Presence Of Multiple Cracks Research Articles

An analysis of the interaction between surface and basal crevasses in ice shelves

Abstract. The prescription of a simple and robust parameterization for calving is one of the most significant open problems in ice sheet modelling. One common approach to the modelling of crevasse propagation in calving in ice shelves is to view crevasse growth as an example of linear elastic fracture mechanics. Prior work has, however, focused on highly idealized crack geometries, with a single fracture incised into a parallel-sided slab of ice. In this paper, we study how fractures growing from opposite sides of such an ice slab interact with each other, focusing on different simple crack arrangements: we consider either perfectly aligned cracks or periodic arrays of laterally offset cracks. We visualize the dynamics of crack growth using simple tools from dynamical systems theory and find that aligned cracks tend to impede each other's growth due to the torques generated by normal stresses on the crack faces, while periodically offset cracks facilitate simultaneous growth of bottom and top cracks. For periodic cracks, the presence of multiple cracks on one side of the ice slab, however, also generates torques that slow crack growth, with widely spaced cracks favouring calving at lower extensional stresses than closely spaced cracks.

Investigation on the interaction evolution and growth behavior of multiple cracks under fatigue loading

In this study, the cracks interaction is investigated on plates with different crack geometry parameters through finite element analysis and experiments. The presence of multiple cracks may lead to an enhancement or shielding effect on stress intensity factors (SIFs) depending on crack relative positions and sizes, thereby potentially accelerating or decelerating the crack propagation rate. When the crack tips of double parallel non-collinear cracks begin to overlap, the interaction between cracks transitions from an enhancement effect to a shielding effect, and the KII values reach their peak at this point, which are explained by the stress field distributions surrounding the cracks. For non-collinear double cracks with an inclined angle α, the shielding effect of inclined cracks becomes increasingly pronounced in comparison to horizontal cracks as the angle α increases. To verify the numerical results, fatigue crack propagation experiments were carried out on Al–Li alloy samples with double non-collinear cracks with different crack vertical distance. The experimental results show that growth direction of two non-collinear cracks underwent a transition when they overlapped, leading to load mode I changing into mixed mode of I + II. Based on both numerical simulations and experimental results, the material parameters C and m in Paris equation are modified, and then a new method for predicting the multiple cracks growth life is presented. By comparing with the experimental values, it was found that this method exhibits high accuracy and reliability.

Estimation of multiple cracks interaction and its effect on stress intensity factors under mixed load by artificial neural networks

One of the goals of fracture mechanics in the analysis of problems involving cracks is to investigate crack growth and propagation. Each crack grows and propagates in the environment based on its geometry and loading conditions, which can occur under pure mode or a combination of modes. The growth and propagation pattern of the crack in these conditions aligns with the fracture mode. In the presence of multiple cracks in the environment, the growth and propagation paths of these cracks differ from the isolated crack case, where they can either grow independently under certain conditions or merge together. Nowadays, extensive research has been conducted on cracks and their mathematical relationships with respect to the geometry and loading conditions of various components. Since in many cases, a large number of cracks may occur in proximity to each other, the intensification and protective effects of each crack on others and their impact on the overall behaviour of components are of great importance. This study focuses on investigating the behaviour of interaction and the stress intensity factor for an infinite plate with parallel adjacent cracks. Remote stress boundary conditions in the form of tensile and compressive stresses have been applied to this plate, and using the J-integral and the finite element method with the Abaqus finite element analysis software, this subject has been examined. The obtained results indicate that depending on the type of vertical and horizontal distances and the angle of their placement between the adjacent crack and the main crack in the first, second, and mixed modes, the adjacent crack can have intensifying, protective, or neutral effects. Furthermore, a good estimation of the secondary crack's influence on the main crack has been provided using a neural network method (MLP), which creates an appropriate weight function for the upcoming sample.

