Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials - Part I: Crack Perpendicular to the Material Gradation

G. H. Paulino, A. C. Fannjiang, Y. S. Chan

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, ℓ and ℓ′, which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the problem is derived assuming that the shear modulus is a function of the Cartesian coordinate y, i.e., G = G(y) = G 0eγγ, where G0 and γ are material constants. The crack boundary value problem is solved by means of Fourier transforms and the hypersingular integrodifferential equation method. The integral equation is discretized using the collocation method and a Chebyshev polynomial expansion. Formulas for stress intensity factors, K III, are derived, and numerical results of KIII for various combinations of ℓ, ℓ′, and γ are provided. Finally, conclusions are inferred and potential extensions of this work are discussed.

Original languageEnglish (US)
Pages (from-to)531-542
Number of pages12
JournalJournal of Applied Mechanics, Transactions ASME
Volume70
Issue number4
DOIs
StatePublished - Jul 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Fingerprint

Dive into the research topics of 'Gradient Elasticity Theory for Mode III Fracture in Functionally Graded Materials - Part I: Crack Perpendicular to the Material Gradation'. Together they form a unique fingerprint.

Cite this