Numerical analysis of the stress intensity factors for repaired cracks from a notch with bonded composite semicircular patch

In this paper, we investigated the crack growth behaviour of cracked thin aluminium plate repaired with bonded composite patch. The finite element method is used to study the performance of the bonded composite reinforcement or repair for reducing the stress concentration at a semicircular lateral notch and repairing cracks emanating from this kind of notch. The effects of the adhesive properties and the patch size on the stress intensity factor variation at the crack tip in mode I were highlighted. The obtained results show that the stress concentration factor at the semicircular notch root and the stress intensity factor of a crack emanating from notch are reduced with the increase of the diameter and the number of the semicircular patch. The maximal reduction of stress intensity factor is about 42% and 54%, respectively, for single and double patch. However, the gain in the patch thickness increases with the increase of the crack length and it decreases when the patch thickness increases. The adhesive properties must be optimised in order to increase the performance of the patch repair or reinforcement.     

Computation of the stress intensity factors for repaired cracks with bonded composite patch in mode I and mixed mode

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity factors according to the crack length in mode I, shows that the stress intensity factor exhibits an asymptotic behaviour as the crack length increases. In mixed mode, the obtained results show that the Mode I stress intensity factor is more affected by the presence of the patch than that of mode II.     

The stress intensity factor for a cracked stiffened sheet repaired with an adhesively bonded composite patch

The problem of a cracked, stiffened metallic sheet adhesively bonded by a composite patch is analyzed. The composite patch is assumed to be either an infinite orthotropic sheet or an infinite orthotropic strip normal to the crack. Due to the high stress concentration around the crack and on the interface, an elliptical disbond is assumed to exist around the crack. The crack is asymmetric with respect to the stiffener's locations as well as to the patch's center. The effect of thermal stresses in curing process is also considered. The fracture problem is solved by the displacement compatibility method, using the complex variable approach and the Fourier integral transform method.The problem is dealt with in two steps. First, starting with an uncracked, patched stiffened sheet, the stress at the prospective location of the crack is determined in a closed-form solution. The second step is to introduce a crack into the stiffened patched sheet. The multivalue of the analytical formulation is treated in detail to ensure proper implement in the computer. The results show that the effect of the stiffeners on the stress intensity factor is not significant for a crack fully covered by a patch.For the repairs by Boron/Epoxy patches, the difference in KI between the infinite sheet patch and the infinite strip model is only minor (less than 5 percent) in the absence of the curing thermal stresses and it becomes more pronounced when these stresses are taken into consideration. The stress intensity factor for a crack repaired by an infinite composite strip also can be estimated with a good or reasonable accuracy via a simplified analysis in which the patch is considered as an infinite strip in the first step and is treated as an infinite sheet in the second step of the solution procedure mentioned above.The latter simplified analysis is based on the approach originally proposed by Rose for a relatively simple repair configuration. For most cases, that approach seems to work well for the repair of a stiffened sheet by an infinite composite strip with the effects of thermal stresses and a disbond included. It should be emphasized that the present methodology can apply to the problem of a crack in a metallic stiffened sheet growing beyond the patch's boundary and also to the repairs by an infinite adhesively bonded composite strip parallel to the crack.     

Evaluation of the stress intensity factor for cracks in elastomers

We analyze the applicability of the method of the J-integral to the solution of problems of fracture mechanics for structures made of low-compressible elastomers. The components of the J-integral are computed by the method of equivalent three-dimensional integration. To take into account weak compressibility, we use the finite-element moment scheme. Lugansk Agricultural Institute, Lugansk, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 81–85, July–August, 1999.     

