whitespace adjustments
This commit is contained in:
Martin Diehl
parent
eecfed7cda
commit
5af6cc288b
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@ -772,66 +772,67 @@ module subroutine nonlocal_LpAndItsTangent(Lp,dLp_dMp, &
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tau, & !< resolved shear stress including backstress terms
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dot_gamma !< shear rate
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associate(prm => param(ph),dst=>dependentState(ph),stt=>state(ph))
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!*** shortcut to state variables
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rho = getRho(ph,en)
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rhoSgl = rho(:,sgl)
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!*** shortcut to state variables
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rho = getRho(ph,en)
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rhoSgl = rho(:,sgl)
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do s = 1,prm%sum_N_sl
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tau(s) = math_tensordot(Mp, prm%P_sl(1:3,1:3,s))
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tauNS(s,1) = tau(s)
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tauNS(s,2) = tau(s)
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if (tau(s) > 0.0_pReal) then
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tauNS(s,3) = math_tensordot(Mp, +prm%P_nS_pos(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%P_nS_neg(1:3,1:3,s))
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else
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tauNS(s,3) = math_tensordot(Mp, +prm%P_nS_neg(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%P_nS_pos(1:3,1:3,s))
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end if
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end do
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tauNS = tauNS + spread(dst%tau_back(:,en),2,4)
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tau = tau + dst%tau_back(:,en)
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! edges
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call kinetics(v(:,1), dv_dtau(:,1), dv_dtauNS(:,1), &
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tau, tauNS(:,1), dst%tau_pass(:,en),1,Temperature, ph)
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v(:,2) = v(:,1)
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dv_dtau(:,2) = dv_dtau(:,1)
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dv_dtauNS(:,2) = dv_dtauNS(:,1)
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!screws
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if (prm%nonSchmidActive) then
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do t = 3,4
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call kinetics(v(:,t), dv_dtau(:,t), dv_dtauNS(:,t), &
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tau, tauNS(:,t), dst%tau_pass(:,en),2,Temperature, ph)
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do s = 1,prm%sum_N_sl
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tau(s) = math_tensordot(Mp, prm%P_sl(1:3,1:3,s))
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tauNS(s,1) = tau(s)
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tauNS(s,2) = tau(s)
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if (tau(s) > 0.0_pReal) then
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tauNS(s,3) = math_tensordot(Mp, +prm%P_nS_pos(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%P_nS_neg(1:3,1:3,s))
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else
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tauNS(s,3) = math_tensordot(Mp, +prm%P_nS_neg(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%P_nS_pos(1:3,1:3,s))
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end if
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end do
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else
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v(:,3:4) = spread(v(:,1),2,2)
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dv_dtau(:,3:4) = spread(dv_dtau(:,1),2,2)
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dv_dtauNS(:,3:4) = spread(dv_dtauNS(:,1),2,2)
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end if
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tauNS = tauNS + spread(dst%tau_back(:,en),2,4)
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tau = tau + dst%tau_back(:,en)
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stt%v(:,en) = pack(v,.true.)
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! edges
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call kinetics(v(:,1), dv_dtau(:,1), dv_dtauNS(:,1), &
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tau, tauNS(:,1), dst%tau_pass(:,en),1,Temperature, ph)
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v(:,2) = v(:,1)
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dv_dtau(:,2) = dv_dtau(:,1)
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dv_dtauNS(:,2) = dv_dtauNS(:,1)
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!*** Bauschinger effect
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forall (s = 1:prm%sum_N_sl, t = 5:8, rhoSgl(s,t) * v(s,t-4) < 0.0_pReal) &
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rhoSgl(s,t-4) = rhoSgl(s,t-4) + abs(rhoSgl(s,t))
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!screws
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if (prm%nonSchmidActive) then
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do t = 3,4
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call kinetics(v(:,t), dv_dtau(:,t), dv_dtauNS(:,t), &
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tau, tauNS(:,t), dst%tau_pass(:,en),2,Temperature, ph)
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end do
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else
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v(:,3:4) = spread(v(:,1),2,2)
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dv_dtau(:,3:4) = spread(dv_dtau(:,1),2,2)
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dv_dtauNS(:,3:4) = spread(dv_dtauNS(:,1),2,2)
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end if
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dot_gamma = sum(rhoSgl(:,1:4) * v, 2) * prm%b_sl
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stt%v(:,en) = pack(v,.true.)
