Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris’ law model. Finally, the performance and capability of the developed program are shown in the application examples.     

Finite Element Simulation of a Crack Growth in the Presence of a Hole in the Vicinity of the Crack Trajectory

The aim of this paper was to present a numerical simulation of a crack growth path and associated stress intensity factors (SIFs) for linear elastic material. The influence of the holes’ position and pre-crack locations in the crack growth direction were investigated. For this purpose, ANSYS Mechanical R19.2 was introduced with the use of a new feature known as Separating Morphing and Adaptive Remeshing Technology (SMART) dependent on the Unstructured Mesh Method (UMM), which can reduce the meshing time from up to several days to a few minutes, eliminating long preprocessing sessions. The presence of a hole near a propagating crack causes a deviation in the crack path. If the hole is close enough to the crack path, the crack may stop at the edge of the hole, resulting in crack arrest. The present study was carried out for two geometries, namely a cracked plate with four holes and a plate with a circular hole, and an edge crack with different pre-crack locations. Under linear elastic fracture mechanics (LEFM), the maximum circumferential stress criterion is applied as a direction criterion. Depending on the position of the hole, the results reveal that the crack propagates in the direction of the hole due to the uneven stresses at the crack tip, which are consequences of the hole’s influence. The results of this modeling are validated in terms of crack growth trajectories and SIFs by several crack growth studies reported in the literature that show trustworthy results.     

Crack Propagation Analysis of Compression Loaded Rolling Elements

The problem of crack propagation from internal defects in thermoplastic cylindrical bearing elements is addressed in this paper. The crack propagation in these elements takes place under mixed-mode conditions—i.e., all three possible loading modes (tensile opening mode I and shear opening modes II and III) of the crack are combined together. Moreover, their mutual relation changes during the rotation of the element. The dependency of the stress intensity factors on the crack length was described by general parametric equations. The model was then modified by adding a void to simulate the presence of a manufacturing defect. It was found that the influence of the void on the stress intensity factor values is quite high, but it fades with crack propagating further from the void. The effect of the friction between the crack faces was find negligible on stress intensity factor values. The results presented in this paper can be directly used for the calculation of bearing elements lifetime without complicated finite element simulations.     

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance.     

Fatigue Crack Growth Analysis under Constant Amplitude Loading Using Finite Element Method

Damage tolerant design relies on accurately predicting the growth rate and path of fatigue cracks under constant and variable amplitude loading. ANSYS Mechanical R19.2 was used to perform a numerical analysis of fatigue crack growth assuming a linear elastic and isotropic material subjected to constant amplitude loading. A novel feature termed Separating Morphing and Adaptive Remeshing Technology (SMART) was used in conjunction with the Unstructured Mesh Method (UMM) to accomplish this goal. For the modified compact tension specimen with a varied pre-crack location, the crack propagation path, stress intensity factors, and fatigue life cycles were predicted for various stress ratio values. The influence of stress ratio on fatigue life cycles and equivalent stress intensity factor was investigated for stress ratios ranging from 0 to 0.8. It was found that fatigue life and von Mises stress distribution are substantially influenced by the stress ratio. The von Mises stress decreased as the stress ratio increased, and the number of fatigue life cycles increased rapidly with the increasing stress ratio. Depending on the pre-crack position, the hole is the primary attraction for the propagation of fatigue cracks, and the crack may either curve its direction and grow towards it, or it might bypass the hole and propagate elsewhere. Experimental and numerical crack growth studies reported in the literature have validated the findings of this simulation in terms of crack propagation paths.     

Effect of the Crack Tip Bifurcation on the Plasticity-Induced Fatigue Propagation in Metallic Materials

This article deals with the influence of the crack path branching (at the micro level) on the plasticity-induced fatigue crack growth. With regard to this, a modeling by means of the finite element method was performed considering a cracked panel subjected to tension with different symmetric and asymmetric configurations of the bifurcated crack tip. The results show the appearance of a retardation effect in the growth rate of the bifurcated crack in relation to the growth rate of the fully straight crack in different cases studied, namely: (i) if the two branches of the bifurcation have different initial projected length, the propagation rate is greater at the crack tip corresponding to the long-branch than that of the short-branch, and the long-branch growth rate increases with the decrease of the initial branch angle and of the initial projected short-branch length and with the increase of the intensity of fatigue; (ii) if the two branches of the bifurcation have identical initial projected length, the retardation effect depends on the initial distance between the two bifurcated crack tips, the growth rate going up with the decrease of such a distance and with the increase of the fatigue intensity.     

Phase Field Models for Thermal Fracturing and Their Variational Structures

It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.     

