Cracked Bar Research Articles

Change in mode shape nodes of multiple cracked bar: I. The theoretical study

In present paper change in position of mode shape nodes induced by multiple cracks in bar is studied with purpose to use for the multiple crack detection from measured mode shape nodes. First, there is derived an explicit expression for natural modes in axial vibration of multiple cracked bar that allows obtaining exact positions of the node in the case of single and double crack. The change in mode shape nodes induced by multiple cracks provides an important indicator for crack localization in bar. Finally, a procedure for multiple crack detection by using mode shape nodes has been proposed and examined in an example of application.

Diagnostic tool for structural health monitoring: effect of material nonlinearity and vibro-impact process

Numerous techniques are available for monitoring structural health. Most of these techniques are expensive and time-consuming. In this paper, vibration-based techniques are explored together with their use as diagnostic tools for structural health monitoring. Finite-element simulations are used to study the effect of material nonlinearity on dynamics of a cracked bar. Additionally, several experiments are performed to study the effect of vibro-impact behavior of crack on its dynamics. It was observed that a change in the natural frequency of the cracked bar due to crack-tip plasticity and vibro-impact behavior linked to interaction of crack faces, obtained from experiments, led to generation of higher harmonics; this can be used as a diagnostic tool for structural health monitoring.

Analysis of a cracked bar under a tensile load in a corrosive environment

This brief study aims at providing a model to predict the time of service of a cracked bar in corrosive environment, in view of both the fracture mechanics and elastic failure criteria. Dolinskii`s assumption on the relationship between stress and the corrosion rate is adopted. It is superimposed with fracture mechanics consideration. A comparison between the time of service of a cracked bar and that of a uniform bar is provided.

Crack as modulator, detector and amplifier in structural health monitoring

A model of a one-dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a nonlinear response as a way to monitor structural health. The effect of the bilinear (nonlinear) character of the crack on the dynamics of the structure is studied. Simulation and experiments were performed to analyse the nonlinear behaviour of the cracked bar. In simulation the nonlinear information is obtained based on a combination of the analytical technique and the Matlab–Simulink computation. From analysis and experiment, it is found that the crack-induced nonlinearity leads to the generation of higher harmonics, whose intensity is a function of a distance from the crack. Side band frequencies were clearly revealed as well. The latter indicate modulation of exciting frequency due to systematic interaction of crack faces. The nonlinear transformation of modulated vibration by crack leads to generation of a low frequency periodic component. Its intensity is proportional to the forced response of the cracked bar at the exciting frequency. The phenomenology revealed can be effective for Structural Health Monitoring.

Vibro-impact response of the cracked structures to monitor structural health

A method of simulation is developed for studying the dynamics of the structures with discontinuities using Matlab-Simulink. Simulation and experiments were performed to analyse the nonlinear behaviour of the cracked bar. It is found that the crack-induced nonlinearity leads to the generation of higher harmonics along with side band frequencies. Their intensity diminishes with increase in distance of measurement from the crack. The presence of sideband frequencies indicates modulation of exciting frequency due to systematic interaction of crack faces. The nonlinear transformation of modulated vibration by crack leads to generation of a low frequency periodic component. Its amplitude is proportional to the forced response of the cracked bar at the exciting frequency. The phenomenology described here can be effective for Structural Health Monitoring (SHM).

On the Stress Intensity Factors of Cracked Beams for Structural Analysis

In this paper simple engineering methods for a fast and close approximation of stress intensity factors of cracked beams and bars, subjected to bending moment, normal and shear forces, as well as torque, are examined. As far as the circular cross section is concerned, comparisons are made on the base of numerical calculations. The agreement between the present results and those previously published is discussed. New formulae for calculating the stress intensity factors are proposed.

On the modelling of dynamic structures with discontinuities

A method of simulation is developed for studying the dynamics of the structures with discontinuities using Matlab–Simulink. The concept of dynamic compliance is used for modeling the continuous elements of the structure and the local discontinuity is modeled as nonlinear feedback. As an example, a one-dimensional model of cracked bar under harmonic loading is considered for the simulation purpose.

Simulation of viscoelastic behavior of defected rock by using numerical manifold method

Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of discontinuities. Firstly, validation of the numerical manifold method is carried out by simulations of a longitudinal stress wave propagating through intact and cracked rock bars. The behavior of the stress wave traveling in a one-dimensional rock bar with randomly distributed microcracks is subsequently studied. It is revealed that the highly defected rock bar has significant viscoelasticity to the stress wave propagation. Wave attenuation as well as time delay is affected by the length, quantity, specific stiffness of the distributed microcracks as well as the incident stress wave frequency. The storage and loss moduli of the defected rock are also affected by the microcrack properties; however, they are independent of incident stress wave frequency.

