Affected depth approach to determine the fatigue strength of materials containing surface defects

This paper explains a novel methodology to determine the High Cycle Fatigue (HCF) reliability of materials with defects. A defect was represented by a semi-spherical void situated at a specimen surface subjected to periodic loading. Then, the Finite Element (FE) method was carried out to find out the stress distribution near the defects for diverse sizes and diverse loadings. The Crossland stress change is studied and interpolated by a mathematical function depending on fatigue limits, defect radius, and profundity from the defect tip. The HCF strength of defect material is computed by the “stress strength” approach via the Monte Carlo sampling. This approach leads to determine Kitagawa–Takahashi diagrams, for a definite reliability, of materials with defects. The calculated HCF reliabilities agree well with fatigue tests. Obtaining Kitagawa–Takahashi diagrams with reliability level permits the engineer to be engaged in an endurance problem to compute the defective fatigue lives in safe and efficient process. As a final point, we discuss the sensitivity effects of defect size, defect free fatigue limits, affected depth, and load amplitude to envisage the fatigue reliability of materials with defects.     

Stress concentrations in bolt-thread roots

The apparent geometric origin of fatigue fractures in oversize shank bolts is considered in this report. Bolt-nut interaction between the bolt and both a standard nut and a special nut are investigated. The “frozen stress” method of three-dimensional stress analysis was used to determine the magnitudes and locations of points of stress concentration in plastic models of both the oversize shank bolt and a standard bolt in combinations with standard and special nuts. The results indicate that, for installations in which the special nut is used, bolt geometry may be the controlling factor in determining the fatigue life of the boltnut combination, because the stress-concentration factors due to the nut loading are of the same order of magnitude as the stress-concentration factors due solely to bolt geometry. On the other hand, for installations in which standard nuts are used, the nut-induced stress-concentration factors are much larger than those due to bolt geometry; so, bolt geometry will have less effect on the fatigue performance of the combination. If the nut is threaded onto the bolt so far that the first loaded thread of the nut is in the thread-runout area of the bolt, fatigue performance of the installation will be greatly reduced due to the combination of stress-concentration factors from thread loading and section change and, again, bolt geometry may be a prominent causative factor.     

The effect of low-frequency biaxial loads on stress-concentration factors in plates

It is generally recognized that stress-concentration factors under stress-wave loading are lower than those under static loads. In this work, the effect of low-range frequency of biaxial sinusoidally varying alternating stresses on the stress-concentration factors for circular and elliptical holes in Plexiglas plates is investigated. The experiments have been performed on a specially designed and built “biaxial cyclic-stress machine” and the results are presented in the form of curves. In the case of biaxial alternating stresses, the stress-concentration factor is defined as the ratio of amplitude of the maximum alternating stress around the geometrical discontinuity to the larger of the amplitudes of the two principal alternating stresses which would occur at the same point, if the geometrical discontinuity was not present. Both values are considered over a stress cycle. The results indicate a slight decrease in the values of stress-concentration factors with increase in frequency.     

Stresses in turbine-blade tenons subjected to bending

The photoelastic method was used to model large steam turbine tenon-shroud attachments under bending loads. Six models were used to investigate three basic tenon geometries: (a) single round tenon—here two different fillet radius-to-tenon diameter ratios were examined; (b) long narrow tenon—for this geometry the influence of shroud-seating clearance and shroud stiffness was investigated; (c) two separated round tenons. Stress-concentration factors for the tenon fillets were determined based on the nominal bending stress in the tenon using the moment of inertia of the tenon cross section. For the single round tenon, stress-concentration factors of 1.3 and 1.6 were found for fillet radius-to-tenon diameter ratios of 0.41 and 0.19. These compared very well with those values obtained by treating the geometry as a stepped round bar with a shoulder fillet subjected to bending. The long-narrow-tenon geometry showed a higher stress-concentration factor than the two separated round tenons—6.1 compared to 2.9. Increasing the shroud stiffness reduced the stress-concentration factor for the long-narrow-tenon design.     

