Elastic Stress Concentration Factor Research Articles

Creep crack growth assessment by means of a crack tip/far field concept

A method has been developed to assess crack initiation and crack growth behaviour in the creep range. The proposed method is based on a two-criteria-diagram, which covers the crack tip/far field situation. The approach is similar to the application of the elastic stress concentration factor K, in the creep rupture range.

Frequency and Hold-Time Effects on Low Cycle Fatigue Life of Notched Specimens at Elevated Temperature

This paper describes the frequency and hold-time effects on high temperature low cycle fatigue for round notched specimens. Unnotched and notched specimens having different elastic stress concentration factors were fatigued under triangular and trapezoidal stress waves at frequencies ranging from 5 Hz to 0.0001 Hz at 873 K. The three specific fracture characteristics were observed: cycle dependent, time dependent, and cycle-time dependent. The respective notch sensitivity occurred in the respective fracture regime. The fatigue life of notched specimens was predicted from the elastic-plastic-creep cyclic FEM analysis using the linear damage rule and the strain range partitioning rule. Both the life prediction methods predicted the creep-fatigue life within almost a factor of two scatter band.

溶接継手止端部の疲労強度

The high cycle fatigue strengths at the toe of the cruciform welded joints of SM41A and HT60 were investigated experimentally under tensile and bending fatigue loading. The effects of welding process (toe treatment), mean stress and welding residual stress on fatigue strength were studied.The main results obtained are as follows.(1) The fatigue limit of SM41A welded joint under tensile loading was increased up to 64% by the toe treatment of CO2 soft plasma welding. Similarly, in the case of HT60 welded joint the fatigue limits under bending loading were increased to 77%, 43% and 25% by the toe treatment of CO2 soft plasma welding, TIG welding and grinding, respectively. These improvements can be attributed to the change of the toe part geometry; lowering the elastic stress concentration factor at the toe.(2) The relation between fatigue limit of welded joint and mean stress can be expressed by the straight line intercepted at the true rupture stress on the axis of mean stress in fatigue limit diagram.(3) The fatigue limit of welded joint was decreased by tensile welding residual stress. This decrease can be well estimated by regarding the welding residual stress as the static stress.

A method of calculating elastoplastic stresses and strains in concentration zones

1. We proposed a method of determining the maximum elastoplastic stresses and strains which is not limited by the values of the elastic stress concentration factor. 2. Comparison of the results obtained by the proposed method with those calculated by FEM for the specimens with a notch and the experimental results of measurements of the strains in the areas of stress concentration indicates that they are in satisfactory agreement. 3. The proposed method can be used to calculate the stresses and strains in cyclic elastoplastic deformation of the material.

Elastoplastic Plane Strain Analysis of Stresses and Strains at the Notch Root

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

Fatigue behaviour of porous polysulphone surface coatings for orthopaedic applications

Porous polysulphone (PPSF) has recently been selected as a candidate material for use as a prosthetic surface coating in orthopaedic applications to acommodate ‘bone ingrowth’ for fixation to the skeletal system. The tension-loaded fatigue behaviour of PPSF was characterized based on the interpretation of stress/life ( S/ N) data. Results of this investigation indicate that the fatigue life of PPSF is governed by crack propagation across the sintered necks of the porous structure. In addition, experimental data revealed that the fatigue strength-reduction factor, K f , remains equivalent to the tensile notch strength-reduction factor for a wide range of fatigue lives. However, analytical results indicate that the material has a low notch sensitivity and that a single application of a theoretical elastic stress-concentration factor in a fatigue analysis would be inappropriate.

