Opening Mode Stress Intensity Factor Research Articles

The opening mode stress intensity factor extraction method from mixed mode crack using single element strain gage.

The opening mode stress intensity factor extraction method from mixed mode crack using single element strain gage.

Flaw-Bridging in Composite Materials

The implicit assumption in the modelling of fibre reinforced materials is that they are defect free. Defects in fibre-reinforced materials can be initated during their service life and can result a variety of damage phenomena. This paper focuses on the mathematical treatment of the case where a defect is present in the matrix of a uni-directionally reinforced composite but the fibres themselves exhibit continuity across the matrix crack. This results in a processes that is referred to as “flaw bridging”. The amplification of the stress intensity factors at the boundary of the matrix crack can be influenced by the bridging action, to the extent that if the the fibres are inextensible, the stress intensity factor can be suppressed. This paper examines the flaw bridging action in a unidirectionally reinforced composite, which can be reduced to the solution of a Fredholm integral equation of the second kind. The mathematical treatment is used to examine the influence of the bridging action on the crack opening mode stress intensity factors at the boundary of a penny-shaped crack.

Estimation of three‐dimensional stress intensity factor for structural ‘T’ details

AbstractThree‐dimensional (3D) opening mode stress intensity factors (SIFs) for structural steel‐welded ‘T’ details were investigated by the finite element method. A 3D shape‐dependent correction factor is proposed for semi‐elliptical surface cracks. The aspect ratio (a/c) of a semi‐elliptical crack plays a key role in the approximation of 3D‐SIF values, and in the present study, it was estimated for a 3D crack analysis. The estimated 3D‐SIF was determined through a correlation between the a/c ratio and the two‐dimensional SIF for semi‐elliptical cracks in the thickness direction adjacent to the web‐flange junction of a welded ‘T’. The resulting equation can be used to estimate the 3D‐SIF values from the two‐dimensional SIF without much ambiguity.

J-Integral Computation in Mixed Mode Ι and ΙΙ

Computation of a path independent contour integration but it yields directly the independent values of the opening mode and shear mode stress intensity factors. The calculations are not sensitive to the choice of contour. To the J-integral calculation, the present scheme calculates separately the factors KI and KII. A simple method to determine the SIFs for the three-dimensional crack is proposed based on the conservation integral.

OS0503 き裂の応力拡大係数解析用ひずみゲージの開発 : 第1報 開口モード応力拡大係数の解析式と精度検証実験

Strain gages to measure only the stress intensity factor are only one or two kinds so far. They are not easy nor practical to analyze the stress intensity factor. Therefore, this paper reports on the development of strain gages dedicated to analyze the stress intensity factor easily and practically. The authors have made the strain gages for trial purpose. The strain gage was pasted to the crack tip of the plate tension specimens, having the opening mode crack. The authors carried out the tensile tests of the test pieces that pasted such strain gauges. As results, the experimental values of the opening mode stress intensity factors to be able to count by calculator were obtained within ±10% compared with analytical values.

Improving accuracy of opening-mode stress intensity factor in two-dimensional media using fundamental solution based finite element model

A hybrid finite element method (FEM) is developed for determining stress intensity factor of opening-mode cracks. The model is based on fundamental solutions and higherorder displacement extrapolation. In the present formulation, linear combination of fundamental solutions and shape functions are respectively used to approximate the element interior and frame fields. The equality of the two approximations is enforced through a hybrid functional and element boundary integrals are involved only. Numerical examples are considered to investigate effects of element size, number of elements and crack length on crack tip singularity. Results show that the proposed approach can achieve better numerical accuracy than conventional FEM.

Extent of Three Parameter Zone and Optimum Strain Gage Location for Eccentric Cracked Configurations

The accuracy of measurement of opening mode stress intensity factor using strain gage techniques mainly depends on location of the strain gages. The present work proposes a finite element based simple procedure for accurate determination of three parameter zone and optimum strain gage location for various eccentric cracked configurations. In this paper, the effect of specimen size and crack length to width of the eccentric cracked plate on optimum location of strain gage is also studied. The results of the present investigation show that specimen size and ratio of crack length to width of the plate strongly influence the optimum location of strain gage.

