Mode Stress Intensity Factors Research Articles

Fatigue crack behaviors under asynchronous biaxial loading

Crack behavior of aluminum alloy 2A12-T4 is investigated experimentally and numerically using cruciform specimens subjected to in-plane biaxial loadings applied in horizontal (x axis) and vertical (y axis) directions. Different cruciform configuration plans, with variant sizes of slots in loading arms and different transitional fillet radius between adjacent arms, are analyzed by means of FEM to confirm a final specimen geometry with relative uniform stress distribution in its central area. The tests for fatigue crack growth behavior under cyclic biaxial sinusoidal loadings with phase differences of 0° or −60° between two orthogonal fatigue loads are conducted by using a biaxial fatigue test system. The biaxial load ratio, Pmaxx/Pmaxy, varies from −0.5 to 1.0. Initial central cracks are inclining in angles of 0°, 45° and 60° to x-axis. Crack growth path and lives are obtained. It is observed that the crack growth behavior under biaxial loading differs from that with only uniaxial loading. A widely accepted fatigue crack growth model, which combines Paris equation, maximum tangential stress (MTS) criterion and an equivalent stress intensity factor (SIF) proposed by Tanaka, is used for mixed mode-I/II crack subjected biaxial loading. The combined model is evaluated by the SIFs analysis based on analytical and numerical solution. The mixed mode SIFs are calculated based on finite element analysis with mesh updating. The simulated crack growth path and growth lives correlate well with the experiments in most cases. Both the experiments and the simulations demonstrate that the tensile load parallel to crack path behaves as the retarder to the crack growth, and the compressive load parallel to crack path behaves as the promoter to the crack growth. It is found that equivalent SIF used in the model overestimates the effect of mode II SIF on the fatigue crack growth rate by Paris equation. It is questionable to use the combined model for the cases with asynchronous biaxial loadings or those leading to crack surface contact.

Polyurethane foam behavior in mixed mode bending

Mixed mode four-point bending testing is performed on polyurethane foams. This paper presents only the results on the stress intensity factors (SIFs) obtained experimentally for a density of 325 kg/m3 , although tests were done for three foam densities. An asymmetric four-point bending setup was used for determining the critical SIFs in Mode I and Mode II, and discussions on the influence of the initial crack length on the SIF values are done. As initial crack length is increased the theoretical predictions give a better comparison to experimentally obtained results. Mode II testing is also performed on a polyurethane foam as a particular case of mixed-mode four-point testing. Crack initiation and propagation in Mode II depends on the geometrical parameters of the testing configuration. Numerical XFEM simulations are done in order to clarify the situations in which the crack doesn't propagate, and failure is produced in the region of supports. A combined experimental-XFEM analysis is recommended to fully understand the particularities of the behavior of cellular materials.

The effects of some parameters on perforation tip initiation pressures in hydraulic fracturing

Perforations play an important role in hydraulic fracturing as channels of fracturing fluid penetrating into reservoirs. The perforation geometry and the geo-stresses of reservoirs could affect the initiation pressures (i.e. the critical hydraulic pressure as perforation tips start to initiate), and the fracture initiation direction which could affect the fracturing fluid flowing into reservoirs. In this paper, two collinear perforations emanating from a wellbore were considered, and by using conformal mapping techniques, the stress intensity factors (SIFs) of mode I and mode II at the perforation tips were obtained. According to the maximum tangential stress criterion, i.e. MTS criterion, the analytical solutions of the initiation pressures and the initiation angles at perforation tips were obtained. The theoretical results were compared with the previous test results by using cubic concrete models and the previous in-situ measuring results. The prediction results of initiation pressures generally agreed with the test results and the in-situ results. Finally, the effects of perforation lengths, perforation angles with the major principal stress and the principal stress difference on hydraulic fracturing were analyzed. The results showed that the optimal perforation angles should lie in the range from 0° to 30°, and the optimal perforation length should 2 or 3 times the wellbore diameter.

