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fixing docs
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@MatthewReid854
MatthewReid854 committed Nov 10, 2021
1 parent a80b6c1 commit c95de20
Showing 1 changed file with 70 additions and 82 deletions.
152 changes: 70 additions & 82 deletions reliability/PoF.py
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Original file line number Diff line number Diff line change
Expand Up @@ -945,13 +945,10 @@ def coffin_manson(eps_tot, sigma_f, E, cycles_2Nf, epsilon_f, b, c):
c=c,
)
use_cycles_2Nf = fsolve(fun_cm, np.array(10))
cycles_2Nt = (epsilon_f * E / sigma_f) ** (
1 / (b - c)
)
cycles_2Nt = (epsilon_f * E / sigma_f) ** (1 / (b - c))
epsilon_total = (
(sigma_f / E) * cycles_2Nf_array ** b
+ epsilon_f * cycles_2Nf_array ** c
)
sigma_f / E
) * cycles_2Nf_array ** b + epsilon_f * cycles_2Nf_array ** c
epsilon_total_at_cycles_2Nt = (
sigma_f / E
) * cycles_2Nt ** b + epsilon_f * cycles_2Nt ** c
Expand Down Expand Up @@ -993,13 +990,12 @@ def morrow(
c=c,
)
use_cycles_2Nf = fsolve(fun_m, np.array(10))
cycles_2Nt = (
epsilon_f * E / (sigma_f - mean_stress)
) ** (1 / (b - c))
epsilon_total = (
((sigma_f - mean_stress) / E) * cycles_2Nf_array ** b
+ epsilon_f * cycles_2Nf_array ** c
cycles_2Nt = (epsilon_f * E / (sigma_f - mean_stress)) ** (
1 / (b - c)
)
epsilon_total = (
(sigma_f - mean_stress) / E
) * cycles_2Nf_array ** b + epsilon_f * cycles_2Nf_array ** c
epsilon_total_at_cycles_2Nt = (
(sigma_f - mean_stress) / E
) * cycles_2Nt ** b + epsilon_f * cycles_2Nt ** c
Expand Down Expand Up @@ -1053,8 +1049,7 @@ def modified_morrow(
cycles_2Nt = (
epsilon_f
* E
* ((sigma_f - mean_stress) / sigma_f)
** (c / b)
* ((sigma_f - mean_stress) / sigma_f) ** (c / b)
/ (sigma_f - mean_stress)
) ** (1 / (b - c))
epsilon_total = (
Expand Down Expand Up @@ -1100,8 +1095,7 @@ def modified_morrow(
)
plastic_strain_line = (
epsilon_f
* ((sigma_f - mean_stress) / sigma_f)
** (c / b)
* ((sigma_f - mean_stress) / sigma_f) ** (c / b)
* cycles_2Nf_array ** c
)
elastic_strain_line = (
Expand All @@ -1128,20 +1122,14 @@ def SWT(
sigma_max=self.max_stress,
)
use_cycles_2Nf = fsolve(fun_swt, np.array(10))
cycles_2Nt = (epsilon_f * E / sigma_f) ** (
1 / (b - c)
)
cycles_2Nt = (epsilon_f * E / sigma_f) ** (1 / (b - c))
epsilon_total = (
(sigma_f ** 2 / E) * cycles_2Nf_array ** (2 * b)
+ sigma_f
* epsilon_f
* cycles_2Nf_array ** (b + c)
+ sigma_f * epsilon_f * cycles_2Nf_array ** (b + c)
) / self.max_stress
epsilon_total_at_cycles_2Nt = (
(sigma_f ** 2 / E) * cycles_2Nt ** (2 * b)
+ sigma_f
* epsilon_f
* cycles_2Nt ** (b + c)
+ sigma_f * epsilon_f * cycles_2Nt ** (b + c)
) / self.max_stress
equation_str = str(
r"$\epsilon_{tot} = \frac{1}{"
Expand All @@ -1164,9 +1152,7 @@ def SWT(
+ ")})$"
)
plastic_strain_line = (
sigma_f
* epsilon_f
* cycles_2Nf_array ** (b + c)
sigma_f * epsilon_f * cycles_2Nf_array ** (b + c)
) / self.max_stress
elastic_strain_line = (
(sigma_f ** 2 / E) * cycles_2Nf_array ** (2 * b)
Expand Down Expand Up @@ -1310,14 +1296,11 @@ def SWT(
plt.gcf().set_size_inches(10, 7)
else: # this is in the case that max stress or strain was not supplied
if show_plot is True:
cycles_2Nt = (epsilon_f * E / sigma_f) ** (
1 / (b - c)
)
cycles_2Nt = (epsilon_f * E / sigma_f) ** (1 / (b - c))
cycles_2Nf_array = np.logspace(1, 8, 1000)
epsilon_total = (
(sigma_f / E) * cycles_2Nf_array ** b
+ epsilon_f * cycles_2Nf_array ** c
)
sigma_f / E
) * cycles_2Nf_array ** b + epsilon_f * cycles_2Nf_array ** c
epsilon_total_at_cycles_2Nt = (
sigma_f / E
) * cycles_2Nt ** b + epsilon_f * cycles_2Nt ** c
Expand Down Expand Up @@ -1429,13 +1412,15 @@ def palmgren_miner_linear_damage(rated_life, time_at_stress, stress):
from reliability.PoF import palmgren_miner_linear_damage
palmgren_miner_linear_damage(rated_life=[50000,6500,1000], time_at_stress=[40/60, 15/60, 5/60], stress=[1, 2, 4])
>>> Palmgren-Miner Linear Damage Model results:
>>> Each load cycle uses 0.01351 % of the components life.
