Nonlinear mode III crack stress fields for materials obeying a modified Ramberg‐Osgood law

In this paper, an analytical study is carried out on the work‐hardening, elastic‐plastic stress distributions in a cracked body under antiplane shear deformation. A modified Ramberg‐Osgood law is introduced to describe the material behaviour, and stress and strain fields are derived in closed form. Compared with the conventional Ramberg‐Osgood formulation, the new law includes the effect of a new parameter, κ, which allows the transition from the ideally elastic behaviour (low stress regime) to the power law behaviour (large stress regime) to be controlled, thus providing 1 more degree of freedom to better fit the actual behaviour of engineering materials. A discussion is carried out on the features of stresses and strains close to and far away from the crack tip.     

Neue Auswertungsmethode zur Bestimmung der Kennwerte der Dehnungswöhlerlinie und der Spannungs‐Dehnungs‐Kurve unter Berücksichtigung der Kompatibilität

New method for evaluation of the Manson‐Coffin‐Basquin and Ramberg‐Osgood equations with respect to compatibility A new method for determining the stress‐strain and strain‐life curves for metals is presented. The method involves fitting the curve to experimental data points in a three‐dimensional strain‐stress‐life space. With the plastic part of strain, stress and fatigue life as coordinates, a straight line is used for fitting the experimental data points. The material constants are calculated directly from the directional vector R and the coordinates of the point P , which determines the fitted straight line. It is shown that the assumption of equality of the plastic and elastic components in Manson‐Coffin‐Basquin and Ramberg‐Osgood equations leads to the so called compatibility condition. This new method retains the mathematical and physical relationships between the considered curves. The results obtained from this new method using high‐strength aluminium alloys subjected to different manufacturing conditions and different test temperatures are presented. These results are compared to results obtained with a conventional method for determining the fatigue parameters.     

Crack closure in friction stir weldment using non‐linear model for fatigue crack propagation

The fatigue crack propagation in a friction stir‐welded sample has been simulated herein by means of two 3‐dimensional finite element method (FEM)‐based analyses. Numerical simulations of the fatigue crack propagation have been carried out by assuming a residual stress field as a starting condition. Two initial cracks, observed in the real specimen, have been assessed experimentally by performing fatigue tests on the welded sample. Hence, the same cracks have been placed in the corresponding FE model, and then a remote load with boundary conditions has been applied on the welded specimen. The material behaviour of the welded joint has been modelled by means of the Ramberg‐Osgood equation, while the non‐linear Kujawski‐Ellyin (KE) model has been adopted for the fatigue crack propagation under small‐scale yielding (SSY) conditions. Owing to the compressive nature of the residual stress field that acts on a part of the cracked regions, the crack closure phenomenon has also been considered. Then, the original version of the KE law has been modified to fully include the closure effect in the analysis. Later, the crack closure effect has also been assessed in the simulation of fatigue propagation of three cracks. Finally, an investigation of the fracture process zone (FPZ) extension as well as the cyclic plastic zone (CPZ) and monotonic plastic zone (MPZ) extensions have been assessed.     

Monotonic and low cycle fatigue behaviour of 2024‐T3 aluminium alloy between room temperature and 300 °C for designing VAWT components

In the present study, the results of the monotonic tension tests and low cycle fatigue tests performed on aluminium alloy EN AW‐2024‐T3 under various operating temperatures are presented in order to assess the fatigue behaviour of the aluminium alloy under evaluated temperatures. Monotonic tests were performed to determine the influence of temperature on mechanical properties of the material. The aim of cyclic tests was to acquire the parameters required for Manson–Coffin equation in order to plot strain–fatigue life curves. Moreover, stress–strain behaviour of the alloy and the cyclic hardening behaviour were evaluated using Ramberg–Osgood equation. Finally, P_SWT‐damage parameters for each temperature have been calculated for further investigation of the effects of the temperature on fatigue life using acquired data while taking the account of mean stress effect into calculations. Variations in the experimental data due to various test temperatures are presented for both monotonic and cyclic tests.     

A local strain method for the evaluation of welded joints fatigue resistance: the case of thin main-plates thickness

Current procedures for evaluating fatigue strength of welded structures may not be consistent with the real fatigue behaviour of welded joints. A local strain method for the prediction of the WELded joints FAtigue REsistance (WELFARE), by local strain measurements at the weld toe, was recently proposed on the basis of fatigue tests on more than 10 series of welded joints (T, cruciform, angular and butt joints) in structural steel, with 10–25 mm main‐plate thickness. This paper reports fatigue test results obtained from 30 cruciform and butt welded joints (3–5 mm thick) under two load ratios (0.1 and ?1) in order to extend the applicability of the method to thin welded joints.     

