The document discusses stress-strain diagrams and the mechanical properties they represent. It begins by describing how to create a stress-strain diagram through experimentation. It then explains the different regions of the diagram - the elastic region, plastic region, strain hardening, and fracture. Key properties are defined, including yield strength, tensile/ultimate strength, modulus of elasticity, resilience, toughness, ductility, and brittleness. Examples of stress-strain diagrams are shown for A36 steel. Common mechanical testing properties are also listed.

1. Material Failure Analyses
Instructor: Group Captain Abdul Munem Khan
STRESS STRAIN RELATIONSHIP

2. Experiment to get Stress-Strain Diagram

3. Stress-Strain Diagram
Strain ( ) (e/Lo)
4
1
2
3
5
Stress(F/A)
Elastic
Region
Plastic
Region
Strain
Hardening Fracture
ultimate
tensile
strength
Slope=E
Elastic region
slope=Young’s(elastic) modulus
yield strength
Plastic region
ultimate tensile strength
strain hardening
fracture
Necking
yield
strength
UTSσ
yσ
εEσ =
ε
σ
E =
ε
12
y
εε
σ
E
−
=

4. A36 Steel
Stress and Strain Diagram

5. • - the extent of plastic deformation that a material undergoes
before fracture, measured as a percent elongation of a material.
% elongation = (final length, at fracture – original length) / original length
Ductility
Common Mechanical Properties
• – the
highest stress a material
can withstand and still
return exactly to its original
size when unloaded.
Yield Strength (Sy)
• - the
greatest stress a material can
withstand, fracture stress.
Ultimate Strength (Su)
• - the
slope of the straight portion of
the stress-strain curve.
Modulus of elasticity (E)
• - the capacity of a material to absorb energy within the elastic
zone (area under the stress-strain curve in the elastic zone)
Resilience
• - the total capacity of a material to absorb energy without fracture
(total area under the stress-strain curve in the elastic zone)
Toughness

6. Stress-Strain Diagram (cont)
• Elastic Region (Point 1 –2)
- The material will return to its original
shape after the material is unloaded( like a
rubber band).
- The stress is linearly proportional to the
strain in this region.
εEσ =
: Stress(psi)
E : Elastic modulus (Young’s Modulus) (psi)
: Strain (in/in)
σ
ε
- Point 2 : Yield Strength : a point at which permanent
deformation occurs. ( If it is passed, the material will
no longer return to its original length.)
ε
σ
E =or

7. • Plastic Region (Point 2 –3)
- If the material is loaded beyond the yield
strength, the material will not return to its
original shape after unloading.
- It will have some permanent
deformation.
- If the material is unloaded at Point 3, the
curve will proceed from Point 3 to Point 4.
The slope will be the as the slope between
Point 1 and 2.
- The distance between Point 1 and 4
indicates the amount of permanent
deformation.
Stress-Strain Diagram (cont)

8. • Strain Hardening
- If the material is loaded again from
Point 4, the curve will follow back to Point
3 with the same Elastic Modulus(slope).
- The material now has a higher yield
strength of Point 4.
- Raising the yield strength by
permanently straining the material is
called Strain Hardening.
Stress-Strain Diagram (cont)

9. • Tensile Strength (Point 3)
- The largest value of stress on the
diagram is called Tensile Strength(TS) or
Ultimate Tensile Strength (UTS)
- It is the maximum stress which the
material can support without breaking.
• Fracture (Point 5)
- If the material is stretched beyond Point
3, the stress decreases as necking and non-
uniform deformation occur.
- Fracture will finally occur at Point 5.
Stress-Strain Diagram (cont)

10. Plastic Deformation

11. Brittleness & Ductility
Brittleness
- Measure of the material’s inability to deform before failure.
- The opposite of ductility.
- Example of ductile material : glass, high carbon steel,
ceramics
Ductile
Brittle
Stress
Strain

12. STRESS-STRAIN CURVES

13. Mechanical properties of Various Materials at
room Temp.

14. Questions ???Questions ???