Top

Journal of Elasticity

Published in:

01-02-2015

On the Influence of Adhesive Stress-Separation Laws on Elastic Stress Singularities

Author: G. B. Sinclair

Published in: Journal of Elasticity | Issue 2/2015

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The stresses occurring at the vertices of two elastic wedges joined together on a common planar interface are considered. The wedges are under the action of in-plane tension and shear, as well as antiplane shear loading. When the wedges are joined with perfectly bonded conditions, stress singularities abound. When, instead, the wedges are joined with adhesive stress-separation laws, asymptotic analysis then shows that, with appropriate care in the implementation of these laws, erstwhile singular configurations can be rendered nonsingular.

previous article On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation

next article Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Strictly \(k'_{\tau}\) depends on whether r is in \(\boldsymbol{\mathcal{R}}_{1}\) or \(\boldsymbol{\mathcal{R}}_{2}\): Because the associated terms in stresses are always of higher order than the dominant terms, we simplify results by ignoring this distinction.

When ϕ ₁=ϕ ₂ as here, singularity exponents are independent of μ ₁/μ ₂ because the asymptotics are insensitive as to what μ _i is assigned to which ϕ _i.

Despite τ _rθ not being equal on θ=0 to τ _rθ on θ=±π/2, equilibrium is still satisfied for a small element containing r=0 by virtue of infinite gradients in normal stresses there (see Reissner [42]).

Absent such reductions, not only are stress singularities removed from interface cracks but also stress concentrations.

Sinclair, G.B.: Stress singularities in classical elasticity—II: asymptotic identification. Appl. Mech. Rev. 57, 385–439 (2004) ADSCrossRef

Williams, M.L.: The stresses around a fault or crack in dissimilar media. Bull. Seismol. Soc. Am. 49, 199–204 (1959)

Zak, A.R., Williams, M.L.: Crack point stress singularities at a bimaterial interface. J. Appl. Mech. 30, 142–143 (1963) ADSCrossRef

Bogy, D.B.: Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 35, 460–466 (1968) ADSCrossRefMATH

Bogy, D.B.: On the problem of edge-bonded quarter planes loaded at the boundary. Int. J. Solids Struct. 6, 1287–1313 (1970) CrossRefMATH

Bogy, D.B.: Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions. J. Appl. Mech. 38, 377–386 (1971) ADSCrossRef

Bogy, D.B.: On the plane elastostatic problem of a loaded crack terminating at a material interface. J. Appl. Mech. 38, 911–918 (1971) ADSCrossRefMATH

Bogy, D.B., Wang, K.C.: Stress singularities at interface corners in bonded dissimilar isotropic elastic materials. Int. J. Solids Struct. 7, 993–1005 (1971) CrossRefMATH

Hein, V.L., Erdogan, F.: Stress singularities in a two-material wedge. Int. J. Fract. Mech. 7, 317–330 (1971)

10.

Rao, A.K.: Stress concentrations and singularities at interface corners. Z. Angew. Math. Mech. 51, 395–406 (1971) CrossRefMATH

11.

Gdoutos, E.E., Theocaris, P.S.: Stress concentrations at the apex of a plane indentor acting on an elastic half plane. J. Appl. Mech. 42, 688–692 (1975) ADSCrossRef

12.

Fenner, D.N.: Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface. Int. J. Fract. 12, 705–721 (1976)

13.

Theocaris, P.S., Gdoutos, E.E.: Stress singularities at vertices of composite plates with smooth or rough interfaces. Arch. Mech. Stosow. 28, 693–704 (1976) MATH

14.

Theocaris, P.S., Gdoutos, E.E.: Stress singularities in cracked composite full-planes. Int. J. Fract. 13, 763–773 (1977) CrossRef

15.

Dempsey, J.P., Sinclair, G.B.: On the singular behavior at the vertex of a bimaterial wedge. J. Elast. 11, 317–327 (1981) CrossRefMATHMathSciNet

16.

Ying, X., Katz, I.N.: A uniform formulation for the calculation of stress singularities in the plane elasticity of a wedge composed of multiple isotropic materials. Comput. Math. Appl. 14, 437–458 (1987) CrossRefMATH

17.

Van Vroonhoven, J.C.W.: Stress singularities in bimaterial wedges with adhesion and delamination. Fatigue Fract. Eng. Mater. Struct. 15, 159–171 (1992) CrossRef

18.

Yong-Li, W.: Crack tip stress singularities in a bimaterial with an inclined interface. Int. J. Fract. 54, R65–R72 (1992) ADSCrossRef

19.

Chen, D.-H., Nisitani, H.: Singular stress field near the corner of jointed dissimilar materials. J. Appl. Mech. 60, 607–613 (1993) ADSCrossRefMATH

20.

Chen, Y.Z., Hasebe, N.: Singularity eigenvalue analysis of a crack along a wedge-shaped interface. J. Appl. Mech. 60, 781–783 (1993) ADSCrossRefMATH

21.

