Dislocation Lecture Summary
for 22.71 on 10_4_2012
Elliott Fray
Outline
• What is a dislocation?
– Localized and Non-localized deformation
– Characterizing dislocations
– Dislocation types
• Stress field of a dislocation
– Edge type , Screw Type
• Slip Systems
• Applications
What is a dislocation?
• A dislocation is a discontinuity at which a material’s
crystal lattice shifts from an un-sheared to a sheared
state
• Dislocations enable a material to deform under shear
stress levels ~ 1/10,000 of its theoretical yield stress
Localized and Non-Localized
Deformation
Dislocation
Line
𝜀𝑡𝑜𝑡𝑎𝑙 = 𝜀𝑒𝑙𝑎𝑠𝑡𝑖𝑐 + 𝜀𝑖𝑛𝑒𝑙𝑎𝑠𝑡𝑖𝑐
•
Crystals deform by dislocations 1 atomic layer thin (𝜀𝑖𝑛𝑒𝑙𝑎𝑠𝑡𝑖𝑐 )
•
Energy stored in the material after deformation is localized around the dislocations
Characterizing Dislocations
• Burgers Vector
– The burgers vector is a property of a dislocation which
characterizes its orientation
– The burgers vector closes the circuit in loop in an
imperfect crystal
Characterizing Dislocations
• Burgers Vector
Dislocation Line
𝜇 = 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 − 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
– Dislocations with the same signs tend to repel,
dislocations with the opposite signs tend to attract
( −𝜖 , −𝑏) ↔ ( −𝜖 , −𝑏) Same, Stress fields repel one another
( 𝜖 , 𝑏) ↔ ( 𝜖 , −𝑏) Opposite, Stress fields repel attract one another
A few Dislocation Types
Screw Dislocation
Edge Dislocation
b
Mixed
b
• Edge
– b is perpendicular to the
dislocation line
• Screw
– b is parallel to the
dislocation line
Stress Field of a Dislocation
• Screw Dislocation
• Edge Dislocation
• Packing of dislocations is limited by the range of the
stress field surrounding a dislocation (R1)
𝐸(𝑅1)
𝐿
= 𝐸𝑖𝑛𝑒𝑙𝑎𝑠𝑡𝑖𝑐 𝑅𝑜 +
𝜇𝑏2
4𝜋
𝑅1
ln(𝑅𝑜) where Ro~b
Slip Systems
• Materials tend to slip first
along the closest packed
plane
– Smallest burgers vector: b
– Largest spacing between
planes: do
• Alternatively one can find
the directions of slip from
the line tension
𝜼=
𝐸𝑠𝑒𝑙𝑓
𝐿
~
𝜇𝑏2
4𝜋
𝑅𝑠𝑐𝑟𝑒𝑒𝑛
)
𝑅𝑜
ln(
Minimize this to find slip systems → 𝐺𝑏2
Close packed plane of FCC Crystal
or 𝜼 = 𝛼𝐺𝑏2 where α = 0.5-1
Applications
• FCC materials tend to yield more before failing than
BCC systems due to the large number of possible slip
directions
• FCC Aluminum Alloys are commonly used in nuts for
traditional rock climbing
Nut
Placing gear during trad climbing
Thanks!
References
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Dr. Meredith Aronson (2001). Materials Science and Art of Archaeological Objects. Retrieved from:
http://www.ic.arizona.edu/ic/mse257/class_notes/disclocation.html
Dr. Ulrich T. Schwarz (2004). Research Topics – Semiconductor Optoelectronics. Retrieved from: http://www.physik.uniregensburg.de/forschung/schwarz/research.html
UC Santa Barbara Materials Research Lab. Finding the Burgers Vector of a Dislocation. Retrieved from:
http://www.mrl.ucsb.edu/~edkramer/LectureVGsMat100B/99Lecture11VGs/
University of Cambridge. (2012). Slip in Close Packed Cubic Crystals. Retrieved from:
http://www.doitpoms.ac.uk/tlplib/slip/slip_in_ccp.php
Iwona Erskine-Kelliw (2009). Trad Rock Climbing Gear. Retrieved from: http://www.flickr.com/photos/iwona_kellie/4584634424/