Search results for: longitudinal crack growth

Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Hamad, H. Kebir

Abstract:

This study concerned the dynamic behavior of the wind turbine rotor. Before all we have studied the loads applied to the rotor, which allows the knowledge their effect on the fatigue, also studied the rotor with longitudinal crack in order to determine stress, strain and displacement. Firstly we compared the first six modes shapes between cracking and uncracking of HAWT rotor. Secondly we show show evolution of first six natural frequencies with longitudinal crack propagation. Finally we conclude that the residual change in the natural frequencies can be used as in shaft crack diagnosis predictive maintenance.

Keywords: Wind turbine rotor, natural frequencies, longitudinal crack growth, life time.

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Authors: M. Benachour, M. Benguediab, A. Hadjoui, N. Benachour

Abstract:

In this paper fatigue crack growth behavior of aeronautical aluminum alloy 2024 T351 was studied. Effects of various loading and geometrical parameters are studied such as stress ratio, amplitude loading, etc. The fatigue crack growth with constant amplitude is studied using the AFGROW code when NASGRO model is used. The effect of the stress ratio is highlighted, where one notices a shift of the curves of crack growth. The comparative study between two orientations L-T and T-L on fatigue behavior are presented and shows the variation on the fatigue life. L-T orientation presents a good fatigue crack growth resistance. Effects of crack closure are shown in Paris domain and that no crack closure phenomenons are present at high stress intensity factor.

Keywords: Fatigue crack, orientation effect, crack closure, aluminum alloy.

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Authors: F. Husem, M. E. Turan, Y. Sun, H. Ahlatci, I. Tozlu

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Residual stress and fatigue crack growth rates are important to determine mechanical behavior of rails. This study aims to make relationship between residual stress and fatigue crack growth values in rails. For this purpose, three R260 quality rails (0.6-0.8% C, 0.6-1.25 Mn) were chosen. Residual stress of samples was measured by cutting method that is related in railway standard. Then samples were machined for fatigue crack growth test and analyze was completed according to the ASTM E647 standard which gives information about parameters of rails for this test. Microstructure characterizations were examined by Light Optic Microscope (LOM). The results showed that residual stress change with fatigue crack growth rate. The sample has highest residual stress exhibits highest crack growth rate and pearlitic structure can be seen clearly for all samples by microstructure analyze.

Keywords: Residual stress, fatigue crack growth, R260, LOM, ASTM E647.

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Authors: Osama A. Terfas, Abdusalam A. Alaktiwi

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Pressure vessels are usually operating at temperatures where the conditions of linear elastic fracture mechanics are no longer met because massive plasticity precedes crack propagation. In this work the development of a surface crack in a pressure vessel subject to bending and tension under elastic-plastic fracture mechanics conditions was investigated. Finite element analysis was used to evaluate the hydrostatic stress, the J-integral and crack growth for semi-elliptical surface-breaking cracks. The results showed non-uniform stress triaxiality and crack driving force around the crack front at large deformation levels. Different ductile crack extensions were observed which emphasis the dependent of ductile tearing on crack geometry and type of loading. In bending the crack grew only beneath the surface, and growth was suppressed at the deepest segment. This contrasts to tension where the crack breaks through the thickness with uniform growth along the entire crack front except at the free surface. Current investigations showed that the crack growth developed under linear elastic fracture mechanics conditions will no longer be applicable under ductile tearing scenarios.

Keywords: Bending, ductile tearing, fracture toughness, stress triaxiality, tension.

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Authors: Wentao He, Jingxi Liu, De Xie

Abstract:

It is necessary to manage the fatigue crack growth (FCG) once those cracks are detected during in-service inspections. In this paper, a simulation program (FCG-System) is developed utilizing the commercial software ABAQUS with its object-oriented programming interface to simulate the fatigue crack path and to compute the corresponding fatigue life. In order to apply FCG-System in large-scale marine structures, the substructure modeling technique is integrated in the system under the consideration of structural details and load shedding during crack growth. Based on the nodal forces and nodal displacements obtained from finite element analysis, a formula for shell elements to compute stress intensity factors is proposed in the view of virtual crack closure technique. The cracks initiating from the intersection of flange and the end of the web-stiffener are investigated for fatigue crack paths and growth lives under water pressure loading and axial force loading, separately. It is found that the FCG-System developed by authors could be an efficient tool to perform fatigue crack growth analysis on marine structures.

