Dynamic stress intensity factor analysis of the interaction between multiple impact-loaded cracks in infinite domains

A.-V. Phan; A.-V. Phan

doi:10.3934/matersci.2016.4.1683

AIMS Materials Science

2016, Volume 3, Issue 4: 1683-1695. doi: 10.3934/matersci.2016.4.1683

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Dynamic stress intensity factor analysis of the interaction between multiple impact-loaded cracks in infinite domains

A.-V. Phan ^,

Department of Mechanical Engineering, University of South Alabama, 307 N. University Blvd, Mobile, AL 36688, USA

Received: 23 August 2016 Accepted: 15 November 2016 Published: 29 November 2016

In this work, the dynamic interaction between multiple cracks whose surfaces are symmetrically impact-loaded in infinite domains is investigated. Toward this end, the symmetric-Galerkin boundary element method (SGBEM) for 2-D elastodynamics in the Laplace-space frequency (LaplaceSGBEM) was employed to compute the dynamic stress intensity factors (DSIFs) for the cracks during their interaction under dynamic loading conditions. Three examples of multi-crack dynamic interaction were considered. The Laplace-SGBEM results show that the DSIFs will reach their maximum value after the cracks are loaded. It is followed by a damped-like oscillation of the DSIFs about their corresponding static value. In addition, as the cracks approach each other, the dynamic stress field in the vicinity of their crack tips interacts which results in an increase or decrease of the maximum DSIFs.
- symmetric-Galerkin boundary element method; Laplace domain; dynamic stress intensity factors; multi-crack dynamic interaction
Citation: A.-V. Phan. Dynamic stress intensity factor analysis of the interaction between multiple impact-loaded cracks in infinite domains[J]. AIMS Materials Science, 2016, 3(4): 1683-1695. doi: 10.3934/matersci.2016.4.1683

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Abstract

In this work, the dynamic interaction between multiple cracks whose surfaces are symmetrically impact-loaded in infinite domains is investigated. Toward this end, the symmetric-Galerkin boundary element method (SGBEM) for 2-D elastodynamics in the Laplace-space frequency (LaplaceSGBEM) was employed to compute the dynamic stress intensity factors (DSIFs) for the cracks during their interaction under dynamic loading conditions. Three examples of multi-crack dynamic interaction were considered. The Laplace-SGBEM results show that the DSIFs will reach their maximum value after the cracks are loaded. It is followed by a damped-like oscillation of the DSIFs about their corresponding static value. In addition, as the cracks approach each other, the dynamic stress field in the vicinity of their crack tips interacts which results in an increase or decrease of the maximum DSIFs.

