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COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL & ARCHITECTURAL ENGINEERING

CVEN 214: STRENGTH OF MATERIALS

Chapter 3: 3: MECHANICAL MECH ANICAL PROPERTIES OF O F MATERIAL MATERIAL Dr Mohammed Elshafie

 The fascinating world of materials!

 The fascinating world of materials!

 The fascinating world of materials!

Stress (σ) – strain (ε) diagrams-Mild Steel

(1) Modulus of Elasticit y: Hooke’s Law:



Hooke’s Law defines the linear relationship between stress and strain within the elastic region.

 E 

σ   =

= stress

E = modulus of elasticity or Youn g’s mo dul us (N/m2) ε 



σ 

ε

= strain

E can be used only if a material has linear–elastic behaviour .

(2) Modulus of Resilience: Strain Energy 





When material is deformed by external loading, it will store energy internally throughout its volume. Energy is related to the strains called strain energy .

Modul us of Resilience 

ur

When stress reaches the proportional limit, the strain-energy density is the modulus of resilience, u r .

1 =

2

2

σ pl ε pl

=

1 σ  pl 2  E 

, Nm

2

−

(3) Modulus of Toughness: Strain Energy 

Toughness is also defined as the resistance to fracture of a material when stressed 



Modulus of toughness, u t , represents the entire area under the stress–strain diagram. It indicates the strain-energy density of the material  just before it fractures.

(4) Poisson’s Ratio



Poisson’s ratio, v, states that in the elastic range, the ratio of its two strains is a constant since the deformations are proportional.

v=−

ε lateral ε longidudinal



Poisson’s ratio is dimensionless. Typical values are 1/3 or 1/4.

Negative sign since longitudinal elongation (positive strain) causes lateral contraction (negative strain), and vice versa.

Limitations

Poisson’s ratio is constant in the linearly elastic range •

Material must be homogeneous (same composition at every point) •

Materials having the same properties in all directions are called isotropic •

If the properties differ in various directions the materials called anisotropic •

SHEAR STRESS-STRAIN DIAGRAM 



Strength parameter G – Shear modulus of elasticity or the modules of rigidity  G is related to the modulus of elasticity E and Poisson’s ratio  v. τ 

=

G=

Gγ    E 

(

2 1+ v

)

EXAMPLE 3.4

E = 200GPa Poission’s Ratio = 0.32

EXAMPLE 3.4 (CONTINUED)

EXAMPLE 3.5

EXAMPLE 3.5 (CONTINUED)

EXAMPLE 3.6

EXAMPLE 3.6 (CONTINUED)

Failure of Materials Due to Creep and Fatigue Creep 







When material support a load for long period of time, it will deform until a sudden fracture occurs. This time-dependent permanent deformation is known as creep. Both stress and/or temperature play a significant role in the rate of creep. Creep strength will decrease for higher temperatures or higher applied stresses.

Fatigue 

 



When metal subjected to repeated cycles of stress or strain, it will ultimately leads to fracture. This behaviour is called fatigue. Endurance or fatigue limit is a limit which no failure can be detected after applying a load for a specified number of cycles. This limit can be determined in S-N diagram.