Approximate weight function methods using a new condition

A method is presented to derive the approximate weight functions, by using a new condition on the crack mouth, for edge cracks in the semi-infinite or finite plate under Mode I loadings. This method requires only one information, say, the reference stress intensity factor (SIF), K_r. Numerical examples show that the present method is efficient in evaluation of the SIFs for edge cracks subjected to the polynomial loadings on the crack faces.     

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

Adhesively bonded composite patch repair is efficient means to regain load carrying capacity, alleviate the crack growth, and improve the service life of the damaged structure. In this paper, three dimensional finite element models are developed to examine the fracture behavior of a single edge V-notched Aluminum plate repaired with Kevlar-49/epoxy or e-glass/epoxy pre-preg patches on both sides. Contour integral method was used for evaluating the stress intensity factor (SIF), an indicator of the crack stability. The load transfer mechanisms, stress distribution, damage variable (D), and crack mouth opening displacement (CMOD), were also presented to estimate the effectiveness of composite patch repair. The influence of the patch material, crack length and the adhesive thickness has been investigated. Results have shown that the crack induced damage increased nonlinearly with a larger crack size. With the composite patch repairs, SIF is reduced to 1/7–1/10 of that of the bare plate and CMOD decreased by 79%. The damage variable is reduced significantly and the load capacity is increased. A thinner adhesive layer results in a higher percentage of load shared by the composite patch.     

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C⁰ finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.     

Modified crack closure integral using six-noded isoparametric quadrilateral singular elements

Six-noded, isoparametric serendipity type quadrilateral regular/singular elements are used for the estimation of stress intensity factors (SIF) in linear elastic fracture mechanics (LEFM) problems involving cracks in two-dimensional structural components. The square root singularity is achieved in the six-noded elements by moving the in-side nodes to the quarter point position. The modified crack closure integral (MCCI) method is adopted which could generate accurate estimates of SIF for a relatively coarse mesh. The equations for strain energy release rate and SIF are derived for mixed mode situations using six-noded quadrilateral elements at the crack tip. The model is validated by numerical studies for a centre crack in a finite plate under uniaxial tension, a single edge notched specimen under uniaxial tension, an inclined crack in a finite rectangular plate and cracks emanating from a pin-loaded lug (or lug attachment). The results compare very well with reference solutions available in the literature.     

Stress intensity factor solution for a semi-elliptical crack in an arbitrarily distributed stress field

An equation for the stress intensity factor (SIF) for semi-elliptical crack has been developed. It is based on the Newman-Raju's solution for the crack in a plate under bending or tension. The equation can be applied when a stress distribution is described by a power function. Using the approach outlined, the SIF for a surface crack in a T-butt welded connection has been estimated. The results obtained can be used in a fracture-mechanics-based fatigue analysis.     

Determination of Fracture Parameters for Multiple Cracks of Laminated Composite Finite Plate

A predictive method for estimation of stress state at zone of crack tip and assessment of remaining component lifetime depend on the stress intensity factor (SIF). This paper discusses the numerical approach for prediction of first ply failure load (F_L), progressive failure load, SIF and critical SIF for multiple cracks configurations of laminated composite finite plate using finite element method (FEM). The Hashin and Chang failure criterion are incorporated in ABAQUS using subroutine approach user defined field variables (USDFLD) for prediction of progressive fracture response of laminated composite finite plate, which is not directly available in the software. A tensile experiment on laminated composite finite plate with stress concentration is performed to validate the numerically predicted subroutine results, shows excellent agreement. The typical results are presented to examine effect of changing the crack tip distance (S), crack offset distance (H), and stacking fiber angle (θ) on F_L, and SIF .     

A new weight function approach using indirect boundary integral method

A new weight function approach to determine SIF (stress intensity factor) using the indirect boundary integral method has been presented. The crack opening displacement field was represented by one boundary integral in the form of a single-layer potential whose kernel was modified from the fundamental solution. The proposed method enables the calculation of SIF using only one SIF formula without any modification of the crack geometries symmetric in a two-dimensional plane, e.g. a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure for this variety of crack geometries is very simple and straghtforward with only one SIF formula. The necessary information in the analysis is two reference SIFs. The analysis results, using several examples, verified that the present closed-form solution was in good agreement with those of the literature and applicable to various crack geometries.     

