Hole-shape optimization in a finite plate in the presence of auxiliary holes

Minimizing the stress concentration around holes in uniaxially loaded finite plates is an important consideration in engineering design. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate is to introduce smaller auxiliary holes on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. This method has been demonstrated by Heywood and systematically studied by Erickson and Riley. Erickson and Riley show that for a central-hole diameter-to-plate width ratio of 0.222, the maximum stress reduction is up to 16 percent. In recent work, Durelliet al. show that the stress concentrations around holes in uniaxially loaded plates can be minimized by changing the hole shape itself till an optimum hole profile with constant stress values respectively on the tensile and compressive segments of the hole boundary is reached. By this technique the maximum stress reduction obtained for the above case is up to 20 percent. In the present work, starting with the optimum sizes and locations of central and auxiliary circular holes for a finite plate given by Erickson and Riley, a systematic study of the hole-shape optimization is undertaken. A two-dimensional photoelastic method is used. For a central-hole diameter-to-plate width ratio of 0.222, the reduction in stress-concentration factor obtained after hole-shape optimization is about 30 percent. It is also shown that it is possible to introduce the ‘equivalent ellipse’ concept for optimized holes.     

Stress concentrations in tensile strips with large circular holes

The purpose of this investigation was to determine more accurately the stress concentrations in tensile strips having large circular holes where the ratio of the hole diameter to strip width is greater than 0.5 Results of numerical elasticity analyses are presented for ratios of hole diameter to bar width ranging from 0.10 to 0.99, and photoelastic data are presented for the range from 0.40 to 0.94. Both numerical results and photoelastic data indicate that the stress-concentration factor based on net area approaches a value of one as the ratio of hole diameter to bar width approaches a value of one.     

Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method

0Introduction Photoelasticityisanopticalmeasurementmethodforstressanalysis.Itcanperformwhole field measurementduetotwo dimensionalsignalprocessingoflight.Alsoitcanperformnon contact measurementbecauseoftransmissionorreflectionoflightonaspecimen.Photoelast…     

高炉炉壳开孔位置对应力集中的影响

考虑到冶金行业中高炉炉壳开孔的实际情况，本文应用有限元分析的方法研究受远场均匀拉伸载荷，二维有限区域内菱形分布的圆孔中间不同开孔位置下的应力分布，得到最大应力集中系数随孔位置变化的三维变化曲面。此外，孔沿座标轴及沿原孔边缘位置变化对应力集中系数的影响被详细研究，从而为合理设计炉壳开孔提供了理论依据。     

Minimizing stress concentrations around circular holes in uniaxially loaded plates

The problem of determining stress distributions and reducing stress concentrations around holes in plates occurs in numerous design situations. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate was demonstrated by Heywood. With this approach, smaller holes are introduced on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. For the one case reported by Heywood (which did not produce the greatest reduction possible), the maximum stress was reduced to 84 percent of that due to a single hole. In the present program, a systematic study was undertaken using two-dimensional photoelasticity method to determine the optimum sizes and locations for the auxiliary holes for a number of plates with different central-hole diameter-to-plate width ratios. Maximum stress reductions from 13 to 21 percent were demonstrated for plates with hole diameter-to-plate width ratios between 0.1 and 0.6. With such reductions in maximum stress level, the improvement in fatigue life of a part can be very significant.     

含圆孔缺陷三点弯曲梁动态焦散实验

应用新型数字激光动态焦散线实验系统,采用含预制裂纹的有机玻璃板试件进行落锤冲击实验,研究了含圆孔缺陷三点弯曲梁的动态断裂行为。通过实验得到了含圆孔缺陷三点弯曲梁裂纹尖端动态应力强度因子的变化情况、裂纹扩展速度的变化情况以及裂纹贯穿空孔的扩展情况等。实验结果表明:三点弯曲梁中的空孔位置对裂纹的扩展轨迹具有明显的导向作用;空孔位置的改变会影响三点弯曲梁的断裂时间;空孔位置的变化对空孔下方裂纹的扩展时间、扩展轨迹影响较小;在空孔位置居中的情况下,空孔上方裂纹的最大扩展速度大于空孔位置偏移时的情况。     

Investigation of the stress field of a near-surface circular hole

By observing experimentally obtained photoelastic fringe patterns and applying classical solutions for an infinite plate containing a circular hole under remote tension and the modified Hertz contact theory, a replaced superposition method is proposed. In this paper we use this method to investigate the state of stress around a near-surface circular hole in a semi-infinite plate under a concentrated load. The well-matched conditions between the reconstructed and experimental photoelastic fringe patterns indicate the applicability of the proposed method. This paper was presented, in part, at a symposium honoring Dr. Christian P. Burger, Novel Applications of Experimental Methods in Mechanicsheld at the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2–4, 2003, Charlotte, North Carolina.     

