Lecture 12 - Hardened Properties of Concrete- Part 2

5/28/2018 Lecture 12 - Hardened Properties of Concrete- Part 2

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Lecture No. 12

Concrete PropertiesHardening and Setting- Part II


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Concrete is a multiphase material containing cement paste

(unhydrated and hydrated compounds), fluids, aggregates,

discountinuities etc..

The overall mechanical and physical properties of such a

composite system depend on the volume fractions and properties

of various constituents , the mechanisms of interaction -whether

mechanical, physical or chemical between the separate phases.

Deformation and Failure Theory

Firstly lets consider the stresses and strains

At a location in an element of material the generalised stress

(strain) state in one, two or three dimensions comprising direct andshear stresses (strains) can be decomposed geometrically to a

system of mutually perpendicular principal stresses (strains) 123 123 acting orthogonal to the principal planes on which the

shear stresses(strains) are zero.


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Since the 18thCentury many theories and models have been proposed to

explain or predict the deformation, fracture and failure of composite systems


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Category 1Predicts failure when a particular function of stress or strain

reaches a critical value and have limited application to concrete.

Category 2Based on fundamental theories of physics and mechanics

and allow evaluation of stresses and strains within composite materials

and for different geometrical arrangements of homogeneous materials.

Category 3Assuming concrete to be a two-phase(matrix and aggregate)

then its stiffness (Elastic Modulus E) can be calculated using models in

which the matrix phase (Em) and aggregate phase (Ea) are arranged in

various configurations and proportions.

The upper bound model, in which both phases experience the same strainfor this arrangement assuming zero Poissons ratio for the constituents,

then

are the volume fractions of the matrix and aggregate

respectively.


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Category 4based on the use of combinations of elements modelling stiffness

(elastic springs), plasticity(yield stress) and viscosity (damper).


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Category 6There is a large discrepancy between the theoreticalstrength of a brittle material ( as calculated from bonding forces

between atoms) and its observed fractured strength.

Theoretical calculations estimate gives values of 10x to 1000x than

those determined experimentally.

In 1920 Griffithexplained the difference by presence of microscopic

flaws or cracks that exist under normal conditions at the surface and

within the interior of a body material, with each crack tip acting as a

stress- raiser.

During crack propagation there is a release of elastic strain engery

Category 5based on statistical distribution of element properties are limited use

for concreteas assumptions must be made before they can be applied.


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During crack propagation there is a release of elastic strain energy (some of theenergy stored as the material is elastically deformed) and new free surfaces arecreated which increase the surface energy of the system.

The critical stress for crack propagation can be calculated by

However for a heterogeneous material such as concrete the task is difficult as

many cracks of different sizes, shapes and orientations either pre-exist or areformed under load . Solid particles of aggregates act both as crack arrestors

and stress intensifiers.


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John NewmanConsider concrete as a thin plate : When stress is graduallyincreased to a certain level the stress and strain intensification near the crack tipscauses small cracks to initiate to stabilize the system.

This stage of the fracture process (Stage 1) has been termed stable fractureinitiation

Stage 2 : Further increases in stress causes the cracks to propagate in direction

essentially parallel to the direction of the applied stress. Termed as stable fracture

propagation

Stage 3 : but when the stress is maintained constant propagation ceases. Termed

as unstable fracture propagation


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Most concretes can be simplified as two-phases materials in which stiffer

and stronger particles are embedded in a softer and weaker matrix.

For such materials experience has shown that most of the theories and

models do not adequately explain or predict the behaviour but can help in

understanding of stresses induced within a composite material under load.

In normal practice it is best to test the concrete and fit the results to

relationships which have been derived on the basis of a knowledge of

fundamental material behaviour.


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Deformation of Concrete

StressStrain relationships for a typical concrete subjected to short

term uniaxial compressive loading to ultimate loading


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Although the axial and lateral relationships appear linear up to 40 to 60 % of

ultimate strength they are not strictly linear. Unlike steel, concrete has no readilyidentifiable elastic limit and for simplicity engineers refer to the tangent and

secant elastic modulusfor design purposes.


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Modulus of Elasticity E- ValueE- Value is the ratio between stress and strain

The stress-strain relationship is non-linear and the material is strictly non-elastic. Therefore 3 types of E-value are used, namely secant modulus,

tangent modulus and initial tangent modulus.


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The secant and tangent moduli can be determined from the stress-strainrelationship from a short term static test in which a specimen is loaded in

uniaxial compression.

The E-value of concrete is influenced generally by the same factors as

strength and relationship between strength and E-Value for normal density of

concrete is


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Poissons RatioFor uniaxial loading Poissons ratio (v) is the ratio between the strain in the

loading direction and that in the unloading direction. It is determined from static

tests. For most concretes v lies within the range 0.15 to 0.2 for loading uptoabout 60% ultimate strength.


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Lecture 12 - Hardened Properties of Concrete- Part 2

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