SIFBench: An Extensive Benchmark for Fatigue Analysis

Jacob Hochhalter; Robert M. Kirby; Shandian Zhe; Tushar Gautam

REVIEW 3 major objections 4 minor 1 cited by

SIFBench: An Extensive Benchmark for Fatigue Analysis

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read SIFBench introduces a benchmark of over five million finite-element-derived stress intensity factors across 37 crack scenarios, with baselines and a unified Python interface.

desk verdict SIFBench is a genuinely useful benchmark resource for ML-for-fatigue work, but the headline 'over 5 million geometries' claim is internally contradicted by the paper's own per-dataset counts, and the lack of FEM validation and baseline variance needs to be addressed before it can be fully trusted. read the letter →

arxiv 2506.01173 v2 pith:HDEKHXVL submitted 2025-06-01 cs.DB cs.LG

Tushar Gautam , Robert M. Kirby , Jacob Hochhalter , Shandian Zhe This is my paper

classification cs.DBcs.LG

keywords stressintensityfactorfatiguecrackgrowthfiniteelementmethodmachinelearningbenchmarkfracturemechanicsdatasetneuraloperatorsdamagetolerancedesign

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

SIFBench is an open benchmark database containing over five million finite-element-derived stress intensity factor (SIF) values for cracks in plates and at bolt holes. Its purpose is to give the machine learning community a large, standardized, transparent training and evaluation resource for SIF prediction, which previously did not exist at this scale. The paper also supplies baseline results from several model families and a unified Python interface so that new users can train and compare models without running expensive fracture simulations. If the underlying finite element data are accurate, this lowers the barrier to applying machine learning to fatigue life prediction and damage tolerance design.

What carries the argument

The load-bearing object is the benchmark database itself, whose records pair normalized crack and component geometry parameters (such as $a/t$, $a/c$, $c/b$, $W/R$, and $R/t$) with SIF values sampled along the crack front at parametric angle $\phi$. The data were produced by finite element and hp-finite element simulations, with SIFs extracted by displacement- and integral-based post-processing, and the geometric parameter ranges and sampling resolutions for each scenario are documented in appendix tables so users know the boundaries of the data. A unified Python interface reads the CSV files and provides training and validation templates, making the dataset the reusable instrument that carries the paper's argument.

What would settle it

Re-run the finite-element computation for one scenario (e.g., the semi-elliptical surface crack in a rectangular plate under tension) with progressively refined meshes and with quarter-point elements, and compare the computed SIF values at matched crack-front angles. If the values shift by more than a few percent across refinements, or if they disagree with the analytical handbook solution in the regime where that solution is valid, then the database's ground-truth quality would be in question for every model trained on it.

Watch

Extended reading notes

Core claim

SIFBench is an open-source benchmark database containing over five million distinct configurations of cracks, component geometries, and loading conditions, generated by high-fidelity finite element simulations and organized into 37 scenarios. The scenarios split into single-crack cases (semi-elliptical surface cracks in plates, quarter-elliptical and through-thickness corner cracks at straight and countersunk bolt holes, each under tension, bending, or bearing) and twin-crack cases (pairs of corner cracks at the same hole types). Each record stores the dimensionless geometric parameters of the configuration together with the stress intensity factor values along the crack front, parameterized by angle $\phi$. The paper's central claim is that this standardized, openly accessible resource, with its unified Python interface, baseline models, and evaluation metrics, removes the data bottleneck that has held back machine-learning approaches to SIF prediction.

Load-bearing premise

The FEM-computed SIF values are accurate enough to serve as ground truth for the represented geometries; the paper does not report mesh-convergence or validation checks against analytical solutions, so any systematic error in the simulations propagates into every model trained on the benchmark.

