Notch Apex Research Articles

Superior Gluteal Nerve Anatomy and Its Injuries: Aiming for a More Secure Surgical Approach of the Pelvic Region.

Because most of the recognized causes of superior gluteal nerve (SGN) injury are iatrogenic, detailed knowledge of the anatomy of the SGN is crucial to prevent its injury associated with surgical procedures. This study aims to describe the precise location of SGN or its branches at the greater sciatic foramen, measure the distances of these neural structures to palpable bony landmarks, and evaluate the possible correlation between these parameters and pelvis size. Twenty human cadaveric hemipelvises were studied. After dissection to expose the SGN or its branches at the greater sciatic foramen, the distances from these neural structures to the greater trochanter (GT), to the anterior superior iliac spine (ASIS), to the posterior superior iliac spine (PSIS), to the ischial tuberosity (IT), and to the greater sciatic notch apex were measured. We found that at the greater sciatic foramen, the SGN emerges as a common trunk in 75% of hemipelvises, and already divided in its superior and inferior branches in 25% of hemipelvises. When the SGN exits the pelvis as a common trunk, it does so, in most cases, in contact with the bone at the apex of the greater sciatic notch or superior to the level of the apex. The median distance from the SGN at the greater sciatic notch to the PSIS, ASIS, GT and IT is 7.6 cm, 10.9 cm, 7.5 cm and 10.8 cm, respectively. We found a positive correlation between some of the analyzed parameters and the size of the pelvis. The anatomical data of this study may serve as pivotal guides during orthopedic pelvic surgery, contributing to minimize SNG iatrogenic lesions with significant implications in the patient's quality of life.

Combined notch and size effect modeling of metallic materials for LCF using plasticity reformulated critical distance theory

Fatigue assessment of notched parts plays imperative performance in structural integrity and reliability of major equipment. The theory of critical distance (TCD) involves determining the fatigue strength of notched parts from the linear elastic stress field surrounding the notch apex. In addition, the fatigue strength of engineering part is also size dependent. Accordingly, by coupling a plasticity reformulated TCD with the weakest link theory, this study elaborates a novel scheme for probabilistic low cycle fatigue (LCF) analysis under notch and size effects. Results of fatigue tests and complementary FE analysis with the proposed model is utilized to compute highly stressed volume (HSV). Furthermore, test data of titanium alloys TC4 (Ti-6Al-4V) and TC11 (Ti-6.5Al-3.5Mo-1.5Zr-0.3Si) as well as aluminum alloy 7075-T6 are utilized for model verification. Results specify that the model predicted P–S–N curves are in good agreement with experimental data.

DEM/FEM simulation of the shot peening process on sharp notches

The residual stress field produced by shot peening on Al-7075-T651 prismatic samples carrying V-edge notches is evaluated through combined Discrete Element Modeling (DEM) and Finite Element Modeling (FEM) simulations. Special care is paid to faithfully model the interaction between peening nozzle, shots and notched target through DEM analyses and to understand the coverage level at the notch root. The simulated stream of shots with randomly distributed size, location and velocity is imported into an explicit dynamic FE model of a neighborhood of the notch tip. The resulting residual stress (RS) field is compared to the RS field computed using thermal fields in a FEM simulation, calibrated with experimental data collected through Micro-hole Drilling, Micro-slot Cutting and Micro-X-ray Diffraction techniques. The obtained results are in good agreement with experimentally reconstructed RS and suggests the hypothesis that the notch tip RS field is dictated only by impacts occurring in the very vicinity of the notch apex.

