Crack Propagation Scenarios Research Articles

Examination of crack path in silicon multi-crystals

Dynamic fracture of silicon multi-crystal merits a systematic investigation given the complexity induced by microstructure defects, in particular grain boundaries. How crack selects its path in the presence of substantial grain boundaries is an issue still under debate in literature. In this work, fracture behavior of multi-crystalline silicon is carefully examined through bending tests, bringing to light new crack propagation scenarios. In the case of multi-cracking, massive branching events emerge, and crack paths are heavily affected by burst waves. When a single crack propagates across grain boundaries, orientation mismatch between cleavage planes generates an important constraint effect, leading the crack to eventually propagate along (112) plane, i.e., a path scarcely seen in single crystal. Perfect crack propagation along coherent Σ3 twin boundary can hardly be achieved, presumably due to the crack inertia effect. Moreover, crack is found to incessantly deviate at the two sides of high order grain boundaries, resulting in a zigzag crack path. The observations suggest that grain boundaries are not prone to break up but significantly affect crack path in silicon multi-crystals.

Crack propagation under thermo-mechanical loadings based on moving mesh strategy

This paper proposes an effective FE modeling for simulating fracture propagation in linear elastic media under mechanical and thermal loadings. The model joins Moving Mesh (MM) technique with Interaction integral (M−integral) method to simulate crack advancing phenomena. MM reproduces growing cracks by moving the mesh nodes around the crack front, according to proper fracture criteria. In particular, the method adopts the Arbitrary Lagrangian-Eulerian (ALE) Formulation, which handles random cracks, reducing the recourse to remeshing processes. In this context, M−integral determines the fracture quantities at crack front, required to find onset conditions and propagation direction. This takes place during the entire analysis, thus ensuring quite smooth crack paths. Comparison results with other numerical strategies serve as primary tests to check the efficacy of the proposed approach. Besides, simulations with multiple growing cracks in both complex geometries and boundary conditions let checking performance. The results denote that the proposed method is a powerful and versatile tool for reproducing complex crack propagation scenarios.

Crack initiation and propagation in braided SiC/SiC composite tubes: Effect of braiding angle

Crack initiation and propagation in three braided SiC/SiC composite tubes with different braiding angles are investigated by in situ tensile tests with synchrotron micro-computed tomography. Crack networks are precisely detected after an image subtraction procedure based on Digital Volume Correlation. FFT based simulations are performed on the full-resolution 3D images to assess elastic stress/strain fields. Quantitative measurements of the crack geometries are performed using a novel method based on grey levels. The results show that braiding angle has no obvious effect on the location of crack onsets (initiation always occurs at tow interfaces), whereas it significantly affects the paths of crack propagation. This work provides an explicit demonstration of the crack propagation scenarios with respect to the mesoscopic fibre architectures.

Mesh stiffness modelling and dynamic simulation of helical gears with tooth crack propagation

In order to identify gear crack failure, modelling the mesh stiffness of a cracked tooth is crucial. In this study, an analytical model of the mesh stiffness for cracked helical gears considering the axial mesh stiffness components and the deflection of the gear body has been proposed. Based on the analytical model, the comparison of the mesh stiffness with and without the axial mesh stiffness components or the deflection of the gear body was carried out. Mesh stiffness of three crack propagation scenarios with different crack sizes has been investigated. Simultaneously, a method to detect the crack length has been deduced based on the time period of the mesh stiffness. Simulation has been conducted using a six-degrees-of-freedom helical gear dynamic model in order to study the effect of tooth crack propagation on the dynamic response. Statistical indicators extracted in the time domain and frequency domain were adopted to evaluate the crack propagation level. The results indicated that the analytical model that has been proposed is able to provide a relatively accurate mesh stiffness, taking into consideration the axial mesh stiffness components and the deflection of the gear body. Mesh stiffness reduced with the propagation of the crack size in either the direction of the crack depth or the crack length. Through analysis of the time period of the residual signal from the dynamic transmission error, the crack length was able to be accurately identified. The shape factor in the selected statistical indicators is most sensitive to the tooth crack propagation in the frequency domain.

Modelling the criticality of silicon nitride surface imperfections under rolling and sliding contact

Ceramic rolling elements of hybrid bearings may initially include surface imperfections. In order to provide reliable operation of a bearing, the criticality of such imperfections under rolling contact fatigue is examined by defining them as Star features: intersecting semi-elliptical surface cracks. Parametric study is conducted using Finite Element Method and discussed with help of previously published experimental observations. The effects of the Star feature morphology and configuration, contact pressure and crack face friction are investigated in terms of stress intensity factors. Possible crack propagation scenarios are explained in the present study.