Vibro-Impact Response of a Cracked Bar

The presence of a crack in a structure affects its dynamic behaviour under working conditions. Cracks introduce nonlinearities into the system; the use of such nonlinearities for damage detection should be investigated. A model of a one-dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a vibro-impact response as a way to monitor structural health. The effect of contact nonlinearity due to crack's faces interaction is considered. This nonlinear information is obtained based on a combination of the analytical technique and the Matlab-Simulink computation. The procedure uses a numerical approximation for dynamic compliance operators and a nonlinear model of contact faces interaction implemented numerically as a nonlinear feedback. Nonlinear resonant phenomena due to vibro-impact interaction in the cracked bar are obtained and analysed. A distribution of the higher harmonics along the bar length, generated due to the nonlinear response of the crack, is revealed as a function of the distance from the crack. Recommendations on structural health monitoring of cracked bars due to contact nonlinearity are presented

Vibro-Impact Response of a Cracked Bar

The presence of a crack in a structure affects its dynamic behaviour under working conditions. Cracks introduce nonlinearities into the system; the use of such nonlinearit ies for damage detection should be investigated. A model of a one- dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a vibro-impact response as a way to monitor structural health. The effect of contact nonlinearity due to crack's faces interaction is considered . This nonlinear information is obtained based on a combination of the analytical technique and the Matlab-Simulink computation. The procedure uses a numerical approximation for dynamic compliance operators and a nonlinear model of contact faces interaction implemented numerically as a nonlinear feedback. Nonlinear resonant phenomena due to vibro-impact interaction in the cracked bar are obtained and analysed. A distribution of the higher harmonics along the bar length, generated due to the nonlinear response of the crack, is revealed as a function of the distan ce from the crack. Recommendations on structural health monitoring of cracked bars due to contact nonlinearity are presented

A finite element ductile failure simulation method using stress-modified fracture strain model

This paper proposes a new method to simulate ductile failure using finite element analysis based on the stress-modified fracture strain model. A procedure is given to determine the stress-modified fracture strain as a function of the stress triaxiality from smooth and notched bar tensile tests with FE analyses. For validation, simulated results using the proposed method are compared with experimental data for cracked bar (tensile and bend) tests, extracted from API X65 pipes, and for full-scale burst test of gouged pipes, showing overall good agreements. Advantages in the use of the proposed method for practical structural integrity assessment are discussed.

A new finite element analysis of free axial vibration of cracked bars

In this paper a new and innovative method for computation of longitudinal dynamic characteristics of multi-cracked bars is proposed. Cracks are modeled by equivalent axial springs with specified flexibility. Making use of the Heaviside step function and Dirac's delta distribution, a single governing equation for the whole bar is developed. The governing equation is an ordinary differential equation. With the help of Laplace Transform, a general analytical solution in terms of several unknown coefficients is determined. Boundary conditions are then used to determine the analytical solution for specific problems. Making use of the proposed governing equation a new finite element formulation is derived. In this formulation the effect of cracks is considered by adding an equivalent mass matrix to the element mass matrix. Through numerical study, the accuracy, efficiency and robustness of the work is verified. Copyright © 2010 John Wiley & Sons, Ltd.

Damage Assessment of a Cracked Bar: Effect of Material Nonlinearity on Vibro-Impact Response

Structural health monitoring is receiving much attention as a means to prevent catastrophic failure in structures in operating conditions. In most cases fracture is caused by the growth of crack, which cannot be precluded in many engineering structures. Moreover, to have an accurate quantitative estimate of crack tolerance of a structure to prevent fracture of load bearing components, an effective non-destructive evaluation procedure becomes necessary to monitor the structure under working conditions.

Sickle-shaped cracks in metallic round bars under cyclic eccentric axial loading

In the present paper, the fatigue propagation of an initial sickle-shaped surface crack in a metallic round bar under eccentric axial loading acting perpendicular to the crack plane is examined. Firstly, the stress-intensity factor (SIF) along the crack front is determined through a three-dimensional finite element analysis and the one-quarter point displacement method, for different values of the loading eccentricity. Then, the fatigue behaviour of the cracked bar is numerically analysed by a step-by-step procedure based on the Paris–Erdogan law. The results are plotted in terms of crack paths, intersection angle and crack depth evolution, by varying the loading eccentricity.

Surface Cracks in Round Bars under Cyclic Tension or Bending

The fatigue growth of a surface crack in a metallic round bar under cyclic tension or bending is analysed. The stress-intensity factor (SIF) along the crack front is computed through a three-dimensional finite element analysis and the one-quarter point displacement method. The results are compared with those presented by other Authors. Then, the fatigue behaviour of the cracked bar is numerically determined by a step-by-step procedure.

