Determination of Stress Intensity Factor for Cracks in Orthotropic Composite Materials using Digital Image Correlation

Abstract: This paper focuses on the application of the digital image correlation (DIC) technique to determine the stress intensity factor (SIF) for cracks in orthotropic composites. DIC is a full‐field technique for measuring the surface displacements of a deforming object and can be applied to any type of material. To determine the SIF from full‐field displacement data, the asymptotic expansion of the crack‐tip displacement field is required. In this paper the expansion of the crack tip displacement field is derived from an existing solution for strain fields. Unidirectional fibre composite panels with an edge crack aligned along the fibre were tested under remote tensile loading and the displacements were recorded using DIC. The SIF was calculated from the experimental data by fitting the theoretical displacement field using the least squares method. The SIF thus determined was in good agreement with theoretical results and therefore demonstrates the applicability of the derived displacement field and DIC technique for studying fracture in composites.     

Dynamic Stress Intensity Factor of Interfacial Finite Cracks in Orthotropic Materials

The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under distributed normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. Bimaterial formulation of a crack problem is shown to converge to the mono-material formulation, derived independently, in the limiting case when both materials are the same.     

A Residual Stress Intensity Factor Solution for Knoop Indentation Cracks

The residual stress intensity factors at the surface and at the deepest point of the semi-elliptical Knoop indentation crack is determined from the stresses in the damaged zone below the indenter. For this purpose, the weight function approach by Cruse and Besuner was used and wide-range expressions of the geometric function are given. The solution is then applied to a commercial silicon nitride for which all relevant geometrical data are available.     

共面三维裂纹应力强度因子干涉的研究

利用奇异有限元理论与方法对三维多裂纹的应力强度因子干涉问题进行了研究,通过构造裂纹前缘位移场的局部解,提出了一种新的裂纹前缘位移场的位移模式,通过最小势能原理和变分原理直接得到裂纹前缘干涉的应力强度因子,较好地解决了含多裂纹有限体的强度分析问题.算例说明了该方法的有效性,其计算结果为多裂纹简化为单裂纹提供了理论依据.     

Experimental Evaluation of Mixed Mode Stress Intensity Factor for Prediction of Crack Growth by Phoelastic Method

Determination of stress intensity factors K _I, K _II, and constant stress term, σ _ox is investigated. A theory of determining the stress intensity factors using photo-elastic method is formulated taking three stress terms. Three-parameter method of fracture analysis for determining the mixed mode stress intensity factors under biaxial loading conditions from photo-elastic isochromatic fringe data is used. A special biaxial test rig is designed and fabricated for loading the specimen biaxially. A simplified and accurate method is proposed to collect the data from isochromatic fringes. Taking specimen geometry and boundary conditions into account, regression models are developed for estimation of fracture parameters.     

Mixed-Mode Stress Intensity Factor Estimation of Inclined Cracks in an Unnotched Round Bar

Journal of Failure Analysis and Prevention - The extent on mixed-mode stress intensity factor (SIF) of inclined multiple cracks in an unnotched bar has been investigated numerically. Opposite...     

On Stress Intensity Factors of Multiple Cracks at Small Distances in 2-D Problems

In the present work a method is proposed to predict stress intensity factors (SIFs) of strongly interacting cracks at spacings that are substantially smaller than crack lengths. The method is intended for applications where cracks are observed in stack-like/staggered arrangements as in damage patterns of some natural materials with dense lamellar microstructures. The new calculation procedure is inspired by the analytical method of Kachanov (1987) that due to its simplicity has shown to be a powerful tool for analysis of crack interactions. Although in 3-D the accuracy of Kachanov’s method remains good at quite close spacings, in 2-D problems it, however, quickly drops as the distance between cracks decreases, underestimating the effect of crack interactions, especially in ordered staggered arrangements. In this work we introduce new modeling assumptions that are suited for problems where stress fields have high gradients – a typical situation in the case of closely spaced parallel cracks. The accuracy of the method is examined on the example of two stacked cracks. The use of SIFs for estimation of material elastic compliance is also discussed.     

Stress Trajectories for Mode I and Mode II Cracks

Maximum shear stress trajectories are obtained for the mode I and for the mode II crack in an isotropic elastic solid in plane strain.     

Mixed-Mode Stress Intensity Factor Determination of Riveted Lap Joints Used in Aircraft Fuselage Structures

Journal of Failure Analysis and Prevention - In the present work, mixed-mode stress intensity factor (SIF) of multiple cracks in a riveted lap joint has been determined, with and without the...     

