Change In Strain Energy Research Articles

Damage detection in wind turbine gearbox using modal strain energy

Damage detection in complex machinery such as Wind Turbine Gearbox (WTG) is a challenging task due to its complex dynamic behavior. However, obtaining modal properties for such a system is not arduous. In this paper, damage detection of WTG is performed using Modal Strain Energy (MSE). Modal analysis of a three-stage WTG is carried out, and modal parameters are used to calculate MSE in various components of WTG. MSE distribution analysis of a healthy WTG is performed for the dynamic characterization of the modes. Two damage indicators, namely Modal Strain Energy Change (MSEC) and Damage Index (DI) based on MSE, are used to indicate the damage. A comparison is made between these two indicators for assessing the capability to locate the damage accurately and effectively. It is observed that DI locates damage more accurately compared to MSEC.

Fracture mechanics analysis of generalized compact tension specimen geometry using the mechanics of net-section

Fracture mechanics analysis of a generalized compact tension specimen, on the basis of the mechanics of deformation of the net-section, is shown to provide a simple and a broadly useful expression for stress intensity factor calculations. A single analytical expression is found to be sufficient for the characterization of crack behavior in compact tension, extended compact tension and wedge splitting test specimens without any restriction on the specimen length (or height) and width. The analysis is enabled by the concept of the change in net-section energy, which is determined by summing the changes in strain energies of the net-section of the generalized specimen for tension and bending deformation modes, which result from the introduction of the crack. This is equivalent in concept to the increase in strain energy upon the introduction of the crack, as in the Griffith’s fracture theory. The square-root of the change in net-section strain energy parameter multiplied by the elastic modulus provides an expression that is equivalent to the conventional stress intensity factor expression. The application of the net-section based expression to the standard compact tension, the extended compact tension and the wedge-splitting test specimens shows very good agreements with the crack behaviors as expressed by the stress intensity factor expressions for the respective geometries. The proposed method enables easy analytical determination of stress intensity factors for any asymmetrically-loaded mode-I crack problem.

Evaluation of The Modification Efficiency of Bituminous Binders with SBS Polymer Based on Changes in Strain Energy in the Ductility Test

Road pavement layers in many cases are done of hot mix asphalt (HMA). It is mixture of mineral aggregate and asphalt binder. The content of the bituminous binder is not very significant (several percent). In fact, asphalt binder decides about every properties of hot mix asphalt in significant range. Traffic condition is still changing (traffic is growing and trucks are heavier). It is reason to find better solution to asphalt pavement and improve parameters asphalt binder. One of important attribute is sensitivity for temperature. Searching for a way to improve cohesion, viscosity and adhesion to mineral aggregate is one of the directions research. One of solution is use application of modifier. The most popular are polymers. Most frequently used copolymers to modify asphalt binder are thermoplastic elastomer styrene - butadiene - styrene (SBS). Thermoplastic polymers are used in practice, which soften upon heating and harden during cooling (reversible process), reminding in this respect the behaviour of asphalts. In article, authors have present tests results of modified asphalt binder by SBS polymer. Tests were made on two types of bitumen, one of them was distilled asphalt, second oxidised. Amount of modifier was variable and was from 0% to 6%. Results of test confirmed usefulness SBS polymer to modify asphalt. In every cases noticed increase penetration index (PI) and change structure of bitumen from sol-gel to typical gel. Effect of this is reduce thermal sensitivity. Resistance to changing of temperature is better. After tests and analyses, the authors stated that amount of polymer above 2% clearly changes asphalt parameters both hard and soft.

On the study of element modal strain energy sensitivity for damage detection of functionally graded beams

In this paper, a modeling framework based on element modal strain energy sensitivity is developed for identifying damage of functionally graded beams. The element damage equation set of functionally graded Euler-Bernoulli beam is established built on element modal strain sensitivity and the rate of change of element modal strain energy from healthy to damage. The Tikhonov regularization algorithm incorporated with the generalized cross validation is used to solve the reliability problem of damage equation set. Numerical illustrative examples contain a simply supported and continuous functionally graded Euler-Bernoulli beams are considered to demonstrate the performance of the method. The influences of gradient index, damage extent, mode shape and noise level are investigated respectively. Damage results imply that the proposed method can give a valid way to accurately detect the damage of beam-like structures, also has excellent resistance to measurement noise.

