Steinberg-Lund Hardening - Revision history

Nairnj: /* Plasticity Theory */

2019-10-30T06:57:24Z

Plasticity Theory

← Older revision		Revision as of 06:57, 30 October 2019
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	=== Plasticity Theory ===		=== Plasticity Theory ===

	The implementation of this hardening law is formally non-associative J<sub>2</sub> plasticity theory as explained [[#Plasticity Theory\|here]].		The implementation of this hardening law is formally non-associative J<sub>2</sub> plasticity theory as explained [[Steinberg-Cochran-Guinan Hardening#Plasticity Theory\|here]].

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj at 06:56, 30 October 2019

2019-10-30T06:56:52Z

← Older revision		Revision as of 06:56, 30 October 2019
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			== Yield Stress ==

	In the Steinberg-Lund [[Hardening Laws\|hardening law]], the yield stress is given by		In the Steinberg-Lund [[Hardening Laws\|hardening law]], the yield stress is given by

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	where J is the relative volume change (V/V<sub>0</sub>), G<sub>P</sub>' and G<sub>T</sub>' are coefficients for pressure and temperature affects, T is current temperature, and T<sub>0</sub> is a reference temperature. For more details, see paper by Steinberg and Lund.<ref>D. J. Steinberg and C. M. Lund, "A constitutive model for strain rates from 10-4 to 106," J. Appl. Phys., 65, 1528-1533 (1989).</ref>		where J is the relative volume change (V/V<sub>0</sub>), G<sub>P</sub>' and G<sub>T</sub>' are coefficients for pressure and temperature affects, T is current temperature, and T<sub>0</sub> is a reference temperature. For more details, see paper by Steinberg and Lund.<ref>D. J. Steinberg and C. M. Lund, "A constitutive model for strain rates from 10-4 to 106," J. Appl. Phys., 65, 1528-1533 (1989).</ref>

			=== Plasticity Theory ===

			The implementation of this hardening law is formally non-associative J<sub>2</sub> plasticity theory as explained [[#Plasticity Theory\|here]].

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj at 22:43, 2 June 2015

2015-06-02T22:43:55Z

← Older revision		Revision as of 22:43, 2 June 2015
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	\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units K<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.		\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units K<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.
	\|-		\|-
	\| C1SL \|\| The C<sub>1</sub> constant in this law entered in ~~units of~~ 1/~~sec~~.		\| C1SL \|\| The C<sub>1</sub> constant in this law entered in [[ConsistentUnits Command#Legacy and Consistent Units\|1/time units]].
	\|-		\|-
	\| C2SL \|\| The C<sub>2</sub> constant in this law entered in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure-time units]].		\| C2SL \|\| The C<sub>2</sub> constant in this law entered in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure-time units]].
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	where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,		where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,
	the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]], and the current plastic strain rate (dα/dt in 1/~~sec~~). These variables are stored as history variables #1, #2, and #3.		the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]], and the current plastic strain rate (dα/dt in [[ConsistentUnits Command#Legacy and Consistent Units\|1/time units]]). These variables are stored as history variables #1, #2, and #3.

	== References ==		== References ==

	<references/>		<references/>

Nairnj at 21:55, 2 June 2015

2015-06-02T21:55:20Z

Nairnj: /* Hardening Law Properties */

2015-06-02T00:41:02Z

Hardening Law Properties

← Older revision		Revision as of 00:41, 2 June 2015
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	\| YP \|\| The Peierls stress (Y<sub>P</sub>) and also the maximum rate-dependent yield stress. Enter in units of MPa.		\| YP \|\| The Peierls stress (Y<sub>P</sub>) and also the maximum rate-dependent yield stress. Enter in units of MPa.
	\|-		\|-
	\| Uk \|\| An energy associated with forming kinks (U<sub>k</sub>). It has units eV.		\| UkOverk \|\| An energy associated with forming kinks (entered as U<sub>k</sub>/k). It has units degrees K.
	\|-		\|-
	\| yieldMax \|\| Maximum yield stress. Enter in units of MPa.		\| yieldMax \|\| Maximum yield stress. Enter in units of MPa.