Optimisation Investigation and Bond-Slip Behaviour of High Strength PVA-Engineered Geopolymer Composite (EGC) Cured in Ambient Temperatures

Engineered geopolymer composite (EGC) is becoming an uprising product in the civil industry as a substitute and solution for conventional geopolymer concrete (GPC) as GPC exhibits brittleness and has poor cracking resistance. In this paper, we explored high strength engineered geopolymer composite (EGC) made of polyvinyl alcohol (PVA) fibre and without coarse aggregate constituents characterised as high-performance geopolymer concrete. Varying alkaline solution to fly ash ratio (AL/FA) was investigated. Bond-slip behaviour and the mechanical properties, including compressive, tensile, and flexural strengths, were studied. PVA-EGC mix designs in this research was optimised using response surface methodology (RSM). Various parameters, including the amount of ground granulated blast slag (GGBS) and silica fume, were included in the parametric and optimisation study. Based on the RSM study, the use of quadratic studies found the responses to be well-fitted. Next, the optimised mix design was utilised for the casting of all the samples for the mechanical and bond-slip tests in this study. The main parameters of bonding behaviour include multiple embedment lengths (7 d, 10 d, 12 d and 15 d) and various sizes of rebar diameter used for pull-out tests. Moreover, the mechanical properties and bond behaviours of EGC were compared with those of conventional geopolymer concrete (GPC). The compressive strength of EGC and GPC at 28 days were designed to be similar for comparison purposes; however, EGC shows higher early compressive strength on day 1 compared to GPC. In addition, results indicate that EGC has superior mechanical properties and bond performance compared to GPC, where EGC is approximately 9 and 150% higher than GPC in terms of flexural and tensile strength, respectively. Pull-out tests showed that EGC samples exhibited higher ductility, as evidenced by the presence of multiple cracks before any exhibited failure in tension and flexure. Ductile failure modes, such as pull-out failure and pull-out splitting failure, are observed in EGC. In contrast, GPC specimens show brittle failure, such as splitting failure.

Experimental and Numerical Study of Concrete Fracture Behavior with Multiple Cracks Based on the Meso-Model.

In this paper, a series of experimental and numerical studies were carried out to investigate the effect of multiple cracks on concrete fracture behavior. Seven groups of double-crack concrete three-point bending (TPB) experiments with different crack lengths and different crack distances were carried out. The experimental results showed that the bearing capacity of double-crack specimens was slightly larger than the standard specimen with one central crack. Additionally, with an increase in the second crack length or with a crack distance reduction, the concrete's bearing capacity increased correspondingly. Based on the experiments, a numerical meso-model was developed based on applying cohesive elements. The aggregate, mortar, interface transition zone (ITZ), and potential fracture surfaces were explicitly considered in the model. In particular, cohesive elements were used to characterize the mechanical behavior of the ITZ and potential fracture surfaces. A modified constitutive concrete model was developed by considering the potential fracture surfaces' damage relation and friction effect. The accuracy of the developed meso-model was validated through a comparison between simulation and experiments. Based on meso-models, the influence of multiple cracks on the concrete bearing capacity was investigated by analyzing the energy evolution. The analysis results showed that the bearing capacity has a linear relation with the proportion of mode II energy consumption during the fracture process, which explains why specimens with multiple cracks have a slightly larger bearing capacity than the standard specimens. In summary, this study has found that in three-point bending fracture tests primarily characterized by mode I fractures, the presence of multiple cracks near the main crack slightly enhances the load-bearing capacity of the specimens. This is attributed to a slight increase in internal energy dissipation associated with the presence of these multiple cracks.

Response probability density function for multi-cracked beams with uncertain amplitude and position of cracks

This paper addresses the determination of the response of beams under static loads, in presence of multiple cracks. The crack is modeled as a rotational internal spring. Both the amplitude and position of the spring are taken as uncertain variables. In particular, its random position characteristic has been modeled as Poisson law distribution along the axial coordinate. By using the theory of generalized functions, the probability transformation method (PTM) has been easily applied to the beam equilibrium equations. The PTM, employing the space transformation laws of random vectors, allows determining the probability density function (PDF) of the system response directly and easily. The results of some numerical applications have confirmed the goodness of the proposed stochastic procedure.

