Mode Stress Intensity Factors Research Articles

Effect of Thermal Load Caused by Tread Braking on Crack Propagation in Railway Wheels on Long Downhill Ramps

To investigate the propagation behavior of thermal cracks on the wheel tread under the conditions of long downhill ramps, a three-dimensional finite element model of a 1/16 wheel, including an initial thermal crack, was developed using the finite element software ANSYS 17.0. The loading scenarios considered include mechanical wheel–rail loads, both with and without the superposition of thermal wheel–brake shoe friction loads. The virtual crack closure method (VCCM) is employed to analyze the variations in stress intensity factors (SIFs) for Modes I, II, and III (KI, KII, and KIII) at the 0°, mid, and 90° positions along the crack tip. The simulation results show that temperature is a critical factor for the propagation of thermal cracks. Among the SIFs, KII (Mode II) is larger than KI (Mode I) and KIII (Mode III). Specifically, the thermal load on the wheel tread during braking contributes up to 23.83% to KII when the wheel tread reaches the martensitic phase transition temperature due to brake failure. These results are consistent with the observed radial propagation of thermal cracks in wheel treads under operational conditions.

Finite element analysis of macro-crack behavior in the cortical bone of a human tibia

The bone is a biological tissue that possesses a highly complicated hierarchical structure; hence, the tissue components of the bone exhibit variable mechanical proper-ties and a complex bone geometry. This is why the creation of a three-dimensional mod-el through CAD software facilitates the study of the mechanical behavior of bones. Com-bining the concepts of linear elastic fracture mechanics and finite element analysis pro-vides a practical solution to study the fracture behavior of the tibial bone. The objective of this study is to analyze the behavior of cracks in the cortical bone of the human tibia us-ing stress intensity factors in mode I, II, and III as rupture criteria to assess the bone damage response. The tibial bone is one of the most common sites for lower limb stress fractures, which pose problematic injuries. The results investigating the effect of the crack position in the bone demonstrate that the risk of crack propagation is mainly due to mode I opening and is highly favored in the distal zone compared to the middle and proximal regions, regardless of bone density. For the second case study, it is observed that regardless of the crack size, the maximum values of stress intensity factors KI are obtained in the distal zone. Regarding the effect of crack orientation, the results indicate the dominance of mode II for angles α = – 45°, 30°, 45°, leading to high values of stress intensity factors KII.

Investigation of the fracture characteristics of mixed-mode I/III crack by using two kinds of sandstone specimens

This study aims to identify specimens that are more suitable for examining the failure properties of I/III mixed-mode cracks under static loads. We employed single-edge notched bending (SENB) and edge-notched disc bending (ENDB) specimens, and used ABAQUS finite element method software to calculate the stress intensity factors for modes I and III at various crack inclination angles θ. Fracture toughness was tested using three-point bending experiments on two types of sandstone specimens. The evolution of mixed-mode I/III fracture morphology and failure patterns was investigated with a monocular microscope. Additionally, the evolution of the strain field and crack tip opening displacement was analyzed using the digital image correlation method. Our findings indicate that the fracture toughness of the ENDB specimens surpassed that of the SENB specimens. The effective fracture toughness of both SENB and ENDB specimens initially increased with crack inclination angle θ but then decreased. The fracture mode correlated with energy release; the energy release rate of the ENDB specimens exceeded that of the SENB specimens, making the former more brittle. For SENB specimens, crack initiation was primarily intergranular, while ENDB specimens exhibited predominantly transgranular fractures. The crack initiation moments for both specimen types increased with higher crack inclination angles. Furthermore, at the same crack inclination angle, ENDB specimens cracked earlier than SENB specimens.

X-IGA Used for Orthotropic Material Crack Growth.

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh's Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries.