Investigation of the Performance of Ti6Al4V Lattice Structures Designed for Biomedical Implants Using the Finite Element Method

The development of medical implants is an ongoing process pursued by many studies in the biomedical field. The focus is on enhancing the structure of the implants to improve their biomechanical properties, thus reducing the imperfections for the patient and increasing the lifespan of the prosthesis. The purpose of this study was to investigate the effects of different lattice structures under laboratory conditions and in a numerical manner to choose the best unit cell design, able to generate a structure as close to that of human bone as possible. Four types of unit cell were designed using the ANSYS software and investigated through comparison between the results of laboratory compression tests and those of the finite element simulation. Three samples of each unit cell type were 3D printed, using direct metal laser sintering technology, and tested according to the ISO standards. Ti6Al4V was selected as the material for the samples. Stress–strain characteristics were determined, and the effective Young’s modulus was calculated. Detailed comparative analysis was conducted between the laboratory and the numerical results. The average Young’s modulus values were 11 GPa, 9 GPa, and 8 GPa for the Octahedral lattice type, both the 3D lattice infill type and the double-pyramid lattice and face diagonals type, and the double-pyramid lattice with cross type, respectively. The deviation between the lab results and the simulated ones was up to 10%. Our results show how each type of unit cell structure is suitable for each specific type of human bone.     

Modelling of Longitudinal Elastic Wave Propagation in a Steel Rod Using the Discrete Element Method

The paper deals with the issue of modelling elastic wave propagation using the discrete element method (DEM). The case of a longitudinal wave in a rod with a circular cross-section was considered. A novel, complex algorithm consisting of the preparation of models and simulation of elastic waves was developed. A series of DEM models were prepared for simulations, differing in discretisation and material parameters. Additional calculations with the finite element method (FEM) were performed. Numerical wave signals were obtained from each simulation and compared with experimental results to choose the best DEM model based on the correlation between the waveforms. Moreover, dispersion curves were prepared for each model to verify the agreement with the Pochhammer-Chree wave propagation theory. Both experimental and theoretical approaches indicated the same model as the most suitable. The analysis results allowed stating that DEM can be successfully used for modelling wave propagation in structural rods.     

The Uniaxial Stress–Strain Relationship of Hyperelastic Material Models of Rubber Cracks in the Platens of Papermaking Machines Based on Nonlinear Strain and Stress Measurements with the Finite Element Method

Finite element analysis is extensively used in the design of rubber products. Rubber products can suffer from large amounts of distortion under working conditions as they are nonlinearly elastic, isotropic, and incompressible materials. Working conditions can vary over a large distortion range, and relate directly to different distortion modes. Hyperelastic material models can describe the observed material behaviour. The goal of this investigation was to understand the stress and relegation fields around the tips of cracks in nearly incompressible, isotropic, hyperelastic accouterments, to directly reveal the uniaxial stress–strain relationship of hyperelastic soft accouterments. Numerical and factual trials showed that measurements of the stress–strain relationship could duly estimate values of nonlinear strain and stress for the neo-Hookean, Yeoh, and Arruda–Boyce hyperelastic material models. Numerical models were constructed using the finite element method. It was found that results concerning strains of 0–20% yielded curvatures that were nearly identical for both the neo-Hookean, and Arruda–Boyce models. We could also see that from the beginning of the test (0–5% strain), the curves produced from our experimental results, alongside those of the neo-Hookean and Arruda–Boyce models were identical. However, the experiment’s curves, alongside those of the Yeoh model, converged at a certain point (30% strain for Pieces No. 1 and 2, and 32% for Piece No. 3). The results showed that these finite element simulations were qualitatively in agreement with the actual experiments. We could also see that the Yeoh models performed better than the neo-Hookean model, and that the neo-Hookean model performed better than the Arruda–Boyce model.     

Direct Computation of 3-D Stress Intensity Factors of Straight and Curved Planar Cracks with the P-Version Finite Element Method and Contour Integral Method

This paper presents direct computations of 3-D fracture parameters including stress intensity factors (SIFs) and T-stress for straight and curved planar cracks with the p-version finite element method (P-FEM) and contour integral method (CIM). No excessive singular element or enrichment function is required for the computation. To demonstrate the accuracy and efficiency of the proposed approaches, several benchmark numerical models of 3-D planar straight and curved cracks with single and mixed-mode fractures are considered and analyzed: a through thickness edge straight crack in a homogeneous material, a through thickness inclined straight crack, a penny-shaped crack embedded in a cube and a central ellipse shaped crack in a homogeneous cube. Numerical results are analyzed and compared with analytical solutions and those reported by the extended finite element method (XFEM) and the scaled boundary finite element method (SBFEM) in the available literature. Numerical experiments show the accuracy, robustness and effectiveness of the present method.     

