SIMULATION OF SHRINKAGE/VOIDS FORMATION IN LEAD CASTING AND ITS EXPERIMENTAL VALIDATION

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 3785-3794 © TJPRC Pvt. Ltd.

SIMULATION OF SHRINKAGE/VOIDS FORMATION IN LEAD CASTING AND ITS EXPERIMENTAL VALIDATION MD. SALIM ANSARI1, AMITESH KUMAR2, KAMLESH KUMAR SINGH3 & B. S. MANJUNATH4 1,2,3

Foundry Technology Department, National Institute of Foundry and Forge Technology, Hatia, Ranchi (Jharkhand), India 4

Bhabha Atomic Research Centre, Mumbai, India

ABSTRACT In this research work a defect-free direct method of lead castings was developed. To achieve this, existing defects in the direct method of lead castings were investigated. This was developed by computing models and simulating the casting process to identify the source of defects and the optimum conditions for the direct method of casting lead. An improved model to the existing casting process was developed. The key parameters of the casting process were established through quantitative and qualitative data collection techniques including temperature sensors and defect analysis. The model was simulated using the key process parameters identified on commercial solidification software, ProCast, to establish the cause and effect of each parameter on the overall quality of lead casting. In this research work, solidification of lead has

results have been validated experimentally for a particular case of lead solidification. The simulated results were found in good agreement with experimental results. Voids appeared at the top and isolated area of castings for defect free direct method used in this study.

KEYWORDS: Solidification; Shrinkage; Simulation; Lead Casting & Defect analysis

Original Article

been carried out in different size of metallic mold to predict the formation of shrinkage during solidification. Theoretical

Received: Jun 10, 2020; Accepted: Jun 30, 2020; Published: Jul 16, 2020; PaperId.: IJMPERDJUN2020359

INTRODUCTION Radioactive materials are packaged and transport in a cask. Cask is generally made of steel shell filled with shielding material lead. [1] Radioactive materials are completely shielded inside the cask. Casks design must meet the standards and guidelines of Atomic Energy Regulatory Board (AERB) in India / International Atomic Energy Agency (IAEA) regulations. The most important aspects of standards are that there should not be any leakage of radiation even in case of major accidents and in the worse condition of fire. Therefore, cask must pass several tests to ensure its performance capability. One of the open pool fire test of 800 0C for 30 minutes is carried out in which lead melts and allowing it to solidify [2]. Solidification of any metal leads shrinkage but in case of lead shrinkage is more because of low melting point and large difference in liquidus and solidus density [3]. Shrinkage may be macro and micro porosity types in the casting. [4] In several cases during solidification molten metal areas get encapsulated with solidified metal, which is also an extended part of micro shrinkage, that areas are known as isolated liquid area. These isolated areas solidified independently and can’t feed them each other and left behind shrinkage cavity due to solidification of liquid in those areas. Both (i.e. micro and macro) decrease the mechanical properties furthermore, macro porosities could not be removed through annealing [5] for producing sound castings even in case of lead if it is used as packaging material for transportation of radioactive material. Reduction in wall thickness and reduction in density due to shrinkage in isolated areas may raise the issue of steaming of radiation. www.tjprc.org

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So, it is necessary to study the formation of shrinkages in lead casting, since solidification of lead is not a well-studied area.

Mathematical modelling is the versatile technique to solve the issue of shrinkage in lead casting economically and time saving without expensive shop floor practice. Extra precaution may be taken while melting lead because it generates harmful fumes and exposure at work may lead to lead poisoning in adults [6]. Investigators have reported different prediction criterions and models for prediction of shrinkage cavities. Niyama criterion was incorporated for prediction of shrinkage porosities [7-8] generally based on inter-dendritic but it is not suitable for macro porosity. Reis et al. [9] has been investigated number of parameters which affects formation of shrinkage porosity are heat transfer, fluid flow in molten condition, natural convection i.e. flow in mushy zone, solidification shrinkage due to density difference of liquidus state and solidus state, deformation of solid interface due to the formation under deformation etc. Samavedam and Sundarrajan [10] estimated shrinkage porosity using virtual casting software which takes accounts of transient heat transfer between solid and liquid phase, however they have not discussed about fluid flow. A large number of investigators predicted shrinkage porosity based heat flow condition [11-14] but it also depends on the alloy content [15]. Pehlke R.D. [16] calculated the porosity formation both due to liquid to solid shrinkage as well as gas porosity. Sarkar et al. [17] studied melting and solidification of lead using neutron radiography. They tried to capture movement of liquid front and solid front during melting and solidification. Similarly, Lokendra et al. [18] studied melting of lead and captured melting front experimentally and validated theoretically using CFD software fluid. However, Sarkar et al. and Lokendra et al. have not discussed about detection of shrinkage cavity. Therefore, it is essential to study the solidification characteristics of pure lead to understand the phenomenon of formation of shrinkage/voids theoretically and experimentally. In this work simulation has been carried out for different diameter of cylindrical moulds with fixed height.

