SOME STRAIGHT CRACK PROBLEMS IN. ELASTIC-PLASTIC MEDIA

Abstract

The ,problems investigated in this thesis are based on Dugdale model. The Dugdale model is for the arrest of a crack weakening an infinite plate. The infinite plate is subjected to tension at infinity which opens the faces of the crack forming plastic zones ahead of the tips of crack. These plastic zones are closed by a uniform constant stress distribution applied at the rims of plastic zones. This model is modified for infinite plate weakened by two cracks where the plastic zones developed are closed by a variable load distribution. The different cases are considered when the cracks are collinear, equal or unequal. They may be symmetrically or asymmetrically situated. The chapterwise description is given below. Chapter 1 is an introduction to the basic concepts of fracture mechanics relevant to the thesis. It also gives an account of developments, applications and scope of the subject. A brief survey of the literature and its development is presented in overview section of this chapter. The main emphasis is on the problems based on Dugdale's "strip yield model" and the problems of multiple cracks weakening an infinite sheet. Chapter 2 recapitulates the concepts of two-dimensional theory of elasticity. The complex variable formulation of the crack problems given by Muskhelishvili (36) forms a part of the chapter. The Griffith's crack propagation criterion is discussed. Dugdale model, plastic zone size and crack opening displacement concepts are also discussed. Thesis is divided into two parts; (i) Part one and (ii) Part two. In part one the crack problems with separated plastic zones are considered. Part one consists of chapters 3, 4, 5 and 6. The modified. Dugdale model proposed for two hairline collinear, equal and straight cracks ' weakening an infinite elastic-perfectly plastic plate, is considered in chapter 3. The infinite plate is subjected to tensile load at infinite boundary. The loads act in a direction perpendicular to the rims of the cracks. As a consequence the rims of the cracks open forming the plastic zones ahead of the tips of the cracks. Thus four plastic zones are formed. These, in turn, are closed by distributing over them, the normal compressive stress distribution Pyy = torye, where aye is the yield point stress of the plate and t is any point on rims of the plastic. zones. Thus the crack is arrested from further opening. A qualitative analysis is carried out to find the behaviour of load ratio. (load applied at infinity / yield point stress) required to close the plastic zone against effecting parameters. Analytical expressions are derived for crack face opening displacement (COD) and its variation against the parameters: crack length, plastic zone size and the inter-crack distance, is studied..