Towards self-driving labs for experimental mechanics: a data-centric approach for fatigue crack analysis in aerospace materials

doi:10.21203/rs.3.rs-3128435/v1

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Towards self-driving labs for experimental mechanics: a data-centric approach for fatigue crack analysis in aerospace materials

https://doi.org/10.21203/rs.3.rs-3128435/v1

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Today’s societal challenges require rapid response and smart materials solutions in almost all technical areas. Driven by these needs, data-driven research has emerged as an enabler for faster innovation cycles. In fields such as chemistry, materials science and life sciences, autonomous data generation and processing is already accelerating knowledge discovery. In contrast, in experimental mechanics, complex investigations like studying fatigue crack growth in structural materials have traditionally adhered to standardized procedures with limited adoption of the digital transformation. In this work, we present a novel infrastructure for data-centric experimental mechanics. The setup is demonstrated using a complex fatigue crack growth experiment for aerospace materials. Our methodology incorporates an open-source Python library that complements a multi-scale digital image correlation and robot-assisted test rig. Our novel approach significantly increases the information-to-cost ratio of fatigue crack growth experiments in aerospace materials compared to traditional experiments. Thus, serves as a catalyst for discovering new scientific knowledge and contributes to the data-driven acceleration of the deployment of new applications in the field of structural materials and structures.

Physical sciences/Materials science/Structural materials/Mechanical properties

Physical sciences/Engineering/Aerospace engineering

Physical sciences/Materials science/Structural materials/Metals and alloys

Physical sciences/Mathematics and computing/Scientific data

Today’s societal challenges require rapid response and smart materials solutions in almost all technical areas. Motivated by these needs, data-driven research has emerged as a new paradigm to enable faster innovation cycles [1, 2]. In this context, self-driving laboratories that autonomously generate and process data are being developed to accelerate knowledge discovery in many fields, such as materials science, chemistry or life sciences [1–14]. In contrast, the number of studies investigating similar concepts for mechanical testing [15] is very limited and especially complex experiments such as fatigue crack growth (FCG) in structural materials have historically followed highly standardized procedures [16] with limited digitalization. These experiments are fundamental to understand the process-microstructure-property relationship in a wide range of applications where fatigue cracks are inherent to structural design, e.g. in aircraft structures [17].

In conventional FCG experiments, the stress intensity factor (SIF) is calculated as a function of specimen geometry, load and crack length using analytical formulas or modelling tools such as finite element analysis. The resulting da/dN-ΔK curves (where da is the crack length increment per load cycle N and ΔK is the respective cyclic SIF) are suitable for lifetime estimations, but do not provide information on physical (and local) crack propagation mechanisms. Moreover, the analysis of such experimental data usually involves manual steps and requires highly qualified domain experts. Consequently, the information-to-cost ratio is notably low.

In fracture mechanics, digital image correlation (DIC) has become a state-of-the-art method for generating full-field information of displacements and strains during crack growth experiments [18–39]. For instance, DIC has been successfully applied together with numerical or analytical approaches to calculate the J-integral, stress intensity factors or T-stress [18, 21, 23–25, 27, 29–32, 35–39], analyse the crack tip plastic zone [19, 20], crack opening displacements [34, 35], or mechanisms acting locally at the crack tip, such as strain accumulation [22]. However, the non-automated acquisition and analysis of DIC data is not readily scalable in terms of time and the amount of information that can be processed. A key requirement for automation is the rapid and robust detection of the fatigue crack path and, even more important, the crack tip. To this purpose, artificial neural networks have recently been trained to reliably and fully automatically detect fatigue cracks in DIC data [40, 41]. Nevertheless, automated DIC remains very challenging, particularly for cases in which variable regions of interest much smaller than the specimen are studied, as it is the case of high resolution DIC (HRDIC). To address this challenge, Paysan et al. recently developed algorithms for a robot-assisted test rig that can be used to automatically scan a specimen surface during fatigue crack growth experiments using an optical microscope for HRDIC analysis [42].

Overall, literature shows that the integration of experimental DIC (especially HRDIC) and algorithmic analyses yields deep understanding of crack growth behaviour and its underlying mechanisms [38]. However, this approach requires entirely new test infrastructures, including interconnected hardware, i.e. the DIC system/s, the robotic systems and the test rig, as well as a robust code base for data management that include data acquisition, analysis, and storage. In addition, it is important to ensure that the generated data meets the criteria of being Findable, Accessible, Interoperable, and Reusable (F.A.I.R.) so that it can be utilized for data-driven research in a sustainable manner [43].

In this work we present a novel test infrastructure for data-centric experimental mechanics. The functionality of the setup is demonstrated using the complex experiment of fatigue crack growth in aerospace materials. Our methodology includes an open source Python package called “CrackPy – Crack Growth Analysis in Python” which complements our multiscale DIC and robotic-assisted test rig. We demonstrate the effectiveness of our experimental setup by comparing it to conventional experiments. Our results show that the integration of experimental mechanics with robotic systems and digital tools enables automation as well as deeper insights into materials behaviour and, as a result, the information-to-cost ratio is increased.

