PARADISCYL:Cylinder-test - Revision history

Iryu: /* TEST4 : Circular glide dislocation loop */

2011-11-17T20:19:57Z

TEST4 : Circular glide dislocation loop

← Older revision		Revision as of 20:19, 17 November 2011
Line 97:		Line 97:
	\|-		\|-
	\|colspan="2" \| Fig.7 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}[1 0 0]</math> and the slip plane is <math>\mathbf{n}=[001]</math>		\|colspan="2" \| Fig.7 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}[1 0 0]</math> and the slip plane is <math>\mathbf{n}=[001]</math>
	In general, the energy of an edge dislocation is greater than that of a screw, <math>\mathbf{E}_e>\mathbf{E}_s</math> and the line tension of an edge dislocation is smaller than that of a screw, <math>\mathbf{T}_e<\mathbf{T}_s</math>.This apparent anomaly arises because when an edge dislocation is bowed out,		In general, '''''the energy of an edge dislocation is greater than that of a screw, '''''<math>\mathbf{E}_e>\mathbf{E}_s</math> ''''' and the line tension of an edge dislocation is smaller than that of a screw, ''''' <math>\mathbf{T}_e<\mathbf{T}_s</math>. '''''This apparent anomaly arises because when an edge dislocation is bowed out,less energetic screw segments are created, while when a screw dislocation is bowed, out more energetic edge segments are created. For this reason it is easier to bow an edge dislocation compared to a screw dislocation.One consequence of the differences in line tension between the edge and screw is that a dislocation segment does not take a circular shape when it is bowed out by the action of a stress'''''.(''Nix,W.D.'' Course note on MATSCI 206)
	less energetic screw segments are created, while when a screw dislocation is bowed, out more energetic edge segments are created. For this reason it is easier to bow an edge dislocation compared to a screw dislocation.One consequence of the differences in line tension between the edge and screw is that a dislocation segment does not take a circular shape when it is bowed out by the action of a stress.(''Nix,W.D.'' Course note on MATSCI 206)
	With this in mind, we put circular glide dislocation loop inside cylinder and watch the time-evolution of dislocation loop.In this model, we use <math>\mathbf{n}_\theta=\mathbf{n}_z=101</math>. As expected,The loop initially becomes oval as the edge components are pulled towards the surface and the screw components are pulled inward. The edge components then leave the cylinder and the dislocation loop becomes two truncated segments, <span style="color:#FF0000"> which ultimately leave the cylinder as well </span>.		With this in mind, we put circular glide dislocation loop inside cylinder and watch the time-evolution of dislocation loop.In this model, we use <math>\mathbf{n}_\theta=\mathbf{n}_z=101</math>. As expected,The loop initially becomes oval as the edge components are pulled towards the surface and the screw components are pulled inward. The edge components then leave the cylinder and the dislocation loop becomes two truncated segments, <span style="color:#FF0000"> which ultimately leave the cylinder as well </span>.
	[[Image:T4_result.jpg\|800px\|center\|Fig.6. ]]		[[Image:T4_result.jpg\|800px\|center\|Fig.6. ]]