Three-dimensional mixed-mode stress intensity factors for deflected internal surface cracks in thin and midsize-thick-walled spherical pressure vessels

In this paper, three-dimensional mixed-mode stress intensity factor solutions are obtained for deflected inner surface cracks contained in thin- and midsize-thick-walled spherical pressure vessels. In an effort to build a library of stress intensity factor solutions for different realistic cases, main parameters affecting the problem, which are crack deflection angle, normalized crack depth and crack shape aspect ratio, are changed systematically to cover all combinations. The results show that as the deflection angle increases, mode-I stress intensity factors decrease and mode-II and mode-III stress intensity factors increase for a given case. It is also observed that as the normalized crack depth increases, stress intensity factors increase along the crack front. The results show that magnitudes of the normalized mixed mode stress intensity factors for midsize-thick-walled vessels are higher than those of thin-walled spherical vessels. Crack deflection angle is shown to have the highest influencing effect among all parameters. It is also observed that especially for higher crack deflection angles, which have higher mode-mixity, crack surfaces may come into contact partially or fully.

Investigation of crack resistance in epoxy/boron nitride nanotube nanocomposites based on multi-scale method

Boron nitride nanotubes (BNNTs) possess superior mechanical, thermal and electrical pro- perties and are also suitable for biocomposites. These properties make them a favorable reinforcement for nanocomposites. Since experimental studies on nanocomposites are time- consuming, costly, and require accurate implementation, finite element analysis is used for nanocomposite modeling. In this work, a representative volume element (RVE) of epo- xy/BNNT nanocomposites based on multi-scale modeling is considered. The bonds of BNNT are modeled by 3D beam elements. Also non-linear spring elements are employed to simu- late the van der Waals bonds between the nanotube and matrix based on the Lennard- -Jones potential. Young’s and shear modulus of BNNTs are in ranges of 1.039-1.041TPa and 0.44-0.52TPa, respectively. Three fracture modes (opening, shearing, and tearing) have been simulated and stress intensity factors have been determined for a pure matrix and nanocom- posite by J integral. Numerical results indicate that by incorporation of BNNT in the epoxy matrix, stress intensity factors of three modes decrease. Also, by increasing the chirality of BNNT, crack resistance of shearing and tearing modes are enhanced, and stress inten- sity factor of opening mode reduced. BNNTs bridge the crack surface and prevent crack propagation.

Investigation of the effect of load distribution along the face width and load sharing between the pairs in contact on the fracture parameters of the spur gear tooth with root crack

Abstract The magnitude and location of stress intensity factor (SIF) in mode I (KI), mode II (KII), mode III (KIII) relies mainly on the geometry and location of the crack tip, variation in magnitude of load due to multiple pair contact along the active profile and the distribution of the load along the face width of a spur gear drive. Mostly, in literature the calculation of SIF in gear were carried out either by using a two dimensional (2D) Finite element model (FEM) with point load for unit width or a three dimensional (3D) FEM with uniform / parabolic load distribution along the face width without considering load sharing effect between the multiple pairs in contact. In the present study, an attempt has been made to explore the significance of the load distribution along the face width and the load sharing between the pairs when the contact moves from the highest point of tooth contact (HPTC) to the lowest point of tooth contact (LPTC) on the SIF calculation. A comparative study has been made by using a validated 3D single tooth spur gear FEM with four different load cases such as case 1: Uniform load distribution along face width without considering load sharing between the pairs, case 2: Uniform load distribution along face width by including the effect of load sharing between the pairs, case 3: Actual load distribution along the face width without considering load sharing between the pairs, case 4: Actual load distribution along the face width by including the effect of load sharing between the pairs. The stiffness based approach was used to calculate the load distribution ratio (LDR) of a contact point along the contact line and the load sharing ratio (LSR) between the pairs in contact. The detailed analysis showed that case 1, case 2 and case 3 load cases overestimate the SIFs comparing to the case 4. The first three load cases overestimate the KI by 39%, 2.5%, and 45% and KII by 390%, 36%, and 129% and KIII by 282%, 47%, and 132% respectively when compared to load case 4. The results of this study provide valuable guidelines for the crack propagation as well as life prediction calculations for spur gear drives.

