Double Edge Cracks Research Articles

Mixed-mode fracture analysis of CORC cables with double-edge cracks under tension and torsion

The Conductor on round core (CORC) refers to a circular cable that is helically wound with rare-earth-barium-copper-oxide ((RE)BCO) high-temperature superconducting (HTS) tapes. This type of cable finds extensive applications in large superconducting magnets. However, the mechanical–electrical performance of CORC cables is hindered by microscopic edge cracks that occur during the mechanical slitting process of HTS tapes. In this paper, the mixed-mode stress intensity factor (SIF) of cracks in CORC cables under different loading conditions is investigated using the extended finite element method (XFEM). The design variables of CORC cables are optimized by considering the effect of various factors such as the crack parameter, the winding angle, the core radius, and the Poisson’s ratio of the winding core on the SIF. The results indicate that the impact of each factor on the mixed-mode SIF varies depending on the loading mode. Notably, the influence of the winding angle on the SIF is particularly significant and intricate. In the case of tensile loading, a smaller winding angle proves advantageous in impeding crack propagation. Conversely, the most dangerous winding angle for torsional loads is 45°. The divergence of these effects can be indirectly indicated by theoretical solutions regarding the tape strain along the helix direction. For the cases examined, the results have shown that the crack propagation path is independent of these factors, and the direction of propagation is perpendicular to the edge of the tape.

Facilitation effect of multiple crack interaction on fatigue life reduction and a quantitative evaluation of interactions factor of two parallel Non-coplanar cracks

Synergistic/interaction action of the multiple cracks can be clearly observed from fracture topography of the post-fatigue test specimen. Based on experimental observations, the interactions of two parallel non-coplanar cracks mounted in double-edge crack specimens under tension loading are investigated. The stress intensity factor (SIF) for a wide range of crack configurations is established using three-dimensional finite element analysis (FEA), and the effects of multiple crack interactions on the SIF values are studied. The effects of crack interactions on the SIF are strongly dependent on the crack geometry. The greater the vertical distance between the two cracks, the more strongly the stress field at the tip of the main crack is impacted. The analytical solutions for calculating SIF under effect of the multiple crack interactions were derived in a matrix form and the accuracy of the estimated equation was confirmed.

Heat Conduction and Cracking of Functionally Graded Materials Using an FDEM-Based Thermo-Mechanical Coupling Model

In this paper, the steady-state and transient heat transfer processes of functionally graded materials (FGMs) are analyzed using a coupled thermo-mechanical model in a GPU parallel multiphysics finite–discrete element software, namely MultiFracS. First, the coupled model to handle the heat transfer problem of heterogeneous materials is verified. Then, the advantages and disadvantages of FGMs and composite materials in response to thermal shock loads are compared and the results indicate that FGMs can overcome extreme environments better than composite materials. Finally, the influence of the geometric distribution characteristics of the double-edge cracks in the gradient material plate on the crack propagation is analyzed. The simulation results show that the interaction between the cracks affects the crack propagation path under the thermal load. The inclination angle and spacing of double-edge cracks greatly influence crack propagation. Specifically, a larger inclination angle and spacing can lead to a smaller crack propagation angle. The approach in this paper provides a new quantitative tool for investigating the thermal, elastic, and cracking of functionally graded materials.

The shear behaviors of concrete-gypsum specimens containing double edge cracks under four-point loading conditions

In this investigation, the fracture behavior of concrete-gypsum samples consisting of edge joints (planer and echelon joints) under four-point bending tests has been investigated using numerical simulation and experimental testing. For this purpose, concrete and gypsum rectangular samples with a dimension of 30 cm * 15 cm * 5 cm have been prepared. These slabs have edge notches in their volume. The lengths of these notches vary by 2 cm in increments of 2 cm, from 2 cm to 6 cm. The slabs were attached with glue. This complex was tested and simulated numerically under four-point loading conditions. The results indicate that the crack growth trajectory is affected by the type of slab material. The strength of samples is controlled by notch length. Numerical simulation outputs are in good accordance with experimental test results.

Mode I stress intensity factor with various crack types

Presence of cracks in mechanical components needs much attention, where the stress field is affected by cracks and the propagation of cracks may be occurred causing the damage. The objective of this paper is to present an investigation of crack type effect on crack severity in a finite plate. Three cases of cracked plate with three different types of cracks are assumed in this work, i.e., single edge crack, center crack and double edge crack. 2D numerical models of cases of cracked plate are established in finite element analysis (FEA), ANSYS software by adopting PLANE 183 element. Values of FEA mode I stress intensity factor SIF and Von-Mises stress at crack apex are determined for cases of cracked plate under tensile stress with different values. To identify the crack severity, the comparison of FEA results for different cracked cases is made. The comparison showed that, single edge cracked plate (SECP) has the maximum values of mode I SIF and Von-Mises stress at crack apex, i.e. the greatest crack severity is considered. Also, values of FEA Von-Mises stress at crack apex for center cracked plate (CCP) are moderate and for double edge cracked plate (DECP) are the minimum. Besides, in case of high crack lengths, it is found that, FEA results of mode I SIF in case of (CCP) are higher than those of in case of (DECP). Consequently, crack severity is considered as moderate in case of (CCP) and the minimum in case of (DECP). Empirical formulas are used to approximately estimate mode I SIF for all the case studies of cracked plate in this study and the results are compared to those of FEA. A good agreement between analytical and FEA results has been showed by this comparison.