Application of the GTN Model to Quantify Constraint Effects on Ductile Fracture of API X65 Steels

This paper quantifies the effects of geometry, the loading mode and the specimen size on fracture toughness of the API X65 steel, via plane strain finite element (FE) damage analyses using the GTN model. The validity of FE damage analyses is checked first by comparing with experimental test data for small-sized, cracked bar test. Then the analyses are extended to investigate the effects of the relative crack depth and the specimen size on fracture toughness. It is shown that fracture toughness of the API X65 steel increases with decreasing the relative crack depth and increasing the specimen size.

Finite Element Analyses for Thickness Effects on J-Integral Testing using Non-Standard Testing Specimens

This paper compiles solutions of plastic η factors for standard and non-standard fracture toughness testing specimens, via detailed three-dimensional (3-D) finite element (FE) analyses. Fracture toughness testing specimens include a middle cracked tension (M(T)) specimen, SE(B), single-edge cracked bar in tension (SE(T)) and C(T) specimen. The ligament-to-thickness ratio of the specimen is systematically varied. It is found that the use of the CMOD overall provides more robust experimental estimation than that of the LLD, for all cases considered in the present work. Moreover, the estimation based on the load- CMOD record is shown to be insensitive to the specimen thickness, and thus can be used for testing a specimen with any thickness.

Stability of Nonuniform Cracked Bars Under Arbitrarily Distributed Axial Loading

This study is concerned with the stability analysis of nonuniform bars with arbitrary number of cracks and with arbitrary distribution of flexural stiffness or arbitrarily distributed axial loading. The homogeneous solutions of the governing differential equation for buckling of a nonuniform uncracked bar are derived for several important cases. A model of massless rotational spring is adopted to describe the local flexibility induced by cracks. Then a new approach that combines the exact buckling solution of a nonuniform uncracked bar, the model of massless rotational spring, and the transfer matrix method is presented for the title problem. The main advantage of the proposed method is that the eigenvalue equation for buckling of a nonuniform bar with an arbitrary number of cracks, arbitrary distribution of flexural stiffness, or arbitrarily distributed axial loading can be conveniently determined from a second-order determinant. The decrease in the determinant order as compared with other methods leads to significant savings in the computational effort. A numerical example is given to illustrate the reliability of the proposed approach through comparisons with numerical solutions and to study the effect of cracks on the stability of a nonuniform bar. Nomenclature ai = depth of the ith crack Ci =fl exibility of the ith rotational spring Ci1, Ci2 = constants of integration 1F2(a1; a2; a3; a4) =h ypergeometric series f () =fl exibility function hi = height of cross section at xi Jν(x) = first Bessel function of the vth order Ki(x) =fl exural stiffness at x in the ith

시편두께 및 균열깊이 영향을 고려한 비표준시편의 J 시험법 및 구속효과의 정량화

This paper compiles solutions of plastic η factors and crack tip stress triaxialites for standard and nonstandard fracture toughness testing specimens, via detailed three-dimensional (3-D) finite element (FE) analyses. Fracture toughness testing specimens include a middle cracked tension (M(T)) specimen, SE(B), single-edge cracked bar in tension (SE(T)) and C(T) specimen. The ligament-to-thickness ratio of the specimen is systematically caried. It is found that the use of the CMOD overall provides more robust experimental J estimation than that of the LLD, for all cases considered in the present work. Moreover, the J estimation based on the load-CMOD record is shown to be insensitive to the specimen thickness, and thus can be used for testing specimen with any thickness. The effects of in-plane and out-of-plane constraint on the crack tip stress triaxiality are also quantified, so that when experimental Ｊ value is estimated accordinng to the procendure recommended in this paper, the corresponding crack tip stress triaxiality can be estimated. Moreover, it is found that the out-of-plane constraint effect is related to the in-plane constraint effect.

3-D constraint effects on J testing and crack tip constraint in M(T), SE(B), SE(T) and C(T) specimens: numerical study

This paper compiles solutions of plastic η factors and crack tip stress triaxialites for standard and non-standard fracture toughness testing specimens, via detailed three-dimensional (3-D) finite element (FE) analyses. Fracture toughness testing specimens studied include a middle cracked tension (M(T)) specimen, SE(B), single-edge cracked bar in tension (SE(T)) and C(T) specimen. The ligament-to-thickness ratio of the specimen is systematically varied. It is found that the use of the CMOD overall provides more robust experimental J estimation than that of the LLD, for all cases considered in the present work. Moreover, the J estimation based on the load–CMOD record is shown to be insensitive to the specimen thickness, and thus can be used for testing a specimen with any thickness. Furthermore, effects of in-plane and out-of-plane constraint on the crack tip stress triaxiality are quantified, so that when an experimental J value is estimated according to the procedure recommended in this paper, the corresponding crack tip stress triaxiality can be estimated. Moreover, it is found that the out-of-plane constraint effect is related to the in-plane constraint effect.