Abstract
It is generally accepted that the cohesive zone model is a common and highly effective method for simulating interlaminar damage in multilayer materials or structures. However, difficulties are encountered in identifying the interfacial parameters of the cohesive zone model, since it is time-consuming and expensive to experimentally obtain these parameters. Especially, some engineering materials or components under real engineering conditions cannot be measured directly. In this paper, based on the bilinear traction–separation relation of coupled mixed-mode cohesive law, a machine learning-based approach is constructed to identify the cohesive interfacial parameters by using the general regression neural network. No separate measurements are required, and seven independent interfacial parameters in mixed-mode fracture problems can be conveniently determined through machine learning-based analysis. In this case, only an experimental force–displacement curve is needed. A numerical example under a mixed-mode displacement load is considered to validate the proposed method. The results show that this machine learning-based approach provides an effective and general pathway to identify the interfacial parameters under mixed-mode fracture.
Similar content being viewed by others
References
Rodriguez-Garcia, V., Herraez, M., Martinez, V., de Villoria, R.G.: Interlaminar and translaminar fracture toughness of automated manufactured bio-inspired CFRP laminates. Compos. Sci. Technol. 219, 109236 (2022)
Lu, S.Z., Dong, H.J., Yu, H.L.: Interlaminar damage assessment method of CFRP laminate based on synchrosqueezed wavelet transform and ensemble principal component analysis. Compos. Struct. 276, 114584 (2021)
Mohammed, Y., Hassan, Mohamed K., Abu El-Ainin, H., Hashem, A.M.: Size effect analysis of open-hole glass fiber composite laminate using two-parameter cohesive laws. Acta Mech. 226, 1027–1044 (2015)
Mei, H.X., Pang, Y.Y., Huang, R.: Influence of interfacial delamination on channel cracking of elastic thin films. Int. J. Fract. 148(4), 331–342 (2007)
Beom, H.G., Jang, H.S., Zhuo, X.R.: Debonding of the interface between a thin film and an orthotropic substrate. Eng. Fract. Mech. 124, 217–233 (2014)
Fang, C., Guo, X., Weng, G.J., Li, J.H., Chen, G.: Simulation of ductile fracture of zirconium alloys based on triaxiality dependent cohesive zone model. Acta Mech. 232, 3723–3736 (2021)
Zhu, M., Wang, Y., Wang, C., Chen, F., Liu, Y.: An improved analytical model for inversely determining multiple interfacial parameters from single fiber micro-Raman and fragmentation tests. Compos. Sci. Technol. 214, 108983 (2021)
Shindo, Y., Narita, F., Sato, T.: Analysis of mode II interlaminar fracture and damage behavior in end notched flexure testing of GFRP woven laminates at cryogenic temperatures. Acta Mech. 187, 231–240 (2006)
Dhanesh, N., Kapuria, S., Achary, G.G.S.: Accurate prediction of three-dimensional free edge stress field in composite laminates using mixed-field multiterm extended Kantorovich method. Acta Mech. 228, 2895–2919 (2017)
Comninou, M.: The interface crack. J. Appl. Mech. 44, 631–636 (1977)
Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8(2), 100–104 (1960)
Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129 (1962)
Zhao, G.H., Zhong, J.J., Feng, C., Liang, Z.: Simulation of ultra-low cycle fatigue cracking of coiled tubing steel based on cohesive zone model. Eng. Fract. Mech. 235, 107201 (2020)
Long, H., Liang, L., Wei, Y.: Failure characterization of solid structures based on an equivalence of cohesive zone model. Int. J. Solids. Struct. 163, 194–210 (2019)
Fan, M., Xiao, Z.M., Luo, J.: Application of cohesive zone model in crack propagation analysis in multiphase composite materials. Mech. Adv. Mater. Struct. 24(13), 1109–1115 (2017)