Iryu at 20:12, 17 November 2011

2011-11-17T20:12:15Z

← Older revision		Revision as of 20:12, 17 November 2011
Line 99:		Line 99:
	In general, the energy of an edge dislocation is greater than that of a screw, <math>\mathbf{E}_e>\mathbf{E}_s</math> and the line tension of an edge dislocation is smaller than that of a screw, <math>\mathbf{T}_e<\mathbf{T}_s</math>.This apparent anomaly arises because when an edge dislocation is bowed out,		In general, the energy of an edge dislocation is greater than that of a screw, <math>\mathbf{E}_e>\mathbf{E}_s</math> and the line tension of an edge dislocation is smaller than that of a screw, <math>\mathbf{T}_e<\mathbf{T}_s</math>.This apparent anomaly arises because when an edge dislocation is bowed out,
	less energetic screw segments are created, while when a screw dislocation is bowed, out more energetic edge segments are created. For this reason it is easier to bow an edge dislocation compared to a screw dislocation.One consequence of the differences in line tension between the edge and screw is that a dislocation segment does not take a circular shape when it is bowed out by the action of a stress.(''Nix,W.D.'' Course note on MATSCI 206)		less energetic screw segments are created, while when a screw dislocation is bowed, out more energetic edge segments are created. For this reason it is easier to bow an edge dislocation compared to a screw dislocation.One consequence of the differences in line tension between the edge and screw is that a dislocation segment does not take a circular shape when it is bowed out by the action of a stress.(''Nix,W.D.'' Course note on MATSCI 206)
	With this in mind, we put circular glide dislocation loop inside cylinder and watch the time-evolution of dislocation loop.In this model, we use <math>\mathbf{n}_\theta=\mathbf{n}_z=101</math>. As expected,The loop initially becomes oval as the edge components are pulled towards the surface and the screw components are pulled inward. The edge components then leave the cylinder and the dislocation loop becomes two truncated segments, which ultimately leave the cylinder as well.		With this in mind, we put circular glide dislocation loop inside cylinder and watch the time-evolution of dislocation loop.In this model, we use <math>\mathbf{n}_\theta=\mathbf{n}_z=101</math>. As expected,The loop initially becomes oval as the edge components are pulled towards the surface and the screw components are pulled inward. The edge components then leave the cylinder and the dislocation loop becomes two truncated segments, <span style="color:#FF0000"> which ultimately leave the cylinder as well </span>.
	[[Image:T4_result.jpg\|800px\|center\|Fig.6. ]]		[[Image:T4_result.jpg\|800px\|center\|Fig.6. ]]

Iryu at 19:07, 17 November 2011

2011-11-17T19:07:01Z

← Older revision		Revision as of 19:07, 17 November 2011
Line 82:		Line 82:
	[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]		[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]
	With more than 45 number of grids, they converge to almost same value.		With more than 45 number of grids, they converge to almost same value.


			<HR>

			==TEST4 : Circular glide dislocation loop==

			In the final test case, we consider time evolution of glide dislocation loop, discretized with 50 equally spaced nodes connected by straight segments, as shown in the following ''Figure''.
			{\|border="0" align="center"
			\|[[Image:T4 geom Isoview.jpg ‎\|frameless\|400px\|caption]]
			\|[[Image:T4_geom_Topview.jpg‎ \|frameless\|400px\|caption]]
			\|-
			\|align="center"\|(a)
			\|align="center"\|(b)
			\|-
			\|colspan="2" \| Fig.7 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}[1 0 0]</math> and the slip plane is <math>\mathbf{n}=[001]</math>
			In general, the energy of an edge dislocation is greater than that of a screw, <math>\mathbf{E}_e>\mathbf{E}_s</math> and the line tension of an edge dislocation is smaller than that of a screw, <math>\mathbf{T}_e<\mathbf{T}_s</math>.This apparent anomaly arises because when an edge dislocation is bowed out,
			less energetic screw segments are created, while when a screw dislocation is bowed, out more energetic edge segments are created. For this reason it is easier to bow an edge dislocation compared to a screw dislocation.One consequence of the differences in line tension between the edge and screw is that a dislocation segment does not take a circular shape when it is bowed out by the action of a stress.(''Nix,W.D.'' Course note on MATSCI 206)
			With this in mind, we put circular glide dislocation loop inside cylinder and watch the time-evolution of dislocation loop.In this model, we use <math>\mathbf{n}_\theta=\mathbf{n}_z=101</math>. As expected,The loop initially becomes oval as the edge components are pulled towards the surface and the screw components are pulled inward. The edge components then leave the cylinder and the dislocation loop becomes two truncated segments, which ultimately leave the cylinder as well.
			[[Image:T4_result.jpg\|800px\|center\|Fig.6. ]]

