×

Phase-field modeling of fracture in high performance concrete during low-cycle fatigue: numerical calibration and experimental validation. (English) Zbl 1507.74416

Summary: The development of an elasto-plastic phase-field model is presented which is able to predict nonlinear behavior of high performance concrete (HPC) during low-cycle fatigue. An elasto-plastic damage model which follows the Drucker-Prager yield criterion is formulated. For the modeling of unsymmetric tension-compression behavior of HPC two different continuous stepwise linearly approximated degradation functions for HPC in tension and in compression are used. The experimental three-point bending tests at low-cycle using notched beams of pure HPC are performed. Load-CMOD (crack mouth opening displacement) curves are plotted using the measured experimental data and residual stiffness-CMOD curves are calculated using these experimental Load-CMOD curves. The data used for the interpolation of degradation functions are calibrated using the experimental results for three-point bending tests. For that purpose the uniaxial tension and uniaxial compression tests and three-point bending beam test for HPC are simulated numerically. The accuracy of the proposed numerical model using the presented integration algorithm is verified by comparing the degradation of stiffness in numerical and experimental results.

MSC:

74R10 Brittle fracture
74E30 Composite and mixture properties
Full Text: DOI

References:

[1] Aïtcin, P. C., High-Performance Concrete (1998), E & FN Spon: E & FN Spon London
[2] High Performance Fiber Reinforced Cement Composites: Proceedings of the International RILEM/ACI Workshop (1992), E & FN Spon: E & FN Spon London
[3] High-Performance Concrete: from Material to Structure (1998), E & FN Spon: E & FN Spon London
[4] Lemaitre, J., A Course on Damage Mechanics (1996), Springer: Springer Berlin, Heidelberg · Zbl 0852.73003
[5] Hsu, T. T.C., Fatigue of plain concrete, ACI J. Proc., 78, 4, 292-305 (1981)
[6] Lubliner, J.; Oliver, J.; Oller, S.; Oñate, E., A plastic-damage model for concrete, Int. J. Solids Struct., 25, 3, 299-326 (1989)
[7] Lee, J.; Fenves, G. L., Plastic-damage model for cyclic loading of concrete structures, ASCE J. Eng. Mech., 124, 892-900 (1998)
[8] Wu, J. Y.; Li, J.; Faria, R., An energy release rate-based plastic-damage model for concrete, Int. J. Solids Struct., 43, 583-612 (2006) · Zbl 1119.74584
[9] Grassl, P.; Jirásek, M., Damage-plastic model for concrete failure, Int. J. Solids Struct., 43, 7166-7196 (2006) · Zbl 1120.74777
[10] Papanikolaou, V. K.; Kappos, A. J., Confinement-sensitive plasticity constitutive model for concrete in triaxial compression, Int. J. Solids Struct., 44, 7021-7048 (2007) · Zbl 1166.74322
[11] Cicekli, U.; Voyiadjis, G. Z.; Abu Al-Rub, R. K., A plasticity and anisotropic damage model for plain concrete, Int. J. Plast., 23, 1874-1900 (2007) · Zbl 1155.74401
[12] Grassl, P.; Xenos, D.; Nyström, U.; Rempling, R.; Gylltoft, K., A damage-plasticity approach to modelling the failure of concrete, Int. J. Solids Struct., 50, 3805-3816 (2013)
[13] Zhang, J.; Li, J., Elastoplastic damage model for concrete based on consistent free energy potential, Sci. China Technol. Sci., 57, 2278-2286 (2014)
[14] Zhou, F.; Cheng, G., A coupled plastic damage model for concrete considering the effect of damage on plastic flow, Math. Probl. Eng., 2015, Article 867979 pp. (2015)
[15] Zhang, J.; Li, J.; Ju, J. W., 3D elastoplastic damage model for concrete based on novel decomposition of stress, Int. J. Solids Struct., 94-95, 125-137 (2016)
