Stress Concentration Coefficient Research Articles

The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity

We consider a two-dimensional system of differential equations of the moment theory of elasticity. The general solution of this system is represented by two arbitrary harmonic functions and solution of the Helmholtz equation. Based on the general solution, an algorithm of constructing approximate solutions of boundary value problems is developed. Using the proposed method, the approximate solutions of some problems on stress concentration on the contours of holes are constructed. The values of stress concentration coefficients obtained in the case of moment elasticity and for the classical elastic medium are compared. In the final part of the paper, we construct the approximate solution of a nonlocal problem whose exact solution is already known and compare our approximate solution with the exact one. Supposedly, the proposed method makes it possible to construct approximate solutions of quite a wide class of boundary value problems.

Bearing characteristics of coal pillars based on modified limit equilibrium theory

There are two states for the coal-mass on the goaf-side which is in stress equilibrium: the state of limit equilibrium (the bearing stress in the coal-mass equals its ultimate bearing stress) and the state of non-ultimate equilibrium (the bearing stress in the coal-mass is less than its ultimate bearing stress). To analyze the bearing characteristics of a coal pillar in the state of limit equilibrium and guide the design of pillar width, we established a mechanical analytical model of the non-ultimate equilibrium zone in the coal-mass on the goaf-side combined with the limit equilibrium theory as well as adopting the methods of theory analysis and mechanical analysis based on the assumption of a state of non-ultimate equilibrium. The width correction coefficient of the limit equilibrium zone has been given. The influence of mining depth, stress concentration coefficient of the surrounding rock, the non-limit strength of the coal-mass and stability of the coal rock interface has been studied. On this basis, we have confirmed that when the width of a longwall mining face roadway protection coal pillar is between 11.6m and 13.16m in No. 4 coal seam of Xinrui coal mine in Lvliang in Shanxi province the elastic core region in the coal pillar can be assured and the roadway will be located in the area of lower stress which is outside the peak stress. So the revised width of the limit equilibrium zone is more practical.

Comparative Spatially Resolved Characterization of a Czochralski-Grown Silicon Crystal by Different Laser-Based Imaging Techniques

The axial distribution of electrical and optical properties of a 4 inch Czochralski-grown silicon single crystal were analyzed by different methods that can be applied in the scanning mode. These methods were tested with respect to the suitability to reveal growth striations. The residual stress was visualized by SIRIS (Scanning Infrared Stress Inspection System) and SIREX (Scanning Infrared Stress Explorer), the electrical resistivity by LPS (Lateral Photovoltage Scanning) and SRP (Spreading Resistance Profiling), and the lifetime of the minority charge carriers by MDP (Microwave Detected Photoconductivity) mapping. The concentration of interstitial oxygen (Oi) across the growth striations was determined by FTIR (Fourier Transform Infrared) spectroscopy. We demonstrate for the first time on the micrometer scale that the Oi scan is very well-correlated with the profile of Δσ (difference of the in-plane principal stress components). The stress field is tensile oriented in growth direction, i. e. perpendicularly to the growth striations. The stress-concentration coefficient has been estimated to be in the order of 10-13 Pa cm-3 what does agree well with previous XRD results.

Stress concentration coefficient in a composite double lap adhesively bonded joint

The main target of this paper is to investigate the effect of peak stress at the extremities of the adhesive layer of a bonded assembly subjected to dynamic shear impact. It is known, that under both static and dynamic loadings such joints endure at their extremities high level of stresses, an aspect known as edge effects. Double lap joint assembly was considered with unidirectional carbon–epoxy substrates and Araldite 2031 adhesive. To quantify this edge effect, a specific coefficient, named coefficient of stress concentration was defined: it is the ratio of the maximum shear stress to the average shear stress. This coefficient helps to calculate maximum strength of the joint since experimentally, only average shear stress could be measured. A numerical analysis at the midplane of the joint was carried out to investigate the effect of geometrical and material parameters on this stress concentration factor. It was found that this factor is constant with the time once the equilibrium is established. Moreover, this stress concentration coefficient decreases with higher Young's modulus of the adherents, lower Young's modulus of the adhesive, thicker and shorter adhesive layer. A unified parameter involving geometrical and mechanical parameters of the specimen was established to quantify this stress concentration factor.

