Crack Propagation Calculations Research Articles

Fatigue Analysis of a Cracked Shaft: a Finite Element Modeling Approach

Shafts are typically used in sophisticated mechanisms and machinery which highly depend on shafts for rotatory motion which could lead to the failure. In today’s contemporary, damages caused by cracking on mechanical components and structures have increased, causing crack and structural failure. The failure could be examined by the calculation of stress intensity factor (SIF). Once the shaft reaches the critical SIF (SIFIC), the flaw is initiated and has a potential to propagate upon loading. Typically, the flaw would spread in many patterns and tenders to the formation and initiation of different types of cracks. Thus, the objective of this research work is to analyse fatigue cracked shafts. Prediction of crack growth via SIF calculation. SIF is usually adapted to predict the stress intensity near the crack tip where crack propagation occurs. Thus, SIF is used to study and analyse the cracked surface in relation to crack initiation and propagation. The SIF is calculated through finite element method (FEM) since the FEM is capable simulating complex geometry. The SIF is calculated based on the deformation in FEM calculation. The results show the predicted crack propagation and SIF calculation. It is crucial to study the resistance of cracked shafts towards cyclic loading for maintenance preceding and retirement of the structure.

Numerical modeling of crack propagation from open and closed flaws in rock

The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (KII) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of KII can be effectively eliminated when the non-singular stress (T-stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T-stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions.

Surrogate model building and error analysis for the damage tolerance life of penetration type fatigue crack

The penetration type cracks are often found in the components of mechanical systems and are a major threat to the operational reliability of mechanical components. There are many factors affecting the fatigue crack damage tolerance life, so the numerical calculation of 3D fatigue crack propagation is a complex process. Therefore, it is significant to improve the calculation efficiency of fatigue crack life with guaranteeing the calculation accuracy. The crack life is the result of the integration of crack propagation length and stress intensity factor(SIF). In this paper, a surrogate model for calculating the damage tolerance life of penetrating fatigue cracks is constructed using Kriging method based on the results of experimental tests and finite element analysis(FEA). The surrogate model is a four-dimensional response-value solution model, which can solve the fatigue crack life under random parameters. Finally, an error analysis is performed on the results of the surrogate model calculation. The results indicate that the error of the surrogate model calculation is relatively low, and the overall error is within 2%. Therefore, the surrogate model is characterized by high efficiency and accuracy.

Fracture-mechanical crack growth parameters of historical mild steels

At the beginning of the 20th century, a large number of steel structures were built in Europe. Many of these buildings—especially railway bridges—are still in use. These structures are mainly composed of rimmed steel. In addition to the stress–life concept, fracture mechanics is often used to assess the safety of these structures in terms of fatigue failure. Based on crack propagation calculations, it is possible to determine inspection intervals and, thus, ensure safe operation. For these calculations, suitable parameters of the Paris law, along with threshold values, are needed. The aim of this study is to experimentally determine a wide range of fracture mechanics parameters for old mild steel with reference to the stress ratio R. The experimental results were compared with values from the literature. Furthermore, the experimental results were fitted to several models considering the stress ratio R during crack growth. The investigated models were compared on the basis of the results for simulated crack growth calculations. The models are assessed according to how closely they represent the experimental results.

Fatigue Crack Propagation Study of Bridge Steel Q345qD Based on XFEM Considering the Influence of the Stress Ratio

In the past, fatigue cracks have appeared in the orthotropic steel decks of bridges shortly after they opened to traffic. Previous studies have shown that high tensile welding residual stress exists in welded joints of steel bridges, which significantly changes the average stress and stress ratio of the joints. However, traditional fatigue crack propagation (FCP) calculations based on the Paris equation do not consider the influence of the stress ratio. Steel Q345qD is a common material used in bridges. Therefore, it is meaningful to study the influence of the stress ratio on the FCP life of steel Q345qD. In this paper, an FCP equation based on the energy release rate considering the influence of the stress ratio is first derived and named the da/dN-ΔG-R equation. Next, three material parameters in the equation are determined based on the results from tests of steel Q345qD under different stress ratios. Then, a user subroutine based on the extended finite element method (XFEM) that considers the influence of the stress ratio is defined and the effects of mesh size are analyzed. Finally, the effects of the stress ratio on FCP are discussed and the adaptability of the da/dN-ΔG-R equation is verified by comparing the values obtained from the equation with experimental results. The results show that: with a 95% guarantee rate, three material parameters in the da/dN-ΔG-R equation are: log(C) = −10.71, m = 2.780, and γ = 0.957; in the numerical simulation, a mesh size of 1 mm is more appropriate than other mesh sizes as it shows better accuracy and efficiency; under the same energy release rate range, the crack growth rate decreases as the stress ratio increases; under the same loading amplitude and cycles, the fatigue life decreases as the stress ratio increases; and finally, the numerical results considering the influence of stress ratio based on the da/dN-ΔG-R equation are close to the test results, while the results without considering the stress ratio based on the Paris equation are inaccurate.