On the performance of a cointegration-based approach for novelty detection in realistic fatigue crack growth scenarios

Abstract Confounding influences, such as operational and environmental variations, represent a limitation to the implementation of Structural Health Monitoring (SHM) systems in real structures, potentially leading to damage misclassifications. In this framework, this study considers cointegration as a state of the art method for data normalisation in fatigue crack propagation scenarios, where monitoring is performed by a distributed network of strain sensors. Specifically, the work is aimed at demonstrating the effectiveness of cointegration on real engineering data in a new context, where the damage is continuously growing. Cointegration is applied at first in a controlled scenario consisting of a numerical strain simulation by means of a finite element model, modified in order to take realistic temperature fluctuations and sensor noise into account. Afterwards, detrending and anomaly detection performances are verified in two different experimental programmes on realistic aeronautical structures subjected to fatigue crack growth, including a full-scale fatigue test on a helicopter tail boom. Strain measurements are taken from a network of Fibre Bragg Grating (FBG) sensors, known to be extremely sensitive to temperature variations, hence delivering challenging scenarios for cointegration testing. Results are shown to be in good agreement with the experimental evidence, with the cointegration algorithm capable of detecting the onset of damage propagation within a 4 mm increment from a baseline condition.

A polymorphic element formulation towards multiscale modelling of composite structures

This paper presents a new polymorphic element modelling approach for multi-scale simulation, with an application to fracture in composite structures. We propose the concept of polymorphic elements; these are elements that exist as an evolving superposition of various states, each representing the relevant physics with the required level of fidelity.During a numerical simulation, polymorphic elements can change their formulation to more effectively represent the structural state or to improve computational efficiency. This change is achieved by transitioning progressively between states and by repartitioning each state on-the-fly as required at any given instant during the analysis. In this way, polymorphic elements offer the possibility to carry out a multiscale simulation without having to define a priori where the local model should be located.Polymorphic elements can be implemented as simple user-defined elements which can be readily integrated in a Finite Element code. Each individual user-defined polymorphic element contains all the relevant superposed states (and their coupling), as well as the ability to self-refine.We implemented a polymorphic element with continuum (plain strain) and structural (beam) states for the multiscale simulation of crack propagation. To verify the formulation, we applied it to the multiscale simulation of known mode I, mode II andmixed-mode I and II crack propagation scenarios, obtaining good accuracy and up to 70% reduction in computational time —the reduction in computational time can potentially be even more significant for large engineering structures where the local model is a small portion of the total.We further applied our polymorphic element formulation to the multiscale simulation of a more complex problem involving interaction between cracks (delamination migration), thereby demonstrating the potential impact of the proposed multiscale modelling approach for realistic engineering problems.

3D reconstruction of cracks propagation in mechanical workpieces analyzing non-stationary acoustic mixtures

Abstract Cracks are one of the main causes of solid bodies weakening and are a hidden threat for mechanical systems. Acoustic emission is an indicator of cracks initiation and propagation and is widely exploited for the localization of cracks in non- or weakly-transparent environments. The present study enriches the functionality of multiple existing algorithms in crack localization using acoustics. The novelty is in the reconstruction of the complex geometry of the crack path and tracking its propagation in time, whereas existing methods focus only on the localization of the crack without any information about its geometry. The algorithm uses sparse acoustic signal representations as relative energies of the narrow frequency bands, extracted with the M-band wavelet transform. Non-linear independent component analysis is applied to de-mix the recorded acoustic signals into a number of separate acoustic patterns. Furthermore, a triangulation, using the time delay arrivals, is applied for each of such patterns separately, thus extracting multiple individual emittance sources. The algorithm was tested using synthetic data that replayed various scenarios of crack propagation together with different detector arrays configurations and its behavior was analyzed. Additional verification with real-time data was carried out by analyzing signals from crack propagation in glass along a known programmed path. The acoustic data was recorded with four fiber Bragg gratings. In both cases, the algorithmic framework showed a high efficiency in recovering the geometrical configuration of the crack.

Vibration feature evolution of locomotive with tooth root crack propagation of gear transmission system

Abstract As the prompt development of modern railway transportation towards high-speed and high load-capacity, the high-power locomotive is urgently required. Under this situation, the wheel–rail dynamic interaction is becoming more and more intensified which will deteriorate the vibration condition of the key elements of locomotive, such as the gear transmissions. Once gear failures are present, such as gear tooth crack or breakage, it is likely to threaten the operation safety of the locomotive. Thus, deep insight into the fault features of the locomotive gear transmission is urgently necessary for prevention of the induced disastrous consequences. This paper is concentrated on the fault vibration feature extraction of a locomotive in presence of gear tooth root crack under the complicated dynamic excitations from both the gear transmissions and the nonlinear wheel–rail interactions. The locomotive–track coupled dynamics model considering the dynamic effect of the mechanical power transmission path is employed, and the time-varying mesh stiffness of the gear pair with tooth root crack fault and the rail geometric irregularities are then incorporated into the dynamics model to obtain the vibration responses. Then, angular synchronous average technique is proposed to enhance the fault vibration features, and the statistical indicators extracted in frequency domain are developed to reveal the evolution law for the crack propagation scenarios along crack depth or tooth width. The analyzed results indicate that the angular synchronous average technique could effectively reveal the fault vibration feature, and the M8A in the selected statistical indicators is most sensitive to the tooth crack propagation in frequency domain.

