The Peak Stress Method to assess the fatigue strength of welded joints using linear elastic finite element analyses

Abstract In fatigue design of welded joints according to the notch stress intensity factor (NSIF) approach, the weld toe profile is assumed to be a sharp V-notch having tip radius equal to zero, while the root side is assumed to be a pre-crack in the structure. The Peak Stress Method (PSM) is an engineering, FE-oriented method to estimate the NSIFs starting from the singular linear elastic peak stresses calculated at the V-notch or crack tips by using a coarse FE mesh. The element type is kept constant and the average element size can be chosen arbitrarily within a given range. The method is used in conjunction with Ansys software. The FE meshes are claimed to be coarse in comparison to those necessary to evaluate the NSIFs from the local stress distributions. Two-dimensional as well as three dimensional FE analyses can be adopted to apply the method. By using the averaged Strain Energy Density (SED, which can be expressed as a function of the relevant NSIFs) as a fatigue strength criterion, a so-called equivalent peak stress is defined to assess either weld toe or weld root fatigue failures in conjunction with a properly calibrated design curve. After presenting the theoretical background of the method, the paper presents a review of applications of the PSM relevant to steel welded joints under uniaxial as well as multiaxial fatigue loadings. Because of the relatively coarse FE analyses required and simplicity of post-processing the calculated peak stresses, the PSM might be useful in the everyday design practice

The Heat Energy Dissipated in a Control Volume to Correlate the Fatigue Strength of Bluntly and Severely Notched Stainless Steel Specimens

Abstract In previously published papers by the authors, the specific heat energy loss per cycle (the Q parameter) was used to rationalize about 120 experimental results generated from constant amplitude, push-pull, stress- or strain-controlled fatigue tests on plain and notched hot rolled AISI 304 L stainless steel specimens as well as from cold drawn un-notched bars of the same steel, tested under fully-reversed axial or torsional fatigue loadings. It has been shown that Q can be estimated starting from the cooling gradient measured at the critical point immediately after the fatigue test has been stopped. Concerning notched specimens, it was noted that a 3 mm notch tip radius was close to the limitation of applicability of the adopted temperature sensor, consisting in 0.127-mm-diameter thermocouples, because of the 1.5-to-2 mm diameter spot of the glue which prevented to measure the maximum temperature level. In this paper, the fatigue-damage-index effectiveness of Q parameter was investigated, carrying out fully reversed axial fatigue tests on 4-mm-thick AISI 304L specimens, having 3, 1 and 0.5 mm notch tip radii. The cooling gradients were measured by using an infrared camera, characterized by a 20 μm/pixels spatial resolution. As a result, all new fatigue data could be rationalized using the same scatter band published previously by the authors

investigation of the crack tip stress field in a stainless steel sent specimen by means of thermoelastic stress analysis

Abstract In this work a Thermoelastic Stress Analysis (TSA) setup is implemented to investigates the Thermoelastic and Second Harmonic signals on a fatigue loaded Single Edge Notched Tension (SENT) specimen made of stainless steel AISI 304L. Three load ratios are in particular applied, R=-1, 0, 0.1. The thermoelastic signal is used to evaluate the Stress Intensity Factor via two approaches, the Stanley-Chan linear interpolation method and the over-deterministic least-square fitting (LSF) method using the Williams' series expansion. Regarding least-square fitting, an iterative procedure is proposed to identify the optimal crack tip position in the thermoelastic maps. The SIF and T-Stress are then evaluated considering the influence of the number of terms (up to 20) in the Williams' series function, and the extent and position of the area used for data input. The study also investigates the Second Harmonic signal observed on the wake of the crack with varying load ratio R. An interpretation is proposed that considers the rise of the Second Harmonic as the result of the modulation of the compression loads between the crack flanks, rather than dissipation phenomena. This interpretation enables the possibility to use this parameter to reveal the presence and extent of crack-closure

Evaluating the specific heat loss in severely notched stainless steel specimens for fatigue strength analyses

Abstract In the last years, a large amount of fatigue test results from plain and bluntly notched specimens made of AISI 304L stainless steel were synthetized in a single scatter band adopting the specific heat loss per cycle (Q) as a damage parameter. During a fatigue test, the Q parameter can be evaluated measuring the cooling gradient at a point of the specimens after having suddenly stopped the fatigue test. This measurement can be done by using thermocouples in the case of plain or notched material; however, due to the high stress concentration at the tip of severely notched components analysed in the present paper, an infrared camera achieving a much improved spatial resolution was adopted. A data processing technique is presented to investigate the heat energy distribution close to the notch tip of hot-rolled AISI 304L stainless steel specimens, having notch tip radii equal to 3, 1 and 0.5 mm and subjected to constant amplitude cyclic loads

