1. Introduction

Semi-solid metalworking is a process in which a partially liquid– partially solid metal mixture is

injected into the die cavity. Although origins of semi-solid metalworking can be traced back over

30 years, the process did not become commercialized for high volume production until the early to

mid-1990s. The process was developed by David Spencer (1) at the Massachusetts Institute of

Technology as an outgrowth from hot-tearing research model Sn-15%Pb alloy in the 1970s. When

inducing hot tears, researchers found that partially solidified metal was thixotropic and could be

deformed under pressure. With an understanding of semi-solid metal behavior, several new net-

shape manufacturing processes were developed based on closed die forging, die casting,

extrusions, rolling, and hybrids of these processes. Semi-solid casting is a relatively new

technology which combines the forming capabilities of pressure die casting with the mechanical

properties of forged products. Semi-solid metalworking has been applied to numerous metal

systems, including aluminium, magnesium, zinc, titanium, and copper as well as numerous ferrous

alloys. The most common commercial alloy systems in use are aluminium and magnesium die

casting alloys. These alloys are ideal for use in semi-solid metalworking due to their wide freezing

ranges. Examples material that is heated to a semi-solid state can be formed, sheared, or cut easily.

During the semi-solid processing, the formation of non-dendritic or globular crystal

microstructure with the appropriate size through shearing can improve the fluidity and uniformity

of materials and eliminate the defects, such as solidification segregation, shrinkage porosity and

shrinkage cavity, which thereby improve the comprehensive mechanical properties of the

materials.

A number of rheocasting processes (“slurry on demand”)are proposed for aluminium alloy; (i)

Direct slurry forming (DSF), (ii) Sub liquidus casting (SLC), (iii) New rheocasting (NRC) (2),

(iv) Thixomoulding, (v) Twin-screw rheocasting (4), (vi) Semi-solid rheocasting (SSR),(vii)

Continuous rheocasting (CRP) (3) and Rapid slurry forming (RSF) (6).The RSF process differs

from other rheocasting processes because heat extraction and temperature control are not

necessary. The RSF process is based on enthalpy exchange of two alloy systems where one alloy

is the low superheat melt (high enthalpy) and the other one act as the cold solid stirring material

(low enthalpy) and is also known as enthalpy exchange material (EEM). During the process, the

EEM is immersed into the melt while stirring action is applied. Heat is absorbed from the melt

during stirring operation. At slurry formation, during melting and dissolution of EEM, a new 1

alloy system will form with a certain enthalpy level and solid fraction depending upon selected

process parameters. The main advantage is that slurry can be produced without temperature

control or outer cooling in a short time.

The implication of rheology in semi-solid metal (SSM) processing is very important. The effect

of several process and metallurgical parameters, such as shear rate, shear time, holding time,

pouring temperature, fraction solid of the primary phase and its morphology, size and

distribution, on the apparent viscosity of the SSM alloys are reviewed and discussed. A variety

of viscometry methods are introduced in characterizing the microstructure and viscosity values

of SSM slurries.

The flow and deformation of metallic alloys “rheological behaviour” are entirely dependent on

the viscosity which itself varies with both metallurgical and process parameters. The followings

give a brief account of the effects of both sets of parameters on the viscosity of SSM slurries.

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2. Rheology

2.1 Introduction to rheology

Thetermrheologywascoinedin1920s,andwasinspiredbyaGreekquotaon,"pantarei","everything

flows".Rheology is defined as the science of the deformation and flow of matter.This involves

the study of what can informally be called "funny fluids" and soft solids. In theory it could

include the study of all materials that deform or flow but, by convention, classical (Hookean)

elastic solids and viscous (Newtonian) liquids are excluded. Both non-Newtonian and elastic

liquids and viscoelastic solids are included in the science.In short, rheology is the study of the

fluid response of a material to an imposed stress.

The rheology is very important to study in these materials to study the flow behavior of the semi-

solid slurry. The rheology is highly dependent on the solid mass fraction, the temperature,

particle size and particle shape. It is generally accepted that the time dependent behaviour results

from the agglomeration and de-agglomeration of the globules.

The concept ofrheological equation of state(orconstitutive equation)occupies the central position

in modern rheology. It is a relationship betweenstresses acting at a point and deformations

occurring as a result of their action.Such a relationship determines all mechanical phenomena

which can be expected in the observation of mechanical behaviour of a material.

Rheologicalequations of state serve the purpose of understanding and describing qualitatively

and (the most desirable) quantitatively various “anomalous” effects observed in real life for real

materials.

The concepts of elasticity and viscosity need to be qualified since real materials can be made to

display either property or a combination of both simultaneously. Which property dominates, and

what the values of the parameters are, depends on the stress and the duration of application of the

stress.

An empirical equation is proposed to correlate viscosity with average aspect ratio and shear rate:

This equation is valid for the shear rates less than 0.01 s−1.