Fatigue and static strength of notched and unnotched aluminum-alloy and steel specimens

This paper describes a method of presentation of fatigue data on three commonly used aircraft materials, 2024-T3 and 7075-T6 aluminum alloys and normalized SAE 4130 steel, such that variations in fatigue strength with stress-concentration factor can be shown. Comparisons of the fatigue strengths of 2024-T3 and 7075-T6 aluminum are made for the most useful range of stress-concentration factors. Static-strength results of notched and unnotched specimens of the three materials are presented to show how the strength varies with some parameters of the stress concentration. Comparison of the data with one theory for the strength of cracked specimens was made.     

Stress redistribution in notched specimens during fatigue cycling

Most materials exhibit a change in stress-strain relationship when subjected to fatigue stresses. In this work, the effect of this change on the stress distribution across the throat of notched-plate specimens of mild steel is examined. Using a set of strain gages, the strain distribution across the specimens was determined under dynamic conditions for various numbers of cycles. Tests of unnotched specimens were used to obtain the cyclic stress-strain properties for corresponding numbers of cycles, and from these data the stress distribution in the notched specimens was determined. Tests in which the strain amplitude at the notch root was held constant revealed a decreasing maximum stress with fatigue cycles. In another series of tests, in which the load amplitude was constant, the maximum stress amplitude was observed to decrease with number of fatigue cycles, despite an increasing strain amplitude. In both types of tests, the stress-concentration factor was observed to decrease with increasing number of fatigue cycles.     

Experimental determination of stress-concentration factors in thick-walled cylinders with crossholes and sideholes

In a companion paper¹ submitted to ASME, the theoretical determination of stress-concentration factors in thick-walled cylinders was reported. The present paper reports the results of experiments conducted to check the predictions of the theory. The configuration is a thick-walled cylinder with crossholes or sideholes oriented perpendicular to the bore. Stress concentrations occur at the “tee” intersections of the holes with the bore. The loadings considered are internal pressure and external pressure. Both steel and plastic models were tested. Experiments were also conducted to determine the reduction of the stress-concentration factor by intersection radii at the crosshole intersection. Experimental results were found to agree well with theory. The best configuration was found to be one with crosshole (or sidehole) diameter equal to the bore diameter, and with an intersection radius at the tee intersection equal to the bore radius.     

Stress-concentration factors at intersecting and closely approaching orthogonal coplanar holes

Using two models, each containing three groups of intersecting or closely approaching holes, 18 different cases were investigated by three-dinensional frozen-stress photoelasticity. In all cases, the coplanar holes were orthogonal to the applied uniaxial tension. Included were three cases of intersecting hoes with square corners and varying hole-diameter ratios. Five cases of intersecting holes with rounded corners were studied for two hole-diameter ratios and varying corner radius. Stresses were determined for two cases where the end of one drilled hole partially penetrated another hole leaving acute corners or feathered edges at the intersection. Three types of closely approaching holes were studied: two cases in which the end of one drilled hole nearly intersected the side of an-other hole, two cases in which the ends of two drilled holes approached each other along a common axis, and four cases (called corner-approach cases) in which the ends of two drilled holes approached each other along orthogonal axes. A stress-concentration factor of 13 was found for one of the partially penetrating drilled-hole cases. The upper limit on stress-concentration factor for a very small hole intersecting a large hole in an infinite body subjected to uniaxial stress is 8.4 for metals. This factor is reduced to 5.2 as the diameters of the intersecting holes become equal. Rounding the corners on intersecting holes reduced the stress concentration by only four to seven percent. Closely approaching drilled holes results in higher stresses than fully intersecting holes when the minimum ligament width is less than ten percent of the hole diameter. Corner approach cases do not result in high stress-concentration factors as long as the ligament width is greater than the percent of the hole diameter.     

On the nullification of stress-concentration factors by stress equalization

During a recent design study involving a critically stressed “tongue-and-groove” type compression joint of dissimilar materials, a novel technique was conceived for nullifying the effects of an otherwise high local stress-concentration factor. In principle, the nominal stresses in the tongue-and-groove portions of the joint are forced to be uniform. For idealizedfit conditions, the stress concentration in the fillet under this stress-equalized condition is theorized to approach unity (1.00). In the present paper, experimental verification is provided.     