XFEM Simulation of Tensile and Fracture Behavior of Ultrafine-Grained Al 6061 Alloy

In the present work, the tensile and fracture behavior of ultra-fine grained (UFG) Al 6061 alloy was simulated using extended finite element method (XFEM). UFG Al 6061 alloy processed by cryorolling (CR) and accumulative roll bonding (ARB) was investigated in this work. Numerical simulations of two-dimensional and three-dimensional models were performed in “Abaqus 6.14” software using an elastic-plastic approach, and the results obtained were validated with the experimental results. The specimens corresponding to the three-point bend test, compact tension test with center crack, and double edge cracks were analyzed using XFEM (eXtended Finite Element Method) approach. In XFEM, the partition of unity (PU) was used to model a crack in the standard finite element mesh. The tensile and fracture properties obtained from the simulation were in tandem with the experimental data. UFG Al alloy showed higher tensile strength and fracture toughness compared to their bulk solution treated counterparts. Fracture toughness was measured in terms of stress intensity factor and J integral. In CR Al alloys, with increasing thickness reduction, an increase in stress intensity factor and a decrease in the J integral was observed. This behavior is attributed to the increase in strength and decrease in ductility of CR samples with increasing thickness reduction. In ARB Al alloys, the strength and ductility have increased with an increase in number of cycles. It also revealed an increase in both the stress intensity factor and J integral in ARB processed Al alloys with increase in number of cycles, as evident from XFEM simulation results.

Determination of vibration analysis in single and double cracked cantilever numerical beam

Constructions are debilitated by crack. At the point when the Crack size builds, the construction turns out to be exceptionally failed; at last the design may Crackdown because of moment Crack. Thusly, Crack recognition is vital. The target of this investigation is free vibration examination of cracked cantilever beam utilizing FEM. This research has focused on both the cases namely single edge crack as well as double edge crack and the frequency characteristics are determined for various mode of crack location and the crack depth by ANSYS software.

Numerical Evaluation of Aluminium 6026-T9 Fracture Toughness

Fracture is the separation of an object into two or more pieces caused by crack growth under the action of applied stress. There are many different methods for fracture evaluation has been made but still lacks information on properties of Aluminium 6026-T9. Aluminium 6026 is non-toxic since it does not contain Tin (Sn) and features a great corrosion resistance. This study focuses on the mechanical properties and fracture toughness of Aluminium 6026-T9. The material is cut and shaped into dog-bone specimens by referring the ASTM E8 and was eventually undergoing a tensile test to evaluate the mechanical properties. A linear elastic analysis of three different crack characteristics which are single edge crack, double edge crack and center crack were performed in Mode I analysis to evaluate its fracture toughness. The stress intensity factor (SIF) value near the crack tip obtained from the simulation process were then compared with analytical value and had been discussed. The percentage of error found that the numerical and analytical values are closed to each other.

Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method

Stress intensity factor (SIF) is one of three important parameters in classical linear elastic fracture mechanics (LEFM). The evaluation of SIFs is of great significance in the field of engineering structural and material damage assessment, such as aerospace engineering and automobile industry, etc. In this paper, the SIFs of a central straight crack plate, a slanted single-edge cracked plate under end shearing, the offset double-edge cracks rectangular plate, a branched crack in an infinite plate and a crucifix crack in a square plate under bi-axial tension are extracted by using the p-version finite element method (P-FEM) and contour integral method (CIM). The above single- and multiple-crack problems were investigated, numerical results were compared and analyzed with results using other numerical methods in the literature such as the numerical manifold method (NMM), improved approach using the finite element method, particular weight function method and exponential matrix method (EMM). The effectiveness and accuracy of the present method are verified.

A study of the double edge cracks and a central crack in an orthotropic strip under the tensile loads

In this article, An elastostatic problem with two symmetrically located edge cracks and a centre crack in an orthotropic elastic material under normal loadings is considered. Two harmonic functions are considered which are expressed in terms of displacement of stress and component of axes. The problem is reduced into a pair of simultaneous singular integral equations of the first kind with Cauchy-type singularities, which are solved using Chebyshev polynomials. The normalized stress intensity factors are found against ratios of cracks’ length are computed for different particular cases for the orthotropic material Steel-Mylar and the results are depicted through graphs.