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

Transient in-plane analysis of cracked general orthotropic planes

An edge dislocation with a time-dependent Burgers vector in an orthotropic plane is analyzed. The stress field caused by a dynamic point force in the intact plane is determined. The displacement discontinuity of dislocation and direction of point load are at arbitrary angles with the Material Principal Axes (MPA), the general orthotropic plane. The density of dislocations is employed to construct integral equations for orthotropic planes weakened by several interacting cracks, making arbitrary angles with the MPA. The numerical solution of integral equations results in the density of dislocations on a crack surface. The results are employed to determine time-dependent Stress Intensity Factors (SIFs) at the tips of a crack and Crack Opening Displacement (COD). In the problem of general orthotropic planes containing cracks subjected to dynamic loads, crack orientations may cause their partial/total closing. Under the hypothesis of frictionless contact, we devise an iterative procedure to handle crack closing, as well. By contrast to cracks in the directions of MPA, expressions for the two modes of SIFs contain the density functions of both the climb and glide of the edge dislocation. Therefore, mode I SIF at an open tip of a crack may not be positive. Conversely, positive mode I SIF may occur at a closed crack tip. Numerical results of the SIFs and COD for several examples of orthotropic planes under dynamic point loads, while weakened by single and double parallel cracks, are presented. Moreover, in double cracks cases, the interaction between cracks is studied.

Double inclined cracks overlapping effect on mixed stress intensity factors using XFEM object-oriented implementation

The object of research is the Mixed Mode Stress Intensity Factor (MMSIF) of a two-dimensional (2D) plate. With the emergence of modern technologies and advanced innovations which contribute to the development and improvement of the design, implementation and management of construction projects, it has become easier. However, it is very difficult to manufacture components free from unavoidable defects, such as cracks, which lead to material deterioration and ultimately shorten its service life. Based on the process of local enrichment region using partition of unity concept, the extended finite element method (XFEM) has overcome the limitations of the standard FEM method in terms of modeling and numerical simulation of discontinuities (cracks) while gaining its general advantages. This makes XFEM a powerful and widely used digital tool in recent years. One of the most frequently raised problems in the discontinuities field (cracks) is the phenomenon of juxtaposition of multiple cracks in a cracked isotropic plate, which must be studied to determine the extent of its effect on the crack stress intensity factor in order to obtain higher safety reliability. On this basis, an improved object-oriented programming (OOP) with extended finite elements was used because of its great importance and well-known benefits. In this paper, the MMSIF of a 2D plate is determined to show the effect of the out-of-phase orientation of the angle, as well as the effect of the juxtaposition of two inclined cracks. As a result of the research, it is shown that, the convergence between the results obtained in this study with those reported in the literature, and to theoretical values is remarkable, and their close agreement was noted. In the future, based on the object-oriented approach characteristics represented by flexibility, scalability, and modularity, which were explained in this research, this proposed approach can be enriched to include heterogeneous materials modeling, whether linear or nonlinear, crack propagation in dynamics, in addition to Complex 3D industrial problems.

Effect of microstructure and local stress on small crack initiation and propagation paths in coarse‐grained FeCrAl alloys

AbstractThis study investigated the high cycle fatigue crack initiation and propagation behaviors in coarse‐grained FeCrAl alloys, with a focus on the relationship between the path of small cracks and the local microstructure. The results show that the small cracks initiate along the {100} slip plane due to the synthetical influence of local microstructure and shear stress. The initiation zone forms inclined areas with layered fine‐grain areas caused by cyclic shear stress. Quantitative analysis of the stress intensity factor (SIF) indicates that in the realm of mixed‐mode loading, the SIF of Mode I takes the lead in determining the intensity of stress and strain fields at the crack tip. As the crack propagates further, the SIF steadily increases. Once it reaches a specific threshold, the propagation mode within a coarse grain shifts from Mode II to Mode I. Moreover, fatigue life increases with a tendency for decreased SIF during crack deflection.

I-II mixed fracture characterization of hot mix asphalt under tensile test using notched semi-circular specimens

