Semicircular Grooves Research Articles

The effect of surface macrotexture and hydroxylapatite coating on the mechanical strengths and histologic profiles of titanium implant materials.

A mechanical and histological evaluation of uncoated and hydroxylapatite-coated titanium implant materials was performed. Cylindrical implants of uncoated commercially pure (CP) titanium and hydroxylapatite-coated Ti-6Al-4V alloy were studied using a transcortical model, with implants evaluated after periods of 3, 5, 10, and 32 weeks. All implants had a surface macrotexture consisting of a series of semicircular annular grooves, approximately 750 micron in maximum depth. The attachment characteristics of interface shear stiffness and interface shear strength were determined by mechanical push-out testing. Nondecalcified histologic and microradiographic techniques, with implants in situ, were used to evaluate the response to the implant materials and the presence of the surface macrotexture. Mechanical testing results indicated that the hydroxylapatite-coated implants exhibited significantly greater values of maximum interface shear strength than the uncoated implants after all time periods. Interface shear stiffness was also significantly greater at all time periods for the hydroxylapatite-coated implants as compared to the uncoated implants. Histological evaluation after 3 weeks revealed an osteoid layer covering on all areas coated with the hydroxylapatite material; mineralization of this layer appeared to be complete after 10 weeks. In all cases, longer-term implants demonstrated mineralization of interface bone directly onto the hydroxylapatite coating, and in no case was a fibrous layer observed between the hydroxylapatite coating and the interface bone. Sections from the uncoated CP titanium implants revealed a thin fibrous layer present in nearly all areas. Only isolated regions of direct bone-implant apposition were observed for the uncoated implants. The presence of this fibrous tissue layer, however, apparently did not adversely affect the development of considerable attachment strength. The results from this study indicate that the hydroxylapatite coating can significantly increase the attachment strength of implants which rely upon bone apposition for fixation. In addition, the hydroxylapatite coating provides an osteophilic surface for bone deposition, and allows for a more rapid development of implant-bone attachment.

Torsion of an elastic solid cylinder with semicircular grooves. Stress mitigations by additional notches.

This paper deals with the stress concentration problem of a circular solid cylinder with a central notch and two supplemental notches under torsion. Stress mitigations due to interference effects of stress concentrations are investigated. The influences of the distances between a central notch and two supplemental notches and the radius of the semicircular notches on the mitigations of stress concentration are considered. The principle of the method of solution used here is to distribute torsional body forces in the interior of a solid cylinder so as to satisfy boundary conditions of the notched surfaces imagined in the solid cylinder with no notch. For this purpose, we apply Green's functions for torsional body force problems of an infinite solid cylinder. Numerical results are shown for stress concentration factors of the problem.

Torsion of an Elastic Finite Solid Cylinder with a Semicircular Groove : Influences of Boundary Conditions on the Stress Concentrations

This paper deals with the stress concentration problem of a finite solid cylinder having a semicircular notch under torsion. The problems treated here are (i) torsion by a pair of rigid chucks attached to the circular cylindrical surfaces and (ii) torsion by surface forces acting on the end faces. Numerical results are compared with the results for an infinite cylinder, and influences of boundary conditions and the length of a finite cylinder on the stress concentration factors are investigated. The principle in the method of solution developed here is an application of Green's functions for torsional body force problems of an infinite thick plate. That is, the method of solution is to distribute torsional body forces in the interior of an infinite thick plate so as to satisfy boundary conditions of a region which is to become a finite solid cylinder having a notch.

Biogenic grooving on glass shards

The occurrence of grooves on the surface of volcanic glass shards in marine and nonmarine environments suggests the existence of microorganisms that can dissolve silica substrates. The etchings occur within a 30-cm-thick marine turbidite bed in the Miocene Obispo Tuff at Shell Beach, central California, and also in a tuff layer (Deep Creek Tuff) in the Miocene John Day Formation of eastern Oregon. The etchings occur in three different patterns with two subtypes, depending on the formation in which they occur. Type A is an anastomosing pattern of semicircular grooves covering the entire grain. Subtypes of A are distinguished by the presence (Obispo Tuff, Type A-1) or lack (John Day, Type A-2) of annulations. Type B has some sinuous, branching grooves covering only part of the grain. Subtypes are the same as those of Type A. Type C, occurring only on Obispo Tuff grains, is a series of straight, nonbranching grooves on one side of platy shards. The grooves range in size from 4–20 µm in the Obispo Formation to 15–18 µm in the John Day Formation. The grooves are strikingly similar to grooves occurring on carbonate grains.