3

The rheological behavior and properties of a substance may sometimes exhibit considerable

changes with time or with continuing deformation. These changes occur either reversiblyor

irreversibly. The break-up or rupture of solids and liquidsinto smaller segments or droplets and

the rejoining and sticking together,“cohesion”, of particles or droplets to make a continuumbody

and mass are often included in rheology . Shearflow is an important type of deformation in

rheology and may bevisualized as a process in which infinitely thin, parallel planesslide over

each other as in a pack of rigid cards.With such simple definition, the inter-relationship of

rheologyand mechanical properties of materials is closely tideup with materials’ viscosity and

deformation behaviour withinmushy state.

2.2 Alloys for Rheological Studies

The alloys studied from a rheological point of view belong essentially to threecategories: the

model alloys like Sn–Pb with a low melting temperature for whichthe experiments are relatively

easy, the aluminium and magnesium alloys, which arethe main thixoformed alloys, and the

alloys with a high melting temperature forwhich only feasibility tests have been carried out.

For the characterization of the rheologicalbehaviour of these semisolid alloys, twoapproaches are

usually adopted.

2.3 Need of Rheology Study

Recently, the rheocasting is a developing manufacturingtechnique which produces near-net-

shape components withlow porosity and good mechanical properties. In rheocasting,the alloy is

sheared continuously during solidification and asemisolid slurry forms which exhibits a complex

non-Newtonian flow behaviour. The flow behaviour of the slurry underdeformation is the

essence of rheocasting and demands adetail rheological study for understanding of the process. It

isfound that the works available in the literature related to therheological behaviour are mainly

experimental. In contrast,the theoretical models are less developed. However, forsuccessful

implementation of the rheocasting process, aplenty of knowledge on the semisolid slurry

behaviour underdeformation is necessary.

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2.4 Rheology parameters

There are various parameters to st

2.4.1 Shear stress

Shear stress is the force acting on the system per unit area which leads to deformation of the

system.A force F applied tangentially to an area A being the interface between theupper plate

and the liquid underneath, leads to a flow in the liquid layer. Thevelocity of flow that can be

maintained for a given force is controlled by the internal resistance of the liquid, i.e. by its

viscosity. Depicted usually as “τ”, it is given by the following formula:

where, F is in Newton, A is in m2 and τ is in Pascal

2.4.2 Shear rate

The shear rate in a system under a force is defined as the rate of change of velocity with distance.

The shear stress τcauses the liquid to flow in a special pattern. A maximumflow speed vmaxis

found at the upper boundary.The speed drops across the gap size y down to vmin= 0 at the lower

boundarycontacting the stationary plate. Laminar flow means that infinitesimally thin liquid

layers slide on top of each other, similar to the cards in a deck of cards. Onelaminar layer is then

displaced with respect to the adjacent ones by a fractionof the total displacement encountered in

the liquid between both plates. Thespeed drop across the gap size is named “shear rate” and in

it’s general for it is mathematically defined by a differential.Generally denoted by the symbol “ϒ

”, , the shear rate is given by the formula:

where, v is in m/s, h in m and is in s-1

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2.4.3 Viscosity

Viscosity is the main parameter for rheology of semi-solid metallic alloys and plays an important

role equivalent to that of “fluidity” concept in liquid metalsand modulus of strength for solids.

Viscosity is an indication of SSM capability in filling the mold and determines the required force

for deformation and flow of materials. According to several recent review articles, viscometry is

identified as an appropriate route for the rheological studies of materials. Ideal viscous body

exhibits flow, with the rate of flow being a function of the stress. One most important type of

flow is due to shear. An ideal viscous body cannot sustain strain for long, since it is relieved by

flow. Of course, extremely viscous materials may exhibit elastic strain for considerable periods

of time; periods which are short with respect to the time needed for appreciable flow. Regardless

of geometry of the body and the deformation, the flow will always be in the form of laminar

shear. Based on Newton’s first law, viscosity is a constant to show the capability of momentum

diffusion through the body of material,

whereV is the momentum velocity, τ the shear stress, η the viscosity and γ0 is the shear rate.

Furthermore, it is a parameter that shows visco-plastic behavior of materials and interprets

viscous flow characteristics in terms of a criterion for comprehension of deformation behavior.

In Newtonian fluids the viscosity, η, is a constant but for non- Newtonian fluids it is a function of

physical properties of the fluid and testing conditions including particle size and distribution,

microstructural degeneration, temperature, shear force and shear rate.

In the eyes of mass producers of metallic artifacts, knowledge of viscosity is equivalent to die

filling characteristics, since lower viscosity causes better movement of material through the die.

The viscosity is always used as an input parameter for prediction of flowability in the simulation

software. Lower viscosity results intricate thin wall component production with lower machine

pressure and reduced rejects and scraps.

2.4.4 Behaviour of fluid flow

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A wide range of information regarding a fluid’s rheological properties can be obtained from

agraph of the shearing stress vs. shear rate in the fluid, commonly known as a “flow curve”.This

curve can be obtained by either varying the shear rate and measuring the shear stress generated in

the fluid or introducing a known shearing stress within the fluid and then recording the shear rate

flow behaviour of the fluid. The major typesoffluid flow behaviour can bedescribedby

meansofbasic shear diagram ofshear rate versus shear stress. Different classifications of the

fluids have different flow curves and similar curves can be grouped together, thereby enabling

researchers to classify various fluids. Thereare two major groups of fluids

a) Newtonian behaviour of fluid

WithNewtonianfluids, the shear rate is directlyproportionalto the shear stress and theplot begins

at the origin. TypicalNewtonianfluids are those containingcompoundsoflowmolecularweight

(e.g., sugars) and that do not contain largeconcentrationsofeitherdissolvedpolymers or insoluble

solids. ExamplesofNewtonianfluids include water, sugar syrups, most honeys, most

carbonatedbeverages, edible oils, filteredjuicesand milk.

