BASIC RHEOLOGY

Chapter 2

BASIC RHEOLOGY

9 APPLICATION TO FRESH CONCRETE

2.1

In its broadest

sense, RHEOLOGY

can

be

considered

as a branch

of

science

dealing with deformation and flow of matter. The term itself comes from Greek ' pant a reV

: everything flows.

It is usual to restrict the application of the term rheology, especially engineering practice, to materials which laws for

flow

and

deformation

of

in their behaviour do not follow

ideal,

elastic,

solids,

simple

in the

(Newtonian)

fluids and gases. There are no rigid boundaries between materials for which the 'ideal' material laws adequately describe their behaviour. Materials studied by practical rheology often show a much more complex behaviour.

Rheological methods for assessment can be therefore aplied of

concrete

both

in

its

fresh

and

in

its

final,

hardened

to the behaviour state.

There

are

circumstances in which the non-elastic behaviour of solid concrete has practical significance. Such cases arise when close

to ultimate

ones

are

'plastic' deformations occur when

applied

to

hardened

concrete

or

when

stresses

long-term,

sustained loading and the resulting creep deformations are considered. However, in most situations the laws of deformation of ideal solids adequately

describe

or predict the behaviour of hardened concrete.

There is a much greater scope for the application of rheologial methods when fresh concrete

is considered.

All

concrete

has

to pass

through

a

shorter

or

longer period of time between the initial mixing of cement and water, which is usually simultaneous with the addition of aggregate and

the stage

in which it

solidifies enough for the laws of ideal solids to apply. The term FRESH

CONCRETE

refers to this period. Fresh concrete together with FRESH CEMENT PASTE, which is one of its principal constituents are materials which fall within the scope of practical rheology.

It is common practice to consider fresh concrete as a dispersion of aggregate in a liquid medium represented by the cement paste. The cement paste itself is a suspension of

solid

particles

(cement)

in a

liquid

medium

(water) and

it

is

probably more appropriate to consider fresh concrete as a multiphase material. Water then becomes the continuous phase in the multi-phase liquids representing fresh concrete.

The

rheological

characteristics

and

equations parameters

which of

determine

fresh

concrete

the are

basic based

rheological on

several

assumptions, namely that concrete when considered as a multiphase material is :

10 a.

A

continuum,

i.e.

a

material

with

no

discontinuity

between

any

two

points. b.

A

homogeneous

mix,

i.e.

a

materials

with

a

uniform

composition

throughout. c.

An

isotropic material,

i.e.

a material

of

the

same properties

in all

directions.

It is easy to see that fresh concrete in practice is unlikely to satisfy all the three assumptions

simultaneously.

The degree of

compliance

tends

to vary

greatly from one type of concrete mix to another. It also depends on how closely the structure of concrete is observed, on a micro-scale the material is unlikely to remain a continuum.

The state in which the material carried

out

shearing.

also

matters.

In practical

The

is when a rheological

most

situations,

common

state

however,

such

has a

measurement

been

state

that is

is being

of

rare.

a

steady

Even

when

fresh mix is being pumped the shear tends to vary or oscillate and in many other forms

of

placing

rheological

or

transport

investigations

the

have

shearing

taken

is dynamic

this

into

and

variable.

account

and

Recent

attempts

to

introduce testing regimes more akin to the conditions in real concrete are being made.

In case of a multiphase shear

strain

applied

while

material

such as fresh

rheological

concrete

characteristics

the magnitude

are

assessed

is

of

also

important. Very small strains are likely to produce different basic parameters from

the

very

large

strains

with

a

large

area

of

change

for

all

strains

in-between. An understanding of the basic rheological parameters and characteristics therefore

a pre-requisite

for

a survey

of

the

current

level

is

of knowledge

of

deformation

or

behaviour of fresh concrete mixes. Rheological

parameters

enable

us

to predict

the

amount

of

flow which will occur when a given stress is applied or, vice versa, the stress caused by a certain amount of deformation. the

limitations of both

theoretical

It is also important to be aware of

and practical

rheology when applied

to a

material as complex as the fresh concrete.

