Notch Effect Research Articles

MEMS capacitive pressure sensor: analysis, theoretical modeling, simulation and performance comparison of the effect of a conical notch

Abstract Micro-Electro-Mechanical Systems (MEMS) pressure sensors are widely used in various applications due to their high sensitivity, low power consumption, and compactness. This work involves the design and simulation of a MEMS-based Touch Mode Capacitive Pressure Sensor (TMCPS). The proposed sensor is based on a substrate with an integrated conical notch featuring a circular diaphragm, aiming to enhance the key performance parameters of the sensor. The integration of a conical notch in the substrate increases the touch area between the diaphragm and substrate compared to the literature, ensuring increased capacitance and capacitive sensitivity. In this work the mathematical analysis of deflection of a circular diaphragm employing thin plate theory, capacitance, and capacitive sensitivity, along with step-by-step explanations, is provided. The results are obtained from MATLAB simulations. The deflection of the diaphragm is validated through Finite Element Analysis (FEA) using COMSOL Multiphysics. The proposed work demonstrates a significant improvement in sensor sensitivity compared to the existing literature.

Notch Effect in Acrylonitrile Styrene Acrylate (ASA) Single-Edge-Notch Bending Specimens Manufactured by Fused Filament Fabrication

This paper analyses the notch effect in the fracture behaviour of acrylonitrile–styrene–acrylate (ASA) material manufactured by fused filament fabrication (FFF). The research is performed on 72 single-edge-notch bending (SENB) specimens containing U-notches with nominal notch radii varying from 0 mm (crack-like defects) up to 2.0 mm, and fabricated with three different raster orientations (0/90, 45/−45, 30/−60). Apparent fracture toughness values are obtained for the different conditions and the resulting notch effect is analysed through the Theory of Critical Distances. A fractographic analysis is also performed using Scanning Electron Microscopy (SEM) in order to justify the fracture (macroscopic) behaviour from the observed fracture micromechanisms. The notch effect observed in the three ASA raster orientations is very similar, and lower than that observed in other FFF polymeric alternatives (ABS, PLA).

Evaluation of U-Notch and V-Notch Geometries on the Mechanical Behavior of PVDF: The DIC Technique and FEA Approach.

The notch effect of semicrystalline PVDF was investigated using U- and V-notch geometries with different depths, and tensile tests were performed at 23 °C using the DIC technique and FEA. Both unnotched and notched dumbbell-shaped specimens were subjected to tensile loading with the DIC technique to obtain mechanical curves and strain maps. The experimental data were compared to a numerical model, analyzing both global mechanical curves and local strain maps around the notch region to assess the accuracy of the simulations. The results demonstrated that the geometry and depth of the notch influence the mechanical behavior of PVDF, presenting a decrease in load and displacement compared to unnotched specimens. This aspect was corroborated by strain maps, which showed the increase in the local strain around the notch tip. For FEA, the global analysis indicated a good correlation with experimental results, and the local analysis demonstrated a reasonable agreement in strain map results within 0.5 mm of the notch neighborhood. Overall, the DIC technique and FEA provided a reliable evaluation of notch behavior on the PVDF used as pressure sheaths with reasonable precision.

Investigating the impact of notch shapes on oxide–oxide ceramic matrix composites strength: A computational approach

AbstractThis study utilizes finite element analysis (FEA) to explore the effect of standardized notch shapes—triangular, circular, and rectangular on the tensile behavior of oxide–oxide (O–O) ceramic matrix composites (CMCs) across various temperature ranges. Findings reveal that unnotched samples exhibited a superior equivalent stress of ∼425 MPa, closely aligning with experimental values. However, under elevated temperatures of 1000°C and 1200°C, degradation occurs, reaching up to 54% decrease at 1200°C. Notched samples demonstrate similar behavior, with all notches acting as stress concentrators. Analysis of single and double notches highlights that circular notches have the most significant stress concentrators due to their smooth surfaces and lack of sharp edges, in contrast to rectangular and triangular notches. Although all notch types influence stress concentration, the absence of non‐sharp corners in circular notches limit stress dissipation, resulting in higher stress concentrations. This trend persists under high temperature as well. The study emphasizes the critical need for a thorough assessment of notch effects, considering their position, orientation, shape, and size, as they significantly affect the mechanical properties of O–O CMCs.