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
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do s = 1,prm%sum_N_sl
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Lp = Lp + dot_gamma(s) * prm%P_sl(1:3,1:3,s)
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forall (i=1:3,j=1:3,k=1:3,l=1:3) &
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dLp_dMp(i,j,k,l) = dLp_dMp(i,j,k,l) &
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+ prm%P_sl(i,j,s) * prm%P_sl(k,l,s) &
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* sum(rhoSgl(s,1:4) * dv_dtau(s,1:4)) * prm%b_sl(s) &
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+ prm%P_sl(i,j,s) &
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* (+ prm%P_nS_pos(k,l,s) * rhoSgl(s,3) * dv_dtauNS(s,3) &
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- prm%P_nS_neg(k,l,s) * rhoSgl(s,4) * dv_dtauNS(s,4)) * prm%b_sl(s)
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end do
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!*** Bauschinger effect
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forall (s = 1:prm%sum_N_sl, t = 5:8, rhoSgl(s,t) * v(s,t-4) < 0.0_pReal) &
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rhoSgl(s,t-4) = rhoSgl(s,t-4) + abs(rhoSgl(s,t))
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dot_gamma = sum(rhoSgl(:,1:4) * v, 2) * prm%b_sl
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
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do s = 1,prm%sum_N_sl
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Lp = Lp + dot_gamma(s) * prm%P_sl(1:3,1:3,s)
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forall (i=1:3,j=1:3,k=1:3,l=1:3) &
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dLp_dMp(i,j,k,l) = dLp_dMp(i,j,k,l) &
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+ prm%P_sl(i,j,s) * prm%P_sl(k,l,s) &
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* sum(rhoSgl(s,1:4) * dv_dtau(s,1:4)) * prm%b_sl(s) &
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+ prm%P_sl(i,j,s) &
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* (+ prm%P_nS_pos(k,l,s) * rhoSgl(s,3) * dv_dtauNS(s,3) &
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- prm%P_nS_neg(k,l,s) * rhoSgl(s,4) * dv_dtauNS(s,4)) * prm%b_sl(s)
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end do
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end associate
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@ -870,7 +871,8 @@ module subroutine plastic_nonlocal_deltaState(Mp,ph,en)
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dUpper, & ! current maximum stable dipole distance for edges and screws
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dUpperOld, & ! old maximum stable dipole distance for edges and screws
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deltaDUpper ! change in maximum stable dipole distance for edges and screws
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associate(prm => param(ph),dst => dependentState(ph),del => deltaState(ph))
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mu = elastic_mu(ph,en)
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@ -1394,78 +1396,79 @@ module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
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belowThreshold
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type(rotation) :: mis
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associate(prm => param(ph))
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ns = prm%sum_N_sl
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ns = prm%sum_N_sl
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en = material_phaseMemberAt(1,i,e)
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!*** start out fully compatible
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my_compatibility = 0.0_pReal
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,:) = 1.0_pReal
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en = material_phaseMemberAt(1,i,e)
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!*** start out fully compatible
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my_compatibility = 0.0_pReal
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,:) = 1.0_pReal
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neighbors: do n = 1,nIPneighbors
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neighbor_e = IPneighborhood(1,n,i,e)
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neighbor_i = IPneighborhood(2,n,i,e)
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neighbor_me = material_phaseMemberAt(1,neighbor_i,neighbor_e)
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neighbor_phase = material_phaseAt(1,neighbor_e)
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neighbors: do n = 1,nIPneighbors
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neighbor_e = IPneighborhood(1,n,i,e)
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neighbor_i = IPneighborhood(2,n,i,e)
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neighbor_me = material_phaseMemberAt(1,neighbor_i,neighbor_e)
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neighbor_phase = material_phaseAt(1,neighbor_e)
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if (neighbor_e <= 0 .or. neighbor_i <= 0) then
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!* FREE SURFACE
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_surface)
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elseif (neighbor_phase /= ph) then
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!* PHASE BOUNDARY
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if (plasticState(neighbor_phase)%nonlocal .and. plasticState(ph)%nonlocal) &
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = 0.0_pReal
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elseif (prm%chi_GB >= 0.0_pReal) then
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!* GRAIN BOUNDARY
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if (any(dNeq(phase_O_0(ph)%data(en)%asQuaternion(), &
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phase_O_0(neighbor_phase)%data(neighbor_me)%asQuaternion())) .and. &
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plasticState(neighbor_phase)%nonlocal) &
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_GB)
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else
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!* GRAIN BOUNDARY ?