2.1 Infrastructure for next generation fatigue crack growth experiments

Figure 1 provides an overview of the infrastructure developed showing the flow of information between hardware and algorithms producing (raw) data and results. Starting with a commercial 3D DIC system (see section 4.1 for details), full-field displacements and strains are calculated on the specimen’s surface (Fig. 1c). At each time step during the experiments, the DIC data is saved in a node-wise neutral (.txt-) format – we call it the “nodemap” file. Then, the current crack tip position and crack path location are detected based on the analysis of the DIC displacement field. To this purpose, we use trained convolutional neural networks (CNNs) (see Fig. 1d) as explained in detail in our previous works [40, 41]. The CNN models were trained using supervised learning on a data set containing DIC displacement fields, manually labelled with the crack path and crack tip position [44]. The network focusses its attention on the characteristic crack tip field ahead of the crack to accurately detect its position [41]. The crack detection can be carried out in situ during the fatigue crack growth experiment to feed the crack tip information to the DIC system, the robot and the test rig controller or ex situ for all acquired time steps. A second DIC system is carried by a cobot using a light optical microscope (LOM) for higher magnification of the displacements and strains. This second system can therefore be used to perform HRDIC by moving the microscope to a region of interest using the crack tip information or by scanning the entire specimen’s surface in a checker board pattern. To ensure that the region of interest appears sharply in the focus of the microscope, the robot’s position can be fine-adjusted fully automated according to the implementation of Paysan et al. [42]. The hardware is fully automated for uniaxial test rigs (Fig. 1a) [42] and was used in this setup to obtain the data discussed in this study. Moreover, the whole system has recently been adapted for a biaxial test rig (Fig. 1b, see also Supplementary Video 1).

The data analysis provides several fracture mechanical parameters such as SIFs, T-Stress or higher order terms of the Williams series based on fitting methods or integral techniques (Fig. 1f). In particular, the utilization of Williams series coefficients condenses the crack tip field into a concise feature vector. This approach enables data-driven evaluation by representing the essential characteristics of the crack tip near-field in a lower dimensional space. These functionalities are implemented in CrackPy [45] and described in detail in the next section. The goal is to generate comprehensive datasets according to F.A.I.R. principles for each experiment.

CrackPy

We developed a Python-based library called CrackPy [45] to automate the data analysis pipeline. The library is structured according to Fig. 2. A Structural Element module provides classes that contain metadata, for instance the Experiment or Material class. The Material class contains information about the material physical parameter, like Young’s modulus, shear modulus, stiffness matrix, etc. As mentioned above, the nodal coordinates, displacement vectors and surface total mechanical strain tensors are stored in a neutral structure as text files (“Nodemap”) together with corresponding metadata. The metadata contain the experiment name, the DIC parameters, the specimen and material investigated, and information on the actual time or load step. A “_connection.txt” file stores the mesh information of the DIC evaluation domain. These files can be generated directly from a commercial DIC system using CrackPy’s DIC module or from a finite element analysis tool using the Simulation module. The "nodemap" and "connection" files can be used to visualize the data or to save all the information in the open-source ".vtk" (Visualization Toolkit) file format. Alternatively, the data structure can be created from any file type or system that provides node-wise results data. Once the nodal DIC data are stored in this format, the actual crack analysis can begin. Crack information such as the crack angle and crack tip position can be detected automatically using the Crack Detection module based on trained convolutional neural networks [40, 41] or set manually (e.g. in case of simulations, where the crack information is known a-priori). The network architectures together with the weights of the trained CNN models are available in [46]. The corresponding training data sets are available in [44]. The crack tip information is then stored in a file “Crack Information” (see Fig. 2) and is used as input for the Fracture Analysis module. CrackPy features a wide range of methods and algorithms. Currently (CrackPy 1.1.1), the following methods are implemented:

Calculation of the energy release rate during crack propagation by the J integral [18, 47]
Calculation of stress intensity factors (mode I, mode II) using the interaction integral technique [48, 49]
Calculation of higher order singular terms (HOSTs) or higher order regular terms (HORTs) of the Williams series [50] (including T-Stress) using Bueckner's conjugate work integral [51] together with the interaction technique described in [52, 53]
Calculation of higher order singular terms (HOSTs) or higher order regular terms (HORTs) of the Williams series [50] (including K_I, K_II and T-Stress) by fitting the theoretical displacement field to the experimentally measured (or simulated) data [54]
Calculation of stress intensity factors that take into account plasticity effects by fitting the theoretical displacement field of the CJP model [55] to the experimentally measured (or simulated) data [56]

More and more attention is being paid to methods 3–5: They describe the whole crack tip field in an alternative way considering higher-order terms of the Williams’ series and plastic effects. While the fitting methods (4 and 5) rely solely on displacements, the integral methods (1–3) also depend on stresses. Since DIC can only provide displacement and strain measurements, the stress fields must be calculated using an appropriate material model. For CrackPy, we use a linear-elastic material law – a good approximation in the absence of plastic deformation – and choose an integration domain away from the plastic zone surrounding the crack. The result of the analysis is then stored in Fracture Mechanics Results as structured text files and plots. The large amount of stored data, in the long-term, enables data-centric analyses, including techniques such as clustering, machine learning, and symbolic regression [57]. All these techniques need data to uncover patterns, make predictions, or build new physical models [43].