>>> The service life of the component is 7400.37951 load cycles.
>>> The amount of damage caused at each stress level is:
>>> Stress = 1 , Damage fraction = 9.86717 %.
>>> Stress = 2 , Damage fraction = 28.463 %.
>>> Stress = 4 , Damage fraction = 61.66983 %.
'''
Palmgren-Miner Linear Damage Model results:
Each load cycle uses 0.01351 % of the components life.
The service life of the component is 7400.37951 load cycles.
The amount of damage caused at each stress level is:
Stress = 1 , Damage fraction = 9.86717 %.
Stress = 2 , Damage fraction = 28.463 %.
Stress = 4 , Damage fraction = 61.66983 %.
'''
"""
if len(rated_life) != len(time_at_stress) or len(rated_life) != len(stress):
raise ValueError("All inputs must be of equal length.")
Expand Down Expand Up @@ -1477,13 +1462,9 @@ class fracture_mechanics_crack_initiation:
different materials and geometries. Resources for finding some of these
parameters if they are not given to you:
- q = 1/(1+a/r) Where r is the notch radius of curvature (in mm), and a is
0.025*(2070/Su). Su is the ultimate strength in MPa. This only applies to
high strength steels where Su>550MPa.
- Kt can be calculated using the `efatigue website <https://www.efatigue.com/constantamplitude/stressconcentration/>`_.
This website will provide you with the appropriate Kt for your notched
geometry.
- q = 1/(1+a/r) Where r is the notch radius of curvature (in mm), and a is 0.025*(2070/Su).
- Su is the ultimate strength in MPa. This only applies to high strength steels where Su>550MPa.
- Kt can be calculated using the `efatigue website <https://www.efatigue.com/constantamplitude/stressconcentration/>`_. This website will provide you with the appropriate Kt for your notched geometry.
Parameters
----------
Expand Down Expand Up @@ -1536,18 +1517,23 @@ class fracture_mechanics_crack_initiation:
cycles_to_failure : float
The number of cycles until failure due to fatigue
Notes
-----
Example usage:
.. code:: python
from reliability.PoF import fracture_mechanics_crack_initiation
fracture_mechanics_crack_initiation(P=0.15, A=5*80, Kt=2.41, q=0.9857, Sy=690, E=210000, K=1060, n=0.14, b=-0.081, c=-0.65, sigma_f=1160, epsilon_f=1.1,mean_stress_correction_method='SWT')
>>> Results from fracture_mechanics_crack_initiation:
>>> A crack of 1 mm will be formed after: 2919.91 cycles (5839.82 reversals).
>>> Stresses in the component: Min = -506.7291 MPa , Max = 506.7291 MPa , Mean = -5.684341886080802e-14 MPa.
>>> Strains in the component: Min = -0.0075 , Max = 0.0075 , Mean = 8.673617379884035e-19
>>> Mean stress correction method used: SWT
'''
Results from fracture_mechanics_crack_initiation:
A crack of 1 mm will be formed after: 2919.91 cycles (5839.82 reversals).
Stresses in the component: Min = -506.7291 MPa , Max = 506.7291 MPa , Mean = -5.684341886080802e-14 MPa.
Strains in the component: Min = -0.0075 , Max = 0.0075 , Mean = 8.673617379884035e-19
Mean stress correction method used: SWT
'''
"""

def __init__(
Expand Down Expand Up @@ -1851,31 +1837,33 @@ class fracture_mechanics_crack_growth:
print('')
fracture_mechanics_crack_growth(Kc=66,C=3.81*10**-12,m=3,P=0.103,W=100,t=5,crack_type='center')
>>> Results from fracture_mechanics_crack_growth:
>>> SIMPLIFIED METHOD (keeping f(g), S_max, and a_crit as constant):
>>> Crack growth was found in two stages since the transition length ( 2.08 mm ) due to the notch, was greater than the initial crack length ( 1 mm ).