The Numerical Modelling Approach with a Random Distribution of Mechanical Properties for a Mismatched Weld

The aim of this work was to include a local variation in material properties to simulate the fracture behaviour in a multi-pass mis-matched X-weld joint. The base material was welded with an over and under-match strength material. The local variation was represented in a finite element model with five material groups in the weld and three layers in the heat-affected zone. The groups were assigned randomly to the elements within a region. A three-point single edge notch bending (SENB) fracture mechanics specimen was analysed for two different configurations where either the initial crack is in the over or under-matched material side to simulate experimentally obtained results. The used modelling approach shows comparable crack propagation and stiffness behaviour, as well as the expected, scatter and instabilities of measured fracture behaviour in inhomogeneous welds.     

Notch Effects on the Stress Intensity Factor and on the Fatigue Crack Path for Eccentric Circular Internal Cracks in Elliptically Notched Round Bars under Tensile Loading

In this paper, stress intensity factor (SIF) solutions are numerically obtained for notched bars subjected to tensile loading containing an eccentric circular inner crack located in the cross-section corresponding to the notch root. The finite element method and the J-integral have been used to obtain the SIF and to analyze the effect on it of three elliptical notch geometries (of equal radial depth). The results show how the SIF is greater in the notched bars than in the smooth bar and within the former when the axial semi-axis of the notch rises, its effect being greater as the diameter and eccentricity of the inner crack increase. In addition, the fatigue growth of an eccentric crack induces an increase in such eccentricity, greater as the notch axial semi-axis increases. The cause of these phenomena can be attributed to the constraint loss caused by the notch, which also facilitates bending of the specimen due to the asymmetry generated by the crack eccentricity.     

Discrete Element Method Modeling for the Failure Analysis of Dry Mono-Size Coke Aggregates

An in-depth study of the failure of granular materials, which is known as a mechanism to generate defects, can reveal the facts regarding the origin of the imperfections, such as cracks in the carbon anodes. The initiation and propagation of the cracks in the carbon anode, especially the horizontal cracks below the stub-holes, reduce the anode efficiency during the electrolysis process. The failure analysis of coke aggregates can be employed to determine the appropriate recipe and operating conditions in order to avoid the formation of cracks in the carbon anodes. In this paper, it will be shown that a particular failure mode can be responsible for the crack generation in the carbon anodes. The second-order work criterion is employed to analyze the failure of the coke aggregate specimens and the relationships between the second-order work, the kinetic energy, and the instability of the granular material are investigated. In addition, the coke aggregates are modeled by exploiting the discrete element method (DEM) to reveal the micro-mechanical behavior of the dry coke aggregates during the compaction process. The optimal number of particles required for the failure analysis in the DEM simulations is determined. The effects of the confining pressure and strain rate as two important compaction process parameters on the failure are studied. The results reveal that increasing the confining pressure enhances the probability of the diffusing mode of the failure in the specimen. On the other hand, the increase of strain rate augments the chance of the strain localization mode of the failure in the specimen.     

Numerical Simulation of Stresses in Functionally Graded HCS-MgO Cylinder Using Iterative Technique and Finite Element Method

In this study, a thick hollow axisymmetric functionally graded (FG) cylinder is investigated for steady-state elastic stresses using an iteration technique and the finite element method. Here, we have considered a functionally graded cylinder tailored with the material property, namely, Young’s modulus, varying in an exponential form from the inner to outer radius of the cylinder. A mathematical formulation for stress analysis of functionally graded cylinder under internal and external pressure conditions is developed using constitutive relations for stress–strain, strain–displacement relations and the equation of equilibrium. The effect of the in-homogeneity parameter on radial displacement, radial and tangential stresses in a functionally graded cylinder made up of a High Carbon Steel (HCS) metal matrix, reinforced with Magnesium Oxide (MgO) ceramic is analyzed. The iterative method implemented is fast and converges to the solution which can be further improved by considering a higher number of iterations. This is depicted graphically by using radial displacement and stresses in a pressurized functionally graded cylinder obtained for the first two iterations. An iterative solution for non-FGM (or homogeneous material) is validated using the finite element method. The mechanical responses of the functionally graded cylinder obtained from the iterative method and the finite element method are then compared and found to be in good agreement. Results are presented in graphical and tabular form along with their interpretations.     

Modelling of the Fine-Grained Materials Briquetting Process in a Roller Press with the Discrete Element Method

By using the Altair^® EDEM™ software, which implements the discrete element method, modelling and further study of the processes occurring in the roller press’s deformation area were carried out. It was shown that the discrete element method makes it possible to accurately describe the phenomena occurring in the area of roller press deformation compared with the finite element method. Models of material compaction in a roller press are developed using calcium hydroxide (slaked lime) and copper ore concentrate. The developed model makes it possible to determine the process’s energy parameters and the material’s compaction characteristics, taking into account the characteristics of its constituent particles. It was shown that discrete element modelling could be used effectively to create roller presses that provide rational characteristics of the briquetting process, taking into account the properties of the material being briquetted and the operating modes of the equipment. The results of the studies provided the basis for the applicability of the development of the discrete element method for describing the phenomena occurring in roller presses and accelerating the design of press equipment and briquetting technological processes.     