Morphing structures and fatigue: The case of an unmanned aerial vehicle wing leading edge

AbstractWith the emergence of novel aircraft structural concepts, which make use of large‐scale shape deflections to achieve improved flight performance across significantly different flight regimes and missions, unusual crack paths and mixed‐mode crack propagation situations may take place. Consequently, morphing concepts require a full understanding of the materials' behaviour in primary or secondary structures to reliably withstand unusual and demanding operating conditions.A case study of a morphing leading edge developed for the wings of an unmanned aerial vehicle is presented in this paper. Leading edges are subjected to damage originated by bird strike or other events, and those damages can compromise the structural integrity and stability of the flight. Due to the deflections during the morphing structure actuation, cracks will propagate eventually until critical sizes. Possible crack propagation scenarios are presented, considering the service operation of the morphing leading edge.

Hybrid technique to assess the fatigue performance of multiple cracked FSW joints

In this paper a numerical–experimental procedure useful to numerically assess the fatigue performance of friction stir welded aluminium joints is presented. The impact of manufacturing residual stresses on crack propagation in the joint driven by a remote fatigue load can be predicted. The proposed sequential procedure starts with the experimental residual stress assessment by the contour method and proceeds through the multiple crack growth simulation by the Dual Boundary Element Method. In the frame of Linear Elastic Fracture Mechanics, the superposition principle is invoked to provide the mathematical foundation supporting the proposed modelling strategy. In order to validate the proposed procedure, simple specimens are fatigue tested, obtaining multiple crack propagation scenarios that are monitored, in order to compare experimental and predicted crack growth rates.

Scenarios of crack propagation in bast fibers: Combining experimental and finite element approaches

This work investigates the rupture of bast fiber type from hemp, to attain better control over the ultimate tensile and fracture strength properties of hemp composites. Crack propagation in both individualized and bundles of hemp fibers is studied. Crack initiation is controlled using generated defects within fibers. A non-contact-ablation apparatus creates these defects using a laser beam directed by high-precision optics. V- and U-type notches are processed, with sizes ranging from 2 to 30μm in depth. The micromechanical testing of damaged fibers is coupled to a high-speed camera, allowing for the measurement of ultimate properties as well as monitoring of the crack propagation.Finite element simulation is developed to identify possible damage scenarios for bundles and elementary fibers. Microcracks are allowed to initiate, grow and coalesce based on non-prescribed crack propagation (i.e., not imposed or with direction update) and stress criteria. High speed camera recording indicate a wide variability in crack propagation speed in the range 2–149m/s. Both longitudinal and transverse cracking are observed depending on the notch geometry. Our results demonstrate that the damage kinetics is a combination of growth and coalescence of microcracks. These damage mechanisms compete depending on the notch geometry and fiber element dimensions.

Measurement of Nonuniformity of Fracture in Structural Steels with Heterogeneous Structure

Different methods for measurement of nonuniformity of fracture in structural steels with heterogeneous structure are studied including the partition of space into Voronoy polyhedrons for measuring the differences in random sets of points in a plane, synthesis of a 3D-picture from several 2D ones (stereophotogrammetry) and indirect analysis of 3D-peculiarities from a 2D-shot, i.e., a “plane” image, for reconstructing scenarios of crack propagation, and solution of problems of linear regression with the use of the principle of maximum likelihood.

Computation of crack propagation in 3‐dimensional anisotropic solids

AbstractThis contribution presents ideas, how crack propagation in three‐dimensional solids composed of anisotropic materials can be predicted using the Griffith energy principle. Since the work of Irwin the change of potential energy caused by a straight elongation of a crack in an isotropic two‐dimensional homogeneous structure can be expressed in quadratic terms of the stress intensities at the crack tip. This result was generalized in the last decades using methods of asymptotic analysis by many authors [1] to more complicated geometries, to anisotropic and inhomogeneous materials. With the energy release rate at hand, quasi‐static scenarios of crack propagation can be simulated for plane problems [2], but this is still a complicated task for three‐dimensional problems [3]. We show an idea how the change of energy caused by propagation of a crack surface in a fully three‐dimensional solid of nearly arbitrary shape can be computed in anisotropic materials. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimization of Numerical Analyses for Maintenance of Fuselage Skins with Rectangular Repairs

