Crack Propagation In Structures Research Articles

On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

AbstractA strategy that combines the global‐local version of the generalized finite element method (GFEM) with a mixed‐dimensional coupling iterative method is proposed to simulate two‐dimensional crack propagation in structures globally represented by Timoshenko‐frame models. The region of interest called the local problem, where the crack propagates, is represented by a 2D elasticity model, where a fine mesh of plane stress/strain elements and special enrichment functions are used to describe this phenomenon accurately. A model of Timoshenko‐frame elements simulates the overall behavior of the structure. A coarse mesh of plane stress/strain elements provides a bridge between these two representation scales. The mixed‐dimensional coupling method imposes displacement compatibility and stress equilibrium at the interface between the two different element types by an iterative procedure based on the principle of virtual work. After establishing the constraint equations for the interface, the 2D elasticity model is related to the small‐scale model by the global‐local enrichment strategy of GFEM. In such a strategy, the numerical solutions of the local problem subjected to boundary conditions derived from the global‐scale problem enrich the approximation of this same global problem in an iterative procedure. Each step of the crack propagation requires a new sequence of this iterative global‐local procedure. On the other hand, the constraint equation for the interface is defined only once. The crack representation in a confined region by the global‐local strategy avoids a remeshing that would require new constraint equations. Two numerical problems illustrate the proposed strategy and assess the influence of the analysis parameters.

A coupled SPH-PD model for fluid–structure interaction in an irregular channel flow considering the structural failure

Understanding fluid–structure interaction (FSI) is important because it dominates diverse natural phenomena and engineering problems. This paper presents an integrated particle model for FSI problems involving irregular channel flows and crack propagation in structures. The proposed model is implemented as follows: (1) we couple weakly compressible smoothed particle hydrodynamics (WCSPH) with bond-based peridynamics (BBPD) in a partitioned approach (this framework has a much simpler algorithm than the previously reported SPH-PD method); (2) we propose a novel periodic boundary conditions (PBCs) algorithm for modeling flows in non-regular channels; and (3) we incorporate crack propagation in structural responses under fluid dynamics, which was rarely considered in previous works. The new framework has been validated and illustrated to be effective and versatile in diverse FSI problems, including hydrostatic pressure-induced solid deformation, violent free-surface flows and channel flows interacting with flexible structures. Compared with conventional grid-based methods, this particle framework is more user-friendly, since no extra effort is required to update meshes, even when a discontinuity appears during the modeling process. The extendibility and potential of this framework is further demonstrated by the simulation of fluid-driven deformation and crack propagation in elastomers.

Damage tolerance analysis of wading structures of amphibious aircraft based on Franc3D

Aiming at the combined action effect of the corrosive environment of amphibious aircraft wading structures and random loads including water surface take-off and landing impact, based on the standard load spectrum TWIST of transport aircraft, considering the load level and frequency corresponding to the hydrodynamic load, the simulated random load spectrum of the wading structure was first compiled; the Willenborg/Chang high-load hysteresis model was used to consider the hysteretic effect of hydrodynamic high-amplitude overload on structural crack propagation, and an engineering method for damage tolerance analysis of amphibious aircraft wading structures was established. Taking the common hole edge crack of a typical wading structure of a certain type of aircraft as an example, based on the Franc3D crack propagation analysis software, the crack propagation life under the combined action of corrosive environment and random load spectrum was analyzed, and the inspection threshold value and check interval for maintaining the airworthiness of the structure were determined by residual strength analysis. The method proposed in this study is simple and feasible, and provides a theoretical basis for the damage tolerance analysis and maintenance plan formulation of amphibious aircraft wading structures.

