Solidification

Alloy Solidification

When a liquid metal at temperature θo is poured in to the mold, at time t=0, the temperature everywhere inside the mold is θo .mold is θo .

Solidification starts with the formation of randomly-oriented small crystals near the mold walls.

Subsequently a temperature gradient exists within the Subsequently a temperature gradient exists within the casting. As solidification progresses inwards, long columnar crystals , with their axis perpendicular to the mold surface grows.

Pure metals have as sharply defined freezing temperature.Pure metals have as sharply defined freezing temperature.Alloys does not have a well defined freezing point. Rather they solidify over a range of temperature. The solids seperating at different temperature have differentThe solids seperating at different temperature have different compositions.

Solidification of an alloy takes place over a range of temperatures.During this process solids separating at different temperaturesposses varying composition.

The direction of crystal growth depends on:The direction of crystal growth depends on:

1. Composition gradient within the casting2 Variation of solidus temperature with composition2. Variation of solidus temperature with composition3. Thermal gradient within the mould.

Freezing diagram for metal inFreezing diagram for metal in ordinary mold Freezing diagram for metal inside chilled

mold

Difficulty of feeding is expressed by “ Centre line feeding Resistance (CFR)

Temperature distribution in different regions during solidification of a castingduring solidification of a casting

• Consider the mold face AB

Solidification of a large casting in an insulating mold

• Consider the mold face AB.• Large mold initially at temperature θo and

extending up to infinity along x .• At t = 0, metal at temperature θp isAt t 0, metal at temperature θp is

poured in to the mold.Assume that mold face temperature is raisedto θf (freezing temperature of metal) at t = 0fand maintained at that temperature tillcomplete solidification.The temperature distribution within the mold at some time t is:p

θx(t) = temperature at distance x from mold wall at instant tth l diff i it (k/ ) k d ti it d it ifi h t fα = thermal diffusivity = (k/ ρc), k = conductivity, ρ = density c= specific heat of

mold

Rate of heat flow through the mold face at any instant t ;

A = cross sectional area of mold-metal interface.

By using eqn (1) and (2) eqn (3) can be writtenBy using eqn. (1) and (2), eqn. (3) can be written as;

The total quantity of heat flow across the mold face up to a certain time t isup to a certain time to is

Heat rejected (QR) by liquid metal during solidification:

where, L= Latent heat of solidification, Cm = specific heat of molten metal and ρ = density of molten metal V = volume of themetal, and ρm = density of molten metal, V = volume of the casting.

Combining eqn (5) and (6), g q ( ) ( )

i.e.,

where,

The above relation is valid for a plane metal-mold interface.In real cases, the contour of the casting is having complex contours. ea cases, t e co tou o t e cast g s a g co p e co tou sConsidering three types of metal mold interfaces:

Solidification time determined above will be overestimation for case (a )Solidification time determined above will be overestimation for case (a,)where as it will be underestimate for case(c).

Defining two non-dimensional parameters, viz.,

and

Eqn (8) can be rewritten in terms of these parameters as:

Solidification distance in the insulating moldDuring solidification of plate shaped casting,g p p g,heat is rejected mainly through side faces,each of cross sectional area A. Solidificationfront moves inwards.If the solidification front moves through adistance δ(t) at any instant t from the metal-mold interface, then heat rejected by each, j ysolidification half is

Let the time taken to reject is heat through the mold face of area A in time t. Eqn(7)

equating eqn. (13) and (7)

or

Solidification with predominant interface resistance

The heat flow is controlled significantly by thermal resistance of the mould-metal interface (region 3). E.g. permanent mold casting and die casting

Considering one-dimensional heat flow,

The Rate of heat flow through the interface is

Let the solidification front at any instant be at δ distance from the mold face. Then,

From eqn.(15) and (16),

Integrating eqn(17) with boundary conditions, at t = 0, δ = 0,

Comparing eqn (14) and (18),

Depth of solidification increases linearly with time in eqn.(18) where as it is proportional to the square root of time in eqn.(14).

The heat flow through the interface during solidification can be obtained by substituting θp = θf in eqn. (6) (since super heat is neglected for the analysis for heat flow during solidification.

From eqn (15), heat flow through the interface during the period of solidification ts is

From eqn(19) and (6), after substituting θp = θf ,

Solidification with constant Casting surface temperature

This is the case of a large slab casting when produced in a thin water cooled metalThis is the case of a large slab casting when produced in a thin, water cooled metal mold having higher conductivity than the solidified casting.The predominant resistance is offered by region 4.

Temperature distribution with constant casting surface temperature

Assumptions:Metal mold interface temperature θ remains constant at its initial value θMetal-mold interface temperature θs remains constant at its initial value θf .Pouring temperature of the metal = Freezing temperature.δ(t) indicates the depth of solidification at any instant t.

The temperature profile within the range 0 < x < δ(t) can be obtained by ,

αs = Thermal diffusivity if solidified metal, θ∞ is a constant of integration.

At x = δ(t) θ = θf Substituting in eqn (21)At x = δ(t), θ = θf. Substituting in eqn (21),

i.e.,

where,

From eqn(23), the depth of solidification varies as the square root of time.

For determining the constant ζ, the following procedure is used.

At the solid-liquid interface, the rate of energy flow balance equation is

k C d L i l h d i i f h lidifi dk s, ρm, Cs and L are respectively the conductivity of the solidified metal, density of the metal, specific heat of the solidified metal and latent heat of fusion.

Differentiating equation (21) ,

Using equation (26) and (25), we can obtain,

Substituting for (θ∞- θs) and δ using eqn(22), (23) and (27)

or,

ζ can be found out by trial and error or by graphical method.

The solidification time ts can then be obtained from eqn(23) using δ(ts) =h/2, as

or,