def aniso_211(self):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
e1 = [1, 0, 0]
e2 = [0, 1, -1]
e3 = [0, 1, 1]
# axes = np.array([e2, e1, e3])
axes = np.array([e1, e2, e3])
burgers = self.pot["lattice"] / 2. * np.array([1., 1., -1.])
burgers = axes_check.axes_check(axes).dot(burgers)
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
self.ckcoeff.K1 = sqrt(2 * self.pot["surf110"] /
abs(Gamma[1, 1] * 1e3))
# theta = np.deg2rad(54.735610317245346)
theta = np.deg2rad(35.2643896828)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose() #
Gamma = np.abs(np.linalg.inv(Gamma))
Gamma = Gamma * 1e9 # Pa
print(self.ckcoeff.K1)
if axes is not None:
burgers = axes_check.axes_check(axes).dot(burgers)
c = c.transform(axes)
G00 = Gamma[0, 0]
usf = 0.57405172613
k1e = np.sqrt(G00 * usf) * 1e-6
print(Gamma)
print(self.ckcoeff.K1, k1e)
self.set_plane_strain_bij(c.Sij)
# self.get_scalarB(self.pot["surf110"]) get the same k1c
self.get_coeffs()
atoms = self.intro_crack_k1(atoms=self.gn_perf_plate())
self.write_lmp_config_data(atoms, 'crack.txt')
def bcc_screw_dipole_alongz_atoms(self, atoms, c1, c2):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, c1, 1)
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, c2, -1)
return atoms
def get_bcc_w_result211(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
e1 = [1, 0, 0]
e2 = [0, 1, -1]
e3 = [0, 1, 1]
# glide plane [2, 1, -1]
axes = np.array([e1, e2, e3])
# x [1, 0, 0], y[0, 1, -1], z[0, 1, 1]
burgers = param['lat'] / 2. * np.array([1., 1., -1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
surf = param['surf']
k1c = sqrt(2 * surf / abs(Gamma[1, 1] * 1e3))
theta = np.deg2rad(54.735610317245346)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose()
Gamma = np.abs(np.linalg.inv(Gamma))
Gamma = Gamma * 1e9 # Pa
# K1c
# G11 = Gamma[1, 1]
# k1c = sqrt(2 * surf / G11) * 1e6
# Ke
if axes is not None:
T = axes_check.axes_check(axes)
burgers = T.dot(burgers)
c = c.transform(axes)
(coeff, Kg) = self.cal_crack(param, c, theta=theta)
print(Kg)
usf = param['ugsf1'] # J/m^2
G00 = Gamma[0, 0]
k1e = np.sqrt(G00 * usf) * 1e-6
k1e = k1e / coeff
print(k1e, k1c, Kg, k1e / k1c)
return (k1e, k1c, k1e / k1c)
def get_cutin_result_mat_k2e(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
# A
axes = np.array([[1, 1, 2], [1, 1, -1], [-1, 1, 0]])
burgers = param['lat'] / np.sqrt(6.) * np.array([1., 1., 2.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
# print A * B.transpose() + B * A.transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
theta = np.deg2rad(0.0)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = np.abs(omega * Gamma * omega)
# phi = 0
# svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
Gamma = np.linalg.inv(Gamma)
Gamma00 = Gamma[0, 0] # in GPa
Gamma11 = Gamma[1, 1]
Gamma00 *= 1e9
Gamma11 *= 1e9
# cal F(theta)
soltrace = np.mat([[stroh.p[0], 0.0, 0.0], [0.0, stroh.p[2], 0.0],
[0.0, 0.0, stroh.p[4]]],
dtype='complex')
Fmat1 = soltrace / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat1 = np.real(B * Fmat1 * np.linalg.inv(B))
Fmat2 = 1.0 / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat2 = np.real(B * Fmat2 * np.linalg.inv(B))
print(Fmat1[0, 1])
# print Gamma
k2e = np.sqrt(Gamma00 * param['ugsf']) * 1e-6 # Mpa
print('k2e', k2e / abs(Fmat1[0, 1]))
def get_cutin_result(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
# A
axes = np.array([[-1, -1, 2], [1, 1, 1], [-1, 1, 0]])
burgers = param['lat'] * np.sqrt(2.) / 2. * np.array([-1., 1., 0])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
# theta = self.theta
# omega = np.mat([[cos(theta), sin(theta), 0.0],
# [-sin(theta), cos(theta), 0.0],
# [0.0, 0.0, 1.0]])
phi = 0
svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
usf = param['ugsf'] # J/m^2
Gamma = np.abs(np.linalg.inv(Gamma))
# Gamma = omega * Gamma * omega
Gamma = Gamma # Pa
Gamma00 = (svect * Gamma * svect.transpose())[0, 0] # in GPa
Gamma11 = Gamma[1, 1]
Gamma00 *= 1e9
Gamma11 *= 1e9
# print Gamma
k2e = np.sqrt(Gamma00 * usf) * 1e-6 # Mpa
coeff, tmp = self.cal_crack(param)
k1e = k2e / coeff
print('Gamma', Gamma00, Gamma11)
print('k1e, k2e', k1e, k2e)