Irwin, G.R.: In: Fracture Dynamics. Fracturing of Metals, ASM Publication, 147–166 (1948)
Xu, X.P., Needleman, A.: Void nucleation by inclusion debonding in a crystal matrix. Model. Simul. Mater. Sci. Eng. 1(2), 111–132 (1993)
Xu, X.P., Needleman, A.: Numerical simulation of fast crack growth in brittle solids. J. Mech. Phys. Solids 42(9), 1397–1434 (1994)
Xu, X.P., Needleman, A.: Analysis of ductile crack growth by means of a cohesive damage model. Int. J. Fract. 81(2), 99–112 (1995)
Mi, Y., Crisfield, M.A., Davies, G.A.O., Hellweg, H.B.: Progressive delamination using interface elements. J. Compos. Mater. 32(4), 1246–1272 (1998)
Guo, X., Chang, K., Chen, L.Q., Zhou. M.: Determination of fracture toughness of AZ31 Mg alloy using the cohesive finite element method. Eng. Fract. Mech. 96(1), 401–415 (2012)
Guo, X., Weng, G.J., Soh, A.K.: Ductility enhancement of layered stainless steel with nanograined interface layers. Comput. Mater. Sci. 55(3), 350–355 (2012)
Tvergaard, V., Hutchinson, J.W.: The relation between crack growth resistance and fracture process parameters in elasticplastic solids. J. Mech. Phys. Solids 40(6), 1377–1397 (1992)
Camacho, G.T., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids. Struct. 33(20–22), 2899–2938 (1996)
Needleman, A.: A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54(3), 525–531 (1987)
Cornec, A., Scheider, I., Schwalbe, K.H.: On the practical application of the cohesive model. Eng. Fract. Mech. 70(14), 1963–1987 (2003)
Li, S., Thouless, M.D., Waas, A.M., Schroeder, J.A., Zavattieri, P.D.: Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite. Compos. Sci. Technol. 65(3–4), 537–549 (2005)
Ramantani, D.A., de Moura, M.F.S.F., Campilho, R.D.S.G., Marques, A.T.: Fracture characterization of sandwich structures interfaces under mode I loading. Compos. Sci. Technol. 70(9), 1386–1394 (2010)
Liu, C., et al.: Mode II fracture toughness related to ply angle for composite delamination analysis. Mech. Adv. Mater. Struct. 28(23), 2417–2428 (2020)
Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. ASTM International (2007)
Reeder, J.R., Demarco, K., Whitley, K.S: The use of doubler reinforcement in delamination toughness testing. Compos. Part A 35(11), 1337–1344 (2004)
Sorensen, B.F., Goutianos, S., Jacobsen, T.K.: Strength scaling of adhesive joints in polymer-matrix composites. Int. J. Solids Struct. 46(3–4), 741–761 (2009)
Vorel, J., Kabele, P.: Inverse analysis of traction-separation relationship based on sequentially linear approach. Comput. Struct. 212(2), 125–136 (2019)
Dreysse, H., Demangeat, C.: Theoretical approaches of magnetism of transition-metal thin films and nanostructures on semi-infinite substrate. Surf. Sci. Rep. 28(34), 65–122 (1997)
Camanho, P.P., Davila, C.G., de Moura, M.F.: Numerical simulation of mixed-mode progressive delamination in composite materials. J. Compos. Mater. 37, 1415–1438 (2003)
Alfredsson, K.S., Högberg, J.L.: Energy release rate and mode-mixity of adhesive joint specimens. Int. J. Fract. 144(4), 267–283 (2007)
Zhou, Q.C., Ju, Y.T., Wei, Z., Han, B., Zhou, C.S.: Cohesive zone modeling of propellant and insulation interface debonding. J. Adhesion 90(3), 230–251 (2014)
Wang, J., Kang, Y.L., Qin, Q.H., Fu, D.H., Li, X.Q.: Identification of time-dependent interfacial mechanical properties of adhesive by hybrid/inverse method. Comput. Mater. Sci. 43(4), 1160–1164 (2008)
Dourado, N., de Moura, M.F.S.F., de Morais, A.B., Pereira, A.B.: Bilinear approximations to the mode II delamination cohesive law using an inverse method. Mech. Mater. 49, 42–50 (2012)