Keywords: Crack path, Fatigue crack, Fatigue live, FCG-System, Virtual crack closure technique.

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Authors: Chinnaiah Madduri, Raghu V. Prakash

Abstract:

This paper presents the results of corrosion fatigue crack growth behaviour of a Ni-Cr-Mn steel commonly used in marine applications. The effect of mechanical variables such as frequency and load ratio on fatigue crack growth rate at various stages has been studied using compact tension (C(T)) specimens along the rolling direction of steel plate under 3.5% saturated NaCl aqueous environment. The significance of crack closure on corrosion fatigue, and the validity of Elber-s empirical linear crack closure model with the ASTM compliance offset method have been examined. Fatigue crack growth rate is higher and threshold stress intensities are lower in aqueous environment compared to the lab air conditions. It is also observed that the crack growth rate increases at lower frequencies. The higher stress ratio promotes the crack growth. The effect of oxidization and corrosion pit formation is very less as the stress ratio is increased. It is observed that as stress ratios are increased, the Elber-s crack closure model agrees well with the crack closure estimated by the ASTM compliance offset method for tests conducted at 5Hz frequency compared to tests conducted at 1Hz in corrosive environment.

Keywords: Corrosion fatigue, oxide induced crack closure, Elber's crack closure, ASTM compliance offset method.

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Authors: T.S.Balasubramanian, V.Balasubramanian, M.A.Muthumanikkam

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This paper reports the fatigue crack growth behaviour of gas tungsten arc, electron beam and laser beam welded Ti-6Al-4V titanium alloy. Centre cracked tensile specimens were prepared to evaluate the fatigue crack growth behaviour. A 100kN servo hydraulic controlled fatigue testing machine was used under constant amplitude uniaxial tensile load (stress ratio of 0.1 and frequency of 10 Hz). Crack growth curves were plotted and crack growth parameters (exponent and intercept) were evaluated. Critical and threshold stress intensity factor ranges were also evaluated. Fatigue crack growth behaviour of welds was correlated with mechanical properties and microstructural characteristics of welds. Of the three joints, the joint fabricated by laser beam welding exhibited higher fatigue crack growth resistance due to the presence of fine lamellar microstructure in the weld metal.

Keywords: Fatigue, Non ferrous metals and alloys, welding

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Authors: Seon Soon Choi

Abstract:

The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: Crack size, Fatigue crack propagation, Magnesium alloys, Probability distribution, Specimen thickness.

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Authors: Rohit, S. Vishnuvardhan, P. Gandhi, Nagesh R. Iyer

Abstract:

The evaluation of energy release rate and centre Crack Opening Displacement (COD) for circumferential Through-Wall Cracked (TWC) pipes is an important issue in the assessment of critical crack length for unstable fracture. The ability to predict crack growth continues to be an important component of research for several structural materials. Crack growth predictions can aid the understanding of the useful life of a structural component and the determination of inspection intervals and criteria. In this context, studies were carried out at CSIR-SERC on Nuclear Power Plant (NPP) piping components subjected to monotonic as well as cyclic loading to assess the damage for crack growth due to low-cycle fatigue in circumferentially TWC pipes.

Keywords: 304LN stainless steel, cyclic J-integral, Elastic- Plastic Fracture Mechanics, J-integral, Through-wall crack

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Authors: S. Lecheb, A. Nour, A. Chellil, A. Basta, D. Belmiloud, H. Kebi

Abstract:

In recent years, a new numerical method has been developed, the extended finite element method (X-FEM). The objective of this work is to exploit the (X-FEM) for the treatment of the fracture mechanics problems on 3D geometries, where we showed the ability of this method to simulate the fatigue crack growth into two cases: edge and central crack. In the results we compared the six first natural frequencies of mode shapes uncracking with the cracking initiation in the structure, and showed the stress intensity factor (SIF) evolution function as crack size propagation into structure, the analytical validation of (SIF) is presented. For to evidence the aspects of this method, all result is compared between FEA and X-FEM.

