## Date of Award

August 2020

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mechanical and Aerospace Engineering

## Advisor(s)

Alan J. Levy

## Keywords

cohesive fracture, elasticity, integral equations, layered composites, mode-III, torsion

## Subject Categories

Engineering

## Abstract

This research examines the mechanics of mode-III cohesive fracture by defect initiation and quasi-static growth in both cylinder and layered systems. The analysis, which is exact, is based on the solution of two fundamental elasticity problems: i) a cylinder subject to an arbitrary shear on one end cap and an equilibrating torque on the other and, ii) a layer subject to arbitrary anti-plane shear traction on one surface and an equilibrating uniform traction on the other. For a particular geometry and defect configuration, these solutions are shown to lead to a pair of interfacial integral equations whose derived cohesive surface fields capture the entire defect evolution process from incipient growth through complete failure. The anti-plane shear separation/slip process is assumed to be modeled by Needleman-type traction-separation relations (e.g., bilinear, Xu-Needleman, frictional) characterized by a shear cohesive strength, a characteristic force length and, in the case of the bilinear law, a finite decohesion cutoff length and possibly other parameters as well. Symmetrically arrayed cohesive surface defects are modeled by a cohesive surface strength function which varies with surface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body movement, are found by eigenfunction approximation of the solution of the governing interfacial integral equations.

General features of the solutions to anti-plane shear cohesive fracture in both cylindrical and layered geometries indicate that quasi-static defect initiation and propagation occur under monotonically increasing load. For small values of characteristic force length, brittle behavior occurs that is readily identifiable with the growth of a sharp crack, i.e., the existence of a strong local stress concentration. At larger values of characteristic force length, ductile response occurs which is more typical of a linear “spring” cohesive surface, i.e., more distributed stress and slip distribution. Both behaviors ultimately give rise to abrupt failure of the cohesive surface. Results for the stiff, strong cohesive surface under a small applied load show consistency with static linear elastic fracture mechanics solutions in the literature. By superimposing a frictional part onto the cohesive law, the solution can be used to predict frictional response. Both decohesion and friction dominated cases show similar quasi-static defect propagation process, stable defect growth till a maximum load is reached, then defect growth becomes dynamic and unstable. However, the difference lies in that the friction dominated cohesive surface can still sustain certain load even after response becomes dynamic, but the decohesion dominated case will not. For friction dominated cohesive surfaces, the cylinder cases have smooth deformation processes whereas the layered systems experience a noticeable displacement jump. Both cylinder and layered systems predict the principal plane (perpendicular to principal stress direction) to be close to 45 degrees which helps to explain the orientation of mode-I microcracks in layered systems and the initiation of a spiral crack plane in cylinder geometries.

The cohesive fracture solution to layered geometries can be extended to obtaining traction fields for more complicated defect geometries (array of cracks and subsurface cracks in nonuniform bilayer) which can be used to predict the sequence of defect propagation. The bifurcation analysis of the uniform two-sublayer system shows the phenomenon of non-unique slip for the same loading. The bifurcation analysis for the multi-sublayer system with such non-uniqueness gives an explanation of the asymmetric configuration. For the analysis of nonuniform multi-sublayer systems, no additional difficulty occurs in the problem-solving process. By studying different geometries and crack patterns, the current study discussed the combined effects of interlaminar and intralaminar crack interaction which are important in predicting the most vulnerable place in the system while multiple defects exist.

## Access

Open Access

## Recommended Citation

song, yueming, "Anti-plane Shear of Cylinders and Layered Systems: Cohesive Fracture and Instability" (2020). *Dissertations - ALL*. 1273.

https://surface.syr.edu/etd/1273