Stress-Strain Diagram Terms

  • Identify the terminology and symbols associated with tension tests.

  • Draw and interpret engineering stress-strain diagram for ductile and brittle material.

  • Be able to identify regions and properties from the stress-strain curve.

  • Identify elastic, yield, strain-hardening, ultimate and necking regions of basic stress-strain diagrams.

  • Read or calculate commonly used values from basic stress-strain diagrams.

Stress-Strain Curve

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.

  1. The stress-strain 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 stress-strain diagram.

    • Stress s = applied Load P divided by the specimen s original cross-sectional Area \(A_0\)

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

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

  3. 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.

  4. 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.

  5. Necking: After the ultimate stress, the cross-sectional 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 Examples

Solved Example:

51-1-01

According to Hooke's law of elasticity, if stress is increased then the ratio of stress to strain:

Correct Answer: D

Solved Example:

51-1-02

The energy stored per unit volume in copper wire, which produces longitudinal strain of 0.1% , is, (Y = 1.1 $\times$ $ 10^{11}$ )

Correct Answer: B

Solved Example:

51-1-03

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. Stress-strain graph will start from residual strain value rather than from origin (0, 0).


Correct Answer: D

Solved Example:

51-1-04

What refers to the stress in the material at the elastic limit?

Correct Answer: B

Solved Example:

51-1-05

Within elastic limit, the shear stress is proportional to shear strain. What is the constant of proportionality of this statement called?

Correct Answer: A

Solved Example:

51-1-06

What does it means when the material is said to be 'yielding'?

Correct Answer: B

Solved Example:

51-1-07

The elastic deformation of a material is:

Correct Answer: B

Solved Example:

51-1-08

The strain energy of a member is:

Correct Answer: C

Solved Example:

51-1-09

Stiffness is:

Correct Answer: A

Solved Example:

51-1-10

__________ is the stress beyond which the material will not return to its original shape when unloaded but will retain a permanent deformation.

Correct Answer: A

Solved Example:

51-1-11

During a tensile test on a specimen of 1 cm cross-section, maximum load observed was 8 tonnes and area of cross-section at neck was 0.5 cm$^2$. Ultimate tensile strength of specimen is:

Correct Answer: B

Solved Example:

51-1-12

For steel, the ultimate strength in shear as compared to in tension is nearly: (SSC JE ME March 2017)

Correct Answer: B

Solved Example:

51-1-13

Which is the false statement about true stress-strain method?

Correct Answer: A

Solved Example:

51-1-14

In a tensile test on mild steel specimen, the breaking stress as compared to ultimate tensile stress is:

Correct Answer: B

Solved Example:

51-1-15

If a part is constrained to move and heated, it will develop: (SSC JE ME March 2017)

Correct Answer: C

Solved Example:

51-1-16

Which of the following materials is most elastic? (SJVNL JE Mech 2018)

Correct Answer: D

Solved Example:

51-1-17

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:

Correct Answer: B

Solved Example:

51-1-18

The property of a material by virtue of which a body returns to its original, shape after removal of the load is called:

Correct Answer: B

Solved Example:

51-1-19

The stress developed in a material at breaking point in extension is called:

Correct Answer: A

Solved Example:

51-1-20

Rupture stress is:

Correct Answer: D

Solved Example:

51-1-21

The elasticity of various materials is controlled by its:

Correct Answer: D

Solved Example:

51-1-22

A material obeys Hook's law up to:

Solution:
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