Sensitivity Analysis of the Nasgro Equation Based on the PZL-130 TC-II Orlik Trainer Aircraft Full Scale Fatigue Test

Abstract The study investigates the sensitivity of numerical crack propagation estimations based on the Nasgro equation. The equation is widely used for crack propagation calculations since it considers the whole range of crack propagation speed from threshold to critical values of stress intensity factor range (ΔK). The presented investigation is based on the actual results of the full scale fatigue test (FSFT) of the PZL-130 ‘Orlik’ TC-II aircraft. We provide a brief description of the test and the general approach followed in crack propagation estimations originally carried out after the test. The obtained results are verified in terms of variation of the input data. Overall results are compared and discussed.

Tensile strength and fracture toughness of steel fiber reinforced concrete measured from small notched beams

Steel fiber reinforced concrete (SFRC) is a kind of multiphase composite material and its tensile strength (ft) and fracture toughness (KIC) cannot be easily measured using small samples due to its highly heterogeneous microstructure. In this study, a novel evaluation is proposed for calculating ft and KIC of brittle heterogeneous solids. The results obtained by this method have been confirmed by three-point bending (TPB) test results of 75 notched SFRC beams in which the length of the corrugated steel fibers is 36 mm. Considering the heterogeneity and discontinuous fracture failure characteristic of SFRC samples, a virtual crack propagation calculation model is established, and the accurate prediction of ft and KIC can be obtained by incorporating the model into the Hu-Duan boundary effect model (BEM). The reasonable range of tensile strength of SFRC used in this paper is about 3.77–5.66 MPa. Compared with the median value of this range, the calculation error of BEM is only 7.69 %. By discussing the influence of α-ratio (defined as the ratio between the height W and the initial notch depth a0) on the predicted results, a value that is less affected by the front and rear boundary is obtained, and the value range is 0.16–0.24. Meanwhile, the exact ft and KIC can be obtained by using only 1–2 groups of samples with reasonable α-ratio. Based on the failure curve of SFRC established by using ft and KIC, the theoretical minimum size of samples with different α-ratio is determined under the condition of linear elastic fracture mechanics (LEFM). This method provides a valuable reference for the estimation of concrete mechanical parameters.

Fatigue Crack Propagation Estimation Based on Direct Strain Measurement during a Full-Scale Fatigue Test.

Military aircraft are subjected to variable loads, which are the main cause of initiation and propagation of cracks in the most stressed locations of the airframe. The aim of a Full-Scale Fatigue Test (FSFT) is to represent actual load conditions in such a way that the results obtained are a good representation of the actual loads and may be used as data that give insight into the development of real fatigue damage in critical locations. The FSFT load spectrum is a generalized depiction of the expected service loads and is designed to give an overall good representation of loads exerted on the airframe’s structural elements during operation. Moreover, the discrete method of load application on the structure (exerting loads with hydraulic actuators rather than pressure fields or inertia loads expected in actual operation) may cause some local effects, which may not be present in operation. The proposed usage of direct strain data from the test include such local effects. Moreover, operational loads may vary between individual aircraft, therefore it is crucial to understand the whole process of fatigue crack onset and development in order to determine safe inspection intervals and thereby mitigate risk. This paper presents crack propagation calculations regarding the development of a crack in a critical location of the PZL-130 “Orlik” TC-II aircraft, discovered during FSFT. The discussed crack was found already developed, hence the information about nucleation and initial propagation of the crack was not available. Therefore, there was a need to recreate the whole propagation process by means of numerical estimations using the FSFT results like location of the crack and total life for model validation. Moreover, in order to gather real load data for calculations a dedicated stain gage was installed on the damaged load path to monitor the actual remote strain in the element during the FSFT. This allowed for the definition of load sequence exerted on the damaged element directly during the test rather than estimating it from the general load conditions of the wing. The calculations allowed for the estimation of crack propagation curves from initiation to critical crack length causing fatal damage. The obtained curves allowed to visualize the crack behavior due to applied load and furthermore define initial and recurring inspection intervals for the entire fleet during operation, which allowed to define which cracks could be found before they reach critical size in order to carry out mitigation actions like repair or replacement of the damaged part. The authors present the methodology for load spectrum development based on direct strain measurements and furthermore crack propagation curves estimation, validated with the actual FSFT results, which allowed to propose nondestructive inspection intervals for future operation.