[16] Hafezolghorani, M.; Hejazi, F.; Vaghei, R.; Jaafar, M. S.B.; Karimzade, K., Simplified damage plasticity model for concrete, Struct. Eng. Int., 27, 1, 68-78 (2017)
[17] Zhang, J.; Ma, L.; Zhang, Z. X., Elastoplastic damage model for concrete under triaxial compression and reversed cyclic loading, Strength Mater., 50, 5, 724-734 (2018)
[18] Sarikaya, A.; Erkmen, R. E., A plastic-damage model for concrete under compression, Int. J. Mech. Sci., 584-593 (2019)
[19] Griffith, A. A., The phenomenon of rupture and flow in solids, Phil. Trans. R. Soc. A, 163-198 (1921) · Zbl 1454.74137
[20] Irwin, G. R., Fracture, (Flügge, S., Elasticity and Plasticity / Elastizität und Plastizität, Handbuch der Physik / Encyclopedia of Physics (1958), Springer: Springer Berlin, Heidelberg), 551-590 · Zbl 0103.16403
[21] Barenblatt, G. I., The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 55-129 (1962)
[22] Francfort, G. A.; Marigo, J. J., Revisiting brittle fracture as an energy minimisation problem, J. Mech. Phys. Solids, 1319-1342 (1998) · Zbl 0966.74060
[23] Bourdin, B.; Francfort, G. A.; Marigo, J. J., The variational approach to fracture, J. Elasticity, 5-148 (2008) · Zbl 1176.74018
[24] Ambrosio, L.; Tortorelli, V. M., Approximation of functionals depending on jumps by elliptic functionals via \(\gamma \)-convergence, Comm. Pure Appl. Math., 999-1036 (1990) · Zbl 0722.49020
[25] Mumford, D.; Shah, J., Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., 577-685 (1989) · Zbl 0691.49036
[26] Karma, A.; David, A. K.; Levine, H., Phase-field model of mode III dynamic fracture, Phys. Rev. Lett., Article 045502 pp. (2001)
[27] Hakim, V.; Karma, A., Laws of crack motion and phase-field models of fracture, J. Mech. Phys. Solids, 342-368 (2009) · Zbl 1421.74089
[28] Miehe, C.; Hofacker, M.; Welschinger, F., A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Engrg., 2765-2778 (2010) · Zbl 1231.74022
[29] Miehe, C.; Welschinger, F.; Hofacker, M., Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Internat. J. Numer. Methods Engrg., 1273-1311 (2010) · Zbl 1202.74014
[30] Kuhn, K.; Müller, R., A continuum phase field model for fracture, Eng. Fract. Mech., 3625-3634 (2010)
[31] Borden, M. J.; Hughes, T. J.R.; Landis, C. M.; Verhoosel, C. V., A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Comput. Methods Appl. Mech. Engrg., 273, 100-118 (2014) · Zbl 1296.74098
[32] Msekh, M. A.; Sargado, J. M.; Jamshidian, M.; Areias, P. M.; Rabczuk, T., Abaqus implementation of phase-field model for brittle fracture, Comput. Mater. Sci., 96, 472-484 (2015)
[33] Ambati, M.; Gerasimov, T.; De Lorenzis, L., A review on phase-field models of brittle fracture and a new fast hybrid formulation, Comput. Mech., 383-405 (2015) · Zbl 1398.74270
[34] Kästner, M.; Hennig, P.; Linse, T.; Ulbricht, V., Phase-field modelling of damage and fracture-convergence and local mesh refinement, (Naumenko, K.; Aßmus, M., Advanced Methods of Continuum Mechanics for Materials and Structures (2016), Springer Singapore: Springer Singapore Singapore), 307-324
[35] Nguyen, T. T.; Yvonnet, J.; Bornert, M.; Chateau, C.; Sab, K.; Romani, R.; Le Roy, R., On the choice of parameters in the phase field method for simulating crack initiation with experimental validation, Int. J. Fract., 197, 2, 213-226 (2016)
[36] Linse, T.; Hennig, P.; Kästner, M.; de Borst, R., A convergence study of phase-field models for brittle fracture, Eng. Fract. Mech., 184, 307-318 (2017)