Fatigue behaviour of welded joints from magnesium alloy (AZ31) according to the local strain concept

In the present study, the results of fatigue tests with the magnesium alloy AZ31 (ISO‐MgAl3Zn1) in the material states base metal, heat affected zone and weld metal obtained under strain control at room temperature within a range from 2·10² to 5·10⁶ cycles are presented. The fatigue behaviour was characterized by the Coffin–Manson–Basquin equations and the stress – strain behaviour by the Ramberg–Osgood equation. The data can be used to assess welded magnesium joints according to the local strain concept.     

A neural network approach for predicting steel properties characterizing cyclic Ramberg–Osgood equation

This paper attempts to demonstrate the applicability of artificial neural networks to the estimation of steel properties, cyclic strain‐hardening exponent and cyclic strength coefficient, characterizing cyclic Ramberg–Osgood equation on the basis of monotonic tensile test properties. For this purpose, steel tensile data were extracted from the literature and two separate neural networks were constructed. One set of data was used for training the two networks and the remaining for testing purposes. Regression analysis and mean relative error calculation were used to check the accuracy of the system in the training and testing phases. Comparison of the results obtained from the neural networks and the values obtained from direct fitting of experimental data, indicated the reasonable prediction of cyclic strain‐hardening exponent and cyclic strength coefficient, which are often used to characterize the cyclic deformation curve by a Ramberg–Osgood type equation.     

A multi‐axial low‐cycle fatigue life prediction model considering effects of additional hardening

It is generally accepted that the additional hardening of materials could largely shorten multi‐axis fatigue life of engineering components. To consider the effects of additional hardening under multi‐axial loading, this paper summarizes a new multi‐axial low‐cycle fatigue life prediction model based on the critical plane approach. In the new model, while critical plane is adopted to calculate principal equivalent strain, a new plane, subcritical plane, is also defined to calculate a correction parameter due to the effects of additional hardening. The proposed fatigue damage parameter of the new model combines the material properties and the angle of the loading orientation with respect to the principal axis and can be established with Coffin‐Manson equation directly. According to experimental verification and comparison with other traditional models, it is clear that the new model has satisfactory reliability and accuracy in multi‐axial fatigue life prediction.     

Multiaxial low‐cycle fatigue life evaluation under different non‐proportional loading paths

This paper presents analytical and experimental investigations for fatigue lives of structures under uniaxial, torsional, multiaxial proportional, and non‐proportional loading conditions. It is known that the rotation of principal stress/strain axes and material additional hardening due to non‐proportionality of cycle loading are the 2 main causes resulting in shorter fatigue lives compared with those under proportional loading. This paper treats these 2 causes as independent factors influencing multiaxial fatigue damage and proposes a new non‐proportional influencing parameter to consider their combined effects on the fatigue lives of structures. A critical plane model for multiaxial fatigue lives prediction is also proposed by using the proposed non‐proportional influencing factor to modify the Fatemi‐Socie model. The comparison between experiment results and theoretical evaluation shows that the proposed model can effectively predict the fatigue life due to multiaxial non‐proportional loading.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

Strain analysis at notch root in laser welded samples using material properties of individual weld zones

This paper presents results of the strain analysis at a notch root in a laser-welded joint subjected to cyclically variable stresses. The examined welds were made of S355JR (PN-EN 10025-2) ferritic steel. A theoretical analysis of strain was performed using cyclic material properties determined for individual weld zones. For the purpose of comparison, values of strains at a notch root were also determined using base metal properties. Experimental verification of determined strain values was performed using the laser grating interferometry method. Cyclic variations of material properties for base metal and welded joint zones were determined as per the standard and the methodology presented in previous study and described with the Ramberg–Osgood relationship. The above material properties were used to calculate strain at the root of two types of geometric notches machined in a laser-welded joint. Analytical calculations were performed using the Neuber’s rule, while numerical calculations with the use of the finite element method by means of the ABAQUS software.Test results confirmed good efficiency of the numerical strain analysis using cyclic material properties of the individual weld zones in low cycle fatigue.     

Studies in elastic fracture mechanics based on the material force method

The object of this work is to discuss a further improvement of the material force method for non‐linear hyperelastostatic fracture mechanics. We investigate the accuracy of the material force method within a ‘modified boundary layer’‐formulation using a Ramberg–Osgood material type for the sake of comparison. The proposed improvement leads to a reliable and very accurate method to compute the vectorial J‐integral in fracture mechanics. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimization research on S‐N curve of ring welding structure based on structural stress method

In engineering, △F‐N curves are usually used to predict the fatigue life of ring welding, which is time‐consuming, laborious, and not universal. To improve the above inadequacies, an S‐N curve for evaluating the fatigue life of the ring welded specimen is proposed. The fatigue life of ring welded specimens with different materials, plate thicknesses, and hole diameters is obtained by tensile and shear fatigue tests. Shell elements, CBar beam elements (a kind of beam element in Nastran that can simulate bending), and rigid elements are used to establish the finite element model of ring welding. The stress of the ring welding structure under tensile shear load is calculated according to the structural stress method. The stress range △ σs of the welding core is taken as the longitudinal coordinate and the experimental life N as the horizontal coordinate, using two‐parameter log‐log model and the least square method of the fatigue data for linear fitting to obtain the S‐N curve equation of fatigue life evaluation. Most of the data are located within five times of the life span, which proves that the predicted life is close to the actual life of the test, and it can provide a certain reference for design and life prediction of the ring welding structures.     