On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics

ABSTRACTWe investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.

Analysis of multi-crack problems by the spline fictitious boundary element method based on Erdogan fundamental solutions

The Erdogan fundamental solutions are derived from an infinite plane containing a crack. When they are used in the formulation of the boundary element method (BEM), the stress boundary conditions on the crack surface are automatically satisfied and the singular behavior at the crack tip can be naturally reflected. Using the multi-domain technique, the multi-crack problem can be transformed into a series of single-crack problems involving displacement continuity conditions along common boundaries. In this paper, the displacements which are expressed in terms of the integral of a complex function in the Erdogan fundamental solutions are derived in closed-form expressions. Then, the multi-domain spline fictitious boundary element method (SFBEM) based on the above fundamental solutions is proposed and formulated for analyzing multi-crack problems. The computational accuracy and stability of the proposed method are verified by comparing the stress intensity factor (SIF) results of a double-inner crack problem with different inclined angles and crack lengths against those calculated by the finite element method. Also, the SIF results of a double-edge crack problem with different crack lengths are compared with those obtained from studies. Finally, the proposed method is applied to the analysis of the triple-crack problem, in which the shielding effects of multi-crack and stress contours are studied with different crack lengths and locations.

Effects of Crack Faults on the Dynamics of Piezoelectric Cantilever-Based MEMS Sensor

The presence of cracks on the surface of MEMS microelectromechanical system (MEMS) devices affects their functional parameter, such as resonance frequency. Overtime, these cracks may cause the devices’ failure. Therefore, it is important to identify the symptoms of the cracks presence so that the affected devices can be removed/bin-out before delivering to the customers thus avoiding failure during applications of these devices. In this paper, we present a predictive and quantitative fault modeling approach using the linear time invariant (LTI) technique for a piezoelectric cantilever-based sensor. The analytical fault model is developed by correlating single edge, double edge, and surface cracks with the resonance frequency of the cantilever. The Simulink is utilized to design the LTI-based faulty device by integrating the dynamic equations associated to actuation and sensing mechanisms of the device under study. The model is validated by comparing it with the finite element method model containing the same design parameters, using the COMSOL Multiphysics. We observed that the presence of cracks at any location on the surface of the device stimulates the amplitude that causes decrease in its resonance frequency. The increase in the amplitude of vibration due to the presence of cracks is electrically sensed by the piezoresistive mechanism. Finally, the fault detection methodology is presented by using the Stateflow technique. We found that the proposed techniques can be significant to study the faulty behavior of the MEMS devices.

Effect of thermomechanical loading on fracture properties of brittle materials: A fully-coupled transient thermoelastic analysis using a lattice approach

The influence of simultaneous thermomechanical loadings on the fracture behavior of linear thermoelastic brittle materials with a propagating crack and transient temperature diffusion is investigated. A planar two-way coupled thermoelastic lattice with a brittle erosion algorithm, implemented in MATLAB, is used in the context of LEFM to study two well-known classic fracture problems in Mode I, i.e., center and double-edge crack configurations, under thermal, mechanical, and thermomechanical loadings for a brittle crystalline Silicon, as an example material. The approach can also be applied to other brittle materials like brick or concrete. Validated by the well-developed analytical solutions for these configurations under separate thermal and mechanical loads, the numerical lattice analyzes the crack tip’s energy release rates and stress intensity factors based on the change of the global stiffness matrix of mesh before and after crack growth with no need for strain/stress calculations. Under the thermomechanical loading scenario, the response of the configurations in terms of the load-displacement and fracture toughness-crack length curves are then analyzed with respect to different loading rates and temperature gradients at crack surface and ambient environment. Having more pronounced effects on the toughness curves than the loading rate does, higher temperature difference results in lower values for the toughness curves. These curves also exhibit a rising jump for very short crack lengths and then approach to constant uniform values as a typical behavior for brittle materials. Considering the average trend of the toughness curves, it is observed that the thermomechanical fracture growth is highly unstable for very short cracks and it approaches a more stable condition as the crack length grows. Having a simple constitutive formulation and failure criterion, the proposed lattice approach is a convenient tool to obtain fracture properties of brittle materials under thermomechanical loading.

On the accuracy of higher order displacement discontinuity method (HODDM) in the solution of linear elastic fracture mechanics problems

The higher order displacement discontinuity method (HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics (LEFM) problems. The paper has selected several example problems from the fracture mechanics literature (with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode I and Mode II SIFs for these problems using HODDM are in excellent agreement with analytical results (reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort (with less than 400 nodes) than the XFEM and the modified XFEM (which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.

