Presence Of Geometric Discontinuities Research Articles

Fracture assessment of polyamide 12 (PA12) specimens fabricated via Multi Jet FusionTM in the presence of geometrical discontinuities

This study aims to study the fracture resistance of additively manufactured polyamide 12 (PA12), specifically when subjected to notches and cracks, and how it varies with the printing direction using Multi Jet Fusion (MJF). The methodology involved conducting tensile tests on V-notched samples, with a focus on different combinations of opening angle (0°-120°) and tip radius (0.2–2 mm). The findings revealed that the sensitivity to the notch opening angle decreased with an increase in the notch tip radius. Furthermore, the fracture resistance for different mode mixities was examined using semi-circular bend (SCB) specimens, with the crack angle varied between 0° and 53°. The results demonstrated two distinct fracture behaviours, namely brittle and ductile, depending on the crack angle. Theoretical analyses revealed that with appropriate tuning, average strain energy density (ASED) can predict the load capacity of notched and cracked PA12 parts manufactured with MJF, within an error range of ± 20 %.

Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Abstract This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.

Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique

Abstract Theoretical and experimental large deflection and stress analysis of a master leaf spring considering stress concentration effect of clamping is reported. The non-uniformly curved master leaf spring under three point bending subjected to moving boundaries is modeled. Geometrically nonlinear strain-displacement relations, as necessary for the theoretical analysis, are derived through visualization of physics behind the large deformation problem. An embedded curvilinear coordinate system is considered, to study the combined effects of non-uniform curvature, bending, stretching and shear deformation including cross-sectional warping. Governing equation of the non-uniformly curved beam system is derived in variational form using energy method, based on linear material constitutive relations and the derived nonlinear kinematic relations. An iterative solution scheme through successive geometry updation is developed and executed in MATLAB® software to solve the governing equation involving strong geometric nonlinearity together with complicating moving boundary effect. Experimental deflection profiles under static loading are obtained through manual image processing technique using AutoCAD® software. Whereas, strain measurements are performed using strain gauges with data acquisition system (HBM-MX840B). Comparison between the theoretical and experimental results lead towards observation on stress concentration effect due to presence of geometric discontinuity in form of a small hole in the physical system. A modified formulation is proposed using domain decomposition method incorporating effect of geometric discontinuity through an equivalent curved beam geometry of variable cross-section. The modified theoretical model is validated successfully with the experimental results, and observations on stress characteristics and effect of hole diameter to beam width ratio are made.

Fatigue analysis of cruciform welded joint with weld penetration defects

For the fabrication of steel structures such as steel bridges, offshore structure etc, welding is nowadays considered as an efficient metal joining process. The type of fillet welded cruciform joint are widely used in construction of long spanned bridges with improved design and increased weld quality. However, the presence of geometrical discontinuities and metallurgical nonuniformities lead to crack initiations from different positions which are difficult to detect. Moreover, when these structures are subjected to repeated loading these cracks start propagating in different directions and lead to fatigue failure of welded structures. Also, the presence of locked in stresses and other factors affect the fatigue life and fatigue crack initiation. In the present work, the cruciform fillet welded joint with full and incomplete penetration were analyzed for both load types i.e load carrying and non-load carrying by using 3D fatigue FEM analysis. The experimental study of non-load carrying cruciform joint was also carried out. The effect of incomplete penetration depth, welding deformation, residual stresses and stress magnitude on fatigue crack initiation and fatigue life of fillet welded cruciform joints was investigated. Also, the S-N curves plotted for comparing with the results of hotspot stress and experiments. The results of 3D fatigue FEM analysis were compared with S-N curves recommended by IIW and DNV GL.

Stress diffusion interactions in an elastoplastic medium in the presence of geometric discontinuity

This paper aims to study the effect of stress-diffusion interactions and its effect on the localization of the plastic strain in an elastoplastic material using a fully coupled chemo-mechanical system. The transient coupled system is solved using a finite element formulation in an open-source finite element solver FEniCS. We investigate the role of geometric discontinuities in scenarios involving diffusing species, namely, a plate with a notch/hole/void and particle with a void/hole/core. We also study the effect of stress concentrations and plastic yielding on the diffusion-deformation.