Iryu: /* TEST2 : Circular prismatic dislocation loop */

2011-11-17T18:12:56Z

TEST2 : Circular prismatic dislocation loop

← Older revision		Revision as of 18:12, 17 November 2011
Line 55:		Line 55:
	[[Image:T2_relative_error.jpg\|frameless\|400px\|right\|Fig.4. ]]		[[Image:T2_relative_error.jpg\|frameless\|400px\|right\|Fig.4. ]]
	Due to the symmetry of this problem, the image forces on all nodes point to the radial direction and		Due to the symmetry of this problem, the image forces on all nodes point to the radial direction and
	have the same magnitude. An estimate of their relative error is plotted as a function of number of grid in the circumferential direction(<math>n_\theta</math>) in the following figure. Because this problem does not have an analytic solution, the reference value is taken to be the value obtained using Method I (Bessel) with <math>n_\theta = 181</math>. As expected, the relative error in radial image force decreases with increasing number of grids.		have the same magnitude. An estimate of their relative error is plotted as a function of number of grid in the circumferential direction(<math>\mathbf{n}_\theta</math>) in the following figure. Because this problem does not have an analytic solution, the reference value is taken to be the value obtained using Method I (Bessel) with <math>\mathbf{n}_\theta=181</math>. As expected, the relative error in radial image force decreases with increasing number of grids.


Line 62:		Line 62:

	<HR>		<HR>

	==TEST3 : Circular inclined glide dislocation loop==		==TEST3 : Circular inclined glide dislocation loop==

Iryu: /* TEST3 : Circular inclined glide dislocation loop */

2011-11-17T18:11:55Z

TEST3 : Circular inclined glide dislocation loop

← Older revision		Revision as of 18:11, 17 November 2011
Line 78:		Line 78:
	The orientation and magnitude of the image force on every node is different. Fig. 10 plots the component		The orientation and magnitude of the image force on every node is different. Fig. 10 plots the component
	of the image force in the direction away from the center of the loop for all 10 nodes with		of the image force in the direction away from the center of the loop for all 10 nodes with
	different values of <math>n_\theta</math> using Method I.		different values of <math>\mathbf{n}_\theta</math> using Method I.
	[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]		[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]
	With more than 45 number of grids, they converge to almost same value.		With more than 45 number of grids, they converge to almost same value.

Iryu: /* TEST3 : Circular inclined glide dislocation loop */

2011-11-17T18:11:14Z

TEST3 : Circular inclined glide dislocation loop

← Older revision		Revision as of 18:11, 17 November 2011
Line 78:		Line 78:
	The orientation and magnitude of the image force on every node is different. Fig. 10 plots the component		The orientation and magnitude of the image force on every node is different. Fig. 10 plots the component
	of the image force in the direction away from the center of the loop for all 10 nodes with		of the image force in the direction away from the center of the loop for all 10 nodes with
	different values of nq using Method I.		different values of <math>n_\theta</math> using Method I.
	[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]		[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]
	With more than 45 number of grids, they converge to almost same value.		With more than 45 number of grids, they converge to almost same value.

Iryu at 18:08, 17 November 2011

2011-11-17T18:08:41Z

← Older revision		Revision as of 18:08, 17 November 2011
Line 6:		Line 6:
	</DIV>		</DIV>