Multifunctional topology optimization of strain-sensing nanocomposite beam structures

Controlling volume fractions of nanoparticles in a matrix can have a substantial influence on composite performance. This paper presents a multi-start topology optimization algorithm that designs nanocomposite structures for objectives pertaining to stiffness and strain sensing. Local effective properties are obtained by controlling local volume fractions of carbon nanotubes (CNTs) in an epoxy matrix, which are assumed to be well dispersed and randomly oriented. Local Young’s modulus, conductivity, and piezoresistive constant drive the global objectives of strain energy and resistance change. Strain energy is obtained via a modified solution of Euler-Bernoulli equations and resistance change is obtained via solution of a bilinear quadrilateral finite element problem. The optimization uses a two-step restart method in which Pareto points from the first step are used as starting conditions in the second step. An efficient method for obtaining analytic sensitivities of the objective functions is presented. The method is used to solve a set of example problems pertaining to the design of a composite beam in bending. The results show that the strain energy may be optimized by placing high volume-fraction CNT elements away from the neutral axis. Resistance change is optimized through a combination of shifting the neutral axis, formation of conductive paths between electrodes, and asymmetric distribution of highly piezoresistive elements. Results also show that the strain energy is governed by the volume fraction constraint and the resistance change is dependent on a combination of the volume fraction constraint and the boundary electrode location.

Net-section based approach for fatigue crack growth characterization using compact tension specimen: Physical correlation of mean stress or stress ratio effects

A new approach is demonstrated here for the correlation of fatigue crack growth (FCG) data, generated using compact tension (CT) specimens, for various mean stress levels or stress ratios (R) of testing. The approach uses the change in the cyclic strain energy of the net-section as a parameter to correlate fatigue crack growth rates. The derivation of the change in net-section strain energy, for the CT specimen, is demonstrated here on the basis of energy principles of solid mechanics. The total change in net-section strain energy is determined as the sum of the changes in the tension and the bending strain energy components, arising from the tensile stress and the bending moment acting on the net-section of the CT specimen. This leads to a compact physical equation for the change in cyclic strain energy, which is expressed as a direct function of applied cyclic load level, crack length, stress ratio, and specimen dimensions. Extensive experimental evaluations, using the data for steels, copper and titanium alloys, were conducted and are presented here to show that the change in net-section strain energy can successfully correlate the fatigue crack growth for various stress ratios or mean stress levels. The present work provides a new direction for physically-based characterizations of fatigue crack growth data generated using CT specimens.

Fault Simulation and Online Diagnosis of Blade Damage of Large-Scale Wind Turbines

Damaged wind turbine (WT) blades have an imbalanced load and abnormal vibration, which affects their safe and stable operation or even results in blade rupture. To solve this problem, this study proposes a new method to detect damage in WT blades using wavelet packet energy spectrum analysis and operational modal analysis. First, a wavelet packet transform is used to analyze the tip displacement of the blades to obtain the energy spectrum. The damage is detected preliminarily based on the energy change in different frequency bands. Subsequently, an operational modal analysis method is used to obtain the modal parameters of the blade sections and the damage is located based on the modal strain energy change ratio (MSECR). Finally, the professional WT simulation software GH (Garrad Hassan) Bladed is used to simulate the blade damage and the results are verified by developing an online fault diagnosis platform integrated with MATLAB. The results show that the proposed method is able to diagnose and locate the damage accurately and provide a basis for further research of online damage diagnosis for WT blades.

Finding Damage Localizations of a Planar Truss Using Modal Strain Energy Change

A novel structural damage localization method based on modal strain energy changes is proposed. The proposed method does not utilize the first several modes together as usual but selectively makes use of some sensitive modes for each element. Both the magnitude of normalized elemental modal strain energy and the capability of each element to resist identification uncertainties are considered to determine the sensitive modes. Elements’ capability to resist identification uncertainties is calculated by using the Monte Carlo method. Based on determined sensitive modes, an in‐turn damage‐checking process is employed to judge the damage state of each element. A typical planar truss is numerically analyzed. The results show that the proposed method is more effective than that based on modal strain energy change ratio even when using the first several modes together as usual. Furthermore, by utilizing some sensitive modes only, the proposed method becomes much more robust, making damage localization more easy and reliable.