Fig2.1: Rheological behaviour of fluid

According to Newton’s first law, the applied shear stress is given as;

It may also be expressed in terms of the applied force F,

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Integrating the above equationfor h = h0 at t = 0 and h = h at t = t, and knowing the initial

pressure, P0 = (Fh0/V), at the onset of deformation, the viscosity–time relationship is given as :

For a Newtonian fluid the average shear rate, γ0av , at any instant during compression is also given

by:

Where vx, η, V, h0, h, F and t are deformation speed, viscosity (Pa s), volume of specimen (mm3),

initial height (mm), instantaneous height (mm), applied dead force (N) and deformation time (s),

respectively. The viscosity is then calculated as the inverse slope of the graph where the left hand

side of Equationis plotted against time.

Fig 2.2: [3Vh0/8πP0(1/h4 − 1/h40 )] is plotted against time for the quasi steady-state part of

the deformation, to calculate the viscosity for different morphologies.

b) Non-Newtonian behaviour of fluid

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All other typesoffluid foods are non-Newtonianwhich means that either theshearstress-shearrate

plot is not linear and/or the plot does not begin at the origin, or the material exhibitstime-

dependentrheological behaviour as a resultof structural changes. Flow behaviour may depend

only on shear rate and not on the durationof shear (time-independent) or may depend also on the

durationofshear (time-dependent).

a) Bingham plastic and plastic behaviour.

b) Shear thinning behaviour.

c) Shear thickening behaviour.

Fig. 2.3.Logarithmic plot representing flow curves in Newtonian, shear thickening and

shear thinning systems

a) Bingham plastic and plastic behaviour

On plotting the rate of shear against the shearing stress, Bingham observed that the relation

between the two quantities was linear over a wide range of shearing stresses; the line when

extrapolated cuts the stress axis at a point above the origin. This point is referred to as the ‘yield

point’ of the fluid and expressed the equation as:

Thus an ideal Bingham plastic is characterized by the fact that the shear rate is proportional to

the shear stress after a finite value of shear stress (yield stress) is achieved. Also, the viscosity of

the ideal Bingham plastic is strongly temperature dependent. This makes the fluid almost

Newtonian above the yield stress. Below the yield stress value the fluid behaves as a plastic

solid. Microscopic analysis of a Bingham plastic reveals that such fluids possess a three-

dimensional network structure which at first resists the shearing stresses until the yield stress

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(hence the plastic solid behaviour at low shear stresses). Beyond yield stress the structure breaks

down leading to the flow behaviour observed. Upon reducing the shear stress below the yield

stress value, the dimensional structure is formed once again.

b) Shear thinning fluids

As the name self suggests these fluids ‘thin’ upon shearing. In more elaborate terms, the apparent

viscosity of such fluids reduces upon increasing the rate of shear on the fluid. Another

representation of such fluids is a logarithmic plot between shearstress and shear rate, which is

generally linear with a slope less than 1. Logarithmic plot representing flow curves in

Newtonian, Shear Thickening and Shear Thinning systems.the slope for shear thinning fluids is

almost unity at the two extremities, i.e. at high and low shear rates these fluids behave as

Newtonian fluids. Due to the linear segment in the logarithmic plot of shear stress to shear rate,

both shear thinning fluids and shear thickening fluids (described later) can be represented by a

power law, which means the fluids can be defined by the following equation:

with n < 1 for shear thinning fluids, n>1 for shear thickening fluids and n = 1 for Newtonian

fluids. From equation the apparent viscosity for such fluids would be defined as,

Some examples of shear thinning fluids include dilute polymer solutions,printing inks with lower

solute content, paints, napalm etc.

c) Shear thickening fluids

These fluids behave in the converse manner to shear thinning fluids and as their name indicates,

these fluids ‘thicken’ on shearing – their apparent viscosity increases with shear rate.Such fluids

are less common in comparison to the shear thinning fluids andalso satisfy the power law

(equation 2.6) with n > 1. Thus the slope of logarithmic plot of shear stress vs. shear rate is

greater than unity. Some researchers have observed this phenomenon of shear thickening at the

beach and have classified sand-water combination type materials, generally called ‘granular

materials’, as shear thickening systems.Recent studies indicate that the phenomenon of shear

thickening occurs during the solidification of molten metals, especially when the molten metal or 10

alloy system transit from a purely molten state to a semi-solid. These semi-solid materials have

exhibited characteristics similar to granular materials including an increase in apparent viscosity.

If the SSM slurry is treated as a non-Newtonian fluid, the results are interpreted in terms of the

power law, relating shear stress (τ) to average shear rate, and the apparent viscosity is the ratio of

shear stress to shear rate.

The expression of viscosity changes in terms of applied stress and resulting shear rates as:

wherem and n are the consistency factor and power-law index, respectively, material constants .