MATHEMATICAL MODELLING The domain of solution with boundary condition is shown in the Figure 1.

Figure 1: Domain of Solidification of Pure Lead The fluid flow module which solves filling of mold, fluid flow, natural and forced convection, dynamic liquid pressure and entrapped gasses by the solution of the Navier- Stokes equation.

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The Navier-Stokes equations are given by ∂ρui ∂t

+

∂(uj ρui +Pδij −σij ) ∂Xj

= 𝜌g i

Where, ρ = density of liquid metal, P = pressure, δij = Kronecker delta, σij = Stokes viscous stress tensor, g i = gravitational acceleration The conservation of mass is balanced through the continuity equation: ∂ρ ∂t

+

∂ρui ∂Xi

=0

Where, ρ = density of liquid metal, ui = fl ui,liq = component of superficial velocity, fl = liquid fraction, ui,liq = Actual liquid velocity The heat flow calculation, latent heat release during solidification is obtained by solving the Fourier heat conduction equation. Temperature distribution, Fraction of solid evolution, Heat flux and thermal gradients, Solidification time, Hot spots, Porosity prediction are obtained by solving the energy equation along with fluid flow. The energy equation according to the characteristics of casting the three dimensional unsteady temperature field was adopted as per the Eq. (1).

Transient non-linear conduction equation is: δH δT

𝜌 δT δt – [k𝛻T] – q(x) = 0

(1)

Where, H= Enthalpy, k = conductivity, T = nodal temperatures, q(x) = volumetric heat source Transient heat transfer analysis of casting is given by enthalpy; Enthalpy of liquid metal is given by T

H(T) = ∫0 Cp dT + L[1 − fs ]

(2)

Where, Cp= specific heat, L = latent heat, fs = Solid fraction Niyama criterion (Ny) was used in near the end of solidification to predict shrinkage micro porosity [19].

Ny= G⁄ √Ṫ Where, G is temperature gradient, Ṫ is cooling rate.

In this modelling work it was assumed that solidification of metal start only after complete feeling of stainless steel mold.

Boundary conditions are shown in the domain Figure 1.

Following boundary and initial conditions were used to simulate the lead solidification.

Boundary Conditions 

There is no movement of liquid metal around the wall of mold.



Mold is stationary.



Heat transfer will start after complete filling.

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

Md. Salim Ansari, Amitesh Kumar, Kamlesh Kumar Singh & B. S. Manjunath

Top of the liquid metal is in direct contact with atmosphere.

Initial Conditions 

Mold is initially at room temperature (30 oC)



Ambient temperature is also 30 oC and heat transfer coefficient between mold wall and surrounding is 25 Wm-2K1



.

Metal is filled at 350 oC. Only movement of liquid metal is due to natural convection.

Convective heat flux boundary condition -k 𝛻T⋅n̂ = h [T-Ta]

(1)

Where, n̂ =unit vector normal to the surface, h = convection heat transfer coefficient between mold to surrounding also known as convective film coefficient, T a = ambient temperature Solution Method Finite element Method (FEM) was used to solve differential equations. The solution domain, Ω was divided into a set of non-overlapping elements which completely fill the space. Temperature in each of these elements interpolated from discrete nodal temperature. This computes a temperature field which approximates the exact solution.

T(x, t) = Ni(x) Ti(t)

(2)

Where, Ni = interpolating or "shape" functions Ti = nodal values of temperature The approximate solution of Eq. (2) was taken as input for the governing field and boundary condition of Eq. (1).

This resulted into a residual error. This error was minimized by the Method of Weighted Residuals, applying the Galerkin procedure [20] of using the shape functions, Ni, as the weighting functions. This results in the symmetric matrix system CṪ +KT = F

(3)

Where, Ṫ = Time derivative of the vector of nodal temperatures, C = capacitance matrix with terms 4

Cij = ∫Ω (ρ

dH dT

)Ni Ni dΩ

K = conductivity matrix with terms 4

4

K ij = ∫Ω ∇Ni . (k∇Nj )dΩ + ∫┌ hNi . Nj d┌2 2

F = source vector with terms 4

Fi = ∫┌ Ni . (q − hTa )d┌2 2

The integrations were performed on an element-by-element basis and assembled to form the global matrices. The first order differential equation system of Eq. (3) was numerically integrated by a two level predictor-corrector method.