Modification of fatigue strain‐life equation for sheet metals considering anisotropy due to crystallographic texture

The fatigue behaviour of cold rolled and annealed sheet metals are influenced by the anisotropy of mechanical properties due to crystallographic texture. However, the existing fatigue strain‐life models are primarily meant for isotropic material behaviour. In the present work, the Coffin‐Manson equation for strain‐life is modified to include the effect of anisotropy using phenomenological plasticity models. It is observed that the variation of strain hardening exponent is critical to model the strain‐life behaviour. Variation of strain hardening exponent with orientation is modelled using existing anisotropic yield criteria. The prediction of fatigue life using the proposed model correlates well with the experimental results of Al6061‐T6 along different orientations. The proposed model can be used to predict the fatigue properties along any orientation from the fatigue data along one orientation and monotonic mechanical properties along longitudinal, transverse and diagonal directions.     

Identification of local cyclic stress‐strain curves at material inhomogeneities on the basis of digital image correlation

Low‐cycle fatigue (LCF) tests on butt‐welded joints revealed that material inhomogeneities become decisive for the fatigue behavior at elastic‐plastic strain amplitudes and the geometrical notch is no longer the failure location – as observed in high‐cycle fatigue (HCF) regime. Digital image correlation techniques enable the measurement of local strains at the surface of the welded region. A new method is proposed that is able to calculate related local stresses and identifies local cyclic material properties in structures of inhomogeneous material and geometry. This method combines strain measurements and Finite Element simulations. It is a fast iteration procedure that is able to perform the identification within less than ten iterative steps at several hundred local points. Transient material behavior is easy to capture and an application at high temperatures is anticipated due to the method is based on materials mechanics.     

Einfluss der Netztopologie der künstlich neuronalen Netze auf das Ergebnis der Abschätzung zyklischer Kennwerte

Several estimation methods have been developed to estimate the cyclic material parameters out of the static material properties. Most of these methods are based on empirical equations. Increasing numbers of input‐ and influencing parameters lead to an rising effort for determining these equations and the accuracy decreases. For this reason new suitable methods are sought to estimate the cyclic material behaviour. A very promising approach is the application of the artificial neural networks, which can derive self‐depended a relationship between in‐ and output parameters. Static parameters such as yield strength, tensile strength …? etc., which can rapidly be determined used as input parameters. The output parameters are the cyclic material parameters of the strain‐life curve and stress‐strain curve according to the Manson‐Coffin‐Basquin‐ and Ramberg‐Osgood curve. Many different artificial neural networks with different structures and complexity can be applied. In this paper the influence of the topology of an artificial neural network on the estimation accuracy will be investigated. Based on the results of a reference artificial neural network it will be shown, that more complex topologies in the network do not lead inevitably to better estimations.     

The local strain energy density approach applied to pre‐stressed components subjected to cyclic load

Ahead of sharp V‐notches, residual stresses, arising from the solidification of a fusion zone, have the same asymptotic nature of the stress field induced by mechanical loads. This stress field significantly affects the engineering properties of structural components, notably fatigue life and corrosion resistance of welded joints. Tensile residual stresses can reduce the fatigue strength of welded joints particularly in the high‐cycle regime, where no stress redistribution due to local plasticity phenomena is expected to be present. The aim of this work is to analyse, by means of the numerical simulation, the residual stress redistribution near a V‐notch tip induced by cyclic loads and to propose a method, based on the local strain energy approach, for the fatigue resistance estimation of pre‐stressed components. The numerical solutions of the problem were carried out under the hypothesis of generalized plane strain conditions by means of SYSWELD and SYSTUS codes.     

Modelling and fatigue life assessment of complex structures

This paper presents some of the motivations and main conclusions from a series of joint Nordic research initiatives in which an integrated research approach to the development of future generations of advanced fabricated structures have been employed. The integrated research approach includes coordinated efforts in several key technologies: high‐speed welding processes, high strength materials, cost‐effective NDE, post‐weld treatments and FE‐based design assessment tools. Traditionally, fatigue assessment methods for welded structures have been developed based on small‐scale test specimens and verification studies for large structures are rarely published. Applications on complex structures have led to several new assessment concepts and areas for future work. A modified structural stress method that proposes a multi‐linear stress distribution through the plate thickness is introduced. Also, a crack growth assessment method in which the constraint equations of a sub‐model are linked to the global model is presented. Both these new methods are promising for complex structures. The crucial role of boundary conditions for complex structures is highlighted as is the future challenge of understanding and making use of the residual stress state for welded structures.     

Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.