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!* Compatibility defined by relative orientation of slip systems:
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!* The my_compatibility value is defined as the product of the slip normal projection and the slip direction projection.
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!* Its sign is always positive for screws, for edges it has the same sign as the slip normal projection.
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!* Since the sum for each slip system can easily exceed one (which would result in a transmissivity larger than one),
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!* only values above or equal to a certain threshold value are considered. This threshold value is chosen, such that
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!* the number of compatible slip systems is minimized with the sum of the original compatibility values exceeding one.
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!* Finally the smallest compatibility value is decreased until the sum is exactly equal to one.
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!* All values below the threshold are set to zero.
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mis = orientation(ph)%data(en)%misorientation(orientation(neighbor_phase)%data(neighbor_me))
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mySlipSystems: do s1 = 1,ns
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neighborSlipSystems: do s2 = 1,ns
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my_compatibility(1,s2,s1,n) = math_inner(prm%slip_normal(1:3,s1), &
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mis%rotate(prm%slip_normal(1:3,s2))) &
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* abs(math_inner(prm%slip_direction(1:3,s1), &
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mis%rotate(prm%slip_direction(1:3,s2))))
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my_compatibility(2,s2,s1,n) = abs(math_inner(prm%slip_normal(1:3,s1), &
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mis%rotate(prm%slip_normal(1:3,s2)))) &
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* abs(math_inner(prm%slip_direction(1:3,s1), &
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mis%rotate(prm%slip_direction(1:3,s2))))
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end do neighborSlipSystems
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if (neighbor_e <= 0 .or. neighbor_i <= 0) then
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!* FREE SURFACE
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_surface)
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elseif (neighbor_phase /= ph) then
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!* PHASE BOUNDARY
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if (plasticState(neighbor_phase)%nonlocal .and. plasticState(ph)%nonlocal) &
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = 0.0_pReal
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elseif (prm%chi_GB >= 0.0_pReal) then
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!* GRAIN BOUNDARY
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if (any(dNeq(phase_O_0(ph)%data(en)%asQuaternion(), &
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phase_O_0(neighbor_phase)%data(neighbor_me)%asQuaternion())) .and. &
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plasticState(neighbor_phase)%nonlocal) &
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forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_GB)
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else
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!* GRAIN BOUNDARY ?
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!* Compatibility defined by relative orientation of slip systems:
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!* The my_compatibility value is defined as the product of the slip normal projection and the slip direction projection.
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!* Its sign is always positive for screws, for edges it has the same sign as the slip normal projection.
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!* Since the sum for each slip system can easily exceed one (which would result in a transmissivity larger than one),
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!* only values above or equal to a certain threshold value are considered. This threshold value is chosen, such that
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!* the number of compatible slip systems is minimized with the sum of the original compatibility values exceeding one.
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!* Finally the smallest compatibility value is decreased until the sum is exactly equal to one.
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!* All values below the threshold are set to zero.