References

[1]	Trinh QT, Mouhoubi S, Chazallon C, et al. (2015) Solving multizone and multicrack elastostatic problems: A fast multipole symmetric Galerkin boundary element method approach. Eng Anal Bound Elem 50: 486–495.
[2]	Guo Z, Liu Y, Mac H, et al. (2014) A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements. Eng Anal Bound Elem 47: 1–9.
[3]	Grytsenko T, Galybin AN (2010) Numerical analysis of multi-crack large-scale plane problems with adaptive cross approximation and hierarchical matrices. Eng Anal Bound Elem 34: 501–510.
[4]	Wang XM, Gao S, Shen YP (1996) Interaction between an interface and cracks. Eng Fract Mech 53: 107–117.
[5]	Jiang ZD, Zeghloul A, Bezine G, et al. (1990) Stress intensity factors of parallel cracks in ﬁnite width sheet. Eng Fract Mech 35: 1073–1079.
[6]	Wu KC, Hou YL, Huang SM (2015) Transient analysis of multiple parallel cracks under anti-plane dynamic loading. Mech Mater 81: 56–61.
[7]	Monfared MM, Ayatollahi M (2013) Dynamic stress intensity factors of multiple cracks in an orthotropic strip with FGM coating. Eng Fract Mech 109: 45–57.
[8]	Ang WT, Athanasius L (2011) Dynamic interaction of multiple arbitrarily oriented planar cracks in a piezoelectric space: A semi-analytic solution. Eur J Mech A-Solids 30: 608–618.
[9]	Wu KC, Chen JC (2011) Transient analysis of collinear cracks under anti-plane dynamic loading. Procedia Eng 10: 924–929.
[10]	Itou S (2016) Transient dynamic stress intensity factors around three stacked parallel cracks in an inﬁnite medium during passage of an impact normal stress. Int J Solids Struct 78–79: 199–204.
[11]	Itou S (2016) Dynamic stress intensity factors for three parallel cracks in an inﬁnite plate subject to harmonic stress waves. Engineering 2: 485–495.
[12]	Dong L, Atluri SN (2013) Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 1: 2D Structures. Comp Model Eng Sci 90: 91–146.
[13]	Dong L, Atluri SN (2013) Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 2: 3D Solids. Comp Model Eng Sci 90: 379–413.
[14]	Sutradhar A, Paulino GH, Gray LJ (2008) Symmetric Galerkin Boundary Element Method, Berlin: Springer-Verlag.
[15]	Chirino F, Dominguez J (1989) Dynamic analysis of cracks using boundary element method. Eng Fract Mech 34: 1051–1061.
[16]	Gray LJ (1991) Evaluation of hypersingular integrals in the boundary element method. Math Comp Model 15: 165–174.
[17]	Gray LJ, Phan AV, Paulino GH, et al. (2003) Improved quarter-point crack tip element. Eng Fract Mech 70: 269–283.
[18]	Fedeli´nski P, Aliabadi MH, Rooke DP (1995) A single-region time domain BEM for dynamic crack problems. Int J Solids Struct 32: 3555–3571.
[19]	Ebrahimi S, Phan AV (2013) Dynamic analysis of cracks using the SGBEM for elastodynamics in the Laplace-space frequency domain. Eng Anal Bound Elem 37: 1378–1391.
[20]	Phan AV, Gray LJ, Salvadori A (2010) Transient analysis of the dynamic stress intensity factors using SGBEM for frequency-domain elastodynamics. Comp Method Appl M 199: 3039–3050.
[21]	Aliabadi MH (2002) The Boundary Element Method – Volume 2: Applications in Solids and Structures, England: John Wiley & Sons.
[22]	Phan AV, Napier JAL, Gray LJ, et al. (2003) Symmetric-Galerkin BEM simulation of fracture with frictional contact. Int J Numer Meth Eng 57: 835–851.
[23]	Henshell RD, Shaw KG (1975) Crack tip ﬁnite elements are unnecessary. Int J Numer Meth Eng 9: 495–507.
[24]	Barsoum RS (1976) On the use of isoparametric ﬁnite elements in linear fracture mechanics. Int J Numer Meth Eng 10: 25–37.
[25]	Blandford GE, Ingraﬀea AR, Liggett JA (1981) Two-dimensional stress intensity factor computations using the boundary element method. Int J Numer Meth Eng 17: 387–404.
[26]	Banks-Sills L (1991) Application of the ﬁnite element method to linear elastic fracture mechanics. Appl Mech Rev 44: 447–461.
[27]	Gray LJ, Paulino GH (1998) Crack tip interpolation, revisited. SIAM J Appl Math 58: 428–455.
[28]	Costabel M, Dauge M, Duduchava R (2003) Asymptotics Without Logarithmic Terms for Crack Problems. Commun Part Diﬀ Eq 28: 869–926.
[29]	Phan AV, Gray LJ, Kaplan T (2007) On some benchmarch results for the interaction of a crack with a circular inclusion. ASME J Appl Mech 74: 1282–1284.
[30]	Durbin F (1974) Numerical inversion of Laplace transforms: an eﬃcient improvement to Dubner and Abate’s method. Comp J 17: 371–376.

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