Skip to main content
SpringerLink
Log in

Fracture analysis of a plane crack problem under chemo-mechanical loading

化学-力学荷载下平面裂纹问题的断裂分析

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model. The flux conductivity is introduced to characterize the influence of the crack defect on the diffusion process. Using Fourier transform and the dislocation density functions, the crack problem is reduced to a set of singular integral equations, which are solved numerically by the Lobatto-Chebyshev method. Parametric studies are conducted to reveal the effects of flux conductivity, geometric configuration, chemical and mechanical loads on the crack tip field. The numerical results show that the stress singularity at the crack tip is usually a mixture of mode I and mode II types.

摘要

基于线性的化学弹性模型, 本文给出了化学-力学荷载下平面裂纹问题的断裂分析. 引入流通系数来描述裂纹缺陷对扩散过程的影响. 利用傅里叶变换和位错密度函数, 裂纹问题被归结为一组奇异积分方程, 采用Lobatto-Chebyshev方法对其进行数值求解. 通过参数研究揭示了流通系数、几何构型、化学和力学载荷对裂纹尖端场的影响. 数值结果表明, 裂纹尖端的应力奇异性通常表现为I型和II型的混合.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. O. Coussy, Poromechanics (John Wiley & Sons, England, 2004).

    MATH  Google Scholar 

  2. S. A. Chester, A constitutive model for coupled fluid permeation and large viscoelastic deformation in polymeric gels, Soft Matter 8, 8223 (2012).

    Article  Google Scholar 

  3. N. Swaminathan, J. Qu, and Y. Sun, An electrochemomechanical theory of defects in ionic solids. Part II. Examples, Philos. Mag. 87, 1723 (2007).

    Article  Google Scholar 

  4. Z. Cui, F. Gao, and J. Qu, A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries, J. Mech. Phys. Solids 60, 1280 (2012).

    Article  MathSciNet  Google Scholar 

  5. S. Cai, and Z. Suo, Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels, J. Mech. Phys. Solids 59, 2259 (2011).

    Article  Google Scholar 

  6. R. Marcombe, S. Cai, W. Hong, X. Zhao, Y. Lapusta, and Z. Suo, A theory of constrained swelling of a pH-sensitive hydrogel, Soft Matter 6, 784 (2010).

    Article  Google Scholar 

  7. J. S. Katz, and J. A. Burdick, Light-responsive biomaterials: development and applications, Macromol. Biosci. 10, 339 (2010).

    Article  Google Scholar 

  8. H. Yang, and J. Qu, Fracture toughness of LixSi alloys in lithium ion battery, Extreme Mech. Lett. 32, 100555 (2019).

    Article  Google Scholar 

  9. L. S. Bennethum, M. A. Murad, and J. H. Cushman, Modified Darcy’s law, Terzaghi’s effective stress principle and Fick’s law for swelling clay soils, Comput. Geotechnics 20, 245 (1997).

    Article  Google Scholar 

  10. M. A. Biot, General theory of three-dimensional consolidation, J. Appl. Phys. 12, 155 (1941).

    Article  Google Scholar 

  11. W. Hong, X. Zhao, J. Zhou, and Z. Suo, A theory of coupled diffusion and large deformation in polymeric gels, J. Mech. Phys. Solids 56, 1779 (2008).

    Article  Google Scholar 

  12. L. Anand, 2014 Drucker medal paper: A derivation of the theory of linear poroelasticity from chemoelasticity, J. Appl. Mech. 82, 111005 (2015).

    Article  Google Scholar 

  13. Q. Yang, Q. Qin, L. Ma, X. Lu, and C. Cui, A theoretical model and finite element formulation for coupled thermo-electro-chemo-mechanical media, Mech. Mater. 42, 148 (2010).

    Article  Google Scholar 

  14. L. Ma, and Q. Yang, in Transient modeling on the coupled chemo-mechanical behaviors of hydrogels in an aqueous environment: Proceedings of SPIE 8409, Third International Conference on Smart Materials and Nanotechnology in Engineering, Shenzhen, 2011.

  15. S. A. Chester, C. V. Di Leo, and L. Anand, A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels, Int. J. Solids Struct. 52, 1 (2015).

    Article  Google Scholar 

  16. P. D. Zarnas, B. L. Boyce, J. Qu, and R. Dingreville, Stress-induced transition from vacancy annihilation to void nucleation near micro-cracks, Int. J. Solids Struct. 213, 103 (2021).