Use of a rotation-invariant linear strain measure for linear elastic crack propagation calculations

The classical stress intensity factor concept requires linear elastic calculations based on infinitesimal strains in order to create the correct stress and strain singularity at the crack tip. Infinitesimal strains, however, are not rotation-invariant and cannot be used in structures undergoing large rotations even if the stretch is small. Therefore, a new strain measure is proposed based on a linearization of the Lagrange strain tensor written in terms of the right stretch tensor instead of the deformation gradient. In that way the local rotation is removed from the linear strain measure. An example of crack propagation of a rotating beam shows the effectiveness of the method.

Rock Dynamic Crack Propagation Behaviour and Determination Method with Improved Single Cleavage Semi-circle Specimen Under Impact Loads

This paper studied the rock dynamic fracture propagation under impact loads elaborately with a determination method proposed to calculate crack propagation dynamic stress intensity factor (DSIF). By utilizing the split-Hopkinson pressure bar, the impact experiments with an improved single cleavage semi-circle (ISCSC) specimen were conducted to illuminate the dynamic crack propagation behaviour. Meanwhile, the fracture characteristics and crack propagation velocity were obtained by the crack propagation gauges. Coordinating experiments with a numerical approach, the crack propagation dynamic stress intensity factors were calculated by an experimental–numerical method with fractal theory. Then, a finite difference model was developed based on the tensile fracture softening damage criterion. With the analysis of numerical and experimental results, the crack propagation behaviour and mechanism of crack arrest were discussed sophisticatedly. The results demonstrate that the novel ISCSC specimen shows a definite advantage in determining crack propagation and arrest DSIF. Additionally, the crack arrest DSIF is larger than the average propagation DSIF with a sharp increase. Meanwhile, the numerical simulation results which agree well with the actual crack propagation illustrate that the crack arrest should be dominated by the compressive stress perpendicular to the crack path, and there were several arrest pauses existing in the transitory crack arrest process.

A TMF crack propagation model considering time dependency and load sequence effects

Due to increasing temperatures and mechanical loads in aero engine turbine components, the prediction of thermomechanical life requires accurate crack propagation calculations under thermomechanical Fatigue (TMF) conditions. Based on a linear elastic crack propagation model which considers pure cyclic crack propagation behavior only, a crack propagation model was developed to accurately predict TMF crack propagation life. It is considering short crack behavior by an El Haddad approach, time dependent effects by a combined creep and oxidation model, as well as cyclic and static time dependent load sequence effects described by a modified Willenborg model. Furthermore, an approach was developed to calculate the time dependent threshold behavior. The model can be applied to arbitrary mission profiles.A total of 29 parameters are required to describe all considered effects. As an example, these were calibrated by isothermal cyclic crack propagation, threshold and creep crack propagation tests on Inconel 718 at three temperatures. TMF crack propagation tests were carried out to validate the capability of the model. It is shown that the calculated crack propagation rates and thresholds, and consequently the predicted crack propagation life, match the measured data very well for isothermal as well as for TMF conditions.

A New Crack Propagation Algorithm Combined with the Finite Element Method

ABSTRACTThe prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.

Crack kinking and tunneling simulation for the single-fiber composite under transverse tension based on phase-field method

Virtual tests for a single-fiber–reinforced composite model subjecting to transverse tension are carried out based on a phase-field method considering a varying interface toughness parameter. Without pre-treating the crack initiation location and propagation path, the complete fracture process is realized for the first time in a three-dimensional numerical model, including nucleation cracks on the fiber/matrix interface at the free end, tunneling cracks along the fiber axis, and kinked interface cracks deviating from the interface and penetrating into the matrix. The numerically calculated crack propagation process is in good agreement with the in situ observations in the literature, indicating that the present model provides a good real-time quantitative numerical method for three-dimensional fracture analysis of fiber-reinforced composites. Tunneling cracks tend to cause macroscopic interface debonding and fiber pull-out. The interface tunneling crack initiation and the transition to the steady state inside the model are captured and analyzed in the numerical model. Kinked interface cracks can merge with other matrix cracks, forming a macroscopic transverse crack fracture mode. The kinking behaviors affected by the initial crack size and the interface properties are investigated. This study for the detailed crack propagation is helpful in understanding the toughening mechanism of fiber-reinforced composites under transverse tension.

