Lecture # 5 and 6Lecture # 5 and 6

Objectives:Objectives:

1): Relating Stress to Strain using experimental method.

2): Plotting Stress verses Strain (Stress – Strain diagram)

3): Extracting mechanical properties from – diagram.

The Tension and Compression Test

Typical steel specimen withattached strain gauge.

Electrical-resistanceStrain gauge.

The Stress – Strain Diagram

0

0

L

A

P

Conventional and true stress-strain diagramsfor ductile material (steel) (not to scale).

True Stress – Strain Diagram

Stress-Strain diagram for mild steel

Stress – Strain Behavior ofDuctile and Brittle Materials

Percent elongation = %1000

0

L

LL f

Percent reduction of area = %1000

0

A

AA f

Hooke’s Law

(mm/mm)

E

Typical Stress-Straincurve showingmodulus of resilience, MR.

Typical Stress-Straindiagram showing

modulus of toughness, MT.

Poission’s ratio.Poission’s ratio.

h

h

b

b

d

d

ensionlateraloriginal

ncontractiolateral

dim

1

(a) Lateral contraction for a bar in tension with

(b) Cross-sectional dimensions.

Deflection Due to Axial Loading

AE

PL (in.) or (mm.)

(a)Undeformed bar and

(b)Bar subject to axial force showing deformation.

Deflection Due to Axial Loading

(in.) or (mm.)ii

ii

iEA

LPN

1

Bar with intermediate axial loads.

Bar with changes in cross section and intermediate loads.

Deflection Due to Axial Loading

(in.) or (mm.)L

dxxExA

xP

0 )()(

)(

(a)Bar with variable cross sectional area and

(b)Bar subjected to loading that varies with x.

Elastic Strain verses Plastic Strain

Strain Hardening