Nairnj: /* Hardening Law Properties */

2015-03-12T16:08:15Z

Hardening Law Properties

← Older revision		Revision as of 16:08, 12 March 2015
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	\| GPpG0 \|\| The (G<sub>p</sub>'/G<sub>0</sub>) ratio term for pressure dependence of shear modulus. Enter in units MPa<sup>-1</sup>. Enter 0 to omit pressure dependence in shear modulus.		\| GPpG0 \|\| The (G<sub>p</sub>'/G<sub>0</sub>) ratio term for pressure dependence of shear modulus. Enter in units MPa<sup>-1</sup>. Enter 0 to omit pressure dependence in shear modulus.
	\|-		\|-
	\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units ~~MPa~~<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.		\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units K<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.
	\|-		\|-
	\| C1SL \|\| The C<sub>1</sub> constant in this law entered in units of 1/sec.		\| C1SL \|\| The C<sub>1</sub> constant in this law entered in units of 1/sec.

Nairnj: /* Hardening Law Properties */

2013-09-10T07:45:01Z

Hardening Law Properties

← Older revision		Revision as of 07:45, 10 September 2013
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	\|}		\|}

	The reference temperature, T<sub>0</sub>, is set using the simulation's [[stress free temperature]] and not set using [[Hardening Laws\|hardening law]] properties.		The reference temperature, T<sub>0</sub>, is set using the simulation's [[Thermal Calculations#Stress Free Temperature\|stress free temperature]] and not set using [[Hardening Laws\|hardening law]] properties.

	== History Data ==		== History Data ==

Nairnj at 00:35, 30 May 2013

2013-05-30T00:35:08Z

← Older revision		Revision as of 00:35, 30 May 2013
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	<math>\sigma_y = \left(\min\left\{~~Y_T~~(\~~dot~~\alpha,T),~~Y_P~~\right\}+\min\left\{~~\sigma_0\bigl~~(~~1 +~~ \~~beta~~ \alpha~~\bigr~~)^n,~~\sigma_y^{max}~~\right\}\right){G(T,P)\over G_0}</math>		<math>\sigma_y = \left(\min\left\{\sigma_0\bigl(1 + \beta \alpha\bigr)^n,\sigma_y^{max}\right\}+\min\left\{Y_T(\dot\alpha,T),Y_P\right\}\right){G(T,P)\over G_0}</math>

	where <math>Y_T(\dot\alpha,T)</math> is a strain rate and temperature dependent term, σ<sub>0</sub> is the initial yield stress, β and n are hardening law properties, α is the cumulative equivalent plastic strain, G(T,P) is the shear modulus (which may depend on temperature and pressure), and G<sub>0</sub> is the initial shear modulus. The strain rate and temperature dependent term is defined in inverse form:		where <math>Y_T(\dot\alpha,T)</math> is a strain rate and temperature dependent term, σ<sub>0</sub> is the initial yield stress, β and n are hardening law properties, α is the cumulative equivalent plastic strain, G(T,P) is the shear modulus (which may depend on temperature and pressure), and G<sub>0</sub> is the initial shear modulus. The strain rate and temperature dependent term is defined in inverse form:

Nairnj at 18:22, 24 May 2013

2013-05-24T18:22:22Z

← Older revision		Revision as of 18:22, 24 May 2013
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	<math>{G(T,P)\over G_0} = 1 + {G_P'\over G_0} P J^{1/3} + {G_T'\over G_0}(T-T_0)</math>		<math>{G(T,P)\over G_0} = 1 + {G_P'\over G_0} P J^{1/3} + {G_T'\over G_0}(T-T_0)</math>

	where J is the relative volume change (V/V<sub>0</sub>), G<sub>P</sub>' and G<sub>T</sub>' are coefficients for pressure and temperature affects, T is current temperature, and T<sub>0</sub> is a reference temperature. For more details, see paper by Steinberg and Lund<ref>D. J. Steinberg and C. M. Lund, "A constitutive model for strain rates from 10-4 to 106," J. Appl. Phys., 65, 1528-1533 (1989).</ref>.		where J is the relative volume change (V/V<sub>0</sub>), G<sub>P</sub>' and G<sub>T</sub>' are coefficients for pressure and temperature affects, T is current temperature, and T<sub>0</sub> is a reference temperature. For more details, see paper by Steinberg and Lund.<ref>D. J. Steinberg and C. M. Lund, "A constitutive model for strain rates from 10-4 to 106," J. Appl. Phys., 65, 1528-1533 (1989).</ref>