Determination of the Stress Intensity Factor of an elliptical breathing crack in a rotating shaft

The failures due to the propagation of fatigue cracks are one of the most frequent problems in rotating machines. Those failures sometimes are catastrophic and are sufficient to provoke the loss of the complete machine with high risks for people and other equipments. When a cracked shaft rotates, the breathing mechanism appears. The crack passes from an open state to a close state with a transition in which a partial opening or closing of the crack is produced. In this work, a new general expression that gives the Stress Intensity Factor (SIF) along the crack front of an elliptical crack in a rotating shaft in terms of the crack depth ratio, the crack aspect ratio, the relative position on the front and the angle of rotation has been developed for linear elastic materials. By the moment, no expressions of the SIF in term of these variables have been found in the literature. To this end, a quasi-static 3D numerical model of a cracked shaft with straight and elliptical cracks subjected to rotary bending using the Finite Element Method (FEM) has been made. To simulate the rotation of the shaft, different angular positions have been considered. The SIF in mode I along the crack front has been calculated for each angular position of the cracked shaft and for different crack geometries. The expression results have been compared with solutions obtained from the literature. It has been found that they are in good agreement. The model has been applied to other crack geometries with good results. The obtained SIF expression allows studying the dynamic behavior of cracked shafts and can be used to analyze the crack propagation.     

焊接桥梁结构的断裂驱动力分析

对焊接桥梁结构的典型单元H型构件进行了简化分析 ,同时考虑了焊接残余应力的影响 ,估计了临界裂纹的长度 ,并将构件按设计应力进行了分类 ,计算出各类应力构件的驱动力。临界裂纹长度 2aC=6 0mm ;H型构件中基体的驱动力KBI=1.12 (α +β1)σs πaC,焊缝的驱动力KWI =1.12 (α +β2 )σs πaC     

Stress Intensity Factor of an Edge Crack in Composite Media

A solution to the 2-D problem of a rigid circular inclusion squeezed by two semi-infinite elastic planes is presented. The size of the contact zone and the length of the opened area as a function of the applied stress, material properties and radius of the inclusion are calculated. The results demonstrate a strong non-linearity of the solution.     

Residual Stresses and Stress Intensity Factor Calculations in T-Welded Joints

In welded joint, the residual stresses effect can be considered using the residual stress intensity factor (K _res). In this study, K _res is calculated using the analytic weight function method (WFM) and the polynomial distribution of residual stresses (σ _res). The different residual stress distributions have been used analytically. It is to be emphasized that the current approach is little investigated. This is because the weight function has already been developed to calculate K for a crack that had already existed, and hence to calculate the stress distribution and stress intensity factor over the crack face. Therefore, the current approach calculates K _res with σ _res consideration for the crack which initiates and propagates until failure. The validity to use the proposed weight function has been shown. The results of K _res have been compared with those obtained from FEM.     

Stress Intensity Factor of an Edge Crack in Bonded Orthotropic Materials

The article presents the problem of an edge crack under normal point loading terminating perpendicular to the surface of an orthotropic strip of finite thickness which is bonded to another orthotropic half plane. Expressing the displacements and stresses in plane strain condition in terms of harmonic functions, the problem is reduced to a pair of simultaneous integral equations with Cauchy type singularities, which are finally been solved by the Hilbert transform technique. The analytical expression of stress intensity factor (SIF) at the crack tip for large thickness of the strip is calculated, which corresponds to the weight function of a crack under normal loading. The influences of elastic constants of two different orthotropic materials, distinct arbitrary locations of normal point loading on the crack surface and length of the crack on the dynamic SIF are depicted through graphs.     

On the Stress Intensity Factor for the Elliptical Crack

Stress intensity factor (SIF) for the elliptical crack under polynomial (uniform, as a special case) loading was first given by Kassir and Sih (1975). However, their expressions contain an error, corrected by Fabrikant (1987). This correction appears to have gone largely unnoticed, and some authors still use the incorrect result. We demonstrate, on the limiting case of a very elongated crack, that the correct expression is indeed the one of Fabrikant. This is hoped to resolve the controversy. It is also pointed out how to correct other results of Kassir and Sih for various loadings. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mixed Mode Fracture of Cracks and Wedge Shaped Notches in Expanded PVC Foam

Fracture initiated from a sharp crack or wedge shaped notch in a homogeneous material, subjected to different loading is considered. Singularities in the stress fields at edges and vertices are discussed. A point-stress criterion is used to predict fracture for sharp cracks as well as 90° wedge notches in expanded PVC foam. The point-stress criterion is formulated in a manner allowing failure predictions in general 3D stress situations. The influence of nonsingular T-stress at cracks is discussed and substantiated by experimental results.     

An Isolated Mode I Three-Dimensional Planar Crack: The Stress Intensity Factor is Independent of The Elastic Constants

It is demonstrated that for an isolated Mode I planar crack embedded in an infinite body, the stress intensity factor along the crack front is a function independent of the elastic constants.