Crack initiation and propagation in coalbed gas reservoir during hydraulic fracturing

The crack initiation and propagation calculation model during hydraulic fracturing in a coalbed methane reservoir with interlayers is established in this paper. The influence of coal elasticity modulus and fracturing fluid displacement on the fracture geometry are studied. Results show that the fracture initiation begins at the perforation interval. Stress inhomogeneity is detrimental for the formation of multiple cracks for the extension of the fracturing area. The cracks at the boundary have changed from less developed to more developed with increasing horizontal stress coefficient. The coal elasticity modulus and fracturing fluid displacement both play a determinative effect on fracture geometry. The study provides a reference basis for implementing hydraulic fracturing of low permeability coal seams with interlayers.

A fast algorithm to racetrack filter multiaxial histories preserving load shape

A fast algorithm is presented to implement a multiaxial version of the racetrack amplitude filter, improved upon the authors’ previous works. The algorithm only requires a single user-defined scalar filter amplitude to eliminate noise and potentially non-damaging events from arbitrary non-proportional multiaxial stress or strain histories, while preserving all key features of the load path. It can be applied as a pre-processing step to both invariant-based and critical-plane multiaxial damage models, highly decreasing the computational cost in assessments involving oversampled or noisy data, much improving the usefulness of computationally-intensive multiaxial models. Since load path shape is well preserved (within the chosen filter resolution), peaks and valleys from subsequent candidate plane projections are not filtered out. Moreover, path-equivalent stress or strain calculations can still be applied after the filtering process, without precision loss beyond the filter resolution. The algorithm is synchronous and preserves load order, becoming suitable for strain-based multiaxial damage models involving plastic memory, as well as for mixed-mode crack propagation calculations. The filter efficiency is validated from oversampled tension-torsion experimental data in 316L stainless steel tubular specimens, following complex non-proportional histories. Finally, a fully-tested computer implementation of the algorithm is presented.

Experimental study of unstable crack propagation velocity for X80 pipeline steel

AbstractUnstable crack propagation velocity following the failure of pipeline steel has always been a problem. In this study, differences between the existing unstable crack propagation calculation models were analysed, and the deficiencies within the crack propagation velocity models were overcome. The hardening coefficient and hardening index of the ductile material were considered, and a velocity model of unstable crack propagation of pipelines based on the Hutchinson‐Rice‐Rosengren (HRR) theory elastic‐plastic stress‐strain field and the displacement field was established. Consequently, the limit propagation velocity was obtained. In full‐scale burst test, the pipe with diameter of 1422 mm was chosen to simulate the natural gas pipeline transportation environment. Compared with the theoretical result, the error was limited in 13%. The research result solved the problem of quantifying the propagation velocity of the crack in X80 pipeline, which was significant for describing the forecast of velocity and length of unstable propagation and failure characteristics of pipelines.

Mechanism Analysis of Liquid Carbon Dioxide Phase Transition for Fracturing Rock Masses

The technique of breaking rocks using carbon dioxide phase transition technology is being widely applied in current research. This article combines theoretical and practical methods to analyze the mechanism by which high-pressure gas breaks rock at different stages. Using the observation that liquid carbon dioxide forms a high-pressure jet from release holes at the moment of release, a formula for calculating the initial pressure on the wall in the direction of release was obtained, and the pattern of initial crack formation on the borehole wall under different initial stress conditions was examined. An experiment using carbon dioxide phase transition technology to fracture rock without an initial stress field was conducted. The mechanism of generation and expansion of subsequent cracks under stress waves and high-pressure gas was analyzed, and the formula for calculating crack propagation radius under stress waves was obtained. The results suggested that under the quasi-static action of high-pressure gas, cracks begin to develop when the stress intensity factor KI at the crack tip is equal to or greater than the fracture toughness KIC of the rock.

