[1]:

%matplotlib inline
%load_ext autoreload
%autoreload 2

[2]:

import numpy as np
import matplotlib.pyplot as plt

from helpr.physics.api import CrackEvolutionAnalysis
from helpr.physics.pipe import Pipe
from helpr.physics.crack_initiation import DefectSpecification
from helpr.physics.environment import EnvironmentSpecification
from helpr.physics.material import MaterialSpecification
from helpr.physics.stress_state import InternalAxialHoopStress
from helpr.physics.cycle_evolution import CycleEvolution
from helpr.physics.crack_growth import CrackGrowth, get_design_curve

from helpr.utilities.unit_conversion import convert_psi_to_mpa, convert_in_to_m
from helpr.utilities.plots import generate_pipe_life_assessment_plot
from helpr.utilities.postprocessing import calc_pipe_life_criteria, report_single_pipe_life_criteria_results, report_single_cycle_evolution

from probabilistic.capabilities.uncertainty_definitions import DeterministicCharacterization

Single Deterministic Pipeline Lifetime Evaluation

Problem Specification

Geometry

[3]:

pipe_outer_diameter = convert_in_to_m(36)  # 36 inch outer diameter
wall_thickness = convert_in_to_m(0.406)    # 0.406 inch wall thickness

Material Properties

[4]:

yield_strength = convert_psi_to_mpa(52_000)      # material yield strength of 52_000 psi
fracture_resistance = 55                     # fracture resistance (toughness) MPa m1/2

Operating Conditions

[5]:

max_pressure = convert_psi_to_mpa(840)   # maximum pressure during oscillation MPa
min_pressure = convert_psi_to_mpa(638)   # minimum pressure during oscillation (or R = 0.75)
temperature = 293                         # K -> temperature of gas degrees C
volume_fraction_h2 = 1                      # % mole fraction H2 in natural gas blend

Initial Crack Dimensions

[6]:

flaw_depth = 25      # flaw 5% through pipe thickness
flaw_length = 0.04   # width of initial crack/flaw, m

Physics Model Choices

[7]:

stress_intensity_method = 'Anderson'  # Stress intensity factor method used

Modular Analysis

Create Pipe Object

[8]:

pipe_module = Pipe(outer_diameter=pipe_outer_diameter,
                   wall_thickness=wall_thickness)

Specify Pipe Material Properties

[9]:

material_module = MaterialSpecification(yield_strength=yield_strength,
                                        fracture_resistance=fracture_resistance)

Specify Defect

[10]:

defect_module = DefectSpecification(flaw_depth=flaw_depth,
                                    flaw_length=flaw_length)

Specify Pipe Gaseous Environment

[11]:

environment_module = EnvironmentSpecification(max_pressure=max_pressure,
                                              min_pressure=min_pressure,
                                              temperature=temperature,
                                              volume_fraction_h2=volume_fraction_h2)

Determine Stress Environment on Pipe

[12]:

stress_module = InternalAxialHoopStress(pipe=pipe_module,
                                        environment=environment_module,
                                        material=material_module,
                                        defect=defect_module,
                                        stress_intensity_method=stress_intensity_method)

Specify Crack Growth Model

[13]:

crack_growth_module = CrackGrowth(environment=environment_module,
                                  growth_model_specification={'model_name': 'code_case_2938'})

Evolve Cracks Over Cycles to Failure

[14]:

pipe_evaluation = CycleEvolution(pipe=pipe_module,
                                 stress_state=stress_module,
                                 defect=defect_module,
                                 environment=environment_module,
                                 material=material_module,
                                 crack_growth_model=crack_growth_module)
load_cycling = pipe_evaluation.calc_life_assessment()

Postprocess QoIs (life criteria)

[15]:

life_criteria = calc_pipe_life_criteria(cycle_results=load_cycling,
                                        pipe=pipe_module,
                                        stress_state=stress_module)

Plot QoI

[16]:

specific_life_criteria_result = report_single_pipe_life_criteria_results(life_criteria, pipe_index=0)
specific_load_cycling = report_single_cycle_evolution(load_cycling, pipe_index=0)
generate_pipe_life_assessment_plot(specific_load_cycling, specific_life_criteria_result, 'Test Pipe')
plt.savefig('./Figures/deterministic_crack_growth.png', format='png', dpi=300)

