ELASTIC BEHAVIOUR OF A MATERIAL – STRESS-STRAIN DIAGRAM

GENERAL OBJECTIVE:

• To assess the elastic behaviour of materials through stress-

strain diagram

SPECIFIC OBJECTIVES:

1. sketch stress-strain curve (S)

2. identify proportional limit, elastic limit and yield point (S)

3. predict ultimate tensile strength and breaking stress(S)

4. list four uses of stress-strain diagram (T)

5. identify ductile and brittle regions from stress-strain curve (E)

STRESS – STRAIN DIAGRAM

• Consider a body subjected to uniform increasing stress,

which results in a change in its dimension.

• The relation between stress and strain is studied using a

graph.

• This graph is called stress – strain graph

STRESS – STRAIN DIAGRAM

• OA – proportionality limit

• OB - elastic limit (perfectly

elastic region)

• B - Yield point (large

increase of strain with less

increase of stress)

• D - Breaking stress

(maximum stress before

rupture)

• E – Rupture or breaking

point (material breaks)

PROPORTIONAL LIMIT

• Proportional limit is point on the curve up to which the value

of stress and strain remains proportional.

ELASTIC LIMIT

• Elastic limit is the limiting value of stress up to which the

material is perfectly elastic.

YIELD STRESS POINT

• Yield stress is defined as the stress after which material

extension takes place more quickly with no or little increase

in load.

Ultimate strength

• The greatest stress that the body can experience without

breaking or rupturing.

breaking stress

• Stress at which the material breaks.

Modulus of Resilience

• The resilience of the material is its ability to absorb

energy without creating a permanent distortion.

Modulus of Toughness

• The toughness of a material is its ability to absorb energy

without causing it to break.

Working Stress

• Working stress is defined as the actual stress of a

material under a given loading.

Allowable Stress

• The maximum safe stress that a material can carry is

termed as the allowable stress.

Factor of Safety

• It is the ratio of the breaking stress of a material or

structure to the calculated maximum stress when in use. It

is also called as safety factor.

USES OF STRESS – STRAIN DIAGRAM

• Strength

• Hardness

• Ductility

• Brittleness

• Toughness

F = 779 N

Example 1. The elastic limit for steel is2.48 x 108 Pa. What is the maximumweight that can be supported withoutexceeding the elastic limit?

F

A 2.48 x 108 PaL Stress

F

F = (2.48 x 108 Pa) AL

F = (2.48 x 108 Pa)(3.14 x 10-6 m2) F = 779 N

A

A

Recall: A = 3.14 x10-6 m2

F = 1536 N

Example 2 The ultimate strengthfor steel is 4089 x 108 Pa. What is themaximum weight that can besupported without breaking the wire?

10-6 m2Recall: A = 3.14 x

F

A 4.89 x 108 PaL Stress

F

F = (4.89 x 108 Pa) AL

F = (4.89 x 108 Pa)(3.14 x 10-6 m2) F = 1536 N

A

A

DUCTILE AND BRITTLE MATERIALS STRESS-STRAIN CURVE

Ductile

Brittle

Strain

MIND MAP

SUMMARY

• Elastic behaviour of a material – stress-strain diagram

• Proportional limit, elastic limit, yield point

• Ultimate tensile strength, breaking stress

• Four uses of stress-strain diagram

STIMULATING QUESTIONS

1. Why does the slope of typical Stress-Strain curve

decrease after yielding?

2. Do soft solids like gels possess elasticity or plasticity?

Comment.

THANK YOU……