Editorial extensions

If this is right

Research groups can train and compare SIF-prediction models on a common, openly hosted dataset instead of each generating their own FEM data, making results directly comparable.
Baseline results establish a reference: feedforward networks typically perform best on single-crack scenarios, random forests on twin-crack scenarios, while the Fourier neural operator lags in accuracy on most of these tasks.
The documented parameter ranges define the current scope of validity for any model trained on the benchmark, so users know where interpolation is supported and where it is not.
The paper states that the benchmark will be expanded to more complex component shapes, broader loading spectra, and experimental data, so the current 37 scenarios are an initial standardized core.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the community adopts SIFBench as a standard evaluation set, stress-intensity-factor prediction could accumulate the kind of direct model-to-model comparability seen in mature ML benchmark suites, accelerating progress that the lack of shared data currently blocks.
Because the benchmark's ground truth is entirely FEM-generated, its ceiling is the accuracy of those simulations; adding mesh-convergence studies or comparisons with analytical solutions for a subset of scenarios would let users know how much of the reported model error is model error versus data error.
The current tabular format (geometric parameters plus angle) suits the baselines tested, but the same database could be reorganized as crack-front coordinate fields or images to enable convolutional and geometry-aware neural operators, a testable extension the paper does not explore.
Since the scenarios center on fastener holes and plates common in aircraft structures, transferring the benchmark to automotive or energy-sector components would require generating new scenarios; the paper's pipeline and interface could be reused for that purpose.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Quick take: this is a real resource paper, not vaporware. The authors have assembled 37 FEM-derived SIF datasets, wrapped them in a unified Python interface, shipped code, and run four baseline models. That artifact -- a common, open, large-scale training/evaluation ground for ML-based fatigue analysis -- did not exist before in this form, and it lowers the entry barrier for the field. The reuse of CAStLE and Merrell data is fine; benchmarks are built from prior sources, and the value is in the standardized access and baseline suite.

But there is a problem you need to know about before citation. The abstract and intro claim "over 5 million different crack and component geometries," and the paper even splits this into 1.6M single-crack and 3.3M twin-crack geometries. I summed the per-dataset counts in Section 3. Adding everything gives 543,806 single-crack configurations and 1,169,194 twin-crack, total about 1.71M. The only way to reach 5M is to count each angle-sampled SIF row as a separate geometry, which contradicts the per-dataset wording of "unique plate and crack geometries." That is a 3x overstatement of the core scale selling point. It is fixable, but it has to be corrected -- the numbers in the abstract, the intro, and the conclusion all need to match the actual data files.

Other soft spots, in decreasing order of severity. No convergence studies or validation against known analytical solutions for the FEM data. Some of this is inherited from trusted sources (Fawaz-Andersson, Merrell), but the paper does not do its own verification, and any systematic FEM error propagates into every downstream model. Baselines are single-split with no variance or repeated runs, so the model comparisons in Tables 1-2 are suggestive, not conclusive. There is a bug in the Listing 1 snippet (extra parenthesis, and the test prediction uses training features), which is embarrassing but easy to fix. And Table 16 has those wild mean-NAE values for the TT countersunk b/t=0.5 scenario (25-215) alongside relative L2 errors around 0.1-0.3 -- that tension needs an explanation or a correction.

The central resource claim is still plausible: 1.7M unique geometries is a large, useful benchmark. But the paper is not ready as-is. It deserves a serious referee, not a desk reject, because the underlying artifact is valuable and the fixes are mechanical. I would send it to review with a request for major revision: correct the count, add FEM verification or at least a clear statement of what is inherited, report baseline variability, fix the snippet, and reconcile the NAE outliers.

Who's it for: anyone working on SIF prediction with ML, and fracture-mechanics researchers looking for a common testbed. Once the numbers are corrected, I'd cite it. For now, I'd bring it to reading group and discuss the discrepancy -- it's a good lesson in checking headline claims.

My recommendation: accept for peer review, but only after the authors fix the counting and validation issues.

Referee Report

3 major / 4 minor

Summary. The paper introduces SIFBench, an open benchmark dataset of finite-element-derived stress intensity factors (SIFs) covering single and twin cracks in plates and around straight and countersunk holes, under tension, bending, and bearing loadings. The authors report baseline results for random forests, support vector regression, feedforward neural networks, and Fourier neural operators, together with evaluation metrics (NAE, relative L2 error, CCDF-NAE) and template Python code. The central claim is that SIFBench contains over five million unique crack and component geometries across 37 scenarios, derived from high-fidelity FEM simulations.

