following DAMASK paper
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Martin Diehl
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@ -4,9 +4,12 @@ references:
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- N. Jia et al.,
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Acta Materialia 60(3):1099-1115, 2012,
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https://doi.org/10.1016/j.actamat.2011.10.047
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- N. Jia et al.,
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Acta Materialia 60:3415-3434, 2012,
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https://doi.org/10.1016/j.actamat.2012.03.005
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v_sb: 0.0001
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xi_sb: 300.0e6 # tau_hat_sb
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gamma_0_sb: 0.0001
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tau_sb: 180.0e6 # tau_hat_sb
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Q_sb: 4.0e-19 # Q_0
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p_sb: 1.15
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q_sb: 1.0
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@ -11,26 +11,26 @@ submodule(phase:plastic) dislotwin
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type :: tParameters
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real(pReal) :: &
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Q_cl = 1.0_pReal, & !< activation energy for dislocation climb
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omega = 1.0_pReal, & !< frequency factor for dislocation climb
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D = 1.0_pReal, & !< grain size
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p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
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q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
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i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning
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i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
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L_tw = 1.0_pReal, & !< length of twin nuclei
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L_tr = 1.0_pReal, & !< length of trans nuclei
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x_c = 1.0_pReal, & !< critical distance for formation of twin/trans nucleus
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V_cs = 1.0_pReal, & !< cross slip volume
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xi_sb = 1.0_pReal, & !< value for shearband resistance
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v_sb = 1.0_pReal, & !< value for shearband velocity_0
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E_sb = 1.0_pReal, & !< activation energy for shear bands
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h = 1.0_pReal, & !< stack height of hex nucleus
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gamma_char_tr = sqrt(0.125_pReal), & !< Characteristic shear for transformation
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a_cF = 1.0_pReal, &
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cOverA_hP = 1.0_pReal, &
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V_mol = 1.0_pReal, &
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rho = 1.0_pReal
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Q_cl = 1.0_pReal, & !< activation energy for dislocation climb
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omega = 1.0_pReal, & !< frequency factor for dislocation climb
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D = 1.0_pReal, & !< grain size
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p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
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q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
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i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning
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i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation
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L_tw = 1.0_pReal, & !< length of twin nuclei
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L_tr = 1.0_pReal, & !< length of trans nuclei
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x_c = 1.0_pReal, & !< critical distance for formation of twin/trans nucleus
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V_cs = 1.0_pReal, & !< cross slip volume
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tau_sb = 1.0_pReal, & !< value for shearband resistance
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gamma_0_sb = 1.0_pReal, & !< value for shearband velocity_0
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E_sb = 1.0_pReal, & !< activation energy for shear bands
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h = 1.0_pReal, & !< stack height of hex nucleus
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gamma_char_tr = sqrt(0.125_pReal), & !< Characteristic shear for transformation
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a_cF = 1.0_pReal, &
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cOverA_hP = 1.0_pReal, &
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V_mol = 1.0_pReal, &
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rho = 1.0_pReal
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type(tPolynomial) :: &
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Gamma_sf, & !< stacking fault energy
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Delta_G !< free energy difference between austensite and martensite
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@ -331,18 +331,18 @@ module function plastic_dislotwin_init() result(myPlasticity)
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!--------------------------------------------------------------------------------------------------
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! shearband related parameters
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prm%v_sb = pl%get_asFloat('v_sb',defaultVal=0.0_pReal)
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if (prm%v_sb > 0.0_pReal) then
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prm%xi_sb = pl%get_asFloat('xi_sb')
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prm%gamma_0_sb = pl%get_asFloat('gamma_0_sb',defaultVal=0.0_pReal)
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if (prm%gamma_0_sb > 0.0_pReal) then
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prm%tau_sb = pl%get_asFloat('tau_sb')
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prm%E_sb = pl%get_asFloat('Q_sb')
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prm%p_sb = pl%get_asFloat('p_sb')
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prm%q_sb = pl%get_asFloat('q_sb')
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! sanity checks
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if (prm%xi_sb < 0.0_pReal) extmsg = trim(extmsg)//' xi_sb'
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if (prm%E_sb < 0.0_pReal) extmsg = trim(extmsg)//' Q_sb'
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if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_sb'
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if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_sb'
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if (prm%tau_sb < 0.0_pReal) extmsg = trim(extmsg)//' tau_sb'
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if (prm%E_sb < 0.0_pReal) extmsg = trim(extmsg)//' Q_sb'
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if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_sb'
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if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_sb'
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end if
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!--------------------------------------------------------------------------------------------------
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@ -569,7 +569,7 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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Lp = Lp * f_matrix
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dLp_dMp = dLp_dMp * f_matrix
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shearBandingContribution: if (dNeq0(prm%v_sb)) then
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shearBandingContribution: if (dNeq0(prm%gamma_0_sb)) then
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E_kB_T = prm%E_sb/(K_B*T)
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call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design?
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@ -580,10 +580,10 @@ module subroutine dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en)
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tau = math_tensordot(Mp,P_sb)
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significantShearBandStress: if (abs(tau) > tol_math_check) then
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StressRatio_p = (abs(tau)/prm%xi_sb)**prm%p_sb
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dot_gamma_sb = sign(prm%v_sb*exp(-E_kB_T*(1-StressRatio_p)**prm%q_sb), tau)
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ddot_gamma_dtau = abs(dot_gamma_sb)*E_kB_T*prm%p_sb*prm%q_sb/prm%xi_sb &
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* (abs(tau)/prm%xi_sb)**(prm%p_sb-1.0_pReal) &
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StressRatio_p = (abs(tau)/prm%tau_sb)**prm%p_sb
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dot_gamma_sb = sign(prm%gamma_0_sb*exp(-E_kB_T*(1-StressRatio_p)**prm%q_sb), tau)
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ddot_gamma_dtau = abs(dot_gamma_sb)*E_kB_T*prm%p_sb*prm%q_sb/prm%tau_sb &
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* (abs(tau)/prm%tau_sb)**(prm%p_sb-1.0_pReal) &
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* (1.0_pReal-StressRatio_p)**(prm%q_sb-1.0_pReal)
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Lp = Lp + dot_gamma_sb * P_sb
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