Experimental and Numerical Study of Shear Fracture in Brittle Materials with Interference of Initial Double Cracks

A simultaneous experimental and numerical study of shear fracture of concrete-like materials is carried out using Brazilian disc specimens with initial double edge cracks and fourpoint bending beam specimens with double edge-notches. The interference effects of two cracks/notches are investigated through varied ligament angles and crack lengths. It is shown that shear fracturing paths change remarkably with the initial ligament angles and crack lengths. The cracked specimens are numerically simulated by an indirect boundary element method. A comparison between the numerical results and the experimental ones shows good agreement.

Stress intensity factors of double edge cracks in large groove plates under mode I tension

The solutions of stress intensity factors (SIFs) of double edge cracks in large groove plates are investigated. The plate is assumed to fulfil the plain strain condition and it is axially stressed. According to the literature, the SIFs of the cracks in circular notches are available. However, the roles of cracks in large groove are difficult to obtain. Therefore, different grooves and crack geometries are modelled numerically using the ANSYS finite element software. The present model is first validated using an existing model of double edge cracks without notches and it is found that both models are in close agreement. The large grooves are then introduced and the cracks are positioned in the mid-point. It is found numerically that the SIFs are strongly affected by the relative crack depth and the groove geometries. It is also found that the large groove is capable of reducing the SIFs in comparison with the circular notched due to lower stress concentration factors.

Modeling Cracks in Nonlinear Viscoelastic Media Subjected to Thermal Loading

The study is concerned with the simulation of cracks in finitely deforming viscoelastic media. The main goal is to establish a computational methodology for crack propagation analyses in bulk material and interface debonding using an extended finite element method and cohesive zone modeling. First, a linear elastic plate with a single-edge crack and a linear viscoelastic plate with a double-edge crack are selected as benchmark problems. Upon verification of the extended finite element method and cohesive zone modeling results against those from the conventional crack propagation method and those from the literature, a nonlinear viscoelastic solid rocket motor subjected to various thermal loadings is analyzed for failure due to bore cracking or interface debonding. For a cooldown the stress distribution along the bond line is determined for the bore cracking mode and results are compared with those from the literature. For the cyclic temperature, the propagation of bore cracks is analyzed using an extended finite element method, and the propagation of initial debonding is studied using cohesive zone modeling. For both failure modes, crack propagation occurs only during the first cooldown. The relation between the crack growth and the initial crack size show parabolic behavior. Overall, it is concluded that the extended finite element method and cohesive zone modeling are suitable methods for crack propagation analysis in nonlinear viscoelastic media.

STRESS INTENSITY FACTOR FOR DOUBLE EDGE CRACKED FINITE PLATE SUBJECTED TO TENSILE STRESS

A finite rectangular plate with double edge crack under uniaxial tension depends on the assumptions of Linear Elastic Fracture Mechanics LEFM and plane strain problem are studied in the present paper. The effect of crack position, crack oblique and the kinked crack orientation are investigated to predict if a crack starts to grow. These problems are solved by calculating the Stress Intensity Factor SIF for mode I (KI) and II (KII) near the crack tip theoretically using mathematical equations and numerically using finite element software ANSYS R15.A good agreement is observed between the theoretical and numerical solutions. The results show that the KI increases with increasing the relative crack length and tensile stress and these values are increased when the crack position draws near the plate edge while in case of parallel cracks the mutual shielding effect reduces KI in each crack.In mixed mode, it is shown that the maximum values of KI and KII occur at crack angle β=0o and 45o, respectively and the orientation of the kinked crack have significant effects on the KI and KII.

Fracture toughness of woven glass and carbon reinforced hybrid and non‐hybrid composite plates

The fracture toughness and strength of materials are adversely affected by the cracks in the materials, which can be induced during manufacturing, assembly, and usage. In this study, the effect of crack length and crack location on the fracture toughness of woven glass and carbon reinforced hybrid and non‐hybrid composite plates were investigated experimentally and numerically. For this purpose, glass/epoxy (G8), and carbon/epoxy (C8) non‐hybrid composite plates and glass‐carbon/epoxy (G2C4G2), and carbon‐glass/epoxy (C2G4C2) hybrid composite plates were produced by using hand lay‐up method. The fracture toughness of hybrid and non‐hybrid composite plates having three different crack locations as single edge crack (SEC), center crack (CC), and double edge crack (DEC) with different crack lengths were obtained by determining failure loads under tensile loading. The ANSYS finite element package program was used in order to determine the fracture toughness of hybrid and non‐hybrid composites by means of J‐Integral methods. The results showed that the highest and the lowest fracture toughness values were obtained in the specimens with SEC and CC, respectively. POLYM. COMPOS., 39:783–793, 2018. © 2016 Society of Plastics Engineers