Stress strain graph of various materials

1. Department of Mechanical Engineering
Approved by AICTE, Government of India & affiliated to Dr. A.P.J. Abdul Kalam Technical
University, Lucknow
Subject : Strength of Material
Subject Code : KME 502
Lecture 3:Stress strain graph of various materials
Prepared by Dr. Nagendra Kumar Maurya

2. Determination of Mechanical Properties
Figure 1 Tensile-test machine with automatic data-processing system.

3. Figure 2 Typical tensile-test specimen with extensometer attached

4. Figure 3 Rock sample being tested in
compression to obtain compressive
strength

5. Figure 4 Stress-strain diagram for a typical structural steel in tension
not to scale)

6. Figure 5 : Necking of a mild-steel bar in tension

7. Figure 6 Tensile test curves for various metals

8. Figure 7 Typical stress strain curves for hard drawn wire material

9. Classification of material
• Ductile materials
• Brittle materials
 Materials with high ductility are termed ductile materials and members with
low ductility are termed brittle materials.
 A quantitative value of the ductility is obtained by measurements of the
percentage elongation or percentage reduction in area.

10. Figure 8: Typical stress-strain diagram for a brittle material showing the
proportional limit (point A) and fracture stress (point B)

11. Elasticity, Plasticity
Figure 9: Stress-strain diagrams illustrating (a) elastic behavior
(b) partially elastic behavior

12. Lateral strain
d
d-Δd
It is the ratio of change in
diameter over original diameter
Figure 10 (a) without loading (b) after applying load P P
P
P

13. Poisson’s Ratio
Figure 11: (a) bar before loading, and
(b) bar after loading.
 Poisson’s ratio is named for the famous French mathematician Simeon Denis
Poisson (1781–1840), who attempted to calculate this ratio by a molecular
theory of materials.
 The lateral strain at any point in a bar is proportional to the axial strain if the
material is linearly elastic.
 The minus (-ve) sign is inserted in the equation to compensate for the fact that
the lateral and axial strains normally have opposite signs.
 For most engineering materials the value of ‘ν’ lies between 0.25 and 0.33

14.  Materials with an extremely low value of Poisson’s ratio include cork, for
which ν is practically zero, and concrete, for which ν is about 0.1 or 0.2.
 A theoretical upper limit for Poisson’s ratio is 0.5. Rubber comes close to
this limiting value.
Limitations
 The material must be homogeneous
 Elastic properties must be the same in all directions perpendicular to the
longitudinal axis.

15. References
Mechanics of materials by James M Gere
MECHANICS OF MATERIALS I by E. J. HEARN