Crack Dynamics in Rotating, Initially Stressed Material Strips: A Mathematical Approach

TL;DR

This paper presents a mathematical analysis of crack behavior in initially stressed, rotating material strips using singular integral equations and Hilbert transforms, highlighting how various factors influence stress intensity factors.

Contribution

It introduces a novel mathematical approach to analyze fracture in rotating, stressed strips, incorporating singular integral equations and numerical analysis for the first time.

Findings

Rotation and initial stress significantly affect the stress intensity factor.

Mathematical model accurately predicts fracture behavior under various conditions.

Comparison shows differences between stressed, rotating strips and standard materials.

Abstract

The current study explores the analysis of crack in initially stressed, rotating material strips, drawing insights from singular integral equations. In this work, a self-reinforced material strip with finite thickness and infinite extent, subjected to initial stress and rotational motion, has been considered to examine the Griffith fracture. The edges of the strip are pushed by constant loads from punches moving alongside it. This study makes waves in the material that affect the fracture's movement. A distinct mathematical technique is utilized to streamline the resolution of a pair of singular integral equations featuring First-order singularities. These obtained equations help us understand how the fracture behaves. The force acting at the fracture's edge is modeled using the Dirac delta function. Then, the Hilbert transformation method calculates the stress intensity factor (SIF) at the fracture's edge. Additionally, the study explores various scenarios, including constant intensity force without punch pressure, rotation parameter, initial stress, and isotropy in the strip, deduced from the SIF expression. Numerical computations and graphical analyses are conducted to assess the influence of various factors on SIF in the study. Finally, a comparison is made between the behavior of fractures in the initially stressed and rotating reinforced material strip and those in a standard material strip to identify any differences.