Su, M., Peng, H., Yuan, M., Li, S.F.: Identification of the interfacial cohesive law parameters of FRP strips externally bonded to concrete using machine learning techniques. Eng. Fract. Mech. 247, 107643 (2021)
Sadeghi, F., Yu, Y., Zhu, X.Q., Li, J.C.: Damage identification of steel-concrete composite beams based on modal strain energy changes through general regression neutral network. Eng. Struct. 244, 112824 (2021)
Specht, D.F.: A general regression neural network. IEEE Trans. Neural Netw. 2(6), 568–576 (1991)
Krajcinovic, D., Fonseka, G.U.: The continuous damage theory of brittle materials. J. Appl. Mech. 48, 809–815 (1981)
Ungsuwarungsri, T., Knauss, W.G.: The role of damage-softened material behaviour in the fracture of composites and adhesives. Int. J. Fract. 35, 221–241 (1987)
Cui, W., Wisnom, M.R., Jones, M.: A comparison of failure criteria to predict delamination of unidirectional glass/epoxy specimens waisted through the thickness. Composites 23(3), 158–166 (1992)
Mohammadi, S., Owen, D.R.J., Peric, D.: A combined finite/discrete element algorithm for delamination analysis of composites. Finite Elem. Anal. Des. 28, 321–336 (1998)
Ding, S., Chang, X.H., Wu, Q.H.: A study on approximation performances of general regression neural network. In: Machinery Electronics and Control Engineering III, editor Li, J.F. 441, 713–716 (2014)
Huang, L.N., Nan, J.C.: Researches on GRNN neural network in RF nonlinear systems modeling. In: 2011 International Conference on Computational Problem-Solving, 21–23 Oct. 577–580. Chengdu, China (2011)
Chang, H.Y., Wen, C.H., Pan, W.T.: Prediction of the return of common fund through general regression neural network. J. Stat. Manag. Syst. 13(3), 627–637 (2010)
Mei, A.K.C.: Applying the general regression neural network to forecast stock closing price. J. Stat. Manag. Syst. 13(3), 639–649 (2010)
Tomandl, D., Schober, A.: A modified general regression neural network (MGRNN) with new, efficient training algorithms as a robust ’black box’-tool for data analysis. Neural Netw. 14(8), 1023–1034 (2001)
Chtioui, Y., Panigrahi, S., Francl, L.: A generalized regression neural network and its application for leaf wetness prediction to forecast plant disease. Chemom. Intell. Lab. Syst. 48(1), 47–58 (1999)
Bengio, Y., Grandvalet, Y.: No unbiased estimator of the variance of k-fold cross-validation. J. Mach. Learn. Res. 5, 1089–1105 (2004)
Bednarz, P.: Finite element simulation of stress evolution in thermal barrier coating systems. Aachen, Forschungszentrum Julich GmbH (2006)
Li, Y., Deng, H.X., Yu, Y.H.: Evaluation of interfacial properties of sisal fiber reinforced high density polyethylene (HDPE) composites. Advances in Composite Materials and Structures in Key Eng. Mater. 334–335(PTS1-2), 625–628 (2007)
Fan, M., Yi, D.K., Xiao, Z.M.: Elastic-plastic stress investigation for an arc-shaped interface crack in composite material. Int. J. Mech. Sci. 83, 104–111 (2014)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 12002256, 11772245), the Fundamental Research Funds for the Central Universities in China (No. xjh012020014), and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2020JQ-011), the Exploration Program-Q of Natural Science Foundation in Zhejiang (Program No. LQ20A020010), the Natural Science Foundation of Jiangsu (No: BK20200246), and funded by China Postdoctoral Science Foundation (No. 2020M673374). The author Qun Li gratefully acknowledges the support of the K.C. Wong Education Foundation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Junling, H., Xuan, L. & Qun, L. Application of general regression neural network in identifying interfacial parameters under mixed-mode fracture. Acta Mech 233, 3909–3921 (2022). https://doi.org/10.1007/s00707-022-03296-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-022-03296-2