Design and mechanical properties analysis of a novel CFRP tendons anchorage structure

To address the challenges of larger size, stress concentration at the loading end, and insufficient anchoring performance at the free end of traditional bonding-type anchors for Carbon Fiber Reinforced Polymer (CFRP) tendons, a novel anchor featuring a variable angle multi-stage cone is proposed. This solution is derived by analyzing the notch effect at the loading end caused by the wedging of the bonding medium in conventional cone-type anchors. A theoretical model for the stress distribution of the variable angle multi-stage conical anchor was developed using elastic deformation theory. The reliability of this model was validated through finite element analysis. Subsequently, a comparative analysis was conducted to evaluate the stress distribution and anchoring performance of the variable angle multi-stage conical anchor against several traditional anchor types. This analysis revealed the mechanical mechanisms and advantages of the variable angle multi-stage conical anchor in enhancing anchoring effectiveness. The study illustrates that the bonding medium between adjacent cone sections of the variable angle multi-stage conical anchor exhibits a specific gap under stress, leading to reduced stress in the tendon at the connection points. This ensures a smooth transition that prevents abrupt changes in stress due to sudden shape alterations, thereby guaranteeing uniform stress distribution within the anchor section. By incorporating a multi-stage cone structure and increasing the cone angle at the free end, compressive stress can be effectively transferred to the free end, mitigating the notch effect and enhancing anchoring performance. Compared to typical conical anchors, the maximum compressive stress of the variable angle multi-stage conical anchor is reduced by 53.5 %, the outer diameter of the anchor cylinder is decreased by 22.7 %, and the anchoring efficiency is improved by 12.2 %. These improvements result in a robust anchoring effect and significant size advantage. The anchor is suitable for multibar anchoring, providing a reliable solution for large tonnage and long-span cable-stayed bridges.

Strengthening effects of indentation notches on metallic glasses and their sensitivity to stress triaxiality

In this study, a metallic glass sample with an annular indentation notch was successfully constructed by a compression rod cyclic compression strategy using molecular dynamics simulation, and the mechanical behaviors of cut-notched metallic glass samples with the same stress triaxiality and notch size under triaxial compression were comparatively analyzed. It is found that the indentation notch further improves the strength and plasticity of the metallic glass, while it is insensitive to the cut-notched metallic glass with the same notch size. During triaxial compression, rejuvenation and shear softening lead to an increase in free volume, while diffusion and residual compressive stresses lead to a decrease in free volume. The stress triaxiality plays a key regulatory role in their competition and affects the final state of free volume change. This study provides a new theoretical basis and process idea for the enhancement of strength and plasticity of metallic glass.

Multiaxial fatigue life assessment of dental implants

As screwed joints, dental restorations may suffer mechanical failures such as screw loosening and implant or prosthetic screw failure due to fatigue. This work is focused on the failure of the implant and develops a numerical methodology to predict its fatigue life under cyclic loading conditions. This methodology is based on the combination of Critical Plane Methods and the Theory of Critical Distances to account for stress multiaxiality and notch effects. The obtained predictions were validated experimentally, which can be used to identify the main geometrical, assembly and operational factors affecting the fatigue behavior of dental implants. As a result, a powerful and efficient design tool for fatigue life prediction of dental implants is presented. This methodology complements a previously presented one focused on the fatigue life prediction of the prosthetic screw, thereby, offering now a complete design tool package regardless the critical component of the dental restoration, predicting accurately the fatigue response of the restoration, with no need for long-term fatigue test campaigns. This is a pioneering work since no other fatigue design methodology for dental implants with such a solid foundation and experimental validation has been published to date.

Fatigue life prediction of notched components based on energy gradient using reconstructed critical distance theory

AbstractIn this paper, a reasonable explanation is given to unify notch effect and geometric size effect into notch geometric feature effect (NGFE), and energy gradient is utilized to depict the influence of the NGFE on the critical distance. The correlation of energy gradient with critical distance and fatigue life is discussed respectively. The weight index of the high energy region is used to quantify the contribution of the high energy region to the fatigue damage. Finally, a model of the reconstructed critical distance theory considering the geometric notch characteristic effect is established. The fatigue test of Q355 (D) alloy steel notched components was carried out, and the evaluation precision of the presented method is compared with Yang’ model and Shen’ model combining with the existing fatigue test data of En8. The results indicate that prediction results of the proposed method are consistent with the test results.

