# Mechanical Metallurgy Questions and Answers – Element of Plasticity Theory – Plastic Stress-Strain Relation

This set of Mechanical Metallurgy Multiple Choice Questions & Answers (MCQs) focuses on “Element of Plasticity Theory – Plastic Stress-Strain Relation”.

1. If the plane strain deformation is occurring parallel to the XY plane, then which of the following is not the correct statement?
a) εz=0
b) εxzyz=0
c) τyzxz=0
d) εxy=0

Explanation: In the case of the plane strain, all the displacement of material is restricted in the XY plane, and strain in the z-direction is zero. Following this condition then;
=> εz=0; εxzyz=0; τyzxz=0
But εx and εy will not be equal to zero.

2. If the plane strain deformation is occurring parallel to the XY plane, then strain in the z-direction is equal to zero. The stress in the z-direction will be equal to _______________
(Given that stress in x and y-direction is σx andσy respectively).
a) σxy
b) (σxy)/2
c) (σxy)/3
d) 0

Explanation: Although the strain in the z-direction is zero, the restraining stress will be acting in the z-direction. So, the stress in the z-direction:
=>σz=(σxy)/2

3. For the state of plane strain, the maximum shear stress and von-mises yield criteria are equivalent.
a) True
b) False

Explanation: According to maximum shear stress yielding criteria:
=> σ12o=2k
where k is yield stress in pure shear.
According to von-mises yielding criteria;
=> σ12=(2/√3)σo
The relationship between the yield stress in pure tension and pure shear is that:
σo = √3 k
So, σ12=(2/√3)σo = 2k.
So, it is assumed that two-dimensional plastic flow will begin when the shear stress reaches a critical value k.

4. The slip line field theory is based on the fact that any general state of stress in plane strain consists of pure shear plus a hydrostatic pressure.
a) True
b) False

Explanation: Every state of stress on an object can be represented as a sum of pure hydrostatic stress and pure shear stress. Slip line theory uses this idea to the calculated stress required for yielding.

Sanfoundry Global Education & Learning Series – Mechanical Metallurgy.

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