The effects of disbonds on the pure mode II stress intensity factor of aluminium plate reinforced with bonded composite materials

Adhesively bonded composite patch repair has been widely used to restore or extend the service life of cracked structural components due to its effectiveness to mechanical repair technique. In this work, the finite element method is applied to analyse the performance of the bonded composite patch for repairing cracks emanating from semicircular notch root in pure mode II. The stress intensity factor was computed at the crack tip repaired using a boron/epoxy patch for different orientation of fibers, taking into account the disbond. In this case, the increase of a patch thickness reduces the negative effects of disbond. When this effect is significant between the patch and the plate, it reduces the repair effectiveness. The maximum reduction obtained by using a boron/epoxy of fibers in the x-direction is of the order of 20% more important compared to a patch having its fibers in the y-direction. The stress intensity factor exhibits an asymptotic behaviour as the disbond size increases.     

加载速率对复合材料粘接修理金属结构力学性能的影响

基于复合材料补片基体和胶层树脂黏弹性的特点, 分别采用光固化和传统热固化方式制备了一系列不同树脂配方的试样, 实验研究了树脂配方对修理结构应变率效应的影响, 测定了复合材料粘接修理结构在不同加载速率下的力学性能。结果表明, 树脂体系的交联度较低时, 应变率效应更明显; 加载速率的提高通常会使补片更好地发挥分担载荷的作用, 但是也会导致变形协调能力的下降; 这两个因素共同影响复合材料粘接结构的最终修理效率。加载速率对于复合材料粘接修理结构的破坏模式也有影响。     

加载速率对复合材料粘接修理金属结构力学性能的影响

基于复合材料补片基体和胶层树脂黏弹性的特点,分别采用光固化和传统热固化方式制备了一系列不同树脂配方的试样,实验研究了树脂配方对修理结构应变率效应的影响,测定了复合材料粘接修理结构在不同加载速率下的力学性能.结果表明,树脂体系的交联度较低时,应变率效应更明显;加载速率的提高通常会使补片更好地发挥分担载荷的作用,但是也会导致变形协调能力的下降;这两个因素共同影响复合材料粘接结构的最终修理效率.加载速率对于复合材料粘接修理结构的破坏模式也有影响.     

Analysis of the plastic zone size ahead of repaired cracks with bonded composite patch of metallic aircraft structures

In this study, the three-dimensional and non-linear finite element method is used to estimate the performance of the bonded composite repair of metallic aircraft structures by analyzing the plastic zone size ahead of repaired cracks. Several calculations have been realized to extract the plasticized elements around the crack tip of repaired crack. The obtained results show that the presence of the composite patch reduces considerably the size of the plastic zone ahead of the crack. The effects of the adhesive properties and the patch thickness on the plastic zone size ahead of repaired cracks were analyzed.     

Accurate stress intensity factor solutions for corner cracks at a hole

Laboratory test and in-service experience shows fatigue cracks at holes exhibit unsymmetric growth; thus, the need for the new solutions is paramount. Stress intensity factor, K, solutions for symmetric and unsymmetric corner cracks at a hole subject to general loading were determined using a hp-version of the finite element method (FEM) in conjunction with a mathematical splitting scheme to enable efficient, accurate calculations. In traditional applications of the FEM, mesh generation is labor intensive; however, using the splitting scheme, stress intensity functions are obtained without explicitly including the crack in the FE mesh of the global structure. By using the hp-version of FEM, a set of K-solutions converging exponentially fast to the exact solution is obtained. The crack is analyzed in the local domain with easily generated FE meshes. All structurally significant crack shapes were considered; specifically, crack depth to crack length ratios (a/c) of 0.1–10.0, crack depth to sheet thickness ratios (a/t) of 0.10–0.99, and hole radius to sheet thickness ratios (r/t)=1.0. The loading conditions were remote tension, remote bending, and pin loading (bearing). In addition, all combinations of a/c and a/t are analyzed at each side of the hole; thus 226,875 solutions were developed with control of the error in the computed K solutions. Calculated relative error is generally much smaller than 1% along the entire crack front including the vertex regions. Comparisons are made to solutions in the open literature. The new K solutions show the literature solutions are, in general, accurate for all three load conditions; however, for the extreme cases of a/c, a/t, and r/t; the literature solutions differ by as much as 26%.     

