Enhancing Stress Intensity Factor Reduction in Cracks Originating from a Circular Hole in a Rectangular Plate under Uniaxial Stress through Piezoelectric Actuation

Circular holes are commonly employed in engineering designs;however, they often serve as locations where cracks initiate and propagate. This paper explores a novel approach to structural repair by utilizing piezoelectric actuators. The primary focus of this study is to investigate the influence of an adhesively bonded piezoelectric actuator patch placed above a circular hole on the stress intensity factor (SIF) in an aluminium plate. The plate is subjected to uniaxial tensile stress, while the piezoelectric actuator is excited with varying voltage levels. The analysis is conducted using the finite element method (FEM), a powerful numerical technique for simulating complex structures. The study assesses the stress distribution and employs the SIF as an adequate criterion for evaluating the impact of different patch configurations. The results indicate a strong correlation between the applied voltage and the SIF. Whether the SIF increases or decreases depends on the polarization of the piezoelectric actuator. Particularly noteworthy is the finding that rectangular patches in a horizontal orientation significantly reduce the SIF compared to other patch geometries. Moreover, double-sided patches exhibit a pronounced decrease in the SIF compared to single-sided patches. In summary, this research underscores the potential of piezoelectric actuators in mitigating stress intensity in structures with circular hole with crack initiation. It offers valuable insights into the influence of applied voltage, patch geometry, and patch placement on the SIF, thereby contributing to developing effective strategies for enhancing structural integrity.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working con- ditions is an essential issue. In this paper, a comprehensive study of stress intensity factors （SIFs） in rotating disks containing three-dimensional （3D） semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical prop- erties, rotational velocity, and orientation of cracks on SIFs in rotating disks under cen- trifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

Evaluation of mixed-mode stress intensity factors by extended finite element method

Extended finite element method (XFEM) implementation of the interaction integral methodology for evaluating the stress intensity factors (SIF) of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationally efficient.

Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors （SIFs） of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

DYNAMIC STRESS INTENSITY FACTORS AROUND TWO CRACKS NEAR AN INTERFACE OF TWO DISSIMILAR ELASTIC HALF－PLANES UNDER IN－PLANE SHEAR IMPACT LOAD

Transient stresses around two collinear cracks which lie in parallel with theinterface of the two dissimilar half-planes are studied in this article.The surfaces ofthe cracks are sheared suddenly. Application of the Fourier and Laplace transforms technique reduces the problem to that of solving dual integrai equations.To solvethese,the differences of.the crack surface displacements are expanded in a series offunctions which are automatically zero outside of the cracks. The unknown coefficients accompanied in the series are determined by the Schmidt method. The stress intensity .factors are defined in the Laplace transform domain and these are inverted numerically in the physical space .As an example ,the dynamic stress intensity factors around two cracks in a ceramic and steel bonded composite are numerically calculated.

An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks

The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.

Digital Image Correlation Using Specific Shape Function for Stress Intensity Factor Measurement

The stress intensity factor(SIF) is a critical parameter associated with the fracture behaviour of materials. In this paper, we select the displacement function around a crack tip as the shape function of the digital image correlation(DIC), which makes it possible to directly calculate the SIF by the correlation scheme. Moreover, we use a non-rectangular subset, which can reduce the influence of plastic deformation and crack width on the DIC measurement accuracy. We measured the SIF of a mode I crack in a super-hard aluminium alloy specimen to verify the performance of the proposed method. Our experimental results show that a DIC with a specific shape function can be used to accurately and efficiently calculate the SIF.Furthermore, we also present a practical application of our proposed method for determining the SIF, crack propagation angle and crack tip displacement.

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC STRESS INTENSITY FACTOR

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

Analysis on Fracture Mechanics of Unstable Rock

Unstable rock is a kind of global geological disaster with high frequency. This paper, considering three kinds of combined loads which are gravity, fracture water pressure and seismic force, constructs a unstable rock mechanics model and it uses a fracture mechanics method to deduce the composite stress intensity factor of the type I - II. Based on the maximum circumferential stress theory, this article calculates the theo-retical fracture angle by triangle universal formula.

Theoretical and numerical studies of crack initiation and propagation in rock masses under freezing pressure and far-field stress

Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Fracture mechanics analysis on Smart-Cut~technology.Part 2:Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that the bonding flaws with large size are prone to cause severe deviation of defect growth, leading to a non-transferred area of thin layer when splitting. In a practical Smart-Cut process where the internal pressure of bonding flaws is very small, large interfacial defects always promote defect growth in the splitting process. Meanwhile, increasing the internal pressure of the bonding flaws decreases the defect growth and its deviation before splitting. The mechanism of relaxation of stiffener constraint is proposed to clarify the effect of bonding flaws. Moreover, the progress of the splitting process is analyzed when bonding flaws are present. After splitting, those bonding flaws with large size and high internal pressure are vulnerable for the blistering of the thin film during high-temperature annealing.

A Study on Propagation Mechanism of Fracture Systems in Rock Masses by Discontinuity Displacement Method

The main task of fracture mechanics of rock masses is the study on the propagating mechanism of fractures in rock masses , which can be efficiently conducted by discontinuty displacement (DD) numerical evaluation . Firstly ,the element stress and displacement are analysed and the principle and steps of the numerical calculation of stress intensity factor and fracture extension force are introduced .The numerical results of parallel and echelon fracture systems ,which are compared with real field fractures .are presented. Finally . a simple engineering application example is presented .