Stress Distribution in an Orthotropic Plate with Circular Holes under Impulsive Loading

The photoelastic method is used to analyze the stress–strain state induced by an impulsive load in an orthotropic plate with circular holes. The distribution of dynamic stress concentration factors along the periphery of the holes is studied, and stresses and strains in representative sections are determined     

Optimization of hole shapes in circular cylindrical shells under axial tension

Hole shapes are optimized in circular cylindrical shells subjected to axial load considering only the predominantly large membrane stresses present around the holes. Two-dimensional photoelastic isochromatics obtained with a special-purpose polariscope are utilized for the optimization process. The process leads to a significant decrease in the membrane stress-concentration factor and a modest decrease in weight, thus yielding a considerable increase in strength-to-weight ratio. This paper presents results for certain typical ratios of hole diameter to shell diameter. Previous theoretical and experimental studies for the circular hole have also been verified     

Elastic-plastic strain concentrations produced by various skew holes in a flat plate under uniaxial tension

The elastic and elastic-plastic surface strain fields around circular holes drilled at various skew angles to a flat plate have been experimentally evaluated in uniaxial tension. A photoelastic coating and moiré technique were used in the low- and high-strain regions, respectively. The maximum strain-concentration factor is shown to increase markedly with horizontal skew angle and decrease slightly with increasing vertical skew angle. Plastic deformation accentuates the differences between normal and skew holes, so that the angular dependence of the strain-concentration factor increases with nominal strain.     

Stress-concentration factors for fatigue configurations

Stress concentrations in thin-plate configurations commonly used in fatigue bending tests were determined by photoelastic means. The test configurations were rectangular and tapered plates with a centrally located hole. These configurations were machined from plates constructed by cementing together two sheets of similar photoelastic material. A reflective-type cement was used. In this manner, photoelastic measurements for the bending case were indicative of the average between maximum fiber stress and the stress at the reflective surface. The maximum fiber stress was then computed assuming that plane sections remain plane. Although bending was of primary concern, tension tests were also performed. The measured stress concentrations are compared with available analytical solutions. In the case of bending, the results are compared with infinite-plate solutions since the perforated finite-width plate bending problem has not been solved.     

Stresses in hollow hexagons under external pressure

A two-dimensional photoelastic study was made of the stresses produced in a regular hexagon with a central, circular hole when subjected to external pressure. Four sizes of the hole were tested, and three types of loading were used. This paper describes the pressure-loading fixtures and the procedure which was used to calibrate them. An experimental confirmation of the theoretical solution of Kawaguchi¹ is given, and typical stress patterns and boundary stress distributions are included.     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

Photoelastic analysis of stresses around oblique holes

A three-dimensional photoelastic analysis was conducted to determine the magnitude and distribution of stresses around oblique holes in a uniaxially loaded plate. The holes were circular and inclined at angles of 45 deg and 60 deg with the faces of the plate. The plate-thickness-to-hole-diameter ratiot/D was 2.40. One end of each hole was blended to the face of the plate through a break radius equal to the radius of the hole. The plate dimensions were sufficiently large to simulate conditions of an infinite plate. The plates were loaded perpendicular to the plane of skewness. Stress distributions were obtained on sections perpendicular to the direction of loading. Results point to two critical areas of stress concentration: one at the acute-angle intersection of the hole and the surface of the plate and the other in the break-radius area. The stress concentrations in the latter area reach values of 4.6 and 6.7 compared to 3.6 and 4.5 at the acute-angle intersection, for the inclination angles of 45 deg and 60 deg, respectively. A simplified analysis used for the break-radius area gave results in agreement with the experiment. Thus, it was shown that break radii in oblique penetrations may have deleterious rather than beneficial effects. Comparison of results for the acute-angle intersection with existing theoretical and experimental values shows a definite and pronounced dependence of the stress-concentration factor on thickness-to-diameter ratio.     

Stress wave fields in plates weakened by curvilinear holes with edge cracks

The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 79–84, February 2006.     