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* History Data */

2013-05-24T18:21:47Z

History Data

← Older revision		Revision as of 18:21, 24 May 2013
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	where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,		where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,
	the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in MPa, and the current plastic strain rate (dα/dt in 1/sec). These variables are stored as history variables #1, #2, and #3.		the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in MPa, and the current plastic strain rate (dα/dt in 1/sec). These variables are stored as history variables #1, #2, and #3.

			== References ==

	<references/>		<references/>

← Older revision		Revision as of 21:55, 2 June 2015
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	! Property !! Description		! Property !! Description
	\|-		\|-
	\| yield \|\| Initial yield stress (σ<sub>0</sub> at zero pressure and the reference temperature). Enter in units ~~of MPa~~.		\| yield \|\| Initial yield stress (σ<sub>0</sub> at zero pressure and the reference temperature). Enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]].
	\|-		\|-
	\| betahard \|\| Yield stress hardening term β. It is dimensionless.		\| betahard \|\| Yield stress hardening term β. It is dimensionless.
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	\| nhard \|\| Exponent on cumulative equivalent plastic strain in hardening term. It is dimensionless.		\| nhard \|\| Exponent on cumulative equivalent plastic strain in hardening term. It is dimensionless.
	\|-		\|-
	\| GPpG0 \|\| The (G<sub>p</sub>'/G<sub>0</sub>) ratio term for pressure dependence of shear modulus. Enter in ~~units MPa~~<sup>-1</sup>. Enter 0 to omit pressure dependence in shear modulus.		\| GPpG0 \|\| The (G<sub>p</sub>'/G<sub>0</sub>) ratio term for pressure dependence of shear modulus. Enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure<sup>-1</sup> units]]. Enter 0 to omit pressure dependence in shear modulus.
	\|-		\|-
	\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units K<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.		\| GTpG0 \|\| The (G<sub>T</sub>'/G<sub>0</sub>) ratio term for temperature dependence of shear modulus. Enter in units K<sup>-1</sup>. Enter 0 to omit temperature dependence in shear modulus.
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	\| C1SL \|\| The C<sub>1</sub> constant in this law entered in units of 1/sec.		\| C1SL \|\| The C<sub>1</sub> constant in this law entered in units of 1/sec.
	\|-		\|-
	\| C2SL \|\| The C<sub>2</sub> constant in this law entered in units ~~of MPa-sec~~.		\| C2SL \|\| The C<sub>2</sub> constant in this law entered in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure-time units]].
	\|-		\|-
	\| YP \|\| The Peierls stress (Y<sub>P</sub>) and also the maximum rate-dependent yield stress. Enter in units ~~of MPa~~.		\| YP \|\| The Peierls stress (Y<sub>P</sub>) and also the maximum rate-dependent yield stress. Enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]].
	\|-		\|-
	\| UkOverk \|\| An energy associated with forming kinks (entered as U<sub>k</sub>/k). It has units degrees K.		\| UkOverk \|\| An energy associated with forming kinks (entered as U<sub>k</sub>/k). It has units degrees K.
	\|-		\|-
	\| yieldMax \|\| Maximum yield stress. Enter in units ~~of MPa~~.		\| yieldMax \|\| Maximum yield stress. Enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]].
	\|}		\|}

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	where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,		where dε<sub>p</sub> is the incremental plastic strain tensor in one time step,
	the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in ~~MPa~~, and the current plastic strain rate (dα/dt in 1/sec). These variables are stored as history variables #1, #2, and #3.		the current rate- and temperature-dependent yield stress (Y<sub>T</sub>) in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]], and the current plastic strain rate (dα/dt in 1/sec). These variables are stored as history variables #1, #2, and #3.

	== References ==		== References ==

	<references/>		<references/>