Evaluation of Brittle Fracture Strength of Tubular T-Joints of Offshore Structures under Tensile Loading (1st Report)

As offshore structures are used in rougher and colder seas, the rigorous safety has been demanded. Nowadays, it becomes more common to conduct CTOD tests for weldments as a steel prequalification test and/or a welding procedure test. However, there have been arguments that the CTOD criterion give a much conservative assessment.In these circumstances, it is essential to establish the precise evaluation method for the structural integrity from fatigue crack growth to brittle fracture in offshore structures. For offshore structures, the most important structural members are tubular joints, where high stress concentration takes place.From this viewpoint, the strain distribution and the fatigue crack growth characteristics in the hot spot area have been investigated with tubular T-joints model specimens under tensile loading, and the brittle fracture strength of the model tests has been evaluated based on the CTOD criterion.The results obtained are summarized as follows.(1) The elastic stress distribution around the connection of the tubular joint is well evaluated by the FEM stress analysis, and the elastic stress concentration factor at the hot spot agrees with the predicted value.(2) The plastic strain concentration factor can be estimated using Eq. (1) as a function of the elastic stress concentration factor and the nominal applied stress. In case where residual stress exists, Eqs. (2) to (6) can be used to analyse the effect of residual stress.(3) The fatigue crack propagation behaviour at tubular joints can be evaluated reasonably using the linear elastic fracture mechanics.(4) The critical CTOD obtained from the tubular joint model test agrees well with that from 3-point CTOD test. Therefore, the CTOD criterion can be applied to the fracture of structural component with 3-dimensional stress concentration such as tubular joints.(5) The brittle fracture strength of the tubular joint models can be evaluated using the estimated hot spot strain and the proposed CTOD design curve by taking into account the welding residual stresses.

Comparison of local strains at the notch root between FEM analysis and experimental strain measurement in creep-fatigue condition.

This paper describes the accuracy of FEM analysis for the estimation of local strain at the notch root in creep-fatigue conditions, comparing the local strain calculated by FEM with the measured strain using high temperature strain gages. The specimens are commercial pure aluminum notched plates with both side grooves whose elastic stress concentration factors are 0.5 and 2.0. The test was made at 473 K in air. The following results are obtained. In no-hold time fatigue tents, FEM analysis accurately estimates the local strains at the notch root. In no-hold time fatigue tents, FEM analysis accurately estimates the local strains at the notch root. In the hold time test, on the other hand, FEM analysis estimates a smaller strain range compared with the actual strain range occurring at the notch root. The reason for the disagreement between FEM analysis and the actual strain results from the change in material response due to creep loading. In the creep-fatigue condition, so-called plastic-creep interaction, the FEM analysis does not take account of, occurs. The local strain calculated from conventional methods, Neuber's rule, Stowell-Hardrath-Ohman, Koe's methods are also compared with the strain measurement for no-hold time tents. All the methods overestimate the strain concentration at the notch root.

Comparison of local strain at the notch root between FEM analysis and experimental strain measurement under creep-fatigue conditions.

This paper describes the accuracy of FEM analysis for the estimation of local strain at the notch root under creep-fatigue conditions, comparing the local strain calculated by FEM with the measured strain using high temperature strain gages. The specimens used are commercial pure aluminum notched plates with both sides grooved, whose elastic stress concentration factors are 1.5 and 2.0. The tests were made at 473 K in air. In no hold-time fatigue test, FEM analysis accurately estimates the local strain at the notch root. In the hold-time test, on the other hand, FEM analysis estimates a smaller strain range in comparison with the actual strain range occurring at the notch root. The reason for the disagreement between FEM analysis and the actual strain results from the change in material response die to creep loading. Under creep fatigue conditions, the so-called plastic creep interaction which FEM analysis does not take account of, occurs. The local strain calculated from conventional methods, Neuber's rule, Stowell-Hardrath-Ohman and Koe's methods are also compared with the strain measurement in no-hold-time tests. All the methods overestimate the strain concentration at the notch root.

Stress concentration factors in finite anti-plane shear: numerical calculations and analytical estimates

In two recent papers [1, 2], an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous isotropic incompressible materials was presented. For the problem of an infinite slab, with a traction-free circular or elliptical cavity, subject to a state of finite simple shear deformation, explicit estimates for the stress concentration factor were obtained in terms of the cavity geometry, applied stress at infinity and constitutive parameters. In this paper, numerical results for these stress concentration factors are obtained using a finite-difference scheme and the analytical and numerical results are compared.

