Machine Design, Strength of Materials

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 =
𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑆𝑎𝑓𝑒𝑡𝑦
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
𝜎 =
𝐹
𝐴 𝑜
Engineering strain or strain
𝜀 =
𝑙 𝑓−𝑙 𝑜
𝑙 𝑜
Tensile Test
The cross-section of specimen can be circular,
square and rectangular (IS 1608-2005)
𝑙0 = 5 × 𝐷 for circular section
𝑙0 = 5.65√𝐴0 for non-circular section
Tensile Test is conducted to know mechanical
strength, elastic constant and ductility of material.
𝑑 𝑜 = 6 𝑚𝑚 𝑙 𝑜 = 30 𝑚𝑚
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

5. 𝜎 =
𝐹
𝐴 𝑜
𝜀 =
𝑙 𝑓−𝑙 𝑜
𝑙 𝑜
Tensile Test : Material Properties
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
𝑑 𝑜 = 6 𝑚𝑚; 𝑙 𝑜 = 30 𝑚𝑚; 𝐴 𝑜 = 26.27 𝑚𝑚2
Stress
(MPa)
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
𝑆 𝑦𝑡 = 190 − 250 𝑀𝑃𝑎
𝑆 𝑢𝑡 = 350 − 470 𝑀𝑃𝑎
𝐸 = 210000 𝑀𝑃𝑎
E =
(34.46 − 19.03)
(0.00017 − 0.0001)
E = 210428 𝑀𝑃𝑎
E = 210.4 𝐺𝑃𝑎
𝐸 = 210 𝐺𝑃𝑎
Representative values for Steel
𝑆(𝑦/𝑢)𝑐 = (1.2 − 1.7)𝑆(𝑦/𝑢)𝑡
𝑆(𝑦/𝑢)𝑠 = 0.5𝑆(𝑦/𝑢)𝑡
𝐺 = 80 𝐺𝑃𝑎 𝜈 = 0.29
𝜈 = − 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
Representative Curve for Mild Steel (Not as per data)
V K Jadon, Professor, Mechanical Engineering
or 0.577𝑆(𝑦/𝑢)𝑡

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
𝑑 𝑜 = 6 𝑚𝑚; 𝑙 𝑜 = 30 𝑚𝑚; 𝐴 𝑜 = 26.27 𝑚𝑚2
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
𝜈 = 0.29
𝜈 = − 𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 𝑠𝑡𝑟𝑎𝑖𝑛
Lateral Strain Reduction in
Diameter (mm)
−1.35 × 10−5
8.1 × 10−5
−2.90 × 10−5 1.74 × 10−4
−4.93 × 10−5 2.96 × 10−4
−6.09 × 10−5 3.65 × 10−4
−8.12 × 10−5 4.875 × 10−4
−17.4 × 10−4
1.04 × 10−3
−72.5 × 10−4
4.35 × 10−3
%
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
% 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑎𝑟𝑒𝑎, 𝑟 =
𝐴 𝑜 − 𝐴 𝑓
𝐴 𝑜
× 100
𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑑𝑖𝑎 = −𝐿𝑎𝑡𝑒𝑟𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 × 𝑑0
% 𝑒𝑙𝑜𝑛𝑔𝑎𝑡𝑖𝑜𝑛 =
𝑙 𝑜 − 𝑙 𝑓
𝑙 𝑜
× 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 (τ) to shear strain
(ϒ) within elastic range and it represents the resistance offered by a material
to geometric distortion. This is also called as Modulus of Rigidity
𝐺 = 𝜏
𝛾 This is related to Modulus of Elasticity 𝐺 = 𝐸
2(1+𝜈)
Bulk Modulus (K) is a measure of the elastic
volume change in a material and is defined as
𝐾 = 𝐻𝑦𝑑𝑎𝑢𝑠𝑡𝑎𝑡𝑖𝑐 𝑆𝑡𝑟𝑒𝑠𝑠
𝑉𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑆𝑡𝑟𝑎𝑖𝑛
This is related to Modulus of Elasticity
𝐾 = 𝐸
3(1−2𝜈)
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.
𝑀𝑅 =
1
2
(𝑆 𝑦𝑡)(𝜀) 𝑀𝑅 =
1
2
𝑆 𝑦𝑡
2
𝐸
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.
𝑀𝑇𝑑𝑢𝑐𝑡𝑖𝑙𝑒 =
1
2
(𝑆 𝑦𝑡 + 𝑆 𝑢𝑡)𝜀𝑓
𝜀𝑓
𝑀𝑇𝑏𝑟𝑖𝑡𝑡𝑙𝑒 =
2
3
(𝑆 𝑢𝑡)𝜀𝑓
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

8. References