Skip to main content
SpringerLink
Log in

Transient Behavior of Multiple Interface Cracks in Two Non-Homogeneous Half-Layers

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In this paper, the analytical solution of two dissimilar orthotropic functionally graded half-layers with interface Volterra-type screw dislocation under anti-plane transient loading is studied using linear elasticity theory. The energy loss is displayed by viscous damping, and the rate of gradual alteration of elastic stiffness, damping constant and mass density of two dissimilar non-homogeneous half-layers are modeled with exponential law. In the first stage, a single dislocation, Laplace and Fourier transform are applied to obtain the stress components with simple Cauchy kernel in the interface of the layers. Then, by means of the image method, the stress fields are derived in the interface of two half-layers. The dynamic stress intensity factors (DSIFs) are calculated in time domain by using numerical Laplace inversion and the distributed dislocation technique. Eventually, various examples are reported to demonstrate the effects of the crack length, cracks location, geometrical parameters, material specifications, viscous damping and the interaction of cracks on the DSIFs.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

\(A_{1} (\zeta ,s),A_{2} (\zeta ,s),A_{3} (\zeta ,s),A_{4} (\zeta ,s)\) :

Unknown coefficients

b mz :

Burger vector

B mzj :

Dislocation density

c :

Wave slowness

g :

Ratio of shear moduli

gmzj (q,t):

Regular terms of dislocation density

h 1 :

Thickness of lower half-layer

h 2 :

Thickness of upper half-layer

H(x):

Heaviside step function

K(t)Li :

Mode-III stress intensity factor of left side of crack

K(t)Ri :

Mode-III stress intensity factor of right side of crack

K 0 :

Mode-III stress intensity factor of a crack in infinite plane

\(\bar{K}_{ij} (q,p,s)\) :

Kernels of integral equations in Laplace domain

l :

Half-lengths of crack

N :

Total number of cracks

s :

Laplace variable

w :

Out-of-plane displacement component

xi(q),yi(q):

Functions describing the geometry of cracks

\(\lambda_{1} ,\lambda_{2}\) :

FGM exponent of the half-layers

\(\mu_{x} (y),\mu_{y} (y)\) :

Shear modules in the x- and y-directions

\(\gamma (y)\) :

Viscous damping coefficient per unit volume

\(\rho (y)\) :

Mass density

\(\sigma_{zx} ,\sigma_{zy}\) :

Out-of-plane stress components

\(\zeta\) :

Fourier variable

References

  • Afshar H, Bagheri R (2018) Several embedded cracks in a functionally graded piezoelectric strip under dynamic loading. Comput Math Appl 76:534–550

    Article  MathSciNet  Google Scholar 

  • Bagheri R (2017) Several horizontal cracks in a piezoelectric half-plane under transient loading. Arch Appl Mech 87:1979–1992

    Article  Google Scholar 

  • Bagheri R, Mirzaei AM (2017) Fracture analysis in an imperfect FGM orthotropic strip bonded between two magneto-electro-elastic layers. Iran J Sci Technol Trans Mech Eng. https://doi.org/10.1007/s40997-017-0129-6

    Article  Google Scholar 

  • Bagheri R, Ayatollahi M, Mousavi SM (2015) Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating. Int J Mech Sci 93:93–101

    Article  Google Scholar 

  • Cohen AM (2007) Numerical methods for Laplace transform inversion. Springer, Berlin

    MATH  Google Scholar 

  • Erdogan F, Gupta GD, Cook TS (1973) Numerical solution of singular integral equations. In: Sih GC (ed) Methods of analysis and solutions of crack problems. Mechanics of fracture, vol 1. Springer, The Netherlands, pp 368–425

    Chapter  Google Scholar 

  • Ershad H, Bagheri R, Noroozi M (2018) Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method. Math Mech Solids 23:1–12

    Article  MathSciNet  Google Scholar 

  • Haghiri H, Fotuhi AR, Shafiei AR (2015) Elastodynamic analysis of mode III multiple cracks in a functionally graded orthotropic half-plane. Theor Appl Fract Mech 80:155–169

    Article  Google Scholar 

  • Hills DA, Kelly PA, Dai DN, Korsunsky AM (1996) Solution of crack problems: the distributed dislocation technique. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Itou S (2007) Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load. Acta Mech 192:89–110

    Article  Google Scholar 

  • Li YD, Wei T, Hongcai Z (2006) Anti-plane transient fracture analysis of the functionally gradient elastic bi-material weak/infinitesimal-discontinuous interface. Int J Fract 142:163–171

    MATH  Google Scholar 

  • Li YD, Lee KY, Dai Y (2008) Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface. Eur J Mech A/Solids 27:808–823

    Article  MathSciNet  Google Scholar 

  • Liu P, Yu T, Bui TQ, Zhang C (2013) Transient dynamic crack analysis in non-homogeneous functionally graded piezoelectric materials by the X-FEM. Comput Mater Sci 69:542–558

    Article  Google Scholar 

  • Liu P, Yu T, Bui TQ, Zhang C, Xu Y, Lim CW (2014) Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method. Int J Solids Struct 51:2167–2182

    Article  Google Scholar 

  • Shi M, Wu H, Li L, Chai G (2014) Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique. Int J Mech Mater Des 10:65–77

    Article  Google Scholar 

  • Shul CW, Lee KY (2001) Dynamic response of subsurface interface crack in multi-layered orthotropic half-space under anti-plane shear impact loading. Int J Solids Struct 38:3563–3574

    Article  Google Scholar 

  • Vafa JP, Baghestani AM, Fariborz SJ (2015) Transient screw dislocation in exponentially graded FG layers. Arch Appl Mech 85:1–11

    Article  Google Scholar 

  • Weertman J (1996) Dislocation based fracture mechanics. World Scientific Publishing Co., Singapore

    Book  Google Scholar 

  • Wei PJ, Zhang SY, Wu YL, Li R (2000) Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading. Int J Fract 105:127–136

    Article  Google Scholar 

  • Wu H, Li L, Chai G, Song F, Kitamura T (2016) Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading. J Therm Stress 39:371–385

    Article  Google Scholar 

  • Yu H, Wu L, Guo L, Wu H, Du Sh (2010a) An interaction integral method for 3D curved cracks in nonhomogeneous materials with complex interfaces. Int J Solids Struct 47:2178–2189

    Article  Google Scholar 

  • Yu H, Wu L, Guo L, He Q, Du Sh (2010b) Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials. Mech Mater 42:435–450

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Mechatronics Faculty, Karaj Branch, Islamic Azad University, Karaj, Alborz, Iran

    R. Bagheri

Authors
  1. R. Bagheri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Bagheri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bagheri, R. Transient Behavior of Multiple Interface Cracks in Two Non-Homogeneous Half-Layers. Iran J Sci Technol Trans Mech Eng 44, 619–629 (2020). https://doi.org/10.1007/s40997-019-00292-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-019-00292-1

Keywords

Search

Navigation