Metals- Schmids Law and OILS Rule

Question 1

What is the slip system?

Answer 1

The combination of the plane and direction that the dislocation moves along

Question 2

What is the slip system operating within a crystal determined by?

Answer 2

The energetics of the crystal and the crystal structure and the nature of binding that occurs within the structure

Question 3

Slip system for fcc metals

Answer 3

{111}<1-10>
Remember Fred Curly Ones
Backwards middle finger direction

Question 4

Slip system for bcc metals

Answer 4

{110}<1-11>
Others occur at high temperatures
Remember opposite if fcc but only negative always in the direction vectors and never negative in planes

Question 5

Slip system for hcp metals

Answer 5

{001}<100>

Remember hcp symmetry

Question 6

Slip system for diamond structure

Answer 6

{111}<1-10>
Same as fcc
Remember diamonds are forever

Question 7

What is Schmid’s law in relation to?

Answer 7

The critical resolved shear stress which is the shear stress at which slip occurs (constant for a given material). If a stress is applied at an arbitrary angle to a single crystal, each available slip system will experience a resolved shear stress acting in the associated slip plane in the slip direction

Question 8

Schmid’s law

Answer 8

τsub(crss)=σy cosφcosλ
Where σy is the tensile yield stress
φ is the angle between the slip plane normal and the tensile force axis
λ is the angle between the slip direction and the tensile force axis

Question 9

Deriving Schmid’s law

Answer 9

Resolve shear stress on any plane is τsubR=Force/Area.
Slip direction at angle λ to tensile axis so resolved component of applied force F parallel to slip direction is Fcosλ. Normal to the slip plane makes angle φ with tensile axis so area is A/cosφ.
So τR=(F/A)cosφcosλ=σcosφcosλ. The value of τR at which slip occurs is τcrss for which σ=σy

Question 10

Schmid’s factor

Answer 10

cosφcosλ from Schmid’s law formula

Think this can only reach a maximum of 1/2

Question 11

Which slip system will yield first?

Answer 11

The one with the greatest Schmid factor. This is because all available slip systems will experience a resolved shear stress and the critical resolved shear stress is the same for all slip systems

Question 12

What can OILS rule be used for?

Answer 12

Identifying the slip system with the greatest Schmid factor for bcc and fcc structures

Question 13

What does OILS stand for?

Answer 13

Zero Intermediate Least Sign

Question 14

Steps of OILS rule

Answer 14

Write down indexes of tensile axis [UVW]
Ignoring signs, identify Highest, Intermediate, Lowest value indices. For fcc the slip direction <110> is the direction with the 0 in the Intermediate index. Preserve the signs from the tensile axis. Slip plane {111} is plane with the sign of the Lowest value index reversed and others preserved from tensile axis.
For bcc the slip plane {110} is plane with 0 in position of Intermediate and others preserve signs from tensile axis. Slip direction <111> is direction with sign of Lowest index reversed and other two preserved.

Question 15

Remembering order for fcc and bcc in OILS rule

Answer 15

FCC is direction then plane (Frank de Poer)

BCC is plane then direction (Beats per dinute)

Question 16

Example of [-214] tensile axis for fcc

Answer 16

[-I L H]. For fcc direction has 0 in I place so [011].
Slip plane has sign in Lowest position reversed from what tensile axis has while others are preserved so (-1-11)
Operating slip system is therefore (-1-11)[011]

Question 17

Example of [-214] tensile axis for bcc

Answer 17

[-I L H]. For bcc zero the I position of the slip plane so (011).
Reverse sign of L position in direction that tensile axis would have given and preserve others so [-1-11].
Operating slip system is therefore (011)[-1-11].

Question 18

Tensile axis rotation

Answer 18

As slip proceeds the slip direction rotates towards the tensile axis leading to a change in the resolved shear stress. Or think about it as the tensile axis rotating towards the slip direction. Direction of tensile axis relative to crystal lattice vectors can also be obtained by adding multiples of the slip direction to the tensile axis. From fcc example
Tensile axis = [-214]+n[011].
Rotation of tensile axis will continue until a second slip system is activated at which point multiples of both slip directions will have to be added.