Stress intensity factor for semi-elliptical surface cracks loaded by stress gradients

The stress intensity factor at the deepest point of a semi-elliptical surface crack is calculated for stress gradients in direction of depth. The method is based on weight functions. The crack opening displacement for the reference problem is calculated with a method proposed by Petroski and Achenbach. The results are compared to finite element solutions given in the literature. As an example, the stress intensity factor is calculated for a crack in a thermally shocked pipe.     

Dynamic stress intensity factor for an unbounded plate having collinear cracks

The steady-state vibration of an infinite plate with collinear cracks is considered for low frequency cyclic loading. The formulation of the mixed boundary value problem leads to a dual trigonometric series. The Schwinger's method gives an automatic perturbation scheme. The dynamic stress intensity factor is found to be higher than the corresponding static one. The inertial effect on the stress intensity factor becomes significant only when the frequency of the external load is close to that of the shear wave.     

Piezoelectric sensor for stress intensity factor measurement of two dimensional cracks

A piezoelectric sensor for the measurement of stress intensity factors (SIFs) of two dimensional cracks induced in a structure is developed. Two small pieces of piezoelectric elements are adhered near the crack tip so that the piezoelectric elements are placed close to each other and the crack tip’s position is between them. The electric currents from the piezoelectric elements are integrated by integration circuits and the output voltages which are proportional to the electric charge induced in the piezoelectric elements are measured. The SIFs of Mode I (K_I) as well as of Mode II (K_II) based on the piezoelectric constitutive law and fracture mechanics are calculated.     

Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor

In this paper we investigate the stress intensity factors (SIFs) of multiple penny-shaped cracks in an elastic solid cylinder under mode I (axial tension) loading. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. The fractal-like finite element method (FFEM) is employed to study the interaction of multiple cracks and to demonstrate the efficiency of the FFEM for multiple crack problems. The results show that the SIF values of the inner cracks, which are denoted as crack number 1,2,3,…,(n+1)/2 of a stack of n parallel cracks, are lower than the SIF values of a single crack by between 16% and 48%. Also, the outermost crack, that is the crack closest to the boundaries of a multiple cracked body, has the highest SIF values and is, therefore, likely to fail first.     

Effect of curvature at the crack tip on the stress intensity factor for curved cracks

In this paper, the numerical solution of the hypersingular integral equation using the body force method in curved crack problems is presented. In the body force method, the stress fields induced by two kinds of standard set of force doublets are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form r ^–2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density functions and power series. The calculation shows that the present method gives rapidly converging numerical results for curved cracks under various geometrical conditions. In addition, a method of evaluation of the stress intensity factors for arbitrary shaped curved cracks is proposed using the approximate replacement to a simple straight crack.     

Green's functions for the stress intensity factor evolution in finite cracks in orthotropic materials

The elastodynamic response of an infinite orthotropic material with finite crack under concentrated 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 example materials are obtained. This solution can be used as a Green's function to solve dynamic problems involving fini te cracks.     

Computing stress intensity factors for curvilinear cracks

The use of the interaction integral to compute stress intensity factors around a crack tip requires selecting an auxiliary field and a material variation field. We formulate a family of these fields accounting for the curvilinear nature of cracks that, in conjunction with a discrete formulation of the interaction integral, yield optimally convergent stress intensity factors. In particular, we formulate three pairs of auxiliary and material variation fields chosen to yield a simple expression of the interaction integral for different classes of problems. The formulation accounts for crack face tractions and body forces. Distinct features of the fields are their ease of construction and implementation. The resulting stress intensity factors are observed converging at a rate that doubles that of the stress field. We provide a sketch of the theoretical justification for the observed convergence rates and discuss issues such as quadratures and domain approximations needed to attain such convergent behavior. Through two representative examples, a circular arc crack and a loaded power function crack, we illustrate the convergence rates of the computed stress intensity factors. The numerical results also show the independence of the method from the size of the domain of integration. Copyright © 2015 John Wiley & Sons, Ltd.