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The solution of Eq. (3) determines temperature distribution of the domain. The above solutions were carried out on the FEM based commercial software ProCast 2014.0 [21]. Mathematical modelling of solidification of pure Pb was carried out to understand the formation of voids and shrinkages.

THERMO-PHYSICAL PROPERTIES Thermo-physical properties of pure lead and stainless steel grade 304 are given in Table 1 and Table 2, which were used as an input for simulation of lead casting.

Table 1: Thermophysical Data for Pure Lead [22] 1 Solidus Temperature, (0C) 326 Liquidus Temperature, (0C) 327 2 Thermal Conductivity, (W/mK), At solidus point 30.5 At liquidus point 24.2 3 Density of solid (g/cc) 11.336 Density of liquid (g/cc) 10.686 4 Latent heat of fusion, kJ/kg 23.20 5 Specific heat, kJ/kg.K 0.1478

Table 2: Thermophysical Data for Stainless Steel 304 [23] 1 Thermal Conductivity, (W/mK) 14.85 2 Density of solid (g/cc) 8.02 3 Specific heat, kJ/kg.K 0.49

EXPERIMENTAL VALIDATION OF MODEL A Cylindrical mold of grade 304 stainless steel 70 mm internal diameter and 210 mm height with shell thickness 3 mm was selected for validation. K-type thermocouples were attached to the surface of the mold wall and at the centre of mold cavity to obtain the temperature profile during solidification of mold wall and liquid metal using data acquisition system.

Schematic sketch of experimental set up is shown in the Figure 2. Experimentally obtained temperature v/s time plot was also used to finalize the heat transfer coefficient between liquid metal and mold wall. Induction furnace was used to melt the pure lead. Molten lead was poured into the mold at 350 oC. Mold was kept in open atmosphere at room temperature (30 o

C).

Figure 2: Schematic Two Dimensional View of the Experimental Setup

RESULTS AND DISCUSSIONS Determination of Heat Transfer Coefficient Between Mold Wall and Liquid Metal www.tjprc.org

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It is essential to give an input of heat transfer coefficient between wall of the mold and molten lead for simulation of solidification of molten lead in stainless steel mold. The value of heat transfer coefficient between liquid metal and mold wall was determined by matching the simulated temperatures vs. time plot at centre of liquid metal and at the wall of the mold wall.

(a)

(b)

Figure 3: (a) Simulated and Experimental Temperatures vs. time plot at a point on Mold Wall, (b) Simulated and Experimental Temperatures vs. time plot at a Point Inside Molten Lead

Locations of temperature determination with respect to times are shown in the Figure 2. Simulated and experimental plots of temperature and time of both points were similar for the value of heat transfer coefficient 300 Wm2

K-1. Therefore, 300 Wm-2K-1 was taken as a fixed value of heat transfer coefficient for further simulation of lead

solidification. Figure 3(a) shows the experimental and simulated temperatures vs. time plots for wall. The temperature vs. time plot for liquid metal experimental and simulated is shown in the Figure 3(b).

Simulation of Pure Lead Casting

(a) (b) Figure 5: Temperature, shrinkage porosity and solidification profile for Casting Diameter (a) 65 mm and (b) 70 mm

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(a) (b) Figure 6: Temperature, shrinkage porosity and Solidification Profile for Casting Diameter (a) 75 mm and (b) 80 mm

(a)

(b)

Figure 7: Temperature, shrinkage porosity and solidification profile for casting diameter (a) 90 mm and (b) 100 mm

Studies on shrinkage characteristics of pure lead were conducted theoretically. The solid models for shrinkage simulations were created using the CATIAV5R19 software.