Crack identification in beam-type structural elements using a piezoelectric sensor

ABSTRACT A crack or any kind of damage induces a sharp discontinuity in the rotational displacement curve in a structure under load. However, if the beam is not loaded sufficiently or crack depth is very small, the discontinuity may not be possible to identify through conventional methods. This study proposes a non-destructive approach to reveal the presence of a crack in structural components based on the measurement of very small discontinuity in rotational displacement by employing a piezoelectric sensor (PZT). An analytical model of a statically loaded cracked beam with PZT attached to the beam is developed for various boundary conditions. The solution is obtained through Ritz approximation. Rotational displacements at different points along the length of the beam are determined. Subsequently, a finite element analysis on ABAQUS platform is carried out for comparison. The results obtained from these analyses are validated with the experimental data published in open literature. Two distinct techniques are employed to monitor the damage in slender and short length beams. the efficacy of the technique in the detection of small cracks in structure is established. It is also shown that the presence of multiple cracks in beams having various boundary conditions can be monitored by a single non-destructive investigation following the method.

Stress Intensity Factor of Inclined Internal Edge Crack in Cylindrical Pressure Vessel

In this work, the stress intensity factor of inclined edge cracks introduced on the inner surface of a cylindrical pressure vessel is analyzed through numerical simulation. The fracture analysis was performed using a two-dimensional axisymmetric finite element model. The results reveal that, as the crack inclination increases beyond 30o, mode II loading becomes dominant. As the crack length increases, mode II loading acts in a profound manner in the component. In addition, the stress intensity factor of inclined crack was examined in the presence of multiple cracks. It was found that after a certain spacing between the inclined and neighboring crack, the ratio of mode I to mode II remains constant due to the non-interaction of stress fields around the crack.

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

Interval static analysis of multi-cracked beams with uncertain size and position of cracks

• Interval static analysis on cracked beams with uncertain size/position of cracks. • Uncertainty in size/position of cracks is handled by proper generalized functions. • Monotonicity of response is tested with respect to all uncertain parameters. • Bounds of monotonic response are obtained by sensitivity-based method. • Bounds of non-monotonic response are computed by global optimization technique. This paper deals with beams under static loads, in presence of multiple cracks with uncertain parameters. The crack is modelled as a linearly-elastic rotational spring and, following a non-probabilistic approach, both stiffness and position of the spring are taken as uncertain-but-bounded parameters. A novel approach is proposed to compute the bounds of the response. The key idea is a preliminary monotonicity test, which evaluates sensitivity functions of the beam response with respect to the separate variation of every uncertain parameter within the pertinent interval. Next, two alternative procedures calculate lower and upper bounds of the response. If the response is monotonic with respect to all the uncertain parameters, the bounds are calculated by a straightforward sensitivity-based method making use of the sensitivity functions built in the monotonicity test. In contrast, if the response is not monotonic with respect to even one parameter only, the bounds are evaluated via a global optimization technique. The presented approach applies for every response function and the implementation takes advantage of closed analytical forms for all response variables and related sensitivity functions. Numerical results prove efficiency and robustness of the approach, which provides very accurate bounds even for large uncertainties, avoiding the computational effort required by the vertex method and Monte Carlo simulation.

The crack propagation path for a system of surface and subsurface cracks and their interactions due to rolling contact fatigue

In this paper, the rolling contact fatigue crack growth in the presence of multiple cracks and their interactions is studied. The proposed formulation is based on linear elastic fracture mechanics and singular integral equations. The body under the rolling contact is modeled by a half-plane weakened by a set of surface, subsurface and surface–subsurface cracks. Rolling contact is simulated by translational motion of an elliptically distributed force along the half-plane boundary. Several parameters, such as the distance between cracks, the value of initial crack lengths, the value of the friction coefficient, and the initial angle between cracks and the boundary of the half-plane are studied. Results obtained from this investigation are in good agreement in a special case with those reported in the literature. It is observed that in the system of two parallel surface and subsurface cracks with equal lengths, changing the distance between the cracks changes the growth paths, and when this distance increases to a critical value, the cracks grow independently. In addition, in the case of two parallel surface cracks when the left crack is shorter, the cracks have a stronger tendency to join together, which leads to pitting phenomena on the contact surface. Furthermore, in the system of two parallel subsurface cracks, it is seen that fast fracture occurs sooner when the initial angle of the cracks increases. In the system of parallel surface and subsurface cracks, the dominant failure mode is spalling.