Experimental and numerical determination of the fatigue notch factor in as‐built wire arc additive manufacturing steel components

AbstractParts manufactured by wire arc additive manufacturing (WAAM) are characterized by a peculiar surface morphology, namely, surface waviness, that negatively affects the fatigue performance. To exploit the full potential of WAAM and minimize the need for postproduction work, it is crucial to utilize the components in the as‐built state. This is because conventional machining techniques, typically employed for postprocessing operations, severely curtail the freedom of geometry of the components. This study focuses on an experimental and numerical characterization of the notch effect of the surface waviness for an AISI 308 LSi stainless steel. This is done by quantifying the fatigue notch factor in a probabilistic fashion, considering the results of ad‐hoc designed fatigue tests. A finite element model is developed by considering a 3D scan of the geometry of WAAMed plates, allowing to determine the theoretical stress concentration factor. The fatigue notch factor is also estimated from the numerical model by making use of the gradient correction according to the FKM guidelines. To validate the numerical approach, test data produced for different testing conditions are correlated by using the local stress approach, showing that classical methods are also applicable to additive manufactured parts.

On the notch sensitivity of as‐built Laser Beam Powder Bed–Fused AlSi10Mg specimens subjected to Very High Cycle Fatigue tests at ultrasonic frequency up to 109 cycles

AbstractThe notch effect significantly influences the fatigue response of components and is particularly relevant for parts produced with additive manufacturing (AM) processes, characterized by complex geometries and possible geometric discontinuities inducing local and critical peak stresses. Moreover, the low surface quality, as well as manufacturing defects and residual stresses, interacts with the local peak stress induced by geometric discontinuities, complicating the assessment of the notch effect for AM parts and requiring extensive experimental fatigue investigations. In the present paper, the notch sensitivity of as‐built AlSi10Mg specimens produced with the laser beam powder bed fusion in the Very High Cycle Fatigue regime is investigated. Ultrasonic fatigue tests up to 109 cycles have been carried out on rectangular bars and rectangular bars with a central through‐thickness hole. The notch effect has been found to significantly affect the fatigue response of the investigated AlSi10Mg specimens, with surface defects having a main role and pointing out the influence of the surface quality on the crack formation.

Assessment of structural materials containing notch-type defects: A comprehensive validation of the FAD-TCD methodology on metallic and non-metallic materials

This paper provides a comprehensive description, and the subsequent validation, of a structural integrity assessment methodology of structural materials containing notch-type defects. The approach is based on the combination of Failure Assessment Diagrams (FAD) and the Theory of Critical Distances (TCD). The former provides the general assessment tool, which is exactly the same one as that used for crack-like defects, whereas the latter provides the notch effect correction required for the analysis of this type of defects. Finally, the proposed methodology is validated on a number of metallic and non-metallic structural materials, with 1,106 experimental results on different types of testing specimens, covering four structural steels, aluminium alloys 7075-T651 and 6060-T66, PVC, PMMA, PA6, fibre-reinforced PA6, 3D printed (Fused Filament Fabrication) ABS, PLA and graphene reinforced PLA, granite and limestone. The results show how the FAD-TCD methodology provides safe reasonably conservative assessments on the mentioned structural materials in the presence of notch-type defects.

Cancelling the effect of sharp notches or cracks with graded elastic modulus materials

Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, σ∼rα, with a modulus varying as E∼rβ. In the inhomogeneous case the order of singularity of the LEFM case decreases if β>0, as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the “rounding” of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which eliminates size-scale effects due to singular stress fields, with potentially very wide applications.

Carbon-Aramid Fiber/Epoxy Hybrid Composite Laminates with the Presence of Defect: An Experimental Study

Abstract Carbon-Aramid fiber-reinforced epoxy has been used extensively in the aerospace and automobile industries. The combination of high-strength carbon fiber and the high toughness of aramid fiber is believed to be beneficial to the structural behavior of composites. In the current study, Aramid fiber was sandwiched between carbon fiber layers to maintain high strength and toughness simultaneously. The behavior of the laminate with the presence of an open hole and single-edge notch was investigated. For justification, the response of the hybrid laminate was compared with two other laminates, one is made totally from carbon fiber-reinforced epoxy (CFRP) and the other is made from aramid fiber-reinforced epoxy (AFRP). The effect of an open hole was assessed by a tension test, while the single-edge notch effect was evaluated by the flexural test. Tensile and flexural tests were also performed on the regular samples. As per the current results, the notch sensitivity of hybrid laminate was found to be less than that of CFRP laminate. The CFRP laminate failure type was dominated by delamination. AFRP composite laminate failure was dominated by fiber breakage and crack propagation through the matrix. The hybrid composite laminates were dominated by fiber breakage of the AFRP laminates and delamination of CFRP outer layers. The flexural modulus of hybrid laminate resulted in the greatest value, followed by CFRP and AFRP. The hybrid laminate’s fracture toughness is significantly higher than that of CFRP but lower than that of AFRP.

