SLIP SYSTEMS
Dislocations do not move with the same degree of ease on all crystallographic planes and directions
There are preferred planes (slip planes) and preferred directions (slip directions)
Slip planes are planes with high planar density of atoms, and slip directions are lines with high linear density
Slip system: the combination of slip plane and slip direction
SLIP SYSTEM: EXAMPLES
• FCC (Al, Cu, Ni, Ag, Au)
– Close packed planes: {111}, e.g., ADF
– Close packed directions: <110>, e.g., AD, DF, AF
– Slip system: {111}<110> (12 independent slip systems)
• BCC (Fe, W, Mo): {110}<111> (12 independent slip systems)
• HCP (Zn, Cd, Mg, Ti, Be): 3 independent slip systems
• FCC & BCC metals: ductile, HCP metals: brittle
• Single crystals easy to treat; can generalize to polycrystals later
• Regardless of what type of external stress is applied to a material, plastic deformation or dislocation motion occurs due to a shear stress
• Some component of the applied stress has to be a shear stress on a slip plane and along a slip direction
• This component is called the resolved shear stress
SLIP IN SINGLE CRYSTALS
All plastic deformation by slip is due to shear stresses
The shear stress resolved onto the slip plane is responsible for slip
When the Resolved Shear Stress (RSS) reaches a critical value →
Critical Resolved Shear Stress (CRSS) →
plastic deformation starts (The actual Schmid’s law)
Schmid’s law
Slip is initiated when CRSS is a material parameter Yield strengh of a single crystal
RSS CRSS
CRSS y
Cos Cos
RESOLVED SHEAR STRESS
Applied tensile stress: = F/A
A F
F
slip
direction
Resolved shear stress: R=Fs/As
As
R
R
Fs
slip
direction slip plane normal, ns
Relation between
and R
R = Fs/As
Fcos A /cos
F
Fs
slip
direction
ns
As A
cos cos
cos /
cos
A F
R
CRITICAL RESOLVED SHEAR STRESS (CRSS)
• Condition for dislocation motion:
• Crystal orientation can make it easy or hard to move disl.
R
CRSS
R cos cos
R= 0
=90°
R= /2
=45°
=45°
R= 0
=90°
• Maximum possible R = /2; thus y = 2CRSS
BCC EXAMPLE
• Slip system: {110} <111>
= 45 degrees
= tan
-1(a2/a) = 54.7 degrees
• From which or can be calculated if one of them is
specified
DISL. MOTION IN POLYCRYSTALS
• • Slip planes & directions (, ) change from one crystal to another.
• • R will vary from one crystal to another.
• • The crystal with the largest R yields first.
• • Other (less favorably oriented) crystals yield later.
• • Polycrystalline materials generally stronger than single crystals, due to geometric constraints & the requirement of larger stresses for yielding
Adapted from Fig. 7.10, Callister 6e.
(Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].)
• Latihan soal
Home work
Jelaskan tentang perbedaan SLIP vs TWINNING
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