I-II mixed mode fracture is a common fracture pattern of asphalt pavement under the coupled tension and shearing loads. To address the roles of reclaimed asphalt pavement (RAP) and loading effect, this study proposed a novel test method to characterize the I-II mixed fracture toughness of two types of asphalt mixture. Within the novel tensile test, direct tension load could be applied on the bottom of the notched semi-circular specimens at −10 °C. I-II mixed fracture could be generated by varying the notch angle. Fracture parameters, including the stress intensity factors of mode I and mode II fracture (KIC and KIIC) and the T stress were obtained for specimens with five notch angles, including 0∘, 15∘, 30∘, 45∘ and 60∘, respectively. Results indicated that from 0∘ to 30∘, pure mode I to pure mode II fracture could be generated. Under the same loading rate, compared to mixture A, mixture B presented superior fracture toughness in terms of mode I and mode II stress intensity factors (KI and KII), which was attributed to the fact that the inclusion of RAP in mixture A deteriorated the fracture resistance. Loading rate played positive effect on the fracture toughness. From 1 mm/min to 5 mm/min, the improvements of KIC were 52% and 33% for mixture A and B, respectively. For KIIC, the increase of loading rate enhanced the pure mode II fracture resistance by 30% and 20% for mixture A and B, respectively. Several fracture criteria were adopted for the fracture prediction. Comparison was performed between the test data and the predictions. It was found that compared to MTS criterion, the inclusion of T stress in GMTS criterion made the prediction closer to the test data. Compared to GMTS and GEMTS criteria, GEMTS criterion could provide better estimates for I-II mixed mode, indicating considering the effect of fracture mode on the critical distance (rc) could make the prediction with a higher reliability.

An innovative model to estimate the tension field inclination considering crack growth for steel plate shear wall

The Steel Plate Shear Walls (SPSWs) are known as a capable system to use in steel structures due to their significant advantages. Despite extensive studies concerning this system, few researchers have scrutinized thecrack effect on SPSW behavior. However, the crack dramatically affected the experimental results. In the currentpaper, the effect of central and edge cracks, therefore, has been studied in jointed plates at mid-height of SPSW.Results indicated that the central crack is more destructive than the edge crack. The central crack having a long initial length also makes a sudden wall fracture in the elastic zone and consequently cannot be used in high seismic regions. Due to the dependence of the wall on the diagonal tension field and its angle, an equationis proposed taking into account shear, axial, and moment actions in columns, axial and moment actions in beams, as well as shear and axial actions in the plate which conform to finite element results. Because of thecomplication of the stress intensity factor for mode I and mode II calculations, this confidence is derived and offered.

Improved XFEM for 3D interfacial crack modeling

The conventional extended finite element method (XFEM) usually suffers from the crack tip enrichment for removing the blending elements. This may be inconvenient when treating the three dimensional (3D) and curved crack modeling since the crack tip enrichment is usually defined in the local coordinate system depending on the crack front. To avoid these shortcomings of the XFEM, an improved enrichment scheme is proposed for the 3D interfacial crack modeling. The proposed enrichment scheme removes the crack tip enrichment and two weight functions are introduced to capture the strong and weak discontinuities in the element including the crack front. The new enrichment scheme has advantages for the 3D curved interfacial cracks since all the enrichment functions are defined in the global system and it is unnecessary to introduce additional coordinate systems. Several benchmark problems including the mixed mode stress intensity factors (SIFs), anti-plane load and curved cracks are analyzed by the proposed method with the local refinement technology. Numerical results demonstrate that the proposed method can obtain accurate 3D energy release rate and SIFs. In addition, the proposed method enhances the applications of XFEM and has the potential abilities to the multiple-fields coupling and interfacial crack growth phenomena due to the fact that compatible enrichment functions are utilized.

Calibration of a Test Method to Measure Mode I, Mode II and Mode III Fracture Toughness of Engineering Materials

A refined finite element model and a new post processing sub program to determine mixed mode stress intensity factors and their variation along a surface crack front in components and structures is presented. The proposed finite element model employs a fine mesh of singular isoparametric pentahedral solid element with user specified number and size from one crack face to another and a number of such segments along a surface crack front. A compatible mesh of regular elements namely hexahedral solid element and pentahedral solid element is used to discretize the rest of the domain under consideration. Consistent with the use of the singular element, formulae to compute the Mode I, Mode II and Mode III stress intensity factors using displacements only of flagged nodes on flagged singular elements are implemented in a special purpose post processing sub program named SIF 1-2-3. In the present work the finite element models developed using ANSYS, a commercial FEA program, and the stress intensity factors determined using SIF 1-2-3 are validated using benchmarks. This finite element model is then used to calibrate a proposed test method to measure Mode I, Mode II and Mode III fracture toughness of engineering materials.