Random-load fatigue tests on a fail-safe structural model

Experiments performed on a ten-member redundant “fail-safe” structural model subjected to randomized load sequences confirm predictions of fatigue life and reliability based on a probabilistic approach. The statistical variation in ultimate strength of 2024-T4 aluminum alloy combined with an exponentially distributed, Markovian, bending load-amplitude sequence with a constant-amplitude S-N relation for single specimens, is utilized in the analysis. Experimental results are presented for the statistical distribution of ultimate bending strength of 2024-T4 aluminum alloy. Constant load-amplitude flat-bending fatigue tests on single specimens and on multimember structures, and variable-amplitude flat-bending tests on fail-safe structures are reported. Life to failure of the weakest member, as well as the remaining “fail-safe” life in the parallel structure, are examined.     

A statistical investigation of the behavior of short fatigue crack in medium carbon steels

Rotary bending fatigue tests were carried out by using smooth specimens of medium carbon steel with two ferrite grain sizes. In order to clarity the physical background of the scatter in fatigue behaviour, the statistical characteristics of the initiation and growth of short fatigue crack were investigated. Results show that the short crack initiation and growth life distribution can be express by two-or three-parameter Weibull distribution. The Weibull distribution of the mixed type is well fitted to the crack length distribution for both steels. The knee values of Weibull plots are related to the grain size. The crack length distribution before the knee point can be expressed by a two-parameter Weibull distribution, and that after the knee point can be represented by two-or three-parameter Weibull distribution. It was found that the initiation Life, growth life and crack length distribution were affected by the grain size.     

Parametric stress-concentration factors in greenstick bone fracture

The reported work is a part of an ongoing research program concerned with structural analysis of fractured long bone and methods of internal fixation. The stress-concentration factors for equine metacarpus bones containing greenstick fractures and “through” fractures (surgically repaired) were determined for the compression, flexural and torsional modes of loading based on whole bone (unfractured) strengths. The greenstick type of fracture was simulated with saw cuts at the mid-span of the bone, and the parameters varied were depth of fracture and orientation of fracture. All specimens consisted of fresh dead bone which had been placed in a freezer within 4 hr after expiration. The maximum stress-concentration factors for the simulated greenstick fractures studied were about 3.4 for compression, 4.3 for torsion and 16 for flexure. The stressconcentration factors for fractured bones surgically repaired with commercial plates were about 3.0 for compression, 2.7 for torsion and 6.1 for flexure.     

An eigenstrain formulation for the prediction of elastic moduli of defective fiber networks

A method for predicting the elastic moduli of a regular network populated by a large number of randomly located defects is presented. The prediction is based exclusively on the stiffness of individual fibers and the location of defects. The method requires a preliminary calibration step in which the eigenstrains associated with “elementary defects” of the regular network are fully characterized. Each type of defect is represented by a superposition of singular point sources in 2D elastostatics producing a field identical to the eigenstrain of the respective defect. The amplitude of the point sources is determined by probing the eigenstrain with a series of path independent integrals. This “spectral decomposition” represents the generalization that allows applying methods developed to account for crack–crack interaction in fracture mechanics to situations in which the interacting sources have eigenstrains obtained by the superposition of multiple types of singularities. Once the representation of each elementary defect is determined, any distribution of defects in the network can be mapped into a distribution of point sources in an equivalent continuum. This allows inferring the elastic behavior of a defective network of any distribution and concentration of defects. The method discussed here provides an efficient way to treat the non-affine deformation of defective regular fiber networks.     

Phase field simulation of heterogeneous cubic → tetragonal martensite nucleation

The mechanisms for heterogeneous cubic → tetragonal martensite nucleation due to different types of microscopic defects (voids, stress-concentration site, inertial inclusion and pre-existing nucleus) and the temporal evolution of martensite morphology are monitored with finite element simulation of phase filed model. The results demonstrate that the nucleation prefers to occur around void and stress-concentration site initially; high residual stress exists around inertial inclusion; pre-existing nucleus promotes nearby martensite phase to develop on it. The effects of various defects on heterogeneous nucleation are different, and stress relaxation behavior is the dominant factor which characterizes the whole microstructure evolution process.     

