Crack Problems Research Articles

Numerical Comparison Research on the Solution of Stress Intensity Factors of Multiple Crack Problems

A newly developed approach without crack surface discretization for modeling 2D solids with large number of cracks in linear elastic fracture mechanics is proposed with the eigen crack opening displacement (COD) boundary integral equations in this paper. The eigen COD is defined as a crack in an infinite domain under fictitious traction acting on the crack surface. Respect to the computational accuracies and efficiencies, the multiple crack problems in finite and infinite plates are solved and compared numerically using three different kinds of boundary integral equations (BIEs): 1) the dual BIEs require crack surface discretization; 2) the BIEs with numerical Green’s functions (NGF) without crack surface discretization, but have to solve a complementary matrix; 3) the eigen crack opening displacement (COD) BIEs in the present paper. With the concept of eigen COD, the multiple crack problems can be solved by using a conventional displacement discontinuity boundary integral equation in an iterative fashion with a small size of system matrix as that in the NGF approach, but without troubles to determine the complementary matrix. Solution of the stress intensity factors of multiple crack problems is solved and compared in some numerical examples using the above three computational algorithms. Numerical results clearly demonstrate the numerical models of eigen COD BIEs have much higher efficiency, providing a newly numerical technique for multiple crack problems. Not only the accuracy and efficiency of computation can be guaranteed, but also the overall properties and local details can be obtained. In conclusion, the numerical models of eigen COD BIEs realize the simulations for multiple crack problems with large quantity of cracks.

Effective Two-Level Domain Decomposition Preconditioners for Elastic Crack Problems Modeled by Extended Finite Element Method

Effective Two-Level Domain Decomposition Preconditioners for Elastic Crack Problems Modeled by Extended Finite Element Method

Road Damage Detection Utilizing Convolution Neural Network and Principal Component Analysis

Roads should always be in a reliable con-dition and maintained regularly. One of the problems that should be maintained well is the pavement cracks problem. This a challenging problem that faces road engineers, since maintaining roads in a stable condition is needed for both drivers and pedestrians. Many meth-ods have been proposed to handle this problem to save time and cost. In this paper, we proposed a two-stage method to detect pavement cracks based on Principal Component Analysis (PCA) and Convolutional Neural Network (CNN) to solve this classification problem. We employed a Principal Component Analysis (PCA) method to extract the most significant features with a di˙erent number of PCA components. The proposed approach was trained using a Mendeley Asphalt Crack dataset, which contains 400 images of road cracks with a 480×480 resolution. The obtained results show how PCA helped in speeding up the learning process of CNN.

The effect of interfacial thermal resistance on interface crack subjected to remote heat flux

We consider the thermoelastic problem of an interface crack between two dissimilar semi-infinite isotropic materials under a uniform remote heat flux in plane deformation. The crack face is assumed to be partially thermopermeable (defined by a partial insulation coefficient of the crack), while the interface is assumed to be perfectly bonded except that a constant thermal resistance is introduced into the interfacial region near the tips of the crack. By using the integral transform method, we obtain the analytic solution for the thermoelastic field in the entire bi-material system. Numerical examples are presented to study the influence of interfacial thermal resistance on the thermal stress intensity factors and the crack opening/sliding displacements. It is shown that the magnitudes of the mode I and mode II TSIFs, as well as the crack opening displacements, increase with the increasing interfacial thermal resistance, while the crack sliding displacement is insensitive to the change of interfacial thermal resistance.

Identification of crack-like defect and investigation of stress concentration in coated bar

The first part of this work is devoted to the location of defects in a coated bar and the identification of their geometrical parameters. Using the methods of finite element modeling, ultrasonic non-destructive testing and machine learning technologies (artificial neural networks), the inverse problem of mechanics has been solved. A finite element model of ultrasonic wave propagation in a bar with a coating and an internal defect is constructed. Compared with previous works, the model used PML (Perfectly Matched Layer) structures, which suppress multiple reflections of the probe ultrasound pulse inside the bar and prevent signal noise. Based on the conducted numerical calculations of the finite element model, a data set was constructed. It contains the geometrical parameters of the defect and the corresponding amplitude-time characteristic of the ultrasonic signal. The architecture of a direct propagation neural network has been developed. The neural network was trained on the basis of previously processed data. As a result, on the basis of ultrasound data obtained from the outer surface of the bar, it is possible to restore the values of such defect parameters as depth, length and thickness. At the second stage, analytical-numerical technology for studying the stress intensity factor (SIF) at the crack tip is described using the example of the problem of a longitudinal internal crack of finite length located in an elastic strip reinforced with a thin flexible coating. The solution to this problem is based on the method of integral transformations, which made it possible to reduce it to a singular integral equation of the first kind with a Cauchy kernel, which is solved by the collocation method in the form of expansion in Chebyshev polynomials with a factor that explicitly takes into account a feature in the vicinity of the crack vertices. The latter allows you to directly find the SIF and evaluate the effect on it of various combinations of geometric and physical parameters of the problem.