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mis = orientation(ph)%data(en)%misorientation(orientation(neighbor_phase)%data(neighbor_me))
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mySlipSystems: do s1 = 1,ns
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neighborSlipSystems: do s2 = 1,ns
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my_compatibility(1,s2,s1,n) = math_inner(prm%slip_normal(1:3,s1), &
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mis%rotate(prm%slip_normal(1:3,s2))) &
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* abs(math_inner(prm%slip_direction(1:3,s1), &
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mis%rotate(prm%slip_direction(1:3,s2))))
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my_compatibility(2,s2,s1,n) = abs(math_inner(prm%slip_normal(1:3,s1), &
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mis%rotate(prm%slip_normal(1:3,s2)))) &
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* abs(math_inner(prm%slip_direction(1:3,s1), &
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mis%rotate(prm%slip_direction(1:3,s2))))
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end do neighborSlipSystems
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my_compatibilitySum = 0.0_pReal
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belowThreshold = .true.
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do while (my_compatibilitySum < 1.0_pReal .and. any(belowThreshold))
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thresholdValue = maxval(my_compatibility(2,:,s1,n), belowThreshold) ! screws always positive
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nThresholdValues = real(count(my_compatibility(2,:,s1,n) >= thresholdValue),pReal)
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where (my_compatibility(2,:,s1,n) >= thresholdValue) belowThreshold = .false.
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if (my_compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
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where (abs(my_compatibility(:,:,s1,n)) >= thresholdValue) &
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my_compatibility(:,:,s1,n) = sign((1.0_pReal - my_compatibilitySum)/nThresholdValues,&
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my_compatibility(:,:,s1,n))
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my_compatibilitySum = my_compatibilitySum + nThresholdValues * thresholdValue
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end do
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my_compatibilitySum = 0.0_pReal
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belowThreshold = .true.
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do while (my_compatibilitySum < 1.0_pReal .and. any(belowThreshold))
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thresholdValue = maxval(my_compatibility(2,:,s1,n), belowThreshold) ! screws always positive
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nThresholdValues = real(count(my_compatibility(2,:,s1,n) >= thresholdValue),pReal)
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where (my_compatibility(2,:,s1,n) >= thresholdValue) belowThreshold = .false.
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if (my_compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
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where (abs(my_compatibility(:,:,s1,n)) >= thresholdValue) &
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my_compatibility(:,:,s1,n) = sign((1.0_pReal - my_compatibilitySum)/nThresholdValues,&
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my_compatibility(:,:,s1,n))
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my_compatibilitySum = my_compatibilitySum + nThresholdValues * thresholdValue
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end do
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where(belowThreshold) my_compatibility(1,:,s1,n) = 0.0_pReal
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where(belowThreshold) my_compatibility(2,:,s1,n) = 0.0_pReal
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where(belowThreshold) my_compatibility(1,:,s1,n) = 0.0_pReal
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where(belowThreshold) my_compatibility(2,:,s1,n) = 0.0_pReal
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end do mySlipSystems
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end if
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end do mySlipSystems
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end if
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end do neighbors
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end do neighbors
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compatibility(:,:,:,:,i,e) = my_compatibility
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compatibility(:,:,:,:,i,e) = my_compatibility
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end associate
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@ -1647,52 +1650,52 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T,
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criticalStress_S !< maximum obstacle strength
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associate(prm => param(ph))
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v = 0.0_pReal
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dv_dtau = 0.0_pReal
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dv_dtauNS = 0.0_pReal
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v = 0.0_pReal
