CE 444 PROPERTIES OF FRESH AND HARDENED

CONCRETE

Gürkan YILDIRIM

Serhat Çelikten

ELASTIC BEHAVIOUR

All objects are deformable. It is possible to change the shape or the size of an object by applying external forces. However, the internal forces in the object resist to deformation.

Stress and Strain

Stress: is a quantity that is proportional to the force causing a deformation. Stress is the external force acting on an object per unit cross sectional area.

Strain: is a measure of the degree of deformation. It is found that for sufficiently small stresses strain is proportional to stress.

The constant of proportionality depends on the material being deformed and on the nature of deformation.

We call this proportionality constant as modulus of elasticity or Young’s modulus.

The elastic modulus is therefore the ratio of stress to the resulting strain

Elastic Modulus = Stress / Strain

In a very real sense it is a comparison of what is done to a solid object (a force is applied) and how that object responds (it deforms to some extent)

The response of a material to applied forces depends on the type and nature of the bond and the structural arrangement of atoms, molecules or ions.

Basic deformation types for load carrying materials are:

1. Elastic deformation (deformations are instantaneously recoverable)

2. Plastic deformation (non-recoverable)

3. Viscous deformation (time dependent deformation)

Elastic means reversible!

Elastic Deformation1. Initial 2. Load 3. Unload

F

d

bonds stretch

return to initial shape

F

d

Linear- elastic

Non-Linear-elastic

Return to the original shape when the applied load is removed.

Plastic means permanent!

Plastic Deformation1. Initial 2. Load 3. Unload

p lanes still sheared

F

delastic + plastic

bonds stretch & planes shear

dplastic

F

dlinear elastic

linear elastic

dplastic delastic

Could not return to the original shape when the applied load is removed.

Viscous Deformation

Plastic deformations in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism. Usually attributed to fluids. But solids may also behave like viscous materials under high temperature and pressure.

Viscous materials deform steadily under stress. Deformations are time dependent.

1. Elastic MaterialsReturn to the their original shape when the applied load is removed.

Unloading

d

P

Loading

2. Plastic MaterialsNo deformation is observed up to a certain limit. Once the load passes this limit, permanent deformartions are observed.

δ

P

Limit

Plastic deformation

UnloadingLoadin

g

Hooke's Law

• Modulus of Elasticity, E:

• Hooke's Law: For elastic materials, stress is linearly proportional to strain and is independent of time.

s = E e

s

Linear- elastic

E

e

F

Fsimple tension test

Example: Uniaxial Loading of a Prismatic Specimen

AfterBefore

10 cm

10 cm

10 cm

10.4 cm

9.9 cm

9.9 cm

Determine E

P=1000 kgf

10cm

10cm

1000 kgf

P=1000 kgfP=1000kgf → σ= 10*1

0

1000

= 10kgf/cm2

E=

σε =

100.0

4

= 250 kgf/cm2

Modulus of Elasticity :

• High in covalent compounds such as diamond

• Lower in metallic and ionic crystals• Lowest in molecular amorphous

solids such as plastics and rubber.

Elastic Constants of Some Materials

E(psi)x106

(GPa)G(psi)x106 (GPa) ν (-)

Cast Iron 16 110 7.4 50 0.17

Steel 30 205 11.8 80 0.26

Aluminum 10 70 3.6 25 0.33

Concrete 1.5-5.5 10-40

0.62-2.30 4-15 0.2

Wood Long 1.81 12Tang 0.10 0.7

0.11 0.7 0.03 0.2

?

PROPERTIES RELATED TO STRENGTH

Strength is the ability of a material to resist applied forces without yielding or fracturing.

Strength of a material may change considerably with respect to the way it is deformed.

Mode of stress, type of stress & rate of stress application may affect the strength of a material.

Strength data are usually obtained from lab. Tests which are performed under strictly standardized specimens under controlled conditions. These tests also serve for obtaining σ-ε relationships.