The Stress Intensity Factor of Opening Mode Determined by Digital Image Correlation

Applications of the digital image correlation method (DIC) for the determination of the opening mode stress intensity factor (SIF) is investigated using an edge cracked aluminum plate in this paper. Standard compact tension test specimen was tested under tensile loading and the full-field displacement fields of the test sample were recorded using DIC. The SIF associated with unavoidable rigid-body displacement translation were calculated simultaneously from the experimental data by fitting the theoretical displacement field using the method of least-squares. Selection of displacement and convergence values is discussed. For validation, the SIF thus determined is compared with theoretical results, confirming the effectiveness and accuracy of the proposed technique. Therefore it reveals that the DIC is a practical and effective tool for full-field deformation and SIF measurement.

Experimental Investigation of Static Interfacial Fracture in Orthotropic Polymer Composite Bimaterials Using Photoelasticity

The effects of static Mode I (opening mode) loading on orthotropic-orthotropic bimaterial interface cracks have been investigated using the experimental technique of transmission photoelasticity. For successful implementation of this experimental technique transparent and birefringent glass fiber reinforced polyester composite materials were developed, enabling the direct observation and recording of photoelastic fringes in the vicinity of the interface crack in the orthotropic bimaterial. It is our belief that this is the first of such experimental investigation. Opening and shearing mode stress-intensity factors and the strain energy release rates have been calculated for various combinations of the bimaterial halves. Results have been verified by mathematically regenerating the observed isochromatic fringe patterns. This study has made it feasible to investigate interfacial fracture in orthotropic-orthotropic bimaterials and orthotropic-isotropic bimaterials using photoelasticity.

On the Mode I stress intensity factor for an external circular crack with fibre bridging

Abstract This paper presents a theoretical analysis of an external matrix crack located in a unidirectional fibre-reinforced elastic solid modelled as a transversely isotropic material. The presence of matrix cracking with fibre continuity introduces bridging action that has an influence on the stress intensity factors at the crack tip of the external crack. This paper presents a model for the bridged crack, where the fibre ligaments induce a constant displacement-dependent traction constraint over the external crack. This gives rise to a Fredholm integral equation of the second kind, which can be solved in an approximate fashion. We examine the specific problem where the bridged external circular crack is loaded by a doublet of concentrated forces. Numerical results are presented to illustrate the influence of the fibre–matrix modular ratio and the location of the loading on the bridged-crack opening mode stress intensity factor.

Characterization of fracture in adhesively bonded double-lap joints

A broad finite element study was carried out to understand the stress fields and stress intensity factors behavior of cracks in adhesively bonded double-lap joints, which are representative of loading in real aerospace structures. The interaction integral method and fundamental relationships in fracture mechanics were used to determine the mixed-mode stress intensity factors and associated strain energy release rates for various cases of interest. The numerical analyses of bonded joints were also studied for various kinds of adhesives and adherends materials, joint configurations, and thickness of adhesive and different crack lengths. The finite element results obtained show that the patch materials of low stiffness, low adhesive moduli and low tapering angles are desirable for a strong double-lap joint. In the double-lap joint, the shearing-mode stress intensity factor is always larger than that of the opening-mode and both shearing and opening mode stress intensity factors increase as the crack length increases, but their amplitudes are not sensitive to adhesive thickness. Results are discussed in terms of their relationship to adhesively bonded joints design and can be used in the development of approaches aimed at using adhesive bonding and extending the lives of adhesively bonded repairs for aerospace structures.

Determination of strain gage locations for the accurate measurement of opening mode stress intensity factors

Determination of strain gage locations for the accurate measurement of opening mode stress intensity factors

ACCURATE DETERMINATION OF STRESS INTENSITY FACTOR OF A CENTRAL CRACK BY DIGITAL PHOTOELASTICITY

In this paper, Irwin's method and two-parameter method are employed to get mode I stress intensity factor KI using photoelastic experiments. The initial images are processed by some software and multiplied and sharpened isochromatic fringes are applied to two different methods to get the accurate stress intensity factor. Irwin's method develops a relation for the opening-mode stress intensity factor in terms of the geometric characteristics of the fringe loops near the crack tip and requires only a single data point on the fringe. But there still is a problem in this method, a small error in the measurement can lead to large errors in determining stress intensity factor. Two-parameter method is tested to improve accuracy by using data from more than one fringe loop. The experimental results are compared with those obtained by the use of approximate empirical equation and FEM. Good agreement shows that the methods utilized in experiments are considerably reliable. The photoelastic results can be used for bench mark in theoretical study and other experiments.