	This tutorial describes test cases to check if cylinder code works well, especially for the image stress calculation. We provide Matlab files which generates ParaDiS inputs and plot the results. The theoretical background is published in Computing Image Stress in an Elastic Cylinder, ''Journal of the Mechanics and Physics of Solids'', '''55''', 2027 (2007). [http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf (PDF)]		This tutorial describes test cases to check if cylinder code works well, especially for the image stress calculation. We provide Matlab files which generates ParaDiS inputs and plot the results. The theoretical background is published in Computing Image Stress in an Elastic Cylinder(''Journal of the Mechanics and Physics of Solids'', '''55''', 2027 (2007)[http://micro.stanford.edu/~caiwei/papers/Weinberger07jmps-image.pdf (PDF)])
	and Dislocation Dynamics Simulations in a Cylinder, ''Proceedings of the Dislocations 2008 International Conference, IOP Conference Series: Materials Science and Engineering'', '''vol 3''',012007 (2009).[http://iopscience.iop.org/1757-899X/3/1/012007/pdf/mse9_3_012007.pdf (PDF)]		and Dislocation Dynamics Simulations in a Cylinder(''Proceedings of the Dislocations 2008 International Conference, IOP Conference Series: Materials Science and Engineering'', '''vol 3''',012007 (2009).[http://iopscience.iop.org/1757-899X/3/1/012007/pdf/mse9_3_012007.pdf (PDF)]).

	<HR>		<HR>
Line 21:		Line 21:
	\|-		\|-
	\|colspan="2" \| Fig.1 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b} = a[1 0 0]</math>.		\|colspan="2" \| Fig.1 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b} = a[1 0 0]</math>.
	Since the image stress field of this configuration is solved analytically[Eshelby, J.D., 1979], we compare the image force between the simulation result and analytic solution.The number of grids in circumferential direction is same as the one along the cylinder axis.To consider periodic images along the cylinder axis under PBC, analytical stress field of edge dislocation is implemented in the function of "AllSegmentStress_no_cell_test1".To use this function, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.		Since the image stress field of this configuration had been solved analytically[Eshelby, J.D., 1979],we compare the image force between the simulation result and analytic solution.The number of grids in circumferential direction is same as the one along the cylinder axis.To consider periodic images along the cylinder axis under PBC, analytical stress field of edge dislocation is implemented in the function of "AllSegmentStress_no_cell_test1".To use this function, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.
	DEFS += -D_CYL_TEST1		DEFS += -D_CYL_TEST1

Iryu at 12:21, 17 November 2011

2011-11-17T12:21:56Z

← Older revision		Revision as of 12:21, 17 November 2011
Line 53:		Line 53:
	DEFS += -D_CYL_TEST23		DEFS += -D_CYL_TEST23

	[[Image:T2_relative_error.jpg\|frameless\|400px\|right\|Fig.2. ]]		[[Image:T2_relative_error.jpg\|frameless\|400px\|right\|Fig.4. ]]
	Due to the symmetry of this problem, the image forces on all nodes point to the radial direction and		Due to the symmetry of this problem, the image forces on all nodes point to the radial direction and
	have the same magnitude. An estimate of their relative error is plotted as a function of number of grid in the circumferential direction(<math>n_\theta</math>) in the following figure. Because this problem does not have an analytic solution, the reference value is taken to be the value obtained using Method I (Bessel) with <math>n_\theta = 181</math>. As expected, the relative error in radial image force decreases with increasing number of grids.		have the same magnitude. An estimate of their relative error is plotted as a function of number of grid in the circumferential direction(<math>n_\theta</math>) in the following figure. Because this problem does not have an analytic solution, the reference value is taken to be the value obtained using Method I (Bessel) with <math>n_\theta = 181</math>. As expected, the relative error in radial image force decreases with increasing number of grids.
Line 72:		Line 72:
	\|align="center"\|(b)		\|align="center"\|(b)
	\|-		\|-
	\|colspan="2" \| Fig.5 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}/\sqrt{2}[\bar{1} 1 0]</math>		\|colspan="2" \| Fig.5 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}/\sqrt{2}[\bar{1} 1 0]</math> and the slip plane is <math>\mathbf{n}= 1/\sqrt{6}[\bar{1} \bar{1} 2]</math>
	~~For simplicity~~, cell is not used for the force calculatoin. To do this, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.		Likewise, cell is not used for the force calculatoin. To do this, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.
	DEFS += -D_CYL_TEST23		DEFS += -D_CYL_TEST23

