The document outlines the fundamental concepts of stress and strain, including definitions, types, and relationships such as Hooke’s law. It explains the calculation of material parameters from stress-strain curves and describes elastic and plastic deformation. Additionally, it includes specific values for Poisson's ratio and material moduli for various materials.

1. By
Priyanka Singh
M.Tech (Applied Mechanics)
Motilal Nehru National Institute of Technology

2. Objectives
1. Define stress & strain.
2. Utilize Hooke’s Law to calculate unknown stresses and strains.
3. Determine material parameters from a stress-strain curve.
4. Recognize elastic and plastic components of deformation in a material.
5. Identify the regions of behavior on a stress-strain diagram.

3. Intensity of Force
Stress = ____ /____

4. Normal : load perpendicular to area

5. Types of Stress
a) Normal
b) Shear : load parallel to area

6. Types of Stress
a) Normal
b) Shear
c) Hydrostatic (uniform pressure)

7. Strain: Intensity of Deformation
e = ____/_____ =dl / lo

8. Normal : deformation in the the direction of
length
Longitudinal Strain
e = u / l
Transverse Strain
e = v / l

11. Poissons Ratio Values
ν = 0.5 constant volume
ν = 0.3 good guess for most materials

12. Types of Strain
Normal
Shear : deformation normal to length

13. Types of Strain
Normal
Shear
Dilatational (volume change)

14. Called a “Constitutive Model”
Simple Linear Model:
“Hooke’s Law”

15. Relating Stress and Strain
Normal
S = E e
Stress = Young’s modulus x strain

16. Relating Stress and Strain
Shear
Hooke’s Law
τ = G γ
Shear Modulus
G = E / [2 (1+ ν )]
τ = shear stress
G = shear modulus
γ = shear strain

17. Relating Stress and Strain
Dilatational (hydrostatic)
Hooke’s Law
P = K ∆
K= E/3(1-2ν)
P = pressure
K = bulk
modulus
∆ = ∆V/ Vo

18. -Hookean to a limiting strain
-Proportional limit : Deviation from linear
-After PL
*Linear
*Flat
*Non linear

19. Tensile Test
Callister, Materials Science & Engineering

20. What is Elastic Deformation?

21. *Recoverable strain (elastic)
*Nonrecoverable strain (plastic)
Real Material Behavior
S
e
Elastic
Elastic/plastic
Plastic Elastic

23. Unload/Reload
Callister, Materials Science & Engineering

24. Yield Strength from S-e Curve

28. Representative Modulii
MaterialMaterial Modulus (psi)Modulus (psi)
AluminumAluminum 10x1010x10^6^6
SteelSteel 30x1030x10^6^6
PolycarbonatePolycarbonate 300 x 10^3300 x 10^3