def extract_slice(self, data='strain', phi=None, az_idx=None, z_idx=None):
""" Extract 2D data slice wrt. azimuthal slice index or angle (phi).
The extracted data is defined using the data variable (str), which
must be one of the following: peaks, peaks error, fwhm, fwhm error,
strain, strain error, shear strain, stress, shear stress.
Certain combinations of data type and azimuthal index/phi will not
work (e.g. can't extract peaks wrt. phi only wrt. az. index).
Note: must define EITHER phi or az_idx
Args:
data (str): Data type to extract (see above)
phi (float): Azimuthal angle in rad
az_idx (int): Azimuthal slice index
z_idx (int): Index of slice height in 3D array
"""
complex_check(data, self.analysis_state, phi, az_idx)
command = text_cleaning(data)
az_command = 'phi' if phi is not None else 'az_idx'
if az_command == 'az_idx':
az_idx = int(az_idx)
if 'stress' not in command:
data_command = {
'peaks': self.peaks,
'peaks error': self.peaks_err,
'fwhm': self.fwhm,
'fwhm error': self.fwhm_err,
'strain': self.strain,
'strain error': self.strain_err
}
data = data_command[command][..., az_idx]
else:
d = self.strain if 'err' not in command else self.strain_err
e_xx, e_yy = d[..., az_idx], d[..., az90(self.phi, az_idx)]
data = self.stress_eqn(e_xx, e_yy, self.E, self.v)
else:
tensor = self.strain_tensor
tensor = tensor[..., 0], tensor[..., 1], tensor[..., 2]
shear = True if 'shear' in command else False
stress = True if 'stress' in command else False
if shear:
e_xy = shear_transformation(phi, *tensor)
data = self.G * e_xy if stress else e_xy
elif stress:
e_xx = strain_transformation(phi, *tensor)
e_yy = strain_transformation(phi + np.pi / 2, *tensor)
data = self.stress_eqn(e_xx, e_yy, self.E, self.v)
else:
data = strain_transformation(phi, *tensor)
data = data[z_idx] if z_idx is not None else data
return data
def extract_slice(self, data='strain', phi=None, az_idx=None, z_idx=None):
""" Extract 2D data slice wrt. azimuthal slice index or angle (phi).
The extracted data is defined using the data variable (str), which
must be one of the following: peaks, peaks error, fwhm, fwhm error,
strain, strain error, shear strain, stress, shear stress.
Certain combinations of data type and azimuthal index/phi will not
work (e.g. can't extract peaks wrt. phi only wrt. az. index).
Note: must define EITHER phi or az_idx
Args:
data (str): Data type to extract (see above)
phi (float): Azimuthal angle in rad
az_idx (int): Azimuthal slice index
z_idx (int): Index of slice height in 3D array
"""
complex_check(data, self.analysis_state, phi, az_idx)
command = text_cleaning(data)
az_command = 'phi' if phi is not None else 'az_idx'
if az_command == 'az_idx':
az_idx = int(az_idx)
if 'stress' not in command:
data_command = {'peaks': self.peaks,
'peaks error': self.peaks_err,
'fwhm': self.fwhm,
'fwhm error': self.fwhm_err,
'strain': self.strain,
'strain error': self.strain_err}
data = data_command[command][..., az_idx]
else:
d = self.strain if 'err' not in command else self.strain_err
e_xx, e_yy = d[..., az_idx], d[..., az90(self.phi, az_idx)]
data = self.stress_eqn(e_xx, e_yy, self.E, self.v)
else:
tensor = self.strain_tensor
tensor = tensor[..., 0], tensor[..., 1], tensor[..., 2]
shear = True if 'shear' in command else False
stress = True if 'stress' in command else False
if shear:
e_xy = shear_transformation(phi, *tensor)
data = self.G * e_xy if stress else e_xy
elif stress:
e_xx = strain_transformation(phi, *tensor)
e_yy = strain_transformation(phi + np.pi / 2, *tensor)
data = self.stress_eqn(e_xx, e_yy, self.E, self.v)
else:
data = strain_transformation(phi, *tensor)
data = data[z_idx] if z_idx is not None else data
return data
def test_angles(self):
self.data.calculate_strain(self.q0)
# Compare angles, same position
for p_idx in [0, 7, 12, 26, 32]:
tensor = e_xx[p_idx], e_yy[p_idx], e_xy[p_idx]
initial = strain_transformation(self.data.phi, *tensor)
processed = self.data.strain[p_idx]
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10**-4, (p_idx, max_diff) # Brittle (linux)?!