Combining phase field method and critical distance theory for predicting fatigue life of notched specimens

Notch features, widely used in engineering components, have negative effect on the fatigue life of structural parts due to the stress concentration caused by their geometry. This highlights the importance of numerical methods to help assessing the adverse effect of geometrical discontinuities like notch on the fatigue properties of structural components. In this study, a new phase field fatigue formulation was proposed to predict the fatigue behavior of metallic notched specimens, suggesting a dimensionless parameter based on the critical distance theory to capture the notch effect. The slope of S-N curve was regarded as a function of the effective stress ratio obtained from different critical distances, and the fatigue damage threshold was varied with the slope of the S-N curve. Two S-N curves of smooth and notched specimens were used to calibrate the fatigue model parameters for each material. Numerical examples validated by experimental data of various configurations in terms of geometry, stress ratio and loading mode indicated the validity of the proposed model and its ability to accurately predict the fatigue life of notched specimens with different notch geometries and materials, as the predicted fatigue lives mostly fell within the ± 2 scatter band. The results indicated that compared with the traditional TCD method the proposed model eliminates the requirement to recalculate the critical distance at different fatigue lives, and the stress ratio effect can be naturally captured without recalibrating the critical distance.

Mechanism of thermal exposure on the mechanical properties of microtextured Ti60 alloys

In this study, the mechanism of thermal exposure on the mechanical properties of two Ti60 alloys with different micro-texture regions (MTRs) was systematically investigated through macro- and microstructural characterization. It was found that when the alloy was exposed to prolonged thermal exposure at 600 °C for 100 h, the strength of the no-MTR samples increased significantly and the plasticity decreased sharply. In contrast, the MTR samples showed a sharp decrease in strength and plasticity due to the transmissibility of dislocation slip and crack propagation, resulting in the formation of a continuous brittle cleavage plane on the fracture. Meanwhile, the oxide film formed on the surface promotes the formation of early cracks and cleavage planes, and the oxide film serves as the location of surface crack nuclei and creates a notch effect leading to premature fracture of the alloy. It is further found that the oxide film is mainly composed of alternating nanocrystalline grains of Al2O3 and TiO2, and there is an oxygen-rich layer of Ti3O near the matrix, and these nano-oxides increased the brittleness of the oxide film. The strengthening and embrittlement mechanism of the alloy was revealed based on the deformation characteristics, i.e. the plasticity reduction was attributed to the formation of the oxide film and precipitation of the α2 phase on the surface, whereas the inhomogeneous distribution of the α2 phase in the interior led to the formation of microcracks in the interior. The precipitation of (Ti, Zr)6Si3 phase at grain boundaries hinders the dislocation motion and leads to a significant increase in the strength of No-MTR alloys. This study reveals the effects of interactions between MTRs, oxide films and precipitated phases on the thermal exposure properties of Ti60 alloys, providing theoretical support for the stability of titanium alloy properties at elevated temperatures.

Effects of Notches on Breakdown Pressures and Fracture Evolution in Hydraulic Fracturing

AbstractSustainable ore extraction in cave mining heavily relies on the effective fragmentation or caveability of the orebody. Since cave mining offers substantial benefits, it has gained popularity after preconditioning was introduced to help improve caveability. Therefore, hydraulic fracturing serves as a vital technique for risk management and cave stimulation. The increased rock competency and high stress levels in the rock mass around the orebody significantly influence fracturing and, thus, cavability processes. In order to improve the çefficiency of preconditioning by hydraulic fracturing to specific parts of the non-caving or poorly caving formations, the use of notches as artificial flaws offers an influence on the directionality of fracture propagation; this approach also has the potential to decrease the necessary breakdown pressures, thereby lifting limitations on the design and mechanical capabilities of fracturing campaigns and reducing required breakdown pressures, which could improve hydraulic fracturing capabilities. In this study, we studied the effects of notches on hydraulic fracturing performance under varying stress conditions. A number of hydraulic fracturing experiments were conducted using different notch quantities and spacings. Notches were created parallel to the axis of confining stress, and specimens were then subjected to constant axial loads of 40 MPa under varying confining pressures ranging from 5 to 40 MPa. A supplementary 3-D discrete element method using 3DEC was performed, and the results were compared with the hydraulic fracturing experiment. The 3DEC models incorporated Darcy's Law to describe fluid flow through fractures, and the Mohr–Coulomb softening yield criterion was used to simulate failures on predefined surfaces, providing a thorough hydro-mechanical coupled solution. We found that introducing notches can effectively reduce the pressures needed for fracture initiation and growth. Moreover, with appropriate spacing, fracture direction can be controlled. This knowledge, combined with the use of numerical modelling, has advanced our understanding of fracture behaviour and the influence of notches on propagation paths under different stress regimes. These findings could potentially revolutionise the field of hydraulic fracturing, making it more efficient and sustainable.