Interpreting the single fiber fragmentation test with numerical simulations

Characterization of the mechanical properties of the fiber/matrix interface is a challenge that needs to be addressed to enable accurate micromechanical modeling of failure in composite materials. In this paper a numerical investigation is presented into one of the tests that has been proposed for measuring these interfacial properties. A new cohesive zone model with friction is presented, as well as an original numerical framework for modeling of embedded fibers. The research generates new insight into the meaning of the single fiber fragmentation test, confirming the applicability of shear lag theory also in presence of multiple cracks, and emphasizing the relevance of matrix plasticity for the development of friction in the test. Although the frictional stress that can be obtained from the test should not be confused with the cohesive strength of the fiber/matrix interface, measurements of fracture process zone length can give indirect information on this cohesive strength.

Evaluation of the multiple embedded cracks interaction effect in creep regime by creep damage method

The crack growth behavior and creep interaction of two coplanar dissimilar embedded cracks subjected to remote tensile load were investigated. The influence of dissimilar crack size, crack configurations on crack growth behavior in the presence of multiple cracks were studied through the variation of crack growth rate, which was achieved using creep damage method. For cases of multiple cracks, crack initiation position depended on crack distance, crack aspect ratio and relative crack length. Moreover, as the difference of crack length between two cracks was large, the interaction intensity was small and had slight effect on crack growth behavior. Furthermore, the creep interaction factor was recommended to be employed as the criterion for evaluating the multiple cracks interaction. According to the magnified ratio of crack growth rates, the critical value of γcreep for combination of multiple embedded cracks was assumed to be 1.10. Finally, a new combination rule for multiple embedded cracks was proposed.

Crack interaction study in piezoelectric materials under thermo-electro-mechanical loading environment

Multiple voids and cracks were generated during material processing techniques, which interact with each other and affects the service performance of piezoelectric components. This work aims to study the behavior of piezoelectric components in presence of multiple cracks under thermo-electro-mechanical loading environment. Extended finite element method has been implemented to model geometrical discontinuities with crack interaction phenomenon. In this work, thermo-electro- mechanical problem has been decoupled into thermal and electro-elastic problems. Temperature distribution has been obtained by solving heat conduction equation and then used as an input to the electro-elastic problem. In post processing phase, interaction integral method and generalized Stroh formalism were used to predict the stress intensity factors. The methodology has been implemented with in-house developed MATLAB code. Set of cases for crack interaction studies were presented using the proposed approach.

On the use of a roving body with rotary inertia to locate cracks in beams

Identifying cracks and damages in structures using measured vibrational characteristics has received considerable attention in the past few decades. The possibility of using frequency changes due to the application of a mass appended to the structure has also been considered. In this paper an analytical proof to show that the natural frequencies of a cracked beam with a roving body possessing mass and rotary inertia will generally change abruptly as the body passes over a crack, provided that the crack permits differential flexural rotations, is presented. A novel explicit closed form solution of the governing equation of an Euler-Bernoulli beam with a roving body possessing mass and rotary inertia, in the presence of multiple cracks is also proposed. The presented exact solution is used to conduct a parametric analysis of cracked beams. Numerical results for natural frequencies are provided and a procedure to exploit the occurrence of frequency shifts to detect and locate each crack, without having to perform any additional calculation, is described.

Characterization of the creep interaction effect for twin semi-elliptical surface cracks under combined tension and bending loading

The interaction of twin semi-elliptical surface cracks subjected to combined tension and bending in the creep regime is studied. Moreover, the crack growth behavior in the presence of multiple cracks is simulated to reveal the effect of creep interaction factor. The tension load produces a larger creep interaction factor than those for pure bending and combined tension and bending. For the combination of cracks, a greater value of the creep interaction factor is permitted compared with the linear-elastic condition. The enhancement of creep crack growth rate in multiple cracks is diminished as the improvement of creep interaction factor is lower than 30%.