2.2

NEWTONIAN FLOW Load applied to an ideal solid will produce deformation. Such a solid

body

will follow Hooke's law : the stress generated by the load will create strain which will be proportional to the amount of stress and inversely proportional to its stiffness (modulus of elasticity).

In this case the application of the load

11 will produce an instantaneous deformation which will not change with time. The body will return to its original shape, the deformation will be recovered, once the load is removed. The same relationship applies when a shear stress The shear strain

γ

τ

acts on an ideal solid.

is proportional to the shear stress, the coefficient of the

proportionality is the the shear modulus G, the relationship is expressed by the equation: τ = G . γ If the shear stress is applied to an ideal Newtonian fluid, the shear stress will cause

the fluid

to deform

and unlike

in the case of an

ideal

solid

fluid will continue to deform as long as the stress is applied.

Fig.2.1

Shear force (P) acting over an area A and the shear deformation.

the

12 The rate at which the deformation occurred, expressed as strain y per unit of time

or

more

generally

as

the

time

differential

of

the

strain,

will

be

proportional to the shear stress τ as in the equation:

dr τ

= η . _

=

η

. γ

In this case the shear modulus G is replaced by the coefficient of viscosity 7).

Shear in fluids is usually represented by two parallel plates, one of which

moves relatively to the other.

SHEAR Fig.2.2

STRAIN

Shear modulus G

of an ideal solid.

The continuous shear strain can be expressed as the velocity the fluid remains in a laminar motion a Newtonian viscous flow shear stress is proportional over

a

unit

length

of

ν . Provided in which

the

to the rate of change of velocity of the laminae

distance

y

between

the

moving

plates

will

occur

(Fig.2.3). The shear stress then can be expressed in more general terms:

= η .D

where

dv/dy = D is the velocity gradient

As the velocity gradient is equivalent to the rate of change in shear strain with time

dv/dt = γ , τ

the equation can be rewritten as: =

η ·

r

The basic rheological characteristic of the laminar flow of a Newtonian fluid is the viscosity

η , determined from the equation:

13 Ή = τ / y = shear stress / rate of shear =

The SI unit

Pa / s

1

=

2

Pa.s

is therefore 1 Pa. s

( lN/mm = 1 Pa )

(pascal second),

the e.g. s unit

previously

2

common was 1 poise = dyne.sec.cm .

Viscosity of Newtonian fluids is determined by a measurement of shear stress at a given rate of shearing of the fluid, expressed as the shear strain rate y. The shear stress distribution in the volume of the fluid tested depends on the geometry of the apparatus flows. However, shear

stress

in which

the viscosity τ

and

the

η

rate

the fluid

is confined

of a Newtonian fluid of

shear

calculated from one single measurement

γ

or

through which

is independent

applied.

It

can

be

of

it the

therefore

providing a pair of data was fitted into

the Shear stress / Rate of shear diagram such as is shown on Fig.2.4.

Fig. 2.3.

Laminar viscous flow.

All Newtonian fluids are represented by straight

lines passing

origin, the constant slopes of the lines indicating the viscosity

through

the

η .

Viscosity of different Newtonian fluids varies considerably, in each case the viscosity

being

strongly

dependent

on

temperature

and

to

a

lesser

degree

on

pressure. The test conditions must be therefore known and correct results are obtained only when the fluid is in a laminar flow

during the test.

Typical viscosities at 20°C are: water lubricating oils bitumens/tars

1 χ 10"

3

Pa. s

15 - 100 1 - 100 χ 1 0

Pa. s 5

Pa. s

14 There is a very large number of methods which are used for determination of viscosity such as those based on

capillary tubes, rotating coaxial cylinders,

orifices, falling sphere etc. There is also a large amount of literature on the topic

of

measurement

of

viscosity,

eg.

by

Whorlow

(ref.l)

who

provided

an

excellent survey of the methods used.

Fig. 2.4.

Viscous flow of a Newtonian fluid

NON-NEWTONIAN FLUIDS AND COARSE SUSPENSIONS

2.3

Many fluids do not follow the simple behaviour of a Newtonian fluid which has been

already

described.