New non-destructive testing approach based on eddy current for crack orientation detection and parameter estimation

Crack orientation is a vital factor in the behavioral study of fractures, especially the study of crack propagation in structures that are under dynamic or fatigue loading. Indeed, many non-destructive testing (NDT) techniques have been developed recently for the detection of cracks such as the eddy current testing (ECT). However, the crack orientation has not been undertaken into consideration. In this paper, a NDT based on eddy current using 3D finite element modeling, is proposed for the determination of the crack orientation. The idea of this proposed technique benefits from the influences of crack orientation, which can be observed on the components of eddy current and the related magnetic flux density following the x, y axes, for the estimation of the crack angle orientation based on an interpolation criteria. The obtained results through the presented simulation prove the validity of the proposed technique for the detection of crack angle orientation.

Detection and tracking of cracks based on thermoelastic stress analysis.

Thermoelastic stress analysis using arrays of small, low-cost detectors has the potential to be used in structural health monitoring. However, evaluation of the collected data is challenging using traditional methods, due to the lower resolution of these sensors, and the complex loading conditions experienced. An alternative method has been developed, using image decomposition to generate feature vectors which characterize the uncalibrated map of the magnitude of the thermoelastic effect. Thermal data have been collected using a state-of-the-art photovoltaic effect detector and lower cost, lower thermal resolution microbolometer detectors, during crack propagation induced by both constant amplitude and frequency loading, and by idealized flight cycles. The Euclidean distance calculated between the feature vectors of the initial and current state can be used to indicate the presence of damage. Cracks of the order of 1 mm in length can be detected and tracked, with an increase in the rate of change of the Euclidean distance indicating the onset of critical crack propagation. The differential feature vector method therefore represents a substantial advance in technology for monitoring the initiation and propagation of cracks in structures, both in structural testing and in-service using low-cost sensors.

Code development for the computational analysis of crack propagation in structures

In this study, the main objective was the creation of a code, which gives the capability to a Finite Element Analysis Program with no built-in crack study tools, to study the propagation of a crack, in a cracked surface. For this purpose, the Finite Element Program FEMAP 11.3.2 with solver the NX NASTRAN has been used, and the proposed code was created, using the Application Program Interface (API) of the program. The Linear Elastic Fracture Mechanics (LEFM) theory has been applied to the code, and can predict, if the crack will propagate, the trajectory of the crack, as well as the number of cycle loads required for the propagation of the crack, for given boundary conditions and loads. Finally, the Stress Intensity Factors (SIF) produced by the program, were compared with results from analytical method. Also, experimental results have been used, for the verification of the results of the trajectory of the propagation, and the cycle loads.

Mixed mode I/II crack growth investigation for bi-metal FSW aluminum alloy AA7075-T6/pure copper joints

Over the past two decades, a large number of papers have been published for investigating mechanical properties and microstructure of Friction Stir Weld (FSW) joints made of several similar and dissimilar alloys. Crack growth resistance of such joints is an important design parameter for integrity and life assessment of FSW components. In practice, propagation of cracks in structures fabricated by the FSW technique, which initiate in the welding region, can occur under multiaxial and complex tensile-shear loadings. However, review of the literature shows that there are only limited research works regarding mixed mode I/II (i.e. tensile-shear) fracture resistance study of FSW weldments. Thus, to fill this research gap in this paper, mixed mode I/II fracture resistance of dissimilar aluminum alloy AA7075-T6 / pure copper butt joints welded by the FSW is investigated both experimentally and theoretically. First, a novel semi-circular bend shape specimen is proposed for conducting mixed mode I/II fracture tests. Then, due to ductile behavior of the cracked specimens, the experimentally obtained load-carrying capacity (LCC) of the tested specimens is predicted theoretically using the maximum tangential stress (MTS) and mean stress (MS) criteria in conjunction with the Equivalent Material Concept (EMC). It is revealed that both EMC-MTS and EMC-MS combined criteria can predict quite well the experimental results.