[37] Zhang, X.; Vignes, C.; Sloan, S. W.; Sheng, D., Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale, Comput. Mech., 59, 5, 737-752 (2017)
[38] Steinke, C.; Kaliske, M., A phase-field crack model based on directional stress decomposition, Comput. Mech., 63, 5, 1019-1046 (2019) · Zbl 1468.74053
[39] Borden, M. J.; Verhoosel, C. V.; Scott, M. A.; Hughes, T. J. R.; Landis, C. M., A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217-220, 77-95 (2012) · Zbl 1253.74089
[40] Hofacker, M.; Miehe, C., A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns, Internat. J. Numer. Methods Engrg., 93, 3, 276-301 (2013) · Zbl 1352.74022
[41] Schlüter, A.; Willenbücher, A.; Kuhn, C.; Müller, R., Phase field approximation of dynamic brittle fracture, Comput. Mech., 54, 5, 1141-1161 (2014) · Zbl 1311.74106
[42] Liu, G.; Li, Q.; Msekh, M. A.; Zuo, Z., Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model, Comput. Mater. Sci., 121, 35-47 (2016)
[43] Ambati, M.; Gerasimov, T.; De Lorenzis, L., Phase-field modeling of ductile fracture, Comput. Mech., 55, 5, 1017-1040 (2015) · Zbl 1329.74018
[44] Duda, F. P.; Ciarbonetti, A.; Sánchez, P. J.; Huespe, A. E., A phase-field/gradient damage model for brittle fracture in elastic-plastic solids, Int. J. Plast., 65, 269-296 (2015)
[45] Kuhn, C.; Noll, T.; Müller, R., On phase field modeling of ductile fracture, GAMM-Mitt., 39, 1, 35-54 (2016) · Zbl 1397.74027
[46] Miehe, C.; Aldakheel, F.; Raina, A., Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory, Int. J. Plast., 1-32 (2016)
[47] Borden, M. J.; Hughes, T. J.R.; Landis, C. M.; Anvari, A.; Lee, I. J., A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects, Internat. J. Numer. Methods Engrg., 130-166 (2016) · Zbl 1439.74343
[48] Miehe, C.; Teichtmeister, S.; Aldakheel, F., Phase-field modelling of ductile fracture: A variational gradient-extended plasticity-damage theory and its micromorphic regularization, Phil. Trans. R. Soc. A, 374, 2066, Article 20150170 pp. (2016) · Zbl 1353.74065
[49] Aldakheel, F.; Wriggers, P.; Miehe, C., A modified gurson-type plasticity model at finite strains: Formulation, numerical analysis and phase-field coupling, Comput. Mech., 62, 4, 815-833 (2018) · Zbl 1459.74024
[50] Yin, B.; Kaliske, M., A ductile phase-field model based on degrading the fracture toughness: Theory and implementation at small strain, Comput. Methods Appl. Mech. Engrg., 366, Article 113068 pp. (2020) · Zbl 1442.74024
[51] Krüger, M.; Dittmann, M.; Aldakheel, F.; Härtel, A.; Wriggers, P.; Hesch, C., Porous-ductile fracture in thermo-elasto-plastic solids with contact applications, Comput. Mech., 65, 4, 941-966 (2020) · Zbl 1462.74143
[52] Noll, T.; Kuhn, C.; Olesch, D.; Müller, R., 3D phase field simulations of ductile fracture, GAMM-Mitt., 43, 2, Article e202000008 pp. (2020) · Zbl 1541.74089
[53] Alessi, R.; Ambati, M.; Gerasimov, T.; Vidoli, S.; De Lorenzis, L., Comparison of phase-field models of fracture coupled with plasticity, (Oñate, E.; Peric, D.; de Souza Neto, E.; Chiumenti, M., Advances in Computational Plasticity: A Book in Honour of D. Roger J. Owen (2018), Springer International Publishing: Springer International Publishing Cham), 1-21 · Zbl 1493.74006
[54] Choo, J.; Sun, W., Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow, Comput. Methods Appl. Mech. Engrg., 330, 1-32 (2018) · Zbl 1439.74184
[55] Kienle, D.; Aldakheel, F.; Keip, M. A., A finite-strain phase-field approach to ductile failure of frictional materials, Int. J. Solids Struct., 172-173, 147-162 (2019)