Controlled manipulation of CNTs in glass/epoxy composites with cut-outs using non-uniform electric field

In this work, an effective methodology to incorporate aligned carbon nanotubes (CNTs) in long fiber composites in the presence of geometric discontinuities has been studied. Unidirectional (UD) glass/CNT-epoxy composites containing circular cut-outs were used as representative of a common discontinuity. Multi-walled (MW) CNTs were introduced in the composites via the epoxy matrix and aligned using low-frequency non-uniform AC electric field. This work discusses the methodology to control CNT alignment around the cut-out with the objective of enhancing the stiffness locally. The effectiveness of CNT alignment was assessed indirectly through the mapping of electrical resistance and polarized Raman spectroscopy. A strong correlation was found between the targeted CNT alignment state and the measured resistance values around the cut-out. As a precursor to developing glass/CNT-epoxy hierarchical composites, the response of MW-CNTs in the epoxy resin system was assessed at various input voltage levels in correlation with the weight fraction (wt.%) of CNTs. While a change in electrical resistance by ~3 orders of magnitude was found along the direction of CNT alignment in the hierarchical composites, a change in electrical resistance by ~5 orders of magnitude was observed in the CNT-epoxy composites in comparison with that of the respective control samples.

Directed Energy Deposition versus Wrought Ti‐6Al‐4V: A Comparison of Microstructure, Fatigue Behavior, and Notch Sensitivity

Laser Engineered Net Shaping (LENS), a Direct Energy Deposition (DED) additive manufacturing process is a 3D manufacturing process generally used to produce fully dense parts or to repair/add additional material to an existing component. The main aim of this work is to evaluate the fatigue behavior of LENS specimens in the presence of geometrical discontinuities and to compare its performance to the one obtained from wrought specimens. For this aim, axial fatigue tests are carried out on three sets of specimens namely, smooth, semi‐circular and V‐notched specimens to determine the fatigue strength and notch sensitivity of the LENS and wrought Ti‐6Al‐4V materials. The LENS material shows higher fatigue strength and notch sensitivity compared to wrought material which is attributed to the unique microstructural features leading to different fatigue failure mechanisms. Further, the fatigue data is assessed by use of strain energy density as a failure criterion.

Failure Theories on Carbon/Kevlar Hybrid Fabric Based Composite Laminate: Notch and Anisotropy Effects

Composite materials have been increasingly used in both researches and industries, given their wide range of innovative applications and configurations. High-performance hybrid fabric-reinforced plastics stand out in this sector. In the present research, an epoxy-based vinyl ester resin laminate reinforced with bidirectional hybrid fabric consisting of carbon and Kevlar fibers is developed. In order to determine its mechanical properties and damage mechanism considering the anisotropy and the presence of geometric discontinuity (circular hole), this research focused on both experimental and analytical aspect. Concerning to geometric discontinuity, in the vicinity of the hole (known as a stress concentration area), characteristic distances ao and do associated to ASC (Average Stress Criterion) and PSC (Point Stress Criterion) failure theories, respectively, were determined. All the study of the composite material mechanical behavior was conducted based on uniaxial tensile tests. Their results show higher losses in the mechanical properties of the hybrid laminate, with respect to the anisotropy and the presence of the central hole, mainly when the orientation of the Kevlar fibers coincides with the direction of the applied load.

A Novel Approach for Assessing the Fatigue Behavior of PEEK in a Physiologically Relevant Environment.

In recent years, the need of surgical procedures has continuously increased and, therefore, researchers and clinicians are broadly focusing on the development of new biocompatible materials. Among them, polyetheretherketone (PEEK) has gained wide interest in load-bearing applications due to its yielding behaviour and its superior corrosion resistance. To assure its reliability in these applications where notches and other stress concentrators weaken implants resistance, a design tool for assessing its tensile and fatigue behaviour in the presence of geometrical discontinuities is highly claimed. Herein, a new fatigue design method based on a local approach is proposed for PEEK implant, and the results are compared with those obtained using the two main biomaterial design approaches available in literature, i.e., the theory of critical distances (TCD) and the notch stress intensity factor (NSIF) approach. To this aim, previously published datasets of PEEK-notched specimens are used, and the proposed method is reported to provide more accurate results and to be robust for different notch geometries.

