In this paper we present several proofs on the extension of M. Riesz fractional integration and di¤erentiation to the contexts of spaces of homogeneous type and measure metric spaces with non-doubling measures. 1. Introduction, some de…nitions, and a basic lemma Professor M. Ash asked me to write a survey article on some of the results that Stephen Vági and I obtained in the nineties on fractio...

Fatigue crack growth can be strongly influenced by crack closure, i. e., the contacting of the opposing faces of a fatigue crack above the minimum load in a loading cycle. This crack closure shields the crack tip from the full stress field, but different views are held regarding the extent of this shielding. The type of closure, whether it be plasticity-induced, or roughness-induced may also pl...

* Corresponding author; Email: [email protected] ABSTRACT Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially straight crack fronts. As a specimen is loaded monotonically, the mid-section of the crack front will advance first, which will be followed by crack growth ...

Theories of toughness of materials depend on an understanding of the characteristic instabilities of the crack tip, and their possible interactions. In this paper we examine the effect of dislocation emission on subsequent cleavage of a crack and on further dislocation emission. The work is an extension of the previously published Lattice Greens Function methodology[1, 2, 3]. We have developed ...

As the number of systems which offer annotations on digital documents increases, robust anchoring of annotations is a key challenge. It is especially important if the annotator lacks write-access to the document being annotated. For example, if someone makes an annotation on a web page today and the web page changes tomorrow, what happens to the annotation? One approach is simply to “orphan” th...

nowadays, textile and woven fabric composites are taken into consideration forapplications in high mechanical properties and every in-plane direction. however, developments inmodelling and characterisation of the fabric reinforced composite materials are considered more inthe effects of element types used in the mesh generation of the crack tip. the type of elementselected for the crack tip, a ...

We present a combined novel methodology to study the three-dimensional complex geometry of a tortuous crack and identify the essential features of the crack and its propagation inside a heterogeneous material. We find that some severe damage events occur unexpectedly below a local mode-I crack within the sample; we realize that the severe plastic zone of the local mode-I crack is shifted down b...

This paper investigates the phenomenon of slant fracture observed in stable tearing tests of many ductile materials, where an initially flat crack, loaded under remote Mode I conditions, tends to grow into a slant crack and stay in the slant configuration until final fracture. In an effort to identify potential reasons why cracks prefer to grow in a slant manner, three-dimensional finite elemen...