def test_angles(self):
self.data.calculate_strain(self.q0)
# Compare angles, same position
for p_idx in [0, 7, 12, 26, 32]:
tensor = e_xx[p_idx], e_yy[p_idx], e_xy[p_idx]
initial = strain_transformation(self.data.phi, *tensor)
processed = self.data.strain[p_idx]
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10**-4, (p_idx, max_diff) # Brittle (linux)?!
def test_angles(self):
self.data.calculate_strain(self.q0)
# Compare angles, same position
for p_idx in [(0, 0), (4, 4), (3, 5), (1, 2), (0, 4)]:
tensor = e_xx[p_idx], e_yy[p_idx], e_xy[p_idx]
initial = strain_transformation(self.data.phi, *tensor)
processed = self.data.strain[p_idx]
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10**-4, (p_idx, max_diff)
def test_angles(self):
self.data.calculate_strain(self.q0)
# Compare angles, same position
for p_idx in [(0, 0), (4, 4), (3, 5), (1, 2), (0, 4)]:
tensor = e_xx[p_idx], e_yy[p_idx], e_xy[p_idx]
initial = strain_transformation(self.data.phi, *tensor)
processed = self.data.strain[p_idx]
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10 ** -4, (p_idx, max_diff)
def test_positions(self):
self.data.calculate_strain(self.q0)
# Compare positions, same angle
for idx in [0, 7, 12, 26, 32]:
tensor = e_xx, e_yy, e_xy
initial = strain_transformation(self.data.phi[idx], *tensor)
processed_1 = self.data.strain[..., idx]
processed_2 = self.data.extract_slice(phi=self.data.phi[idx])
for processed in [processed_1, processed_2]:
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10**-4, (idx, max_diff) # Brittle (linux)?!
def test_positions(self):
self.data.calculate_strain(self.q0)
# Compare positions, same angle
for idx in [0, 7, 12, 26, 32]:
tensor = e_xx, e_yy, e_xy
initial = strain_transformation(self.data.phi[idx], *tensor)
processed_1 = self.data.strain[..., idx]
processed_2 = self.data.extract_slice(phi=self.data.phi[idx])
for processed in [processed_1, processed_2]:
max_diff = np.abs(np.max(initial - processed))
assert max_diff < 10**-4, (idx, max_diff) # Brittle (linux)?!
def extract_strain_array(self, phi):
"""
Add valus for phi
:param phi:
:return:
"""
strain = np.nan * np.ones((self.x.shape + (1, ) + phi.shape))
for idx, tt in enumerate(phi):
e_xx1 = strain_transformation(tt, self.e_xx, self.e_yy, self.e_xy)
strain[:, :, 0, idx] = e_xx1
return strain
def extract_strain_array(self, phi):
"""
Add valus for phi
:param phi:
:return:
"""
strain = np.nan * np.ones((self.x.shape + (1,) + phi.shape))
for idx, tt in enumerate(phi):
e_xx1 = strain_transformation(tt, self.e_xx, self.e_yy, self.e_xy)
strain[:, :, 0, idx] = e_xx1
return strain
def plot_strain_fit(self, pnt=None, figsize=(11, 5)):
""" Plots fitted in-plane strain field and tensor for given data point.
Plots strain wrt. phi and associated tensor fit. The tensor fit is
represented as a Mohr's circle, with e_xx, e_yy (for that point) being
highlighted on both plots.
Args:
pnt (tuple): Define data point (index) else point (0, ) x ndim.