Modal Strain Energy-based Structural Damage Identification: A Review and Comparative Study

Thanks to its sensitive characteristics to damages, modal strain energy (MSE) has been widely utilized for structural damage identification. Various MSE-related techniques on structural damage identification are surveyed and classified as damage index (DI) method, modal strain energy change (MSEC) method, cross-modal strain energy (Cross-MSE) method, and other methods. Four typical MSE-related methods are selected and firstly overviewed. Then damage identification of 1-D beam and 3-D offshore platform structures, considering the issues of spatial incompleteness, noise contamination, etc., are examined systematically with numerical simulation and experimental data. The ability of these four methods to locate damage is compared. Finally, some generalized criteria on these methods for damage identification are concluded, and suggestions for future work are discussed. This brief review aims to help readers identify starting points for research in vibration-based damage identification and health monitoring, and guide researchers and practitioners in better implementing available MSE-based damage identification algorithms.

Development of Finite Element Models for Predicting the Mechanical Behavior of the Cracked Pipe

In this paper, two theoretical models, micro and macro model, are presented to investigate the effect of circumferential cracks on the structural characteristics of a pipe. In the micro model, the equivalent bending stiffness is obtained based on the energy method and fracture mechanics. Because of the high change of strain energy near the crack location, the variation is represented by reduction in the bending stiffness along the length of the pipe. The development of the macro model is based on a simplified procedure, i.e., the pipe is separated into two segments without any change in the cross section property. Two separated pieces are connected by a rotational massless spring of the infinitesimal length inserted at the crack location. Moreover, it is shown that in the macro model so smaller number of elements are required than the micro model to provide a sufficient accuracy. Finally, the experimental measurements are utilized to validate the proposed models. The deflections and frequencies obtained for several cases through the displacement and vibration method, using the proposed models agree reasonably well with the experimental measurement data.

Mechanical Response of Nano-Porous Copper under Different Temperature and Strain Rate through Molecular Dynamics Simulations

As a type of nanostructured material with nanosized porosity and ultrahigh specific surface area, nanoporous metals attract much attention in both industrial and theoretical fields. Through molecular dynamics simulations, the strain energy of nanoporous copper is investigated with special consideration on the effect of temperature and strain rate. First, with the variation of temperature and strain rate, the change of both stress and strain energy is plotted. Dislocation movement and structural response of nanoporous copper are explored in different stages of strain. Secondly, yield points under different conditions are analyzed to demonstrate the super plasticity of nanoporous copper. It is interesting that critical points appears. Based on above mentioned investigation, it is expected to provide a simple description on mechanical property and performance of nanoporous metals.

Numerical study on complex shaped cracks in cantilever beams concerning frequency and stiffness changes

The paper presents a mathematical relation to express the effects of a T-shaped crack on beam-like structures. The study is performed by using the finite element method (FEM) and contrived analytical formulas for proving the existing correlation between deflection, strain energy, and natural frequency changes. The damaged beam static and dynamic behaviors are analyzed by means of the FEM. The frequency shift for the first mode of vibration derived directly was compared with the frequency alteration calculated involving the change in the beam deflection for several scenarios of the T-shaped crack. The frequency shift is derived using the relations between deflection and natural frequency. As the final step in the research, we compared the outcomes for the same crack with the results achieved from a beam suffering a loss of stiffness.

Mechanics of fatigue crack growth under large-scale plasticity: A direct physical approach for single-valued correlation of fatigue crack growth data

The major challenge in the mechanics of elastic-plastic fatigue crack growth is to find a physically based driving force parameter to correlate the crack growth rates under different loading conditions. Specifically, a parameter that can provide single-valued correlation of crack growth rates, in stress-controlled and strain-controlled fatigue, is needed. Approaches of the past used either cyclic strain (strain intensity factor) or nonlinear-fracture-mechanics based (cyclic J-integral, ΔJ) parameter, to correlate fatigue crack growth. The validity of these approaches, however, has not been established. Further, the J-integral based approach requires experimental load-deflection curves, recorded after every crack length increment, and geometry-correction factors, which are numerically determined and complicated. In the present work, a physically based approach, based on thecumulative change in the cyclic strain energy of the net-section, is used to develop new parameters that can successfully correlate fatigue crack growth behavior in a variety of loading situations. The driving force parameter, capturing the change in the net-section cyclic strain energy, is determined analytically from elastic-plastic behavior of material and from the relative sizes of cracked and uncracked sections in the crack plane. Load-deflection measurements, geometric correction factors, or numerical methods are not needed in the present approach. Remarkably, excellent correlations of fatigue crack growth, in a variety of specimen geometries and for various stress/strain levels, have been found in both stress- or strain-controlled fatigue conditions. This work, extending the author’s earlier works for elastic fatigue crack growth, validates that the change in net-section strain energy is a fundamental quantity in the mechanics of fatigue crack growth.