Significance. If the scale and FEM-accuracy claims hold, SIFBench would be a valuable community resource for ML-based fatigue analysis: it aggregates 37 scenarios, provides a unified Python interface, ships baseline code, and includes a neural-operator baseline, all of which lower the entry barrier for researchers and engineers. The paper is honest about limitations such as the absence of dynamic, thermal, and multi-axial loadings. However, the dataset's value as ground truth depends on FEM validation that is not supplied, and the headline scale claim is not supported by the paper's own enumeration. These issues must be resolved before the benchmark can be trusted as a reference standard.

major comments (3)

[Abstract, §3.1–3.2, Conclusion] The headline scale claim is not supported by the paper's own counts. Summing the per-dataset numbers in §3.1–3.2 yields 543,806 single-crack configurations (2,956 + 28,781 + 5,426 + 114,442 + 127,884 + 85,360 + 72,275 + 22,417 + 84,265) and 1,169,194 twin-crack configurations (72,000 + 3,055 + 1,091,419 + 2,720), for a total of 1,713,000, yet §3 states 'roughly 1.6 million and 3.3 million geometries' and the abstract and conclusion claim 'over 5 million different crack and component geometries.' The 5M figure cannot be obtained from the enumeration unless angle-sampled SIF rows are counted as distinct geometries, which contradicts the wording 'unique plate and crack geometries' used throughout §3.1–3.2. Please reconcile the counts and state exactly what is measured: unique geometry configurations, geometry-loading pairs, or SIF rows.
[§3.1.1–3.1.3, Appendix A] The benchmark's value as ground truth rests on FEM accuracy, but the paper provides no validation for its own datasets. Sections 3.1.1–3.1.3 describe 'high-fidelity FEM simulations' (Abaqus/FRANC3D for the surface-crack dataset, hp-FEM from CAStLE for the hole datasets) without mesh-refinement or convergence studies, and without comparison to available analytical or handbook solutions such as Raju-Newman or Fawaz-Andersson, both cited in the paper. Because the datasets are intended to train ML models, any systematic FEM error in a scenario would be inherited by all downstream models. Please add, for each geometry family (or at least one representative case per Appendix Table 3–15), a convergence check and a validation subset against a known solution, reporting maximum and mean relative deviations.
[§3.3, Appendix Tables 16–17] The reported mean NAE values for the TT CC (Countersunk, b/t=0.5) datasets are in the tens to hundreds (e.g., RFR 25.9 under tension, SVR 214.9) while the corresponding relative L2 errors in Table 1 are modest (0.12–0.30). This is likely because some crack-front locations have SIF values near zero, making NAE = |y−ŷ|/|y| ill-conditioned or unbounded. This is not necessarily an arithmetic mistake, but it means mean NAE is not a stable evaluation metric for these sign-changing SIF fields. The paper should state this behavior explicitly, consider reporting median NAE or a thresholded NAE, and advise users of the benchmark accordingly.

minor comments (4)

[Listing 1] The test block in Listing 1 loads SURFACE_CRACK_TEST.csv but then calls rfr.predict(d[:,:-1]), i.e., predictions are made on the training rows rather than the test rows, and no comparison is made to the test labels; line 9 also contains an extra closing parenthesis. The template should be corrected so that users' first-run experience evaluates on held-out data.
[Tables 1, 2, 16, 17; Appendix B] Baseline tables report a single run per model with no standard deviations or repeated seeds, while Appendix B describes random subsampling (e.g., 'randomly selected subset ... capped at 100,000') without a fixed seed. Please provide seeds or repeated-run statistics so the baseline numbers are reproducible.
[Appendix Tables 5 and 13] The entries '1,05' in the a/t and a1/t rows should read '1.05'; the paper should use a single decimal separator throughout.
[§3.1–3.2, §3.3] The paper states that SIF values are sampled at 'a resolution of 0.024 radians' but never reports the number of angular points per crack front. Reporting the number of angle samples per scenario would let readers convert geometry counts into SIF-row counts and better interpret the stated dataset sizes.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: SIFBench is an empirical data benchmark whose SIF values come from external FEM simulations; self-citations appear only as dataset provenance.