The Effect of Stacking Sequence and Ply Orientation with Central Hole on Tensile Behavior of Glass Fiber-polyester Composite

An experimental investigation was carried out to study the effect of circular cross-holes on the failure behavior of unidirectional glass fiber reinforced with unsaturated polyester resin composites, varying cross-ply laminates that were subjected to axial tensile load. This paper deals with the effects of the circular notch and the number of plies on nominal tensile and net tensile strengths. Tensile strengths were investigated for composites with cross-ply([0/90]. [90°/0°/90°] and [0°/90°/0°].90°), orientation and varying the laminate layers with a central hole, and effects of volume fraction and number of ply on mechanical properties for un-notched (smooth) and notched specimens were also studied. The results showed that increasing the number of plies has a marginal effect on tensile strength values. The fraction of volume has significant effects and for increasing the number of plies about 9% decreases in nominal tensile strength and about 11% decrease in the net tensile strength was observed. The same results were obtained with finite element analysis.

Fatigue lifetime predictions of notched specimens based on the critical distance and stress concentration factors

The theory of critical distances is used for evaluation of effects of notches on load-bearing capacity of notched components under static or cyclic fatigue loading. The theory can also be used to predict the fatigue life of notched components. One of the assumptions for a reliable prediction is that the critical distance is independent of the notch geometry and its stress concentration level. The study shows that the critical distance depends not only on the number of cycles to failure (under fatigue loading), but also on the notch radius. In this case, direct use of the critical distance leads to unreliable predictions. The study quantifies the relation between the model notch (from which the critical distance is determined) and the predicted notch by means of the ratio of their stress concentration factors. The predictions modified by the ratio of stress concentration factors provide results that are in satisfactory agreement with the experimental data. The predictions were made and verified on the basis of fatigue data measured on two stainless steels 1.4306 and 1.4307, and high strength structural steel S690QL. Smooth and notched specimens were tested on an ultrasonic fatigue machine in a symmetrical tension–compression mode. The results were evaluated in the regions of high cycle and very high cycle fatigue.

Influence of the as-built surface and a T6 heat treatment on the fatigue behavior of additively manufactured AlSi10Mg

As the fatigue strength of materials manufactured via lase-based powder bed fusion (PBF-LB) is highly influenced by process-induced defects and the “as-built” surface, in this work fatigue tests at specimens made of AlSi10Mg with “as-built” and polished surface condition were conducted. In this context also the defect tolerance of the material, and hence its ability to counteract process-induced notch effects, was analyzed. For this, specimens in a not heat-treated and an artificially aged (T6) condition were tested. For the not heat-treated specimens, a high reduction of the fatigue strength due to the “as-built” surface is observed, while the heat-treated specimens exhibit no influence of the surface condition. Using the √area approach, it is demonstrated that the smaller fatigue strength due to “as-built” surface observed for the not heat-treated condition results from process-related residual tensile stresses, which are removed by T6 heat treatment and polishing, respectively. Moreover, the results show that the “as-built” surface leads to similar stress concentrations than defects in the specimen volume, and thus, polishing had no influence on the fatigue performance after heat treatment. In addition to these findings, an increased fatigue strength after T6 heat treatment was observed, which is caused by an increased defect tolerance.

Comparison of analytical and numerical methods for estimating notch strains**

AbstractIn fatigue assessments, local strains and stresses can be easily evaluated using accurate finite element analysis in a case of an individual fatigue‐critical notch or structural detail. In practical design and analysis of global models, the consideration of local notch effects using suitable estimation rules in the combination with linear elastic analysis is reasonable. Various notch rules exist but the current knowledge lacks understanding how applicable different notch rules are for estimating notch strains from elastic stresses. This work studies the Neuber′s rules for sharp and mild notches, Glinka′s equivalent strain energy density method, the correction of Neuber′s rule proposed by Sonsino for mild notches, as well as the Seeger‐Beste method. The application of different estimation rules for notch strains, applied to the elastic‐perfectly plastic steel material and to Ramberg‐Osgood material model for the aluminum material, including work hardening effect, was studied in this work by comparing the estimations with the corresponding experimental data and finite element analysis results. The Neuber′s rule for mild notches and Sonsino′s averaging method gave best correlations with the experimental data and numerical (finite element analysis) results and can be thus recommended for such analyses in compatible cases studied in this work.