Studying Thermal Shock Resistance of Ceramic Materials Based on Their Structural Sensitivity to a Stress Concentrator

A method for determining the thermal shock resistance of ceramic materials is proposed based on their structural sensitivity to a stress concentrator controlling fracture during thermal loading. For this purpose, a prismatic sample with a specially created notch (stress concentrator) was subjected to thermal cycling realized by heating it to 850°C and cooling with a water jet (20°C). The coolant was supplied to the notch apex of the heated sample (local thermal shock (LTS) technique). By using the LTS technique, the thermal shock resistance of the following 3 types of ceramic materials was studied: α-Al2O3(type 1), α-Al2O3– β-SiC whiskers (20 vol.%) (type 2) and t-ZrO2 partially stabilized with Y2O3 (3.5 mol.%) (type 3). Type 2 ceramics has the highest thermal shock resistance, type 3 ceramics—the lowest, and type 1 ceramics occupies an intermediate position among the studied materials, which is associated with the specifics of formation and distribution of thermal defects in the structure of these ceramic materials as a result of using the LTS technique. The advantage of the latter consists in an explicit reproducibility of the results of determining thermal shock resistance (RT) within the studied batch of samples (measurement accuracy 3 – 5%).

Cortical Bone Thickness and Morphological Variation in the Greater Sciatic Notch of the Human Pelvis

This study analyzes the relationship between cortical bone thickness and shape in the greater sciatic notch (GSN). This bony feature is sexually dimorphic in humans, with males typically exhibiting narrow GSNs and shorter posterior aspects, or cords. In contrast, females typically exhibit wide notches with expanded posterior aspects and more even anterior and posterior cords. The expanded posterior aspect in females appears to contribute to spacious birth canals and is often attributed to obstetric selection. Nevertheless, the proximate mechanisms that produce pelvic sexual dimorphism are unclear.Here I assess GSN variation in 48 females and 50 males aged 0–20 years using decedent computed tomography (CT) data from the Center for Forensic Imaging at the University of New Mexico. I measured cortical bone thickness at the GSN edge and at the pelvic and gluteal aspects adjacent to the notch in Amira software on CT slice planes axial to the posterior and anterior cords. Paired t‐tests assessed cortical thickness differences between the anterior and posterior cords in the three regions. Relative cortical thicknesses were calculated in each of the three regions as the ratio of cortical thickness of the posterior GSN cord to that of the anterior cord. Two‐block partial least‐squares (2B‐PLS) analysis assessed the relationship between relative cortical thicknesses and GSN shape as measured by Procrustes‐aligned 3D landmark coordinates.I also tested for the effects of age on GSN shape and relative cortical bone thickness. For example, results from the 12–14 year and 15–20 year age cohorts indicate that the difference in cortical bone thickness between the posterior and anterior GSN cords at the gluteal aspect is significant (p<0.01), with the posterior cord typically showing greater cortical thickness in this region. Results from the 2B‐PLS analyses suggest moderate but not significant covariation between GSN shape and relative cortical thickness. Among 12–14 year‐olds, deeper GSNs trend with a greater amount of cortical bone in the posterior cord relative to the anterior cord. Among 15–20 year‐olds, greater relative cortical bone in the posterior cord at the GSN edge and gluteal aspect tends to be associated with a lack of a piriform tubercle and a posteriorly displaced notch apex, such that the posterior GSN cord appears shorter. Less relative cortical thickness in the posterior cord tends to be associated with a prominent piriform tubercle and anterior expansion of the superior portion of the anterior cord, such that the notch appears relatively wider. Variables do not clearly associate by sex.Greater cortical thickness in the posterior GSN cord's gluteal aspect relative to that in the anterior cord suggests that the former can better withstand compressive strains related to bipedal posture. Despite insignificant covariation, moderate relationships between relative cortical bone thickness and GSN shape, particularly in terms of notch expansion patterns, suggests that biomechanical mechanisms contribute to GSN morphological variation.This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Estimating Lifetime of Notched Components Subjected to Variable Amplitude Fatigue Loading According to the Elastoplastic Theory of Critical Distances