full rationale

SIFBench makes no derivation claim that reduces to its inputs. The central object is a collection of SIF values generated by FEM (Abaqus, FRANC3D, and CAStLE hp-FEM meshes), which are external, independently established computational methods; the paper does not fit a parameter and then relabel it as a prediction. The baseline ML results in Tables 1 and 2 are measured against these FEM outputs, so they are empirical evaluations, not circular constructions. The only self-citations (Merrell et al. 2024 for the surface-crack data and Gautam et al. 2025 as motivation) are provenance and background, and they are not load-bearing for the benchmark's scale claim or for any numerical result. The apparent mismatch between the headline "over 5 million" geometries and the sum of per-dataset counts in Sections 3.1 and 3.2 is a consistency and arithmetic defect, but it is not circularity: it does not make any output equal to its input by definition. Accordingly, no circular step can be exhibited by quote, and the paper should be regarded as essentially free of circularity aside from minor self-citation.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No physical entities are invented. The load-bearing input from outside the paper is FEM accuracy and geometric completeness, inherited from simulation pipelines and prior datasets. Free parameters are limited to ML baseline hyperparameters, which affect reference results but not the dataset itself.

free parameters (4)

Random forest max_depth = None
Chosen hyperparameter for RFR baseline; affects reported reference errors only, not the dataset itself.
SVR hyperparameters = scikit-learn defaults (C=1.0, epsilon=0.1, RBF kernel)
Default choices for SVR baseline; no tuning reported.
FNN architecture = 5 hidden layers, 15 neurons each, leaky ReLU
Hand-specified network size for NN baseline; affects reported errors.
FNO architecture = 64 Fourier modes, width 64, 4 spectral layers
Hand-specified operator hyperparameters; affects FNO baseline.

assumptions (4)

domain assumption FEM-computed SIF values in the database are accurate ground truth for the represented geometries.
Sections 3.1 and 3.2 describe data as high-fidelity FEM, but the paper provides no convergence study, mesh-refinement verification, or validation against analytical solutions for these datasets.
domain assumption The dimensionless feature sets (a/c, a/t, c/b, W/R, R/t, phi) uniquely and completely characterize each crack and component configuration.
Section 3.1 uses these ratios as input features; completeness and uniqueness of this representation is assumed for ML generalization.
domain assumption Source databases from CAStLE (Fawaz and Andersson) and Merrell et al. are reliable and were correctly processed.
Sections 3.1.2 through 3.2 inherit FEM results from these sources without independent fidelity checks in this paper.
standard math Linear elastic fracture mechanics provides the correct framework for the SIF values.
Section 2 gives background LEFM equations; this is standard theory and not the main risk.

how reviews work

0 comments

Cite this review

Pith. "Pith review of SIFBench: An Extensive Benchmark for Fatigue Analysis." pith.science (2026). https://pith.science/paper/HDEKHXVL

@misc{pith2026250601173,
  author       = {Pith},
  title        = {Pith review of: SIFBench: An Extensive Benchmark for Fatigue Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HDEKHXVL}},
  note         = {Machine review of arXiv:2506.01173}
}

read the original abstract

Fatigue-induced crack growth is a leading cause of structural failure across critical industries such as aerospace, civil engineering, automotive, and energy. Accurate prediction of stress intensity factors (SIFs) -- the key parameters governing crack propagation in linear elastic fracture mechanics -- is essential for assessing fatigue life and ensuring structural integrity. While machine learning (ML) has shown great promise in SIF prediction, its advancement has been severely limited by the lack of rich, transparent, well-organized, and high-quality datasets. To address this gap, we introduce SIFBench, an open-source, large-scale benchmark database designed to support ML-based SIF prediction. SIFBench contains over 5 million different crack and component geometries derived from high-fidelity finite element simulations across 37 distinct scenarios, and provides a unified Python interface for seamless data access and customization. We report baseline results using a range of popular ML models -- including random forests, support vector machines, feedforward neural networks, and Fourier neural operators -- alongside comprehensive evaluation metrics and template code for model training, validation, and assessment. By offering a standardized and scalable resource, SIFBench substantially lowers the entry barrier and fosters the development and application of ML methods in damage tolerance design and predictive maintenance.