Sinclair, G.B.: On the singular eigenfunctions for plane harmonic problems in composite regions. J. Appl. Mech. 47, 87–92 (1980) ADSCrossRefMATH

22.

Aksentian, O.K.: Singularities of the stress-strain state of a plate in the neighborhood of an edge. J. Appl. Math. Mech. 31, 193–202 (1967) CrossRef

23.

Sinclair, G.B.: On the influence of cohesive stress-separation laws on elastic stress singularities. J. Elast. 44, 203–221 (1996) CrossRefMATHMathSciNet

24.

Meng, L., Zhou, S.P., Yang, F.T., Lin, D.Z.: Microstructure and elemental distribution of multicrystal Ag/Cu interface in bimetallic strips with diffusion treatment. Mater. Res. Bull. 36, 1729–1735 (2001) CrossRef

25.

Bolz, R.E., Ture, G.L. (eds.): CRC Handbook of Tables for Applied Engineering Science. Chemical Rubber Co., Cleveland (1970), pp. 94, 125, 286

26.

Delta Technologies Ltd.: Loveland, CO (2014). Web page. http://www.delta-technologies.com

27.

Cease, H., Derwent, P.F., Diehl, H.T., Fast, J., Finley, D.: Measurement of mechanical properties of three epoxy adhesives. Report Fermilab-TM-2366-A, Fermi National Accelerator Lab, Batavia, IL (2006)

28.

Hymel, P.J.: Fabrication and enhancement of aluminum-based microchannel devices. MS Thesis, Dept. of Mech. Eng., Louisiana State University, Baton Rouge, LA (2014)

29.

Munro, R.G.: Evaluated properties of sintered alpha Al₂O₃. J. Am. Ceram. Soc. 80, 1919–1928 (1999) CrossRef

30.

Franco, A., Royer-Carfagni, G.: Cohesive debonding of a stiffner from an elastic substrate. Compos. Struct. 111, 401–414 (2014) CrossRef

31.

Sinclair, G.B.: A note on the influence of cohesive stress-separation laws on elastic stress singularities in antiplane shear. J. Elast. 94, 87–93 (2009) CrossRefMATHMathSciNet

32.

Sinclair, G.B., Meda, G., Smallwood, B.S.: On crack-tip stresses as crack-tip radii decrease. J. Appl. Mech. 78, 011004 (2011) ADSCrossRef

33.

Antipov, Y.A., Avila-Pozos, O., Kolaczkowski, S.T., Movchan, A.B.: Mathematical model of delamination cracks on imperfect interfaces. Int. J. Solids Struct. 38, 6665–6697 (2001) CrossRefMATH

34.

Vellender, A., Mishuris, G., Piccolroaz, A.: Perturbation analysis for an imperfect interface crack problem using weight function techniques. Int. J. Solids Struct. 50, 4098–4107 (2013) CrossRef

35.

Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1987)

36.

Williams, M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19, 526–528 (1952)

37.

Seweryn, A., Molski, K.: Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Eng. Fract. Mech. 55, 529–556 (1996) CrossRef

38.

Dempsey, J.P., Sinclair, G.B.: On the stress singularities in the plane elasticity of the composite wedge. J. Elast. 9, 373–391 (1979) CrossRefMATHMathSciNet

39.

Kolossoff, G.: On some properties of the plane problem of elasticity theory. Z. Math. Phys. 62, 384–409 (1991)

40.

Mishuris, G.S., Kuhn, G.: Asymptotic behavior of the elastic solution near the tip of a crack situated at a nonideal interface. Z. Angew. Math. Mech. 81, 811–826 (2001) CrossRefMATHMathSciNet

41.

Zak, A.R.: Stresses in the vicinity of boundary discontinuities in bodies of revolution. J. Appl. Mech. 31, 150–152 (1964) ADSCrossRef

42.

Reissner, E.: Note on the theorem of the symmetry of the stress tensor. J. Math. Phys. 23, 192–194 (1944) MATHMathSciNet

43.

Turteltaub, M.J., Wheeler, L.T.: Line integral representations for the traction problem of the elastic halfspace and their application to the study of the singular effects of load jumps. J. Elast. 6, 161–178 (1976) CrossRefMATH

Title: On the Influence of Adhesive Stress-Separation Laws on Elastic Stress Singularities
Author: G. B. Sinclair
Publication date: 01-02-2015
Publisher: Springer Netherlands
Published in: Journal of Elasticity / Issue 2/2015
Print ISSN: 0374-3535
Electronic ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-014-9493-2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 2/2015

Reverse Poynting Effects in the Torsion of Soft Biomaterials

A Note on the Convexity of C↦h(detC)

Scale-Dependent Homogenization of Random Hyperbolic Thermoelastic Solids

On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation

Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity

Foundation of Polar Linear Elasticity for Fibre-Reinforced Materials II: Advanced Anisotropy

Premium Partners