A virtual environment for casting solidification process is created based on FEM. It predicts and analyse the occurrence of shrinkage defects. The input for the casting process simulations are solid model of the casting, material properties, boundary conditions and initial conditions. Software consists of three major processes; Pre-processing, Solving the Governing Equations and Post-processing or Visualization of results. In the present research work, interfacial heat transfer coefficient between mold wall and molten pure lead was taken experimentally and theoretically determined value 300 Wm-2K-1 for simulation. Solid model domain of lead casting and mold were divided into small elements. Every element was assigned boundary conditions, initial conditions and thermo-physical properties. Based on above boundary conditions and initial conditions grid independent test were carried out. The relative mesh size 5 out of from 1 to 10 was selected for simulation based on grid independent test. The minimum time step was 0.01second. Solidification simulation was carried out till 100% liquid solidified i.e. solid fraction from 0 to 1. Simulations were carried out for the lead casting to study the formation of shrinkage/defect formation. Solidification of pure lead was carried out in different size of stainless www.tjprc.org

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steel mold. Simulations were carried out for 65 mm, 70 mm, 75 mm, 80 mm, 90 mm and 100 mm diameter of stainless steel mold for a fixed height of mold i.e. 210 mm.

Temperature profile, shrinkage porosity profile and solid fraction profiles are shown in the Figures 5-7 for different diameter of casting. The least solidification time was observed 307 seconds for the smallest diameter casting (65 mm diameter mold), while maximum solidification time (687 Seconds) was observed in the case of highest diameter (100 mm) of mold. The variations of solidification time for different molds are different because of difference in material content. The heat content is directly proportional to the mass not the pouring temperature or initial temperature of molten metal. The solidification times are shown in the Figures 5-7 on solid fraction profile. Temperature profiles show the temperature distribution in the casting with respect to colour gradient as shown in the Figures 5–7. Maximum temperature after solidification is just below the top of the casting as presented in the temperature profile. It means last liquid to solidify at that point. Therefore, there is appearance of shrinkage porosity just below the top solidified region. In 65 mm and 70mm diameter molds casting simulated results do not show isolated shrinkage, it may be due to high cooling rate from wall to centre as shown in Figures 5(a) and 5(b). Therefore, it did not appear in experiment as shown in Figure 8(b). But isolated shrinkages were observed for lead casting for diameter 80mm and above as presented by simulated results shown in Figures 6(a)–7(b). Isolated shrinkage size below top is increasing as the diameter of mold increases as shown in the shrinkage profile Figure (Figures 6(a)-7(b)). It is well connected from the top void/shrinkage in case of casting in 100 mm diameter mold. It is just like a pipe as shown in the shrinkage profile of Figure 7(b). In comparisons to the isolated shrinkage of connected piping type of shrinkage large amounts of voids/shrinkage were observed at the top of the casting for all size of mold. It is macro size shrinkage and well known as voids at the top of casting. Simulated results of voids are shown in the shrinkage profile at the top of castings (Figures 5 - 7). The tendency for formation of shrinkage is related to liquid temperature, freezing range and materials. Volume deficit or shrinkage happens in metallic materials during solidification and cooling due to reduction in specific volume, which is a physical characteristic of materials. The molten metal volume decreases during solidification due to the atoms drawing nearer and coming to fixed lattice positions resulting in shrinkage. This shrinkage occurs in three stages as shrinkage of the molten metal during cooling, shrinkage due to solidification, shrinkage from solidification temperature to room temperature. The amount of shrinkage is large in the lead casting because of large variation in density with temperature particularly solid to liquid condition. That is why it is necessary to study the lead casting to avoid any kind of shrinkage, while it is used as a packaging transport of radioactive material. Shrinkage may cause reduction in optimum wall thickness of cask.

EXPERIMENTAL VALIDATION To validate mathematical model, experiments were carried out as shown in the Figure 2. The pure lead melt was poured into the stainless steel mold of diameter 70 mm. Casting was cut throughout the cross section to observe the exact depth of void/shrinkage at the top of casting. The simulations were carried out for solidification of pure lead in the same size of mold under same boundary and initial conditions as per experimental. Simulated and experimental shrinkage porosity observed similar which validating the simulation work. Shrinkage porosity for 70 mm diameter and 210 mm height of mold casting are shown in the Figure 8. The maximum depth of voids at the top of casting was observed 26 mm as indicated by vertical line shown in the Figure 8.

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Figure 8: Cross Section of Solidified Pure Lead Casting (a) Simulated (b) Experimental

CONCLUSIONS AND SUMMARIES In the present work the shrinkage porosity of lead was analysed. The most important conclusions that can be drawn are: 

Mathematical model has been developed.



This model can predict temperature profile, liquid fraction profile, voids/shrinkage in casting.



Model predicts formation of voids/shrinkage as well as isolated shrinkage in Lead Castings.



Experimental profile of Void/shrinkage matched well with the simulated result.

ACKNOWLEDGMENT This study was financially supported by Bhabha Atomic Research Centre, Mumbai, India. We also thank for their continuous suggestions and improvement.

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