The methodology for fatigue crack growth (fcg) experiments has not changed for decades and usually still relies on the concept that a theoretical stress intensity factor is calculated with respect to a standardized specimen geometry, applied load, and projected crack length measured by integral methods like direct current potential drop [1]. Such conventional fcg experiments are time-consuming and therefore very expensive. On the other hand, these experiments only result in a single material curve, i.e. a-N, which is hard to reproduce even under identical testing conditions. Consequently, the experimental outcome-to-cost ratio is relatively low.
Digital image correlation (DIC) has become a state-of-the-art tool to increase the insight in experimental mechanics due to its wide availability, and the possibility to gain full field information (displacements and strains) fully automatically. In particular, it is well-suited to analyze (fatigue) cracks [2, 3].
This Python package provides a pipeline, which takes an arbitrary number of DIC or simulation results and calculates various fracture mechanical parameters.
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| Schematic overview of data flow in CrackPy |
To do so, we use a specific DIC data format which is stored as a "Nodemap".txt text file. This file contains the nodal full-field displacement and strain data as well as information about the experiment and metadata. For every single file (referring to one time step of the experiment), the crack tip location and crack path geometry is detected using a trained artificial neural network [4]. After that, the crack tip information together with the displacements and strains are used by our fracture analysis module. This module contains a pipeline that computes stress intensity factors based on J-, interaction, and conjugate-work integrals, fits the Williams expansion to calculate arbitrary Williams series coefficients or fits the CJP model to calculate stress intensity factors which take effects of plasticity into account.
The following graph shows an overview over the main CrackPy modules structure elements, dic, simulation, crack detection, and fracture analysis.
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| Overview of main modules, functions and files in CrackPy |
The structure element module provides classes for any structural elements like experiment or data file. Most of these are currently just placeholders to add functionality later on. However, a very important structural element is the Material class containing information about the material law (elastic & shear moduli, stiffness matrix, etc.) as well as the Nodemap class, containing information about the data structure of the nodemap. We provide two modules, i.e. dic and simulation, which feature utilities to generate nodemaps from a specific software. Therefore, these modules can only be used if CrackPy is installed on an Aramis system equipped with an actual GOM Aramis Professional software >v2020 (in case of dic) or if a valid version and license of Ansys is available (in case of simulation). For more details, we refer to our Wiki. Once you have stored your nodemap files either from dic, simulation or from a different source, you reach the heart of our fracture analysis. You can detect crack paths and crack tips fully automatically using our crack detection module. This module provides two independent methodologies for crack detection - our line intercept method together with an iterative crack tip correction algorithm based on the Williams expansion [15] and our trained convolutional neural networks [4, 9]. We store the crack tip information in a file (this can also be generated manually) and use it as input for the fracture analysis pipeline. Here we offer a wide range of methods and algorithms:
- Calculate J-integral [5, 10]
- Calculate stress intensity factors (mode I, mode II) by interaction integral technique [11, 12]
- Calculate stress intensity factors and Williams series coefficients using Bueckner's conjugate work integral [6, 14]
- Calculate higher order singular terms (HOSTs) or higher order regular terms (HORTs) of the Williams series [7] by fitting the theoretical displacement field to the experimental (or simulated) data.
- Calculate CJP stress intensity factors which may take effects of plasticity into account by fitting the theoretical displacement field of the CJP model [8] the experimental (or simulated) data [13]
Here is an example for the output plot of one single time step...
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| Example output for a single input |
... and an example how these methods can enable hybrid approaches of mechanical and data-driven analysis.
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| Various possible calculated stress intensity factors for a complete crack growth experiment. Each data point refers to one DIC measurement, i.e. one set of experimental displacements and strains |
For us, it was important that all these methods are implemented independent of the source of displacement and strain data, i.e. you can also apply all these methods on data from other sources such as finite element simulations, as long as the format of displacements and strains matches the one used here (Checkout our Wiki for detailed information) and fulfills the plane stress condition. We believe that a wider availability of automated analysis - and, therefore, more data-driven methods - will be very beneficial for the experimental mechanics community. This is why we aim to make them easily accessible and applicable. However, this package only covers the topic of (fatigue) cracks in ductile materials. Although most of our methods are (theoretically) independent of the investigated material, we only tested them on aluminium alloys so far.