Keywords: 3D fatigue crack growth, FEA, natural frequencies, stress intensity factor (SIF), X-FEM.

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Authors: M. Benachour, N. Benachour

Abstract:

Stainless steel has been employed in many engineering applications ranging from pharmaceutical equipment to piping in the nuclear reactors and storage to chemical products. In this attempt, simulation of fatigue crack growth based on experimental results of austenitic stainless steel 304L was presented using AFGROW code when NASGRO mode laws adopted. Double through crack at hole specimen is used in this investigation under constant amplitude loading. Effect of mean stress is highlighted. Results show that fatigue crack growth rate (FCGR) and fatigue life were affected by maximum applied load and dimension of hole. An equivalent of Paris law for this material was estimated.

Keywords: Fatigue crack, stainless steel, mean stress, amplitudeloading.

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Authors: Gürol Önal, Ahmet Avcı

Abstract:

This paper presented the results of an experimental investigation into the axial fatigue behavior of a 5086 aluminum alloy which have several notch-aspect ratios a0/c0 and notch thickness ratio a/t with semi-elliptical surface cracks. Tests were conducted in la b air for stress levels of 50 % of their yield strength. Experiments were carried out for various notch to thickness ratios. Crack growth rates of test specimens both in surface and depth directions were determined by using die penetration method. Fuzzy Logic method was used to predict the deep direction crack growth because the dept of the crack is considerably difficult to measure.

Keywords: Axial fatigue, Crack growth rate, surface crack, Al-Mg alloy.

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Authors: M. Benachour, N. Benachour, M. Benguediab

Abstract:

In this investigation variation of cyclic loading effect on fatigue crack growth is the studied. This study is performed on 2024 T351 and 7050-T74 aluminum alloys, used in aeronautical structures. The propagation model used in this study is NASGRO model. In constant amplitude loading (CA), effect of stress ratio has been investigated. Fatigue life and fatigue crack growth rate were affected by this factor. Results showed an increasing in fatigue crack growth rates (FCGRs) with increasing stress ratio. Variable amplitude loading (VAL) can take many forms i.e. with a single overload, overload band… etc. The shape of these loads affects strongly the fracture life and FCGRs. The application of a single overload (ORL) decrease the FCGR and increase the delay crack length caused by the formation of a larger plastic zone compared to the plastic zone due without VAL. The fatigue behavior of the both material under single overload has been compared.

Keywords: Fatigue crack growth, overload ratio, stress ratio, generalized willenborg model, retardation, Al-alloys.

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Authors: M. Benachour, N. Benachour, M. Benguediab

Abstract:

In this paper fatigue crack initiation and propagation in notched plate under constant amplitude loading through tensile residual stress field of 2024 T351 Al-alloy plate were investigated. Residual stress field was generated by plastic deformation using finite element method (FEM) where isotropic hardening in Von Mises model was applied. Simulation of fatigue behavior was made on AFGROW code. It was shown that the fatigue crack initiation and propagation were affected by level of residual stress filed. In this investigation, the presence of tensile residual stresses at notch (hole) reduces considerably the total fatigue life. It was shown that the decreasing in stress reduces the fatigue crack growth rates.

Keywords: Residual stress, fatigue crack initiation, fatigue crack growth, Al-alloy.

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Authors: S. Lecheb, A. Chellil, H. Mechakra, A. Zeggane, H. Kebir

Abstract:

In this work, repaired crack in 6061- T6 aluminum plate with composite patches presented, firstly we determine the displacement, strain and stress, also the first six mode shape of the plate, secondly we took the same model adding central crack initiation, which is located in the center of the plate, its seize vary from 20 mm to 60 mm and we compare the first results with second. Thirdly we repair various cracks with composite patch (carbon/ epoxy) and for (2 layers, 4 layers). Finally the comparison of stress, strain, displacement and six first natural frequencies between un-cracked specimen, crack propagation and composite patch repair.

Keywords: Composite patch repair, crack growth, aluminum alloy plate, stress.

