Reduction in the Stress Intesity Factior for Cracks Starting from A Circular Hole in an Infinite Plate

Reduction in the Stress Intesity Factior for Cracks Starting from A Circular Hole in an Infinite Plate

Mr. A. A. Kshirsagar and Prof. P. R. Kulkarni

Fracture Mechanics, Mechanical Dept.,Walchand Institute of Technology, Solapur, Maharashtra, India

Abstract

This paper concerns with the reduction of stress intensity factors (SIFs) of crack starting from circular hole in infinite plate subjected to internal pressure. Software ANSYS is used for modeling & analysis purpose. Considering the symmetry of the model condition about the x axis and the y axis, only quarter model is prepared with 2-D solid 8 node 82 elements. Moreover, Analytical formula of the SIFs of the crack problem is examined and compared. It is found that very large reduction in the SIFs occurs due to the application of the pressure in Stress reducing feature hole near crack tip but this is applicable to the geometry where only remote load are applied.

Keywords

Fracture Mechanics, Cracked plate under pressure, Finite element Method, Reduction in the Stress Intensity Factor.

1. Introduction

   During manufacturing process and fabrication sometimes cracks may appear in structural materials. Such cracks may grow in time would affect the load-bearing capacity, leading to a loss of strength and reduction in the service life of the structures; it is needed for crack to arrest to enhance residual strength and service life of the cracked structures. [1] If the structure is concerned with either static or fatigue loading, the behavior of the crack must be assessed, in order to avoid catastrophic failure. For this knowledge of the crack size, service stress, material properties and SIF (as a fundamental parameter in linear elastic fracture mechanics) are required. Fracture Mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. Hence Fracture mechanics plays an important role as it provides useful tools which allow for an analysis of materials which exhibits cracks. In a modern era, fractures have been a frequent, dangerous, and costly structural failure mode. Notable examples include collapse of aero-structures, automobile and railway bridges, pressure vessel and pipeline explosion.

2. Literature review

   The task deals with the determination and reduction in the SIFs by various methods and a review of following papers have been studied as listed below:

   Finite element Analysis combining with the concepts of linear elastic fracture mechanics provides practical and convenient means to study the fracture and crack growth of the material. 2-D FEM model is developed for two different geometries.

   A rectangular plate with crack starting from a circular hole and double edge notched plate. Both geometries are in tensile loading and under mode-I conditions. In this paper a displacement extrapolation technique is employed particularly to predict the crack propagations direction and to calculate SIFs and validated with the relevant numerical and analytical results obtained by other researcher. [1]

   Multiple site damage is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor of an infinite plate containing multiple hole-edge cracks was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve stress intensity factor problems on multiple holes. Few numerical examples of an infinite plate containing two hole edge cracks are examined by the method. By comparing the analytical and finite element analysis results it was realized that the analytical results are accurate and reliable. [2]

   This note deals with the stress intensity factors (SIFs) of cracks emanating from a rhombus hole in a rectangular plate subjected to internal pressure by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is very accurate for evaluating the SIFs of the crack problem. [5]

   Boundary value problem of a plate with crack and defect such as the circular and/or elliptical holes is a multi-connected domain problem; this kind of problem is suitable for solving by boundary element method with its higher precision. The sub- region method is used in the paper, a center cracked plate subjected to remote tensile and shear loading is studied numerically. The effect of the circular hole on Mode-I and Mode-II stress intensity factors is studied assuming the plane strain condition; the results are more precise than that of using FEM. The effect of the elliptical hole on Mode-I stress intensity factors are studied as well and some significant results are obtained. [6]

   Several methods have been employed to arrest the crack growth i.e. strip or patch repaired method, Artificial crack closure by crack filling, Welding repaired, Indendation The method of external adhesive patching across the crack is commonly used in aircraft industry, bridge and civil structures. Problems of adhesive patching have been analysed analytically and numerically. Commonly, the method of complex variable formulation has been used to analyses these problems. Some conventional numerical methods such as Finite Element Method have been studied for aircraft structures using bonded composite patches. [7]

   Several methods have been employed to reduce stress intensity factor i.e. stop hole drill method, crack flank holes method, cold hole expansion process. The method of drilling stop holes were drilled in front of crack tip so that the approaching crack towards the hole will get blunt and get arrested. These holes can also be cold expanded to enhance crack reinitiating time. Experimental investigation has been made on crack growth by drilling holes on crack flank side; it is shown that the crack growth can be reduced. [8]

   1. Problem Definition

      An infinite rectangular plate with a central circular hole & cracks emanating from the hole will be modeled. Pressure will be applied inside the hole for one case & pressure will be applied in hole as well as on crack face for the second case. Stress intensity factor will be calculated using Plane Strain Condition & for Linear Elastic Fracture Mechanics condition. Another hole near the crack tip will be tested as a stress reducing feature. Also effect of pressure applied in this stress reducing feature will be studied. Number of different parameters will be changed and its effect on SIFs will be observed.

      The plate is shown as below. Pressure is applied inside the hole & also to the crack faces.

      Figure 2.1 An infinite rectangular plate with central circular hole & two symmetrical cracks starting from it with pressure applied in hole & crack face Table2.1 Geometry of the plate model (Quarter)

      Width of the plate (mm)	250	a	25
      Height of the plate(mm	300	R	20

3. Research Methodology

   After the identification of the problem and after findings literature survey thus it is essential to mention the research method for the perfect solution of the problem. Analytical solution determined first and then FEM is used to solve the problem.

   Analytical Method

   Stress Intensity Factor KI = F (,a/R) P .The values of the boundary correction factor

   F are directly available in the literatures. [3] The

   same are used in the present case. For this particular case i.e. for an infinite plate with hole size 20 mm & crack length 5 mm & pressure applied inside the hole & also to the crack face, the value of the BCF is 0.7929.Pressure is 200 MPa.By using the above empirical formula obtained the SIF is 1405.66 MPamm½[4].

   1. Finite Element Method

      The finite element method is numerical method for solving problems of engineering and mathematical physics. It is useful for problems with complicated geometries, loading and material properties where analytical solution cannot be obtained and it is highly difficult. In such situation the numerical method (FEM) is employed. By this

      method we may get approximate but acceptable solution. After solve this problem byusing ANSYS software, the output of the SIF is obtained.

      i. e. KI = 1417.3 N mm-3/2

      % Error = {(K Ansys – K Analytical) / K Analytical} x 100

      = {(1417.3 -1405.67) / 1405.67} x 100

      = 0.827 %

      The error in the finite element solution is determined by comparing the same with analytical solution obtained by using Newmans equation. The error is 0.827 % which is within acceptable range. [4]

4. Results and Discussions

   1. Reduction in the SIF by Drilling hole near to the crack tip.