σ-ε curves can be grouped into three as:

• Ductile Materials → exhibit both elastic - plastic behavior

• Brittle Materials → exhibit essentially elastic behavior

• Viscoelastic Materials → exhibit large elastic deformation

SPECIAL FEATURES OF STRESS-STRAIN DIAGRAMS

σPL

σE

σY

σF

σU

A B

C

D

E

Point A (Proportional Limit): The greatest stress (σPL) that can be developed in the material without causing a deviation from the law of proportionality of stress to strain. In other words it is the stress upto which the material responds following Hooke’s Law.

Point B (Elastic Limit): Maximum stress (σE) that can be developed in a material without causing permanent deformation. In other words it is the stress upto which the deformations are recoverable upon unloading.

Point C (Yield Point): The stress at which the material deforms appreciably without an increase in stress. Sometimes it can be represented by an upper and lower yield points. σY,U represents the elastic strength of the material and σY,L is the stress beyond which the material behaves plastically.

Point D (Ultimate Strength): It is the maximum stress that can be developed in a material as determined from the original X-section of the specimen.

Point E (Fracture Strength): The stress at which the material breaks, fails.

A ductile material is the one which deforms appreciably before it breaks, whereas a brittle material is the one which does not.

Brittle materials such as concrete do not have a yield point and do not strain-harden. Therefore, the ultimate strength and breaking strength are the same. They do not show any plastic deformation but fail while the deformation is elastic.

DETERMINATION OF E FROM σ-ε DIAGRAMS

For materials like concrete, cast iron & most non-ferrous metals, which do not have a linear portion in their σ-ε diagrams, E is determined by approximate methods.

1. Initial Tangent Method: Tangent is drawn to the curve at the origin

2. Tangent Method: Tangent is drawn to the curve at a point corresponding to a given stress

3. Secant Method: A line is drawn between the origin & a point corresponding to a given stress

32

1

ε

σ

CREEP

It can be defined as the slow & progressive (increasingly continuing) deformation of a material with time under a constant stress.

It is both a time & temperature dependent phenemenon.

The method of carrying out creep tests is to subject the specimen to a constant stress while maintaining the temperature constant and measuring the extent of deformation.

The resulting data are presented as deformation (strain)-time curve.

Instantaneous elastic strain

Deformation (strain)

Time

A

V0

E

D

C

B

Primary

Creep

Secondary Steady-State

Creep

Tertiary

Creep

When a load is applied at the beginning of a creep test, the instantaneous elastic deformation (AB) is followed by transient or primary creep (BC) then the secondary or steady-state creep (CD) and finally by tertiary or accelerated creep (DE).

Instantaneous deformations Elastic

The primary creep rate has a decreasing rate because of work hardening. It is similar to delayed elasticity (retarded elasticity) and the deformations are recoverable.

Secondary creep is essentially viscous in character. The minimum creep rate (V0) is determined by the slope Δε/Δt.The secondary creep stage is highly temperature-sensitive. It can be related to temperature with an equation similar to that in viscosity.

RTEn eA

t

Tertiary creep occurs at an accelerated rate. Time to rupture & stress relationship can be given as:

nr at

tr: time to failure

a, n: material constants

The two parameters determined from creep tests are:

1.Δε/Δt (Steady state creep rate): engineering design parameter for long-life applications.

2.Rupture lifetime (tr): relatively short-life applications

Both temperature & applied stress adversely affect the creep strains. Usually under the same temperature different stress levels are applied & the creep strains are determined.

Creep Strain

T1 or σ1

Time

T2 or σ2

T3 or σ3

T4 or σ4 T1<T2<T3<T4

σ1<σ2<σ3<σ

4

When the slope of two curves (dε/dt) are determined the material constants can then be determined. In practice, however, three or more stress levels are usually used for discrepancies in lab data.

dε/dt

dε/dt

dε/dt

σ1=55MPa

σ3=69MPa σ2=62MP

a

Creep

Strain

Time