Call Girls in Ramesh Nagar Delhi ๐ฏ Call Us ๐9953056974 ๐ Escort Service
ย
tensile test - stress strain curve
1. Tensile Test
V K Jadon
V K Jadon, Professor, Mechanical Engineering
2. V K Jadon, Professor, Mechanical Engineering
Tensile Test
Elongation(%) and Reduction in Area(%)
Resilience and Toughness
Material Properties
3. V K Jadon, Professor, Mechanical Engineering
Maximum induced stress at any point in a loaded machine member <= Design Stress
Design Stress =
๐๐ก๐๐๐๐๐กโ
๐น๐๐๐ก๐๐ ๐๐ ๐๐๐๐๐ก๐ฆ
How many design equations are needed for one component to fix one dimension of a member?
?
Design equation for Strength (Static Load)
?
4. Engineering stress or stress
๐ =
๐น
๐ด ๐
Engineering strain or strain
๐ =
๐ ๐โ๐ ๐
๐ ๐
Tensile Test
The cross-section of specimen can be circular,
square and rectangular (IS 1608-2005)
๐0 = 5 ร ๐ท for circular section
๐0 = 5.65โ๐ด0 for non-circular section
Tensile Test is conducted to know mechanical
strength, elastic constant and ductility of material.
๐ ๐ = 6 ๐๐ ๐ ๐ = 30 ๐๐
Representative Curve for Mild Steel (Not as per data)
V K Jadon, Professor, Mechanical Engineering
Load
(kN)
Elongation
(mm)
0.25 0.01
0.50 0.05
0.91 0.10
1.15 0.30
1.57 0.50
3.32 0.80
8.36 1.5
6. Load
(kN)
Elongation
(mm)
0.25 0.0013
0.50 0.0030
0.91 0.0051
1.15 0.0063
1.57 0.0085
3.32 0.0180
8.36 0.0750
๐ ๐ = 6 ๐๐; ๐ ๐ = 30 ๐๐; ๐ด ๐ = 26.27 ๐๐2
Stress
(MPa)
Longitudinal
Strain
9.51 0.000045
19.03 0.00010
34.46 0.00017
43.78 0.00021
59.76 0.00028
126.38 0.00060
318.23 0.0025
๐ = 0.29
๐ = โ ๐๐๐ก๐๐๐๐ ๐ ๐ก๐๐๐๐
๐๐๐๐๐๐ก๐ข๐๐๐๐๐ ๐ ๐ก๐๐๐๐
Lateral Strain Reduction in
Diameter (mm)
โ1.35 ร 10โ5
8.1 ร 10โ5
โ2.90 ร 10โ5 1.74 ร 10โ4
โ4.93 ร 10โ5 2.96 ร 10โ4
โ6.09 ร 10โ5 3.65 ร 10โ4
โ8.12 ร 10โ5 4.875 ร 10โ4
โ17.4 ร 10โ4
1.04 ร 10โ3
โ72.5 ร 10โ4
4.35 ร 10โ3
%
Elongation
% reduction
in Area
0.00433 0.00261
0.01 0.0058
0.017 0.00986
0.021 0.01218
0.02833 0.016239
0.06 0.034797
0.25 0.144947
% ๐๐๐๐ข๐๐ก๐๐๐ ๐๐ ๐๐๐๐, ๐ =
๐ด ๐ โ ๐ด ๐
๐ด ๐
ร 100
๐ ๐๐๐ข๐๐ก๐๐๐ ๐๐ ๐๐๐ = โ๐ฟ๐๐ก๐๐๐๐ ๐๐ก๐๐๐๐ ร ๐0
% ๐๐๐๐๐๐๐ก๐๐๐ =
๐ ๐ โ ๐ ๐
๐ ๐
ร 100
A material is accepted as ductile if it shows more than 5 percent elongation at fracture.
In general, the tendency of a material to be brittle increases with decrease in temperature; increases with rate of loading;
and change in state of stress from uniaxial to triaxial tension.
Ductility is the most desirable property for the operations like bending, drawing, forming etc.
The ductility and brittleness of a material may also be affected due to manufacturing process e.g. the casting of a
material is less ductile than the cold/hot working of the same material.
Tensile Test : Material Properties
V K Jadon, Professor, Mechanical Engineering
7. Shear, Bulk, Resilience and Toughness Modulus
Shear Modulus (G) is defined as the ratio of shear stress (ฯ) to shear strain
(ฯ) within elastic range and it represents the resistance offered by a material
to geometric distortion. This is also called as Modulus of Rigidity
๐บ = ๐
๐พ This is related to Modulus of Elasticity ๐บ = ๐ธ
2(1+๐)
Bulk Modulus (K) is a measure of the elastic
volume change in a material and is defined as
๐พ = ๐ป๐ฆ๐๐๐ข๐ ๐ก๐๐ก๐๐ ๐๐ก๐๐๐ ๐
๐๐๐๐ข๐๐๐ก๐๐๐ ๐๐ก๐๐๐๐
This is related to Modulus of Elasticity
๐พ = ๐ธ
3(1โ2๐)
Reciprocal of the bulk modulus is called compressibility.
Resilience
When the material undergoes elastic deforma
tion, positive work is done on the material
WD=product of average load and total change in length
This ability of a material to absorb energy when
deformed elastically and release the energy when
unloaded is known as resilience.
Stress
Strain
Modulus of Resilience (MR) is the area under
the stress-strain curve till elastic limit.
๐๐ =
1
2
(๐ ๐ฆ๐ก)(๐) ๐๐ =
1
2
๐ ๐ฆ๐ก
2
๐ธ
Modulus of Toughness (MT) is the area
under the stress-strain curve till fracture.
Toughness is a measure of the ability to absorb energy in
plastic range i.e. the ability of a material to withstand
occasional stress above yield strength without failure.
๐๐๐๐ข๐๐ก๐๐๐ =
1
2
(๐ ๐ฆ๐ก + ๐ ๐ข๐ก)๐๐
๐๐
๐๐๐๐๐๐ก๐ก๐๐ =
2
3
(๐ ๐ข๐ก)๐๐
This property is desirable in the components such as freight
car, gears, crane hooks etc., where shock loading is present.
MR is desirable property for the components not
undergo permanent deformation (springs etc.)
V K Jadon, Professor, Mechanical Engineering