			The orientation and magnitude of the image force on every node is different. Fig. 10 plots the component
⚫	[[Image:~~T2_relative_error~~.jpg\|frameless\|~~400px~~\|~~right~~\|Fig.2. ]]
	~~Due to~~ the ~~symmetry~~ of ~~this problem,~~ the ~~image~~ ~~forces~~ on ~~all~~ ~~nodes~~ ~~point to~~ the ~~radial~~ ~~direction~~ ~~and~~		of the image force in the direction away from the center of the loop for all 10 nodes with
			different values of nq using Method I.
	have the same magnitude. An estimate of their relative error is plotted as a function of number of grid in the circumferential direction(<math>n_\theta</math>) in the following figure. Because this problem does not have an analytic solution, the reference value is taken to be the value obtained using Method I (Bessel) with <math>n_\theta = 181</math>. As expected, the relative error in radial image force decreases with increasing number of grids.
		⚫	[[Image:T3_Fr_img_tot.jpg\|frameless\|800px\|center\|Fig.6. ]]
			With more than 45 number of grids, they converge to almost same value.

Iryu at 12:11, 17 November 2011

2011-11-17T12:11:24Z

← Older revision		Revision as of 12:11, 17 November 2011
Line 66:		Line 66:
	In the third test case, we consider more general shaped dislocation loop, discretized with 10 equally spaced nodes connected by straight segments, as shown in Fig. 5.		In the third test case, we consider more general shaped dislocation loop, discretized with 10 equally spaced nodes connected by straight segments, as shown in Fig. 5.
	{\|border="0" align="center"		{\|border="0" align="center"
	\|[[Image:T3_geom_Isoview~~.jpg~~.jpg‎ \|frameless\|400px\|caption]]		\|[[Image:T3_geom_Isoview.jpg‎ \|frameless\|400px\|caption]]
	\|[[Image:T3_geom_Topview~~.jpg~~.jpg‎ \|frameless\|400px\|caption]]		\|[[Image:T3_geom_Topview.jpg‎ \|frameless\|400px\|caption]]
	\|-		\|-
	\|align="center"\|(a)		\|align="center"\|(a)
	\|align="center"\|(b)		\|align="center"\|(b)
	\|-		\|-
	\|colspan="2" \| Fig.3 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b} = a[~~001~~]</math>.		\|colspan="2" \| Fig.5 (a) Isoview (b) Topview.The Bergurs vector is <math>\mathbf{b}= \mathbf{a}/\sqrt{2}[\bar{1} 1 0]</math>
	For simplicity, cell is not used for the force calculatoin. To do this, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.		For simplicity, cell is not used for the force calculatoin. To do this, modify '''makefile''' in ParaDiS/cylinder directory so that the following line is active.
	DEFS += -D_CYL_TEST23		DEFS += -D_CYL_TEST23

Iryu at 12:04, 17 November 2011

2011-11-17T12:04:44Z

← Older revision		Revision as of 12:04, 17 November 2011
Line 58:		Line 58:


⚫	==TEST3 : Circular inclined ~~prismatic~~ dislocation loop==


⚫	In the third test case, we consider a ~~generalized~~ shaped dislocation loop~~. a circular prismatic dislocation loop concentric with the cylindrical axis~~, discretized with 12 equally spaced nodes connected by straight segments, as shown in Fig. ~~3, where the dislocation loop radius is 0.8 times to the cylinder radius~~.

			<HR>
		⚫	==TEST3 : Circular inclined glide dislocation loop==

		⚫	In the third test case, we consider more general shaped dislocation loop, discretized with 10 equally spaced nodes connected by straight segments, as shown in Fig. 5.
	{\|border="0" align="center"		{\|border="0" align="center"
	\|[[Image:T3_geom_Isoview.jpg.jpg‎ \|frameless\|400px\|caption]]		\|[[Image:T3_geom_Isoview.jpg.jpg‎ \|frameless\|400px\|caption]]