Evaluation of the Ground Response of a Pre-driven Longwall Recovery Room Supported by Concrete Cribs

Pre-driven recovery rooms allow for the safe and rapid extraction of longwall panel face equipment. Optimum support design requires an understanding of the loading mechanisms of pre-driven longwall recovery rooms subjected to large abutment pressures. This paper presents a case study evaluating the ground response of a pre-driven recovery room. The recovery room was supported by a rock bolt and cable support system in conjunction with two rows of concrete cribs. A numerical analysis of the pre-driven recovery room was conducted using the distinct element code UDEC. The numerical results were found to be in good agreement with field observations in terms of the patterns and magnitude of stress changes, roof-to-floor convergence and failure patterns. The present results suggest that the stresses carried by the outby pillar and inby fender began to significantly increase when the longwall face was approximately 20 m away. When the longwall face entered the recovery room, the stress concentration coefficient ranged from 3.0 to 3.5 in the inby fender and from 2.0 to 2.5 in the oubty pillar, resulting in spalling failure of the room ribs. The set of longwall face equipment was safely and successfully recovered. The concrete cribs, in conjunction with the rock bolts and cables, were considered effective, but conservative. It was also found that the stiffness of the concrete crib is critical to the ground response and must be considered when determining the required capacity. From the study results, design guidelines for determining the optimal support requirement of a pre-driven recovery room are proposed.

Effect of Double Shot Peening on Room-Temperature Notched Fatigue Property of TC4 Titanium Alloy

Single shot peening (SSP) with cast-iron shot and double shot peening (DSP) with cast-iron shot and ceramic shot were applied to investigate the relationship between surface integrity status and the fatigue property of titanium alloy TC4 on the notched specimens (stress concentration coefficient Kt=1.7). Surface roughness, residual stress profile and fatigue curve of the notched specimens were tested using scanning profilometer, XRD residual stress tester and rotating-bending fatigue testing machine, respectively. The results showed that surface roughness decreased 18.3% from Ra 1.09 μm post SSP to Ra 0.89 μm after DSP. Moreover, the position of the maximum value of residual stress migrated out close to the surface and the value of surface residual stress raised 12.6% to-800MPa from SSP. Additionally, the fatigue limit of the notched specimens pose SSP increased 64.7% to 467MPa from 283 MPa of AM, furthermore, edged up by 8% from 432MPa on unpeened smooth samples. It may be concluded that the double shot peening on titanium alloy has, therefore, eliminated the weakness of fatigue property caused by stress concentration.

Development of a time-dependent energy model to calculate the mining-induced stress over gates and pillars

Generally, longwall mining-induced stress results from the stress relaxation due to destressed zone that occurs above the mined panel. Knowledge of induced stress is very important for accurate design of adjacent gateroads and intervening pillars which helps to raise the safety and productivity of longwall mining operations. This study presents a novel time-dependent analytical model for determination of the longwall mining-induced stress and investigates the coefficient of stress concentration over adjacent gates and pillars. The model is developed based on the strain energy balance in longwall mining incorporated to a rheological constitutive model of caved materials with time-varying parameters. The study site is the Tabas coal mine of Iran. In the proposed model, height of destressed zone above the mined panel, total longwall mining-induced stress, abutment angle, induced vertical stress, and coefficient of stress concentration over neighboring gates and intervening pillars are calculated. To evaluate the effect of proposed model parameters on the coefficient of stress concentration due to longwall mining, sensitivity analysis is performed based on the field data and experimental constants. Also, the results of the proposed model are compared with those of existing models. The comparative results confirm a good agreement between the proposed model and the in situ measurements. According to the obtained results, it is concluded that the proposed model can be successfully used to calculate the longwall mining-induced stress. Therefore, the optimum design of gate supports and pillar dimensions would be attainable which helps to increase the mining efficiency.

Determination of Longwall Mining-Induced Stress Using the Strain Energy Method

Extraction of the coal seam causes stress redistribution around the mined panel in longwall mining. The weight of bridging strata and strata that cantilevers over the destressed zone is shifted to adjacent gates, pillars, and abutments surrounding the longwall panel. Thus, knowledge of the mining-induced stress is very important to enable accurate design of gate supports and pillar dimensions. In this paper, an analytical model based on the strain energy balance in longwall coal mining is developed to determine the mining-induced stress over gates and pillars. In the proposed model, the height of the destressed zone above the mined panel, total induced stress, abutment angle, vertical component of induced stress, and coefficient of stress concentration over gates and pillars are determined analytically. As a case study, the proposed model is used to determine the coefficient of stress concentration over the gates and pillars in Tabas coal mine of Iran. In order to evaluate the effect of the proposed model’s incorporated parameters on the coefficient of stress concentration, a sensitivity analysis is conducted based on the actual data of Tabas coal mine. Also, the proposed model is validated against the in-situ measurement as well as numerical and analytical models with the same boundary conditions. The validation results show that the proposed model is in agreement with the in-situ measurement and numerical model, but has differences compared with the available analytical models. Considering the obtained results, it can be concluded that the proposed analytical model can be used to calculate the mining-induced stress, aiming to reach the optimum design of gate supports and pillar dimensions.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ИЗГИБА ГУСТО ПЕРФОРИРОВАННЫХ ПЛАСТИН