Experimental Determination of KI for Short Internal Cracks

Since the pioneering discussion by Irwin, a significant effort has been devoted to determining stress intensity factors (K) using experimental methods. Techniques have been developed to determine stress intensity factors from photoelastic, strain gage, caustics, and moire´ data. All of these methods apply to a relatively long single-ended-edge crack. To date, the determination of K for internal cracks that are double-ended by experimental methods has not been addressed. This paper describes a photoelastic study of tension panels with both central and eccentric internal cracks. The data recorded in the experiments was analyzed using a new series solution for the opening-mode stress intensity factor for an internal crack. The data was also analyzed using the edge-crack series solution, which is currently employed in experimental studies. Results indicated that the experimental methods usually provided results accurate to within three to five percent if the series solution for the internal crack was employed in an overdeterministic numerical analysis of the data. Comparison of experimental results using the new series for the internal crack and the series for an edge crack showed the superiority of the new series.

The Bridged External Circular Crack

This paper examines the axisymmetnc problem of an external circular crack, which is located in a fibre-reinforced elastic solid. In contrast to the classical problem where the surfaces of the crack region are traction free, this paper considers the situation in which fibres exhibit continuity across the external crack thereby inducing a displacement dependent traction boundary condition. The influence of the bridging action on the crack opening mode stress intensity factor at the crack tip, created by axisymmetnc loading of a doublet of concentrated forces, is examined.

The penny-shaped crack at a bonded plane with localized elastic non-homogeneity

This paper examines the axisymmetric problem pertaining to a penny-shaped crack which is located at the bonded plane of two similar elastic halfspace regions which exhibit localized axial variations in the linear elastic shear modulus, which has the form G(z)=G1+G2e±ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The resulting mixed boundary value problem associated with the penny-shaped crack is reduced to a Fredholm integral equation of the second kind which is solved in a numerical fashion to generate the crack opening mode stress intensity factor at the tip.

The in-plane loading of rigid disc inclusion embedded in a crack

The paper examines the in-plane loading of a disc shaped rigid disc inclusion which is embedded in bonded contact with the plane surfaces of a penny-shaped crack. The mixed boundary value problem governing the elastostatic problem is reduced to the solution of a system of coupled integral equations, which are solved numerically to determine results of engineering interest. These results include the in-plane stiffness of the disc inclusion and the crack opening mode stress intensity factor at the boundary of the penny-shaped crack.

Interacting cracks and inclusions in a solid by multipole expansion method

An accurate series solution is obtained of the elastic problem for a solid containing penny-shaped cracks and spheroidal inclusions of cavities. The method of solution is based on the general solution procedure developed by Kushch [(1996) Elastic equilibrium of a solid containing a finite number of aligned inclusions. International Journal of Solids and Structures33, 1175–1189] and consists in representation of the displacement vector by a series of the vectorial partial solutions of Lame's equation, written in a spheroidal basis. By using the addition theorems for these partial solutions the primary boundary-value problem is reduced to an infinite set of linear algebraic equations. An asymptotic analysis of the problem is performed and the series expansion of the opening-mode stress intensity factor is obtained. Numerical analysis of model problems is performed and some results demonstrating the effect on the stress intensity factor of the pair interactions in crack-crack, crack-cavity and crack-inclusion geometries are presented.

Improved sour gas resistance of X-80 steel after quenching and tempering

Abstract The sour gas susceptibility of X-80 steel was investigated after quenching and tempering. Self-loaded modified wedge opening loading (M-WOL) specimens were exposed to an NACE sour gas solution under an applied opening mode stress intensity factor KI of 40 MPa m1/2 In this microstructural condition, crack arrest was exhibited at a threshold stress intensity value (KISSC) of 32 MPa m1/2. The relatively good performance of the steel after quenching and tempering was closely related to the development of a fine distribution of (Nb, Ti) containing carbides along ferrite lath boundaries. Apparently, the main crack path exhibited a significant number of bifurcations as it shifted continuously to follow the ferrite interlath boundaries as well as the prior austenitic grain boundaries.

Strain gage methods for measurement of opening mode stress intensity factor

In this study, the determination of the opening mode stress intensity factor by using strain gage methods is investigated both experimentally and analytically. The results are compared with the finite element solution. In the experimental program, cracks are opened at the tip of crack starter slot on the standard compact tension test specimens by using Electrical Discharge Machining (EDM) and Wiring Discharge Machining (WDM). Strain gage data from the crack tip region are used to calculate stress intensity factors with some limitations.