Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T05:50:16.624Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Crack Propagation Algorithm Combined with the Finite Element Method

Published online by Cambridge University Press:  01 April 2020

L.D.C. Ramalho Open the ORCID record for L.D.C. Ramalho [Opens in a new window] ,
J. Belinha  and
R.D.S.G. Campilho
L.D.C. Ramalho
Affiliation:
INEGI, Institute of Mechanical Engineering, Porto, Portugal
J. Belinha*
Affiliation:
School of Engineering, Polytechnic of Porto, ISEP-IPP, Porto, Portugal
R.D.S.G. Campilho
Affiliation:
School of Engineering, Polytechnic of Porto, ISEP-IPP, Porto, Portugal
*
*Corresponding author ([email protected])
Get access

Abstract

The prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.

Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.

Keywords

Crack propagationFractureFEMRemeshing
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 4 , August 2020 , pp. 405 - 422
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kuna, M., Finite Elements in Fracture Mechanics, Dordrecht, Springer, (2013)CrossRefGoogle Scholar
Clough, R., “The stress distribution of Norfork Dam,” Berkeley, (1962)Google Scholar
Bouchard, P. O., Bay, F., Chastel, Y. and Tovena, I., “Crack propagation modelling using an advanced remeshing technique,” Computer Methods in Applied Mechanics and Engineering, 189(3), pp. 723–42, (2000)CrossRefGoogle Scholar
Dhondt, G., “Cutting of a 3-D finite element mesh for automatic mode I crack propagation calculations,” International Journal for Numerical Methods in Engineering, 42(4), pp. 749–72, (1998)3.0.CO;2-F>CrossRefGoogle Scholar
Colombo, D. and Giglio, M., “A methodology for automatic crack propagation modelling in planar and shell FE models,” Engineering Fracture Mechanics, 73(4), pp. 490–504, (2006)CrossRefGoogle Scholar
Henshell, R. D. and Shaw, K. G., “Crack tip finite elements are unnecessary,” International Journal for Numerical Methods in Engineering, 9(3), pp. 495–507, (1975)CrossRefGoogle Scholar
Soghrati, S., Xiao, F. and Nagarajan, A., “A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems,” Computational Mechanics, 59(4), pp. 667–84, (2017)CrossRefGoogle Scholar
Park, K., Paulino, G. H., Celes, W. and Espinha, R., “Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture,” International Journal for Numerical Methods in Engineering, 92(1), pp. 1–35, (2012)CrossRefGoogle Scholar
Moës, N., Dolbow, J. and Belytschko, T., “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, 46(1), pp. 131–50, (1999)3.0.CO;2-J>CrossRefGoogle Scholar
Areias, P. M. A. and Belytschko, T., “Analysis of three-dimensional crack initiation and propagation using the extended finite element method,” International Journal for Numerical Methods in Engineering, 63(5), pp. 760–88, (2005)CrossRefGoogle Scholar
Chin, E. B., Lasserre, J. B. and Sukumar, N., “Modeling crack discontinuities without element-partitioning in the extended finite element method,” International Journal for Numerical Methods in Engineering, 110(11), pp. 1021–48, (2017)CrossRefGoogle Scholar
Sutula, D., Kerfriden, P., van Dam, T. and Bordas, S. P. A., “Minimum energy multiple crack propagation. Part I: Theory and state of the art review,” Engineering Fracture Mechanics, 191, pp. 205–24, (2018)Google Scholar
Sutula, D., Kerfriden, P., van Dam, T. and Bordas, S. P. A., “Minimum energy multiple crack propagation. Part-II: Discrete solution with XFEM,” Engineering Fracture Mechanics, 191(September 2017), pp. 225–56, (2018)Google Scholar
Sutula, D., Kerfriden, P., van Dam, T. and Bordas, S. P. A., “Minimum energy multiple crack propagation. Part III: XFEM computer implementation and applications,” Engineering Fracture Mechanics, 191, pp. 257–76, (2018)Google Scholar
Chen, L. et al., “Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth,” Computer Methods in Applied Mechanics and Engineering, 209–212, pp. 250–65, (2012)CrossRefGoogle Scholar
Peng, X., Kulasegaram, S., Wu, S. C. and Bordas, S. P. A., “An extended finite element method (XFEM) for linear elastic fracture with smooth nodal stress,” Computers and Structures, 179, pp. 48–63, (2017)CrossRefGoogle Scholar
Prange, C., Loehnert, S. and Wriggers, P., “Error estimation for crack simulations using the XFEM,” International Journal for Numerical Methods in Engineering, 91(13), pp. 1459–74, (2012)CrossRefGoogle Scholar
Bordas, S., Duflot, M. and Le, P., “A simple error estimator for extended finite elements,” Communications in Numerical Methods in Engineering, 24(11), pp. 961–71, (2008)CrossRefGoogle Scholar