References:
- ASTM International E-647 Standard Test Method for Measurement of Fatigue Crack Growth Rates
- Roux et al. (2006) Stress intensity factor measurement from digital image correlation: post-processing and integrated approaches. International Journal of Fracture 140: 141-157 https://doi.org/10.1007/s10704-006-6631-2
- Réthoré J et al. (2005) Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral. International Journal of Fracture 132: 65-79 https://doi.org/10.1007/s10704-004-8141-4
- Melching D et al. (2022) Explainable machine learning for precise faticue crack tip detection. Scientific Reports 12, 9513 https://doi.org/10.1038/s41598-022-13275-1
- Becker T et al. (2012) An approach to calculate the J-integral by digital image correlation displacement field measurement. Fatigue and Fracture of Engineering Materials and Structures 35 (10): 971-984 https://doi.org/10.1111/j.1460-2695.2012.01685.x
- Chen Y Z (1985) New path independent integrals in linear elastic fracture mechanics. Engineering Fracture Mechanics 22 (4): 48-51 https://doi.org/10.1016/0013-7944(85)90131-6
- Williams M L (1961) The Bending Stress Distribution at the Base of a Stationary Crack. Journal of Applied Mechanics 28 (Issue 1) https://doi.org/10.1115/1.3640470
- Yang B et al. (2021) New algorithms for optimised fitting of DIC data to crack tip plastic zone using the CJP model. Theoretical and Applied Fracture Mechanics 113, 10295 https://doi.org/10.1016/j.tafmec.2021.102950
- Strohmann T et al. (2021) Automatic detection of fatigue crack paths using digital image correlation and convolutional neural networks. Fatigue and Fracture of Engineering Materials and Structures 44: 1336-1348 https://doi.org/10.1111/ffe.13433
- Rice J R (1968) A Path Independent Integral and the Approximation Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics 35: 379-386 https://doi.org/10.1115/1.3601206
- Stern M et al. (1976) Contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture 12(3): 359-368 https://doi.org/10.1007/BF00032831
- Breitbarth E et al. (2019) Determination of stress intensity factors and J integral based on digital image correlation. Frat ed Integrita Strutt. 13: 12–25 https://doi.org/10.3221/IGF-ESIS.49.02
- Christopher C et al. (2007) Towards a new model of crack tip stress fields. International Journal of Fracture 148(4): 361-371 https://doi.org/10.1007/s10704-008-9209-3
- Melching D et al. (2023) Advanced crack tip field characterization using conjugate work integrals. International Journal of Fatigue 107501, 169 https://doi.org/10.1016/j.ijfatigue.2023.107501
- Melching D et al. (2024) A universal crack tip correction algorithm discovered by physical deep symbolic regression. Preprint https://arxiv.org/abs/2403.10320
Just install via pip from the github repository
pip install --upgrade git+https://github.com/dlr-wf/crackpy.git
To check out how to use the package please read our Wiki.
The package is developed for research only and must not be used for any production or specification purposes. The Package is under current development and all functionalities are on a prototype level. Feel free to use the code, however, we do not guarantee in any form for its flawless implementation and execution. However, if you run into errors in the code or find any bugs, we will be happy if you cantact us.
Licensed under MIT License (see LICENSE file)
Please cite as
Strohmann T, Melching D, Paysan F, Klein A, Dietrich E, Requena G and Breitbarth E
Crack Analysis Tool in Python - CrackPy (2022)
DOI: 10.5281/zenodo.7319653
If you are interested in the code, or in our work in general, feel free to contact us via email at [email protected].
If you want to contribute to this repository just get in touch, too. We will be happy.
This package is property of the German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt e.V. - DLR) and was developed in the Institute of Materials Research. Feel free to check out our LinkedIn channel.
Authors:
Tobias Strohmann
David Melching
Florian Paysan
Eric Dietrich
Guillermo Requena
Eric Breitbarth
Contributors:
We thank
Vanessa Schöne
Alina Klein
Ferdinand Dömling
Erik Schultheis
for continuous support regarding tests and user feedback for the package.