3-D boundary element method for cracks in a plate

New fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3-D boundary element method (BEM) for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations, ‘Part-through’ elliptic cracks in an elastic plate with traction-free surfaces are analysed and the stress intensity factor (SIF) values along the crack front are found to compare favourably with widely accepted numerically obtained SIF results by Raju and Newman.¹     

On the through-thickness crack with a curve front in center-cracked tension specimens

Three-dimensional finite element analyses are performed on through-thickness cracks with slightly wavy front in center-cracked plates. Considering there is an inherent relationship between the crack shape and the corresponding stress intensity factor (SIF) distribution of a crack, the curved configuration of the crack is determined using a heuristically derived iterative procedure if the SIF distribution function is known. Several simple SIF distribution functions, for instance the constant SIF distribution along the crack front, are assumed to determine the crack shape. Under the assumption that the rate of fatigue crack growth depends on the SIF range or the effective SIF range, possible effects of plate thickness, crack length and crack closure level gradient on the behaviour of crack tunneling are investigated. The stability of the curved shape of a through-thickness crack in fatigue is also discussed, i.e. whether a crack can maintain its shape satisfying the conditions of constant SIF distribution or other distribution along the crack front during fatigue growth. This study will be useful for a better understanding of the behaviour of crack tunneling and help to evaluate the validity of the two-dimensional linear elastic fracture mechanics in cracked plates.     

Thermal striping fatigue damage in multiple edge-cracked geometries

Thermal fatigue striping damage may be caused when incompletely mixed hot and cold fluid streams pass over the surface of a component or structure containing a defect. Stress intensity factor (SIF) fluctuations are developed in response to the surface temperature fluctuations. An existing methodology for the analysis of striping damage in geometries containing a single edge‐crack geometry is extended to such an analysis of multiple edge cracks. SIFs are calculated as functions of crack depth, when an edge‐cracked plate and semi‐infinite solid, each containing multiple cracks, are subjected to thermal striping. The effect of various restraint conditions and striping frequencies on the SIF values for a stainless steel plate is examined. The degree of conservatism is shown when an assessment of thermal fatigue striping damage is based on a single, rather than multiple, crack analysis. Accurate curve fits are developed resulting in practical weight functions for an edge‐cracked plate and semi‐infinite solid.     

Irreversible growth of a spherical cavity in rubber-like material: A fracture mechanics description

A procedure is presented for determining stress intensity factors for single and double edge cracks in simply supported undamped Bernoulli–Euler beams under a moving load. The approach is based on using modal analysis to determine the equivalent load on the beam, then linear elastic fracture mechanics is used to calculate stress intensity factors (SIF). The results show that SIF is a function of time, speed of the moving load and crack size and location.     

Anti-plane shear problem for an edge crack in a finite orthotropic plate

The problem of an edge crack in a finite orthotropic plate under anti-plane shear is considered. The boundary collocation method is used to calculate the mode III stress intensity factor (SIF). For the case in which the material is isotropic, the present results agree very well with those obtained by using the integral equation method. Furthermore, the method can be extended readily for general cases with arbitrary geometrical and boundary loading conditions and material properties.     

Stress intensity factors for through-thickness cracks in a wide plate: Derivation and application to arbitrary weld residual stress fields

Exact closed-form stress intensity factor (SIF) solutions have been developed for mode-I, II and III through-thickness cracks in an infinite plate. Centre-crack problems have been analysed comprehensively in the literature, but the focus has been on the effect of simple loading about the crack centre. In the current work, the formula of Sih-Paris-Erdogan was extended to consider the difference in SIF on the left and right crack tips under an asymmetric stress field. Mathematical manipulations were performed to derive exact stress magnification factors for SIF computations and simultaneously circumvent the problem of crack-tip stress singularity. The solutions so obtained are applied to derive the residual SIFs that would act on a crack growing under the influence of the residual stress fields associated with VPPA (variable polarity plasma arc) and friction stir welds, using measured residual stress profiles.     

Calculating stress intensity factors for a semi-elliptical surface crack in a heterogeneous stress field

The author proposes an equation for calculating the stress intensity factor (SIF) for a semi-elliptical surface crack for uniform, linear, and quadratic laws of variation of the load applied to its edges. The derivation of the equation is based on the well-known Newman—Raju solution for a bent plate. The distribution of the values of SIF along the crack front, obtained using the empirical equations, coincides with the results of calculations carried out using the finite element method (FEM).Translated from Problemy Prochnosti, No. 7, pp. 38–41, July, 1990.     

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.     