    Article  Google Scholar 

  17. J. Christensen, and J. Newman, Stress generation and fracture in lithium insertion materials, J. Solid State Electrochem. 10, 293 (2006).

    Article  Google Scholar 

  18. H. Haftbaradaran, and J. Qu, Two-dimensional chemo-elasticity under chemical equilibrium, Int. J. Solids Struct. 56–57, 126 (2015).

    Article  Google Scholar 

  19. X. Gao, D. Fang, and J. Qu, A chemo-mechanics framework for elastic solids with surface stress, Proc. R. Soc. A. 471, 20150366 (2015).

    Article  Google Scholar 

  20. P. L. Bishay, J. Sladek, N. Fabry, V. Sladek, and C. Zhang, Perturbation finite element solution for chemo-elastic boundary value problems under chemical equilibrium, Acta Mech. Sin. 35, 981 (2019).

    Article  MathSciNet  Google Scholar 

  21. C. Xu, M. K. Mudunuru, and K. B. Nakshatrala, Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions, Continuum Mech. Thermodyn. 28, 1847 (2016).

    Article  MathSciNet  Google Scholar 

  22. X. Zhang, and Z. Zhong, A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials, Sci. China-Phys. Mech. Astron. 60, 084611 (2017).

    Article  Google Scholar 

  23. X. Zhang, and Z. Zhong, A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction, J. Mech. Phys. Solids 107, 49 (2017).

    Article  MathSciNet  Google Scholar 

  24. Z. Zhong, B. Qin, and J. Chen, A coupled theory for soft materials at finite strain with heat conduction, diffusion and chemical reactions, Comput. Mater. Sci. 188, 110189 (2021).

    Article  Google Scholar 

  25. H. Haftbaradaran, and J. Qu, A path-independent integral for fracture of solids under combined electrochemical and mechanical loadings, J. Mech. Phys. Solids 71, 1 (2014).

    Article  MathSciNet  Google Scholar 

  26. M. Zhang, J. Qu, and J. R. Rice, Path independent integrals in equilibrium electro-chemo-elasticity, J. Mech. Phys. Solids 107, 525 (2017).

    Article  MathSciNet  Google Scholar 

  27. N. Bouklas, and R. Huang, Swelling kinetics of polymer gels: comparison of linear and nonlinear theories, Soft Matter 8, 8194 (2012).

    Article  Google Scholar 

  28. Y. Yu, C. M. Landis, and R. Huang, Poroelastic effects on steady state crack growth in polymer gels under plane stress, Mech. Mater. 143, 103320 (2020).

    Article  Google Scholar 

  29. Y. Lee, and F. Erdogan, Interface cracking of FGM coatings under steady-state heat flow, Eng. Fract. Mech. 59, 361 (1998).

    Article  Google Scholar 

  30. Y. D. Li, and K. Y. Lee, Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions, Int. J. Fract. 165, 47 (2010).

    Article  Google Scholar 

  31. F. Erdogan, G. D. Gupta, and T. Cook, Numerical solution of singular integral equations. In: G. C. Sih, ed. Methods of Analysis and Solutions of Crack Problems (Noordhoff International Publishing, Leyden, 1973), pp. 368–425.

    Chapter  Google Scholar 

  32. W. K. Binienda, and S. M. Arnold, Driving force analysis in an infinite anisotropic plate with multiple crack interactions, Int. J. Fract. 71, 213 (1995).

    Article  Google Scholar 

  33. I. Laresgoiti, S. Käbitz, M. Ecker, and D. U. Sauer, Modeling mechanical degradation in lithium ion batteries during cycling: Solid electrolyte interphase fracture, J. Power Sources 300, 112 (2015).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Juntao Shi  (时俊涛) & Zheng Zhong  (仲政)

  2. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Zheng Zhong  (仲政)

Authors
  1. Juntao Shi  (时俊涛)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Zhong  (仲政)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng Zhong  (仲政).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11932005 and 11772106).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, J., Zhong, Z. Fracture analysis of a plane crack problem under chemo-mechanical loading. Acta Mech. Sin. 38, 421439 (2022). https://doi.org/10.1007/s10409-022-21439-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-022-21439-2

Keywords

Search

Navigation