2.2 Application

Figure 3a shows the mode I SIF at minimum and maximum load as well as the cyclic mode I SIF as a function of the x coordinate of the crack tip for a cold rolled AA2024-T3 aluminum alloy tested in L-T orientation. Figure 4a presents the same data plotted as da/dN vs. ΔK. For this experiment, we integrated our robot-based infrastructure into a servo-hydraulic uniaxial test rig [42]. The whole system is shown in Fig. 1a. We applied a sinusoidal cyclic load at 20 Hz ranging from F_min = 4.5 kN to F_max = 15 kN, i.e. R = F_min/F_max = 0.3 on a middle tension specimen of width W = 160 mm and thickness t = 2 mm.

We compare the conventional analysis, i.e. using ASTM E647 [16],

$${\Delta }{\text{K}}_{\text{A}\text{S}\text{T}\text{M}}={\Delta }{\text{K}}_{\text{I}, \text{A}\text{S}\text{T}\text{M}}=\frac{{\Delta }\text{F}}{\text{t}}\cdot \sqrt{\frac{{\pi }{\alpha }}{2\text{W}\text{cos}\left(0.5 {\pi }{\alpha }\right)}},$$

where α = 2a/W, with the DIC-based results calculated using the interaction integral [48, 49, 45]. The conventional analysis assumes a symmetric crack growth. Thus, the overall crack length can be estimated by direct current potential drop (DCPD), i.e. a_x = 2a/2. One advantage of the DIC-based method is that both sides of the crack can be analyzed individually. Here, we show only one side of the crack – referred to as “left” side, i.e. the crack growths along the negative x direction with respect to the coordinate system located in the specimen center – and detected the actual crack tip position using our trained CNN. Overall, the novel method yields similar results to the conventional one in terms of K-a and da/dN-ΔK (Fig. 3a and Fig. 4a, respectively). The curves are well aligned for small ΔK = 7.0–9.5 MPa√m. In contrast, the curves from the two methods seem to be shifted away from each other for ΔK > 9.5 MPa√m. This effect is due to the difference between the conventional and the DIC-based methods in terms of calculated SIFs (since da/dN is almost identical for both methods). In contrast to conventional methods, the continuous access to the DIC and HRDIC data enables now a detailed analysis of such effects: Fig. 3c-e and Fig. 4b-c show the von Mises equivalent strains and the vertical (y) displacement around the crack tip and crack path obtained by HRDIC for representative crack growth states during the experiment, respectively. While the crack path is mostly straight at low ΔK (Fig. 3c), a tortuous crack path propagates later (Fig. 3d and e). From a fracture mechanics perspective, it can be inferred that this zig-zag-like crack path may be a consequence of secondary cracks that result in a reduction of the effective stress intensity at the primary crack tip [58]. This has a large effect on the SIF at maximum load but a smaller one at minimum load. Consequently, the effective cyclic SIF (based on DIC results) is lower and more realistic than that obtained using the conventional method based on the ASTM that assumes a fully straight crack. The effect is well aligned with the evolution of K_II throughout the experiment: Conventionally, K_II is considered to be zero using the ASTM method because the crack path is assumed to be perfectly straight, and thus, a pure mode I state is assumed. However, we find that K_II,DIC ranges from − 2 to 2 MPa√m (Fig. 3b) as soon as crack branching begins (Fig. 3d and e, Fig. 4c). These effects are captured locally and continuously throughout the experiment by our method because the results are a consequence of the actual displacements and strains. We show more data of several time steps in Supplementary Video 2. In contrast, the conventional method is unable to detect such phenomena because the SIFs are calculated based only on crack length, load and specimen geometry. Furthermore, we compare results for K_II based on three different approaches computed simultaneously in CrackPy: the interaction integral [48, 49], the Bueckner integral [52] and a fit of the theoretical displacements to the experimental data with respect to Williams’ formulation [50] using the Levenberg-Marquardt algorithm [59]. Although the three methods yield quantitatively different values for K_II, i.e. the interaction integral underestimates K_II compared to the other two methods, the overall trend is similar for all of them.

Figure 5 shows the evolution of the T-Stress as a function of the crack length (in terms of the crack tip’s x coordinate). The T-Stress acts parallel to the crack and is associated to the first non-singular term of the Williams series expansion. In literature, it is usually correlated to crack path stability [60]. Here, we determine the T-Stress using the experimental DIC data and the interaction integral method and compare it with the theoretical finite element method (FEM) solution. The finite element model considers a linear-elastic constitutive law (E = 72 GPa, ν = 0.33) and a structured 2D plane element mesh with an element size of 0.04 × 0.04 mm². Again, two regions can be identified: a first region between − 20 mm > x > -38 mm where both results are close and the DIC results are scattered around the FEM solution. Beyond − 38 mm, the DIC results are higher than the FEM solution. We associate this characteristic with the transition from an almost straight crack path in the first region, to a more tortuous and branched crack path in the second region (see Fig. 3c-e, respectively).