[56] Pise, M.; Bluhm, J.; Schröder, J., Elasto-plastic phase-field model of hydraulic fracture in saturated binary porous media, Int. J. Multiscale Comput. Eng., 17, 2, 201-221 (2019), 10.1615/IntJMultCompEng.2019027066
[57] Späth, M.; Herrmann, C.; Prajapati, N.; Schneider, D.; Schwab, F.; Selzer, M.; Nestler, B., Multiphase-field modelling of crack propagation in geological materials and porous media with drucker-prager plasticity, Comput. Geosci., 25, 1, 325-343 (2021) · Zbl 1453.86008
[58] Aldakheel, F., A microscale model for concrete failure in poro-elasto-plastic media, Theor. Appl. Fract. Mech., 107, Article 102517 pp. (2020)
[59] You, T.; Zhu, Q.-Z.; Li, P.-F.; Shao, J.-F., Incorporation of tension-compression asymmetry into plastic damage phase-field modeling of quasi brittle geomaterials, Int. J. Plast., 124, 71-95 (2020)
[60] Alessi, R.; Vidoli, S.; De Lorenzis, L., A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case, Eng. Fract. Mech., 190, 53-73 (2018)
[61] Carrara, P.; Ambati, M.; Alessi, R.; De Lorenzis, L., A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach, Comput. Methods Appl. Mech. Engrg., 361, Article 112731 pp. (2020) · Zbl 1442.74195
[62] Seiler, M.; Linse, T.; Hantschke, P.; Kästner, M., An efficient phase-field model for fatigue fracture in ductile materials, Eng. Fract. Mech., 224, Article 106807 pp. (2020)
[63] Ulloa, J.; Wambacq, J.; Alessi, R.; Degrande, G.; François, S., Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation, Comput. Methods Appl. Mech. Engrg., 373, Article 113473 pp. (2021) · Zbl 1506.74342
[64] Aldakheel, F.; Schreiber, C.; Müller, R.; Wriggers, P., Phase-field modeling of fatigue crack propagation in brittle materials, (Aldakheel, F.; Hudobivnik, B.; Soleimani, M.; Wessels, H.; Weißenfels, C.; Marino, M., Current Trends and Open Problems in Computational Mechanics (2022), Springer International Publishing: Springer International Publishing Cham), 15-22 · Zbl 1516.74091
[65] Schreiber, C.; Kuhn, C.; Müller, R.; Zohdi, T., A phase field modeling approach of cyclic fatigue crack growth, Int. J. Fract., 225, 1, 89-100 (2020)
[66] Yan, S.; Schreiber, C.; Müller, R., An efficient implementation of a phase field model for fatigue crack growth, Int. J. Fract. (2022)
[67] Seleŝ, K.; Aldakheel, F.; Tonković, Z.; Sorić, J.; Wriggers, P., A general phase-field model for fatigue failure in brittle and ductile solids, Comput. Mech., 67, 5, 1431-1452 (2021) · Zbl 1468.74056
[68] Gebuhr, G.; Pise, M.; Sarhil, M.; Anders, S.; Brands, D.; Schröder, J., Analysis and evaluation of single fibre pull-out behaviour of hooked steel fibres embedded in high performance concrete for calibration of numerical models, Struct. Concr., 20, 1, 1254-1264 (2019)
[69] Pise, M.; Brands, D.; Sarhil, M.; Schröder, J.; Gebuhr, G.; Anders, S., Numerical calibration of elasto-plastic phase-field modeling of fracture for experimental pullout tests of single steel fibres embedded in high-performance concrete, (Zingoni, A., Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications: Proceedings of the 7th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2019, Cape Town, South Africa (2019), Taylor & Francis Group: Taylor & Francis Group London), 1391-1396
[70] Storm, J.; Pise, M.; Brands, D.; Schröder, J.; Kaliske, M., A comparative study of micro-mechanical models for fiber pullout behavior of reinforced high performance concrete, Eng. Fract. Mech., 243, Article 107506 pp. (2021)
[71] Drucker, D. C.; Prager, W., Soil mechanics and plastic analysis or limit design, Quart. Appl. Math., 157-165 (1952) · Zbl 0047.43202
