StressStrain Diagrams
StressStrain Diagram Terms
Learning Objectives:

Identify the terminology and symbols associated with tension tests.

Draw and interpret engineering stressstrain diagram for ductile and brittle material.

Be able to identify regions and properties from the stressstrain curve.

Identify elastic, yield, strainhardening, ultimate and necking regions of basic stressstrain diagrams.

Read or calculate commonly used values from basic stressstrain diagrams.
The strength of a material depends on its ability to sustain a load without undue deformation or a failure. The tension or Compression test is primarily used to determine the relationship between the average normal stress and average normal strain.

The stressstrain diagram: From the data of a tension test, it is possible to compute various values of the stress and corresponding strain in the specimen and then plot the result. The resulting curve is called the stressstrain diagram.

Stress s = applied Load P divided by the specimen s original crosssectional Area \(A_0\)

Strain e = the change in the specimen s gauge length d divided by the specimen s original gauge Length \(L_0\).


Elastic behavior: If the specimen returns to its original length when the load acting on it is removed, it is said to response elastically.

Yielding:A slight increase in stress above the elastic limit will result in permanent deformation. This behavior is called yielding for ductile materials. The stress that causes yielding is called yield stress \(s_y\). The deformation that occurs is called plastic deformation.

Strain Harding: When yielding has ended, a further load can be applied to the specimen, resulting a cure that rises continuously but becomes flatter until it reaches a maximum stress referred to as ultimate stress, \(s_u\). The rise in the curve is called Strain Harding.

