Wcash: New page: =Simulation and observation of dislocation pattern evolution in the early stages of fatigue in a copper single crystal= '''J. Yang, Y. Li, S. Li, C. Ma, G. Li''' '''Materials Science & En...

2009-11-03T23:14:52Z

New page: =Simulation and observation of dislocation pattern evolution in the early stages of fatigue in a copper single crystal= '''J. Yang, Y. Li, S. Li, C. Ma, G. Li''' '''Materials Science & En...

New page

=Simulation and observation of dislocation pattern evolution in the early stages of fatigue in a copper single crystal=
'''J. Yang, Y. Li, S. Li, C. Ma, G. Li'''

'''Materials Science & Engineering A, 2001'''
*Experimental and numerical study of single-crystal copper oriented for single-slip under constant plastic strain amplitude of 2e-4 at a frequency of 0.2 Hz
*Only modeled parallel edge dislocations of magnitude +/- b
*Initially a random distribution of 20 + and 20 - dislocations
*Only consider multiplication; annihilation is ignored
*Climb and cross-slip are ignored
*simulation area of 3.6 x 3 <math>\mu m ^2</math> with PBCs in x&y
*using the typical singular elastic stress fields
**If distance between dislocations is <10b, a distance of 10b is used in the stress field calculation to avoid singularity since they don't consider annihilation.
*Mobility: <math>v=v_o \left ( \frac{\tau}{\tau _o} \right ) ^m</math>
*It appears that if they had an initial dislocation density on the order of <math>10^{10} m^2</math> that the dislocations would randomly arrange after cycling? If they used an initial density of $10^{12} m^2</math> the dislocation patterns would emerge - this is why they chose 40 initial dislocations. (It's hard to tell because this section was poorly written
*State they use triangular waveform, but appear to indicate it's the applied shear stress. (confusing)
*During cyclic deformation the maximum stress increases until saturation at about 28 MPa.
*Only consider 5 values of resolved shear stress (10, 15, 20, 25, 28 MPa) to speed up calculations?
*If strain rate is <2e-4 when the resolved shear stress is 28 MPa, then dislocation multiplication occurs
**20 to 200 dislocations with an equal distribution of +/- b are added based on the how far below the predicted strain rate the simulation was.
**Makes no mention of where these new dislocations are located
*Dislocations initially pattern themselves into "matrix walls" (not the same as PSB walls), which become veins with continued cycling.
**vertical walls are comprised of dislocations with the same Burgers vector
**Dislcations of opposite sign form walls oriented at 45 degrees.
**Says this is an equilibrium distribution according to classical dislocation theory, but cites a Chinese book I can't find.
*claim that cross-slip of screw dislocations is unimportant in the early stages of fatigue prior to PSB emergence.
*claim that screw dislocations spanning the matrix walls cause them to fragment and form into veins.
**In the simulation they select 6-8 cutting positions randomly, but I can't understand what they were doing because it is poorly written.

=Evolution of persistent slip bands and simulation of its stress field in a fatigued copper single crystal=
'''J. Yang, Y. Li, Z. Cai, S. Li, C. Ma, E. Han, W. Ke'''

'''Materials Science & Engineering A, 2003'''
*claims to be a 3D "discrete dislocation method", but the edge and screw dislocations are treated as perfectly straight
**Never clearly explained if they are using dynamics at all
**No mention of how their structures are generated and if they're even stable
*constant plastic strain amplitude of 1e-3
*only edge dislocations of +/-b in the matrix veins and PSB walls; only screw dislocations in the channels
*equal distribution of left/right screw and +/- edge
*Simulate a volume of 6 x 5 x 4 <math>\mu m^3</math> with PBCs
*edge dislocations are distributed randomly in the veins/walls and screw dislocations were distributed randomly in the channels, "according to an actual experimental photograph"
*Edge dislocation density of ~3e14 and screw dislocation density on the order of <math>10^12</math>
*again using the singular elastic stress fields, but with a critical distance of 3b this time
*DD is used to calculate the internal stress distributions and FEM is used to calculate the external stress distributions
**In the FEM mesh the veins and walls has a yield stress of 100 MPa and a Young's modulus of 110 GPa, while the matrix between veins has 60 MPa and a modulus of 108 GPa and the matrix between PSB walls is only 56 MPa and a modulus of 106 GPa.
**Claim PSB channels are softer due to vacancies
*

2D Dislocation Dynamics - Revision history

Wcash: New page: =Simulation and observation of dislocation pattern evolution in the early stages of fatigue in a copper single crystal= '''J. Yang, Y. Li, S. Li, C. Ma, G. Li''' '''Materials Science & En...