钢桥面板对接焊缝表面多缺陷疲劳效应研究

为探明钢桥面板对接焊缝焊趾区域共面及异面表面多缺陷在裂纹扩展过程中的形态变化及相互作用机制,以钢桥面板U肋下翼缘对接焊缝简化后的基本焊接构造为研究对象,探明对接焊缝焊接区域的应力强度因子KI分布,并在验证ABAQUS与FRANC3D数值模拟方法可靠性的基础上,对焊趾区域植入的共面或异面多裂纹进行多裂纹扩展分析。研究结果表明:含余高对接焊缝在轴拉荷载作用下,焊趾线附近存在应力强度因子KI的峰值点;相邻共面裂纹在扩展至临界深度的过程中存在裂纹融合前、裂纹融合时及裂纹融合后3个典型的扩展阶段,不同阶段裂纹前沿形态及扩展速率da/dN变化可通过等效应力强度因子幅值ΔK_(eff)的分布来体现;共面裂纹融合前,单裂纹靠近另一裂纹长轴端点的裂纹相互作用比例因子随净间距s1与裂纹深度a比值呈幂次负相关性;对接焊缝异面裂纹中焊趾处裂纹对热影响区裂纹存在抑制作用,并随着裂纹尺寸差异的累计增加,焊趾处裂纹对热影响区的抑制作用呈线性扩大,最终使得热影响区裂纹ΔK_(eff)低于门槛值ΔKth而失去活性停止扩展,上述抑制作用随异面净间距s2的增加而减弱。

Effects of stick-slip on stress intensity factors for subsurface short cracks in rolling contact

This paper theoretically investigates the effects of stick-slip in rolling contact zone on stress intensity factors(SIFs)for subsurface short cracks.New mathematical models for SIFs including stick-slip ratio are deduced in two cases.One is a subsurface short crack parallel to surface,and the numerical analysis shows that the value of KⅡincreases with the increase of stick-slip ratio;the other is a subsurface short crack perpendicular to the surface,and the numerical analysis indicates that the positive value of KⅠdecreases with the increase of stick-slip ratio.As △KⅠand △KⅡare necessary to evaluate the fatigue crack propagation rate or fatigue lifetime,the influences of stick-slip ratio on them are then discussed.It is found that the maximum variations of △KⅠand △KⅡare both around 3.0%due to stick-slip ratio variation.

Extraction of Stress Intensity Factors by Using the P-Version Finite Element Method and Contour Integral Method

The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral method.Several numerical experiments,e.g.,crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length,unequal-length hole-edge cracks,respectively,at a rectangular plate,an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model,are used to demonstrate the accuracy and effectiveness of the approaches.SIFs are presented for the effects of various crack lengths and length-width ratio.Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method,boundary element method,high-order extended finite element method(high-order XFEM)and commercial finite element software ABAQUS in the available literature.Numerical results are in good agreement with the benchmark problems and show faster convergence rate,higher accuracy and better numerical stability.

Variation of stress intensity factors for several interface crack problems under arbitrary material combinations

In this paper the variation of interface stress intensity factors is considered under arbitrary material combinations for several problems such as central internal interface cracks,periodic interface cracks,and edge interface cracks.The stress intensity factors for all these problems have been determined in terms of Dundurs' parameters,by the application of FEM in the authors' previous papers.In this paper,the variations of the stress intensity factors for all these problems are discussed under arbitrary,,then the maximum and minimum values of dimensionless stress intensity factors F I,max,F II,max,F I,min,F II,max are indicated on the map of,.As an example,it is found that F I,max always appears when(,)=(0.2,0.3),and F I,min always appears when(,)=(1,0),for the central internal interface cracks independent of crack length.

Stress intensity factors under combined bending and torsion moments

This paper discusses stress intensity factor (SIF) calculations for surface cracks in round bars subjected to combined torsion and bending loadings. Different crack aspect ratios, a/b, ranging from 0.0 to 1.2 and relative crack depths, a/D, ranging from 0.1 to 0.6 were considered. Since the loading was non-symmetrical for torsion loadings, a whole finite element model was constructed. Then, the individual and combined bending and torsion loadings were remotely applied to the model. The equivalent SIF method, F*EQ, was then used explicitly to combine the individual SIFs from the bending and torsion loadings. A comparison was then carried out with the combined SIF, F*FE, obtained using the finite element analysis (FEA) under similar loadings. It was found that the equivalent SIF method successfully predicted the combined SIF for Mode I. However, discrepancies between the results determined from the different approaches occurred when FIII was involved. It was also noted that the predicted F*FE using FEA was higher than the F*EQ predicted through the equivalent SIF method due to the difference in crack face interactions.

基于比例边界有限元法计算应力强度因子的不确定量化分析

应力强度因子是预测荷载作用下结构中裂纹产生和扩展的重要参数。半解析的比例边界有限元法结合了有限元和边界元法的优势,在裂纹尖端或存在奇异应力的区域不需要局部网格细化,可以直接提取应力强度因子。在比例边界有限元法计算应力强度因子的框架下,引入随机参数进行蒙特卡罗模拟(Monte Carlo simulation, MCS),并提出一种新颖的基于MCS的不确定量化分析。与直接的MCS不同,采用奇异值分解构造低阶的子空间,降低系统的自由度,并使用径向基函数对子空间进行近似,通过子空间的线性组合获得新的结构响应,实现基于MCS的快速不确定量化分析。考虑不同荷载状况下,结构形状参数和材料属性参数对应力强度因子的影响,使用改进的MCS计算应力强度因子的统计特征,量化不确定参数对结构的影响。最后通过若干算例验证了该算法的准确性和有效性。