The final results from power-law model analysis yields the followings:

Where,

Briefly, this involves plotting the experimental data using the following equation, valid for

longer times of deformation:

So, the values of m and n may be obtained from the slope and intercept of a plot of log(1−e)

versus log times .

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Fig2.4: Effect of primary α-Al particle aspect ratio on the consistency (m) index

Average aspect ratio

Fig2.5: Effect of primary α-Al particle aspect ratio on the power law (n) index.

It is noteworthy that the equations for m and n do not include the applied pressure and the

resulting shear rate. This is because of the negligible effect that applied pressure has on m and n

values each representing a specific applied pressure for each fraction solid, do not vary much. As

for the effect of primary phase morphology, the graphs in together with the respective

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Equationsshow the reducing and increasing trends for n and m, respectively, with increasing the

average aspect ratio at a constant fraction solid.

The above equation is plotted to emphasize the importance of solid phase morphology on the

viscosity value. This equation also justifies the concept of rheology, where the viscosity of

slurries could be altered by changing the morphology of solid phase.

Fig 2.6: The predicted effect of shear rate on the viscosity of SSM billets for different

morphologies of the solid particles.

AR = 1.4 (globular) AR = 1.8 (dendritic)

The above graph further shows the pseudoplastisity of SEED prepared SSM A356 billets

within low shear rates range, where the viscosity decreases with increasing shear rate.

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3. Effect of various parameters on rheology of slurry3.1. Metallurgical parameters

The most important metallurgical characteristics of SSM alloys to have an effect on viscosity are

as follows.

3.1.1. Fraction solid

One of the most important parameters affecting viscosity of the mush is the fraction solid of the

primary phase, e.g. α-Al dendrites in case of Al–Si alloys. Fraction solid may be calculated by

Scheil’s equation. Thermal data during solidification extracted from cooling curve, and image

analysis of the resulted structure may also be used to calculate and measure fraction solid,

respectively.

wherefS, Tm, TL and k are fraction solid, melting point of solvent (for example, for Al–Si alloys, it

is 660◦C, the melting point of Al), liquidus temperature of the alloy and equilibrium partition

ratio, respectively. Chen and Fandeveloped a microstructural model, to describe the relationship

between viscosity and effective solid fraction, rheological behaviour, of liquid-like SSM slurries

under simple shear flow. In this model, liquid-like SSM slurry is considered as a suspension in

which interacting spherical solid particles of low cohesion are dispersed in a liquid matrix. In a

simple shear flow field, the state of agglomeration and de-agglomeration is described by a

structural parameter n, which is defined as the average number of particles in each agglomerated

chunk. Through effective solid fraction, φeff, viscosity can be expressed as a function of the

structural parameter n.

Fig 3.1: Schematic representation of mushy zone and solidification range, formation of α

phase, in binary Al–Si alloys.

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The effective fraction solid is given as;

where η is instantaneous viscosity, η0 the viscosity of liquid matrix, A the model parameter

related to packing mode which decreases with increasing the packing density, nthe structural

parameter and φeff is the sum of the actual solid fraction and entrapped liquid fraction, effective

fraction solid. the effective solid fraction is influenced by the actual solid fraction, agglomerate

size, and the packing mode in the agglomerated chunks. It is interesting to note that the viscosity

of semi-solid slurry is a direct function of the viscosity of the liquid matrix and the effective

solid fraction.

Fig. 3.2. Schematic representation of viscosity changes with fraction solid at different DCP

points.

The flow conditions affect viscosity only indirectly through changing the effective solid fraction.

Viscosity rises up steadily with increasing of solid fraction till dendrite coherency point (DCP) ,

after which it increases abruptly . As solidification proceeds, both the solid and liquid within the

mushy zone move to compensate for solidification shrinkage, but there is a point during

solidification where the solid can no longer move easily and the already solidified segment tends

to develop strength; a 3D solid skeleton is formed. This is the dendrite coherency point, which

marks the transition from mass feeding to interdendritic feeding during solidification.

In SSM processing, the DCP is postponed due to the forced convection or shallow temperature

gradient within the melt. The breakdown of dendrites due to stirring coupled with

15

multidirectional growth of fragmented dendrites due to more uniform temperature distribution

within the mould, shallow temperature gradient, resulting from forced convection, encourages

the formation of equiaxed grains, thus postponing the rapid rise of viscosity to higher fractions of

solid.

3.1.2. Primary phase morphology

The morphology of primary phase has a pronounced effect on the flow behaviour of semi-solid

metal slurries. It is found that dendritic structures at the same solid fraction exhibit flow

resistance approximately several orders of magnitude greater than the equiaxedstructures. In fact,

the globular particles move easier over each other than dendritic phases which tend to interlock

during application of external force, resistance against flow. In addition, since the beginning of

SSM processing research, it was the non-dendritic structure which imparted the interesting and

useful rheological characteristics, such as psuedoplasticity and thixothropy. Therefore, a good

understanding of the effect of particle morphology on the rheological behaviour is not only of

scientific interests but also has great significance on the development of new SSM processes.