Their

characteristics,

namely

viscosity,

are

not

independent of the magnitude of shear and the rate of shear strain applied. Such fluids also often change their flow with the length of time for which shear is applied. The manner in which the rate of shear varies also matters. Some fluids require a certain minimum level of shear stress called the

T

YIELD STRESS

q

to

be applied before they begin to flow at all. The

straight

shear stress τ

line

showing

a

simple

and shear rate y

proportional

relationship

shown on Fig. 2.4

between

changes. The relationship

becomes either non-linear and/or the fluid exhibits the yield stress τ The

diagram

on

Fig.2.5

shows

the

behaviour

of

different

Non-Newtonian fluids expressed by the shapes of the curves of

The

non-Newtonian

classified

fluids

as pseudoplastic

which fluids.

do

The

shear diagram then indicates the plastic

The curve

b

on Fig.

2.5

not

possess

slope

of

viscosity

represents a

the

yield the

of

τ = f (y).

stress

shear

. types

are

stress

generally /

rate

of

T^.

typical

case of

the

pseudoplastic

behaviour in which there is a decrease in the plastic viscosity when the rate of

15 shear increases but the change called

itself

is not

linear. This phenomenon

is often

shear-thinning.

The curve

c

represents a case of shear-thickening,

also called

dilatancy.

Some materials increase their volume when subjected to increasing shear and this phenomenon

is called

volumetric

dilatancy.

The

curve

c

also

indicates

an

increase of viscosity with the rate of shear.

The

relationship

between

the

shear

stress

and

the

shear

rate

for

the

pseudoplastic fluids generally follows an exponential curve governed by a power law, eg.

N

τ

A = A . γ

where: A η

0 Fig.2.5

is a constant related to the consistency of the fluid is the index of flow, for

η < 1

the behaviour is shear-thinning,

for

η > 1

the behaviour is shear-thickening

SHEAR RATE Relationships between shear stress and shear rate for different types of non-Newtonian fluids.

16 Many of the non-Newtonian fluids show a time dependent behaviour. The τ - γ relationship depends on

the

length of

time

for which

a

certain

level

of

the

shear rate is maintained and the time it takes both to reach the given rate(s) and to return to the zero rate again (acceleration, deceleration).

Two basic types of a non-Newtonian fluid are recognised according time-dependent behaviour:

Thixotropic subjected

to

fluids a

thixotropic

show

constant

a

and anti-thixotropic

decrease

rate

of

of

shear.

apparent

(rheopectic).

viscosity

Alternatively,

to their

the

with

time

same

effect

when is

indicated by a reduction of the shear stress measured. The r.ate of decrease of the shear stress diminishes with time and tends to level-off. Once the rate of shear is brought back to zero, most thixotropic materials begin to recover and after a period

of

Anti-thixotropic

time at rest fluids

behave

the same in

the

test

results can be obtained

opoposite

way.

Typical

flow

again. curves

indicating thixotropic behaviour are shown on Fig.2.6.

Fig. 2.6.

Flow curves of a thixotropic fluid.

The acceleration and deceleration of the rate of shear often causes different shear stresses and the plot takes on a shape of a hysteresis loop. If the start and

end

coincide

the

material

indicates such behaviour.

is

If there

truly

thixotropic;

curve

is a difference and

(a) on

the material

Fig.

2.6.

does not

recover fully once the shear rate has been brought back to zero it is sometimes classified behaviour.

as

pseudo-thixotropic;

curve

(b)

on

Fig.2.6.

indicates

such

17 A group concrete

of non-Newtonian

technology

are

fluids

of

particular

the fluids or plastic

interest

bodies which

in

the

context

require a

of

certain

minimum level of shear stress, the yield stress x Q, before they begin to deform. Such materials are often classed as Bingham fluids or plastics. The behaviour of a Bingham fluid

is represented by the curve

(a) shown

on Fig.2.5. The basic relationship for a Bingham fluid is : τ

where

= τ

ο

+ η

ρ

γ

is the plastic viscosity.