Enhancement Mechanism of the Dynamic Strength of Concrete Based on the Energy Principle.

This paper analyzes the relationship between the rates of change of elastic strain energy, the strength during the concrete failure process, and proposes that the increased dynamic strength of concrete was caused by the hysteresis effect of energy release—according to the basic principle of energy conversion. Dynamic Brazilian disc tests were carried out on concrete specimens, with diameter of 100 mm, by using the split Hopkinson pressure bar. Test results were obtained through using a gas gun, with an impact pressure of 0.15 MPa, 0.20 MPa and 0.25 MPa, respectively. The dynamic failure process of concrete is then reproduced by numerical calculation methods. Finally, the energy characteristics during the concrete failure process at different strain rates are studied, and the enhancement mechanism of the dynamic strength of concrete is verified. The results showed that the dynamic tensile strength of concrete increased by 9.79% when the strain rate increased by 61% from 60.25 s−1; and when the strain rate increased by 92.8% from 60.25 s−1, the dynamic tensile strength of the concrete rose by 46.28%. The rates of change of both input energy and dissipated energy meet at the peak stress of the material. The increases in rates of change for the two kinds of energy were not synchronized, so excess input energy could be stored as concrete strength increased. As a result, the extra energy stored after peak stress led to a higher degree of concrete fragmentation and greater kinetic energy of the fragment. These results offer research directions for improving the dynamic strength of concrete.

Shear Strain Energy Change Caused by the Interplate Coupling Along the Nankai Trough: An Integration Analysis Using Stress Tensor Inversion and Slip‐Deficit Inversion

AbstractIn the Nankai Trough, southwest Japan, the Philippine Sea plate descends beneath the Eurasian plate. The locking on the plate interface causes stress change in the seismogenic lithosphere of the Eurasian plate. This interplate locking does not always result in stress accumulation but can cause stress release. The present study employs shear strain energy to determine whether the stress is accumulated or released in the seismogenic zone. While most studies employed a shear stress assuming a fault plane, the shear strain energy is more feasible for the stress accumulation/release mapping because the assumption of the fault plane is not required. First, we estimated the directions of the principal stress axes and the stress ratio of the background stress field by analyzing ~8,000 focal mechanisms. In the Chugoku region, the maximum compression axis is in the E‐W direction. We then calculated the stress change due to the slip deficit along the Nankai Trough. The stress change showed that the maximum compression is in the N‐S direction in the Chugoku region. By using both the background stress and the stress fluctuation, we estimated the shear strain energy change caused by the slip deficit. The shear strain energy is decreased due to the interplate locking in the Chugoku region. We also statistically compared the shear strain energy change with the seismicity in southwestern Japan and found that the seismicity is high where the strain energy increases.

Damage assessment in plate-like structures using a two-stage method based on modal strain energy change and Jaya algorithm

ABSTRACTThe paper presents an effective two-stage approach based on modal strain energy change and Jaya algorithm for damage assessment in plate-like structures. In the first stage, a newly developed damage indicator, named as normalized modal strain energy-based damage index (nMSEBI), is proposed to help locate potential damage elements more effectively. After eliminating most of the healthy elements, the actual damaged sites and its extent in plate structure are determined in the second stage by minimizing an objective function, which is solved using Jaya algorithm. For finding a suitable objective function used in optimization process, two different objective functions are considered to examine their effects on the performance of the utilized optimization algorithm. The efficiency and accuracy of the proposed two-stage damage detection method are investigated by two numerical examples comprising a concrete plate and a four-layer (0°/90°/90°/0°) laminated composite plate with multiple damage locations. All of the obtained results indicate that even under measurement noise, the proposed method can identify the actual damage sites and estimate the extent of damage with high precision. In addition, the numerical results also show that the computational cost of the optimization process using the objective function based on modal flexibility change is much lower than that using the objective function based on mode shapes change.