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dv_dtau = 0.0_pReal
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dv_dtauNS = 0.0_pReal
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do s = 1,prm%sum_N_sl
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if (abs(tau(s)) > tauThreshold(s)) then
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do s = 1,prm%sum_N_sl
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if (abs(tau(s)) > tauThreshold(s)) then
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!* Peierls contribution
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tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s))
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lambda_P = prm%b_sl(s)
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activationVolume_P = prm%w *prm%b_sl(s)**3
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criticalStress_P = prm%peierlsStress(s,c)
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activationEnergy_P = criticalStress_P * activationVolume_P
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tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
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tPeierls = 1.0_pReal / prm%nu_a &
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* exp(activationEnergy_P / (K_B * T) &
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* (1.0_pReal - tauRel_P**prm%p)**prm%q)
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dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (K_B * T) &
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* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), &
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0.0_pReal, &
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tauEff < criticalStress_P)
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!* Peierls contribution
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tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s))
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lambda_P = prm%b_sl(s)
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activationVolume_P = prm%w *prm%b_sl(s)**3
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criticalStress_P = prm%peierlsStress(s,c)
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activationEnergy_P = criticalStress_P * activationVolume_P
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tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
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tPeierls = 1.0_pReal / prm%nu_a &
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* exp(activationEnergy_P / (K_B * T) &
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* (1.0_pReal - tauRel_P**prm%p)**prm%q)
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dtPeierls_dtau = merge(tPeierls * prm%p * prm%q * activationVolume_P / (K_B * T) &
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* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal), &
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0.0_pReal, &
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tauEff < criticalStress_P)
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! Contribution from solid solution strengthening
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tauEff = abs(tau(s)) - tauThreshold(s)
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lambda_S = prm%b_sl(s) / sqrt(prm%c_sol)
|
||||
activationVolume_S = prm%f_sol * prm%b_sl(s)**3 / sqrt(prm%c_sol)
|
||||
criticalStress_S = prm%Q_sol / activationVolume_S
|
||||
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
|
||||
tSolidSolution = 1.0_pReal / prm%nu_a &
|
||||
* exp(prm%Q_sol / (K_B * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
|
||||
dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (K_B * T) &
|
||||
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), &
|
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0.0_pReal, &
|
||||
tauEff < criticalStress_S)
|
||||
! Contribution from solid solution strengthening
|
||||
tauEff = abs(tau(s)) - tauThreshold(s)
|
||||
lambda_S = prm%b_sl(s) / sqrt(prm%c_sol)
|
||||
activationVolume_S = prm%f_sol * prm%b_sl(s)**3 / sqrt(prm%c_sol)
|
||||
criticalStress_S = prm%Q_sol / activationVolume_S
|
||||
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
|
||||
tSolidSolution = 1.0_pReal / prm%nu_a &
|
||||
* exp(prm%Q_sol / (K_B * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
|
||||
dtSolidSolution_dtau = merge(tSolidSolution * prm%p * prm%q * activationVolume_S / (K_B * T) &
|
||||
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal), &
|
||||
0.0_pReal, &
|
||||
tauEff < criticalStress_S)
|
||||
|
||||
!* viscous glide velocity
|
||||
tauEff = abs(tau(s)) - tauThreshold(s)
|
||||
!* viscous glide velocity
|
||||
tauEff = abs(tau(s)) - tauThreshold(s)
|
||||
|
||||
|
||||
v(s) = sign(1.0_pReal,tau(s)) &
|
||||
/ (tPeierls / lambda_P + tSolidSolution / lambda_S + prm%B /(prm%b_sl(s) * tauEff))
|
||||
dv_dtau(s) = v(s)**2 * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2))
|
||||
dv_dtauNS(s) = v(s)**2 * dtPeierls_dtau / lambda_P
|
||||
v(s) = sign(1.0_pReal,tau(s)) &
|
||||
/ (tPeierls / lambda_P + tSolidSolution / lambda_S + prm%B /(prm%b_sl(s) * tauEff))
|
||||
dv_dtau(s) = v(s)**2 * (dtSolidSolution_dtau / lambda_S + prm%B / (prm%b_sl(s) * tauEff**2))
|
||||
dv_dtauNS(s) = v(s)**2 * dtPeierls_dtau / lambda_P
|
||||
|
||||
end if
|
||||
end do
|
||||
end if
|
||||
end do
|
||||
|
||||
end associate
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue