Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-29T11:29:30.525Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculation of Stress Intensity Factor using Displacement Extrapolation Method in Peridynamic Framework

Published online by Cambridge University Press:  17 January 2020

N. Zhu Open the ORCID record for N. Zhu [Opens in a new window]  and
E. Oterkus
N. Zhu*
Affiliation:
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, UK
E. Oterkus
Affiliation:
Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, UK
*
*Corresponding author ([email protected])
Get access

Abstract

This paper introduces a new approach to calculate stress intensity factors based on a combination of Displacement Extrapolation Method and Peridynamic Theory. After obtaining the displacement field from Peridynamic Theory, by appropriately selecting nodes at the crack tip region and their displacements yield stress intensity factors at the crack tips. To demonstrate the capability of the proposed approach, three different benchmark problems are considered including plate with a central crack, plate with an edge crack and plate with a slanted crack. Results evaluated from the current approach are compared against analytical and finite element analysis results, and good agreement is obtained between three different approaches. This shows that coupled Displacement Extrapolation Method and Peridynamic Theory approach can be an alternative method to calculate stress intensity factors.

Keywords

Stress Intensity FactorPeridynamicsDisplacement Extrapolation Method.
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 2 , April 2020 , pp. 235 - 243
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

REFERENCES

Irwin, G. R., “Analysis of stresses and strains near the end of a crack traversing a plate,” Journal of Applied Mechanics, (1957).Google Scholar
Schijve, J., “Stress Intensity Factors of Cracks,” in Fatigue of Structures and Materials, Dordrecht: Springer Netherlands, (2009), pp. 105–140.CrossRefGoogle Scholar
Rooke, D. P. and Cartwright, D. J., “Compendium of stress intensity factors,” Procurement Executive, Ministry of Defence. H. M. S. O., p. 330, (1976).Google Scholar
Liu, M., Gan, Y., Hanaor, D. A., Liu, B. and Chen, C., “An improved semi-analytical solution for stress at round-tip notches,” Engineering Fracture Mechanics, 149, pp. 134–143, (2015).CrossRefGoogle Scholar
Sih, G. C., Paris, P. C. and Erdogan, F., “Crack-tip, stress-intensity factors for plane extension and plate bending problems,” Journal of Applied Mechanics, 29, no. 2, pp. 306–312, (1962).CrossRefGoogle Scholar
Kishimoto, K., Aoki, S. and Sakata, M., “Simple formula for dynamic stress intensity factor of pre-cracked Charpy specimen,” Engineering Fracture Mechanics, 13, no. 3, pp. 501–508, (1980).CrossRefGoogle Scholar
Xiao, Z. M. and Chen, B. J., “Stress intensity factor for a Griffith crack interacting with a coated inclusion,” International Journal of Fracture, 108, no. 3, pp. 193–205, (2001).CrossRefGoogle Scholar
Blandford, G. E., Ingraffea, A. R. and Liggett, J. A., “Two-dimensional stress intensity factor computations using the boundary element method,” International Journal for Numerical Methods in Engineering, 17, no. 3, pp. 387–404, (1981).CrossRefGoogle Scholar
Shih, C. F., de Lorenzi, H. G. and German, M. D., “Crack extension modeling with singular quadratic isoparametric elements,” International Journal of Fracture, 12, no. 4, pp. 647–651, (1976).CrossRefGoogle Scholar
Barsoum, R. S., “On the use of isoparametric finite elements in linear fracture mechanics,” International Journal for Numerical Methods in Engineering, 10, no. 1, pp. 25–37, (1976).CrossRefGoogle Scholar
Ingraffea, A. R., “On discrete fracture propagation in rock loaded in compression,” in Proceedings, First International Conference on Numerical Methods in Fracture Mechanics, pp. 235–248, (1978),.Google Scholar
Petroski, H. J. and Achenbach, J. D., “Computation of the weight function from a stress intensity factor,” Engineering Fracture Mechanics, 10, no. 2, pp. 257–266, (1978).CrossRefGoogle Scholar
Guinea, G. V., Pastor, J. Y., Planas, J. and Elices, M., “Stress intensity factor, compliance and CMOD for a general three-point-bend beam,” International Journal of Fracture, 89, no. 2, pp. 103–116, (1998).CrossRefGoogle Scholar
Paris, P. C., “The Mechanics of Fracture Propagation and Solutions to Fracture Arrester Problem,” in “Document D2-2195,” The Boeing Company, (1957).Google Scholar
Lim, I. L., Johnston, I. W. and Choi, S. K., “Comparison between various displacement-based stress intensity factor computation techniques,” International Journal of Fracture, 58, no. 3, pp. 193–210, (1992).CrossRefGoogle Scholar
Lazzarin, P. and Tovo, R., “A notch intensity factor approach to the stress analysis of welds,” Fatigue & Fracture of Engineering Materials & Structures, 21, no. 9, pp. 1089–1103, (1998).CrossRefGoogle Scholar
Gross, B. and Mendelson, A., “Plane elastostatic analysis of V-notched plates,” International Journal of Fracture Mechanics, 8, no. 3, pp. 267–276, (1972).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, no. 4, pp. 931–938, (1977).CrossRefGoogle Scholar
Dominguez, J. and Gallego, R., “Time domain boundary element method for dynamic stress intensity factor computations,” International Journal for Numerical Methods in Engineering, 33, no. 3, pp. 635–647, (1992).CrossRefGoogle Scholar