Greatly reduced inspection intervals of skin damage repairs pose a significant financial problem for aging commercial aircraft fleets. Such intervals for visual inspections are the result of simplified conservative repair substantiation analyses, based on the same crack propagation scenarios and curves that were established in the initial project development. These neglect the structural role of external repair (“doubler”) and consider only the increase in hidden crack path. A more refined approach to reassessing inspection intervals after a repair may keep maintenance jobs in accordance with common C-check routines in most cases. This approach, based on new crack growth simulations for worst case scenarios that could occur at the region of repair, uses respective kinetic equation and new geometric stress intensity factor functions, obtained in additional FEM (Finite Element Method) analyses. In particular, for standard rectangular repairs, the number of possible geometric configurations is astonishing considering length, width, skin and “doubler” thickness, reinforced panel dimensions, and frame and stringer cross sections. This investigation deals mainly with defining a minimum sufficient number of intermediate crack length values for FEM analyses in each propagation scenario. A conservative but efficient definition of most relevant parameters for a new numerical analysis campaign is another important issue. The results obtained are helpful for the improvement of the operational efficiency and safety of an aging fleet.

Crack propagation in anisotropic composite structures

A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053-1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.

Vibration signal analysis for gear fault diagnosis with various crack progression scenarios

There are different analytical scenarios assumed for crack propagation in the gear tooth root. This paper presents an investigation of the performance of statistical fault detection indicators (the RMS and kurtosis) for three different series of crack propagation scenarios, to compare these scenarios from a fault diagnostics point of view. These scenarios imply different forms of cracks with propagation by a certain step of crack depth. The first scenario assumes a crack being extended through the whole tooth width with a uniform crack depth distribution, while the second scenario assumes the crack being extended through the whole tooth width with a parabolic crack depth distribution, and finally in the third scenario the crack is assumed to be propagating in both the depth and the length directions simultaneously. The time-varying gear mesh stiffness has been investigated using the programme code developed in the present research, and the crack propagation can be modelled with any of the presented crack propagation scenarios. Dynamic simulation has been performed to obtain the residual signals of all the studied cases for each crack propagation scenario. The comparison of the statistical indicators applied to the residual signals shows that in the first scenario the faults are most easily detectable, since in this scenario there is a change in the indicators implying a dramatic decrease in the gear mesh stiffness. The fault detection in the 2nd scenario is more difficult, as the crack propagates with no significant reflection on the mesh stiffness loss. The 3rd proposed scenario should receive more attention in research because it could occur in reality in case of non-uniform load distribution. However, with this scenario it is difficult to perform early fault detection, since there is a very slight change in the statistical indicators at the beginning of the crack propagation. After which, these indicators show a significant change when the crack grows deeper which implies a serious crack propagation condition.

Analytical Crack Propagation Scenario for Gear Teeth and Time-Varying Gear Mesh Stiffness

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.

Micro-scale modelling of bovine cortical bone fracture: Analysis of crack propagation and microstructure using X-FEM

Bone-fracture susceptibility is increased by factors such as bone loss, microstructure changes, and variations in material properties. Therefore, investigation of the effect of microstructure and material properties of bone on crack propagation in it and of its global response at macro-scale is important. A non-uniform distribution of osteons in a cortical bone tissue results in a localization of deformation processes. Such localization can affect bone’s performance under external loads and initiate fracture or assist its propagation. Once the fracture initiates, that distribution can play an important role in the crack propagation process at micro-scale; subsequently, the global response at macro-scale could also be affected. In this study, a two-dimensional numerical (finite-element) fracture model for osteonal bovine cortical bone was developed with account for its microstructure using extended finite element method (X-FEM). The topology of a transverse-radial cross section of a bovine cortical bone was captured using optical microscopy. Mechanical properties for the bone’s micro-structural features in the cross section were obtained with a use of the nanoindentation technique. Both the topology and nanoindentation data were used as input to the model formulated with the Abaqus finite-element software. The area, directly reflecting micro-scale information, was embedded into the region with homogenised properties of the cortical bone. Numerical simulations provide the macro-scale global response, crack propagation paths and distribution of maximum principal stress at the microscopic level for three different topologies – homogeneous, three-phase composite and four-phase composite model under tensile loading conditions.The calculated stress fields for various cases of topologies demonstrate different patterns due to implementation of micro-structural features in the finite-element models, confirming an important role of the microstructure in the crack propagation scenarios. The suggested approach emphasizes the importance of micro-structural features, especially cement lines, in development of bone failure.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113–2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent −1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.