We have shown the first and second term of the Williams expansion, i.e. K_I, K_II, and T-Stress. Moreover, as described in the section “CrackPy”, it is possible to calculate higher order terms of the Williams expansion using Bueckner’s conjugated work integral or by fitting the theoretical displacement field to the experimental data. There is no evidence in the literature about the physical meaning of these higher-order terms although some studies show an effect on crack growth: Higher-order terms can be necessary to match the crack tip near field with the remote geometry or boundary conditions [61]. Moreover, at least theoretically, the third regular term is responsible for crack propagation stability [62]. We refer to[53] for a parameter study of higher-order terms carried out on FE simulations of different standard specimen geometries. A systematic analysis of these higher-order terms, especially for experimental DIC data, will enable new perspectives to investigate their influence on e.g. fracture modes, crack path stability or crack branching. Furthermore, higher order terms can be used to condense the complexity of the crack tip field into a discrete feature vector. This feature vector allows a data-centric approach while it also enables a complete reconstruction of the crack tip field. Exemplary, we show terms A₁-A₄ and B₁-B₄ for the presented experiment in the supplementary material (Supplementary Fig. 1) by fitting the theoretical displacements to the experimental ones using CrackPy (version 1.1.1).

With our new test infrastructure, we have continuous access to displacement and strain data throughout the experiment and at two different length scales, i.e. global 3D DIC and local 2D HRDIC. This alone is a tremendous increase of the information-to-cost ratio for FCG experiments because local effects on the specimen surface can be captured for any number of time and load steps. This opens up the possibility of analyzing intrinsic and extrinsic crack growth effects, individually. Table 1 shows a comparison of the conventional and the robot-assisted DIC-based methods for fatigue crack growth experiments on eight criteria.

Both methods are capable to generate a-N and da/dN-ΔK data. However, the robot-assisted DIC-based methodology has several further advantages: First, the DIC images can be used to calculate fracture mechanics parameters such as SIFs, T-stress, etc. using integral techniques based on actual experimental data rather than analytically, which permits eliminating assumptions. Apart from SIFs, higher order terms of the Williams expansion are conventionally calculated using FEM, i.e. rely on an idealized material, geometry, etc., neglecting e.g. microstructural effects. By means of Chen’s approach using the conjugated work integral [52] it is possible to calculate these parameters based on the experimental DIC data. In addition, the use of full-field data increases confidence in experimental results. Moreover, redundancy is achieved through multiple data sources, overlapping data and independent evaluation algorithms. This comprehensive approach promotes data reliability and facilitates the differentiation between scatter, anomalies and true effects.

The overall time needed to run one single experiment strongly depends on the investigated material, load conditions, specimen size and environmental conditions. For our experiments, the time needed increased from 1–2 days using the conventional ASTM method to ~ 1 week with the new test infrastructure. In both cases, the test procedure is almost completely automatized and we believe that the additional time needed is compensated by the much larger outcome from the experiment.

A notable feature of the methodology introduced in this work is the large amount of data acquired per experiment (> 100 GB). This requires a significant increase of data storage capabilities compared to conventional testing methods. Handling such large amounts of data requires a storage strategy in line with the principals of findable, accessible, interoperable, and reusable data [63, 64]. Our data is publicly available on Zenodo, with a digital object identifier (DOI) [65] serving as persistent and unique identifier. Thus, the data is stored for open, long-term access and is findable by anyone. The data and metadata can be accessed via a web browser or the Zenodo REST application programming interface (API) [66]. We distinguish between metadata at different levels. More precisely, we store metadata describing the whole experiment, the material with its manufacturing process separated from the data [65] accessible and interoperable even if the data was no longer available [63]. On the other hand, we store metadata describing a respective time step directly within the data files to minimize the risk of mixing up metadata or data. To this purpose, we designed the “nodemap”-file as a specific structure of text file including a long header containing all relevant metadata as keyword value pairs. We describe the experiments accurately on the highest level of metadata meeting fracture mechanics community standards. In addition, we explain the vocabulary of the metadata using dictionaries to avoid confusion of any terms. We believe that these accurate descriptions make it easier for humans to understand the origin of the data, while it remains hard for machines to understand the metadata fully automatically. Thus, it becomes more and more important to design standards describing experiments, material and processes of the domain of experimental mechanics for the purpose of machine interoperability, and therefore, reusable data.

Table 1

Comparison of the conventional fatigue crack growth testing and our new methodology
	Conventional FCG experiments	Robot-assisted FCG experiments
a-N	The direct current potential drop (DCPD) technique provides integral values assuming a straight crack and symmetrical crack growth	Both sides of the crack can be analyzed individually; the actual crack path is detected during the experiment. Applicable also for non-straight crack geometries.
da/dN-ΔK	Straight crack is assumed, i.e. K_II = 0 with idealized loading conditions	Calculation of K based on experimental DIC-measured displacement and strain field reflecting actual loading conditions and crack deflection.
T-Stress	Can be calculated using analytical formulations or finite element analysis. Necessitates idealized assumptions.	Calculated based on experimental DIC data
Higher-order terms	Can be calculated using finite element analysis assuming idealized test conditions and material properties	Calculated based on experimental DIC data
Local effects (e.g. crack deflection, crack branching / bifurcation, crack closure)	Captured as integral effects on the crack growth rate; A local analysis is only possible by post-mortem fractography.	Captured in situ locally using high resolution DIC; Can be combined with traditional methods like fractography post-mortem.
Specimen geometry	Standard geometry	Arbitrary geometry
Duration of one experiment	~ 1–2 days, depending on frequency, material and specimen size; This time usually involves few or no manual steps.	~ 5–6 days; This time usually involves few or no manual steps.
Data set size for one experiment	~ KBs to MBs	> 100 GB