Stress-concentration factors for countersunk holes

This paper describes a method of determining the elastic stress-concentration factors for countersunk holes. Local stresses were determined by the birefringent-plastic-coating method on plain-hole specimens, and the stresses were compared with theoretical values. Local stresses were then determined by the same method at all points around countersunk holes except at the base of the countersink. A series of fatigue tests was conducted on groups of plain-hole and countersunkhole specimens, and the elastic stress-concentration factors for the base of the countersinks were determined from the results.     

Low-cycle fatigue-crack indications by strain gages operating in elastic strain fields

This paper describes the response of bonded electrical-resistance strain gages to low-cycle fatigue cracking of four, cyclically pressurized, boxlike structures. The strain-pressure “signatures” of gages installed on flexural parts of the structures were recorded semicontinuously. By observing the changes in signatures of certain gages, it was possible to follow indirectly the initiation and propagation of internal low-cycle fatigue cracks. The described technique appears feasible as a crack-detection system, or as an adjunct to some other type of damage-warning system. It is suggested that the sensitivity and accuracy of this technique make it possible to substitute “crack initiation” for “through cracking” as a criterion for fatigue failure in design.     

含类焊接裂纹十字接头的疲劳特性

为探讨含类焊接裂纹结构的疲劳性能,设计了部分熔透焊接接头的拉一拉疲劳试验,并进行了有限元分析,研究了不同裂纹尺寸下接头的疲劳强度、应力集中系数、应力强度因子范围和疲劳寿命的变化规律.结果表明,当未熔透尺寸2a/T＜0.5时,疲劳性能无明显减弱;而当未熔透尺寸2a/T＞0.5时,则接头的抗疲劳性能显著降低.     

Investigation of stress-concentration factors in tensile strips

A photoelastic and a numerical investigation has been carried out to determine the stress-concentration factors at the edge of a central circular hole in a tensile strip for different ratios of hole diameter to width of the strip. The photoelastic data and the numerical results indicate that the stress-concentration factor at the minimum cross-sectional area tends to a value of two if the ratio of the hole diameter to the strip-width approaches a value of one.     

基于裂纹闭合效应的高载迟滞预测模型修正

裂纹闭合效应通常是导致I 型裂纹扩展在高载作用下发生迟滞效应的主要因素之一．本文采用汽车薄板QSTE340TM 材料，针对不同应力比，高载比条件下疲劳裂纹扩展行为进行了实验研究．论文通过断面分析，针对各参数对裂纹闭合效应的具体影响进行了分析讨论，认为裂纹作用区域随裂纹扩展而动态变化，从而提出了一种对有效应力强度因子幅的修正方法．通过在原有模型中引入幂函数形式的动态变量α，表征裂纹闭合效应的作用比例随裂纹长度的动态变化，取得了较好的效果．     

Local stress measurement using the thermoelastic effect

A technique for measuring local stresses in metallic specimens is proposed and tested. The technique depends on the experimental measurement of temperature changes in stressed members due to adiabatic elastic deformation. At a free boundary in a body under plane stress, these temperature changes are directly related to the value of the tangential principal stress. The technique is suited for measurement of stress-concentration effects, since the temperature changes can be measured with thermocouples featuring extremely small junctions. A simple stress-concentration geometry, the finitewidth strip with a central circular hole, is chosen as a model system for this study. Heat transfer in this geometry due to the temperature gradients produced by elastic deformation is analyzed. It is shown that the ratio of the temperature change at a reference section to the change at the locale of the stress concentration can be used to determine the stress-concentration factor, allowing for heat-transfer effects. An experimental measurement system capable of obtaining reproducible results with the thermal-measurement technique is described, and experimental results are given for the model geometry which agree favorably with theoretical predictions. Application of the technique to other problems is discussed.