A method for analyzing densely perforated plates loaded in pure bending is described. The problem is solved based on the plate theory using a structurally orthotropic model. The parameters of the orthotropic material in the form of stiffness reduction coefficients were determined from the solution of the problem of deformation of a cyclically reiterating structural element with different perforation densities (porosity) loaded in tension and shear. The structural element was analyzed using the methods of continuum mechanics and the theory of Timoshenko-type shells and plates. As a result, stiffness reduction coefficients were obtained for different porosity values, and the scope of applicability of the theory of plates for such problems was assessed. The numerical results obtained were compared with the analytical evaluations of E.I. Grigolyuk and L.A. Filshtinskiy. The numerically obtained orthotropy parameters were verified by solving the problem of bending of a plate with a single row of perforations. It is shown that the use of finite elements of a structurally orthotropic shell with the parameters determined from the solution of a 3D problem of tension and shear of the structural element is justified in bending problems with long waves. Stress distribution in the perforation area of densely perforated plates was studied for different thicknesses and porosities in the geometrically linear and nonlinear formulations. Stress concentration coefficient values were obtained as a function of porosity and thickness of the pate for tension and bending. Keywords: densely perforated plate, orthotropic material, finite element method, pure bending, stress concentration coefficient.

Analysis of the specific features of determining the coefficients of stress concentration in hull structures

Analysis of the specific features of determining the coefficients of stress concentration in hull structures

Stress Concentration Resulting from Irregular Shape of Explosively Cladded Materials Connections - Fem Simulation

Abstract The paper contains a numerical analysis of interface zone steel-titanium bimetal obtained by explosive cladding method. Due to the waviness of the zone, and various properties of the constituent material of the materials type contain structural notch. Therefore it is important inter alia in terms of presentation of the results of fatigue are the maximum stresses that occur just in the area of the zone. In the paper the stress concentration factor and the proposed method of modelling the joint zone of a sinusoidal profile, characterized by the same coefficient of stress concentration at the actual profile.

Calculations of notch stress factor of a thin-walled spreader bracket fillet weld with the use of a local stress approach

Presence of geometric notches in welded joints causes concentration of strains and stresses, therefore reducing fatigue strength of such joints. This article presents an analysis of stress concentrations in a fillet weld of a spreader mounting bracket on a small sailing yacht. The aim of this article is to direct the attention of designers, manufacturers and regulatory bodies to issues of fatigue cracks that form in brackets fastening spreaders to masts. The issue concerns mainly yachts with overall length of a hull below 10m. Despite frequent defects the solution is still being chosen by designers, mainly for technological reasons. Current design regulations of classification societies and other regulatory bodies for small recreational yachts do not specify a technical solution for spreader fastening. With the use of finite element analysis it was shown that for short term design loads structural strength of a bracket is sufficient. Then, with the use of the notch stress approach, it was proven that the spreader bracket welded of thin plates is a structural solution that runs a risk of fatigue cracks. The below presented calculations of the geometric concentration factor of weld section in the locations of fatigue cracks were performed for different geometric cases of joints. The analysis results indicate the need for greater attention that should be paid to the problem of fatigue cracks that form in welds of brackets fastening spreaders to masts. The determined values of effective stress concentration coefficients show the need for conducting fatigue calculations of brackets welded of thin plates, or choosing an alternative solution for fastening spreaders to masts. In both cases it seems appropriate to conduct fatigue calculations for a structural element which is “a weak link” of the main drive on a sailing yacht.

Finite Element Calculation about Stress Concentration Coefficient of Welded Butt Joints of Magnesium Alloy

Geometrical parameters of welded joint affect the stress concentration coefficient seriously. In order to increase the fatigue property of welded structure, it has great significance to reduce stress concentration coefficient of welded structures by researching and improving the geometry of welded joints. In this paper, the effects of weld toe inclination angle θ and weld edge transition arc radius r on the stress concentration coefficient of welded butt joints of magnesium alloy were analyzed by using ABAQUS finite element program, and the change rule of stress concentration coefficient with the variation of the two parameters was also researched. The calculation results indicate that reducing weld toe inclination angle or increasing transition arc radius can effectively decrease the stress concentration coefficient of welded butt joints, so as to improve the fatigue property of welded structures. For the safe use of welded structures, the true weld edge transition arc radius r should be greater than 3mm, and weld toe inclination angle θ should be smaller than 30°.

