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An incremental elastic-plastic cohesive constitutive model with considering damage

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Abstract

The interface has a significant influence on the macroscopic mechanical behaviors of composite materials, with interface cracking being a typical failure event. The ability to precisely describe the mechanical behavior of the interface is critical for analyzing the failure of composite materials. Based on plasticity theory and damage mechanics, an elastic-plastic interface constitutive model is developed to simulate the irreversible plastic deformation at the interface under the cyclic loading condition. Furthermore, by incorporating a damage factor in scalar form, the model is able to simulate mixed loading forms (Modes I and II). The influence of interfacial strength and toughness on the overall mechanical properties of unidirectional fiber reinforced composites under transverse loading is studied with this model. The simulation results are consistent with the experimental data in the literature, demonstrating the model’s effectiveness. The model can be used to simulate the mechanical behavior of composites with interfaces under cyclic loading, and it is helpful for understanding the plastic behavior and damage accumulation at the interfaces in the composites.

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References

  1. Tan W, Martínez-Pañeda E. Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites. Compos Sci Tech, 2021, 202: 108539

    Article  Google Scholar 

  2. Yang L, Yan Y, Liu Y J, et al. Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression. Compos Sci Tech, 2012, 72: 1818–1825

    Article  Google Scholar 

  3. Guo F L, Huang P, Li Y Q, et al. Multiscale modeling of mechanical behaviors of carbon fiber reinforced epoxy composites subjected to hygrothermal aging. Compos Struct, 2021, 256: 113098

    Article  Google Scholar 

  4. Sharma A, Daggumati S. Computational micromechanical modeling of transverse tensile damage behavior in unidirectional glass fiber-reinforced plastic composite plies: Ductile versus brittle fracture mechanics approach. Int J Damage Mech, 2020, 29: 943–964

    Article  Google Scholar 

  5. González C, LLorca J. Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling. Compos Sci Tech, 2007, 67: 2795–2806

    Article  Google Scholar 

  6. Sepasdar R, Shakiba M. Micromechanical study of multiple transverse cracking in cross-ply fiber-reinforced composite laminates. Compos Struct, 2022, 281: 114986

    Article  Google Scholar 

  7. Barenblatt G I. The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech, 1962, 7: 55–129

    Article  MathSciNet  Google Scholar 

  8. Dugdale D S. Yielding of steel sheets containing slits. J Mech Phys Solids, 1960, 8: 100–104

    Article  Google Scholar 

  9. Yin S H, Gong Y, Li W C, et al. A novel four-linear cohesive law for the delamination simulation in composite DCB laminates. Compos Part B-Eng, 2020, 180: 107526

    Article  Google Scholar 

  10. Lu Z X, Xu Q. Cohesive zone modeling for viscoplastic behavior at finite deformations. Compos Sci Tech, 2013, 74: 173–178

    Article  Google Scholar 

  11. Xu Q, Tao W M, Qu S X, et al. A cohesive zone model for the elevated temperature interfacial debonding and frictional sliding behavior. Compos Sci Tech, 2015, 110: 45–52

    Article  Google Scholar 

  12. Sun S Y, Chen H R. The interfacial fracture behavior of foam core composite sandwich structures by a viscoelastic cohesive model. Sci China-Phys Mech Astron, 2011, 54: 1481–1487

    Article  Google Scholar 

  13. Li H, Chandra N. Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. Int J Plast, 2003, 19: 849–882

    Article  MATH  Google Scholar 

  14. Kolluri M, Hoefnagels J P M, Dommelen J A W, et al. A practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment. Int J Fract, 2013, 183: 1–18

    Article  Google Scholar 

  15. Sarrado C, Turon A, Costa J, et al. An experimental analysis of the fracture behavior of composite bonded joints in terms of cohesive laws. Compos Part A-Appl Sci Manuf, 2016, 90: 234–242

    Article  Google Scholar 

  16. Kolluri M, Hoefnagels J P M, Dommelen J A W, et al. Irreversible mixed mode interface delamination using a combined damage-plasticity cohesive zone enabling unloading. Int J Fract, 2014, 185: 77–95

    Article  Google Scholar 

  17. Meng L, Tabiei A. An irreversible bilinear cohesive law considering the effects of strain rate and plastic strain and enabling reciprocating load. Eng Fract Mech, 2021, 252: 107855

    Article  Google Scholar 

  18. Turon A, Camanho P P, Costa J, et al. A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech Mater, 2006, 38: 1072–1089

    Article  Google Scholar 

  19. ASTM. Standard Test Method for Mixed Mode I-Mode II Interlaminar Fracture Toughness of Unidirectional Fiber Reinforced Polymer Matrix Composites. West Conshohocken: American Society for Testing and Materials, 2019. D6671/D6671M-19

    Google Scholar 

  20. ASTM. Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites. West Conshohocken: American Society for Testing and Materials, 2013. D5528-13

    Google Scholar 

  21. ASTM. Standard Test Method for Determination of the Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites. West Conshohocken: American Society for Testing and Materials, 2014. D7905/D7905M-14