The present paper is concerned with the use of the elastoplastic theory of critical distances (TCD) to perform the fatigue assessment of notched components subjected to in-service variable amplitude (VA) fatigue loading. The elastoplastic TCD takes as its starting point the assumption that the detrimental effect of stress/strain concentrators of any kind can efficiently be taken into account by directly postprocessing the entire elastoplastic stress/strain field in the vicinity of the notch apex. Thanks to its specific features, the TCD can be formalized in different ways by simply changing size and geometrical features of the domain used to calculate the required effective stress. The so-called point method (PM) is the simplest form in which this theory can be applied. This formalization of the TCD postulates that the elastoplastic stress/strain state to be used to estimate fatigue damage has to be determined at a given distance from the tip of the notch being assessed. According to the TCD's philosophy, such a distance is treated as a fatigue property. Therefore, given the material, this critical length does not change as either the features of the assessed stress/strain concentrator or the profile of the investigated loading path vary. In the present study, the above design strategy is attempted to be used to estimate lifetime of notched component subjected to VA loading, the required critical distance being determined under constant amplitude (CA) loading. The accuracy and reliability of the devised approach were checked by using a number of experimental results generated by testing, under both concave upward and concave downward spectra, notched samples containing geometrical features having a different sharpness. Such a validation exercise allowed us to prove that the elastoplastic TCD, used in the form of the PM, is highly accurate in estimating fatigue damage also in notched components subjected to in-service VA loading.

Strength of polymer composites used in automotive industry

The article is devoted to research on the impact of the size of a curvature radius of fracture-like notch apex on the critical values ​​of the stress intensity factors in the dispersion-reinforced composite materials.

Prediction the Charpy impact energy of functionally graded steels

Article history: Received September 20, 2013 Received in Revised form October, 14, 2013 Accepted 15 December 2013 Available online 20 December 2013 Functionally Graded Steels (FGSs) are possible solutions to improve the properties of steels made by Martensite and Bainite brittle phases. These phases are usually present in the interface between the carbon ferritic steel and the stainless austenitic steel. FGSs materials are widely investigated in the recent literature but only few works have been devoted to investigate the impact energy in the case of crack arresters. To partially fill this gap, the effect of the distance between the notch tip and the position of the median phase on the Charpy impact energy is investigated in the present paper. The results show that when the notch apex is close to the median layer the impact energy reaches its maximum value due to the increment of the absorbed energy by plastic deformation ahead of the notch tip. On the other hand, when the notch apex is far from the median layer, the impact energy strongly decreases. Keeping into account the relationship between the Charpy impact energy and the plastic volume size, a new theoretical model has been developed to link the composite impact energy with the distance from the notch apex to the median phase. The results of the new model show a sound agreement with previous results taken from the literature. © 2013 Growing Science Ltd. All rights reserved.

Numerical analysis of the singularities for a magneto-electro-elastic notch under anti-plane deformation

Due to the capability of the conversion between mechanical, electric and magnetic energy, magneto-electro-elastic (MEE) materials can be applied to design sensors, actuators and other smart products. The notch and interfacial edge problem can always be encountered in these products. The singularity phenomenon is that the stress, electric displacement and magnetic induction may become theoretical infinite due to the materials or geometrical discontinuities at the vertex of notch. In practices, the mechanical failure or dielectric breakdown may initiate from the notch apex due to this high singularity. The present paper is trying to establish a new method to study the singularity at the vertex of notch encountered in MEE structures. Basing on the asymptotic assumption for the physical field near the notch tip, the singularities for a MEE notch under anti-plane deformation are investigated by the eigenfunction expansion approach. The characteristic differential equations respects to the singularities of the MEE notch are built from the equilibrium equations and Maxell equations. At the same time, the mechanical and electric boundary conditions together with the interfacial continuous conditions are expressed by the combination of the singularity orders and characteristic angle functions. Thus, the evaluation of the notch singularity orders is transformed into the problem of solving the ordinary differential equations under the designated boundary conditions. The singularity orders and the corresponding characteristic angle functions can be achieved by applying the interpolate matrix method to solve the obtained characteristic differential equations. The achieved results can provide the guidelines for the selection of notch angles and materials to reduce the singularity for the structure design of MEE products.