Figures

Figures reproduced from arXiv: 2506.01173 by the authors.

**Figure 1.** Surface crack in a rectangular plate. The first type represents semi-elliptical surface cracks embedded in rectangular plates subjected to Mode I tensile loading Merrell et al. (2024). The SIFs (KI) were extracted from FEM-computed displacement fields using Abaqus2 , in conjunction with the fracture mechanics software FRANC3D (Wawrzynek et al., 2010). The KI values were calculated from the stress fields via the meth… view at source ↗

**Figure 2.** A load of unit 1 acts on the plate with a straight shank-hole. The second geometry type involves corner cracks originating at a straight shank-hole in a plate. Three distinct loading conditions were considered independently: tension, bending, and bearing/pin loading [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Single corner crack from a straight shank-hole in a plate. Shaded is the crack front. Quarter-Elliptical Corner Crack. In the first case, one end of the crack front is at the front of the plate and and the other end is at the hole, forming a quarter-elliptical shape (see Figure 3a). The dataset comprises 28,781 simulations, each representing a unique combination of plate and crack geometries. The geometries are desc… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: A plate with a countersunk hole. The third geometry type involves corner cracks originating from a countersunk hole in a plate. As in Section 3.1.2, FEM results were obtained from the Center for Aircraft Structural Life Extension (CAStLE) at the U.S. Air Force Academ…

**Figure 5.** Figure 5: Single corner crack from a countershank hole in a plate. Shaded is the crack front. at a resolution of 0.024 radians. Detailed statistics for each b/t case are provided in Appendix Tables 6—9. Through-Thickness Corner Crack. In the second configuration, the two ends of…

**Figure 6.** Figure 6: Twin corner cracks from a straight shank-hole in a plate. Shaded are crack fronts. (a) Quarter-Elliptical (b) Through-Thickness [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Twin corner cracks from a countershank hole in a plate. Shaded are the crack fronts. • Normalized Absolute Error (NAE): defined as |yϕ − yˆϕ|/|yϕ|. • Relative L2 Error: a metric used to evaluate the predictive performance on a whole crack. Denote all the ground-truth S…

**Figure 8.** Figure 8: CCDF-NAE. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

When is the combined load identifiable from a stress-intensity profile? A coupled forward-inverse study on SIFBench finite-element data
math.NA 2026-07 conditional novelty 6.0 of 10

For fixed crack geometry, combined tension–bending–bearing load is identifiable from the SIF profile iff the three elementary load profiles are affinely independent; recovery error is controlled by the minimum singula...

Reference graph

Works this paper leans on

35 extracted references · 34 canonical work pages · cited by 1 Pith paper

[1]

and Yamada, K

Albrecht, P. and Yamada, K. (1977). Rapid calculation of stress intensity factors. Journal of the Structural Division , 103(2):377--389

work page 1977
[2]

Aliabadi, M., Rooke, D., and Cartwright, D. (1987). An improved boundary element formulation for calculating stress intensity factors: application to aerospace structures. The Journal of Strain Analysis for Engineering Design , 22(4):203--207

work page 1987
[3]

Anderson, T. L. and Anderson, T. L. (2005). Fracture mechanics: fundamentals and applications . CRC press

work page 2005
[4]

Azizzadenesheli, K., Kovachki, N., Li, Z., Liu-Schiaffini, M., Kossaifi, J., and Anandkumar, A. (2024). Neural operators for accelerating scientific simulations and design. Nature Reviews Physics , 6(5):320--328

work page 2024
[5]

and Suri, M

Babu s ka, I. and Suri, M. (1990). The p-and hp versions of the finite element method, an overview. Computer methods in applied mechanics and engineering , 80(1-3):5--26

work page 1990
[6]