Duflot, M. and Bordas, S., “A posteriori error estimation for extended finite elements by an extended global recovery,” International Journal for Numerical Methods in Engineering, 76(8), pp. 1123–38, (2008)CrossRefGoogle Scholar
González-Estrada, O. A. et al., “Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method,” Computers and Structures, 152, pp. 1–10, (2015)CrossRefGoogle Scholar
Ródenas, J. J., González-Estrada, O. A., Tarancón, J. E. and Fuenmayor, F. J., “A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting,” International Journal for Numerical Methods in Engineering, 76(4), pp. 545–71, (2008)CrossRefGoogle Scholar
Ródenas, J. J., González-Estrada, O. A., Fuenmayor, F. J. and Chinesta, F., “Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM,” Computational Mechanics, 52(2), pp. 321–44, (2013)CrossRefGoogle Scholar
Jin, Y., González-Estrada, O. A., Pierard, O. and Bordas, S. P. A., “Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation,” Computer Methods in Applied Mechanics and Engineering, 318, pp. 319–48, (2017)CrossRefGoogle Scholar
Wu, J.-Y. et al., Phase field modelling of fracture, Vol. 53, Advances in Applied Mechanics., (2018 Jul 8)Google Scholar
Miehe, C., Welschinger, F. and Hofacker, M., “Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations,” International Journal for Numerical Methods in Engineering, 83(10), pp. 1273–311, (2010)CrossRefGoogle Scholar
Miehe, C., Hofacker, M. and Welschinger, F., “A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits,” Computer Methods in Applied Mechanics and Engineering, 199(45–48), pp. 2765–78, (2010)CrossRefGoogle Scholar
Zhou, S., Zhuang, X., Zhu, H. and Rabczuk, T., “Phase field modelling of crack propagation, branching and coalescence in rocks,” Theoretical and Applied Fracture Mechanics, 96(May), pp. 174–92, (2018)CrossRefGoogle Scholar
Rabczuk, T., Zi, G., Bordas, S. and Nguyen-Xuan, H., “A simple and robust three-dimensional cracking-particle method without enrichment,” Computer Methods in Applied Mechanics and Engineering, 199(37–40), pp. 2437–55, (2010)CrossRefGoogle Scholar
Bordas, S., Rabczuk, T. and Zi, G., “Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment,” Engineering Fracture Mechanics, 75(5), pp. 943–60, (2008)CrossRefGoogle Scholar
Rabczuk, T., Bordas, S. and Zi, G., “On three-dimensional modelling of crack growth using partition of unity methods,” Computers and Structures, 88(23–24), pp. 1391–411, (2010)CrossRefGoogle Scholar
Rabczuk, T., Bordas, S. and Zi, G., “A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics,” Computational Mechanics, 40(3), pp. 473–95, (2007)CrossRefGoogle Scholar
Peng, X., Atroshchenko, E., Kerfriden, P. and Bordas, S. P. A., “Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment,” International Journal of Fracture, 204(1), pp. 55–78, (2017)CrossRefGoogle Scholar
Peng, X., Atroshchenko, E., Kerfriden, P. and Bordas, S. P. A., “Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth,” Computer Methods in Applied Mechanics and Engineering, 316, pp. 151–85, (2017)CrossRefGoogle Scholar
Beer, G. et al., “Boundary element analysis with trimmed nurbs and a generalized IGA approach,” 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, (June), pp. 2445–56, (2014)Google Scholar
Marussig, B., Zechner, J., Beer, G. and Fries, T. P., “Fast isogeometric boundary element method based on independent field approximation,” Computer Methods in Applied Mechanics and Engineering, 284, pp. 458–88, (2015)CrossRefGoogle Scholar
Azevedo, J. M. C., “Fracture mechanics using the Natural Neighbour Radial Point Interpolation Method,”, Faculdade de Engenharia da Universidade do Porto, (2013)Google Scholar
Belinha, J., Azevedo, J. M. C., Dinis, L. M. J. S. and Natal Jorge, R. M., “The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study,” International Journal of Computational Methods, 14(04), pp. 1750045, (2017)CrossRefGoogle Scholar
Natarajan, S. and Song, C., “Representation of singular fields without asymptotic enrichment in the extended finite element method,” International Journal for Numerical Methods in Engineering, 96(13), pp. 813–41, (2013)CrossRefGoogle Scholar
Yang, Z. J., Wang, X. F., Yin, D. S. and Zhang, C., “A non-matching finite element-scaled boundary finite element coupled method for linear elastic crack propagation modelling,” Computers and Structures, 153, pp. 126–36, (2015)CrossRefGoogle Scholar
Kachanov, M., “Elastic Solids with Many Cracks and Related Problems,” In, Hutchinson JW, Wu TYBT-A in AM, editors. Advances in Applied Mechanics, Elsevier, p. 259–445, (1993)Google Scholar