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Authors: Thomas Jin-Chee Liu

Abstract:

In this paper, the thermo-electro-structural coupledfield in a cracked metal plate is studied using the finite element analysis. From the computational results, the compressive stresses reveal near the crack tip. This conclusion agrees with the past reference. Furthermore, the compressive condition can retard and stop the crack growth during the Joule heating process.

Keywords: Compressive stress, crack tip, Joule heating, finite element.

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Authors: H. M. Mobarak, Helen Wu, Keqin Xiao

Abstract:

In this work, a three-dimensional finite element model was developed to investigate the crack breathing behavior at different crack locations considering the effect of unbalance force. A two-disk rotor with a crack is simulated using ABAQUS. The duration of each crack status (open, closed and partially open/closed) during a full shaft rotation was examined to analyse the crack breathing behavior. Unbalanced shaft crack breathing behavior was found to be different at different crack locations. The breathing behavior of crack along the shaft length is divided into different regions depending on the unbalance force and crack location. The simulated results in this work can be further utilised to obtain the time-varying stiffness matrix of the cracked shaft element under the influence of unbalance force.

Keywords: Crack breathing, crack location, slant crack, unbalance force, rotating shaft.

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Authors: Seon Soon Choi

Abstract:

It is necessary to predict a fatigue crack propagation life for estimation of structural integrity. Because of an uncertainty and a randomness of a structural behavior, it is also required to analyze stochastic characteristics of the fatigue crack propagation life at a specified fatigue crack size. The essential purpose of this study is to find the effect of load ratio on probability distribution of the fatigue crack propagation life at a specified grown crack size and to confirm the good probability distribution in magnesium alloys under various fatigue load ratio conditions. To investigate a stochastic crack growth behavior, fatigue crack propagation experiments are performed in laboratory air under several conditions of fatigue load ratio using AZ31. By Anderson-Darling test, a goodness-of-fit test for probability distribution of the fatigue crack propagation life is performed. The effect of load ratio on variability of fatigue crack propagation life is also investigated.

Keywords: Load ratio, fatigue crack propagation life, Magnesium alloys, probability distribution.

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Authors: N. Benachour, A. Hadjoui, M. Benachour, M. Benguediab

Abstract:

This study reports an empirical investigation of fatigue crack initiation and propagation in 2024 T351 aluminium alloy using constant amplitude loading. In initiation stage, local strain approach at the notch was used and in stable propagation stage NASGRO model was applied. In this investigation, the flat plate of double through crack at hole is used. Based on experimental results (AFGROW Database), effect of stress ratio, R, is highlights on fatigue initiation life (FIL) and fatigue crack growth rate (FCGR). The increasing of dimension of hole characterizing the notch effect decrease the fatigue life.

Keywords: Fatigue crack growth, initiation life, Al-Alloy, stressratio, notch effect

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Authors: H. M. Mobarak, Helen Wu, Chunhui Yang

Abstract:

In this study, an analytical model is developed to study crack breathing behavior under the effect of crack location and unbalance force. Crack breathing behavior is determined using effectual bending angle by studying the transient change in closed area of the crack. The status of the crack of a balanced shaft is symmetrical about shaft rotational angle and the duration of each crack status remains unchanged. The global stiffness of the balanced shaft is independent of crack location. Different crack breathing behavior for the unbalanced shaft has been observed. The influence of crack location on the unbalanced shaft stiffness can be divided into three regions. When the crack is located between 0.3L and 0.8335L, where L is the total length of the shaft, the unbalanced shaft is less stiff and when located outside this region it is stiffer than the balanced shaft. It was also found that unbalanced shaft stiffness has a maximum value with a crack at 0.1946L, a minimum value at 0.8053L and same value as balanced shaft at 0.3L and 0.8335L.

Keywords: Cracked shaft, crack location, shaft stiffness, unbalanced force.