Theoretical analysis and fracture process of elliptical tunnel with symmetric cracks subjected to water pressure and ground stress

The water diversion tunnel played an important role in the allocation of water resources in the water diversion project. In the process of actual use, some cracks or joints at the edge of the tunnel could produce further cracking under the action of internal water pressure and in-situ stress, which was dangerous to the safety of the tunnel. The analytical solution formulas of stress intensity factors (SIFs) of the elliptical tunnel with two cracks were derived by using the complex function method, and the external factors affecting the stability of the elliptical tunnel were analyzed. The failure process of the specimens was analyzed by using the high-speed camera and digital image correlation (DIC) method to obtain the evolution laws of crack initiation behavior and tunnel fracture modes. The results can conclude that both sides of the elliptical tunnel and the crack tip were stress concentration areas. As the inclination angle α of the elliptical tunnel is varied from 0° to 45°, tensile cracks occur at the top and bottom of the elliptical tunnel caused by tensile stress, and the compressive strength is smallest when the elliptical tunnel with α is 45°. As the inclination angle α is 75°, two penetrating cracks appear at the edge of the elliptical tunnel and crack tips. The initiation pressure increases with the inclination angle α. The SIF of mode II rises with the ellipse major semi axis and the crack length.

Comparative evaluation of mitigation methods for traffic-induced reflective cracking in airport composite pavement

Composite pavement provides an effective and quick solution to restore structural and functional capacity of airfield pavement. However, discontinuities of concrete slabs cause initiation and propagation of reflective cracking in asphalt overlay. This study aims to evaluate and compare the effectiveness of mitigation methods for traffic-induced reflective cracking in airport composite pavements. Finite element (FE) models were developed and validated to predict pavement responses under heavy weight deflectometer (HWD) and aircraft tire loading. The load transfer efficiency (LTE) of existing rigid pavement were evaluated under common deterioration scenarios like base erosion and concrete damage. The crack potential was indicated by pseudo J-integral considering stress intensity factors (SIFs) of different fracture modes. The results show that thicker asphalt overlay, stress absorbing interlayer, and increase of LTE can help mitigate reflective cracking. Increasing 51-mm overlay (from 76 mm to 127 mm) and applying 25-mm interlayer show the similar reduction in reflective cracking fracture potential by about 35% at early crack stage. However, applying interlayer has more benefit on cost effectiveness and pavement elevation control. On the other hand, dowel bar retrofit and base treatment can improve LTE and thus reduce the crack potential at early crack stage of 76-mm overlay by 40% on doweled pavement and 60% on un-doweled pavement, respectively.

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

AbstractThe cracked rock mass could slide along the weak side under the action of compressive loads and shear loads in landslides; thus, the stability evaluation of the crack in rock mass media is of particular importance. The formulas of stress intensity factors (SIFs) for each crack tip are theoretically derived by implementing complex function theory. The results of the analytical solutions are then compared with the predicted results of the finite element analysis via ABAQUS software, revealing a slight relative error. Photo elastic experiment and static compression tests are conducted to verify the correctness of theoretical results. The obtained results reveal that the internal pressure leads to the increasing SIFs of mode II at crack tips. Further, the larger the difference between the horizontal and vertical compressive stresses, the more likely the occurrence of shear failure in the cracked rock mass. For the two cracks, the most dangerous point is the inner crack tip of the longer crack.

Mixed mode stress intensity factors of single edge cracked/notched plates under different boundary conditions using strain energy approach

This paper presents the mixed mode I/II stress intensity factors (SIFs) of slanted cracks/notches under tension loading. A two-dimensional finite element analysis (FEA) was employed using the ABAQUS program. Based on the literature survey, there is a lack of solutions for SIFs of slanted cracks in plane stress plates. The strain energy approach (SEA) was adopted to analyze the notched cases. Mode I and II SIFs are derived via the SEA method from the strain energy computed using the FEA technique. The results show excellent agreement with other researchers' work. The key contribution of the present paper is the presentation of the effect of the crack/notch length to plate width ratio on the mode I and II SIFs of a slant-edge-cracked/notched plate under different boundary conditions. Sets of new data of mode I and II SIFs are provided herein in tabular and graphical formats.

Mode (I, II, III) Stress Intensity Factors of Composite-Coated Gas Turbine Blade Using Semi-Elliptical Crack

Mode (I, II, III) Stress Intensity Factors of Composite-Coated Gas Turbine Blade Using Semi-Elliptical Crack

Amino Acids as Bio-Based Curing Agents for Epoxy Resin: Correlation of Network Structure and Mechanical Properties.

