Deformation und Versagen von StE460 und AlMg4,5Mn bei mehrachsig-proportionalen Beanspruchungen mit konstanten und variablen Amplituden

Deformation and failure behaviour of FeE460 and AlMg4.5Mn under multiaxial proportional loading with constant and variable amplitudes To calculate the fatigue life-to-crack initiation of engineering components under combined cyclic loading, experimentally secured knowledge on the cyclic deformation and failure behaviour of the materials used under the certain multiaxial cyclic stress and strain conditions are required. To obtain this, strain-controlled fully reversed experimental tests at tensional, torsional and combined loading with constant and variable amplitudes have been conducted using thin-walled tube specimens of FeE460 and AlMg4.5Mn. Experimental tests on standard uniaxially loaded hourglass specimens have also been conducted to study specimen form effects. Cyclic deformation behaviour can be uniformly described by the stabilised cyclic σ-ε-curve, if stresses and strains are expressed as equivalent values according to the von Mises criterion. Failure behaviour at constant and variable amplitude loading is characterized by the initiation and growth of short cracks at right angle to the direction of the greatest principal stress (mode I) in the case of tensional or combined loading and by short crack growing in both shear stress directions (mode II+III) in the case of torsional loading. At fully reversed constant amplitude loading, all three types of load can be described by one constant amplitude strain life-to-crack initiation curve. At variable amplitude loading (notch strain simulation with gaussian spectrum, H₀=10⁵), the experimental fatigue life-to-crack initiation values are lower than estimated values based on Miner-calculations using an equivalent stress-strain supported P_SWT-N-curve. The question of mean stresses and their evaluation is discussed.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

In engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter Γ_T is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.     

Selection of the critical plane orientation in two-parameter multiaxial fatigue failure criterion under combined bending and torsion

The present paper is focused on engineering application of the algorithm of fatigue life calculation under multiaxial fatigue loading. For that reason, simple two-parameter multiaxial fatigue failure criterion is proposed. The criterion is based on the normal and shear stresses on the critical plane. Experimental results obtained under multiaxial proportional, non-proportional cyclic loading and variable-amplitude bending and torsion were used to verify the proposed two-parameter criterion and other well-known multiaxial fatigue criteria. Elastic–plastic behaviour of the bulk material was taken into account in calculation of the stress/strain distribution across the specimen cross-section. It is shown that the proposed two-parameter multiaxial fatigue failure criterion gives the best correlation between the experimental and calculated fatigue lives.     

Modelling Residual Strains During Cycling of Ti–Ni and Ti–Ni–Cu Shape Memory Alloys in a Pseudoelastic Range of Behaviour Conditions

Abstract: Pseudoelastic behaviour of three types of Ti–Ni shape memory alloys in a pseudoelastic state has been studied under conditions of maximum strain‐ and maximum stress‐controlled cycling. Experimental results proved that residual deformation after unloading increases with the number of cycles; however, critical stress for the induction of martensite and the energy dissipated in one cycle decline during cycling. A higher critical stress for slip, and more intense cyclic dislocation hardening promoted by greater maximum deformation and greater maximum applied stresses, generally reduce the rate at which residual elongation grows with the number of cycles, and tend to stabilise the cyclic stress‐elongation diagrams. The small magnitude of critical stress for slip in low‐nickel alloys, and also cyclic strain hardening, induce greater internal stresses and a more marked decrease in critical stress for the induction of martensite as cycling progresses. Detailed analysis of plastic deformation propagation in cyclically loaded specimen helped develop a model of dependence of residual elongation on the number of cycles. This model enables identification of three main factors that govern the magnitude of residual elongation: one residual plastic elongation caused by dislocation hardening after the alloy is heat treated, and two cyclic strain hardening parameters describing how residual elongation grows with number of cycles, and how this residual elongation is reduced, as cycles increase, by the rising critical stress level for slip. The model has proved to yield very close agreement with experimental findings.     