The flow behaviour of the semi-solid slurries depends on the morphology of the primary phase,

whether it is dendritic or globular. Dendritic structure exhibit greater resistance to flow as

comparison to globular structure having the same solid fraction, this is due to interlocking of

dendritic phase during application of external phase whereas the globular particles move easier

over each other.

Different microstructures are being shown in the figure 3.3.

Fig. 3.3 Different morphology

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3.1.3. Particle size and distribution

It is expected to have better flow in finer microstructure as there is easier movement and less

collision amongst particles, lower viscosity. There are always tendencies for the suspended

particles in the liquid matrix to agglomerate. Such tendency is intensified with application of

external forces on the semi-solid mush. The dynamic interaction amongst solid particles causes

the formation of chunks, agglomerated particles, within semisolid slurries and makes the flow of

mush harder. After a while under the influence of viscous forces, the equilibrium takes place

between agglomeration and deagglomeration processes, where the viscosity changes reach a

steady state and uniform distribution of particles observed.

3.1.4. Alloy chemistry and pouring temperature

Effects of solute elements on reducing grain size and consequently improving mechanical

properties of as-cast products are well-established facts. The alloy chemical composition directly

affects the percentage of primary phase solidifies within mushy zone.

It is generally believed that small addition of alloying elements interferes with grains growth and

provides conditions required for new nuclei to form, i.e. to promote the formation of finer grains.

The solutes form an enriched boundary layer ahead of the solidification front in which the actual

temperature is lower than the solidification temperature, constitutional undercooling zone .

Constitutional undercooling is responsible for dendritic growth. In other words, by controlling

alloy chemical composition, the type and percentage of solute elements, constitutional

undercooling and thus the growth rate and morphology of primary phase, dendritic or equiaxed

growth, may be controlled. Pouring temperature or superheat is one of the important parameters

to affect the evolution of primary phase during solidification. Several researchers have

investigated the effect of pouring temperature on the microstructure of as-cast semi-solid metals

in recent years. Low superheats are instrumental in establishing shallower temperature gradient

within the slurry, thus encouraging equiaxedgrowth. Shallow temperature gradient removes

directional heat extraction from the melt and prevents the formation of dendrites within the

mush. This is an effective way to control the morphology of primary phase forms in the recently

introduced SSM processes, since agitation of the slurry is no longer the principal factor in

promoting globular morphology.

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Fig 3.3: Strain–time graphs for SSM billets cast at different pouring temperatures, (a) 4.8

KPa, (b) 11.2 KPa.

Fig 3.4 : Optical micrographs to show the effect of pouring temperature on the Al–Si 356

alloy microstructure

Generally all types of materials whose solidification extendsover a temperature range, mushy

zone, are suitable to be SSMprocessed. This is particularly true for metallic alloys havinga wide

solidification range with dendritic growth. Themushy zone contains the solid and liquid phases,

“the mush”,simultaneously. A wider solidification range is translated intoeasier and more

controllable “mush”. The alloys with narrowsolidification range or single point transformation

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such as eutecticalloys may not be SSMprocessed. It was found sheared dendriticalloys with

broken dendrites have lower viscosity, closeto oil viscosity at room temperature. Such simple yet

importantconcept opened up new frontiers to casting engineers wherenear or net-shape parts

could be fabricated at lower temperatures,by the so-called rheocasting and

thixoformingprocesses. Rheocasting is based on direct casting of the mush, slurry,while

solidification is in progress. Thixoforming and thixomoldinghowever, deal with reheating of the

feedstock materials tothe mushy state temperatures and injecting the reheated alloywithin close

die, thixocasting and thixomolding or open die,thixoforging.

3.2.Process parameters

In addition to metallurgical characteristics of SSM alloys, the process parameters such as

temperature or shear rate could also influence the viscosity and thus the flow behavior of SSM

slurries. The following process parameters are discussed briefly.

3.2.1 Shear stress (force) and rate

One of the most important factors affecting the viscosity of SSM slurries is the applied shear

force. It imposes laminar or turbulent flow within the slurry and induces disintegration of

dendrites and the agglomeration or deagglomeration of the dendrite fragments, the main drive for

fine distribution of primary phase particles. The applied shear force could eventually establish

some sort of equilibrium between agglomeration and deagglomeration phenomena within SSM

slurries, “steady state”, and prevent the formation of bulky particles; the main obstacle to SSM

slurries flow within mould cavity. The term “apparent viscosity”, used for SSM slurries, is to

express the viscosity of steady state flow and varies with shear rate and fraction of solid.