In summary, we developed, implemented, and showcased a new generation test infrastructure for experimental mechanics using the example of highly complex crack growth experiments. Therefore, we combined DIC, robotics and a robust code base as a digital backbone. The novel methodology increases the information-to-cost ratio for one experiment tremendously making local effects accessible throughout the experiment. Data are obtained and stored according to F.A.I.R principals. As a consequence, results are more usable, understandable and reliable compared to results following the conventional method. The adoption of F.A.I.R. data ensures the long-term preservation of expert domain knowledge. Therefore, adopting these principles will not only improve reproducibility and transparency, but also drive significant advances, making these practices a key factor in accelerating scientific progress.

4.1 Digital image correlation

We acquired data using the commercial 3D DIC System GOM Aramis 12M and the software GOM Aramis Professional 2021. We supported the commercial system with CrackPy to store metadata when images are captured, to control the experiment, i.e. by on-the-fly crack detection, and to store the results as human-readable text files that combine metadata and facet results in terms of displacements and strains. We used a facet size of 20×20 pixels with a 16 pixels facet distance. One facet covered an area of 0.614×0.614 mm².

4.2 Robot-assisted high-resolution digital image correlation

We used a KUKA LBR iiwa cobot which carries a Zeiss STEMI 206C light optical microscope equipped with a Basler a2A5320-23µmPRO global shutter CMOS camera to take high resolution images. The test rig is explained in detail by Paysan et al. in [42]. The chosen field of view was 10.2×5.7 mm² which was covered by facets with a size of 40×40 pixels and a facet distance of 30 pixels corresponding to a spatial resolution (distance between two facet center points) of 0.05 mm.

4.3 Crack detection

The detection of crack paths and crack tips can be performed in situ or ex situ using the Crack Detection module of CrackPy[45] on any number of load steps. Therefore, we used two trained convolutional neural networks, i.e., the so-called ParallelNets to find the crack tip and the so-called UNetPath to detect the crack path. Both network architectures can be found in CrackPy. Moreover, their trained weights are separately published [67]. For the crack detection, we use the global 3D DIC displacement fields as input data. The crack angle is approximated by fitting a line through the detected crack path near the tip. Moreover, the crack tip detection model is explainable and can be monitored using attention visualizations based on Grad-CAM [68]. For further details we refer to [40, 41].

4.4 Experimental procedure

4.4.1 Material

A commercially available AA2024-T3 aluminium alloy was used for the FCG experiments. This alloy was chosen because it represents one of the most relevant alloys used in the aircraft industry, particularly for fuselage structures. The material was tested in L-T orientation, i.e. rolling direction (L, elongated grains) parallel to the load axis and transverse direction (T) perpendicular to the load axis. A middle tension (MT) specimen with a thickness of 2.0 mm and a width of 160 mm was cut from a rolled sheet. The material has a Young’s modulus E = 72.0 GPa and poisson’s ratio µ = 0.3.

4.4.2 Fatigue crack growth

We used a standard uniaxial test rig. The whole system is shown in Fig. 1a. We applied a cyclic load ranging from F_min = 4.5 kN to F_max = 15 kN, i.e. R = F_min/F_max = 0.3 on a MT specimen (width W = 160 mm, thickness t = 2 mm). We measured the crack length by direct current potential drop (DCPD) following ASTM E-647 [16] to control the experiment. However, when we analyzed the experiment, we used DCPD for the conventional method (ASTM) and used the crack tip achieved from the trained neural network (see section 4.3) for the novel method.

4.4.3 Image acquisition during fatigue crack growth

We acquired reference images for the DIC calculations before the experiment. For the global DIC, this is simply an image of the unloaded specimen. For the local HRDIC the reference images are acquired in a checker board pattern with an overlap of 70% covering the whole specimen surface. The depth of focus is calibrated for each image and the camera is aligned to the specimen’s surface according to Paysan et al. [42]. The spatial position of the robot (and consequently of the microscope) are saved as metadata for each of these reference images. The test was stopped every 0.5 mm of crack extension. Then, the crack length was used to determine the region of interest around the crack tip and the robot moved to the corresponding reference images’ positions to acquire new images at the current loading conditions. Therefore, the region of interest was defined as a square covering the crack tip region of 18 × 9.2 mm². This was done for F_max, F_min, and F_min + 0.5 (F_max-F_min).

Acknowledgement

The authors acknowledge Alina Klein who supported the authors during the implementation of CrackPy as a student assistant. We also acknowledge Vanessa Schöne and Ferdinand Dömling for continuous tests of CrackPy.

The authors acknowledge the financial support of the German federal ministry of Economic Affairs and Climate Action (BMWK) within the LuFo project ATON. The research is also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) –Project number BR 6259/2-1. The authors acknowledge the financial support of the DLR Aeronautics Directorate.

