Strain Rate Sensitivity for Linear Mobility Model - Revision history

Caiwei: /* Elastoplastic Response in One Dimension */

2007-12-18T22:44:42Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 22:44, 18 December 2007
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	Now we don't get anything...		Now we don't get anything...

			We still don't know what kind of constraints a linear mobility law puts on the dislocation dynamics. If you believe there is such a constraint, please let us know.

2007-12-18T22:37:55Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 22:37, 18 December 2007
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	<math> \dot{e} = \frac{\dot{\sigma}}{E} + M \rho b^{2} \sigma </math>		<math> \dot{e} = \frac{\dot{\sigma}}{E} + M \rho b^{2} \sigma </math>

			Now we don't get anything...

2007-12-18T22:36:52Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 22:36, 18 December 2007
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	<math> \dot{e}^{p} = \rho v b </math>		<math> \dot{e}^{p} = \rho v b </math>

	where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the ~~burger's~~ vector. If we now assume a linear mobility, then the average dislocation velocity can be related to the applied stress as		where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the Burgers vector. If we now assume a linear mobility, then the average dislocation velocity can be related to the applied stress as

	<math> v = M \sigma b </math>		<math> v = M \sigma b </math>

2007-12-18T21:22:24Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 21:22, 18 December 2007
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	==Elastoplastic Response in One Dimension==		==Elastoplastic Response in One Dimension==
	In order to answer the above questions, we will start with a simple analytical model in one dimension. ~~This~~ ~~avoids~~ the ~~unnecessary~~ complications that ~~occur~~ ~~with~~ tensors ~~and ultimately should be easily generalized. Thus, we~~ will ~~deal~~ ~~with~~ ~~one~~ ~~dimensional~~ ~~strain,~~ ~~stress,~~ ~~and Young's~~ ~~modulus~~.		In order to answer the above questions, we will start with a simple analytical model in one dimension. A one dimensional model will avoid the complications that arise using tensors but will still capture the important points of the analysis.

	From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts		From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts

2007-12-18T21:19:42Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 21:19, 18 December 2007
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	From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts		From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts

	<math> \dot{e} = \dot{e}^{el} + \dot{e}^{pl} </math>		<math> \dot{e} = \dot{e}^{e} + \dot{e}^{p} </math>

	The elastic strain rate must be related to the stress rate through Hooke's law		The elastic strain rate must be related to the stress rate through Hooke's law

	<math> \dot{e}^{el} = \frac{\dot{\sigma}}{E} </math>		<math> \dot{e}^{e} = \frac{\dot{\sigma}}{E} </math>

	and the plastic strain rate can be approximated as		and the plastic strain rate can be approximated as

	<math> \dot{e}^{pl} = \rho v b </math>		<math> \dot{e}^{p} = \rho v b </math>

	where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the burger's vector. If we now assume a linear mobility, then the average dislocation velocity can be related to the applied stress as		where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the burger's vector. If we now assume a linear mobility, then the average dislocation velocity can be related to the applied stress as

2007-12-18T19:24:14Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 19:24, 18 December 2007
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	<math> \dot{e}^{pl} = \rho v b </math>		<math> \dot{e}^{pl} = \rho v b </math>

	where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the burger's vector.		where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the burger's vector. If we now assume a linear mobility, then the average dislocation velocity can be related to the applied stress as

			<math> v = M \sigma b </math>

			and the resulting stress strain relationship becomes

			<math> \dot{e} = \frac{\dot{\sigma}}{E} + M \rho b^{2} \sigma </math>

2007-12-18T19:18:32Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 19:18, 18 December 2007
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	<math> \dot{e}^{pl} = \rho v b </math>		<math> \dot{e}^{pl} = \rho v b </math>

			where <math>\rho</math> is the dislocation density, v is the average dislocation velocity, and b is the burger's vector.

2007-12-18T19:17:31Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 19:17, 18 December 2007
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	The elastic strain rate must be related to the stress rate through Hooke's law		The elastic strain rate must be related to the stress rate through Hooke's law

	<math> \dot{e}^{el} = \frac{\dot{\sigma}}}{E} </math>		<math> \dot{e}^{el} = \frac{\dot{\sigma}}{E} </math>

	and the plastic strain rate can be approximated as		and the plastic strain rate can be approximated as

2007-12-18T19:17:14Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 19:17, 18 December 2007
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	<math> \dot{e} = \dot{e}^{el} + \dot{e}^{pl} </math>		<math> \dot{e} = \dot{e}^{el} + \dot{e}^{pl} </math>

			The elastic strain rate must be related to the stress rate through Hooke's law

			<math> \dot{e}^{el} = \frac{\dot{\sigma}}}{E} </math>

			and the plastic strain rate can be approximated as

			<math> \dot{e}^{pl} = \rho v b </math>

2007-12-18T18:46:41Z

Elastoplastic Response in One Dimension

← Older revision		Revision as of 18:46, 18 December 2007
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	From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts		From an experimental point of view, we generally impose a constant strain rate and measure the materials stress response. The strain rate can generally be decomposed into elastic and plastic parts

	<math> \dot{e} = \dot{e}^{el} + \dot{e}^{pl} </math>		<math> \dot{e} = \dot{e}^{el} + \dot{e}^{pl} </math>