However, before reaching equilibrium, the viscosity bears a transient state and varies at different

shear rates or fractions solid. Shear rate is a material related parameter which varies linearly with

shear force in Newtonian fluids and non-linearly in non-Newtonian fluids. Shear rate plays the

same role as shear force where the increasing of shear rate decreases the viscosity within non-

Newtonian fluids. For ideal Newtonian fluids, the viscosity numbers are independent of shear

rate . The implementation of shear force and the resulted agitation of the slurry is brought about

by different means including mechanical stirring, magneto hydrodynamic (MHD), stirring ,

ultrasonic vibrationor swirling of the melt as in “Swirled Enthalpy Equilibration Device—

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SEED” process . Application of shear force also plays an important role during the course of

preparing the primary feedstock for thixocasting and rheocasting processes, where the

mechanical impeller or agitator, is the means by which the SSM billets are produced. The current

authors have reported the effect of swirling on microstructural evolution of A356 aluminum

alloy during SEED process. Swirling as an external applied force is believed to bring thermal

homogeneity within the SSM slurry and establishes shallow temperature gradient to alleviate

nucleation barrier within the bulk liquid. In addition, swirling may assist in disintegration of

secondary and tertiary dendrite arms. Such phenomenon is the main recipe for equiaxed grain

growth in SSM cast billets with distinct deformation and flow characteristics shows the effect of

swirling on the engineering strain for A356 Al–Si alloy prepared at high superheat and tested at

different initial pressures. Such difference is attributed to the microstructural evolution of SSM

billets due to swirling intensity.

Fig 3.5: Strain–time graphs for different primary α-Al morphologies and pressures

When viscosity of a semi-solid metal slurry is measured during continuous cooling, it is found to

be a strong function of shear rate, decreasing with increasing shear rate. Thus results in denser

and more rounded particles which move more easily past one another. The general shape of the

curve is as shown in figure 2. Viscosity is high at the low shear rates, partly because of

somewhat dendritic form of the grains and partly because of agglomeration of these grains. At

higher shear rates, the agglomeration decreases and the grains become more rosette like resulting

in the decreased viscosity.

A variety of models have been used for the description of shear thinning, one such model is the

cross model, given by

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η−η∞

η0−η∞= 1

1+K (γ̇ )m

The four parameters in this model are η0 , η∞ , K∧m. This model correctly predicts that the

viscosity tends to η0for γ̇ →0, and to η∞for K ( γ̇)¿>>1.

Other similar models can be used such as carreau model

η−η∞

η0−η∞= 1

[1+K ( γ̇ )2]m1 /2

In the intermediate limit where η≪η0and η≫η∞, the equation for the viscosity has the form

η=η0 K (γ̇ )−m = K 2( γ̇ )n−1

This is called Óstwald de Weale model and is valid at intermediate values of strain rate, and n is

called power law index and is useful parameter in rheological measurements.

In the high strain rate region where η≪η0 the shear viscosity can be approximated as

η=η∞+η0

K ( γ̇)m =η∞+K2( γ̇ )n−1

If we set n equal to zero in the above equation, we get

η=η∞+K 2

γ̇

When inserted into stress strain relationship it yields

σ=σ 0+ηP γ̇

Fig.2 Effect of shear rate on viscosity

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3.2.2 Temperature

Temperature is as important as fraction solid and plays the same role. It means the higher

temperature results in lower fraction solid and better deformability and flow. It is not easy to

differentiate between temperature and fraction solid effect on viscosity in semi-solid situation

due to their intertwined close relationship in mushy state. However, there is an inverse

relationship for temperature and viscosity, where higher temperatures impart lower viscosity

values. This equation is only valid for systems where there is not any phase changes due to

temperature variation as, for instance, in polymeric materials.

For SSM mush, the effect of temperature was investigated by the current authors through special

casting procedure where alloys with similar compositions were cast in such a way to have equal

fraction solid at different temperatures by varying the percentage of decanted liquid . The

morphology of solid phase was also the same. The billet with higher temperature, 602 ◦C,

showed greater deformation than that of 594 ◦C. Such behavior may be attributed to both liquid

matrix and primary -Al particles which flow and deform easier at higher temperatures,

respectively. However, it is not yet known if the viscosity values fit into similar relationshipand

further studies need to be carried out.

Fig 3.6: Strain–time graph for the same primary α-Al morphology and fraction solid at

different temperatures of 602 and 594 ◦C, respectively

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3.2.3 Sample size

Generally the sample size effect on viscosity is not a matter of concern if the homogeneity of

temperature or shear rate distribution within the samples is maintained. Nonetheless, it is

preferred to perform tests on small size specimens to reduce the cost of testing, since for larger

specimens more powerful machines are needed. In addition smaller specimens may render less

diverse results. Parallel plate compression viscometry methodalso uses small size samples. Such

matter refers back to mathematical calculation of viscosity, described in some paragraphs later,

for cylindrical samples under parallel plate compression test. Such calculation has been done for

Newtonian and non-Newtonian fluid assumptions. The mathematical solution of the equations in

the non-Newtonian conditions was always for the samples with h_D, (height_diameter), to make

mathematical treatments less complex. For parallel plate compression viscometry and assuming

the SSM samples behaving as “Newtonian fluid”, there is no limit on the sample size as tested in

authors’ laboratory.

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4 Study of forces developed during semi-solid process

The inertial forces within the fluid, enclosed in the annulus of the concentric cylinders, play a

vital role in determining the stability of the fluid during an experiment. Based on which cylinder

rotates, the inertial forces play different roles in maintaining the required laminar flow within the

fluid. With the inner cylinder rotating, the fluid near the inner cylinder tends to move outwards

but the presence of the outer cylinder prohibits this movement. Thus the fluid starts circulating

outwards locally in a small axisymmetric cellular secondary motion known as Taylor vortices.