Bio-based alternatives for petroleum-based thermosets are crucial for implementing sustainable practices in fiber-reinforced polymer composites. Therefore, the mechanical properties of diglycidyl ether of bisphenol a (DGEBA) cured with either l-arginine, l-citrulline, γ-aminobutyric acid, l-glutamine, l-tryptophan, or l-tyrosine were investigated to determine the potential of amino acids as bio-based curing agents for epoxy resins. Depending on the curing agent, the glass transition temperature, Young’s modulus, tensile strength, and critical stress intensity factor range from 98.1 ∘C to 188.3 ∘C, 2.6 GPa to 3.5 GPa, 39.4 MPa to 46.4 MPa, and 0.48 MPam0.5 to 1.34 MPam0.5, respectively. This shows that amino acids as curing agents for epoxy resins result in thermosets with a wide range of thermo-mechanical properties and that the choice of curing agent has significant influence on the thermoset’s properties. After collecting the results of dynamic mechanical analysis (DMA), tensile, flexural, compression, and compact tension tests, the functionality f, cross-link density νC, glass transition temperature Tg, Young’s modulus ET, compression yield strength σCy, critical stress intensity factor in mode I KIC, fracture energy GIC, and diameter of the plastic zone dp are correlated with one another to analyze their inter-dependencies. Here, the cross-link density correlates strongly positively with Tg, ET, and σCy, and strongly negatively with KIC, GIC, and dp. This shows that the cross-link density of DGEBA cured with amino acids has a crucial influence on their thermo-mechanical properties and that the thermosets considered may either be stiff and strong or tough, but hardly both at the same time.

Закономірності росту плоских тріщин в пластинах

The general regularities of the influence of the geometric parameters of a fatigue crack on the direction of its growth in elastic plates under uniaxial tension were studied. Straight cracks, cracks in the form of a full cosine period, cracks in the form of a circle arc and kinked cracks were considered in a broad range of their geometric parameters variations. The direction of crack growth was determined in accordance with the criteria of maximum tangential (circumferential) stresses. The stress intensity factor of mode I and mode II of fracture were determined numerically using the finite element method. The obtained results made it possible to conclude that in the case of smooth crack faces, the direction of its growth primarily depends on the angle between the tangent at the crack tip and the direction of tension. It was established that the presence of a corner point of the faces near crack tip significantly affects the direction of crack growth in the case of small angles, between the tangent and the direction of tension. For such cases, numerically, it was not possible to achieve a continuous limiting transition in the results when the corner point approaches the tip. This circumstance complicates the issue of choosing the size of the initial crack growth step.

Three-dimensional X-FEM modeling of crack coalescence phenomena in the Smart CutTM technology

A new 3D X-FEM approach is proposed to model crack coalescence phenomena in the Smart Cut TM technology. An adaptive mesh is developed based on a 3D fractal mesh allowing a significant gain in computing time compared to regular meshes. In order to calculate stress intensity factors (SIFs), the term corresponding to internal pressure, that is normal loading on crack faces has been determined, added to the interaction integral and the results of SIFs in mode I have been compared to their analytical values with mean error less than 1%. An implicit algorithm is implemented to predict the evolution of the internal pressure for growing cracks of any shape; a constitutive law in pressure correlated with the equation of state of ideal gases has therefore been used. Compared to the analytical solution, numerically evaluated pressure is accurate with maximum errors less than 1% for relevant convergence tolerance. Finally, the coalescence of two cracks is taken into account in the model. Qualitative local stress analysis makes it possible to explain some phenomena experimentally observed in the Smart Cut TM such as neighboring effects of growing cracks, the outgrowth of nearby cracks or influence of the presence of concave areas at a front on growth. • A 3D X-FEM model has been proposed to model crack coalescence phenomena under variable pressure (Smart Cut TM process). • The interaction integral has been adapted to take into account the internal pressure when computing 3D stress intensity factors. • Prediction of the internal pressure of propagating cracks whatever are their shapes. • Analysis of neighboring effects by stress analysis on a two penny-shape crack coalescence model.