364 J. Mater. Sci. Technol., Vol.24 No.3, 2008

Numerical Simulation of Stress and Deformation for a Duplex

Stainless Steel Impeller during Casting and Heat

Treatment Processes

Lugui CHEN1), Yong LING2), Xiuhong KANG1), Lijun XIA1) and Dianzhong LI1)†1) Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,Shenyang 110016, China

2) WTCM Foundry Center, Zwijnaarde, Belgium

[Manuscript received September 3, 2007]

A large-scale, thin wall duplex stainless steel impeller with complex geometry was deformed severely andunpredictably during casting and heat treatment processes resulted in dimensional failure for the final part.In this paper, the distortion of the impeller during casting and heat treatment was calculated. A commercialsoftware, Experto-ViewCast, was used to simulate the transient heat transfer, solidification and mechanicalbehaviors during the casting and the heat treatment process. The coupled set of governing differential equationsfor mass, energy and mechanical balance were solved by finite control volume and finite element method. Athermoelastic-visco-plastic rheological model was used to compute the constrained shrinkage of the casting.At each time increment, a coupling of the heat transfer and mechanics was performed. Comparison ofthe experimental measurements with the model predictions showed good agreement. From the calculateddisplacements of key points of the blade, the proper inverse displacements were determined to provide anoptimum casting pattern and to achieve a uniform and reasonable machining allowance for both faces of theblade.

KEY WORDS: Numerical simulation; Impeller casting; Heat treatment; Distortion; Modeling

1. Introduction

During casting and heat treatment processes, ther-mal stresses arise because of uneven cooling, phasetransformation and mechanical constraint[1]. Dimen-sional changes and distortions resulted from ther-mal stresses can particularly affect the final shape ofcastings. With todays emphasis on near-net-shape,stringent dimensional reproducibility and economicrequirements, the traditional trial-and-error retoolingprocedures have been gradually replaced by the nu-merical simulation technology. Numerical modelingcan predict the final dimensional changes and resid-ual stress distribution of cast products. It is able toaid engineers to optimize the process. Much efforthas been done to simulate the thermal stress in pastdecades. Most of the numerical models are basedon the finite element method[2,3]; only a few usedthe finite difference method[4], or the finite volumemethod[5]. As for the material behavior, thermoelas-tic behavior was assumed by Hattel et al.[4] and Fryeret al.[5], whereas thermoelastic-plastic behavior wasassumed by Tszeng[6], and thermoelastic-visco-plasticbehavior by Fjaer et al.[7] and Wise et al.[1]. For therefinement of the heat transfer studies, Hwang[8] in-troduced the influence of the formation of an insu-lating air gap between the casting and mould on theheat exchange.

Although many works for simulating stress and de-formation of the casting have been made up to date, itis not enough to predict the final shape of the casting,especially the machining allowance. Not only in thesolidification and cooling stage but also the shake-outof the casting from the mould, the cutting-off of thegating system and heat treatment all have a strong

† Prof., Ph.D., to whom correspondence should be addressed,E-mail: dzli@imr.ac.cn.

effect on the thermal stress and the deformation ofthe casting. Unfortunately most of the numerical sim-ulations for stress and deformation have been aimedsolely at the solidification and cooling stage, and haveoverlooked the succeeding processes. In order to moreaccurately predict the dimensional change of the cast-ing and estimate the machining allowance, before thecasting is set on the machine tool, there is a need foran integrated model that simulates the solidification,cooling, shake-out, de-gating and heat treatment ofthe casting.

The present work deals with the developmentof the thermal stress and distortion of a large-scale impeller during the casting and heat treatmentprocesses. Based on the simulation results, the properinverse displacements were determined, which pro-vided the corrected geometry of the pattern to en-sure that the casting had a correct shape and min-imum uniform machining allowance. A commercialsoftware, Experto-ViewCast, was used to simulatethe heat transfer and mechanical behavior in theprocesses.

2. Mathematical Model Formulation

2.1 Physical descriptionA three dimensional schematic diagram of a six-

bladed impeller casting is shown in Fig.1. The im-peller is 900 mm in diameter and 300 mm in height.The outer diameter of the hub is 700 mm and the in-ner is 622 mm. The duplex stainless steel used in theimpeller is 00Cr25Ni6Mo3N and the chemical compo-sition is shown in Table 1. The blade has a variablecamber geometry, which is controlled by a number ofkey points. The initial machining allowance at sin-gle side of the blade was 30 mm to ensure that thefinal shape of the blade was not out of the machiningallowance. In order to avoid any cold shuts (i.e.