return
def get_bcc_w_result(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
# axes = np.array([[0, 1, 1],
# [2, 1, -1],
# [-1., 1., -1.]])
e1 = [1, 0, 0]
e2 = [0, 1, -1]
e3 = [0, 1, 1]
# glide plane [2, 1, -1]
axes = np.array([e1, e2, e3])
# x [1, 0, 0], y[0, 1, -1], z[0, 1, 1]
burgers = param['lat'] / 2. * np.array([-1., 1., -1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
Gamma = np.abs(np.linalg.inv(Gamma))
Gamma = Gamma * 1e9 # Pa
# K1c
G11 = Gamma[1, 1]
surf = param['surf']
k1c = sqrt(2 * surf / G11) * 1e6
# Ke
# phi = 0
usf = param['ugsf1'] # J/m^2
# svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
# Gamma = (svect * Gamma * svect.transpose())[0, 0] # in GPa
G00 = Gamma[0, 0]
k2e = np.sqrt(G00 * usf) * 1e-6
coeff, tmp = self.cal_crack(param)
k1e = k2e / coeff
print(k1e, k2e, k1c, tmp)
return (k1e, k2e, k1c)
def bcc_screw_dipole_alongz_with_image(self, atoms, center):
# x direction +10.5 unitx, +21
# -10.5 unitx, -21
# y direction +(11 + 1./3.) unity + 22
# -(11 - 1./3.) unity - 22
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
px = 10.5
py = 11
# ydisp = [4 * py, 3 * py + 1. / 3., 2 * py, py + 1. / 3.,
# 0., -py + 1. / 3., -2 * py, -3 * py + 1. / 3., -4 * py]
# xdisp = [-4 * px, -3 * px, -2 * px, -1 *
# px, 0.0, px, 2 * px, 3 * px, 4 * px]
ydisp = [2 * py, py + 1. / 3., 0., -py + 1. / 3., -2 * py]
xdisp = [-2 * px, -1 * px, 0.0, px, 2 * px]
pos = atoms.get_positions()
ux = np.sqrt(6) / 3. * self.pot['lattice']
uy = np.sqrt(2) / 2. * self.pot['lattice']
sign = 1.0
for dy in ydisp:
for dx in xdisp:
ctmp = np.array([center[0] + dx * ux, center[1] + dy * uy])
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, ctmp,
sign)
sign *= -1
atoms.wrap(pbc=[1, 1, 1])
return atoms
def print_dis_constants(self):
struct = "hex"
if struct in ["cubic"]:
# Cubic
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
axes = np.array([[1, -1, 1], [2, 1, -1], [0, 1, 1]])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
print(stroh.A[0])
# hexagonal
if struct in ["hex"]:
print(self.pot["lattice"])
axes = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
burgers = self.pot['lattice'] / 2 * np.array([1., 1, 0])
c = am.ElasticConstants()
c.hexagonal(C11=326.08, C33=357.50, C12=129.56, C13=119.48, C44=92.54)
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
print(stroh.A)
print(stroh.L)
def bcc_screw_dipole_configs_alongz(self, sizen=1):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
atoms = self.set_dipole_box()
atoms_perf = atoms.copy()
pos = atoms.get_positions()
ux = sqrt(6) / 3. * self.pot['lattice']
uy = sqrt(2) / 2. * self.pot['lattice']
uz = sqrt(3) / 2. * self.pot['lattice']
sx = 10.0 * sizen
sy = 5 * sizen
ix = 10.5 * sizen
# c1 = 1. / 3. * np.sum(self.pot['core1'], axis=0)
# c2 = 1. / 3. * np.sum(self.pot['core2'], axis=0)
# shiftc1 = \
# np.ones(np.shape(pos)) * np.array([c1[0, 0], c1[0, 1], 0.0])
# shiftc2 = \
# np.ones(np.shape(pos)) * np.array([c2[0, 0], c2[0, 1], 0.0])
opt = 'original'