Approximate Green's functions for singular and higher order terms of an edge crack in a finite plate

An edge crack in a finite plate (FSECP) subjected to wedge forces is solved by the superposition of the analytical solution of a semi-infinite crack, and the numerical solution of a FSECP with free crack faces, which is solved by the Williams expansion. The unknown coefficients in the expansion are determined by a continuous least squares method after comparing it with the direct boundary collocation and the point or discrete least squares methods. The results are then used to validate the stress intensity factor (SIF) formula provided by Tada et al. that interpolates the numerical results of Kaya and Erdogan, and an approximate crack face opening displacement formula obtained in this paper by Castigliano's theorem and the SIF formula of Tada et al. These approximate formulae are accurate except for point forces very close to the outer edge, and can be used as Green's functions in the crack-closure based crack growth analysis, as well as in interpreting the size effect of quasi-brittle materials. Green's functions for coefficients relevant to the second to the fifth terms in the crack tip asymptotic field are also provided. Finally, a FSECP with a uniform pressure over a part of the crack faces is solved to illustrate the application of the obtained Green's functions and to further assess their accuracy by comparing with a finite element analysis.     

Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading

The stress intensity factor is a traditional topic in mechanics and there have been many solutions for many different cases. The closed frictional crack problem has been modeled in the rock mechanics field where fractures are mostly under compression. Further, the effect of finite plate dimensions under biaxial loading has not been considered in the literature. The key contribution of the present paper is to evaluate the effect of the crack length to plate width ratio on the mode I and II stress intensity factors (SIF) of a central slant crack with frictional surfaces in plates with biaxial loading of different patterns, i.e. tension-tension, tension-compression, compression-tension or compression-compression. A plane strain elastic two-dimensional finite element analysis was adopted. Crack length to plate width ratios equal to 0.1, 0.3 and 0.5 with biaxial ratios from –1 to 1, crack angles from 0° to 90° and friction coefficients from 0 to 1 were considered. Contact regimes and the effect of the crack length to plate width ratio were found dependent on biaxial ratio and pattern, friction coefficient and crack angle.     

Determination of dynamic fracture toughness for PMMA

A dynamic FEM (finite element method) and a strain gage method are applied to analyze the dynamic fracture toughness and SIF (stress intensity factor) for PMMA (polymethyl methacrylate). The analyses are carried out for plates with an edge crack subjected to one-point bending in a plane of the plate. A simple procedure that the present author has proposed is applied to the problem of using a triangular element of assumed constant strain on finite element analysis. The numerical simulation by FEM provides values for the applied forces as measured with the strain gages. Also, a crack initiation time is measured with the strain gage mounted around the crack tip. The dynamic fracture toughness is determined by adapting the crack initiation time to the simulation curve of the dynamic SIF calculated by the FEM. In this study, the usefulness of the method to determine the dynamic fracture toughness is investigated by comparing predictions with the experimental results for dynamic stresses and SIFs.     

弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的有限元分析

对表面裂纹复合型应力强度因子的研究一直是线弹性断裂力学中的重要课题,例如弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的计算,到现在也没有一个正确的分析解。考虑到裂尖的应力奇异性,在裂纹前沿手动设置三维奇异单元,用三维有限元法中的1/4点位移法计算弯扭组合载荷下圆管表面椭圆裂纹前沿的Ⅰ型、Ⅱ型和Ⅲ型应力强度因子,并分析其随裂纹深度增加时的变化规律。运用该方法计算了有关模型的应力强度因子,并与该模型的实验值进行了比较,计算结果和实验结果吻合良好。     

Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates

The effect of crack surface friction on mode II stress intensity factor (SIF) of a central slant crack in a plate uniformly loaded in uniaxial compression is quantified. A previously developed two-dimensional finite element analysis was utilised after its modification to accommodate the friction between the crack surfaces. The plane strain state was assumed. A new numerical technique was devised to avoid the iteration procedures, which had to be employed due to the existence of frictional forces.

The crack inclination angle varied between zero and 75° measured from the horizontal direction. The coefficient of friction of the crack surfaces changed from zero to 1. In case of relatively sliding crack surfaces, mode II SIF existed. As is well known, the resulting mode II SIF decreased with increasing the coefficient of friction of the crack surfaces. Further, mode II SIF increased with increasing crack line inclination angle and then decreased after reaching a maximum value. The angle corresponding to that maximum SIF increased as the coefficient of friction of the crack surfaces increased.