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Table 1 Chemical composition of the duplex stainless steel 00Cr25Ni6Mo3N (wt pct)

C Si Mn S P Cr Ni Mo N Fe≤0.03 ≤1.0 ≤1.0 ≤0.006 ≤0.02 24.0-26.0 6.5-7.5 1-2 0.1-0.2 Balance

Table 2 Thermal and Mechanical Properties of the duplex stainless steel 00Cr25Ni6Mo3N

Properties Value Temperature/◦CConductivity λ=30 W/m/◦C T <1517

λ=42 W/m/◦C T <1700Specific heat Cp=879 J/kg/◦C T <680

Cp=2071 J/kg/◦C T <730Cp=880 J/kg/◦C T <850Cp=737 J/Kg/◦C T <1700

Density ρ=7200 kg–7800 kg TLiquid–Tsolid

Modulus of elasticity E=5.0E–02 GPa T > Tsolid

E=5.0E+01 GPa T <=Tsolid

E=1.20E+02 GPa T <=910E=1.30E+02 GPa T <=800E=1.41E+02 GPa T <=700E=1.53E+02 GPa T <=600E=1.64E+02 Gpa T <=500E=1.75E+02 Gpa T <=400E=1.85E+02 GPa T <=300E=1.93E+02 GPa T <=200E=2.02E+02 Gpa T <=100

Thermal expansion coefficient α=1.8E–5/◦C T < Tsolid

α=1.6E–5/◦C T <1500α=1.55E–5/◦C T <1000α=1.52E–5/◦C T <900α=1.49E–5/◦C T <800α=1.45E–5/◦C T <700α=1.42E–5/◦C T <600α=1.38E–5/◦C T <500α=1.35E–5/◦C T <400α=1.32E–5/◦C T <300α=1.28E–5/◦C T <200α=1.26E–5/◦C T <100

Poisson ratio v=0.4–0.3 TLiquid–Tsolid

Fig.1 Three dimensional model of the casting system ofthe impeller

incomplete filling) of the blade, a supporting ring isconnected to the tip of the blade. The liquid metal isfilled into the mould through a bottom gating system.

The thermal and mechanical model is based onthe following assumptions. (1) Initially the castingmould is filled with liquid metal. The temperaturedistribution of the casting and sand mould is the re-sult of a previous mould filling simulation. (2) Naturalconvection effects are neglected, no mass transfer ofthe solid phase and no segregation effects in the cast-ing. (3) The mould is assumed rigid. Thermoelastic-visco-plastic model is applied at high temperature andthermoelastic-plastic model is adopted at low temper-ature of the casting. All of thermal and mechanical

properties are temperature dependent as listed in Ta-ble 2.

2.2 Heat transfer modelThe classical isotropic Fourier conduction law is

considered as

ρCp(T )dT

dt= div(k(T )gradT ) + Q (1)

where k(T ) is the thermal conductivity, Cp(T ) thespecific heat, ρ the density and Q an internal powersource. The parameters k(T ), Cp(T ) and ρ can varywith space (x, y, z), time (t) and temperature (T ).When solving the transient heat transfer equation, theinterface heat transfer coefficient between casting andmould is considered and the liquid/solid phase changehas also been taken into account. The gap formationwas taken into account by the heat transfer coefficientindirectly. The value of the interface heat transfer co-efficient varies from 1100 W/m2/◦C to 520 W/M2/◦C,while the temperature changes from TLiquid to TSolid.2.3 Stress model

The constitutive model of this study represents thebehavior of metal alloy when temperature changes,the interaction between the casting and the mould,the interaction between the casting product and thegating system. The total strain rate ε is

ε = εe + εvp + εT (2)

where εe is elastic strain rate, depending on thetemperature-dependent material properties such as

366 J. Mater. Sci. Technol., Vol.24 No.3, 2008

elasticity modulus, Poisson′s ratio. εT is thermalstrain rate and can be defined by

εT = αT (3)

where α is the thermal linear expansion coefficient, Tthe temperature rate. The viscoplastic strain rate εvp

for casting metals can be written as

εvp = γ(σeq

σ0− 1

) 1m 3

2σeqS (4)

where σeq is the von Mises equivalent stress; σ0 isthe static yield stress below which no viscoplastic de-formation occurs; S is the deviatoric stress tensor; γis the fluidity of material; m is the strain rate sen-sitivity coefficient. When m equals zero, the behav-ior is elastic-plastic. When m equals one, it corre-sponds to a fluid with a Newtonian viscosity. A valueof m between one and zero is a first approximationfor hot metals (for common metals m lies between0.1 and 0.2). Since the constitutive model tracksdisplacements, stresses, strains and forces, the multi-step thermal loading and time stepping increment wasused. The mesh of the casting and mould is composedof 3-D eight nodes or hexahedral elements.

3. Numerical Results and Discussion

The temperature profile, stress distribution anddisplacement during casting and heat treatment weresimulated by Experto-ViewCast software. And thecasting process includes four stages: the solidifica-tion, cooling, shake-out and de-gating system. Thefull general heat transfer equation and the constitu-tive equation associated with the assigned boundaryconditions were solved by finite element method.