Multiple cracks failure rule for TBM cutterhead based on three-dimensional crack propagation calculation

Abstract Practically, there is multiple cracks interpenetrating in TBM cutterhead, which gives rise to its failure prematurely. While the existing theoretical formulas and calculating methods cannot calculate its fatigue failure process under dynamic loading. In view of such situation, crack cutting sampling of TBM cutterhead after service and its fracture failure analysis were performed to clear that its fracture failure is mainly brittle fracture, based on which, A three-dimensional finite element crack propagation model was established to calculate the crack propagation process under dynamic loading. Stress intensity factor of compact test specimens is calculated by standard formula, and the growth paths of crack are got from multiple cracks fatigue tests, compared the two results obtained above to verify respectively the accuracy of the proposed method in calculating stress intensity factor and its growth path. It is confirmed that the two results about the change of stress intensity factor is basically match, and the maximum error of the growth path of the multiples crack model and the test result is about 3.7% within the permissible range. It is proved that the proposed method is feasible to calculate the multiple cracks failure process under the dynamic loading. Finally, the growth processes of collinear multiple cracks, parallel multiple cracks, nonparallel multiple cracks, and penetrating multiple cracks were calculated. The results show that the stress intensity factor at the intersection of collinear cracks decreased by about 26%, compared with a single crack. Parallel and non-parallel multiple cracks are attracted to each other as the cracks propagate in the process of growth and the stress intensity factor gradually decreases. Although the growth path and stress intensity factor do not change, the crack stops expanding, with the crack tip penetrates through another crack. The failure criterion of TBM cutterhead and the rule of interpenetration of multiple cracks proposed in this paper are the theoretical basis and technical support for the its life prediction and risk prediction.

Crack Propagation Calculations for Optical Fibers under Static Bending and Tensile Loads Using Continuum Damage Mechanics.

Static fatigue behavior is the main failure mode of optical fibers applied in sensors. In this paper, a computational framework based on continuum damage mechanics (CDM) is presented to calculate the crack propagation process and failure time of optical fibers subjected to static bending and tensile loads. For this purpose, the static fatigue crack propagation in the glass core of the optical fiber is studied. Combining a finite element method (FEM), we use the continuum damage mechanics for the glass core to calculate the crack propagation path and corresponding failure time. In addition, three factors including bending radius, tensile force and optical fiber diameter are investigated to find their impacts on the crack propagation process and failure time of the optical fiber under concerned situations. Finally, experiments are conducted and the results verify the correctness of the simulation calculation. It is believed that the proposed method could give a straightforward description of the crack propagation path in the inner glass core. Additionally, the predicted crack propagation time of the optical fiber with different factors can provide effective suggestions for improving the long-term usage of optical fibers.

Сравнение критериев моделирования разрушения трубопроводов методом конечных элементов

The work is devoted to the simulation of pipeline’s fracture. Application of modern viscous pipe steels does not completely solve the problem of brittle fracture of these structures, because the desire to increase the thickness of the wall and the operating pressure and the need to use a pipe in a cold climate shifts the fracture mode toward brittle – but, of course, does not make it completely brittle and require the application of nonlinear fracture mechanics. Simulation of the fracture by formation of large longitudial cracks should take into account the inertial forces of the pipe material coming into motion at crack propagation, and the possibility of a pressure drop in the pipe at the loss of its impermeability. These features of the problem can be modeled using finite element package LS-DYNA. However, LS-DYNA offers a limited set of a fracture criteria, which doesnot include the classic criteria of nonlinear fracture mechanics. The aim of the work is the selection of a criteria that is implemented in the LS-DYNA program and at the same time is in good agreement with the experimental data. As such a criterion equivalent plastic strain isconsidered – with the proviso that the plastic deformation near the crack tip is calculated using a weighted averaging procedure on some representative volume to exclude effect of the finite element sizes on results. Parameters of the weighting function are selected to ensure that the loads corresponding to the beginning of the crack growth are the same for the model of viscous fracture and for the nonlinear fracture mechanics. It is shown that the problem of parameter selection is ill-conditioned. However, the obtained values of parameters will subsequently allow to perform the dynamic calculation of longitudial crack propagation in pipes taking into consideration the effects treated by the LS-DYNA code – inertia forces of the material of the pipe wall, velocity of the perturbation wave in the gas or liquid filling the pipe and decompression.