Author Contributions

T.S. designed and wrote the code base, wrote the manuscript, analyzed and visualized the experimental results, designed and managed the project. D.M. designed and wrote the codebase and wrote the manuscript; F.P. designed and implemented the test infrastructure and performed and analyzed the crack growth experiments; E.D. supported the implementation of the infrastructure and the crack growth experiments. G.R. designed and managed the project, supervised the work, and wrote the manuscript, E.B. wrote the code base, designed and managed the project, supervised the work, and wrote the manuscript. All authors reviewed and commented on the manuscript.

Data Availability

The research data are publicly available as Zenodo dataset [65].

Code Availability

The code, i.e. CrackPy (version 1.1.1) is available on github https://github.com/dlr-wf/crackpy[45] under MIT licence. The code to reproduce results using CrackPy will also be made available on our github repository.

Pyzer-Knapp EO, Pitera JW, Staar PWJ et al. (2022) Accelerating materials discovery using artificial intelligence, high performance computing and robotics. npj Comput Mater 8. https://doi.org/10.1038/s41524-022-00765-z
Yang J, Ahmadi M (2023) Empowering scientists with data-driven automated experimentation. Nat Synth 2:462–463. https://doi.org/10.1038/s44160-023-00337-z
Granda JM, Donina L, Dragone V et al. (2018) Controlling an organic synthesis robot with machine learning to search for new reactivity. Nature 559:377–381. https://doi.org/10.1038/s41586-018-0307-8
Häse F, Roch LM, Aspuru-Guzik A (2019) Next-Generation Experimentation with Self-Driving Laboratories. Trends in Chemistry 1:282–291. https://doi.org/10.1016/j.trechm.2019.02.007
Burger B, Maffettone PM, Gusev VV et al. (2020) A mobile robotic chemist. Nature 583:237–241. https://doi.org/10.1038/s41586-020-2442-2
MacLeod BP, Parlane FGL, Morrissey TD et al. (2020) Self-driving laboratory for accelerated discovery of thin-film materials. Sci Adv 6:eaaz8867. https://doi.org/10.1126/sciadv.aaz8867
MacLeod BP, Parlane FGL, Brown AK et al. (2022) Flexible automation accelerates materials discovery. Nat Mater 21:722–726. https://doi.org/10.1038/s41563-021-01156-3
Soldatov MA, Butova VV, Pashkov D et al. (2021) Self-Driving Laboratories for Development of New Functional Materials and Optimizing Known Reactions. Nanomaterials (Basel) 11. https://doi.org/10.3390/nano11030619
MacLeod BP, Parlane FGL, Rupnow CC et al. (2022) A self-driving laboratory advances the Pareto front for material properties. Nat Commun 13:995. https://doi.org/10.1038/s41467-022-28580-6
Svensson HG, Bjerrum E, Tyrchan C et al. (2022) Autonomous Drug Design with Multi-armed Bandits. https://doi.org/10.48550/arXiv.2207.01393
Abolhasani M, Kumacheva E (2023) The rise of self-driving labs in chemical and materials sciences. Nat Synth 2:483–492. https://doi.org/10.1038/s44160-022-00231-0
Volk AA, Epps RW, Yonemoto DT et al. (2023) AlphaFlow: autonomous discovery and optimization of multi-step chemistry using a self-driven fluidic lab guided by reinforcement learning. Nat Commun 14:1403. https://doi.org/10.1038/s41467-023-37139-y
Peng X, Wang X (2023) Next-generation intelligent laboratories for materials design and manufacturing. MRS Bull 48:179–185. https://doi.org/10.1557/s43577-023-00481-z
Rao Z, Tung P-Y, Xie R et al. (2022) Machine learning-enabled high-entropy alloy discovery. Science 378:78–85. https://doi.org/10.1126/science.abo4940
Gongora AE, Xu B, Perry W et al. (2020) A Bayesian experimental autonomous researcher for mechanical design. Sci Adv 6:eaaz1708. https://doi.org/10.1126/sciadv.aaz1708
ASTM International ASTM E-647-13: Standard Test Method for Measurement of Fatigue Crack Growth Rates:684–732
Schijve J (2003) Fatigue of structures and materials in the 20th century and the state of the art. International Journal of Fatigue 25:679–702. https://doi.org/10.1016/S0142-1123(03)00051-3
BECKER TH, MOSTAFAVI M, TAIT RB et al. (2012) An approach to calculate the J -integral by digital image correlation displacement field measurement. Fatigue & Fracture of Engineering Materials & Structures 35:971–984. https://doi.org/10.1111/j.1460-2695.2012.01685.x
Besel M, Breitbarth E (2016) Advanced analysis of crack tip plastic zone under cyclic loading. International Journal of Fatigue 93:92–108. https://doi.org/10.1016/j.ijfatigue.2016.08.013
Breitbarth E, Besel M (2017) Energy based analysis of crack tip plastic zone of AA2024-T3 under cyclic loading. International Journal of Fatigue 100:263–273. https://doi.org/10.1016/j.ijfatigue.2017.03.029
Camacho-Reyes A, Vasco-Olmo JM, James MN et al. (2022) Towards a new methodology for the characterisation of crack tip fields based on a hybrid computational approach. International Journal of Fatigue 162:106942. https://doi.org/10.1016/j.ijfatigue.2022.106942