Crack propagation in structures with uncertain-but-bounded parameters via interval perturbation method

Fatigue crack growth prediction plays a crucial role in structure design. This paper presents a method for crack propagation analysis in structures with uncertain-but-bounded parameters. Although the parameters of engineering structures are uncertain due to many factors, the range across which they vary can be determined from practical experience and engineering knowledge. The crack growth boundary over the life of the structure has great significance in preventing structural failure. Uncertain-but-bounded parameters are regarded as interval numbers in the proposed method, and expressed alongside time-varying crack length under Paris law as a perturbation series after introducing a small parameter. By combining the perturbation method with interval mathematics, boundaries of each term in the perturbation series of time-varying crack length are determined to obtain the upper and lower boundaries of time-varying crack length. The proposed method is verified based on two examples; both the Monte-Carlo method and probabilistic method are applied for the sake of validation. The results demonstrate the feasibility and efficiency of the proposed method for predicting crack propagation in structures with uncertain-but-bounded parameters.

Fatigue crack growth rate in CFRP reinforced constructional old steel

PurposeThe purpose of this paper is twofold: first, to observe an influence of different Composite Fibre-Reinforced Polymer (CFRP) patches, whose application to metals is very easy, in suppling and significantly elongating the service time; and second, the numerical calculation of the reduced stress intensity factor (SIF) range for strengthened cracked steel specimens.Design/methodology/approachOne of the successful strengthening methods is the CFRP patching along the fatigue crack paths. The presented approach has been studied and discussed in this paper on the background of the numerical and experimental data. As it was expected, the proposed strengthening method is efficient and promising in case of the “immediate” repairs of critical members with cracks. The manufacturing process of specimens and test methodology as well as numerical approach to calculate SIFs for various reinforcements of steel specimens are presented. For this purpose, the Extended Finite Element Method was involved and described.FindingsThe main mechanism of fatigue crack growth retardation is associated with local ΔK reduction due to CFRP patches; any type of reinforcement results in an increase in af and a significant decrease in SIF values. The beach-marking method is described as a good, reliable and comprehensive method to capture the crack propagation in structures consisting of various materials and could be applied successfully for mixed mode testing.Originality/valueA detailed experimental-numerical approach for fatigue crack growth in long-term operated structures made of steel is presented. The strengthening methodology is presented with consideration of the various CFRP patches configurations.

Crack propagation monitoring using an image deformation approach

Summary An image deformation method is herein proposed to monitor the crack propagation in structures. The proposed approach is based on a computational algorithm that uses displacements measured by photogrammetry or image correlation to generate a virtual image of the surface, from an initial input to any given stage of analysis. This virtual image is then compared with the real image of the specimen to identify any discontinuities that appeared or evolved during the monitored period. The procedure was experimentally validated in the characterisation of crack propagation in concrete specimens. When compared with other image processing techniques, for instance, based on edge detectors, the image deformation approach showed insensitiveness to any discontinuity previously existing on the surface, such as cracks, stains, voids, or shadows, and did not require any specific surface treatments or lighting conditions. With this approach, the global crack maps could be extracted from the surface of the structure and extremely small changes occurring within a given time interval could be characterised, such as the movement associated with the opening of cracks. It is highlighted that the proposed procedure is general and therefore applicable to detect and characterise surface discontinuities in different materials and test set-ups.

Modelling of Crack Propagation in Layered Structures Using Extended Finite Element Method

Crack propagation in structures is an important issue which is engineers and designers should consider. Modeling crack propagation in structures and study the behavior of this phenomenon can give a better insight to engineers and designers for selecting the construction’s materials. Extended finite element method (XFEM) was used successfully in the past few years for simulating crack initiation and propagation in sophisticated and complex geometries in elastic fracture mechanics. In this paper, crack propagation in three-point bending beam including initial crack was modeled based on ABAQUS software. The following consequences were attained through the study of simulation data. First, the effects of young’s modulus and fracture energy on force-displacement curve at three-point bending beam were investigated. It was observed that, by increasing the value of young’s modulus and fracture energy, three-point bending beam was showed more load carrying against initiation. Second, in multi-layer beam, the effect of young’s modulus on force-displacement curve was investigated. In case I (the thin upper layer is harder than the substrate) the value of young’s modulus in substrate was kept constant and the amount of young’s modulus in thin layer was risen in each step rather than the substrate, the peak in force-displacement curve was ascended and three-point bending beam resisted better against crack initiation. Next, similar conditions was considered in case II (the thin upper layer is softer than the substrate), by decreasing the value of young’ modulus in top layer, peak in force-displacement curve was declined and crack initiation was happened in lower loading in each step. Finally, sensitivity analysis for thickness of top layer was conducted and the impact of this parameter was studied.

