Analysis of an Unsteadily Propagating Crack under Mode Ⅰ and Ⅱ Loading

Kwang Ho Lee,Gap Su Ban 대한기계학회 2007 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.21 No.3

Stress and displacement fields for an unsteadily propagating crack under mode I and II loading are developed through an asymptotic analysis. Dynamic equilibrium equations for the unsteady state are developed and the solution to the displacement fields and the stress fields for a crack propagating with high crack tip acceleration, deceleration and rapidly varying stress intensity factor. The influence of transients on the higher order terms of the stress fields are explicitly revealed. Using these stress components, isochromatic fringes around the propagating crack are generated for different crack speeds, crack tip accelerations and the time rate of change of stress intensity factor, and the effects of the transients on these fringes are discussed. The effects of the transients on the dynamic stress intensity factor are discussed when a crack propagates with high acceleration and deceleration. The effect of transient on the time rate of change of dynamic stress intensity factor below Rayleigh wave speed in an infinite body is also studied.

용접 잔류응력장 중에서의 Aluminum-Alloy 용접재의 피로균열 성장거동 연구(Ⅱ) : 잔류응력 재 분포 Redistribution of the Residual Stress

최용식,정영석 成均館大學校 科學技術硏究所 1988 論文集 Vol.39 No.1

It is well known that welding residual stress has a great influence on fatigue crack growth rate in welded structure. In the general area of fatigue crack growth in the presence of residual stress, it is noted that the correction of stress intensity factor(K) to account for residual stress is important for the determination of both stress intensity factor range(ΔK) and stress ratio (R) during a loading cycle. The superposition technique can be applied generally for determination of K. The crack growth rate of the welds correlated with the effective stress intensity factor range, ΔK_eff, which was estimated by superposition of the respective stress intensity factors for the residual stress fields and for the applied stresses. However, redistribution of residual stress occurs during crack growth and its effect is not negligible. In this study, fatigue crack growth characteristics of the weld joint were examined by using superposition of redistributed residual stress and examined in comparison with that of the initial residual stress superposition.

Experimental and numerical analysis of fatigue behaviour for tubular K-joints

Shao, Yong-Bo,Cao, Zhen-Bin Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.19 No.6

In this paper, a full-scale K-joint specimen was tested to failure under cyclic combined axial and in-plane bending loads. In the fatigue test, the crack developments were monitored step by step using the alternating current potential drop (ACPD) technique. Using Paris' law, stress intensity factor, which is a fracture parameter to be frequently used by many designers to predict the integrity and residual life of tubular joints, can be obtained from experimental test results of the crack growth rate. Furthermore, a scheme of automatic mesh generation for a cracked K-joint is introduced, and numerical analysis of stress intensity factor for the K-joint specimen has then been carried out. In the finite element analysis, J-integral method is used to estimate the stress intensity factors along the crack front. The numerical stress intensity factor results have been validated through comparing them with the experimental results. The comparison shows that the proposed numerical model can produce reasonably accurate stress intensity factor values. The effects of different crack shapes on the stress intensity factors have also been investigated, and it has been found that semi-ellipse is suitable and accurate to be adopted in numerical analysis for the stress intensity factor. Therefore, the proposed model in this paper is reliable to be used for estimating the stress intensity factor values of cracked tubular K-joints for design purposes.

Stress intensity factors for double-edged cracked steel beams strengthened with CFRP plates

Hai-Tao Wang,Gang Wu,Yu-Yang Pang,Habeeb M. Zakari 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.33 No.5

This paper presents a theoretical and finite element (FE) study on the stress intensity factors of double-edged cracked steel beams strengthened with carbon fiber reinforced polymer (CFRP) plates. By simplifying the tension flange of the steel beam using a steel plate in tension, the solutions obtained for the stress intensity factors of the double-edged cracked steel plate strengthened with CFRP plates were used to evaluate those of the steel beam specimens. The correction factor <i>α</i>₁ was modified based on the transformed section method, and an additional correction factor <i>φ</i> was introduced into the expressions. Threedimensional FE modeling was conducted to calculate the stress intensity factors. Numerous combinations of the specimen geometry, crack length, CFRP thickness and Young's modulus, adhesive thickness and shear modulus were analyzed. The numerical results were used to investigate the variations in the stress intensity factor and the additional correction factor <i>φ</i>. The proposed expressions are a function of applied stress, crack length, the ratio between the crack length and half the width of the tension flange, the stiffness ratio between the CFRP plate and tension flange, adhesive shear modulus and thickness. Finally, the proposed expressions were verified by comparing the theoretical and numerical results.

Analysis of a mode-I crack perpendicular to an imperfect interface

Zhong, Xian-Ci,Li, Xian-Fang,Lee, Kang Yong Elsevier 2009 International journal of solids and structures Vol.46 No.6

<P><B>Abstract</B></P><P>The elastostatic problem of a mode-I crack embedded in a bimaterial with an imperfect interface is investigated. The crack is in proximity to and perpendicular to the imperfect interface, which is governed by linear spring-like relations. The Fourier transform is applied to reduce the associated mixed-boundary value problem to a singular integral equation with Cauchy kernel. By numerically solving the resulting equation, stress intensity factors near both crack tips are evaluated. Obtained results reveal that the stress intensity factors in the presence of the imperfect interface vary between that with a perfect interface and that with a completely debonding interface. Moreover, an increase in the interface parameters decreases the stress intensity factors. In particular, when crack approaches to the weakened interface closer, the stress intensity factors become larger for a sliding interface, and become larger or smaller for a Winkler interface, depending on the crack lying in a stiffer or softer material. The influences of the imperfection of the interface on the stress intensity factors for a bimaterial composed of aluminum and steel are presented graphically.</P>

Hybrid determination of mixed-mode stress intensity factors on discontinuous finite-width plate by finite element and photoelasticity

백태현,Lei Chen,홍동표 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.10

For isotropic material structure, the stress in the vicinity of crack tip is generally much higher than the stress far away from it. This phenomenon usually leads to stress concentration and fracture of structure. Previous researches and studies show that the stress intensity factor is one of most important parameter for crack growth and propagation. This paper provides a convenient numerical method, which is called hybrid photoelasticity method, to accurately determine the stress field distribution in the vicinity of crack tip and mixed-mode stress intensity factors. The model was simulated by finite element method and isochromatic data along straight lines far away from the crack tip were calculated. By using the isochromatic data obtained from finite element method and a conformal mapping procedure,stress components and photoelastic fringes in the hybrid region were calculated. To easily compare calculated photoelastic fringes with experiment results, the fringe patterns were reconstructed, doubled and sharpened. Good agreement shows that the method presented in this paper is reliable and convenient. This method can then directly be applied to obtain mixed mode stress intensity factors from the experimentally measured isochromatic data along the straight lines.

Efficient methods for integrating weight function: a comparative analysis

Gaurav Dubey,Shailendra Kumar 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.55 No.4

This paper introduces Romberg-Richardson’s method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson’s method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

REMARKS ON FINITE ELEMENT METHODS FOR CORNER SINGULARITIES USING SIF

Kim, Seokchan,Kong, Soo Ryun The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.3

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

Remarks on finite element methods for corner singularities using SIF

김석찬,공수련 호남수학회 2016 호남수학학술지 Vol.38 No.3

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

A FINITE ELEMENT METHOD USING SIF FOR CORNER SINGULARITIES WITH AN NEUMANN BOUNDARY CONDITION

Kim, Seokchan,Woo, Gyungsoo The Youngnam Mathematical Society 2017 East Asian mathematical journal Vol.33 No.1

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.