[72] Leusmann, T.; Basutkar, G.; Lunardelli, M., Characterizing the 3D mesostructure of high performance concrete with the help of computed tomography, (Gabrijel, I.; Grosse, C.; Skazlic, M., Proceedings of International Conference on Sustainable Materials, Systems and Structures, SMSS 2019 - Novel Methods for Characterization of Materials and Structures, Rovinj, Croatia (2019), RILEM: RILEM Paris, France)
[73] Scheiden, T.; Oneschkow, N., Influence of coarse aggregate type on the damage mechanism in high-strength concrete under compressive fatigue loading, Struct. Concr., 20, 1212-1219 (2019)
[74] Amor, H.; Marigo, J. J.; Maurini, C., Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, J. Mech. Phys. Solids, 1209-1229 (2009) · Zbl 1426.74257
[75] Kuhn, C.; Schlüter, A.; Müller, R., On degradation functions in phase field fracture models, Comput. Mater. Sci., 374-384 (2015)
[76] Benallal, A.; Botta, A. S.; Venturini, W. S., Consolidation of elastic-plastic saturated porous media by the boundary element method, Comput. Methods Appl. Mech. Engrg., 197, 4626-4644 (2008) · Zbl 1194.74496
[77] Kossa, A., Analytical strain solution for the Drucker-Prager elastoplasticity model with linear isotropic hardening, Period. Polytech. Mech. Eng., 56, 1, 27-31 (2012)
[78] Simo, J. C.; Hughes, T. J.R., (Computational Inelasticity. Computational Inelasticity, Interdisciplinary Applied Mathematics (2000), Springer: Springer New York) · Zbl 0934.74003
[79] Ambati, M.; De Lorenzis, L., Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements, Comput. Methods Appl. Mech. Engrg., 351-373 (2016) · Zbl 1439.74338
[80] C̆ermák, M.; Sysala, S.; Valdman, J., Efficient and flexible MATLAB implementation of 2D and 3D elastoplastic problems, Appl. Math. Comput., 355, 595-614 (2019) · Zbl 1428.74043
[81] Gebuhr, G.; Pise, M.; Anders, S.; Brands, D.; Schröder, J., Damage evolution of steel fibre-reinforced high-performance concrete in low-cycle flexural fatigue: Numerical modeling and experimental validation, Materials, 15, 3 (2022)
[82] van Mier, J. G.M.; Shah, S. P.; Arnaud, M.; Balayssac, J. P.; Bascoul, A.; Choi, S.; Dasenbrock, D.; Ferrara, G.; French, C.; Gobbi, M. E.; Karihaloo, B. L.; König, G.; Kotsovos, M. D.; Labuz, J.; Lange-Kornbak, D.; Markeset, G.; Pavlovic, M. N.; Simsch, G.; Thienel, K. C.; Turatsinze, A.; Ulmer, M.; van Geel, H. J.G. M.; van Vliet, M. R.A.; Zissopoulos, D., Strain-softening of concrete in uniaxial compression, Mater. Struct., 30, 4, 195-209 (1997)
[83] fib, Materials, (fib, Fib Model Code for Concrete Structures 2010 (2013), John Wiley & Sons, Ltd), 74-150
[84] Oneschkow, N., Analysis of the Fatigue Behavior of Concrete Based on Strain Development (German Title: aNalyse des ErmÜdungsverhaltens Von Beton Anhand Der Dehnungsentwicklung) (2014), Gottfried Wilhelm Leibniz Universität Hannover, Hannover, Germany, (Ph.D. thesis)
[85] Uebing, S.; Brands, D.; Scheunemann, L.; Schröder, J., Residual stresses in hot bulk formed parts: Two-scale approach for austenite-to-martensite phase transformation, Arch. Appl. Mech., 91, 2, 545-562 (2021)
[86] Pise, M.; Brands, D.; Schröder, J.; Gebuhr, G.; Anders, S., Macroscopic model for steel fiber reinforced high performance concrete based on unit cell calculations, Proc. Appl. Math. Mech., 21, 1, Article e202100180 pp. (2021)
[87] Fang, J.; Wu, C.; Rabczuk, T.; Wu, C.; Sun, G.; Li, Q., Phase field fracture in elasto-plastic solids: A length-scale insensitive model for quasi-brittle materials, Comput. Mech., 66, 4, 931-961 (2020) · Zbl 1464.74158
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.