Notch stress intensity factor for center cracked plates with crack stop hole strengthened using CFRP: A numerical study

It is well known that drilling a hole ahead of crack tip is one of the most common techniques to prevent crack propagation in structures subjected to fatigue load. An adequate size crack stop hole is necessary to convert a sharp crack into a blunt notch thereby preventing crack propagation. However, fatigue cracks typically occur at locations where drilling a crack-stop hole of required dimensions may not be possible due to geometrical constraints. In such situations, the crack may initiate again from the hole within its service life. Hence, there is a need to strengthen undersized crack-stop holes. In the present study, a combination of crack-stop hole and carbon fiber reinforced polymer (CFRP) overlays under static loads are studied numerically using finite element analysis (FEA) to evaluate its potential as a viable repair technique. A steel plate with an initial central crack subjected to static tensile loading (mode-I) is considered. A hole is modelled ahead of a crack tip and CFRP patches are applied on either side of the crack. The numerical analysis is performed using general purpose FEA ANSYS. A total of 1008 models, i.e 112 unstrengthened and 896 strengthened specimens are used to evaluate the stress intensity factor at notch tip. The material behaviour is assumed to be elastic in case of linear analysis and as a multi linear isotropic hardening material type for nonlinear analysis. The results from linear analysis are used to compare Crack Stress Intensity Factor (CSIF,KI/ρ) and Notch Stress Intensity Factor (NSIF, KI/ρα). The results indicate the need to include the stress gradient α in arriving at adequate crack stop hole radius for both bare steel and CFRP patched specimens. Nonlinear FEA, which takes into account the post yield material behaviour, is carried out to propose a modified NSIF expression by including a Reduction Factor (RF) that is a function of the ratio of the radius of crack stop hole to crack length (ρ/2a), the ratio of stiffness of CFRP to steel (SR) and the ratio of applied stress to yield stress (σapplied/σys). Numerical examples are provided to demonstrate the applicability of the proposed equation.

Stochastic model of crack propagation in brittle heterogeneous materials

The explanation of experimentally observed phenomena of correlation of crack increments is required for consideration of stochastic crack propagation in structures and solids. The proposed model provides an explanation based on Brownian Motion with reflection from effective boundaries of a zone around main crack tip. The model is based on an assumption that there is a micro crack layer near the main crack tip, in which micro cracks are stabilized by inclusions. Main crack tip is advancing in surrounding micro crack layer with higher speed than the speed of boundaries of the micro crack layer, and it is assumed that there exists a positive probability for main crack tip to reflect from effective boundaries of its micro crack layer. The defined process is different from Reflected Brownian Motion in that only a fraction of crack paths get reflected. Results of stochastic Monte Carlo simulation for crack in infinite plate showed that crack trajectories are characterized, in general case, by quicker then linear growing variance, strong long range dependence and non-Normal distribution corresponding to non-Gaussian process. Questions related to usage of additional random parameters for case of long term loading and long term strength are also considered.