多元数据融合在无人机结构-健康监测中的应用

Structural health monitoring is an important means to guarantee the continuing safe operation of aircrafts, and makes a key technique for unmanned aerial vehicles’ (UAVs’) development and certification. For a UAV fuselage, the structural acceleration responses, strain signals and modal parameters were acquired on-line from different sensor measurements in dynamic structure simulation. The normalized wavelet packet energy change rate index, the strain energy change rate index, the modal frequency change rate index and the mixed damage evaluation indices were built to indicate the structural health condition. The integrated multi-source data fusion technique, including data-level fusion, feature-level fusion and Bayesian probabilistic neural network-based decision-level fusion, was used with the rough set reduction successively to significantly decrease the spatial dimension of data. The mapping between structural damage information, like damage severity, damage locations and health evaluation indices, was established, and the comprehensive decision of the structural damage model was achieved. An example for the health monitoring of an unmanned helicopter was demonstrated. The experimental results verify the accuracy of the proposed data fusion technique for damage identification of multi-damage aircraft structures, and show the validity of multi-data fusion in UAV health monitoring.

Insight on physical meaning of finite-width-correction factors in stress intensity factor (K) solutions of fracture mechanics

The physical meaning of the finite-width-correction factors (FWCF), which commonly appear in stress intensity factor solutions of fracture mechanics, is mysterious. The present work is an attempt to resolve this mystery. Specifically, it is shown that for the middle-crack-tension (M(T)) specimen and for the embedded-circular-crack in a specimen of round cross-section, the FWCF factor is related to the average net-section stress for a given crack size. An increase in K at the crack tip means an increase in the average net-section stress ahead of the crack, in addition to the increase in the level of normal stress in the near-tip (or singularity-dominated) zone of fracture mechanics. It is also shown that this increase in net-section stress can be determined, in a straightforward manner, using a simple approach based on strength of materials (SOM). The agreement between the net-section stress determined from the strength of materials approach and that from fracture mechanics is surprisingly good. This connection between the finite-width-correction factor and the net-section stress has not been demonstrated before, and, hence it provides a new point of view to analyze fracture mechanics problems. More importantly, the connection validates the correlation of fatigue crack growth on the basis of the change in the net-section cyclic strain energy, which has recently been demonstrated by the author elsewhere.

Peridynamic simulations of the tetragonal to monoclinic phase transformation in zirconium dioxide

Whether present as a manufactured stabilised ceramic, or as an oxide layer on zirconium alloys, mechanical degradation in zirconia is influenced by the tetragonal to monoclinic phase transformation. Peridynamic theory was implemented within the Abaqus finite element framework to understand how the tetragonal to monoclinic phase transformation can itself cause fracture in zirconia. In 2D these simulations represent a single grain, transforming via an isometric dilational expansion, surrounded by a homogenous monoclinic oxide. The effect of transformation time, applied bi-axial pressure, and the fracture strain were assessed using the change in strain energy and the amount of damage in the oxide surrounding the transformed grain. Reducing the applied compressive stress or applying a tensile stress reduces the transformation strain energy. The introduction of a fracture strain leads to damage in the surrounding oxide region largely in the form of cracks, and reduces the transformation strain energy further by reducing the constraint on the transforming grain. The extent of the fracture, and reduction in constraint on the transformed grain, is more significant with the application of a biaxial tensile pressure.

A new approach to the mechanics of fatigue crack growth in metals: Correlation of mean stress (stress ratio) effects using the change in net-section strain energy

An unsolved problem in the mechanics of fatigue crack growth is why mean stress or stress ratio in a fatigue cycle has a profound effect on growth rate when compared in terms of stress intensity factor range (ΔK). Specifically, there has not been any fracture-mechanically-consistent theory to explain the effects of mean stress on fatigue crack growth. In this work, a new and generalized driving force parameter for fatigue crack growth, which effectively incorporates the mean stress or stress ratio effect, is developed from energy principles of solid mechanics. A successful explanation of the effect of mean stress on the growth rate is provided. The driving force is the accumulated change in net-section strain energy, which develops as a function of increasing crack length and decreasing net-section size in fatigue. A generalized mechanics analysis, showing how to account for the stress amplitude and the maximum stress of a fatigue cycle in the change in net-section strain energy, is presented. Equivalently, the new crack growth parameter can also be interpreted as the cumulative work done by cyclic loading at the crack length at which the crack growth data is determined. Several experimental data, including some historically significant fatigue crack growth data, generated on aluminum, steel and titanium alloys, are used to demonstrate the success of the correlation. As a further validation of the proposed concept, it is shown that the empirical Walker parameter (ΔK0.5Kmax0.5), which had some success in correlating stress ratio effect, is in fact related to the change in net-section strain energy.