Carroll JD, Abuzaid W, Lambros J et al. (2013) High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. International Journal of Fatigue 57:140–150. https://doi.org/10.1016/j.ijfatigue.2012.06.010
Chen C, Qian X (2022) Quantifying through-thickness J for plane strain specimens using digital image correlation considering constraint effects. Engineering Fracture Mechanics 267:108430. https://doi.org/10.1016/j.engfracmech.2022.108430
Dehnavi MY, Khaleghian S, Emami A et al. (2014) Utilizing digital image correlation to determine stress intensity factors. Polymer Testing 37:28–35. https://doi.org/10.1016/j.polymertesting.2014.04.005
Gonzáles GL, González JA, Castro JT et al. (2017) A J-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects. Theoretical and Applied Fracture Mechanics 90:14–21. https://doi.org/10.1016/j.tafmec.2017.02.008
Hosdez J, Witz J-F, Martel C et al. (2017) Fatigue crack growth law identification by Digital Image Correlation and electrical potential method for ductile cast iron. Engineering Fracture Mechanics 182:577–594. https://doi.org/10.1016/j.engfracmech.2017.05.037
Lopez-Crespo P, Shterenlikht A, Patterson EA et al. (2008) The stress intensity of mixed mode cracks determined by digital image correlation. The Journal of Strain Analysis for Engineering Design 43:769–780. https://doi.org/10.1243/03093247JSA419
Panwitt H, Köster P, Sander M (2022) Fatigue crack growth determination under in-phase and out-of-phase mixed-mode loading conditions using an automated DIC evaluation tool. International Journal of Fatigue 164:107122. https://doi.org/10.1016/j.ijfatigue.2022.107122
Réthoré J, Roux S, Hild F (2011) Optimal and noise-robust extraction of Fracture Mechanics parameters from kinematic measurements. Engineering Fracture Mechanics 78:1827–1845. https://doi.org/10.1016/j.engfracmech.2011.01.012
Roux S, Hild F (2006) Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches. Int J Fract 140:141–157. https://doi.org/10.1007/s10704-006-6631-2
Réthoré J, Gravouil A, Morestin F et al. (2005) Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral. Int J Fract 132:65–79. https://doi.org/10.1007/s10704-004-8141-4
Silva A, Jesus A de, Xavier J et al. (2017) Combined analytical-numerical methodologies for the evaluation of mixed-mode (I + II) fatigue crack growth rates in structural steels. Engineering Fracture Mechanics 185:124–138. https://doi.org/10.1016/j.engfracmech.2017.04.016
Sutton MA (2003) Deformations in wide, center-notched, thin panels, part I: three-dimensional shape and deformation measurements by computer vision. Opt Eng 42:1293. https://doi.org/10.1117/1.1566001
Sutton MA (2007) Three-dimensional digital image correlation to quantify deformation and crack-opening displacement in ductile aluminum under mixed-mode I/III loading. Opt Eng 46:51003. https://doi.org/10.1117/1.2741279
Yates JR, Zanganeh M, Tai YH (2010) Quantifying crack tip displacement fields with DIC. Engineering Fracture Mechanics 77:2063–2076. https://doi.org/10.1016/j.engfracmech.2010.03.025
Réthoré J, Roux S, Hild F (2009) An extended and integrated digital image correlation technique applied to the analysis of fractured samples. European Journal of Computational Mechanics 18:285–306. https://doi.org/10.3166/ejcm.18.285-306
Roux S, Réthoré J, Hild F (2009) Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks. J Phys D: Appl Phys 42:214004. https://doi.org/10.1088/0022-3727/42/21/214004
Hebert J, Khonsari M (2022) The application of digital image correlation (DIC) in fatigue experimentation: A review. Fatigue Fract Eng Mat Struct. https://doi.org/10.1111/ffe.13931
Réthoré J (2015) Automatic crack tip detection and stress intensity factors estimation of curved cracks from digital images. Int J Numer Meth Engng 103:516–534. https://doi.org/10.1002/nme.4905
Strohmann T, Starostin‐Penner D, Breitbarth E et al. (2021) Automatic detection of fatigue crack paths using digital image correlation and convolutional neural networks. Fatigue Fract Eng Mater Struct 44:1336–1348. https://doi.org/10.1111/ffe.13433
Melching D, Strohmann T, Requena G et al. (2022) Explainable machine learning for precise fatigue crack tip detection. Sci Rep 12:9513. https://doi.org/10.1038/s41598-022-13275-1
Paysan F, Dietrich E, Breitbarth E (2023) A robot-assisted microscopy system for digital image correlation in fatigue crack growth testing. Experimental Mechanics. https://doi.org/10.1007/s11340-023-00964-9
Scheffler M, Aeschlimann M, Albrecht M et al. (2022) FAIR data enabling new horizons for materials research. Nature 604:635–642. https://doi.org/10.1038/s41586-022-04501-x
Melching D, Strohmann T, Requena G et al. (2022) Full-field displacements and strains obtained by digital image correlation during fatigue crack growth experiments. Zenodo. https://doi.org/10.5281/zenodo.5740216
Strohmann T, Melching D, Paysan F et al. (2022) Crack Analysis Tool in Python - CrackPy. Zenodo. https://doi.org/10.5281/zenodo.7472202
