11.8: Questions

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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!

What is meant by a "misfit strain"?

Answer: A

Why does curvature tend to arise in a coating-substrate system, as a result of the stresses in each constituent caused by imposing a force balance?

Answer: C

Which of these conditions is sufficient to ensure that the Stoney equation is a good approximation for the relationship between coating stress and curvature?

Answer: D. The other three conditions will all tend to favour conditions in which the Stoney equation is likely to be reliable, but they are not sufficient individually for this to be the case.

What is meant by the "Biaxial Modulus" of a coating (or a substrate) and why is it greater than the conventional (Young's modulus)?

a	It corresponds to the stress-strain ratio in any in-plane direction, for an equal biaxial stress state, and it is larger than the Young's modulus because of Poisson effects.
b	It corresponds to the stress-strain ratio (in an elastic system) in any in-plane direction, for an equal biaxial stress state, and it is larger than the Young's modulus because of Poisson effects.
c	It corresponds to the stress-strain ratio (in an elastic system) in any in-plane direction and it is larger than the Young's modulus because of Poisson effects.
d	It corresponds to the stress-strain ratio (in an elastic system) in any in-plane direction, for an equal biaxial stress state, and it is larger than the Young's modulus because of the Poisson contraction arising from a stress in another in-plane direction.

Answer: B

Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

How is the neutral axis (strictly, the neutral plane) of a beam defined?

Answer: A. It is important to note that, while the adoption of curvature will not change the (in-plane) strain at the neutral axis, the strain will only be zero at that location if that was the case before the curvature was created.

Which of these definitions of the curvature of a beam is correct?

Answer: D. It is often instructive to think of the curvature as a through-thickness strain gradient (rather than in terms of the location of the centre of curvature).

Which of these statements regarding debonding (spallation) of coatings is incorrect?

Answer: A. The magnitude of the driving force for debonding is independent of the sign of the stress - it appears in a squared term. A compressive stress may be preferable in terms of conferring resistance to certain types of damage, such as through-thickness cracking, but only the magnitude of the stress is relevant to the driving force for spallation.

a	A strain corresponding to the difference in stress-free dimensions of two constituents that are bonded together in some way.
b	A strain that needs to be imposed on a coating in order to make it stress-free.
c	A strain resulting from imposition of the condition that coating and substrate remain bonded together.
d	A strain that arises between coating and substrate as a result of temperature change

a	The curvature arises because it allows the stress in the coating to be completely relaxed.
b	The force balance cannot be satisfied unless it is accompanied by curvature.
c	There is a lateral separation between the axes along which the corresponding forces act, so a bending moment is generated, creating a curvature.
d	The forces that arise act along axes that are not parallel, so a bending moment is generated, creating a curvature.

a	The stress state is an equal biaxial one.
b	The coating is thinner than the substrate.
c	The stiffness of the coating is lower than that of the coating
d	The magnitude of the average stress in the coating is much greater than that in the substrate.

a	It is the line along which, when an initially unstressed beam is subjected to a bending moment, no strains arise while the beam becomes curved.
b	It is the line along which there are no shear strains in the beam.
c	It is the line along which there is no strain when the beam becomes curved.
d	It is the line along which there is no stress when the beam becomes curved.

a	Beam stiffness times applied moment.
b	Through-thickness gradient of the in-plane stress (in the plane of curvature) induced by the adoption of curvature.
c	Beam thickness divided by radius of curvature.
d	Through-thickness gradient of the in-plane strain (in the plane of curvature) induced by the adoption of curvature.

a	If the residual stress in a coating is compressive, rather than tensile, then it is less likely to debond from the substrate.
b	Coatings are more likely to debond if the coating / substrate interface is brittle (has a low toughness).
c	The main driving force for debonding of many coatings is the stored elastic strain energy associated with the residual stresses in them.
d	Thick coatings tend to debond more readily than thin ones.