Variation Of Stress Intensity Factor Research Articles

Simple formula for dynamic stress intensity factor of pre-cracked Charpy specimen

It has been reported that consideration of inertia effect is important to estimate the stress intensity factor for impact loading. In the present paper a simple expression for the dynamic stress intensity factor of a pre-cracked Charpy specimen is derived by making use of an approximate solution for one-dimensional beam equations. The time variation of the dynamic stress intensity factor obtained retaining only the fundamental mode of bending vibration is in good agreement with the two-dimensional finite element solutions for step-loading and also for final-peak-sawtooth-pulse loading.

Diffraction of Torsional Waves by a Flat Annular Crack in an Infinite Elastic Medium

The problem of diffraction of normally incident torsional waves by a flat annular crack embedded in an infinite, isotropic, and homogeneous elastic medium is considered. Using an integral transform technique, the problem is reduced to that of solving a singular integral equation. The solution of the singular integral equation is obtained in the form of the product of the series of Chebyshev polynomials of the first kind and their weight functions. Thus the essential feature of the dynamic singular stress field near the crack is preserved and the crack tip dynamic stress-intensity factor is easily evaluated. Numerical calculations are also carried out and the variations of dynamic stress-intensity factors with the normalized frequency for the ratio of the inner radius to the outer one are shown graphically.

A METHOD FOR ESTIMATING FATIGUE CRACK PROPAGATION IN PRE‐STRAINED AND MEAN STRESSED SPECIMENS

Abstract A method for quantifying the effect of plane stress, plane strain, mean stress and pre‐strain on fatigue crack propagation rates in plates of different thicknesses is proposed. Experimental verification was carried out on mild steel plates of 0·2, 0·4, 0·6, 0·8, 1·0, 1·2 and 1·4 mm thick specimens. The conflicting effects of variations in stress intensity factors along the crack front and changes from plane stress to plane strain conditions along the crack front are also discussed.

Finite element analysis of the compact shear specimen

Mode II stress intensity factors were generated for the compact shear specimen through finite element techniques. Results are compared to those obtained in a boundary collocation analysis with general agreement being shown but with somewhat greater variation in stress intensity factor indicated over the range of crack lengths investigated. Correction factors for three specimen configurations are tabulated and are used to determine the Mode II fracture toughness for 2024-T4 aluminum specimens tested in a previous investigation. Mode II fracture toughness for this material was found to be approximately 50% higher than the Mode I fracture toughness, and a tendency toward Mode I deformation at crack initiation was evident. Correction factors obtained in this investigation should prove useful in the determination of material fracture toughness and fatigue crack growth thresholds.

3D analyses of surface flaws in thick-walled reactor pressure-vessels using displacement-hybrid finite element method

Solutions of stress intensity factors for external and internal unpressurized and pressurized surface cracks in internally pressurized thick-walled reactor pressure vessels are determined directly by a three-dimensional displacement-hybrid finite element method. The finite element method is based on a rigorous modified variational principle of the total potential energy, with arbitrary element interior displacements, interelement boundary displacements and element boundary tractions as variables. Special crack front elements, developed using the hybrid displacement model, which contain the proper square root and inverse square root variations of displacements and stresses, are used in this analysis and the three stress intensity factors, K I, K II and K III are solved directly along with the unknown nodal displacements. Stress intensity factor variations for pressurized and unpressurized semi-elliptical inner surface cracks in pressurized cylinders with crack aspect ratios of 0.2 and 1.0, crack depth to cylinder wall thickness ratios of 0.5 and 0.8 and outer to inner diameter ratios of 1.5 and 2.0, are presented. Also, for unpressurized outer surface cracks in pressurized cylinders, the solutions are presented for crack aspect ratios of 0.6 and 1.0, crack depth to cylinder wall thickness ratios of 0.4, 0.6 and 0.8, and outer to inner diameter ratio of 1.5.

Stress intensities for nozzle cracks in reactor vessels

A series of six frozen stress photoelastic tests was conducted to investigate the distribution of stress-intensity factor (SIF) along a crack which occurred at the juncture of a pipe (nozzle) with a cylindrical pressure vessel. Typical photoelastic-fringe patterns are shown for slices which were taken mutually orthogonal to the flaw border and the flaw surface. A typical plot of normalized apparent SIF vs. square root of normalized distance from the crack tip is presented. The variation in SIF along the flaw border is given for all six different crack geometries and, also, the variation of SIF with varyinga/T is presented.

Stress Analysis and Stress-Intensity Factors for Finite Geometry Solids Containing Rectangular Surface Cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids.

Three-Dimensional Analysis of Stress Intensity Factors of Cracks Penetrating through the Thickness of Plates

The variation of stress intensity factors along the crack front of a crack penetrating through the thickness of a plate is analysed by the finite-element method on the basis of concept of the superposition of analytic and finite-element solutions, which has been successfully employed for two-dimensional and axi-symmetric three-dimensional crack problems.In three-dimensional problems, difficulties exist in finding analytic solutions of the governing differential equations, which have the singularity for cracks. In the present paper the authors propose a method of constructing appropriate series of analytic solution which does not satisfy the governing equation but can easily approximate the variation of stress intensity factors.As a numerical example the stress intensity factor of a compact tension specimen is calculated. It is shown that the stress intensity factor takes the maximum on the middle-surface, which is 7-15% higher than the two-dimensional value.

The effect of a circular inclusion on the stresses around a line crack in a sheet under tension

Based on the two-dimensional theory of elasticity and by the use of Muskhelishvili technique, the effect of a circular inclusion of different elastic material on the stress state around a line crack in an infinite plate subject to tension is discussed. Here, the circular inclusion is supposed to be on the line of prolongation of the crack. Numerical calculations were carried out and the variation of the crack-tip stress intensity factor due to the geometry and elastic properties of two media was clarified.