Necking: After the ultimate stress, the crosssectional area begins to decrease in a localized region of the specimen, instead of over its entire length. So, a neck is formed as the specimen elongated further.
Solved Example: 51101
According to Hooke's law of elasticity, if stress is increased then the ratio of stress to strain:
A. Decreases
B. Becomes zero
C. Increases
D. Remains constant
Correct Answer: D
Solved Example: 51102
The energy stored per unit volume in copper wire, which produces longitudinal strain of 0.1% , is, (Y = 1.1 $\times$ $ 10^{11}$ )
A. 11 $\times$ $10^3$ J/$m^3$
B. 5.5 $\times$ $10^4$ J/$m^3$
C. 5.5 $\times$ $10^3$ J/$m^3$
D. 11 $\times$ $10^4$ J/$m^3$
Correct Answer: B
Solved Example: 51103
If a factor of Safety is considered too high, which of the following can happen?
I. Cost can be high.
II. Elastic limit and constant of proportionality points are affected.
III. Safe working stress is lowered.
IV. Stressstrain graph will start from residual strain value rather than from origin (0, 0).
A. I, II and III only
B. I and II only
C. I, II, III and IV
D. I and III only
Correct Answer: D
Solved Example: 51104
What refers to the stress in the material at the elastic limit?
A. Working stress
B. Yield stress
C. Ultimate stress
D. Maximum stress
Correct Answer: B
Solved Example: 51105
Within elastic limit, the shear stress is proportional to shear strain. What is the constant of proportionality of this statement called?
A. Modulus of rigidity
B. Modulus of elasticity
C. Young’s modulus
D. Bulk modulus
Correct Answer: A
Solved Example: 51106
What does it means when the material is said to be 'yielding'?
A. The material has pass through plastic range and enter the elastic range
B. The material has pass through elastic range and enter the plastic range
C. The material is in the elastic range only
D. The material is in the plastic range only
Correct Answer: B
Solved Example: 51107
The elastic deformation of a material is:
A. Directly proportional to crosssectional area of the material
B. Inversely proportional to the modulus of elasticity of material
C. Inversely proportional to the force acting on the material
D. Inversely proportional to the initial length of the material
Correct Answer: B
Solved Example: 51108
The strain energy of a member is:
A. Inversely proportional to the square of the force acting on the member
B. Directly proportional to the modulus of elasticity
C. Inversely proportional to the crosssectional area of the member
D. Inversely proportional to the initial length of the member
Correct Answer: C
Solved Example: 51109
Stiffness is:
A. Ratio of force to deformation
B. Ratio of force to modulus of elasticity
C. Ratio of product of crosssectional area and initial length to deformation
D. Ratio of initial length to crosssectional area
Correct Answer: A
Solved Example: 51110
__________ is the stress beyond which the material will not return to its original shape when unloaded but will retain a permanent deformation.
A. Elastic limit
B. Proportional limit
C. Yield limit
D. Yield strength
Correct Answer: A
Solved Example: 51111
During a tensile test on a specimen of 1 cm crosssection, maximum load observed was 8 tonnes and area of crosssection at neck was 0.5 cm$^2$. Ultimate tensile strength of specimen is:
A. 4 tonnes/cm$^2$
B. 8 tonnes/cm$^2$
C. 16 tonnes/cm$^2$
D. 22 tonnes/cm$^2$
Correct Answer: B
Solved Example: 51112
For steel, the ultimate strength in shear as compared to in tension is nearly: (SSC JE ME March 2017)
A. Same
B. Half
C. Onethird
D. Twothird
Correct Answer: B
Solved Example: 51113
Which is the false statement about true stressstrain method?
A. It does not exist
B. It is more sensitive to changes in both metallurgical and mechanical conditions
C. It gives, a more accurate picture of the ductility
D. It can be correlated with stressstrain values in other tests like torsion, impact, combined stress tests etc.
Correct Answer: A
Solved Example: 51114
In a tensile test on mild steel specimen, the breaking stress as compared to ultimate tensile stress is:
A. More
B. Less
C. Same
D. More/less depending on composition
Correct Answer: B
Solved Example: 51115
If a part is constrained to move and heated, it will develop: (SSC JE ME March 2017)
A. Principal stress
B. Tensile stress
C. Compressive stress
D. Shear stress
Correct Answer: C
Solved Example: 51116
Which of the following materials is most elastic? (SJVNL JE Mech 2018)
A. Rubber
B. Plastic
C. Brass
D. Steel
Correct Answer: D
Solved Example: 51117
The total elongation produced in a bar of uniform section hanging vertically downwards due to its own weight is equal to that produced by a weight:
A. Of same magnitude as that of bar and applied at the lower end
B. Half the weight of bar applied at lower end
C. Half of the square of weight of bar applied at lower end
D. Onefourth of weight of bar applied at lower end
Correct Answer: B
Solved Example: 51118
The property of a material by virtue of which a body returns to its original, shape after removal of the load is called:
A. Plasticity
B. Elasticity
C. Ductility
D. Malleability
Correct Answer: B
Solved Example: 51119
The stress developed in a material at breaking point in extension is called:
A. Breaking stress
B. Fracture stress
C. Yield point stress
D. Ultimate tensile stress
Correct Answer: A
Solved Example: 51120
Rupture stress is:
A. Breaking stress
B. Maximum load/original crosssectional area
C. Load at breaking point/A
D. Load at breaking point/neck area
Correct Answer: D
Solved Example: 51121
The elasticity of various materials is controlled by its:
A. Ultimate tensile stress
B. Proof stress
C. Stress at yield point
D. Stress at elastic limit
Correct Answer: D
Solved Example: 51122
A material obeys Hook's law up to:
A. Plastic limit
B. Elastic limit
C. Yield point
D. Limit of proportionality
The extension of a spring or wire is directly proportional to the force applied provided the limit of proportionality is not exceeded.
The limit of proportionality is the is the point beyond which Hooke’s law is no longer true when stretching a material.
The elastic limit is the point beyond which the material you are stretching becomes permanently stretched so that the material does not return to its original length when the force is removed.
Correct Answer: D
True Vs. Engineering StressStrain Curve
Learning Objectives:

Understand the deviation of stressstrain curve due to necking.
The engineering stress is the load borne by the sample divided by a constant, the original area. The true stress is the load borne by the sample divided by a variable the instantaneous area. Note that the true stress always rises in the plastic, whereas the engineering stress rises and then falls after going through a maximum.
The maximum represents a significant difference between the engineering stressstrain curve and the true stressstrain curve. In the engineering stressstrain curve, this point indicates the beginning of necking. The ultimate tensile strength is the maximum load measured in the tension test divided by the original area.
Solved Example: 51201
Engineering stressstrain curve and True stressstrain curve are equal up to:
A. Proportional limit
B. Elastic limit
C. Yield point
D. Tensile strength point
Correct Answer: C
Solved Example: 51202
True stressstrain curve for materials is plotted between:
A. Load/original crosssectional area and change in length/original length
B. Load/instantaneous crosssectional area original area and log.
C. Load/instantaneous crosssectional area and change in length/original length
D. Load/instantaneous area and instantaneous area/original area
Correct Answer: B