mathematical modeling of heat reatment

7/28/2019 Mathematical Modeling of Heat Reatment

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Metallurgia delle polveriMemorie >>

la metallurgia italiana >> giugno 2009 57

MATHEMATICAL MODELING

OF HEAT TREATING

POWDER METALLURGY STEEL

COMPONENTS

V. S. Warke, M. M. Makhlouf

A mathematical model to predict the response of powder metallurgy steels to heat treatment is presented

and discussed. The model is based on modication of commercially available software that was originallydeveloped for wrought alloys so that it can account for the effect of porosity. An extensive database had to bedeveloped specically for PM steels and includes porosity- and temperature-dependent phase transformation

kinetics, and porosity- and temperature-dependent phase-specic mechanical, physical, and thermal properties.This extensive database has been developed for FL-4065 PM steel and has been used in the model to predictdimensional change, distortion, and type and quantity of metallurgical phases that develop in a typical PM

component upon heat treatment. The model predictions are compared to measured values and are found to be inexcellent agreement with them.

KEYWORDS: powder metallurgy, modelling, steel, heat treatment

INTRODUCTION

Components that are manufactured by the powder metallur-gy process (PM) experience considerable changes during heattreatment. These include changes in their mechanical proper-ties, dimensions, magnitude and sense of residual stresses, andmetallurgical phase composition. Since most of the quality as-surances criteria that these components have to meet includeprescribed minimum mechanical properties and compliancewith dimensional tolerances, it is necessary for producers ofPM components to be able to accurately predict these changes

in order to take appropriate measures to insure the productionof parts that meet the required specications. Several softwarepackages that are capable of predicting the heat treatment re-sponse of wrought steels are available commercially [1-3], butnone of them can predict the response of PM components. Inthis work, we developed a nite element-based model to pre-dict the response of PM steels to heat treatment. The model is

based on a modication of the commercially available softwareDANTE [3]. DANTE is comprised of a set of user-dened sub-routines and can be linked to the nite element solver ABAQUS.

Virendra S. Warke, Makhlouf M. Makhlouf

Department of Mechanical Engineering - Worcester PolytechnicInstitute - Worcester, MA 01609

Paper presented at the International ConferenceInnovation in heat treatment for industrial competitiveness,

organised by AIM, Verona, 7-9 May

The DANTE subroutines contain a mechanics module, a phasetransformation module, and a diffusion module that are cou-pled to a stress/displacement solver, a thermal solver, and amass diffusion solver, respectively. A block diagram showingthe combined DANTE/ABAQUS model is shown in Fig. 1. Themodel requires an extensive database, which includes tempera-ture- and porosity-dependent phase transformation kinetics,and temperature- and porosity-dependent phase-specic me-chanical, physical, and thermal properties of the steel. We de-

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Fig. 1Solution procedure or the DANTE/ABAQUS

model.Procedura di soluzione per il modello DANTE/ABAQUS.


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hibit transformation plasticity, i.e., plastic ow caused by changein the relative proportions of the various metallurgical phases inthe microstructure brought about by the phase transformation.We used Low Stress Dilatometry in order to characterize thistransformation-induced plasticity in FL-4605 PM steel. The pro-cedure entails applying an external compressive static load toa standard specimen in a Gleeble machine just before the startof the transformation. We chose the magnitude of the appliedload such that the magnitude of the resulting stress is less thanthe ow stress of austenite at the temperature of application ofthe load. We performed transformation induced plasticity meas-urements on samples of three densities (90%, 95%, and 100% ofthe theoretical density of the material) for each of the austen-ite to martensite and the austenite to bainite transformations.

Fig. 8 (a) and Fig. 8(b) show the measured dilatation data forthe 100% density sample at three the different applied stressesduring the austenite to bainite and the austenite to martensitetransformations, respectively. We performed similar measure-ments on samples with 90 % and 95% of theoretical density andused a tting routine to t this data to mathematical equationsthat were then used to create a transformation induced plastic-ity database.

MODEL CONSTRUCTION AND MATHEMATICALSIMULATIONS

The capabilities of the model are demonstrated using the testpart shown in Fig. 9. The dimensions of the part are summarized

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Fig. 4

Measured strain vs. time or the austenite to

bainite transormation at dierent isothermal holdingtemperatures.Misura della deormazione in unzione del tempo per latrasormazione da austenite a bainite durante trattamentiisotermi a temperature diverse.

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Fig. 5

Measured strain vs. temperature at dierent

cooling rates during continuous cooling transormationmeasurements.Misura della deormazione in unzione della temperaturaper velocit di rareddamento dierenti durante lemisure di trasormazione in rareddamento continuo.

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Fig. 6

TTTP diagram or 90% and 100% density FL-4605 PM steel plotted or the austenite to bainite andthe austenite to martensite transormations.

Diagramma TTTP per densit 90% e 100% dellacciaioFL- 4605 PM tracciato per le trasormazioni da austenitea bainite e da austenite a martensite.

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Fig. 7

True stress vs. true strain curve or austenitemeasured at three dierent temperatures or sampleswith 90% density at 1 s-1 strain rate.

Curva sollecitazione vs. deormazione per austenite,misurata a tre temperature diverse per campioni condensit 90% e velocit di deormazione 1 s-1.


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FL-4605 PM steel component of conguration and dimensionssimilar to those used in the model.Sample production We admixed AUTOMET 4601 steel pow-der with Asbury 1651 graphite powder to yield 0.5 wt% carbonin the nal product. We added zinc sterate to the powder as a lu-

bricant, then placed the admixed powder in a die and pressed itusing 216 tons of pressure. We sintered the green parts at 1100Cfor 30 minutes in a continuous sintering furnace under a con-trolled atmosphere and then we air-cooled them to room tem-perature. The average measured density of the parts was 95%of theoretical density with negligible variation within each partand from part to part.Heat treatment The heat treatment cycle for the sintered partsconsisted of furnace heating to 850C, holding at this tempera-ture for 20 minutes, and then quenching in oil with the partsplaced in an upright position with their thinner section point-

ing down. Twenty parts were heat treated in an internal quenchbatch furnace under an endothermic atmosphere with 0.5 wt.% carbon.In order to characterize the amount of distortion in the partscaused by the heat treatment we designed a xture to hold theparts at the same location in a coordinate measurement ma-chine (CMM). We measured the circular hole before and afterheat treating the sample at locations around the periphery in 5increments. We repeated the measurements at four depths alongthe thickness of the part and in each case we converted the xymeasurement into a radius, r, and an angle at each measuredpoint. We then normalized the radius by dividing it by the aver-age radius before heat treatment. Fig. 10 and Fig. 11 compare themeasured and model-predicted changes in dimensions of thecentral hole due to heat treatment.

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Fig. 11

Change in radius at dierent locations aroundthe circular hole as predicted by the modeland as measured by a CMM.Variazione del raggio in diverse posizioni intorno ai oricircolari secondo la previsione del modello e misuratomediante CMM.

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Fig. 10

Coordinates o the circular hole beore andater heat treatment. (a) Measured using a CMM. (b)Predicted by the model.Coordinate del oro circolare prima e dopo trattamentotermico. (a) Misurato mediante CMM. (b) Previsione del

modello.

b

a

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Fig. 12

Section lines showing where cuts were madeor measuring retained austenite.Linee di sezione che mostrano dove sono stati eettuati i

tagli per misurare laustenite residua.


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mathematical modeling of heat reatment

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