Efficient Temporal Third/Fourth-Order Finite Element Method for a Time-Fractional Mobile/Immobile Transport Equation with Smooth and Nonsmooth Data

In recent years, the numerical theory of fractional models has received more and more attention from researchers, due to the broad and important applications in materials and mechanics, anomalous diffusion processes and other physical phenomena. In this paper, we propose two efficient finite element schemes based on convolution quadrature for solving the time-fractional mobile/immobile transport equation with the smooth and nonsmooth data. In order to deal with the weak singularity of solution near t=0, we choose suitable corrections for the derived schemes to restore the third/fourth-order accuracy in time. Error estimates of the two fully discrete schemes are presented with respect to data regularity. Numerical examples are given to illustrate the effectiveness of the schemes.     

The Biomechanical Impact of Loss of an Implant in the Treatment with Mandibular Overdentures on Four Nonsplinted Mini Dental Implants: A Finite Element Analysis

The aim of this study was to evaluate the biomechanical impact, in terms of stress and displacement, at the level of a mandibular overdenture, on four mini dental implants (MDIs) after the loss of an implant. A three-dimensional virtual model was obtained by scanning the overdenture, and a biomechanical analysis was carried out, using the finite element method (FEM). The displacements of the overdenture and the equivalent von Mises stresses were evaluated using logarithmic scales. In the case of a mandibular overdenture on four MDIs inserted in the interforaminal area, the frontal loading generated the lowest values for the von Mises stresses, and the bilateral loading generated the least displacement when two implants were inserted in the canine area and two in the molar area. The highest von Mises stress was observed during frontal loading in the situation of the mandibular overdenture on four MDIs, two of which were inserted in the canine area and two in the molar area, following the loss of an implant in the canine area. The largest displacement was noted in the mandibular overdenture on four interforaminal MDIs during unilateral loading, following the loss of a distally inserted implant. The FEM analysis showed aspects that correlated with clinical observations, with predictive value. The concentration of von Mises stresses, and the occurrence of some displacements of the prosthodontic restoration, can explain the emergence of some complications in the overdenture’s biodynamics, and the increased risk of fracture. Complications can be prevented by choosing a certain number of implants and a topographical distribution correlated with biomechanical aspects, and by proposing a correct occlusal scheme with optimal functional loading.     

Investigation of Adhesive’s Material in Hermetic MEMS Package for Interfacial Crack between the Silver Epoxy and the Metal Lid during the Precondition Test

A hermetic Micro-Electro-Mechanical Systems (MEMS) package with a metal lid is investigated to prevent lid-off failure and improve its reliability during the precondition test. While the MEMS package benefits from miniaturization and low cost, a hermetic version is highly sensitive to internal pressure caused by moisture penetration and the reflow process, thus affecting its reliability. In this research, the finite element method is applied to analyze the contact stress between the metal lid and the silver epoxy by applying the cohesive zone model (CZM). Moreover, the red dye penetration test is applied, revealing a microcrack at the metal lid/silver epoxy interface. Further analyses indicate that the crack is caused by internal pressure. According to the experimental testing and simulation results, the silver epoxy material, the curing process, the metal lid geometry, and the bonding layer contact area can enhance the bonding strength between the metal lid and the substrate.     

Residual Stress Build-Up in Aluminum Parts Fabricated with SLM Technology Using the Bridge Curvature Method

In metal 3D printing with Selective Laser Melting (SLM) technology, due to large thermal gradients, the residual stress (RS) distribution is complicated to predict and control. RS can distort the shape of the components, causing severe failures in fabrication or functionality. Thus, several research papers have attempted to quantify the RS by designing geometries that distort in a predictable manner, including the Bridge Curvature Method (BCM). Being different from the existing literature, this paper provides a new perspective of the RS build-up in aluminum parts produced with SLM using a combination of experiments and simulations. In particular, the bridge samples are printed with AlSi10Mg, of which the printing process and the RS distribution are experimentally assessed with the Hole Drilling Method (HDM) and simulated using ANSYS and Simufact Additive. Subsequently, on the basis of the findings, suggestions for improvements to the BCM are made. Throughout the assessment of BCM, readers can gain insights on how RS is built-up in metallic 3D-printed components, some available tools, and their suitability for RS prediction. These are essential for practitioners to improve the precision and functionality of SLM parts should any post-subtractive or additive manufacturing processes be employed.