A discussion on various estimations of elastic stress distributions and stress concentration factors for sharp edge notches

The elastic stress distributions in some edge-notched geometries have been estimated from Creager and Paris's and Neuber's expressions. Close to the notch root, these approximate solutions agree well with the finite element results. Further away from the notch, the approximate methods give overestimations. A simple formula derived from Creager and Paris's expression provided accurate stress concentration factor solutions for some edge-notched geometries.

Static strength analysis of pin-loaded lugs

A new method of analysis is presented for predicting the static strength of straight and tapered pin-loaded lugs. The method of analysis is applicable to both tension and shear bearing types of failure. It is shown that the bearing efficiency factor KBR is uniquely related to the elastic tension stress concentration factor at the edge of the lug hole. Based on this relationship, a method of static strength analysis is developed that accounts for lug eccentricity and loading angle. The ratio of predicted load divided by test load for 243 lug tests made from 24 materials was 0.85-1.19, with a mean of 1.003. Based on these results, the method of analysis could be applied to other lug geometries if the elastic tension stress concentration factors are known.

Kinetics of deformation and damage accumulation in concentration zones with nonisothermal low-cycle loading

Data are given for endurance with nonisothermal loading of steel 15Kh2MFA specimens with elastic stress-concentration factors of 2.5 and 3.5. Results and test procedure are given in detail. Specimen heating was carried out in a lowintertial furnace with a quartz-halogen lamp of the KGM type. It was established that the heating method used provides quite a uniform field around the concentrator in the specimen plane. In order to isolate the thermal component of deformation, prior thermal cycling was carried out without a load. The authors note that the difference in endurance values for the test material in concentration zones with isothermal and nonisothermal loading schedules is caused by deformation properties of the material in the temperature range considered.

An Investigation on Formulation of Cyclic Local Strain Range and Estimation of Fatigue Life in Notched Plate (2nd Report)

In order to evaluate the fatigue life in the stress-concentrated region of structures using the results of strain-controlled fatigue tests, it is necessary to know the cyclic local strain range rather than the monotonous strain behavior. In the present study, a simple method to estimate the local strain range under cyclic loading was investigated.Namely, the elastic-plastic finite element analyses under cyclic tensile load were conducted on the highly stress-concentrated models besides the results in the first report. Then an investigation was made into the effects of applied cyclic stress condition, elastic stress concentration factor and material properties on the shakedown and the behaviors of local stress, strain ranges and their concentration factors.As a result, the formulae to estimate the shakedown limit and the cyclic local strain range were derived. Therefore, when the elastic stress concentration factor and the material properties such as cyclic yield stress, workhardening modulus and parameter of the Bauschinger effect are given, the cyclic local strain range can be estimated for a certain applied cyclic stress range. Then, by substituting the estimated strain range into a relationship between the strain range and the failure life obtained by the strain-controlled fatigue test, the fatigue evaluation can be done reasonably for the structural members.The stress-controlled fatigue test on notched plates and the strain-controlled low cycle fatigue test on small smooth specimens were conducted on 50 kgf/mm2 class steel. Then the estimated local strain range and fatigue life were compared to the experimental results. As a result, the estimated values agreed well with the measured values. In addition, the comparisons were made between the estimated fatigue lives on notched plates and the results so far published. Then it was found that the method proposed in this study can be applied to evaluate well the fatigue lives in the wide range from 5 × 102 to 5 × 106 cycles in the notched plates of 41 to 80 kgf/mm2 strength levels.