Tension of a Circular Solid Cylinder with Two Semicircular Grooves : Interference Effects of Stress Concentrations due to Two Notches

This paper is concerned with the stress concentration problem of an elastic solid cylinder with two semicircular grooves under tension. The principal results are as follows: Interference effects of stress concentration due to two notches (a phenomenon leading to α2/α1 0.5, there are cases of α2/α1 > 1.0, as was suggested by Nisitani et al. for an infinite number of periodic notches. The interference effects of two notches are smaller than those of periodic infinite notches and larger in tension than in torsion. The method of solution used here is an application of Green's functions for axisymmetric body force problems of a solid cylinder.

Evaluation of Schmidt Hammer Rebound Hardness Test Holders

Abstract An evaluation is made of three different holders for Schmidt hammer tests on rock core in the laboratory, including steel angle, V-notch, and semicircular groove holders. The differences are small, but it is shown that the V-notch holder gives consistently higher rebound hardness values. It is also easier and more economical to build. These qualities indicate that the V-notch holder would be a better selection for conventional use.

Tension of circular solid cylinder with two semicircular grooves (Interference effects of stress concentrations due to two notches)

This paper is concerned with the stress concentration problem of an elastic solid cylinder with two semicircular grooves under tension. The principal results are as follows: Interference effects of stress concentration due to two notches (a phenomenon leading to α2/α1 0.5, there are cases of α2/α1 > 1.0, as was suggested by Nisitani et al. for an infinite number of periodic notches. The interference effects of two notches are smaller than those of periodic infinite notches and larger in tension than in torsion. The method of solution used here is an application of Green's functions for axisymmetric body force problems of a solid cylinder.

Torsion of an Elastic Solid Cylinder with One or Two Semicircular Grooves

The stress concentration problem of an elastic circular shaft with one or two circumferential grooves of a semicircular form under torsion is investigated in this paper. The torsion problem of an elastic circular shaft with a groove has been investigated by several authors, but it seems that these results do not always agree with one another. The present results for the problem are in fairly good agreement with Nisitani's results calculated by the so called body force method and Kato's experimental results. There are few investigations on the torsion problem of a shaft with two notches. In this paper, the effects of the distance between two grooves and the radius of semicircular grooves on the stress concentration factors are shown. The method of solution employed here is an application of Green's functions for axisymmetric torsional body force problem of a solid circular cylinder. For this purpose, Green's functions mentioned above are shown.

Boundary integral equation analysis of axisymmetric thermoelastic problems

The boundary integral equation (BIE) numerical method for linear elastic stress analysis is applied to axisymmetric problems which also involve temperature variations due to steady-state thermal conduction. The boundary of the two-dimensional solution domain is discretized into isoparametric quadratic line elements, which provide an excellent modelling capability. Satisfactory agreement is obtained with both exact analytical solutions for test problems and numerical results obtained by the finite difference and finite element methods. The BIE method is applied to the problem of a hollow cylinder with an external semi-circular groove, subjected to axial tensile loading and a temperature difference across the cylinder wall. The results emphasise the very high stress concentrations which can be obtained when the effects of thermal and mechanical loading are superimposed. An important practical advantage of the BIE method is the small amount of labour involved in preparing the mesh data.

Torsion of an Elastic Solid Cylinder with One or Two Semicircular Grooves

1個または2個の半円形環状みぞをもつ丸軸のねじりの応力集中問題を三次元弾性論で考察.みぞが1個のときの報告結果は西谷らの計算値にほぼ一致し,加藤の実験値にきわめて近い.2個のみぞをもつときの形状係数に及ぼすみぞ間距離とみぞ半径の影響を考察し,丸軸内の応力分布を明らかにした.また,みぞが周期的に無限個存在するときの従来の結果と比較した.ねじり物体力の働く円柱問題のグリーン関数を応用した解法である.

One Solution of Three-Dimensional Boundary Value Problems in the Couple-Stress Theory of Elasticity

This paper describes a numerical approach for elastic boundary value problems in the linear, couple-stress theory on the basis of the “indirect fictitious-boundary integral method.” In this approach we introduce appropriate potentials corresponding to those for a concentrated force and a couple in an infinite medium, and reduce the problem to solving the simultaneous Fredholm type integral equations of the first kind. As an example, the stress concentration problem is analyzed for a circular cylinder with a semicircular annular groove under uniaxial tension. The results are obtained for various values of parameters such as Poisson’s ratio ν, characteristic length l, and the ratio ηr of bending, twisting moduli.