Термопружна поведінка біматеріалу з міжфазною щілиною, заповненою нестисливою рідиною

Thermo-stressed state of the bimaterial with the interfacial crack filled with an incompressible fluid is investigated. The bimaterial with zero Dundurs parameter is considered. The thermo-elastic problem is reduced to nonlinear systems of singular integro-differential equations for a temperature jump between the cracks faces and an opening crack. The pressure of the fluid is determined from the equation of the incompressible fluid. Using the method of successive approximations a numerical solution of the problem is constructed. The opening crack and temperature jump are determined by the finite sum for Chebyshev polynomials of the second kind. The coefficients for Chebyshev polynomials are determined from the system of linear algebraic equations. Having made numerical calculations, the dependences of the pressure of the fluid and the opening crack from the mechanical loads and density and direction of the heat flow have been constructed. The influence of fluid pressure on the stress intensity factor mode I are analyzed.

A Numerical Study of Creep Crack Growth in an Aero-engine Turbine Disc using XFEM

In this paper, a turbine disc of an aero-engine having a macro crack under creep loading is studied to predict the creep crack growth. Extended finite element method (XFEM) is used as it does not require conformal meshing and remeshing due to change in the topology during crack growth. The elasto-plastic behavior of the material is modelled by Ramberg-Osgood model and von-Mises yield criterion. The creep behavior is modelled by coupling of spatial and temporal dimensions to capture the effect of stress relaxation and redistribution due to creep strain. The creep crack growth rate is computed by the C(t)-integral which includes small-scale creep, transition creep and extensive creep. The crack growth direction is estimated by the maximum principal stress criterion using mode-I and mode-II stress intensity factors (SIFs). The interaction integral approach is implemented for the evaluation of stress intensity factors of different modes. The history fields of plasticity and creep are transferred properly from the old configuration to new configuration after the crack growth which is the main challenge in this analysis. This proposed numerical scheme is then utilized to obtain the creep crack growth in the component made of elasto-plastic-creeping material. The creep crack growth variation with time is estimated by the XFEM to evaluate the life of an aero-engine turbine disc under creep conditions.

Applications on Three-Dimensional Mixed Mode Fatigue Crack Propagation Using Fracture and Crack Propagation Analysis System (FCPAS)

In this study, results from two applications on three-dimensional fatigue crack propagation using the in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” are presented. FCPAS uses finite element models to calculate three-dimensional mixed mode stress intensity factors and other sub-modules to predict shapes of the incrementally growing crack fronts and the resulting fatigue crack propagation lives. The evolving crack surfaces are generated by successively adding the incremental growth surfaces and re-meshing and re-solving the finite element model using the standalone program FRAC3D, a finite element-based standalone program employing three-dimensional enriched finite elements. The results show that the fracture surfaces evolve into a mode-I type three-dimensional crack as expected. Very good agreements are obtained between the results of the current studies and those of numerical applications in terms of both evolving crack surfaces and crack propagation lives. Therefore, it is concluded that the applied method is capable of accurately predicting linear elastic three-dimensional mixed mode fatigue crack propagation problems.

Mixed mode stress intensity factors of slanted edge cracked plate with hole subjected to various in-plane loadings using XFEM

Mixed mode stress intensity factors of slanted edge cracked plate with hole subjected to various in-plane loadings using XFEM

Mixed mode stress intensity factors of slanted edge cracked plate with hole subjected to various in-plane loadings using XFEM

This manuscript presents the fracture behaviour of a slanted edge cracked plate with a circular hole subjected to various in-plane loadings, such as tensile, shear and combined (tensile and shear) ...

