the sample was made to rotate around its longitudinal axis. In this way the results were averaged over the whole sample circumference and could be compared with the results obtained from the neutron diffraction technique.
Mechanical isothermal tests
Cylindrical specimens, with a diameter of 5mm and a gauge length of 10mm, were machined in the coating with the longitudinal axis parallel to the plasma deposited direction ; the thickness of the coating being about 16mm.
The low cycle fatigue tests were carried out on a servo hydraulic push-pull Mayes machine at different temperatures in the range (20-500°C) ; specimens were heated by a joule effect furnace. Before testing, the reduced section is first polished with grinding paper and chemically etched.
The mechanical isothermal tests were conducted, under constant plastic strain in the range (0.2 ; 0.5 ; 1%), to failure applying a triangular wave form signal (R = -1) at a nominal strain rate of 1.10-3 s-1; the total strain being controlled by means of a strain gauge extosometer stuck on the specimen length. Scanning electron microscopy (SEM) analyses of fracture surfaces of the specimens were observed on a Jeol JSM 840 microscope.
The foils were prepared from fatigued specimens with a twin jet electro polishing technique using a 95% acetic acid and 5% perchloric acid solution ; a Philips CM 200 transmission electron microscope (TEM) operating at 200Kv and equipped with a tilting specimen stage was used for the examination of the foils.
The cyclic mechanical behaviour expressed in terms of stress versus strain is modelized by using the viscoplastic J.L. CHABOCHE model according to its constitutive equations . The twelve parameters of this model are determined by an integration process using the identification-optimization code SiDoLo .
Thermal fatigue cycling
Ten temperature measures are realized for the stabilized cycle using an infra-red pyrometer and thermocouples. The highest temperature measured is 500°C ; the temperature axis temperature is near 40°C.
A thermal calculation is then performed according to the two codes of calculation : ZיBuLoN and SiDoLo an optimized temperature cylinder map is given in figure 5; for the most experimental points chosen, better results are obtained for the ones located at the cylinder surface and also for the ones located near the central axis.
For the mechanical calculation, we consider that every cylinder temperature point vary during a cycle, then the thermal conditions have to turn in order to account for the cylinder rotation. According to the considered boundary conditions , the thermomechanical calculation results (von Mises stress) are established (fig.6). The maximal value of von Mise stress is found at the interface of coating and substrate ; the minimal one being near the central axis.
|Fig 5: Optimization of the experimental temperature map (T°C).||Fig 6: Mises’s stress state ; t=3s (half cylinder).|
Residual stresses determined by neutron and X-ray diffraction showed a strong compressive tangential component for the coating with a steep gradient at the interface with the substrate. On the contrary, in the radial direction the residual stress state is tensile, showing a good uniformity and continuity at the interface (fig.7).
|Fig 7: Comparison between the radial (sR) and tangential (sT) measured by neutronic and X-rays diffraction techniques.|
Observation of fatigue microstructure
Hardness of the as-received material was measured at approximatively 450Hv. The examination of X-ray diffraction diagrams permitted the identification of the crystallographic structure of the stainless steel ; this latter has a parameter of 0.2866nm, identical to the ferrite parameter, in the as-received material as well as in all the specimens tested at different temperatures .
Moreover,some observations on specimens cycled at 20 and 500°C were carried out using SEM and TEM microscopes. Martensite laths with a high dislocation density and ferritic subgrains were observed at 20°C. At 500°C, a cell type dislocation structure occur (rearrangement of dislocations) (fig.8 (a,b)). A precipitation of M23C6, M7C3 and ((Nb,V)(C,N)) carbides in the ferritic sub grains was observed.
|Fig 8a:||Fig 8b:||Fig 8: TEM observations after cycling at Dep/2 = 0.2% :
(a)Ferrite structure embedded in the laths Martensite with a high dislocation density ; T = 20°C,
(b) Cell type dislocation structure with a low dislocation density ; T = 500°C.
Cyclic stress-strain response
The evolution of cyclic stress has been reported elsewhere . The variation of the maximum stress amplitude with the cumulated applied plastic strain p shows that at every temperature for every plastic strain amplitude, the stress amplitude decreases, before it stabilizes : the material displays cyclic softening behavior (fig.9 (a,b)).
|Fig 9: Evolution of the stress amplitude vs. the applied plastic strain :
(a) Stress levels vs. the cumulated plastic strain p (Dep/2 = 1%),
(b) Stress amplitude vs. the plastic strain amplitude (Dep/2 = 0.5%).
These results are correlated with hardness decreasing from 450Hv to approximatively 360Hv measured after fatigue tests at 20 and 500°C (e p = 1%).
As first result, since the first cycles until failure, the cyclic plastic deformation is essentially accommodated by the ferrite. This can be explained by the low hardness after cycling and by the ferrite island sizes relative to the tempered martensite lath sizes .
At high strain level, it has pointed out, [7,17] that the ferrite cannot by itself accommodate the plastic deformation ; this leads to an increasingly important contribution of the martensite laths themselves.
At low strain amplitude, mechanical cycling result in formation of dipolar walls and cells in ferrite islands (fig.8 (a,b)). The cells are found to be equiaxe but also elongated. These observations suggest that ferrite is highly strained since cell formation requires multislip and dipolar walls are expected to be double polygonized .
In the other hand, the fatigued specimens observed using SEM microscope showed micro cracks developing preferentially along most favourably oriented extrusions where plastic strain is localized by stress concentration effect (fig.10 (a,b)).
|Fig 10a:||Fig 10b:||Fig 10: SEM micrographs showing microcracks and cupules after the fatigue tests :|
(a) Specimen tested at T = 20°C ; Dep/2 = 1%,
(b) Specimen tested at T = 500°C ; Dep/2 = 1%.
Identification of the viscoplastic model
For each mechanical tests, two loops were necessary to identify the material parameters : the initial cycle and the stabilized one. A good correlation was found for several steady state loops under different strain amplitudes and at various temperatures between the experimental response (symbols) and the numerical simulation (solid line) (fig. 11 (a,b)).
|Fig 11: Comparison between model (solide lines) and experimental responses (symbols).|
(a) T = 20°C ; Dep/2 = 0.5%, (b) T = 500°C ; Dep/2 = 0.5%.
For this study, three main axis were investigated according to the considered experimental conditions.
For the thermal fatigue tests, the mechanical calculation of temperature and stresses has shown a good agreement with the experimental measurements. In the other hand, the residual stresses measurements, by the appropriate techniques, have shown a strong compressive tangential component for the coating while the radial component is tensile. This result has been related to the high stress levels obtained during the low cycle fatigue tests ; especially at 20°C and 450°C. For these last tests, the following conclusions can be drawn :
The authors would like to thank Professor G. Bיranger of L.G.2m.S and Dr P. Revel of S.M.H.P for their scientific contribution in this study ; G. Marichal of L.G.2m.S, Compiטgne University (France), for his participation in performing the fatigue tests ; M. Ceretti and M. Perrin of LLB (CEN-Saclay, France) for their participation in performing the residual stress measurements ; J. Copereaux of IRSID (France) for his participation in performing the examination of the foils by TEM microscopy. The Z10C12 coatings were supplied by H. Michaud from Usinor-Sacilor Cie (France).
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