Photoelastic analysis of a thick plate with an elliptical hole subjected to simple out-of-plane bending

A three-dimensional photoelastic analysis using the stress freezing and slicing techniques was employed to study the stress distribution and the stress-concentration factors around an elliptical hole in a plate of finite thickness. The plate was subjected to simple out-of-plane bending. A special bending device was designed to produce uniform bending moment at the two opposite free edges of the plate. Six plates with various elliptical holes were studied. The stress variation across the plate thickness at the periphery of the elliptical hole was also investigated. The experimental results were correlated with the existing theoretical solutions.     

Photoelastic analysis of an asymmetrically reinforced circular cut-out in a flat plate subjected to uniform unidirectional stress

Three-dimensional photoelastic studies of stresses around an asymmetrically reinforced circular cut-out in a flat plate under uniform unidirectional stress are reported. The frozen-stress technique, with Hysol 4290 material, was used to determine the stress distribution through four critical points on the boundary of the reinforced hole. Included were models with different cross sections of reinforcement, with various interface fillet radii and with different plate widths. For the majority of models, the ratio of volume of reinforcement to volume of hole was unity. It is concluded that, for reducing the stress concentration, there is a limit on the effectiveness of increasing the fillet radius beyond half the plate thickness. It was found that a reinforcement having a thickness of approximately 40 percent of the plate thickness was optimum and that the stress concentration decreases with volume of reinforcement. The authors believe that, with judgment, some of the conclusions reached may be applied, for design purposes, beyond the specific dimensional ranges and loading conditions of the tests.     

Evolution of plastic damage in welded joint of steel truss with pre-existing defects

Experimental analyses are made for the local damage evolution of structural response for a steel truss structure with pre-existing defects in welded joints. Employing a scaled down specimen of the steel truss present in decks of long-span bridges, the photoelastic coating method is adopted to obtain data information on local hot-spot strains near the welded joints while strain and displacement gauges are employed for collecting information on the response of the global structure. Initially, a finite element model of the steel truss is established for the purpose of pre-experimental evaluation. Defects such as holes and a crack are pre-existing near the welded joints. The local plastic damage evolution is captured by photoelastic images and evaluated in relation to the global structural mechanical performance. Local defects tend to affect the weldment details and structural rigidity more appreciably than changes in the structural nominal strains.     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 1. Whole-field determination of isochromatics and isoclinics

Two correlative methods are developed for the computer-aided photoelastic analysis of orthogonal 3D textile composites comprising 6 mm×6 mm highly heterogeneous unit cells in-plane. The first method, presented in Part 1, is used for the whole-field determination of isochromatics and isoclinics; the second method, presented in Part 2, is applied for subsequent photoelastic stress analysis. Part 1 delineates precisely how one circular polariscope and two plane polariscope photoelastic images are implemented to extract the isochromatic parameterR and isoclinic parameter α using the digital image processing technique. The photoelastic experiments were performed with orthogonal 3D textile composite as well as aluminum plates containing a hole under the uniaxial tension loading. The obtained values ofR and α, for the case of the aluminum plate, are smoothly distributed over the field and show consistent agreement with those computed from finite element analysis (FEM). In the case of the composite plate, the global distribution ofR and α also agree well with FEM results employing the homogenized composite properties. However, bothR and α exhibit local variations according to the 3D fabric structure, and the varying amplitude of α is relatively larger than that ofR.     

Effect of two drille holes on the elastic and elastic-plastic strain distribution around a Charpy V-notch

Two small holes (0.0292 in.), appropriately drilled near the root of a Charpy V-notch, have been shown to reduce markedly the Charpy V-notch transition temperature of various steels. In the present study, three experimental techniques were used to define the effect of two holes on the mechanics of deformation and fracture of notched bars loaded in three- and four-point bending: (1) two-dimensional photoelastic stress analyses were performed on models of both the standard Charpy and drilled geometries; (2) a sensitive dislocation etch-pitting technique was used to observe directly the plastic-strain fields developed in V-notch samples of Fe?3% Si alloy loaded in slow bending; and (3) the Charpy striker was instrumented to record load-time curves during impact-bending and thereby determine the dynamic fracture strength of notched and drilled mildsteel samples. It was determined that two holes donot significantly reduce the elastic stress-concentration factor although they cause considerable redistribution of the local shear stresses around the notch. Consequently, the elastic-plastic state develops quite differently in the presence of two holes, and hole drilling can increase the load-carrying capacity of notched mild-steel bars by more than 100 percent even when bars fail by brittle cleavage prior to general yielding. The implications of these results with respect to other forms of “stress-relieving notches” are discussed.