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Field Manual
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.