Three-Dimensional Mixed Mode Stress Intensity Factors for Inclined Elliptical Surface Cracks in Plates under Uniform Tensile Load

In this study, main results from parametric analyses of three-dimensional inclined elliptical surface cracks using FRAC3D are presented in terms of normalized mixed mode stress intensity factors (SIFs) along crack fronts. FRAC3D is the solver of in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” and is a finite element-based standalone program employing three-dimensional enriched finite elements. In the analyses, values of the main parameters affecting the problem, which are normalized crack depth with respect to plate thickness (a/t=0.2, 0.4, 0.6, 0.8), crack aspect ratio (a/c=0.25, 0.50, 1.0, 2.0, 4.0) and crack inclination angle (β=0°, 15°, 30°, 45°, 60°, 75°), are changed systematically in their realistic ranges to obtain a wide library of solutions representing the general problem and to develop empirical SIF equations that are valid for all values of the main parameters in their pre-determined ranges. This resulted in a total of 120 three-dimensional fracture analyses. The results show that as the inclination angle of the surface crack increases, mode-I SIF decreases along the crack front, while mode-II and mode-III SIFs increase up to β=45°, which contains the plane with maximum in-plane shear stress. For higher values of β, mode-II and mode-III SIFs start decreasing as expected. As the normalized crack depth increases, the normalized SIFs also increase. When the depth point and the free-surface point are compared with each other, it is seen that the crack aspect ratio also has big effect on the relative values of the normalized SIFs.

Crack initiation and propagation on CT specimens of two polymers (ABS and PMMA), under cyclic constant displacement loading

Cyclic constant displacement tests on CT (compact tension) specimens, according to the ASTM E647-00 standard, have been carried out in order to investigate the crack initiation and propagation for two polymeric materials: the ABS (Acrylonitrile Butadiene Styrene) and PMMA (Polymethyl methacrylate). Experimental cyclic tests have been performed on a self-designed and constructed machine working under constant displacement at frequency of 0.25 Hz and with maximum displacement of 390 μm. The displacement control is implemented using the Arduino software, a personal computer together with an inductive proximity sensor, which allows determining the displacement with ±4 μm of precision. The stress intensity factor in mode I (KI), is obtained for different crack lengths “a”, different amplitudes of displacement, for the two polymeric materials. In addition, the energy release rate G for plane stress and plane strain are obtained by using the stress intensity factors in mode I, previously calculated. Finally, the fracture surfaces are analyzed by scanning electron microscope in order to examine the general trends for crack initiation and propagation under the loading conditions being described.

Three-dimensional mode-I/III fatigue crack propagation: Computational modeling and experiments

Three dimensional mixed mode-I/III fatigue crack growth simulations and experiments are performed on Al 7075-T651 aluminum under different mode mixity ratios. The crack growth surfaces obtained from numerical models are compared to experimental results. Good agreement is achieved with experimental results on prediction of crack growth surfaces for up to upper intermediate levels of mixed mode loadings. Based on the computed mixed mode stress intensity factors from the numerical analyses, fatigue crack propagation lives are also predicted using different criteria. The results show that all of the mixed mode criteria evaluated in this study underestimate fatigue crack growth lives.

Mixed-mode fracture parameters estimation by genetic programming

The linear elastic fracture phenomenon has been characterized with stress intensity factors (SIFs). In this study a general function is obtained in order to predict the fracture parameters. Numerical calculation of the SIFs in a mixed-mode condition is a cumbersome task. In this research, more than 6800 numerical analyses using extended finite element method are conducted to simulate the fracture problem. States are considered for a plate with an arbitrary edge or center crack. Mixed mode SIFs were calculated using of interaction integral. Then, Gene Expression Programming (GEP) method is utilized to extraction of a function. Results show acceptable correlations between numerical calculations and genetic programming functions. R-square (R2) values are in a range of 0.91 to 0.96 that guarantees the accuracy of the inferred functions.