Melching D, Strohmann T, Requena G et al. (2022) Explainable machine learning for precise fatigue crack tip detection. Zenodo. https://doi.org/10.5281/zenodo.6605441
Rice JR (1968) A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics 35:379–386. https://doi.org/10.1115/1.3601206
Stern M, Becker EB, Dunham RS (1976) A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12:359–368. https://doi.org/10.1007/BF00032831
Breitbarth E, Strohmann T, Besel M et al. (2019) Determination of Stress Intensity Factors and J integral based on Digital Image Correlation. Frattura ed Integrità Strutturale 13:12–25. https://doi.org/10.3221/IGF-ESIS.49.02
Williams ML (1961) The Bending Stress Distribution at the Base of a Stationary Crack. Journal of Applied Mechanics 28:78–82. https://doi.org/10.1115/1.3640470
Bueckner HF (1973) Field singularities and related integral representations. In: Sih GC (ed) Methods of analysis and solutions of crack problems. Springer Netherlands, Dordrecht, pp 239–314
Chen YZ (1985) New path independent integrals in linear elastic fracture mechanics. Engineering Fracture Mechanics 22:673–686. https://doi.org/10.1016/0013-7944(85)90131-6
Melching D, Breitbarth E (2023) Advanced crack tip field characterization using conjugate work integrals. International Journal of Fatigue. https://doi.org/10.1016/j.ijfatigue.2023.107501
AYATOLLAHI MR, NEJATI M (2011) An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue & Fracture of Engineering Materials & Structures 34:159–176. https://doi.org/10.1111/j.1460-2695.2010.01504.x
Christopher CJ, James MN, Patterson EA et al. (2007) Towards a new model of crack tip stress fields. Int J Fract 148:361–371. https://doi.org/10.1007/s10704-008-9209-3
Yang B, Wei Z, Díaz FA et al. (2021) New algorithm for optimised fitting of DIC data to crack tip plastic zone using the CJP model. Theoretical and Applied Fracture Mechanics 113:102950. https://doi.org/10.1016/j.tafmec.2021.102950
Zhou S, Yang B, Xiao S et al. (2023) Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression. Chin J Mech Eng 36. https://doi.org/10.1186/s10033-023-00876-8
Meggiolaro MA, Miranda A, Castro J et al. (2005) Stress intensity factor equations for branched crack growth. Engineering Fracture Mechanics 72:2647–2671. https://doi.org/10.1016/j.engfracmech.2005.05.004
Moré JJ (1978) The Levenberg-Marquardt algorithm: Implementation and theory. In: Watson GA (ed) Numerical Analysis, vol 630. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 105–116
Gupta M, Alderliesten RC, Benedictus R (2015) A review of T-stress and its effects in fracture mechanics. Engineering Fracture Mechanics 134:218–241. https://doi.org/10.1016/j.engfracmech.2014.10.013
Baldi A, Santucci PM (2022) Kinematic estimation of fracture mechanics parameter with automatic crack-tip identification. Engineering Fracture Mechanics 259:108082. https://doi.org/10.1016/j.engfracmech.2021.108082
Cotterell B (1966) Notes on the paths and stability of cracks. Int J Fract 2:526–533. https://doi.org/10.1007/BF00193691
Wilkinson MD, Dumontier M, Aalbersberg IJJ et al. (2016) The FAIR Guiding Principles for scientific data management and stewardship. Sci Data 3:160018. https://doi.org/10.1038/sdata.2016.18
Sbailò L, Fekete Á, Ghiringhelli LM et al. (2022) The NOMAD Artificial-Intelligence Toolkit: turning materials-science data into knowledge and understanding. npj Comput Mater 8. https://doi.org/10.1038/s41524-022-00935-z
Strohmann T., Paysan F, David Melching et al. (will be published along with this article) Digital image correlation displacements and strains around a growing fatigue crack in an AA2024-T3 aluminium alloy. https://doi.org/10.5281/zenodo.8013173
CERN Data Centre & Invenio Zenodo REST API. https://developers.zenodo.org/#rest-api. Accessed 10 Jan 2023
David Melching, Tobias Strohmann, Guillermo Requena et al. (2022) Crack detection models based on digital image correlation and convolutional neural networks. Zenodo. https://doi.org/10.5281/zenodo.7245516
Selvaraju RR, Cogswell M, Das A et al. (2020) Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization. Int J Comput Vis 128:336–359. https://doi.org/10.1007/s11263-019-01228-7

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Towards self-driving labs for experimental mechanics: a data-centric approach for fatigue crack analysis in aerospace materials

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Abstract

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1 Introduction

2 Results

2.1 Infrastructure for next generation fatigue crack growth experiments

2.2 Application

3 Discussion

4 Methodology

4.1 Digital image correlation

4.2 Robot-assisted high-resolution digital image correlation

4.3 Crack detection

4.4 Experimental procedure

4.4.1 Material

4.4.2 Fatigue crack growth

4.4.3 Image acquisition during fatigue crack growth

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