Effect of notch on fatigue behaviour of a directionally solidified superalloy at high temperature

ABSTRACTThe effect of notch types and stress concentration factors (Kt) on low cycle fatigue life and cracking of the DZ125 directionally solidified superalloy has been experimentally investigated. Single‐edge notched specimens with V and U type geometries were tested at 850 °C with stress ratio R = 0.1. High temperature in situ optical method was used to observe crack initiation and short crack propagation. Scanning electron microscope observation of fracture was used to analyse the failure mechanism. The results reveal that fatigue resistance decreases with Kt increasing from 1.76 to 4.35. The ratcheting is found to be affected by both Kt and the nominal stress from the displacement–force curve. In situ observations indicate that the cracking does not occur at the notch apex but at the location where the max principal stress or Hill's stress is the highest. According to the scanning electron microscope observations, the failure of the notched specimens strongly depends on the anisotropy microstructures.

A new analytical expression for the relationship between the Charpy impact energy and notch tip position for functionally graded steels

The effect of the distance between the notch tip and the position of the middle phase in the FGSs on the Charpy impact energy is investigated in the present paper. The results show that when the notch apex is close to the middle layer, the Charpy impact energy reaches its maximum value. This is due to the increment of the absorbed energy by plastic deformation ahead of the notch tip. On the other hand, when the notch tip is far from the middle layer, the Charpy impact energy strongly decreases. Another fundamental motivation of the present work is that for crack arrester configuration, no accurate mathematical or analytical modelling is available up to now. By considering the relationship between the Charpy impact energy and the plastic volume size, a new theoretical model has been developed to link the Charpy impact energy with the distance from the notch apex to the middle phase. This model is a simplified one and the effect of different shapes of the layers and the effect of microstructure on the mechanical properties and plastic region size will be considered in further investigation. The results of the new developed closed form expression show a sound agreement with some recent experimental results taken from the literature.

Staging of a localized plastic deformation upon the tension of Д16AT alloy specimens on the basis of acoustic emission, surface deformation mapping, and strain gauging data. II. Specimens with notches of different depths

Studies of the development of deformations and damage in Д16AT alloy specimens with side notches, which modeled cracks in objects, were performed by combining the acoustic emission, surface deformation mapping, and strain gauging methods. It was shown that a significant portion of the loading time is associated with crack propagation, which is accompanied by the appearance of a segment with a negative value of the strain strengthening coefficient in loading diagrams. According to the data from the correlation of digital images at the plastic deformation stage (within stage 2), two substages were distinguished: the first is related to the deformation localization directly at the notch apex, while the second is associated with an increase in the area of this region to dimensions that are comparable with the specimen cross section. It was revealed that, in the case of a significantly localized deformation, the staging-based approach to the analysis of deformation and fracturing processes is characterized by the better correlation between data that are recorded by different in situ methods.

Two approaches to taking nonsingular T-stresses into account in the criteria of fracture mechanics for bodies with notches

Two possible models and criterion equations of fracture mechanics for bodies with notches taking into account nonsingular expansion terms of stresses at the notch (crack) apex based on crack-growth resistance diagrams and a master curve are considered. A criterion equation of a generalized crack-growth resistance diagram admissible for a body with a crack and a notch and taking into account the changes in the degree of strain constraint at the notch apex due to finiteness of its apex radius rounding and a nonsingular stress component (T-stresses) is given. The notion of effective T-stresses determined using averaging of T-stresses in front of the notch apex in the pre-fracture zone characterized by effective scattering in introduced. A basic dependence of fracturing viscosity in the function of effective T-stresses (a master curve) of pipe steel is constructed for the given notch geometry.

A microsystem for the fracture characterization of polysilicon at the micro-scale

Abstract To characterize the effective fracture energy G IC of polysilicon wafers at room temperature, an on-chip MEMS test structure has been designed and fabricated. The device can provide fatigue pre-cracking at the notch apex and subsequently impose a monotonical load up to failure. The proposed procedure combines the experimental data with outcomes of numerical simulations. A continuously monitored decrease in stiffness of the system is linked to the crack length and the effective fracture energy for the non-standard geometry of the testing device. An average value of G IC = 12.0 ± 1.8 N m −1 is found. These values are then used in numerical micro-scale fracture analyses taking into account the material heterogeneity due to the grain structure and reproducing the crack propagation process with a cohesive approach.