The determination of the stress intensity factor solutions for the new pipe-ring specimen using FEA

For safe transport and reliable supply of petrochemical substances, it is crucial to ensure the structural integrity of the equipment, pipelines in particular. Regarding the large diameters and high mass per distance, pipelines for natural gas are designed as thin-walled cylindrical structures. To ensure the structural integrity of the unknown material means to measure and therefore empirically test the material fracture properties of the laboratory specimen for giving an assessment of the accepted defect size. Compared to standards and regulations, such as the ASTM E-1820, BS 7448 standards and the GKSS procedure, the production of standard specimens for measuring the fracture toughness is commonly very difficult or even impossible for applications. On the basis of the Slovenian–Russian bilateral project, we investigate and propose a solution for this issue with a new kind of specimen, called the pipe-ring specimen. The specimens were made from a segment of the observed thin-walled pipeline from the construction filed or stored in a warehouse. The measurement procedure is similar as for the standard SENB specimens and extensometer because of the geometry of the specimen, which is cut from the pipe and contains only a machine-made notch. The next step is to test specimens axially on the three-point bending load test on the hydraulic machine. Because the ring as the specimen is not standardized, it is necessary to show and prove how, and if it is possible to use ring specimens as an alternative option to the standard specimens for testing and determining fracture properties of testing material for thin-walled pipelines. In the frame of the three main experimental, analytical and numerical approaches, this publication shows the numerical approach of defining the stress intensity factor (SIF) for crack opening mode I with and without prior fatigue pre-cracking. Besides the limit load, the SIF presents one of two main parameters for developing the failure assessment diagram and estimating the possible accepted defects in a material relating to its’ structural integrity.

Inclined surface cracks in a graded half-plane subjected to frictional sliding contact

Fracture parameters of an inclined surface crack in a graded half-plane subjected to sli- ding frictional contact are investigated in this study. The problem is modelled via the finite element method (FEM) under the plane strain assumption employing a newly developed di- splacement boundary condition. The shear modulus of the half-plane is graded exponentially through the thickness direction by means of the homogeneous finite element approach. The augmented Lagrange algorithm is selected as an iterative contact solver. The mixed mode stress intensity factors (SIFs) which are induced by the contact stresses are evaluated utili- zing the Displacement Correlation Technique (DCT). The accuracy of the present procedure is ensured comparing the SIF results to those calculated by an analytical method for verti- cal surface cracks. Additional SIF curves are generated as functions of the crack inclination in order to reveal the effects of non-homogeneity, punch location, crack length and friction coefficient. The prominent conclusion of this study indicates that the crack orientation has profound effects on the behavior of SIF curves, which has not been presented in any study published so far. Hence, consideration of crack inclination is proved essential to successfully predict fracture behavior of a graded medium under frictional contact.

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C0 finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.

Relationship between crack propagation and the stress intensity factor in cutting parallel to the grain of hinoki (Chamaecyparis obtusa)

The method of digital image correlation (DIC) was applied to the digital image of orthogonal cutting parallel to the grain of hinoki, and the strain distribution near the cutting edge was evaluated. The wood fracture associated with chip generation was considered as mode I fracture, and the stress intensity factor KI for fracture mode I was calculated from the strain distribution according to the theory of linear elastic fracture mechanics for the anisotropic material. The calculated KI increased prior to crack propagation and decreased just after the crack propagation. The change in KI before and after crack propagation, ΔKI, decreased in accordance with the crack propagation length, although the variance in ΔKI should depend on the relationships between the resolution of DIC method and the dimensions of cellular structure. The calculated KI in this study was almost on the same order as reported in the literatures. It was also revealed, for the case of chip generation Type 0 or I, the stress intensity factor for fracture mode II could be negligible due to the higher longitudinal elastic properties of wood in the tool feed direction than the one radial ones, and the mode I fracture was dominant.

Effect of the angles of the cracks of corroded plate in bonded composite repair

In this study a three-dimensional finite element method analysis of repairing plate with bonded composite patch subjected to tensile load was presented. The effect of the corrosion on the damage of the adhesive (FM73) in the length of inclined crack is presented. The obtained results show that the increase of (DR) is due to the increase of the inclination of the crack against it leads to the decrease of the values of the stress intensity factor in mode I (KI).