Anti-plane crack problem of a functionally graded piezoelectric materials strip with arbitrarily distributed properties

This paper treats the anti-plane crack problem of a functionally graded piezoelectric material (FGPM) strip with arbitrarily distributed properties. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric constant of the FGPM vary continuously along the thickness of the medium, and the strip is under anti-plane mechanical and in-plane electric impact loadings. By using the Fourier transform and defining unknown discontinuous functions across the crack surfaces, the anti-plane crack problem of FGPM is reduced to a group of singular integral equations, which are solved numerically. The stress and electric displacement intensity factors are presented, and the influences of the nonhomogeneous and geometric parameters on stress and electric displacement intensity factors are also included.

Solving the runner blade crack problem for a Francis hydro-turbine operating under condition-complexity

Runner blade crack is a problem that affects the operation security of hydro-turbines. In this study, penetrating cracks were found by inspection on the runner blade of a Francis turbine near hub and shroud on trailing-edge. To solve this problem, prototype test was conducted to find the conditions under strong hydraulic instabilities. The turbine vibration region was classified based on the test and found mainly at small guide vane opening angles or low-head high-load conditions. In these regions, vibration was strong and the numerical-predicted flow regime was disordered. Analyzed by fluid-solid interaction method, stress concentrations were found on the blade-hub and blade-shroud connections on trailing-edge. By excluding the influence of resonance, the runner blade crack problem was found as the combination of concentrating static stress, hydraulic excited pulsating stress and residual stress. Triangle-blocks, which were helpful for eliminating the concentrating static stress, were welded on the blades after cutting-off the old crack sites. Polishing and buffing were conducted for reducing potential residual stress. After a long-time re-operation, the improved runner was found without runner blade cracks. Prototype re-testing showed no impacts on the efficiency. This study provided a good solution for the Francis turbine runner blade crack problem under condition-complexity.

An asymptotic finite plane deformation analysis of the elastostatic fields at a crack tip in the framework of hyperelastic, isotropic, and nearly incompressible neo-Hookean materials under mode-I loading

In this work, stress and displacement fields were computed around a crack tip in the case of nearly incompressible and isotropic neo-Hookean material. The constitutive equation was linearized, so that the Cauchy stress tensor could be written as a sum of two components: the linear response in term of elastic Hooke’s law and the nonlinear one. Based on this decomposition, an asymptotic analysis has been developed, the fields of linear elastic fracture mechanics (LEFM-theory) are the zero-order terms of the asymptotic expansion. The validity of the proposed theory has been checked in the case of a mode-I crack problem. A numerical model was constructed using a finite element method. It has shown that the computed fields arising from this theory are qualitatively in agreement with those of the finite element simulations.

Visualizing the crack driving force through fluid analogy

AbstractIt is shown that the crack driving force for a fundamental antiplane crack problem is analogous to the limiting case of the force acting on an ideal fluid on free streamlines that form at the ends of flow around two parallel plates.

Size Dependent Thermo-Piezoelectricity for In-Plane Cracks

The finite element method (FEM) is developed to analyse the size effect (flexoeletricity) for 2-D crack problems in thermo-piezoelectricity. Flexoelectricity is observed in micro/nanoelectronic structures, where large strain gradients destroy the symmetric structure of atoms in crystals and thereby causing polarization, even in dielectric materials. In contrast to using classical Fourier heat conduction theory, a finite speed of the thermal wave is considered in the higher order transport equation. The variational principle is applied to derive the FEM equations and C1-continuous elements are employed in the implementation of the FEM. An example is presented to demonstrate the effect of the characteristic time parameter on the crack opening displacement and temperature distribution.

Analysis of 3-Dimensional Creased Cracks

A method of analysis for calculating a precise distribution of a stress intensity factor alonga front of 3D crack was improved by introducing a closed-form integral. In the present study, the crackface is discretized with number of triangular boundary elements on which the weighting function ofbody force doublet varies linearly with coordinate variables. A closed form solution of a resultant forceover an arbitrary planar-triangular area due to a presence of an isolated point force was derived andused to satisfy a stress boundary condition of a creased crack problem. In principle, arbitrary shaped3D cracks which may contain asperities and multiple creased lines in its face can be solved by presentapproach.

