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

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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
View Answer

Answer: d
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.
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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
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

Answer: a
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.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn