Cracked Bar Research Articles

Detection of crack bar deterioration at offshore wind turbine supports using generative adversarial networks and autoencoders

Detection of crack bar deterioration at offshore wind turbine supports using generative adversarial networks and autoencoders

Dynamic torsional analysis of a functionally graded coated circular shafts weakened by multiple radial cracks

Analytical transient analysis of a functionally graded (FG) coated cylindrical bar weakened by multiple radial cracks under torsional transient loading is presented. The solution corresponding to a Volterra-type screw dislocation is achieved using the Fourier and Laplace transforms in the spatial and temporal domains, respectively. The obtained dislocation stress field is used to develop singular integral equations in terms of the unknown dislocation density function for the evaluation of multiple radial cracks. The resulting Cauchy integral equations are reduced to a set of algebraic equations and are solved numerically to determine the dislocation density functions. The achieved results are employed to evaluate the dynamic stress intensity factors (DSIFs) at the crack tips and the torsional rigidity of the FG coated circular cross-section bar with multiple embedded radial cracks. In addition, several numerical examples are presented to verify the results and to explore the effects of transient loading, FG coating layer, cracks position and interaction between them on the DSIFs and torsional rigidity of the FG coated cracked bars.

Influence of the interphase between laser-cladded metal layer and steel substrate on fatigue propagation of a short edge crack

Laser cladding is a relatively new technology how to combine properties of various materials. Thus, bi-material interfaces are presented in real structures and can affect the fatigue crack propagation. A cracked bar subjected to pure tensile loading is numerically simulated in this work in order to analyze the effect of the interphase layer between the cladded metal layer and the steel substrate on crack growth in the surface layer. Particularly, the influence of various Young’s modulus of the interphase on the stable/unstable edge crack propagation is assessed. Moreover, the number of cycles necessary for achievement of the defined critical crack length is calculated and it is summarized that knowledge of elastic properties of the thin interphase is crucial for fracture and fatigue analyses.

Effects of crack location and depths for an iron bar: A Finite Element approach

Structural Health Monitoring has become a significant issue in numerous engineering fields and industries. Early detection of damage such as cracks, as well as their depth and location, could be a major research topic. In this research, the natural frequency of a cylindrical solid shapes iron bar together with two half-circle surface crack has been investigated by Finite Element Method (FEM). Vibration Analysis has been used to predict response and different crack depths are the main parameters for analysis to access structural integrity performance of the domain. It is found that lowest frequency of intact bar was higher than the lowest frequency of the cracked bar, and frequencies decreased as the crack depth increased. Using this method very small sizes crack (minimum 0.05 mm) can be defined in any structural body.

Approximate analytical analysis of longitudinal natural frequencies of a cracked beam

PurposeIn this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.Design/methodology/approachThe crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.FindingsEffect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.Originality/valueA new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.

Analytical solutions of a circular bar with an orthotropic coating involving mode III cracks and cavities under Saint-Venant torsion

This article presents a formulation for a circular bar reinforced by an orthotropic coating containing multiple arbitrarily oriented cracks and cavities subjected to Saint-Venant torsional loading. First, the stress field of a circular bar with an orthotropic coating containing a Volterra-type screw dislocation is found via Fourier transform. At the next step, the problem is reduced to a set of integral equations with Cauchy singularity in the domain via distributed dislocation method. The integral equations are evaluated via a numerical approach to find the stress intensity factors of the singular crack tips, hoop stresses on cavities, and torsional rigidity of the cracked bar with its coating. In addition, von Mises yield criterion is used to find the boundary of the plastic zone via the stress filed around crack tips. Finally, there are multiple examples to indicate the efficiency and correctness of the current approach in torsion problems of cracked circular bars with an orthotropic coating.

Resonant and antiresonant frequencies of multiple cracked bar

The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant ones.

Characteristic equation for antiresonant frequencies of multiple cracked bars and application for crack detection

ABSTRACTThe present paper addresses study and use of antiresonant frequencies for multi-crack detection in bar. First, there is an established new form of the exact characteristic equations for resonant and antiresonant frequencies in longitudinal vibration of bars with a finite number of cracks. Some asymptotic approximations of the equations are therefore derived and examined to evaluate their applicability in solving the forward problem of the multiple cracked bar. Then, the characteristic equations established in this study are used for analysis of change in antiresonant frequencies due to cracks. Finally, based on the characteristic equations and analysis, an efficient procedure is proposed to detect a number of cracks from given resonant and/or antiresonant frequencies. Numerical examples have been examined to illustrate and validate the proposed theory applied for detecting single crack in fixed-free end bar and double cracks in bar with free ends.

Dynamic analysis of a cracked bar by the method of characteristics

PurposeThe purpose of this paper is to introduce a new numerical approach for studying a cantilever bar having a transverse crack. The crack is modeled by an elastic longitudinal spring with a stiffness K according to Castiglione’s theorem.Design/methodology/approachThe bar is excited by different longitudinal impulse forces. The considered problem based on the differential equation of motion is solved by the method of characteristics (MOC) after splitting the second-order motion equation into two first-order equivalent equations.FindingsIn this study, effects of the crack size and crack’s position on the reflected waves from the crack are investigated. The results indicate that the presence of the crack in the cantilever bar generates additional waves caused by the reflection of the incident wave by the crack.Originality/valueA numerical approach developed in this paper is used for detecting the extent of the damage in cracked bars by the measurement of the difference between the dynamic response of an uncracked bar and a cracked bar.

The Effect of Nano-Sized Air Bubbles on the Mechanical Properties and Natural Frequencies of a Multi-Cracked Composite Bar

In this research, the effect of nanosized air bubbles embedded within carbon nanotubes (CNTs) coated by various thicknesses of alumina (Al2O3) reinforced epoxy resin based composite on the natural frequencies of a multi-cracked bar is investigated in details. The impact of cracks’ locations and depths within the hybrid composite structure on the natural frequency profiles is investigated. The volume fraction of CNTs is fixed to 0.5 wt. % due to the significant improvements reported in the literature when the composite is reinforced with this volume fraction of CNTs. The results of the multi-scale finite element analysis are verified by comparing with previous studies and a good agreement is shown relating to the longitudinal natural frequencies. The results of the research show that the dynamic response of cracked bar is highly sensitive to the volume fractions of nanosized air bubbles located within the composite. The results of the study supported the hypothesis that the nanosized air bubbles can be used to reduce the weight of heavy composite structures along with using of suitable coatings to improve the mechanical properties of the hybrid composite. Furthermore. The results of the study can be employed to detect multiple cracks located within similar structures like wind turbine blade (WTB) fabricated from a hybrid composite structure composed of carbon fiber reinforced modified epoxy resin which contains nanosized air bubbles and CNTs nanofillers coated by Al2O3 at different thicknesses.

Analysis of cracked bars with rectangular cross-section and isotropic coating layer under torsion

The solution to problem of a Volterra-type screw dislocation in a rectangular cross section bar with an isotropic coating is first achieved by means of a finite Fourier cosine transform. The bar is under axial torque which is governed by Saint-Venant torsion theory. The series solution is then derived for warping function and stress fields in the rectangular cross section with an isotropic coating. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of smooth cracks. The solution of these equations is used to determine the torsional rigidity of bar and the stress intensity factors for the crack tips. Finally, several examples are presented to show the accuracy and efficiency of the dislocation technique in Saint-Venant torsion problems.

Crack analysis by using the enriched singular boundary method

In this paper, we make the first attempt to extend the singular boundary method to crack problems in conjunction with the domain decomposition technique. In order to characterize singular behaviors around cracks, enriched functions are analytically derived from the governing equations and the corresponding conditions containing singularities. We verify the present enriched singular boundary method to the torsion problem of a cracked bar and the acoustic propagation problem in crack media, which are governed by Laplace and Helmholtz equations, respectively. Numerical results demonstrate the accuracy and efficiency of the proposed scheme.

Averaged strain energy density estimated rapidly from the singular peak stresses by FEM: Cracked bars under mixed-mode (I + III) loading

The strain energy density (SED) averaged over a material dependent control volume proved to control fracture and fatigue behaviour of different materials in many engineering problems. A method to rapidly estimate the averaged SED at the tip of cracks under in-plane mixed mode I+II loading has been recently proposed. It is based on the peak stresses evaluated from finite element (FE) analyses, according to the peak stress method (PSM). Coarse finite element meshes automatically obtained from the free mesh generation algorithm available in a commercial FE code can be adopted. In the present paper Ansys® software has been adopted. The aim of the present contribution is to extend the FE approach to cracks subjected to out-of-plane mixed mode I+III loading. The advantage of the proposed approach is two-fold: there is no need of mesh refinement in the close neighbourhood of the points of singularity, so that coarse FE meshes can be adopted; moreover, geometrical modeling the control volume in FE models is no longer necessary. Bars weakened by circumferential outer cracks subjected to out-of-plane mixed mode (I+III) loading have been analysed taking into consideration different crack lengths, mode mixities and average sizes of the adopted FE meshes. A comparison between approximate values of the averaged SED according to the peak stress approach and accurate values calculated directly from the FE strain energy by adopting very refined FE meshes has been successfully performed within a range of applicability.

Nonlinear Dynamic Structures with Developing Discontinuity

Discontinuity is one of the most important nonlinear factors challenging both methods of nonlinear analysis and its applications. The problem becomes more complicated when the discontinuity is developing under the influence of dynamic processes in the structures. This paper presents the methodology for analysis and simulation of the systems with the developing discontinuity. It is based on the combination of analytical technique using nonlinear integral equations and the Matlab-Simulink computation. This methodology is applied to analysis of nonlinear dynamics of the cracked bar. Some new nonlinear phenomena have been revealed and validated.

Crack detection in pile by measurements of frequency response function

Explicit expressions of either frequency equation or frequency response function (FRF) have been derived for multiple cracked bar. The expressions allow to thoroughly investigate the effect of cracks on the modal parameters such as natural frequencies and FRF of bar with different boundary conditions. The exact expression of FRF provides a basis to propose an efficient procedure for multi-crack detection in pile by modal testing technique. Numerous examples are numerically examined for illustrating the developed theory, and an experimental study is accomplished for validating the proposed crack detection procedure.

Revisit of the Dual Bem using SVD Updating Technique

AbstractThe boundary element method (BEM) is easier than the finite element method (FEM) on the viewpoint of the discretization of one dimension reduction rather than the domain discretization of finite element method. The disadvantage of BEM is the rank deficiency in the influence matrix,e.g., degenerate boundary, degenerate scale, spurious eigenvalues and fictitious frequencies, which do not occur in the FEM. The conventional BEM can not be straightforward applied to solve a problem which contains a degenerate boundary without decomposing the domain to multi-regions. A hypersingular integral equation is used to ensure a unique solution for the problem containing a degenerate boundary. By combining the singular and hypersingular equations, it’s termed the dual BEM due to its dual frame. Following the successful experience on the retrieval of information using the singular value decomposition (SVD) updating term and updating document, this technique is also used to extract out the degenerate-boundary information and the rigid-body information in the dual BEM. It is interesting to find that true information due to a rigid-body mode in physics is found in the right singular vector with respect to the corresponding zero singular value while the degenerate-boundary mode (geometry degeneracy) in mathematics is imbedded in the left singular vector with respect to the corresponding zero singular value. The role of the common right and left singular vectors of SVD for the four influence matrices in the dual BEM is also discussed in this paper. Two examples, a potential flow problem across a cutoff wall and a cracked bar under torsion were demonstrated to see the mathematical SVD structure of four influence matrices in the dual BEM.

Use of Circumferentially Cracked Bar sample for CTOD fracture toughness determination in the upper shelf regime

In this work, the use of circumferentially cracked bar (CCB) sample to determine material fracture toughness in the upper shelf regime for carbon steels has been investigated. Since high fracture toughness materials are known to exhibit extensive crack tip blunting before ductile crack initiation, accurate specimen design is required to provide realistic fracture toughness measurement. Here, a CCB was designed to have similar loss of constraint as for SENT sample. Continuum damage mechanics was used to predict the occurrence of ductile crack initiation and propagation. Finite element analysis was performed to predict specimen response and to compare computed J-integral crack driving force with measured CTOD. Finally, experimental tests were performed on X65 carbon steel and the measured critical CTOD was compared with available fracture data obtained with SENT.

Evolution of crack paths and compliance in round bars under cyclic tension and bending

The aim of this paper is to calculate how the surface crack front and the dimensionless compliance evolve in cracked cylindrical bars subjected to cyclic tension or bending with different initial crack geometries (crack depths and aspect ratios). To this end, a computer application (in the Java programming language) that calculates the crack front’s geometric evolution and the dimensionless compliance was made by discretizing the crack front (characterized with elliptical shape) and assuming that every point advances perpendicularly to the crack front according to the Paris law, and using a three-parameter stress intensity factor (SIF). The results show that in fatigue crack propagation, relative crack depth influences more on dimensionless compliance than the aspect ratio, because the crack front tends to converge when the crack propagates from different initial geometries, showing greater values for tension than for bending. Furthermore, during fatigue crack growth, materials with higher values of the exponent of the Paris law produce slightly greater dimensionless compliance and a better convergence between the results for straight-fronted and circular initial cracks.

Modelling of structures with developing discontinuity

Discontinuity is one of the most important factors which contribute to the nonlinearity, challenging both methods of nonlinear analysis and its application for the analysis of interacting mechanical processes. The problem becomes more complicated when the discontinuity is developing under the influence of dynamic processes in the structures. This paper presents the methodology for analysis and simulation of the systems with the developing discontinuity based on the combination of analytical technique and the Matlab–Simulink computation. As an example, model of a cracked bar subjected to longitudinal excitation is used to analyse a nonlinear response as a way to monitor structural health. Different strategies of monitoring are compared based on the tracking the qualitative transformation of the bar׳s vibration.

Dynamic Crack Tip Opening Displacement (DCTOD) as governing parameters for material fragmentation

Fragmentation in metals can be approached either by Mott statistical or by Energy-based fragmentation theory. Recently, Grady showed that the two theories can be reconciled showing that the material parameter that drives tendency to fragmentation and fragment size is the dynamic fracture toughness. Experimental data do not completely agree with these conclusions. In this paper, the dynamic crack tip opening displacement (CTOD) is proposed as fracture parameter which can account for plastic deformation occurring prior fracture. Here, an experimental procedure for determining the critical dynamic CTOD is presented. The circumferential crack bar tension (CCB(T)) was investigated for its use with tensile Hopkinson bar testing equipment. The calibration function in the dynamic range was determined via finite element analysis (FEA). The critical dynamic CTOD was measured using both high speed video recording, with digital image correlation (DIC) technique, and clip gauge at the crack mouth. The proposed procedure has been used to investigate dynamic fracture resistance of high purity copper (99.98%) and to correlate it with available fragmentation data.