Salimi-Majd, D., Shahabi, F. and Mohammadi, B., “Effective local stress intensity factor criterion for prediction of crack growth trajectory under mixed mode fracture conditions,” Theoretical and Applied Fracture Mechanics, 85, pp. 207–16, (2016)CrossRefGoogle Scholar
Mirsayar, M. M., “Mixed mode fracture analysis using extended maximum tangential strain criterion,” Materials & Design, 86, pp. 941–7, (2015)CrossRefGoogle Scholar
Griffith;, A. A. and Eng, M., “VI. The phenomena of rupture and flow in solids,” Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character, 221(582–593), pp. 163 LP – 198, (1920 Jan 1)Google Scholar
Hussain, M. A., Pu, S. L. and Underwood, J., “Strain energy release rate for a crack under combined mode I and mode II,” In, Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II, (1974)Google Scholar
Sih, G. C., “Strain-energy-density factor applied to mixed mode crack problems,” International Journal of Fracture, 10(3), pp. 305–21, (1974)CrossRefGoogle Scholar
Irwin, G. R., “Analysis of stresses and strains near the end of a crack traversing a plate,” Journal of Applied Mechanics, 24(September), pp. 351–69, (1957)Google Scholar
Chan, S. K., Tuba, I. S. and Wilson, W. K., “On the finite element method in linear fracture mechanics,” Engineering Fracture Mechanics, 2(1), pp. 1–17, (1970)CrossRefGoogle Scholar
Rice, J. R., “A path independent integral and the approximate analysis of strain concentration by notches and cracks,” Journal of Applied Mechanics, 35(2), pp. 379, (1968)CrossRefGoogle Scholar
Rybicki, E. F. and Kanninen, M. F., “A finite element calculation of stress intensity factors by a modified crack closure integral,” Engineering Fracture Mechanics, 9(4), pp. 931–8, (1977)CrossRefGoogle Scholar
Banks-Sills, L., “Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Applied Mechanics Reviews, 44(10), pp. 447–61, (1991)CrossRefGoogle Scholar
Banks-Sills, L., “Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Applied Mechanics Reviews, 63(2), pp. 020803, (2010)CrossRefGoogle Scholar
Krueger, R., “Virtual crack closure technique: History, approach, and applications,” Applied Mechanics Reviews, 57(2), pp. 109, (2004)CrossRefGoogle Scholar
Erdogan, F. and Sih, G. C., “On the Crack Extension in Plates Under Plane Loading and Transverse Shear,” Journal of Basic Engineering, 85(4), pp. 519, (1963)CrossRefGoogle Scholar
Bouchard, P. O., Bay, F. and Chastel, Y., “Numerical modelling of crack propagation: Automatic remeshing and comparison of different criteria,” Computer Methods in Applied Mechanics and Engineering, 192(35–36), pp. 3887–908, (2003)CrossRefGoogle Scholar
Kaung Jain, Chang, “On the maximum strain criterion-a new approach to the angled crack problem,” Engineering Fracture Mechanics, 14(1), pp. 107–24, (1981)CrossRefGoogle Scholar
Rooke, D. P. and Cartwright, D. J., Compendium of stress intensity factors, , Procurement Executive, Ministry of Defence. H. M. S. O., (1976)Google Scholar
Budiansky, B. and Rice, J. R., “Conservation Laws and Energy-Release Rates,” Journal of Applied Mechanics, 40(1), pp. 201–3, (1973)CrossRefGoogle Scholar
Azevedo, J. M. C., Belinha, J., Dinis, L. M. J. S. and Natal Jorge, R. M., “Crack path prediction using the natural neighbour radial point interpolation method,” Engineering Analysis with Boundary Elements, 59, pp. 144–58, (2015)CrossRefGoogle Scholar
Rao, B. N. and Rahman, S., “A coupled meshless-finite element method for fracture analysis of cracks,” International Journal of Pressure Vessels and Piping, 78(9), pp. 647–57, (2001)CrossRefGoogle Scholar
Geniaut, S. and Galenne, E., “A simple method for crack growth in mixed mode with X-FEM,” International Journal of Solids and Structures, 49(15–16), pp. 2094–106, (2012)CrossRefGoogle Scholar
Bittencourt, T. N., Wawrzynek, P. A., Ingraffea, A. R. and Sousa, J. L., “Quasi-automatic simulation of crack propagation for 2D lefm problems,” Engineering Fracture Mechanics, 55(2), pp. 321–34, (1996)CrossRefGoogle Scholar
Ventura, G., Xu, J. X. and Belytschko, T., “A vector level set method and new discontinuity approximations for crack growth by EFG,” International Journal for Numerical Methods in Engineering, 54(6), pp. 923–44, (2002)CrossRefGoogle Scholar
Ingraffea, A. R. and Grigoriu, M., “Probabilistic Fracture Mechanics: A Validation of Predictive Capability,” DTIC Document., (1990)Google Scholar
Suo, Z. and Hutchinson, J. W., “Interface crack between two elastic layers,” International Journal of Fracture, 43(1), pp. 1–18, (1990)CrossRefGoogle Scholar
Mirsayar, M. M., “On fracture of kinked interface cracks - The role of T-stress,” Materials and Design, 61, pp. 117–23, (2014).CrossRefGoogle Scholar