Bathe, K.-J. (2006). Finite element procedures . Klaus-Jurgen Bathe

work page 2006
[7]

Callister Jr, W. D. and Rethwisch, D. G. (2020). Materials science and engineering: an introduction . John wiley & sons

work page 2020
[8]

Courtin, S., Gardin, C., Bezine, G., and Hamouda, H. B. H. (2005). Advantages of the j-integral approach for calculating stress intensity factors when using the commercial finite element software abaqus. Engineering Fracture Mechanics , 72(14):2174--2185

work page 2005

Show all 35 references

[9]

Dehning, P., Thiede, S., Mennenga, M., and Herrmann, C. (2017). Factors influencing the energy intensity of automotive manufacturing plants. Journal of cleaner production , 142:2305--2314

2017
[10]

and Pook, L

Dixon, J. and Pook, L. (1969). Stress intensity factors calculated generally by the finite element technique. Nature , 224(5215):166--167

1969
[11]

and Andersson, B

Fawaz, S. and Andersson, B. (2004). Accurate stress intensity factor solutions for corner cracks at a hole. Engineering Fracture Mechanics , 71(9-10):1235--1254

2004
[12]

M., Settgast, R

Fu, P., Johnson, S. M., Settgast, R. R., and Carrigan, C. R. (2012). Generalized displacement correlation method for estimating stress intensity factors. Engineering Fracture Mechanics , 88:90--107

2012
[13]

Gali \'c , I., C ular, I., Vu c kovi \'c , K., and Tonkovi \'c , Z. (2018). Comparison of sif solutions obtained by xfem and conventional fem for cracks in complex geometries like valve body. Procedia structural integrity , 13:2109--2113

2018
[14]

M., and Lindgren, E

Gautam, T., Hochhalter, J., Zhe, S., Kirby, R. M., and Lindgren, E. (2025). Developing robust stress intensity factor models using fourier-based data analysis to guide machine learning method selection and training. Available at SSRN 5226340

2025
[15]

and Shen, G

Glinka, G. and Shen, G. (1991). Universal features of weight functions for cracks in mode i. Engineering Fracture Mechanics , 40(6):1135--1146

1991
[16]

Han, Q., Wang, Y., Yin, Y., and Wang, D. (2015). Determination of stress intensity factor for mode i fatigue crack based on finite element analysis. Engineering Fracture Mechanics , 138:118--126

2015
[17]

Hou, J., Lv, J., Ricoeur, A., Hu, Y., Zuo, H., Chen, Y., and Li, Q. (2022). The m-integral in fracture and damage mechanics: A review of developments and applications. Engineering Fracture Mechanics , 273:108741

2022
[18]

Irwin, G. R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate

1957
[19]

Launey, M. E. and Ritchie, R. O. (2009). On the fracture toughness of advanced materials. Advanced Materials , 21(20):2103--2110

2009
[20]

Liu, X., Xiao, Q., and Karihaloo, B. L. (2004). Xfem for direct evaluation of mixed mode sifs in homogeneous and bi-materials. International Journal for Numerical Methods in Engineering , 59(8):1103--1118

2004
[21]

M., and Hochhalter, J

Merrell, J., Emery, J., Kirby, R. M., and Hochhalter, J. (2024). Stress intensity factor models using mechanics-guided decomposition and symbolic regression. Engineering Fracture Mechanics , 310:110432

2024
[22]

Mitl \"o hner, J., Neumaier, S., Umbrich, J., and Polleres, A. (2016). Characteristics of open data csv files. In 2016 2nd International Conference on Open and Big Data (OBD) , pages 72--79. IEEE

2016
[23]

Newman, J. C. (2000). Irwin's stress intensity factor--a historical perspective. ASTM special technical publication , 1389:39--53

2000
[24]

and Raju, I

Newman Jr, J. and Raju, I. (1981). An empirical stress-intensity factor equation for the surface crack. Engineering fracture mechanics , 15(1-2):185--192