figsize (tuple): Figure size
"""
pnt = (0,) * (self.strain.ndim - 1) if pnt is None else pnt
fig, (ax_1, ax_2) = plt.subplots(1, 2, figsize=figsize)
p = self.strain_tensor[pnt]
ax_1.plot(self.phi, self.strain[pnt], 'k*')
phi_2 = np.linspace(self.phi[0], self.phi[-1], 1000)
ax_1.plot(phi_2, strain_transformation(phi_2, *p), 'k-', linewidth=0.5)
ax_1.set_xlabel(r'$\phi$ (rad)', size=14)
ax_1.set_ylabel(r'$\epsilon$', size=14)
ax_1.ticklabel_format(axis='both', style='sci', scilimits=(-3, 3))
ax_2.ticklabel_format(axis='both', style='sci', scilimits=(-3, 3))
ax_2.set_xlabel(r'$\epsilon$', size=14)
ax_2.set_ylabel(r'$\gamma}$', size=14)
e_xx, e_yy, e_xy = self.strain_tensor[pnt]
mean = (e_xx + e_yy) / 2
e_1 = mean + (e_xy**2 + ((e_xx - e_yy) / 2)**2)**0.5
e_2 = e_xx + e_yy - e_1
radius = (e_1 - e_2) / 2
for x, text in zip([self.phi[0], self.phi[0] + np.pi/2],
[r'$\epsilon_{xx}$', r'$\epsilon_{yy}$']):
ax_1.axvline(x, ymax=0.93, linewidth=0.5, ls='--', color='k')
y = ax_1.get_ylim()[1] * 0.96
ax_1.text(x, y, text, ha='center', va='bottom')
circ = plt.Circle((mean, 0), radius=radius, color='k', fill=False)
ax_2.add_patch(circ)
for x, y, text in zip([e_1, e_2, e_xx, e_yy],
[0, 0, e_xy, -e_xy],
[r'$\epsilon_{1}$', r'$\epsilon_{2}$',
r'$(\epsilon_{xx}$, $\epsilon_{xy})$',
r'$(\epsilon_{yy}$, $\epsilon_{yx})$']):
ax_2.plot(x, y, 'k.')
ax_2.annotate(' %s' % text, xy=(x, y), xytext=(x, y), ha='left')
ax_2.plot([e_xx, e_yy], [e_xy, -e_xy], 'k--', linewidth=0.5)
fig.tight_layout()
def plot_strain_fit(self, pnt=None, figsize=(11, 5)):
""" Plots fitted in-plane strain field and tensor for given data point.
Plots strain wrt. phi and associated tensor fit. The tensor fit is
represented as a Mohr's circle, with e_xx, e_yy (for that point) being
highlighted on both plots.
Args:
pnt (tuple): Define data point (index) else point (0, ) x ndim.
figsize (tuple): Figure size
"""
pnt = (0, ) * (self.strain.ndim - 1) if pnt is None else pnt
fig, (ax_1, ax_2) = plt.subplots(1, 2, figsize=figsize)
p = self.strain_tensor[pnt]
ax_1.plot(self.phi, self.strain[pnt], 'k*')
phi_2 = np.linspace(self.phi[0], self.phi[-1], 1000)
ax_1.plot(phi_2, strain_transformation(phi_2, *p), 'k-', linewidth=0.5)
ax_1.set_xlabel(r'$\phi$ (rad)', size=14)
ax_1.set_ylabel(r'$\epsilon$', size=14)
ax_1.ticklabel_format(axis='both', style='sci', scilimits=(-3, 3))
ax_2.ticklabel_format(axis='both', style='sci', scilimits=(-3, 3))
ax_2.set_xlabel(r'$\epsilon$', size=14)
ax_2.set_ylabel(r'$\gamma}$', size=14)
e_xx, e_yy, e_xy = self.strain_tensor[pnt]
mean = (e_xx + e_yy) / 2
e_1 = mean + (e_xy**2 + ((e_xx - e_yy) / 2)**2)**0.5
e_2 = e_xx + e_yy - e_1
radius = (e_1 - e_2) / 2
for x, text in zip([self.phi[0], self.phi[0] + np.pi / 2],
[r'$\epsilon_{xx}$', r'$\epsilon_{yy}$']):
ax_1.axvline(x, ymax=0.93, linewidth=0.5, ls='--', color='k')
y = ax_1.get_ylim()[1] * 0.96
ax_1.text(x, y, text, ha='center', va='bottom')
circ = plt.Circle((mean, 0), radius=radius, color='k', fill=False)
ax_2.add_patch(circ)
for x, y, text in zip([e_1, e_2, e_xx, e_yy], [0, 0, e_xy, -e_xy], [
r'$\epsilon_{1}$', r'$\epsilon_{2}$',
r'$(\epsilon_{xx}$, $\epsilon_{xy})$',
r'$(\epsilon_{yy}$, $\epsilon_{yx})$'
]):
ax_2.plot(x, y, 'k.')
ax_2.annotate(' %s' % text, xy=(x, y), xytext=(x, y), ha='left')
ax_2.plot([e_xx, e_yy], [e_xy, -e_xy], 'k--', linewidth=0.5)
fig.tight_layout()