Model‐Based Analysis of Spur Gears’ Dynamic Behavior in the Presence of Multiple Cracks

Early detection of tooth cracks is crucial for effective condition‐based monitoring and decision making. The scope of this work was to bring more insight into the vibration behavior of spur gears in the presence of single and multiple simultaneous tooth cracks. The investigation was conducted in both time and frequency domains. A finite element analysis was performed to determine the variation in stiffness with respect to the angular position for different combinations of crack lengths. A simplified nonlinear lumped parameter model of a one‐stage gearbox with six degrees of freedom was then developed to simulate the vibration response of faulty external spur gears. Four different multiple‐crack scenarios were proposed and studied. The performances of various statistical fault detection indicators were considered and investigated. The simulation results obtained via MATLAB indicated that, as the severity of a single crack increases, the values of the time domain statistical indicators increase also, but at different rates. Moreover, the number of cracks was found to have a negative effect on the values of all the performance indicators, except for the RMS. The number and amplitude of the sidebands in the frequency spectrum were also considered, while assessing the severity of the faults in each scenario. It was observed that, in the case of consecutive tooth cracks, the number of spectrum peaks and the number of cracks were consistent in the frequency range of 4‐5 kHz. The main finding of this study was that the peak spectral amplitude was the most sensitive indicator of the number and severity of cracks.

Numerical modelling on degradation of mechanical behaviour for engineered cementitious composites under fatigue tensile loading

A multiscale modelling framework is developed in this paper for analysing the degradation of mechanical behaviour of Engineered Cementitious Composites (ECCs) under fatigue tensile loading. Degradation models for calibrating fatigue-induced deterioration of the fibre-matrix interface and fibre fatigue rupture are proposed at the microscale. Based on these, the cycle-dependent crack bridging relation is derived at the mesoscale. At the macroscale, the degradation behaviour of the bridging stress in ECC with presence of multiple cracks is modelled using extended finite element method. This multiscale characterisation method is validated by comparing the computed degradation relation of the bridging stress to that obtained from the experiment. Good agreement is obtained, which demonstrates the effectiveness of the developed multiscale modelling framework for the analysis of fatigue behaviour of ECCs. In addition, the deterioration of the fibre-matrix interface is found to be responsible for a steady decreasing bridging stress, while the fibre fatigue rupture is found to contribute to an accelerated loss of bridging stress.

Crack localization in beams by frequency shifts due to roving mass with rotary inertia

The problem of crack localization has been tackled in the past by detecting frequency changes due to the application of a mass appended to the structure. However the effect of the rotary inertia of the mass on the natural frequencies of a cracked beam has not been deeply investigated. In this paper a novel explicit closed form solution of the governing equation of a beam with a concentrated mass, with rotary inertia, in the presence of multiple cracks is proposed. Furthermore, an analytical proof to show that the natural frequencies of a cracked beam with a roving body with a rotary inertia will generally change abruptly as the body passes over a crack, provided that the crack permits differential flexural rotations, is presented. Numerical results in terms of natural frequencies are provided and the procedure to exploit the occurrence of frequency shifts to detect and locate each crack is described.

The influence of multiple cracks on tensile and compressive buckling of shear deformable beams

In this work the static stability of the uniform Timoshenko column in presence of multiple cracks, subjected to tensile or compressive loads, is analyzed. The governing differential equations are formulated by modeling the cracks as concentrated reductions of the flexural stiffness, accomplished by the use of Dirac’s delta distributions. The adopted model has allowed the derivation of the exact buckling modes and the corresponding buckling load equations of the Timoshenko multi-cracked column, as a function of four integration constant only, which are derived simply by enforcing the end boundary conditions, irrespective of the number of concentrated damage. Since shear deformability has been taken into account, the buckling load equation allows capturing both compressive and tensile buckling. The latter phenomenon has been recently investigated with reference to rubber bearing isolators, modeled as short beams, but it has been shown to occur also in slender beams characterized by high distributed shear deformation, like composite and layered beams. The influence of multiple concentrated cracks on the stability of shear deformable beams, particularly under the action of tensile loads, has never been assessed in the literature and is here addressed on the basis of an extensive parametric analysis. All the reported results have been compared with the Euler multi-cracked column in order to highlight its limits of applicability.