These Taylor vortices dissipate energy and lead to the increase in the measured torque values.

For formulating the equations of flow, a laminar flow is assumed.

Fig 4.1: Side view of crucible during slurry formation process. It shows the vortex flow

To check this assumption, the Reynolds number (Re) for the fluid is calculated; well defined for

Newtonian fluids in concentric cylinders:

Taylor (Taylor, 1923c), demonstrated the stability of the fluid (in his case: water) in the annulus

and proved that at specific speeds Taylor vortices are introduced into the system, thereby

increasing the torque and producing an apparent shear thickening behaviour. The criterion is

given by the equation

Where

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This criterion helped the formulation of the Taylor Number (Ta) employed in calculating the

criterion of stability. Defined as:

The Taylor Number predicts the onset of Taylor vortices for inner cylinder rotating concentric

cylinders technique, even when the flow is laminar in nature. (Atkinson, 2008) list the

importance of dimensionless numbers in predicting flow behaviour.

a) For inner cylinder rotating: Ta > 3400 – introduction of Taylor vortices; flow laminar.

b) For outer cylinder rotating: Re > 50000 – laminar to turbulent transition; no vortices.

It should be noted that presence of Taylor vortices within a fluid system is not the same as

“turbulent”.

In comparison to the flow between the cylinders when the inner cylinder rotates, when the outer

cylinder is rotated, the inertial forces stabilize the flow through the centrifugal action, thus

leading to the transition from laminar to the turbulent state at a much greater Reynolds number

than for the inner cylinder rotating.

Fig 4.2: Formation of Taylor vortex motion

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5 Measuring rheological properties

5.1 Rheometry

‘Rheometry’ is a measuring technology used to quantitatively determine the rheological

parameters. It involves measuring systems, instruments, analysis and various tests, all aimed to

understand better the behaviour of the solid or fluid under a deformation. Rheometry includes

viscous behaviour characterization in fluids by rotational and oscillatory tests as well as studying

the viscoelastic behaviour through creep tests and relaxation tests in solids. One of the key

outputs in Rheometry is the viscosity of the fluids. Based on the specific properties of the fluid, a

diverse range of measurement apparatus exist, each with their own principle of working,

advantages and disadvantages as well as the diversity of the results obtained from them. In

general, the key output necessary from such apparatus is the fluid flow curve, i.e., the functional

dependence of shear stress in the fluid on the shear rate.

Fig 5.1: Rheological model of RSF process where velocity of melt increases 0 (stationary) to Maximum V (EEM)

5.2 Viscometer

There are several test procedures to study the visco-plastic behavior of SSM slurries. These

methods are based on measuring the viscosity of slurries and are divided into two main

categories depending on the fractions solid, low fraction solid up to 0.4, and high fraction solid,

in excess of 0.4–0.5. The simplest methods to measure the viscosity of low fraction solid slurries

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are the direct methods where the induced torque in the slurries is measured. In general, there are

two types of viscometers, the “Couette” and “Searle” types.

5.2.1 Searle type viscometer

The Searle type viscometer is primary equipment which consists of a torque measuring unit,

which is housed with the motor rotating the inner cylinder. Connected through a steel tube to the

inner cylinder, the steel tube along with the inner cylinder can be detached from the torque

measuring unit to adjust the concentricity of the inner cylinder with a dial test indicator. The

torque measuring unit is connected to the computer through cable wires which transmit the data

after passing through an A-D converter. The motor is in a cage supported on precision bearings.

The inner and outer cylinders are housed in a muffle furnace open at both ends. Through one end

of the furnace, the outer cylinder is raised into position and through the other; the inner cylinder

is lowered into position. The lowering and raising of the cylinders is made possible by gears.

Attached with the viscometer and the computer is a control box which provides the temperature

control, adjustment of the speed of rotation (both increasing from zero and reducing to zero) and

control on the duration of rotation.

Fig 5.2: The types of viscometers: (a) Couette type with rotary outer cylinder and (b) Searle

type with rotary inner cylinder.

5.2.2 Couette type viscometers

In Couette type viscometers, the liquid is between an outer cylinder (cup) and inner cylinder

(bob). Rotation of the cup while holding the bob stationary produces shear stress on the surface

of the bob which are measured as torque. In both apparatus, the temperature of slurry during

stirring process is maintained almost constant by using electric heating elements inside the body 27

of the apparatus. Temperatures are controlled by using thermocouples which are embedded in

different sections. The Couette type viscometer is primary equipment which consists of a cabinet

housed on an iron framework. The cabinet consists of steel panels on 5 sides and a glass door in

the front. At the bottom of the cabinet, is an opening through which the steel shaft connected to

the motor underneath, passes through. The motor, an asynchronous servo motor, enables the

rotation of the outer cylinder. The steel shaft ends in a conical taper which enables fitting the

outer cylinder to the shaft. Inside the cabinet, a vertical air bearing, mounted on an iron frame,

supports the torque measuring unit. Employing a bob-spider, the bob-rod with the inner cylinder

(bob) atone end, is fitted to the air bearing and the torsion wire. On top of the air bearing is the

A-D converter and other electronic components. The electronics are also connected to the torsion

wire, whose deflection due to the deflection of the inner cylinder immersed in the liquid,

measures the torque. Under the glass door of the cabinet, is the control panel of the equipment

which controls the temperature, speed of rotation and the option to evacuate the chamber to fill

with nitrogen gas: purge. The electronics associated with the control unit, is connected to the

computer controller which then monitors the variables through the software. The inner and outer

cylinders are enclosed in two halves of the induction electric furnace during an experiment. The

copper chilling unit under the vertical air bearing helps prevent the bearing from overheating

when the furnace is switched on. The chilling unit cools the air bearing through the continuous

flow of water circulating in the chilling unit. The cabinet enclosure when shut, has provision to

evacuate the chamber and fill with nitrogen gas during experiments with molten metals.