Numerical Modelling of Crack Propagation in Friction Stir Welded Joint Made of Aluminium Alloy

In this work, fatigue crack propagation in thin-walled aluminium alloy structure with two friction stir welded (FSW) joints has been numerically modelled. Crack propagation in unstiffened part of the structure between two FSW joints is analyzed. Numerical method, so-called eXtended Finite Element Method (XFEM) has been used, including software Abaqus, as well as Morfeo, for modelling and results display. Tensile fatigue loading is applied, with stress ratio R=0. The analyzed model is made from aluminium alloy 2024-T351. Material properties in joints zones and geometry measures of FSW joint are adopted from available experiments.Following results are obtained by numerical analysis:•stress-displacement state in the structure, where special attention is dedicated to the crack tip zone,•coordinates of the crack front (x, y, z) for every propagation step,•distributions of stress intensity factors - KI, KII, KIII and Keq along the crack front for each propagation step,•structural life in form of change of applied number of load cycles, N, for each step of propagation.Besides numerical results, Abaqus provides visualization of crack propagation in the structure. On the basis of obtained data, analysis of crack growth stability is done.

Two-dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

When the loading or the geometry of a structure is not symmetrical about the crack axis, rupture occurs in mixed mode loading and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation. The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method in a FE code and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors. In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we presented the examples of crack propagation in structures containing inclusions and cavities.

Strain energy density prediction of crack propagation for 2D linear elastic materials

When the loading or the geometry of a structure is not symmetrical about the axis of the crack, the rupture occurs in mixed mode loading, and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation.The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method (DEM) and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors (SIFs). In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we present the examples of crack propagation in structures containing inclusions and cavities.

Finite Element Analysis of the Crack Propagation for Solid Materials

Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT). Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET) was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs). Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published results. Conclusion: A developed a source program of finite element model showed that is capable of demonstrating the SIF evaluation and the crack path direction satisfactorily. Therefore, the numerical finite element analysis with displacement extrapolation method, had been successfully employed for linear-elastic fracture mechanics problems.

Crack propagation in structures subjected to periodic excitation

In the present paper, a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten (mimicking crack growth) if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

Modelling crack propagation in structures: Comparison of numerical methods

AbstractCrack propagation in concrete structures is a very complicated process, and the distribution of cracks may significantly affect the behaviour of the structures under time‐dependent loading. If enough damage or extensive cracks exist in a structure, strengthening or repair using external carbon fibre‐reinforced polymer (CFRP) reinforcement may be needed. Therefore, an understanding of the influence of the CFRP strengthening system on behaviour is crucial for the proper design of a structural reinforcement strategy. In this paper, we compare three major methods: the discrete crack method, the smeared crack method and the element‐free method. By using these methods to study the fracture pattern of a beam with dapped ends, we can compare the capabilities and efficiencies of the three methods. When modelling the crack formation in reinforced concrete structures, the smeared crack approach gives better results than the discrete model in terms of crack spacing and regularity, however, it does not follow the crack growth well. The element‐free Galerkin method seems to be superior to the other methods in the sense that it deals with the irregular cracks well and is very efficient in saving computing time. The preferred choice of method depends on the type of problem and the solution accuracy required, and this also depends on a certain balance between the accurate tracing of individual cracks and the computing efficiency. In addition, new algorithms are required for the efficient simulations of dynamic crack propagation, especially in the case of pre‐cracked structures strengthened with prestressed CFRPs. Copyright © 2007 John Wiley & Sons, Ltd.

Joule Heating and its Implications on Crack Detection/Arrest in Electrically Conductive Circular Cylindrical Shells

Distribution of Joule heating and the corresponding electromagnetic field in the vicinity of the crack in a thermo- and electro-conductive thin-walled shell carrying a non-stationary electrical current is investigated. Specifically, a circular cylindrical shell with one finitely long crack that is perpendicular to the current direction is considered. The crack is free of mechanical loads. The underlying boundary-value problem is addressed via the use of Fourier series expansion and the solution reduces to that of a singular integral equation with Hilbert-type singular kernel. The influence of the presence of crack, and the effect of non-stationarity of the current on the distribution of current and Joule heating in the shell are investigated and pertinent conclusions are drawn. The results are instrumental toward crack detection and active arrest of crack propagation in structures made of electro-conductive materials or aged structure components in aerospace industry.