The initial temperature of the casting and mouldwas the last step of the temperature data from amould filling simulation. The temperature distribu-tion at 19.5 s after pouring is shown in Fig.2. It isobserved that the temperature in the impeller wasnonuniform at the early cooling stage. The temper-ature of the supporting ring and the tip of the bladefell quickly. The root of the blade remained around1520◦C and some parts (the hub, four risers and thegating system) were still above 1540◦C. Figure 3 dis-plays the temperature profile at 80000 s (over 22 h)after pouring. It was observed that significant tem-perature differences still existed, the maximum tem-perature around 245 being in the four risers, whereasother parts had cooled to around 88◦C.

Figure 4 shows both deformation and residualstress distribution at 80000 s (over 22 h) after pour-ing. Here, Von Mises stress values are shown in thecolor scale. The white frame shows the original geom-etry. The colored frame represents the deformation,and this new geometry of deformation is doubled forclarity. It was observed that the residual stress inthe blade was high. In Fig.5, both the deformationand residual stress distribution after shake-out areshown for the central section of the impeller. Thesupporting ring and the hub have shrunk inward andbeen distorted. The upper part of the blade hasbeen distorted downwards, but in contrast, the tip of

Fig.2 Temperature field at 19.5 s after pouring(Tmax=1556◦C, Tmin=1395◦C)

Fig.3 Temperature field at 80000 s (over 22 h) afterpouring (Tmax=245◦C, Tmin=88◦C)

Fig.4 Residual stress distribution at 80000 s (over 22 h)(white frame is the original mesh. Mag. x2)

the lower part rose. As expected, the central partof the blade (off-center section of the impeller) keptits original position (Fig.6) and the displacement ofthe tip of the blade was larger than that at the root.Interestingly, the residual stress in the tip of the bladewas higher than that of other parts of the blade.

Figure 7 displays the deformation and residualstress after cutting off the gating system. The resid-ual stress was relieved to some extent after removingthe constraint of the gating system.

The deformation and residual stress distributionafter heat treatment are shown in Figs.8, 9 and 10.The geometry of the blade has clearly been deterio-rated even further. The supporting ring and hub have

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Fig.5 Deformation and residual stress distribution of themiddle section of the impeller after shake-out (De-formation x 2 for clarity; element size 5 mm)

Fig.6 Deformation and residual stress distribution of themiddle section of the blade (off-center section ofthe impeller) after shake-out

Fig.7 Deformation and residual stress distribution afterremoving the gating system

shrunk further inward. The root of the blade has con-tinued to deform downwards; the tip of the upper parthas bent upwards; the tip of the lower part more badlythan the upper part. The middle part was also bent.The residual stress in the impeller increased to around50 MPa. From the comparison with original geometry(white frame), the final shape of the blade is clearlyseen to be seriously wrong, having no machining al-lowance in several places. The part failed. However,the accuracy of this simulation was confirmed by mea-surement of the locations of the key points.

Fig.8 Deformation and residual stress distribution afterheat treatment

Fig.9 Deformation and residual stress distribution of themiddle section of the impeller after heat treatment

Fig.10 Deformation and residual stress distribution of themiddle section of the blade (off-center section ofthe impeller) after heat treatment

Because the geometry of the blade is checked bythe coordinates of key points, an effective method toachieve a qualified impeller is to modify the coordi-nates of the key points. Based on the simulation re-sult of the deformation of the blade, proper inversedisplacements were added to the original coordinates(x, y, z) of key points, as shown in Fig.11. In a Zaxis section of the impeller, the original coordinatesof the key point is on the white frame mesh, the newcoordinates on X and Y axes can be determined byfollowing equations,

Xn = X0 + D∗cosα (5)

368 J. Mater. Sci. Technol., Vol.24 No.3, 2008

Fig.11 Schematic diagram of defining the new coordi-nates of a key point

Fig.12 Simulated deformation of modified model com-pared with the geometry of the impeller casting( the brown outline is the geometry of the finishmachined part, the yellow is the modified patternand the blue is the deformation after heat treat-ment)

Yn = Y0 + Dr ∗ sinα (6)

And in an X or Y axis section, the new coordinateson Z axis can be determined by following equation,

Zn = Z0 + Dr (7)

A modified geometry of impeller pattern was con-structed after new coordinates of all key points weredetermined. Then new processing simulations wererepeated. If the simulative final shape of the blade isout of the machining allowance, one should modify thecoordinates of key points until the final shape matchesthe required geometry and should assure a uniformmachining allowance on both faces of the blade. Themodified model simulation result associated with thepart geometry is shown in Fig.12. It is seen that thecasting after heat treatment had an even machiningallowance. With the simulation tools, the machiningallowance at single side of the blade can be reducedto 5 mm.

4. Conclusions

(1) The temperature profile, thermal stress distri-bution and deformation of a impeller during the cast-ing and heat treatment were simulated in this studyby Experto-ViewCast software package. The simula-tion results agreed with the measurement carried outon the key points of the casting.

(2) Based on the simulation results, a modifiedpattern was made to achieve the required machiningallowance, and dramatically reduce the machining al-lowance at single side of the blade from 30 mm to 5mm.

(3) The exercise demonstrates that the conven-tional trial-and-error method of pattern design canbe simplified and shortened significantly.

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