New analytical solutions for modified polarization saturation models in piezoelectric materials

In this paper, we present new analytical solutions for modified polarization saturation (PS) models for arbitrary polarized and semipermeable 2-D piezoelectric media. The PS model is modified to various other non-linear fracture models by varying the normal electric displacement saturated conditions in place of a constant saturated value. These variations are hereby defined as interpolating linear, quadratic and cubic type’s polynomials into saturated value interpolated on the basis of possible electric displacement values at the centre of the crack, actual crack tip and saturated zone tip. To present the analytical study, a centre crack problem in 2-D semipermeable piezoelectric media under arbitrary poling direction and combined in-plane mechanical and electric displacement loadings is considered. Using extended Stroh formalism and complex variable approach, these models are mathematically reduced into generalized non-homogeneous Riemann–Hilbert problems. Applying Riemann–Hilbert technique, the solution of these problems is obtained in terms of generalized complex potential functions representing traction forces and electric displacement components. These lead to obtain the explicit expressions for saturated zone length, crack opening displacement, crack opening potential and local intensity factor in each case. Also, the results of saturation zones and local intensity factor are obtained in each case and compared with the established numerical results. The studies show that saturated zone length increases with increasing electric loading for each case and also depends on the polynomial varying saturation condition. For a particular electric loading applied within the range of critical value, it increases with increasing degree of polynomial type saturated condition i.e. from constant to cubic type’s normal electric displacement saturated condition.

Simultaneous Enhancement of the Thermoelectric and Mechanical Performance in One-Step Sintered n-Type Bi2Te3-Based Alloys via a Facile MgB2 Doping Strategy.

The Bi2Te3-based alloys have been commercialized for the applications of energy harvesting and refrigeration for decades. However, the commercial Bi2Te3-based alloys produced by the zone-melting (ZM) method usually show poor mechanical strength and crack problems as well as the sluggish figure of merit ZT, especially for the less-progressed n-type samples. In this work, we have simultaneously enhanced the thermoelectric and mechanical performance of the one-step spark plasma sintering (SPS)-derived n-type Bi2Te2.7Se0.3 alloys just by doping a small amount of superconducting material MgB2 where Mg and B atoms can play significant roles in carrier density optimization and hardness enhancement. Besides the optimization of carrier density, the MgB2 doping can also increase the carrier mobility but decrease the lattice and bipolar thermal conductivity, leading to a peak ZT of 0.96 at 325 K and an average ZT of 0.88 within 300-500 K in the 0.5% MgB2-doped Bi2Te2.7Se0.3 (BTSMB) alloys. The peak ZT and average ZT of our optimized BTSMB samples are comparable and higher than those of the state-of-the-art commercial ZM ingot. Moreover, the optimized BTSMB sample also exhibits almost 70% enhancement in hardness compared with the ZM ingot. Our results demonstrate the great potential of the MgB2 doping strategy for mass production of SPS-derived Bi2Te3-based alloys in one-step sintering.

The mode III problem of a Dugdale-Barenblatt interfacial crack in a FGM strip bonded to a homogeneous strip by the integral method

The elasto-static anti-plane problem of a Dugdale-Barenblatt interfacial crack in a functionally graded strip bonded to a homogeneous substrate is formulated in term of a singular integral equation. The functionally graded strip is modeled with an exponentially variable shear modulus. The singular integral equation is solved using Tchebychev polynomials. The influence of the non-homogeneity parameter, the shear modulus of the homogeneous strip, the widths of the functionally graded strip and the homogeneous strip, and the critical sliding displacement jump in the Dugdale-Barenblatt cohesive model on the fracture load are discussed.

Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

Anti-plane fracture mechanics analysis of a piezoelectric material layer with strain and electric field gradient effects

The problem of an anti-plane crack in a polarized ceramic layer with both the strain and electric field gradient effects is studied. This model includes two characteristic length parameters l and m which describes the strain gradient and the electric field gradient effects, respectively. The analysis demonstrates that the near-tip asymptotic stress and electric displacement are governed by r−3/2 singularities. Due to stain gradient effect, stresses ahead of the crack tip are significantly higher than those in the classical linear piezoelectricity fracture mechanics. When the strain and electric field gradient parameters decrease to sufficiently small, the solutions reduce to the conventional linear elastic fracture mechanics results. The new contribution of this research is that it includes the effects of the strain gradient and electric field gradient simultaneously for a finite crack in a finite piezoelectric layer.

