MEC 2403-Lecture 2_Summary

Engineering

MEC2403-Lecture 2

Stress & Strain-Axial Loading

Objective

To show how stress can be related to strain by using experimental methods to determine stress-strain diagram for a particular material

To discuss the properties of the stress-strain diagram for materials commonly used in engineering

To discuss other mechanical properties and tests related to the development of mechanics of materials

MEC2403-Lecture 2 2

MEC2403-Lecture 2 3

Elasticity of Modulus

or Modulus Youngs

E

E

Normal Strain

Strength is affected by alloying,

heat treating, and manufacturing

process but stiffness (Modulus of

Elasticity) is not.

Hooks Law

L

Stress-Strain Diagram: Ductile Materials

MEC2403-Lecture 2 4

Stress-Strain Diagram: Brittle Materials

Fig 2.1 Stress-strain diagram for a typical brittle material.

MEC2403-Lecture 2 5

No necking

Faster time of rupture

No difference between ultimate

strength ad

rupture strength

Elastic vs. Plastic Behavior

If the strain disappears when

the stress is removed, the

material is said to behave

elastically.

When the strain does not

return to zero after the stress

is removed, the material is

said to behave plastically.

The largest stress for which

this occurs is called the elastic

limit.

Fig. 2.18

MEC2403-Lecture 2 6

Fatigue

When the stress is reducedbelow the endurance limit,

fatigue failures do not occur for

any number of cycles.

Fig. 2.21

MEC2403-Lecture 2 7

Deformations Under Axial Loading

AE

PL

With variations in loading, cross-section or material properties,

i ii

ii

EA

LP

Fig. 2.22

MEC2403-Lecture 2 8

Thermal Stresses

coef. expansion thermal

TE

MEC2403-Lecture 2 9

T is the change in temperature

Poissons Ratio

Poissons ratio is defined as

x

z

x

y

strain axial

strain lateral

MEC2403-Lecture 2 10

EEE

EEE

EEE

zyxz

zyxy

zyxx

Generalized

Hookes Law

Dilatation: Bulk Modulus

Change in unit volume is

dilatation E

21

e

zyx

zyx

modulus bulk

213

Ek

210


Shearing Strain

For small strains,

zxzxyzyzxyxy GGG Fig. 2-46

Fig. 2-47


where G is the modulus of rigidity or

shear modulus.

Components of normal and shear

strain are related

Composite Materials

z

zz

y

yy

x

xx EEE

For anisotropic materials, properties are different foreach direction

x

zxz

x

yxy

Materials with directionally dependent mechanicalproperties are anisotropic.


Saint-Venants Principle

Saint-Venants Principle:Stress distribution may be assumed

independent of the mode of load

application except in the immediate

vicinity of load application points.


Elastoplastic Materials

Deformations of an elastoplastic materialare divided into elastic and plastic ranges

Permanent deformations result fromloading beyond the yield stress


Stress Concentration: Hole

ave

max

K

Discontinuities of cross section may result

in high localized or concentrated stresses.

K is stress-concentration factor.

Residual Stresses

Residual stresses also result from the uneven heating orcooling of structures or structural elements

Residual stresses will remain in a structure afterloading and unloading if

- only part of the structure undergoes plastic

deformation

- different parts of the structure undergo different

plastic deformations


Documents

MEC 2403-Lecture 2_Summary