    Google Scholar 

  22. Kenane M, Benzeggagh M L. Mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites under fatigue loading. Compos Sci Tech, 1997, 57: 597–605

    Article  Google Scholar 

  23. Nguyen N H T, Bui H H, Nguyen G D, et al. A cohesive damage-plasticity model for DEM and its application for numerical investigation of soft rock fracture properties. Int J Plast, 2017, 98: 175–196

    Article  Google Scholar 

  24. Hashin Z, Rotem A. A fatigue failure criterion for fiber reinforced materials. J Compos Mater, 1973, 7: 448–464

    Article  Google Scholar 

  25. Ye L. Role of matrix resin in delamination onset and growth in composite laminates. Compos Sci Tech, 1988, 33: 257–277

    Article  Google Scholar 

  26. Fan X L, Xu R, Zhang W X, et al. Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system. Appl Surf Sci, 2012, 258: 9816–9823

    Article  Google Scholar 

  27. Greco F, Leonetti L, Lonetti P. A two-scale failure analysis of composite materials in presence of fiber/matrix crack initiation and propagation. Composite Struct, 2013, 95: 582–597

    Article  Google Scholar 

  28. Callaway E B, Christodoulou P G, Zok F W. Deformation, rupture and sliding of fiber coatings in ceramic composites. J Mech Phys Solids, 2019, 132: 103673

    Article  MathSciNet  Google Scholar 

  29. Kolluri M, Hoefnagels J P M, van Dommelen J A W, et al. An improved miniature mixed-mode delamination setup for in situ microscopic interface failure analyses. J Phys D, 2011, 44: 34005

    Article  Google Scholar 

  30. van den Bosch M J, Schreurs P J G, Geers M G D. An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion. Eng Fract Mech, 2006, 73: 1220–1234

    Article  Google Scholar 

  31. Kolluri M. An in-situ experimental-numerical approach for interface delamination characterization. Dissertation for the Doctoral Degree. Netherlands: Eindhoven University of Technology, 2011. 91–92

    Google Scholar 

  32. Lu Z X, Xia B, Yang Z Y. Investigation on the tensile properties of three-dimensional full five-directional braided composites. Comput Mater Sci, 2013, 77: 445–455

    Article  Google Scholar 

  33. Naya F, Gonzalez C, Lopes C S, et al. Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects. Compos Part A-Appl Sci Manuf, 2017, 92: 146–157

    Article  Google Scholar 

  34. Kaddour A S, Hinton M J. Input data for test cases used in benchmarking triaxial failure theories ofcomposites. J Compos Mater, 2012, 46: 2295–2312

    Article  Google Scholar 

  35. Asp L E, Berglund L A, Talreja R. A criterion for crack initiation in glassy polymers subjected to a composite-like stress state. Compos Sci Tech, 1996, 56: 1291–1301

    Article  Google Scholar 

  36. Jordan J L, Foley J R, Siviour C R. Mechanical properties of Epon 826/DEA epoxy. Mech Time-Depend Mater, 2008, 12: 249–272

    Article  Google Scholar 

  37. Fiedler B, Hojo M, Ochiai S, et al. Failure behavior of an epoxy matrix under different kinds of static loading. Compos Sci Tech, 2001, 61: 1615–1624

    Article  Google Scholar 

  38. Kaddour A S, Hinton M J, Smith P A, et al. Mechanical properties and details of composite laminates for the test cases used in the third world-wide failure exercise. J Compos Mater, 2013, 47: 2427–2442

    Article  Google Scholar 

  39. Paris F, Correa E, Mantič V. Kinking of transversal interface cracks between fiber and matrix. J Appl Mech, 2007, 74: 703–716

    Article  Google Scholar 

  40. Romanowicz M. Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics. Int J Solids Struct, 2014, 51: 2549–2556

    Article  Google Scholar 

  41. Hui X Y, Xu Y J, Zhang W H. An integrated modeling of the curing process and transverse tensile damage of unidirectional CFRP composites. Composite Struct, 2021, 263: 113681

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University (BUAA), Beijing, 100083, China

    Tong Xia, YiXing Qian, ShengYao Xu, ZhenYu Yang & ZiXing Lu

  2. Aircraft & Propulsion Laboratory, Ningbo Institute of Technology (NIT), Beihang University (BUAA), Ningbo, 315832, China

    ZhenYu Yang

Authors
  1. Tong Xia
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  2. YiXing Qian
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  3. ShengYao Xu
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  5. ZiXing Lu
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Corresponding author

Correspondence to ZhenYu Yang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11972057, 12272021, and 11972058), the National Science and Technology Major Project (Grant No. 2017-VII-0003-0096). The support from Super Computing Center ScGrid/CNGrid of CAS was also gratefully acknowledged.

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Xia, T., Qian, Y., Xu, S. et al. An incremental elastic-plastic cohesive constitutive model with considering damage. Sci. China Technol. Sci. 66, 3651–3662 (2023). https://doi.org/10.1007/s11431-022-2314-3

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  • DOI: https://doi.org/10.1007/s11431-022-2314-3

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