8.4.1: Questions

Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

Which of these statements about deviatoric and hydrostatic stresses and strains is correct, in the context of plastic deformation?

a	The deviatoric (von Mises) stress can be positive (tensile) or negative (compressive).
b	The equivalent plastic strain (von Mises strain) is always zero.
c	The deviatoric (von Mises) stress is a second rank tensor.
d	The hydrostatic component of the strain state is always zero.

Answer

D

Which of these statements about true and nominal stresses and strains is correct?

a	Conversion of nominal stresses and strains to true values, using analytical equations, is only correct if they are uniform throughout the sample.
b	It is acceptable to use nominal stress v. nominal strain relationships obtained from uniaxial tests when predicting the behaviour under multi-axial loading.
c	The nominal strain is always greater than the true strain.
d	The true stress is always greater than the nominal stress.

Answer

A

Which of these statements about using constitutive “laws” to describe plastic deformation is correct?

a	Constitutive laws are implemented taking account of both the deviatoric and the hydrostatic components of the stress state.
b	There is no reason to expect the actual plastic deformation behaviour to conform accurately to any constitutive law.
c	Constitutive laws for metal plasticity must predict a continuously decreasing work hardening rate as the strain increases.
d	Constitutive laws are based on the assumption that plasticity depends on the peak shear stress generated within the sample.

Answer

B

Which of these statements about tensile testing of metals is correct?

a	Necking arises in a location where the sample initially has a slightly smaller sectional area.
b	Necking arises when the true stress in the location concerned starts to exceed the yield stress.
c	Necking of the sample is predicted to start when the gradient of the plot of nominal stress against nominal strain starts to become negative.
d	Necking of the sample is predicted to start when the gradient of the plot of true stress against true strain starts to become negative.

Answer

C

Which of these statements about compressive testing of metals is correct?

a	It is always acceptable to assume that friction between sample and platen has a negligible effect on the outcome, provided that surface is lubricated.
b	The complete absence of barreling implies that friction between sample and platen is negligible.
c	If there is no sliding between sample and platen, then it is safe to assume that the stress and strain are uniform throughout the test.
d	The nominal stress v. nominal strain plot can be converted to a true stress v. true strain plot, using analytical equations, provided there is no interfacial sliding.

Answer

B

Which of these statements about hardness testing is correct?

a	A hardness number can be used to obtain an accurate value for the yield stress.
b	Hardness is defined, for any given applied force, as that force divided by the contact area.
c	During hardness testing, the deviatoric stress throughout the plastic zone under the indenter is equal to the yield stress.
d	For a given type of hardness test, the value obtained when testing a given sample is independent of the applied force.

Answer

B

Which of these statements about indentation plastometry is correct?

a	The technique involves repeated numerical simulation of the indentation process, using a constitutive law to represent the true stress v. true strain relationship that applies between the von Mises stress and the equivalent plastic strain.
b	The technique involves repeated numerical simulation of the indentation process, using a constitutive law to represent the nominal stress v. nominal strain relationship that applies between the von Mises stress and the equivalent plastic strain.
c	The technique involves repeated numerical simulation of the indentation process, using a constitutive law to represent the true stress v. true strain relationship that applies between the hydrostatic stress and the hydrostatic strain.
d	The deduced true stress v. true strain relationship will be identical to the curve obtained experimentally during tensile testing, after conversion of nominal stresses and strains to true values, using analytical equations.

Answer

A