Evaluation on Brittle Fracture Initiation from Surface Notch at Fillet Weld Toe using COD Design Curve

As a model of the stress concentrators in the welded structures, a wide plate test with stiffener was carried out, and the brittle fracture characteristics from a surface notch at the toe of the fillet weld was studied. The results of the investigation are summarized as follows.CTOD values obtained from the wide plate test are agreed well with those from COD test with a/w=0.5, even for the very shallow surface notch in the wide plate test. It is confirmed from this results that CTOD criterion can be applied to elastic-plastic fracture from the surface crack in the highly deformed region.The brittle fracture strength from the surface notch at the fillet weld toe is evaluated using COD design curve, which is obtained by modifying WES 2805. The strain at the toe used in the evaluation is estimated for the average value in the cracked area. The strain concentration factor at the toe is caluculated from the elastic stress concentration factor by means of the modified Neuber's relation. Using such strain and COD design curve, the brittle fracture strength is well estimated.

高温クリープ域での長周期疲労寿命推定法に関する一考察

This paper describes a method of predicting low-cycle fatigue life in long-term hold-time tests at elevated temperatures. In order to develop a proper life prediction method under creep-fatigue conditions, especially for the case of long hold-time, the correlation between the static creep rupture data and the low-cycle fatigue data in hold-time tests was examined. The specimens used were an unnotched and three round notched ones of austenitic stainless steels of SUS 304 and SUS 316 having elastic stress concentration factors of 2.6, 4.2 and 6.0. Zero-to-tension low-cycle fatigue tests were carried out by four modified creep machines at 873K using trapezoidal stress waves with 10, 30, 60, and 1440min hold-time. Static creep tests were also carried out on those specimens.Two fracture regions were found to exist in the failure cycles-test frequency plot: one is the cycle-time dependent fracture region where the elastic stress cocnentration reduces the low-cycle fatigue life and the other is the pure time dependent fracture region where it does not. A new prediction method of fatigue life of the unnotched and the notched specimens in low-cycle tests with various hold times from the static creep rupture time and low-cycle fatigue life data obtained in no hold-time and comparatively short hold-time tests was proposed.

Stress Analysis Applications to Service Failures of Traveling-Wave Tubes

By utilizing the mathematical analogy between the electrostatic fields and the elastic stress field, the electrostatic stresses in high voltage electronic device such as Traveling Wave Tubes (TWT) can be obtained from finite element technique. A new point of view about the vacuum electrical breakdown from the theory of elastic stress concentration has been proposed. The elastic stress concentration factors may be used as a good reference figure for TWT design works.

Finite anti-plane shear of an infinite slab with a traction-free elliptical cavity: Bounds on the stress concentration factor

This paper provides an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous, isotropic, incompressible materials. The problem of an infinite slab with traction-free elliptical cavity subject to a state of finite simple shear deformation is considered. Explicit estimates are obtained for the maximum shear stress in terms of the cavity geometry, applied stress at infinity and constitutive parameters. The analysis is based on application of maximum principles for second-order quasilinear uniformly elliptic equations.

Bounds on stress concentration factors in finite anti-plane shear

This paper provides an analytical approach for obtaining bounds on elastic stress concentration factors in the theory of finite anti-plane shear of homogeneous, isotropic, incompressible materials. The problem of an infinite slab with traction-free circular cavity subject to a state of finite simple shear deformation is considered. Explicit estimates are obtained for the maximum shearing stress in terms of the applied stress at infinity and constitutive parameters. The analysis is based on application of maximum principles for second-order quasilinear uniformly elliptic equations.

Estimation of Stress and Strain at the Notch Root in the Elastic-plastic Range using the J-integral

An elastic-plastic analysis of notched plates was made. The J-integral of the notched plates was computed, and the relations between the value of J-integral and the stress and strain at the notch root were discussed. It was found that a master-curve representation of the stress σ or the strain e at the notch root was possible on a σ/σY (or e/eY)-J/Jyield diagram( σY : yield stress, eY : yield strain, Jyield : the J-integral value at which notch root yielding starts). The J-integral was found to be approximately given as J=Jlinear ( = elastic J-integral) when P/PGY≤1, regardless of the stress condition, the elastic stress concentration factor Kt and the strain hardening characteristics of the material (P : the applied load, PGY : the gross yield load of the respective notched plate) By combining these two findings, a simple method was proposed to estimate the stress and strain at the notch root in the elastic-plastic range up to gross yielding.