Martínez, J. and Domínguez, J., “On the use of quarter-point boundary elements for stress intensity factor computations,” International Journal for Numerical Methods in Engineering, 20, no. 10, pp. 1941–1950, (1984).CrossRefGoogle Scholar
Zhu, Z., Wang, L., Mohanty, B. and Huang, C., “Stress intensity factor for a cracked specimen under compression,” Engineering Fracture Mechanics, 73, no. 4, pp. 482–489, (2006).CrossRefGoogle Scholar
Chen, Y. M., “Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method (the HEMP code),” Engineering Fracture Mechanics, 7, no. 4, pp. 653–660, (1975).CrossRefGoogle Scholar
Nagashima, T., Omoto, Y. and Tani, S., “Stress intensity factor analysis of interface cracks using X-FEM,” International Journal for Numerical Methods in Engineering, 56, no. 8, pp. 1151–1173, (2003).CrossRefGoogle Scholar
Parks, D. M., “A stiffness derivative finite element technique for determination of crack tip stress intensity factors,” International Journal of fracture, 10, no. 4, pp. 487–502, (1974).CrossRefGoogle Scholar
Miyazaki, N., Ikeda, T., Soda, T. and Munakata, T., “Stress intensity factor analysis of interface crack using boundary element method—application of contour-integral method,” Engineering Fracture Mechanics, 45, no. 5, pp. 599–610, (1993).CrossRefGoogle Scholar
Imachi, M., Tanaka, S. and Bui, T. Q., “Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics,” Theoretical and Applied Fracture Mechanics, 93, pp. 97–104, (2018).CrossRefGoogle Scholar
Hu, W., Ha, Y. D., Bobaru, F. and Silling, S. A., “The formulation and computation of the nonlocal J-integral in bond-based peridynamics,” International Journal of Fracture, 176, no. 2, pp. 195–206, (2012).CrossRefGoogle Scholar
Panchadhara, R. and Gordon, P. A., “Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation,” International Journal of Fracture, 201, no. 1, pp. 81–96, (2016).CrossRefGoogle Scholar
Stenström, C. and Eriksson, K., “The J-contour integral in peridynamics via displacements,” International Journal of Fracture, 216(2), pp.173–183, (2019).CrossRefGoogle Scholar
Paris, P. C. and Sih, G. C., “Stress analysis of cracks,” in Fracture toughness testing and its applications: ASTM International, pp. 30–81, (1965).CrossRefGoogle Scholar
Madenci, E. and Oterkus, E., Peridynamic Theory and Its Applications. New York: Springer, (2014).CrossRefGoogle Scholar
Oterkus, S., Madenci, E. and Oterkus, E., “Fully coupled poroelastic peridynamic formulation for fluid-filled fractures,” Engineering Geology, 225, pp. 19–28, (2017).CrossRefGoogle Scholar
De Meo, D., Zhu, N. and Oterkus, E., “Peridynamic modelling of granular fracture in polycrystalline materials,” Journal of Engineering Materials and Technology, 138, no. 4, 041008, (2016).CrossRefGoogle Scholar
Oterkus, E., Guven, I. and Madenci, E., “Impact damage assessment by using peridynamic theory,” Open Engineering, 2, no. 4, pp. 523–531, (2012).CrossRefGoogle Scholar
Galadima, Y., Oterkus, E. and Oterkus, S., “Two-dimensional implementation of the coarsening method for linear peridynamics,” AIMS Materials Science, 6, no. 2, pp. 252–275, (2019).CrossRefGoogle Scholar
Basoglu, M. F., Zerin, Z., Kefal, A. and Oterkus, E., “A computational model of peridynamic theory for deflecting behavior of crack propagation with micro-cracks,” Computational Materials Science, 162, pp. 33–46, (2019).CrossRefGoogle Scholar
Javili, A., Morasata, R., Oterkus, E. and Oterkus, S., “Peridynamics review,” Mathematics and Mechanics of Solids, 1081286518803411, (2018).Google Scholar
Gao, Y. and Oterkus, S., “Ordinary state-based peridynamic modelling for fully coupled thermoelastic problems,” Continuum Mechanics and Thermodynamics, pp. 1–31, (2018).Google Scholar
Madenci, E. and Oterkus, S., “Ordinary state-based peridynamics for thermoviscoelastic deformation,” Engineering Fracture Mechanics, 175, pp. 31–45, (2017).CrossRefGoogle Scholar
Gao, Y. and Oterkus, S., “Fully coupled thermomechanical analysis of laminated composites by using ordinary state based peridynamic theory,” Composite Structures, 207, pp. 397–424, (2019).CrossRefGoogle Scholar
Oterkus, S. and Madenci, E., “Fully coupled thermomechanical analysis of fiber reinforced composites using peridynamics,” 55th AIAA/ASME/ASCE/AHS/SC Structures, Structural Dynamics, and Materials Conference-SciTech Forum and Exposition 2014, National Harbor, Maryland, USA (January 13-17, 2014).CrossRefGoogle Scholar
Oterkus, E. and Madenci, E., “Peridynamics for failure prediction in composites,” 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, USA (April 23-26, 2012).CrossRefGoogle Scholar
Silling, S. A., “Reformulation of elasticity theory for discontinuities and long-range forces,” Journal of the Mechanics and Physics of Solids, 48, no. 1, pp. 175–209, (2000).CrossRefGoogle Scholar
Silling, S. A. and Askari, E., “A meshfree method based on the peridynamic model of solid mechanics,” Computers & Structures, 83, no. 17-18, pp. 1526–1535, (2005).CrossRefGoogle Scholar
Seleson, P. and Parks, M., “On the role of the influence function in the peridynamic theory,” International Journal of Multiscale Computational Engineering, 9, no. 6, pp. 689–706, (2011).CrossRefGoogle Scholar
Macek, R. W. and Silling, S. A., “Peridynamics via finite element analysis,” Finite Element in Analysis and Design, 43, pp. 1169–1178, (2007).CrossRefGoogle Scholar