Maximum principles and bounds on stress concentration factors in the torsion of grooved shafts of revolution

This paper provides an analytical approach for obtaining bounds for stress concentration factors in the theory of axisymmetric torsion of circumferentially grooved shafts of revolution. The analysis is based on application of maximum principles for linear second-order elliptic partial differential equations. The particular case of a straight shaft with a semi-circular groove is considered in detail. Explicit estimates are obtained and compared with existing results for this problem.

On the Stress Concentration Problem of a Shaft with a Semicircular Groove under Tension : 2nd Report, Influence of Poisson's Ratio

半円形の切欠きをもつ丸軸が引張り(圧縮)を受けるときの形状係数(応力集中係数)αと応力分布におよぼすポアソン比νの影響を三次元弾性論で考察.αにおよぼすν影響は切欠き半径bによって異なる.丸軸半径とbの比が0.2～0.4のとき最大で8%弱の影響を受けるが,bが非常に大きくても小さくても影響はなくなる.νが小さくなると横断面上の応力σzの分布の不均一性は大きくなり,bが同じなら,ν=0のときαは最大になる.

A Modal Theory Solution to Diffraction from a Grating with Semi-circular Grooves

A modal expansion formalism is presented to solve the scalar-wave diffraction problem for a perfectly conducting reflection grating whose grooves are semi-circular in cross-section. The theory is given for both of the fundamental polarizations, together with efficiency calculations for the first-order Littrow mounting. Similarity between the results and those of other profile shapes is observed and the groove radius which produces optimum blazing performance is determined. Resonance anomalies are observed in the efficiency spectra and are attributed to complex poles in the mode amplitudes. The positions of these poles are traced as a function of groove radius.

Stress Concentration Factors of Semi-Circular Grooves in Torsion

Stress concentration factors of grooves in round shafts under torsion have been investigated by several investigators theoretically and experimentally. But those previous results disagree considerably. In this investigation, the accuracy of those results was examined for semi-circular grooves by means of the electro-plating technique. the experiment was carried out by using a particular procedure so as not to allow an error to be caused by a preconception of the investigator and the difference of experimental conditions. The result shows that the numerical values obtained by Nishitani et al. and Matthews et al. are reasonable.

On the Stress Concentration Problem of a Circular Shaft with a Semicircular Groove Under Tension : An Application of Green's Functions for Body Force Problems of a Solid Cylinder

This paper is concerned with the stress concentration problem of an elastic circular shaft with an annular groove of a semicircular form under tension. The problem has been treated by several authors, but is seems that these results do not always agree with one another. In the present problem, the author's results are in fairly good agreement with Sato's results analyzed by F.E.M. and measured by strain gages. It may be also said that the form factors shown in the paper conform to Neuber's results in the case of large radii of a groove compared with the radius of the shaft and also conform to Peterson's results in the case of small radii of a groove. A fundamental principle of the method of solution employed in the paper is to superpose Green's functions for axisymmetric body force problems of a solid circular cylinder. This method can be easily applied to other annular grooves besides a semicircular one treated here.

Stress Concentration Factors of Semi-Circular Grooves in Torsion

Stress Concentration Factors of Semi-Circular Grooves in Torsion

On Interference of Circular Notches and Loaded Ends : 2nd Report, Axisymmetric Problems

The problems of the interference of notch and loaded ends which must be considered especially in the material test are discussed quantitatively. For this purpose, in the 2nd report, the cases of a circular cylinder having semicircular groove under several tensile load conditions on its partial surfaces, with the positions varied, are taken up. For the analysis, the point matching method is adopted to obtain the stress field superposed two solutions for each cylinder loaded on its partial surfaces. Furthermore, by the same method of solution, the problems of stress concentration due to circular groove are treated.

Stress Concentration Factors From Overlapping Stress Fields in Uniaxial Tension

Standard transmission photoelastic techniques were used to determine the resultant stress concentration factors produced by multiple stress raisers in flat, rectangular bars under uniaxial tension. Observations were made on the overlapping stress fields due to various combinations and orientations of holes and semicircular grooves. Two cases of directly superposed discontinuities were also investigated. The results of this investigation indicate that the sizes and relative positions of the discontinuities had a substantial effect on the resultant stress concentration factor. In some cases the stress concentration factor would be decreased while in other cases it would be increased. In the case of superposed stress raisers considered in this investigation, the resultant stress concentration factor can be taken as the product of the individual stress concentration factors; this is in agreement with the results of other investigators. However, for other cases, much judgment and experience will be required to decide when this can be done. And even then this product should be considered only as the probable upper limit of the actual stress concentration factor.

Analysis of thick cylinders with internal semicircular grooves subjected to internal pressure

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