Wiener Hopf Analysis of Transient Mode-I/Mode-II Fracture in Rotating Heterogeneous Magnetoelastic Orthotropic Media under Initial Stresses

TL;DR

This paper presents an analytical study of fracture behavior in rotating, magnetoelastic, orthotropic media with spatial gradation, revealing how grading, rotation, and magnetoelastic effects influence stress intensity factors over time.

Contribution

It introduces a Wiener Hopf analytical approach to model transient Mode I/II fractures in complex rotating magnetoelastic composites with material gradation.

Findings

Material grading affects SIF magnitude and evolution.

Rotation stabilizes fracture behavior.

Magnetoelastic effects vary with mode and influence SIFs.

Abstract

This study investigates the fracture behavior under both opening (Mode I) and in-plane sliding (Mode II) conditions for a semi-infinite crack in a rotating, spatially graded magnetoelastic orthotropic strip with combined horizontal and vertical initial normal stresses. The strip is assumed infinite in extent, with the crack aligned along its longitudinal axis and parallel to the rotation axis. The governing field equations are reduced to an analytically tractable form by employing the Fourier transform in the spatial domain and the Laplace transform in the temporal domain. The effect of a sudden application of traction, represented by a Heaviside step function, is analyzed for both normal and shear loading conditions. The resulting boundary-value problem is addressed through the Wiener Hopf method, yielding analytical representations of the stress intensity factors (SIFs). The near tip asymptotic stress fields are evaluated to derive explicit SIF representations for each loading configuration. Laplace inversion is performed using the generalized Chebyshev Laguerre polynomial method. Numerical simulations are conducted for Uranium and Graphite--Epoxy, with isotropic materials considered for comparison to assess the role of anisotropy. The temporal evolution of the SIFs is investigated for varying material gradation parameters, rotation rates, magnetoelastic coupling, and initial stresses. Results reveal that functional grading significantly influences both the magnitude and time evolution of the SIFs, rotation introduces a stabilizing effect, and magnetoelasticity exhibits mode-dependent impacts. These findings provide valuable insight into fracture behavior in advanced magnetoelastic composites, with relevance to high-performance rotating structures such as surface acoustic wave devices, aircraft wings, and helicopter blades.