Effects of stress-diffusion interactions in an isotropic elastic medium in the presence of geometric discontinuities

Effects of stress-diffusion interactions in an isotropic elastic medium in the presence of geometric discontinuities

SENSITIVITY ANALYSIS OF VIBRATING MOTION OF NONUNIFORM AFM PIEZOELECTRIC MICROCANTILEVER

Piezoelectric MCs (MCs) are a special type of MCs. Having self-actuating and selfsensing abilities, they can be used as micro-robots in AFM, sensors and actuators. This paper analyzes sensitivity of vibrating motion of a piezoelectric MC with the presence of geometrical discontinuities. As resonance amplitude and natural frequency are of paramount importance in vibrating motions and they are considered in most engineering applications such as AFM and MEMS, sensitivity analysis of these two parameters is conducted. Vibrating analysis is performed based on the nonuniform beam model and the Euler-Bernoulli theory. The Sobol method is used to conduct sensitivity analysis of MC’s vibrating motion into the geometrical dimensions of layers and tip in order to specify the sensitive and insensitive parameters and their effects on vibrating motion of piezoelectric cantilever. The simulation results show that to achieve actuation ability, it is better to select a piezoelectric layer, which is thin, wide and long, and a tip, which is thin and short. The results also show that the piezoelectric layer has a different effect on natural frequency, as Lp/L becomes 0.66; natural frequency reaches its maximum amount, while the effect of other parameters on frequency is either absolutely ascending or absolutely descending.

Stress Concentration Factor in Functionally Graded Plates with Circular Holes Subjected to Anti-plane Shear Loading

Stress concentration factors due to the presence of geometrical discontinuities (circular holes) in functionally graded plates are derived. The material property inhomogeneity is assumed to be in the radial direction originating at the center of the plate. Variable separable closed-form solutions are obtained for the stresses and displacements in functionally graded plates (without and with holes) subjected to anti-plane shear loading. The stresses in functionally graded plates without a hole are not homogeneous as it is in the case of homogeneous plates. Either a stress concentration (more than the applied stress) or dilution (less than the applied stress) occurs depending on whether the modulus increases (hardening graded material) or decreases (softening graded material) away from the center of the graded plate without a hole. A novel definition of the stress concentration factor due to the geometrical discontinuity in functionally graded plates is derived. The effect of the circular hole in functionally graded plates is to magnify (compared to homogeneous plates) the stress concentration when the modulus decreases away from the center of the hole (softening material). Beneficial reduction of the stress concentration factor is achieved in hardening functionally graded materials.

Notched GFRP: anisotropy, residual strength, and fracture characteristics

This research aims to analyze a study of the mechanical response, in the presence of geometric discontinuity, of glass fiber-reinforced plastics to the uniaxial tensile test. Geometric discontinuity is characterized by a circular hole in the longitudinal section (with reduction of the cross-section) of the composite. In this study, different configuration types are tested, with and without hole, to provide a better understanding of the mechanical properties, with respect to residual strength, anisotropy, and fracture characteristics. The residual strength determined using the precepts given by the ASTM D 5766-07 standard is used in the point-stress criterion and average-stress criterion failure theories for the semi-empirical calculation of the distances ( d0 and a0) in the vicinity of the hole, the region where stress failure occurs. Semi-empirical distances are determined for the composite laminate whose configuration is considered isotropic. The results show the direct influence of the presence of geometric discontinuity and residual strength in all the parameters studied, in addition to fracture characteristics.

Numerical experiments and theoretical analysis of the flow of an elastic liquid of the upper-convected Maxwell type in the presence of geometrical discontinuities

The upper-convected Maxwell model of an elastic liquid is solved by means of the finite element method, using a penalty function approach. It is shown that the algorithm produces oscillations in the stresses in the presence of geometrical discontinuities, for increasing Deborah number De. The cause of this problem is explored and an indication of how to solve this problem is given.

On the Representation of the Electric and Magnetic Fields Produced by Currents and Discontinuities in Wave Guides. I

Electromagnetic scattering problems in cylindrical wave guides, including free space, involve the calculation of the fields produced in the presence of geometrical discontinuities by arbitrary currents. Such discontinuities may be replaced by equivalent electric and magnetic currents. The over-all calculation then leads to two distinct problems: first, the calculation of the fields produced by the prescribed and induced currents in a discontinuity—free guide; second, the self-consistent determination of the induced currents by the condition that the fields so produced satisfy the boundary conditions at the discontinuity surfaces. The first problem is treated herein by representation of the fields in terms of a complete set of vector modes characteristic of the possible transverse field distributions in the guide cross section. This representation transforms the over-all field problem into one-dimensional modal problems of conventional transmission line form. The eigenvalue problem of finding the characteristic modes is discussed in detail for the case of a uniform guide with perfectly conducting walls. The transformation procedure and the solution of the resulting transmission line problem are treated from an impedance point of view. A typical modal analysis and synthesis is presented for the explicit determination of the fields produced by arbitrary electric and magnetic currents in an infinite and semi-infinite wave guide of arbitrary cross section. The connection with a corresponding dyadic Green's function representation (to be treated in Part II) is pointed out.