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Authors: Farhad Asgari Mehrabadi, Mohammad Reza Khoshravan

Abstract:

In the present study, fracture behavior of woven fabric-reinforced glass/epoxy composite laminates under mode III crack growth was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance calibration (CC) method and the Virtual Crack Closure Technique (VCCT). To achieve this aim ECT (Edge Crack Torsion) was used to evaluate fracture toughness in mode III loading (out of plane-shear) at different crack lengths. Load–displacement and associated energy release rates were obtained for various case of interest. To calculate fracture toughness JIII, two criteria were considered including non-linearity and maximum points in load-displacement curve and it is observed that JIII increases with the crack length increase. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of woven glass/epoxy laminates in mode III.

Keywords: Mode III, Fracture, Composite, Crack growth Finite Element.

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Authors: Guang Zou, Kian Banisoleiman, Arturo González

Abstract:

Crack initiation and propagation threatens structural integrity of welded joints and normally inspections are assigned based on crack propagation models. However, the approach based on crack propagation models may not be applicable for some high-quality welded joints, because the initial flaws in them may be so small that it may take long time for the flaws to develop into a detectable size. This raises a concern regarding the inspection planning of high-quality welded joins, as there is no generally acceptable approach for modeling the whole fatigue process that includes the crack initiation period. In order to address the issue, this paper reviews treatment methods for crack initiation period and initial crack size in crack propagation models applied to inspection planning. Generally, there are four approaches, by: 1) Neglecting the crack initiation period and fitting a probabilistic distribution for initial crack size based on statistical data; 2) Extrapolating the crack propagation stage to a very small fictitious initial crack size, so that the whole fatigue process can be modeled by crack propagation models; 3) Assuming a fixed detectable initial crack size and fitting a probabilistic distribution for crack initiation time based on specimen tests; and, 4) Modeling the crack initiation and propagation stage separately using small crack growth theories and Paris law or similar models. The conclusion is that in view of trade-off between accuracy and computation efforts, calibration of a small fictitious initial crack size to S-N curves is the most efficient approach.

Keywords: Crack initiation, fatigue reliability, inspection planning, welded joints.

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Authors: M. Benachour, N. Benachour, M. Benguediab, A. Hadjoui

Abstract:

The knowledge of the nature of loading is very important in order to hold account on the total behavior such as vibration, shock, fatigue, etc. Fatigue present 90% of failure when loadings fatigues are very complex. In this paper a study of double through crack at hole for plate subjected to fatigue loading is presented. Various modes loading are studied where the applied load is the same one. The fatigue life is given where the effect of stress ratio is highlighted. This work is conducted on aluminum alloy 2024 T351 used for much aerospace and aeronautics applications. The fatigue crack growth behavior with constant amplitude is studied using the AFGROW code when Forman model is applied. The fatigue crack growth rate and fatigue life for different loading modes are compared with variation of others geometrical parameter such as thickness and dimensions of notch hole.

Keywords: Fatigue crack, mode loading, aluminum alloy

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Authors: M. F. V. Montezuma, E. P. Deus, M. C. Carvalho

Abstract:

Steel bridges are normally subjected to random loads with different traffic frequencies. They are structures with dynamic behavior and are subject to fatigue failure process, where the nucleation of a crack, growth and failure can occur. After locating and determining the size of an existing fault, it is important to predict the crack propagation and the convenient time for repair. Therefore, fracture mechanics and fatigue concepts are essential to the right approach to the problem. To study the fatigue crack growth, a computational code was developed by using the root mean square (RMS) and the cycle-by-cycle models. One observes the variable amplitude loading influence on the life structural prediction. Different loads histories and initial crack length were considered as input variables. Thus, it was evaluated the dispersion of results of the expected structural life choosing different initial parameters.

Keywords: Fatigue crack propagation, life prediction, variable loadings, steel bridges.

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Authors: H. W. Ker

Abstract:

Longitudinal data typically have the characteristics of changes over time, nonlinear growth patterns, between-subjects variability, and the within errors exhibiting heteroscedasticity and dependence. The data exploration is more complicated than that of cross-sectional data. The purpose of this paper is to organize/integrate of various visual-graphical techniques to explore longitudinal data. From the application of the proposed methods, investigators can answer the research questions include characterizing or describing the growth patterns at both group and individual level, identifying the time points where important changes occur and unusual subjects, selecting suitable statistical models, and suggesting possible within-error variance.

