# Numerical Analysis of the Effect of the Pre-Existing Crack Opening on the Direction of the Secondary Crack Propagation

Li, Mingzhou (2017) Numerical Analysis of the Effect of the Pre-Existing Crack Opening on the Direction of the Secondary Crack Propagation. Master's Thesis, University of Pittsburgh. (Unpublished)

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## Abstract

This study involves an analysis of the development and direction of secondary crack propagation starting from openings of different shapes located in brittle prismatic samples subjected to either uniaxial compression or direct shear stress conditions. The findings from the study were then used to understand how notches (cracks) located at the toe of slopes made of brittle materials influence their failure. For the first part of the study, a theoretical analysis that uses closed form solutions, linear elastic fracture mechanics (LEFM) and a numerical analysis that uses a finite element software (ABAQUS) were conducted to understand how the degree of curvature of circular and elliptical openings develops critical stresses that were the locations of the failure of the openings. The theoretical and numerical analysis established that the degree of curvature of the openings had a tremendous influence on where the secondary cracks developed. For the case of the elliptical samples, the attitude of the ellipse also had an influence on how the secondary cracks extend.
For the case of the rock slopes with a notch (crack) at their toe, an extended finite element method (XFEM) based on linear elastic fracture mechanics (LEFM) theory was utilized to model the secondary crack propagation that takes place from the tip of the notch subjected to gravity induced compression and gravity induced lateral pressure. The analysis that used XFEM established that the ratio between the shear stress acting parallel to the axis of the toe crack, and the vertical overburden compression normal to the axis of the notch had a marked influence on how the secondary cracks developed from the notch. If the ratio was less than one, the secondary crack developed at angles greater than 90° with respect to the crack axis. If the ratio was equal to one, the secondary crack developed exactly at 90°. If ratio was greater than one, the secondary crack was inclined at angles less than 90°. XEFM study also indicated that the opening of the notch has also an influence on the angle of secondary crack propagation from the tip of the notch.

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## Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
Li, Mingzhoumil106@pitt.edumil106
ETD Committee:
Committee ChairVallejo, Luis E.vallejo@pitt.edu
Committee MemberVandenbossche, Julie M.jmv7@pitt.edu
Committee MemberIannacchione, Anthony T.ati2@pitt.edu
Date: 13 June 2017
Date Type: Publication
Defense Date: 31 March 2017
Approval Date: 13 June 2017
Submission Date: 3 April 2017
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 101
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Civil and Environmental Engineering
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: XFEM, LEFM, Crack propagation, slope, notch
Date Deposited: 13 Jun 2017 14:27
URI: http://d-scholarship.pitt.edu/id/eprint/31345

### Available Versions of this Item

• Numerical Analysis of the Effect of the Pre-Existing Crack Opening on the Direction of the Secondary Crack Propagation. (deposited 13 Jun 2017 14:27) [Currently Displayed]