1981
[25]

Perez, N. (2004). Linear elastic fracture mechanics . Springer

2004
[26]

Pommier, S., Sakae, C., and Murakami, Y. (1999). An empirical stress intensity factor set of equations for a semi-elliptical crack in a semi-infinite body subjected to a polynomial stress distribution. International Journal of Fatigue , 21(3):243--251

1999
[27]

and Newman, J

Raju, I. and Newman, J. (1979). Stress-intensity factors for two symmetric corner cracks. In Fracture Mechanics: Proceedings of the Eleventh National Symposium on Fracture Mechanics: Part I . ASTM International

1979
[28]

Spencer, A. J. M. (2004). Continuum mechanics . Courier Corporation

2004
[29]

Wang, C. H. (1996). Introduction to fracture mechanics . DSTO Aeronautical and Maritime Research Laboratory Melbourne, Australia

1996
[30]

and Lambert, S

Wang, X. and Lambert, S. (1995). Local weight functions for semi-elliptical surface cracks in finite thickness plates. Theoretical and applied fracture mechanics , 23(3):199--208

1995
[31]

Wawrzynek, P., Carter, B., Hwang, C.-Y., and Ingraffea, A. (2010). Advances in simulation of arbitrary 3d crack growth using franc3dv5. Journal of the Computational Structural Engineering Institute of Korea , 23(6):607--613

2010
[32]

Williams, C. K. and Rasmussen, C. E. (2006). Gaussian processes for machine learning , volume 2. MIT press Cambridge, MA

2006
[33]

Xia, B., Ma, Z., Hu, H., Li, Y., and Zhao, W. (2022). A prediction method of stress intensity factor for mode-i crack in coal rock based on deep learning. Theoretical and Applied Fracture Mechanics , 122:103645

2022
[34]

Xu, T., Ding, S., Zhou, H., and Li, G. (2022). Machine learning-based efficient stress intensity factor calculation for aeroengine disk probabilistic risk assessment under polynomial stress fields. Fatigue & Fracture of Engineering Materials & Structures , 45(2):451--465

2022
[35]

Zhang, X., Zhao, T., Liu, Y., Chen, Q., Wang, Z., and Wang, Z. (2023). A data-driven model for predicting the mixed-mode stress intensity factors of a crack in composites. Engineering Fracture Mechanics , page 109385

2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

and Yamada, K

Albrecht, P. and Yamada, K. (1977). Rapid calculation of stress intensity factors. Journal of the Structural Division , 103(2):377--389

work page 1977

[2] [2]

Aliabadi, M., Rooke, D., and Cartwright, D. (1987). An improved boundary element formulation for calculating stress intensity factors: application to aerospace structures. The Journal of Strain Analysis for Engineering Design , 22(4):203--207

work page 1987

[3] [3]

Anderson, T. L. and Anderson, T. L. (2005). Fracture mechanics: fundamentals and applications . CRC press

work page 2005

[4] [4]

Azizzadenesheli, K., Kovachki, N., Li, Z., Liu-Schiaffini, M., Kossaifi, J., and Anandkumar, A. (2024). Neural operators for accelerating scientific simulations and design. Nature Reviews Physics , 6(5):320--328

work page 2024

[5] [5]

and Suri, M

Babu s ka, I. and Suri, M. (1990). The p-and hp versions of the finite element method, an overview. Computer methods in applied mechanics and engineering , 80(1-3):5--26

work page 1990

[6] [6]

Bathe, K.-J. (2006). Finite element procedures . Klaus-Jurgen Bathe

work page 2006

[7] [7]

Callister Jr, W. D. and Rethwisch, D. G. (2020). Materials science and engineering: an introduction . John wiley & sons

work page 2020

[8] [8]

Courtin, S., Gardin, C., Bezine, G., and Hamouda, H. B. H. (2005). Advantages of the j-integral approach for calculating stress intensity factors when using the commercial finite element software abaqus. Engineering Fracture Mechanics , 72(14):2174--2185

work page 2005