Keywords: Data exploration, exploratory analysis, HLMs/LMEs, longitudinal data, visual-graphical methods.

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Authors: Sedigheh Mirzaei S., Debasis Sengupta

Abstract:

Parametric models have been quite popular for studying human growth, particularly in relation to biological parameters such as peak size velocity and age at peak size velocity. Longitudinal data are generally considered to be vital for fittinga parametric model to individual-specific data, and for studying the distribution of these biological parameters in a human population. However, cross-sectional data are easier to obtain than longitudinal data. In this paper, we present a method of combining longitudinal and cross-sectional data for the purpose of estimating the distribution of the biological parameters. We demonstrate, through simulations in the special case ofthePreece Baines model, how estimates based on longitudinal data can be improved upon by harnessing the information contained in cross-sectional data.We study the extent of improvement for different mixes of the two types of data, and finally illustrate the use of the method through data collected by the Indian Statistical Institute.

Keywords: Preece-Baines growth model, MCMC method, Mixed effect model

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Authors: K. Krishnaprasad, Raghu V. Prakash

Abstract:

Constant amplitude fatigue crack growth (FCG) tests were performed on dissimilar metal welded plates of Type 316L Stainless Steel (SS) and IS 2062 Grade A Carbon steel (CS). The plates were welded by TIG welding using SS E309 as electrode. FCG tests were carried on the Side Edge Notch Tension (SENT) specimens of 5 mm thickness, with crack initiator (notch) at base metal region (BM), weld metal region (WM) and heat affected zones (HAZ). The tests were performed at a test frequency of 10 Hz and at load ratios (R) of 0.1 & 0.6. FCG rate was found to increase with stress ratio for weld metals and base metals, where as in case of HAZ, FCG rates were almost equal at high ΔK. FCG rate of HAZ of stainless steel was found to be lowest at low and high ΔK. At intermediate ΔK, WM showed the lowest FCG rate. CS showed higher crack growth rate at all ΔK. However, the scatter band of data was found to be narrow. Fracture toughness (Kc) was found to vary in different locations of weldments. Kc was found lowest for the weldment and highest for HAZ of stainless steel. A novel method of characterizing the FCG behavior using an Infrared thermography (IRT) camera was attempted. By monitoring the temperature rise at the fast moving crack tip region, the amount of plastic deformation was estimated.

Keywords: Dissimilar metal weld, Fatigue Crack Growth, fracture toughness, Infrared thermography.

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, L. Addar, H. Kebir

Abstract:

This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems.

Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: Aluminium alloys, plate, crack, failure.

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Authors: M. Saravani, M. Azizi,

Abstract:

The V-notches are most possible case for initiation of cracks in parts. The specifications of cracks on the tip of the notch will be influenced via opening angle, tip radius and depth of V-notch. In this study, the effects of V-notch-s opening angle on stress intensity factor and T-stress of crack on the notch has been investigated. The experiment has been done in different opening angles and various crack length in mode (I) loading using Photoelasticity method. The results illustrate that while angle increases in constant crack-s length, SIF and T-stress will decrease. Beside, the effect of V-notch angle in short crack is more than long crack. These V-notch affects are negligible by increasing the length of crack, and the crack-s behavior can be considered as a single-edge crack specimen. Finally, the results have been evaluated with numerical finite element analysis and good agreement was obvious.

Keywords: Photoelasticity, Stress intensity factor, T-stress, V-notch.

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Authors: Omar D. Mohammed, Matti Rantatalo, Uday Kumar

Abstract:

In this paper an analytical crack propagation scenario is proposed which assumes that a crack propagates in the tooth root in both the crack depth direction and the tooth width direction, and which is more reasonable and realistic for non-uniform load distribution cases than the other presented scenarios. An analytical approach is used for quantifying the loss of time-varying gear mesh stiffness with the presence of crack propagation in the gear tooth root. The proposed crack propagation scenario can be applied for crack propagation modelling and monitoring simulation, but further research is required for comparison and evaluation of all the presented crack propagation scenarios from the condition monitoring point of view.

Keywords: Crack propagation, Gear tooth crack, Time varying gear mesh stiffness.

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