              Cycles to a(crit)  Cycles to 25% a(crit)  Cycles to 1/2 Nc
Total cycles        5669.414257               1.000000       2834.707129
a/t                    0.333509               0.083377          0.270803

Interact with Modular Analysis Through API

Specify Problem, Initiate Crack, and Evolve Crack to Failure

[17]:

analysis = CrackEvolutionAnalysis(outer_diameter=DeterministicCharacterization(name='outer_diameter', value=pipe_outer_diameter),
                                  wall_thickness=DeterministicCharacterization(name='wall_thickness', value=wall_thickness),
                                  flaw_depth=DeterministicCharacterization(name='flaw_depth', value=flaw_depth),
                                  max_pressure=DeterministicCharacterization(name='max_pressure', value=max_pressure),
                                  min_pressure=DeterministicCharacterization(name='min_pressure', value=min_pressure),
                                  temperature=DeterministicCharacterization(name='temperature', value=temperature),
                                  volume_fraction_h2=DeterministicCharacterization(name='volume_fraction_h2', value=volume_fraction_h2),
                                  yield_strength=DeterministicCharacterization(name='yield_strength', value=yield_strength),
                                  fracture_resistance=DeterministicCharacterization(name='fracture_resistance', value=fracture_resistance),
                                  flaw_length=DeterministicCharacterization(name='flaw_length', value=flaw_length),
                                  stress_intensity_method=stress_intensity_method)
analysis.perform_study()

Postprocess and Plot QoI

[18]:

analysis.postprocess_single_crack_results()
analysis.get_design_curve_plot()
plt.savefig('./Figures/deterministic_crack_growth_rate.png', format='png', dpi=300)

analysis.assemble_failure_assessment_diagram()

              Cycles to a(crit)  Cycles to 25% a(crit)  Cycles to 1/2 Nc
Total cycles        5669.414257               1.000000       2834.707129
a/t                    0.333509               0.083377          0.270803

[19]:

analysis.save_results()

[19]:

'Results/date_16_04_2024_time_11_39/'

[20]:

analysis.gather_single_crack_cycle_evolution()

[20]:

	a/t	a (m)	Delta a (m)	c (m)	Kmax (MPa m^1/2)	F	Q	Delta K (MPa m^1/2)	Delta N	Total cycles	Toughness ratio	Load ratio
0	0.250000	0.002578	0.000000	0.020000	37.883303	1.962206	1.049829	9.110032	0.000000	0.000000	0.688787	0.71618
1	0.250250	0.002581	0.000003	0.020020	37.926981	1.962842	1.049829	9.120536	45.569690	45.569690	0.689581	0.71618
2	0.250500	0.002583	0.000003	0.020040	37.970700	1.963479	1.049829	9.131049	45.229724	90.799414	0.690376	0.71618
3	0.250750	0.002586	0.000003	0.020060	38.014460	1.964116	1.049829	9.141573	44.892363	135.691777	0.691172	0.71618
4	0.251001	0.002588	0.000003	0.020080	38.058481	1.964756	1.049829	9.152159	44.778700	180.470477	0.691972	0.71618
...	...	...	...	...	...	...	...	...	...	...	...	...
554	0.985078	0.010159	0.000040	0.078806	245.722047	5.555129	1.049829	59.090302	0.084100	6509.550468	4.467674	0.71618
555	0.989001	0.010199	0.000040	0.079120	247.470510	5.583550	1.049829	59.510766	0.082355	6509.632824	4.499464	0.71618
556	0.992943	0.010240	0.000041	0.079435	249.236162	5.612213	1.049829	59.935363	0.080641	6509.713465	4.531567	0.71618
557	0.996906	0.010280	0.000041	0.079752	251.019189	5.641118	1.049829	60.364138	0.078957	6509.792422	4.563985	0.71618
558	1.000888	0.010322	0.000041	0.080071	252.819783	5.670269	1.049829	60.797138	0.077303	6509.869725	4.596723	0.71618

559 rows × 12 columns