>>> Stage 1 (a_initial to transition length): 6802 cycles
>>> Stage 2 (transition length to a_final): 1133 cycles
>>> Total cycles to failure: 7935 cycles.
>>> Critical crack length to cause failure was found to be: 7.86 mm.
>>> ITERATIVE METHOD (recalculating f(g), S_max, and a_crit for each cycle):
>>> Crack growth was found in two stages since the transition length ( 2.45 mm ) due to the notch, was greater than the initial crack length ( 1 mm ).
>>> Stage 1 (a_initial to transition length): 7576 cycles
>>> Stage 2 (transition length to a_final): 671 cycles
>>> Total cycles to failure: 8247 cycles.
>>> Critical crack length to cause failure was found to be: 6.39 mm.
>>> Results from fracture_mechanics_crack_growth:
>>> SIMPLIFIED METHOD (keeping f(g), S_max, and a_crit as constant):
>>> Crack growth was found in a single stage since the transition length ( 0.0 mm ) was less than the initial crack length 1.0 mm.
>>> Total cycles to failure: 281359 cycles.
>>> Critical crack length to cause failure was found to be: 32.67 mm.
>>> ITERATIVE METHOD (recalculating f(g), S_max, and a_crit for each cycle):
>>> Crack growth was found in a single stage since the transition length ( 0.0 mm ) was less than the initial crack length 1.0 mm.
>>> Total cycles to failure: 225827 cycles.
>>> Critical crack length to cause failure was found to be: 18.3 mm.
'''
Results from fracture_mechanics_crack_growth:
SIMPLIFIED METHOD (keeping f(g), S_max, and a_crit as constant):
Crack growth was found in two stages since the transition length ( 2.08 mm ) due to the notch, was greater than the initial crack length ( 1 mm ).
Stage 1 (a_initial to transition length): 6802 cycles
Stage 2 (transition length to a_final): 1133 cycles
Total cycles to failure: 7935 cycles.
Critical crack length to cause failure was found to be: 7.86 mm.
ITERATIVE METHOD (recalculating f(g), S_max, and a_crit for each cycle):
Crack growth was found in two stages since the transition length ( 2.45 mm ) due to the notch, was greater than the initial crack length ( 1 mm ).
Stage 1 (a_initial to transition length): 7576 cycles
Stage 2 (transition length to a_final): 671 cycles
Total cycles to failure: 8247 cycles.
Critical crack length to cause failure was found to be: 6.39 mm.
Results from fracture_mechanics_crack_growth:
SIMPLIFIED METHOD (keeping f(g), S_max, and a_crit as constant):
Crack growth was found in a single stage since the transition length ( 0.0 mm ) was less than the initial crack length 1.0 mm.
Total cycles to failure: 281359 cycles.
Critical crack length to cause failure was found to be: 32.67 mm.
ITERATIVE METHOD (recalculating f(g), S_max, and a_crit for each cycle):
Crack growth was found in a single stage since the transition length ( 0.0 mm ) was less than the initial crack length 1.0 mm.
Total cycles to failure: 225827 cycles.
Critical crack length to cause failure was found to be: 18.3 mm.
'''
"""

def __init__(
Expand Down Expand Up @@ -2302,10 +2290,10 @@ def creep_failure_time(temp_low, temp_high, time_low, C=20, print_results=True):
temperature (temp_high).
This relation requires the input temperatures in Fahrenheit. To convert
Celsius to Fahrenheit use F = C*(9/5)+32
Celsius to Fahrenheit use :math:`F = C \times \left(\frac{9}{5}\right)+32`
Note that the conversion between Fahrenheit and Rankine used in this
calculation is R = F+459.67
calculation is :math:`R = F+459.67`
For more information see `Wikipedia <https://en.wikipedia.org/wiki/Larson%E2%80%93Miller_relation>`_.
Expand Down Expand Up @@ -2343,9 +2331,9 @@ class acceleration_factor:
"""
The Arrhenius model for Acceleration factor due to higher temperature is:
:math: `AF = exp\left(\frac{Ea}{K\left(\frac{1}{T_{use}}-\frac{1}{T_{acc}}\right)}\right)`
:math:`AF = exp\left(\frac{Ea}{K\left(\frac{1}{T_{use}}-\frac{1}{T_{acc}}\right)}\right)`
K is the Boltzmann constant: 8.617333262145*10^-5 eV/Kelvin
K is the Boltzmann constant: :math:`8.617333262145 \times 10^{-5}` eV/Kelvin
This function accepts T_use as a mandatory input and the user may specify
any two of the three other variables, and the third variable will be found.
Expand Down

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