In both methods, the apparent viscosity is calculated by a set of equations given below using

torque data:

WhereT is the measured torque, L the liquid altitude inside the cylinder, γthe shear rate, Ω the

angular speed of rotor, η the apparent viscosity, ri the inner cylinder radius, ro the outer cylinder

radius and r is the actual annular gap radius.

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For the solid fraction of 0.45 or more, viscosity is not generally measured by the rotational

viscometers. Such slugs show mush like behaviourwhich may be characterized by other methods.

5.3 Parallel plate compression test

Parallel plate compression test, direct or indirect extrusion, indentation test and tensile test are

some of these methods.The simplest way to examine rheological behaviour of paste like

materials is by parallel plate compression test.

Fig 5.3: The schematic diagram of a simple parallel plate compression test machine

In this method a dead weight is applied on the top surface of SSM slug and its deformation

behaviour is investigated by analysing strain variation with time. The resulted strain–time graph

is further treated mathematically to characterize the rheological behaviour of tested alloy,

viscosity. The interpretation of results obtained from such graphs can be treated differently

depending on the assumption of the SSM slurries as Newtonian or non-Newtonian fluids. In the

case of low applied shear rates of less than 0.01 (s−1), the resulted graphs could be treated

similar to Newtonian fluids.

A cylindrical sample with low aspect ratio is compressed between two parallel plates at constant

deformation rate or under constant load. Fig.5 shows the schematic of parallel plate compressor.

In this case, the axial velocity becomes insignificant compared to the radial velocity of the alloy

during the later stage of deformation. The stress–strain field in this experiment is highly

inhomogeneous due to the presence of friction therefore the comparison of results should be

made with caution, especially when there are specimen size differences. Advantage of this

technique is it can be used to investigate SSM slurries with high solid fraction, and to detect the 29

presence of yield stress. However, the flow conditions are complex, it is difficult to define the

steady state and, more importantly, it is difficult to prevent solid/liquid segregation.

6. Conclusion

The rheological behaviour of semi-solid metal slurries has been reviewed. Viscosity

measurement is shown to be the appropriate parameter to describe rheological behaviour of

semi-solid metal billets. Attempts were made to generate a better understanding of viscosity

relationships with rheological behaviour of SSM billets on one hand and the metallurgical

properties of SSM billets and process parameters on the other. Fraction solid, particle shape, size,

and distribution, chemical analysis and pouring temperature are the most important metallurgical

parameters influencing the viscosity of SSM billets. Rotational viscometer test and parallel plate

compression test are the two most versatile methods to measure the viscosity for low and high

fractions solid, respectively.

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Appendix

Dendritic coherency point (DCP) -As solidification proceeds, both the solid and liquid within

the mushy zone move to compensate for solidification shrinkage, but there is a point during

solidification where the solid can no longer move easily and the already solidified segment tends

to develop strength; a 3D solid skeleton is formed. This is the dendrite coherency point

Newtonian fluid- A Newtonian fluid (named after Isaac Newton) is a fluid whose stress versus

strain rate curve is linear and passes through the origin. The constant of proportionality is known

as the viscosity.

Non- Newtonian fluid- In a non-Newtonian fluid, the relation between the shear stress and the

shear rate is different, and can even be time-dependent. Therefore, a constant coefficient of

viscosity cannot be defined.

Rheocasting- A process in which a liquid metal is vigorously agitated during initial stages of

solidification to produce a globular semisolid structure which remains highly fluid when more

than 60% solidification has occurred.

Rheology- Rheology is the study of the flow of matter, primarily in the liquid state, but also as

'soft solids' or solids under conditions in which they respond with plastic flow rather than

deforming elastically in response to an applied force.

Shear rate- Shear rate is the rate at which shear is applied.

Thixocasting- Thixocasting utilizes a pre-cast billet with a non-dendritic microstructure that is

normally produced by vigorously stirring the melt as the bar is being cast. Induction heating is

normally used to re-heat the billets to the semi-solid temperature range, and die casting machines

are used to inject the semi-solid material into hardened steels dies.

Psuedoplasticity - psuedoplasticity is an effect where a fluid's viscosity—the measure of a

fluid's resistance to flow—decreases with an increasing rate of shear stress. It is also known as

shear thinning.

Thixotropic fluids-The fluids which exhibit an isothermal reversible decrease of viscosity with

increase in shear rate.

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Viscosity- The viscosity of a fluid is a measure of its resistance to gradual deformation by

shear stress or tensile stress.

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