Calculation about Stress Concentration Coefficient of Welded Cruciform Joints of Magnesium Alloy Based on FEM

Geometrical parameters of welded joint affect the stress concentration coefficient seriously. In order to increase the fatigue property of welded structure, it has great significance to reduce stress concentration coefficient of welded structures by researching and improving the geometry of welded joints. In this paper, the effects of weld tangent line angle θ on the stress concentration coefficient of welded cruciform joints of magnesium alloy were analyzed by using ABAQUS finite element program, and the change rule of stress concentration coefficient with the variation of the parameter was also researched. The calculation results indicate that reducing the weld tangent line angle θ can effectively decrease the stress concentration coefficient of welded cruciform joints, so as to improve the fatigue property of welded structures. In order to have high reliability and safety of welded structures of magnesium alloy, the true weld tangent line angle θ should be controlled less than 25°.

Control of Mechanical Properties of Three-Dimensional Ti-6Al-4V Products Fabricated by Electron Beam Melting with Unidirectional Elongated Pores

Aligned, unidirectional, elongated pores were incorporated in Ti-6Al-4V products fabricated by electron beam melting in order to control the mechanical properties of the products such that they became suitable for biomedical applications. Unidirectional pores were successfully produced when the scan spacing of the electron beam was greater than the diameter of the beam. By changing the scan spacing of the electron beam, the size of the unidirectional pores could be varied. As a result, both the Young’s moduli and the yield stresses of the products with unidirectional pores decreased linearly with an increase in their porosity, owing to the stress concentration coefficient being 1 in the equation representing the relation between strength and porosity for porous materials. Further, low (<35 GPa) Young’s moduli were obtained when the scan spacing was 1 mm or higher, with these values being were close to the typical Young’s modulus of human cortical bone. This suggested that these porous materials could be used to fabricate customized bone implants that exhibited desired mechanical properties and suppressed the stress shielding of bone that is normally noticed when implants made of Ti alloys are used.

Study on the Relationship between the Diameter and the Stress Concentration

In order to find out how much a relief groove can change the stress distribution in a shaft, In this paper, finite element technology and test technique have been used to study the stress concentration dates caused by a escape by different shaft models. Their diameters are all less than M30mm. The research solutions show that the stress concentration coefficients caused by the escapes grow with the increase of the diameters. The pressure on the shaft should be reduced to about 0.68 times of the normal one so that the shafts have the same lifetime as before. Stress concentration coefficient is the only parameter to estimate the stress concentration degree. The calculate dates were compared with the test one in this paper in order to check the models accuracy. The conclusions show that the error rate is less than 5%.It can be taken as a new method to replace the destructive test in the design products.

Study of Multiple Holes Influence on Theoretical Stress Concentration Coefficient in Case of Cylindrical Vessels

In the construction of pressure vessels, especially for steam boilers used in power plants, cylindrical vessels are commonly used. For this important class of mechanical structures, through holes also frequently cause stress concentration which must be taken into account in the design and estimation of their lifetime. In the scientific literature which addresses stress concentration effects for such structures are studied in cases of which the presence of through holes is singular. This paper studies the effect of stress concentration in case of two or more holes placed at a small distance between them, according to construction requirements. In these cases the simplifying assumption of Saint Venant according to which at sufficient distance from the analyzed area the state of stress is not influenced by how the load is applied cannot be accepted. In this paper we study the stress concentration coefficient with numerical methods using the finite element method and more precisely, ABAQUS software package, version 6.9. Different constructive cases of multiple holes are studied: two and three successive holes with the same diameter and different diameters placed on the generating line with variable distance, for which the ratio between the diameter and the distance between the holes varies. Numerical model validation was done by comparing the results obtained for specific computational models in case of which results are known and presented in the literature [1,2]. Based on the results, variation curves of the theoretical stress concentration coefficient were drawn for all cases listed above.

Stress concentration in symmetric two-arm crank with transverse flexure

The stress concentration in a plane crank with a filled hole is considered, in the case of transverse flexure. The stress-concentration coefficient is expressed as a function of the tightness (gap), bending torque, transverse force, and relative width of the plate.

Influence of cavity on scattering of wave field in half space saturated soil using boundary element method

(1) School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China; (2) School of Civil Engineering and Architecture, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

Analysis of stress distribution in the dangerous section area of specimens with fillets under bending using the finite-element modeling method

The results of testing specimens with the diameter of 12 mm made of steel 20 with fillets of various radii (0,5 mm, 1 mm, 3 mm and 5 mm) both non-hardened and hardened by peening have been analyzed by the finite- element modeling method. It is experimentally established that the fillet radius increase results in the dangerous section moving to the specimen smallest section and reaching it at the extreme. This fact is confirmed by thecalculation method. The dependences of the stress concentration coefficient in the dangerous section area of cylindrical specimens with fillets of various radii under bending regularities have been obtained out by the finite- element modeling method.