Fracture mechanics approaches in the analysis of strains and fractures of bodies with notches and scotches

Fracture mechanics models and criteria for bodies with cracks have been developed to analyze strains and fractures of bodies with notches and scotches. Criterion equations and corresponding crack growth resistance diagrams for a body with a notch taking into account the changes in the degree of strain constraint at the notch apex due to finiteness of its apex radius rounding and a nonsingular stress component (T-stresses) have been considered. Analytical relations for calculating the J-integral in the case of bodies with blunt U-and V-notches under elastic and plastoelastic loading have been given. Capabilities of the method of separable functions for the experimental study of plastoelastic crack growth resistance for nonstandard samples with scotches have been presented.

Evaluation of the Thermal Resistance of Structural Ceramics in Testing Notched Prismatic Samples

The considered approach to determining thermal resistance in structural ceramics involves thermal cycling of samples with a special notch. The proposed thermal resistance characteristics include the loss of crack resistance after a thermal shock, the insensitivity of the material structure to defects formed at the notch apex as the result of a thermal shock, and the degree of defect accumulation at the notch apex. The testing results of ceramics made of Al2O3, ZrO2, partly stabilized Y2O3 (molar part 3%), and cermet ZrO2 – Y2O3 (molar part 3%) with metallic chromium additive (50 vol.%) are indicated.

On the extraction of notch stress intensity factors by the post-processing of stress data on the free edges of the notch

Following on the lines of a previous paper dedicated to cracked components by Ciavarella et al., here the case of a notch of semi-angle α is considered. Contrary to the crack case (α = 180°), the free edges of the notch are easily accessible to experimental analysis; moreover they provide information about all the terms of the Williams series expansion of the stress field about the notch apex, including the most important, i.e. the symmetric and antisymmetric singular term notch stress intensity factors (N-SIFs), whereas for the crack case the mode I N-SIFs cannot be extracted from those stresses. Another important different feature is that symmetric and antisymmetric N-SIFs have different singularities, and in several cases they are so close that their contributions tend to overlap. Therefore, a simple procedure is here proposed to use radial stresses, to separate their symmetric and antisymmetric contributions a priori by computing the sum and difference of the stresses on the two edges, to post-process these quantities in the ‘asymptotic region’ with standard least-squares techniques and to extract the N-SIFs. The method is applied to a simple case known in the literature and solved by means of a boundary element code, and the results are almost coincident with previous results, even with quite coarse mesh discretizations.

The elastic interaction between solute atoms and stress field at the tip of cracks and notches

As for a mechanical interaction between a general stress singularity and an-environmental factor (e.g. hydrogen) which has influence on delayed failure characteristics of materials, it has not hitherto been analysed, although it is an important problem. In the present article an analytical basis is given for the problem of elastic interaction between solute atom as an environmental factor accelerating delayed failure and stress field around a crack and further a general V-shaped notch. The result of analysis shows that the number of solute atoms which accumulate to crack tip due to elastic interaction is proportional to a parameter. ρ 0( DKt kT ) 4 5 where K is stress intensity factor,ρ 0 initial uniform density of the solute atom, D diffusion constant, t time, k Boltzman's constant and T absolute temperature. It is further shown that the abovementioned parameter is generalized to ρ 0( Dkt kT ) 2 (2+q) for the number of what accumulate to the apex of a general V-shaped notch due to elastic interaction where k is a factor representing a stress singularity of the notch apex and q is a constant related to apex angle a. The above analysis indicates that it is possible to describe development of delayed failure in terms of a parametre of fracture mechanics K, when viewed from a standpoint inclusive of diffusion and mechanical processes, since it is shown that the rate of concentration to crack tip of solute atoms as an environmental factor is uniquely determined by a factor ρ 0( DK kT ) 4 5 .