The flow of ideal Newtonian and Bingham

fluids

through a pipe

is shown on

Fig. 2.7. The shear stress is the greatest at the wall of the pipe, the stress reduces away from the wall until,

in case of a Bingham fluid,

it reaches

the

level of the yield stress. Shear stress below the yield value will not cause any deformation, the fluid in the central region of the pipe will move on as a solid

in a manner called a

plug flow.

b

0

ο

Newtonian

Fig.2.7

Stress

distribution

in

ideal

Bingham Newtonian

and

Bingham

fluids

flowing

through a pipe. Laminar flow is assumed.

The majority of true liquids behave under normal fluid

and

the same applies

to suspensions

suspended solid matter is either uniformly dispersed.

in which

low or the matter

conditions the

like Newtonian

concentration

of

the

is very finely divided and

In such cases the basic effect of the solid matter is an

increase in the viscosity of the suspension.

18 The effect can be approximately calculated using Einstein's basic equation:

\

= "ο

( 1 + 2

5

v

C

> where:

η = viscosity of the suspension J η = viscosity of the medium ο C = volumetric fraction of the particles ν

Einstein's relationship predicts viscosity of suspensions of rigid

spherical

particles in very dilute concentrations. It ceases to apply when an interaction between

the

suspended

particles

occurs.

The

interaction

can

take

several

different forms. There can be attraction or repulsion between the particles or the shape of the particles may cause them to interlock during the flow. and

orientation

of

the

suspended

particles,

eg.

fibres,

can

Shape

change

and

anisometric particles such as fibres are likely to align with the direction of the

principal

stress.

Such

behaviour

affects

greatly

any

rheological

measurements carried out in an unsteady state, namely during start-up or end of flow.

As

the

concentration

of

the

suspended

matter

increases

it

becomes

necessary to examine its effect on the liquid medium itself.

Stress and gradients of rate of deformation can also affect the distribution of the suspended matter. high, the fluid

When the concentrations of the particles become very

is often considered as a composite material and shear

modulus

rather than viscosity is calculated.

Suspensions

which

do

not

follow

Einstein's

relationship

often

behave

as

non-Newtonian fluids no matter whether the liquid phase were Newtonian or not. The behaviour depends on the type of flow, higher

concentrations

only

the Newtonian behaviour extends to

in case of a unidirectional

steady

flow where

the

particles, even if they were of an irregular shape, could become orientated and their

interaction reduced.

However, a simple Newtonian

liquid with

sufficient

concentration of the solid phase can show a yield stress and different types of non-Newtonian rheological behaviour (ref. 3 ) .

Rheological parameters of concentrated

suspensions are difficult

to measure

because the shear stresses and the rates of deformation during tests can affect the distribution of the suspended particles of the solid matter.

Theoretical

models of rheological

suspensions were proposed

behaviour

(eg. ref.2).

of Newtonian

and

non-Newtonian

These models took account of the size,

shape, particle distribution of the solid matter but most of the models still rely

on

parameters

obtained

by

the

fitting

of

the

models

into

curves

from

19 particular tests.

It was very difficult

to correlate the rheological

behaviour

with structure of the fluid, for example, to indicate whether the existence of a yield stress was due

to mechanical

interlocking

of

the solid

particles or

to

interactions between the particles.

The complexities of rheology, particularly of the non-Newtonian fluids have been dealt with in a number of fundamental reference books on the topic, such as refs.

4

and

5.

The

results

of

the

continuing

research

appear

in

many

new

publications and conference proceedings. 2.4 1 2 3 4

REFERENCES R.W.Whorlow, Rheological Techniques, J.Wiley, Chichester, Great Britain, 1980. A.A.Collyer, D.W.Clegg, Rheological Measurement, Elsevier Applied science, London, Great Britain, 1988. E.R. Eirich (Ed.), Rheology, Theory and Applications, Vols. I-V., Academic Press, New York, U.S.A., 1956 - 1969. Z.Sobotka, Rheology of Materials and Engineering Structures, Elsevier Science Publishers, Amsterdam, The Netherlands, 1984.