Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material. Issue 1 (20th February 2020)

• Record Type: Journal Article
• Authors: Wang, Xu; Schiavone, Peter
• Is Part Of: Quarterly journal of mechanics and applied mathematics. Volume 73:Issue 1(2020:Feb.)
• Page Start: 76
• Page End: 83
• Publication Date: 2020-02-20
• Subjects: Mechanics -- Mathematics -- Periodicals; Applied mathematics -- Periodicals; 530.1
• DOI: 10.1093/qjmam/hbaa001
• Languages: English
• ISSNs: 0033-5614

Abstract

Summary: We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{-3/4\pm i\varepsilon }$ and $r^{-1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index) as well as the real power-type singularities $r^{-3/4}$ and $r^{-1/4}$ . Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.