if opt in ['split']:
c1 = self.pot['posleft'] + \
np.array([0.0, 0.21 * self.pot['yunit']])
c2 = self.pot['posrigh'] + \
np.array([0.0, -0.21 * self.pot['yunit']])
elif opt in ['move']:
c1 = [(sx + 0.5) * ux, (sy + 1. / 3. - 0.95 * 1. / 3.) * uy]
c2 = [(sx + ix + 0.5) * ux, (sy + 2. / 3. + 0.95 * 1. / 3.) * uy]
else:
c1 = [(sx) * ux, (sy + 1. / 3.) * uy]
c2 = [(sx + ix) * ux, (sy + 2. / 3.) * uy]
shiftc1 = np.ones(np.shape(pos)) * np.array([c1[0], c1[1], 0.0])
shiftc2 = np.ones(np.shape(pos)) * np.array([c2[0], c2[1], 0.0])
disp1 = stroh.displacement(pos - shiftc1)
disp2 = stroh.displacement(pos - shiftc2)
if opt in ['pull']:
radius = 2.0 # find the atoms near the center
for ps, dp in zip(pos, disp1):
dis = np.linalg.norm(ps[:2] - c1)
if (dis < radius):
dp[2] += 1. / 6. * uz
# add shirt
for ps, dp in zip(pos, disp2):
dis = np.linalg.norm(ps[:2] - c2)
if (dis < radius):
dp[2] -= 1. / 6. * uz
atoms.set_positions(pos + np.real(disp1) - np.real(disp2))
# periodic boundary conditions ???
# c2l = [(sx - ix + 0.5) * ux, (sy + 2. / 3. + 0.95 * 1. / 3.) * uy]
# shft = np.ones(np.shape(pos)) * np.array([c2l[0], c2l[1], 0.0])
# disp3 = stroh.displacement(pos - shft)
# atoms.set_positions(atoms.get_positions() - np.real(disp3))
atoms.wrap(pbc=[1, 1, 1])
ase.io.write("perf_poscar", atoms_perf, format='vasp')
ase.io.write('POSCAR', atoms, format='vasp')
return (atoms, atoms_perf)
def get_cutin_result_mat_k1e(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
axes = np.array([[-1, -1, 2], [1, 1, 1], [-1, 1, 0]])
burgers = param['lat'] / np.sqrt(6.) * np.array([-1., -1., 2.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
v1 = np.array([-1, -1, 2])
v2 = np.array([1, 1, 2])
theta = (np.arccos(
np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))))
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose()
# phi = 0
# svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
Gamma = np.linalg.inv(Gamma)
Gamma = np.abs(Gamma)
Gamma00 = Gamma[0, 0] # in GPa
Gamma11 = Gamma[1, 1]
Gamma00 *= 1e9
Gamma11 *= 1e9
if axes is not None:
T = axes_check.axes_check(axes)
burgers = T.dot(burgers)
c = c.transform(axes)
(coeff, Kg) = self.cal_crack(param, c, theta)
# print((cos(0.5 * theta))**2 * sin(0.5 * theta))
# cal F(theta)
soltrace = np.mat([[stroh.p[0], 0.0, 0.0], [0.0, stroh.p[2], 0.0],
[0.0, 0.0, stroh.p[4]]],
dtype='complex')
Fmat1 = soltrace / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat1 = np.real(B * Fmat1 * np.linalg.inv(B))
Fmat2 = 1.0 / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat2 = np.real(B * Fmat2 * np.linalg.inv(B))
# print(((Fmat1 + Fmat2) * Gamma) * 1e-3 * param["ugsf"])
k1e = sqrt(Gamma00 * param['ugsf']) * 1e-6 # Mpa
print('k1e', k1e)
print('k1e / coeff', k1e / coeff)