Fat classes of welded steel details derived from the master design curve of the peak stress method

In this paper, the peak stress method (PSM) is adopted to analyse the fatigue strength of steel welded joints. According to this method, a single design curve is expressed in terms of a properly defined equivalent peak stress and it is valid for fatigue design of arc-welded steel joints. Private companies often need simple finite element beam models for fatigue strength assessments, because of the large dimensions of the structures. However, beam elements provide nominal stresses (and not local stresses) that must be compared with appropriate fatigue strength values (the FAT classes) available in design standards. Due to the limited number of FAT classes available, finding the appropriate one is frequently troublesome, particularly when complex geometries are considered. The objective of this work is to define FAT classes in terms of nominal stress for a number of geometrically complex structural details, starting from the design curve of the PSM. FAT classes have also been determined using the hot spot stress approach. Then the results obtained with the two methods are compared. The structural details analysed in the present paper are typically adopted in amusement park structures and are not classified in common design standards

the peak stress method combined with 3d finite element models to assess the fatigue strength of complex welded structures

Abstract The Peak Stress Method (PSM) is a rapid and engineering application of the notch stress intensity factor (NSIF) approach for the fatigue strength assessment of welded structures, which employs the singular linear elastic peak stresses calculated by FEM using coarse meshes. First, the PSM was calibrated to rapidly estimate the NSIFs by adopting 3D, eight-node brick elements and by using the submodeling technique. Given the increasing 3D modelling of large and complex structures in the industry, the application of the PSM combined with 3D FE models has recently been speeded up by calibrating ten-node tetra elements, which allow to directly discretize complex 3D geometries making submodeling unnecessary. In the present contribution, the PSM has been calibrated by analysing several 3D mode I, II and III V-notch problems, by adopting either four-node or ten-node tetra elements. In particular, the 3D PSM with ten-node tetra elements has been extended to V-notch opening angles that had not been taken into account in a previous calibration, namely (i) 120° under mode I and (ii) 90° and 120° under mode III loadings. Then, an applicative example has been considered, which is relevant to a large-scale and rather complex steel welded structure, having overall size on the order of meters. The mesh density requirements to apply the PSM to the considered large-scale welded structure using either four-node tetra elements or ten-node tetra elements have been compared in order to assess the solution time required by the two types of FE meshes

definition of nominal stress based fat classes of complex welded steel structures using the peak stress method

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correlation among energy based fatigue curves and fatigue design approaches

Abstract In this paper, with reference to the strain controlled fatigue characterization of AISI 304L stainless steel, the correlations between plain material fatigue curves based on different definitions of the strain energy densities, namely the elastic, plastic and elastoplastic strain energy densities evaluated under the cyclic stress-strain curve and the plastic strain hysteresis energy density (per cycle and total at fracture) are investigated. On this basis, a diagram showing the link among the different energy-based fatigue curves is proposed and is applied to find the correlation between plain material strain energy density fatigue curves and some fatigue strength assessment methods for notched structural components, namely the one based on the experimental evaluation of the heat energy dissipated by the material per cycle and the one based on the evaluation of the linear elastic strain energy density, averaged in a properly defined structural volume

use of the peak stress method to assess the fatigue life of large welded steel structures

Abstract A precise life assessment of weld seams in large welded steel structures such as the ones from crawler excavators is very important in order to be able to optimize these structures. The local stress approaches with fictitious notch radius have been proved to be necessary to achieve the desired precision in some cases. Unfortunately, these methods are very time and resources consuming making it impossible to be applied systematically on large steel structures. The Peak Stress Method (PSM) could be an alternative since its precision seems to be good and that the method is much easier to apply. This paper shows the results of the tests that have been done on PSM applied to large steel structures from hydraulic excavators. Comparisons have been made in terms of precision and speed with the fictitious notch radius method

On the use of the Peak Stress Method for the calculation of Residual Notch Stress Intensity Factors: a preliminary investigation

Residual stresses induced by welding processes significantly affect the engineering properties of structural components. If the toe region of a butt-welded joint is modeled as a sharp V-notch, the distribution of the residual stresses in that zone is asymptotic with a singularity degree which follows either the linear-elastic or the elastic-plastic solution, depending on aspects such as clamping conditions, welding parameters, material and dimension of plates. The intensity of the local residual stress fields is quantified by the Residual Notch Stress Intensity Factors (R-NSIFs), which can be used in principle to include the residual stress effect in the fatigue assessment of welded joints. Due to the need of extremely refined meshes and to the high computational resources required by non-linear transient analyses, the R-NSIFs have been calculated in literature only by means of 2D models. It is of interest to propose new coarse-mesh-based approaches which allow residual stresses to be calculated with less computational effort. This work is aimed to investigate the level of accuracy of the Peak Stress Method in the R-NSIFs evaluation