CPOT: A suitable tool for crack propagation path optimization based on image recognition

A Crack Path Optimization Tool (CPOT) is developed in this study, and it is designed as a plugin for ABAQUS/CAE. The CPOT provides a friendly graphical user interface, which can control crack propagation along the specified path effectively. With the arrangement strategy of holes, the tool can deflect the crack propagation path and avoid the critical domains or structures. In this application, optimization algorithm assisted extended finite element method (XFEM) is applied to crack propagation analysis. Meanwhile, the image recognition technique is employed to extract the related crack coordinates from crack path image. The grayscale processing and binarization methods are used to obtain the pixels of crack path in the image processing module. Then, a conversion coefficient is proposed to convert the pixel coordinate into physical coordinate. Compared with the single crack optimization strategy, a recognition method for multiple cracks is added to distinguish different cracks path. Additionally, three-dimensional optimization problem is also considered in the application. Finally, several examples which utilize the deformation plasticity theory for the ductile crack problem are employed to illustrate the superiority of the application. The results indicate the high accuracy and efficiency of the application for controlling arbitrary crack propagation along the specified path.

Hypersingular integral equation for triple inclined cracks problems in half plane elasticity

Hypersingular integral equation associated with the modified complex potential is formulated to solve the three inclined cracks problems in an elastic half-plane with free traction boundary condition. The modified complex potential possesses two parts; the principal and the complementary parts. The principal part is derived from the original complex potential of the crack problem in an infinite plate. The complementary part eliminates the traction along boundary of half-plane caused by the principal part. The crack opening displacements (COD) is the unknown function and the traction is the right hand terms. The appropriate quadrature formula is adapted to solve the integral equation numerically and the stress intensity factor (SIF) is computed. The behaviour of SIF at crack tips is analysed. Numerical examples show that the SIF increases as the angle of inclined cracks and the distance of cracks from the boundary of half-plane increase. Our results are agreeable with the previous works.

A Study of the Effect of Post-Heating Pulse on Hot Cracking Susceptibility in Pulsed Laser Welding of Invar Alloy

Hot cracking is one of the major challenges in laser welding of Invar alloy. In this study, welding hot cracking susceptibility experiments are conducted with fish-bone-type Invar alloy sheets under pulsed laser welding condition. The pulse wave consists of two distinct power levels: welding pulse and post-heating pulse. The welding temperature field can be controlled by changing the duration of the post-heating pulse. The results of experimental measurements and finite element method calculation show that increasing of the post-heating pulse duration leads to a decline in the cooling rate of weld metal within the brittle temperature range, although the welding hot cracking susceptibility decreases at first and then increases. Neither the heat input nor the cooling rate is the only decisive factor for hot cracking during the welding process. 1. Introduction Invar alloy is widely applied in precision measurement devices and low-temperature-resistant structures for its low linear expansion coefficient at ambient temperature, which is less than 1.6 × 10—6 k—1, about 1/10 of the low carbon steel, and it changes very little within a large temperature range (Corbacho et al. 1998; Park et al. 2011; Zhao et al. 2015; Qiu et al. 2016). With the increase in demand for natural gas, the liquefied natural gas (LNG) carrier has been developed rapidly as a means of long-distance transport. The material of primary and secondary barriers on the containment insulation system of membrane-type LNG carrier is welded Invar alloy with a thickness of .7 mm, which directly contacts the — 163°C LNG (American Bureau of Shipping 2006; Bureau Veritas 2011; Wang et al. 2006). The total weld length of Invar alloy on an LNG carrier over 13 million cubic meters can reach up to 100 km according to statistics. Hot cracking is the major problem in the welding of Invar alloy, and currently Tungsten inert gas (TIG) arc welding is commonly used. However, the problem of hot cracking cannot be solved completely, and requires that the operator have good technical knowledge. Invar alloy has high hot cracking susceptibility during the welding process because of its single-phase austenite structure and high content of Ni (Kou 2003). Studies show that the welding hot cracking susceptibility of Invar alloy can be reduced when elements such as Ti, Mn, and Mo are added (Hirata et al. 2001), but these alloying elements will increase the linear expansion coefficient of the weld, resulting in the deterioration of mechanical properties at low temperature. Thus, laser welding and friction stir welding are proposed by researchers to solve the welding hot cracking problem of Invar alloy from the aspect of reducing welding heat input.

Dynamic stress intensity factor of a rectangular crack in an infinite saturated porous medium: Mode I problem

A scattering problem of a harmonic plane compressional wave disturbed by a fluid filled rectangular crack, which is embedded in an infinite saturated poro-elastic solid, is investigated. With the aid of the two-dimensional Fourier integral transform technique, the original boundary value problem is formulated by a pair of dual integral equations in terms of the crack surface displacement. By expressing the crack surface displacement into a series of Jacobi polynomials, the solution of the dual integral equations is derived, where the coefficients involved are obtained with the aid of the Schmidt method. The stress intensity factors of the Mode I crack problem are obtained. Numerical results are performed to discuss the influence of the frequency of the incident compressional wave and the geometric parameter of the rectangular crack on the stress intensity factor and crack surface displacement in detail. The present analytical solutions may benefit future simplified and numerical studies.