Standing contact fatigue with a cylindrical indenter

A hardened steel cylinder was repeatedly pressed against a flat case‐hardened steel specimen that was equally wide as the cylinder was long. Some contact end effects were noted as a result of limited plastic deformation. A strain gauge on the contact surface, just outside the contact and oriented perpendicular to the cylinder detected a surface strain when the cylinder was loaded. The non‐zero surface strain was the result of boundary effects of the finite specimen. Four different types of contact fatigue cracks developed in and below the specimen contact surface. The cracks were named lateral, median, contact end and edge cracks. Changes in the measured surface strain values could be used to determine when the lateral and edge cracks developed. The order in which all four crack types typically developed was determined from optical crack observation at test termination, strain measurements and stress computations. Numerical computations using finite‐element (FE) analyses were used to verify the surface strain behaviour due to loading and cracking; to verify contact end effects; crack locations and crack orientation by aid of the Findley multi‐axial fatigue criterion.     

Numerical and experimental validation of residual stresses of laser‐welded joints and their influence on the fatigue behaviour

In this work laser‐welded tube‐tube specimens made of aluminium alloys AlMg3.5Mn and AlSi1MgMn T6 were experimentally tested under constant and variable amplitude loading, under pure axial and pure torsion loading. In order to evaluate the influence on fatigue behaviour of the residual stresses, because of the welding process, some specimens were subjected to postweld heat treatment and then were tested. The numerical analyses, using finite element (FE), were carried out to obtain a reliable estimation of the residual stress in the specimen. The numerical results were in a good agreement with experimental ones obtained by means of hole‐drilling method. Finally, the residual stress distribution was superimposed to stress distribution because of fatigue loads obtained by FE analyses applying local concept, to calculate the stresses in the crack initiation zone and to understand the different types of failure that occurred in as‐welded and relieved specimens.     

Numerical simulation of residual stress relaxation around a cold‐expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models

Cold expansion of fastener holes creates compressive residual stresses around the hole. This well‐known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.     

Generation of residual stress and plastic strain in a fracture mechanics specimen to study the formation of creep damage in type 316 stainless steel

Residual stresses are created in type 316H stainless steel fracture mechanics specimens using the process of local out‐of‐plane compression (LOPC). Three sets of LOPC tools are used to create different distributions of residual stress near to the crack tip. Also the tools create different levels of prior plastic strain. Residual stresses are measured using the neutron diffraction method and compared with the stress predictions obtained from finite element (FE) simulations of LOPC. The specimens are then subjected to thermal exposure at 550 °C for several thousand hours. A creep deformation and damage model is introduced into the FE analysis to predict the relaxation of stresses and creation of damage in the specimens. Neutron diffraction experiments are undertaken to measure the relaxed residual stresses and fractographic analysis of thermally exposed samples measured the extent of creep damage. A comparison between measured and simulated results demonstrates that the prior plastic strain has a significant effect on damage accumulation but this is not accounted for in the current creep damage models.     

FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.     

Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction

This study deals with simulation for cyclic stress/strain evolutions and redistributions, and evaluation of fatigue parameters suitable for estimating fatigue lives under multiaxial loadings. The local cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures of ABAQUS finite element code for both smooth and notched specimens made of three materials: a medium carbon steel in the normalized condition, an alloy steel quenched and tempered and a stainless steel, respectively. Emphasis is on the studying of ‘intelligent’ material behaviors to resist fracture, such as stress redistribution and relaxation through plastic deformations, etc. For experimental verifications, a series of tests of biaxial low cycle fatigue composed of tension/compression with static and cyclic torsion were carried out on a biaxial servo-hydraulic testing machine (Instron 8800). Different multiaxial loading paths were used to verify their effects on the additional cyclic hardening. The comparisons between numerical simulations and experimental observations show that the FEM simulations allow better understanding on the evolutions of the local cyclic stress–strain and it is shown that strong interactions exist between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the local cyclic elastic–plastic stress–strain responses, the energy-based multiaxial fatigue damage parameters are applied to correlating the experimentally obtained lives. Improved correlations between the predicted and the experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses.     

Untersuchungen zur Dauerfestigkeit carbonitrierter Proben aus den Einsatzstählen 18CrNiMo7‐6und 20MnCr5

The endurance limit of carbonitrided specimens of 18CrNiMo7‐6 and 20MnCr5 case hardening steels were examined under bending conditions. Four variants were manufactured differing in heat treatment and surface conditions. Besides conventional gas carburised variants, carbonitrided specimens with a low and a raised nitrogen content of 0.2 and 0.45% at the surface as well as a carbonitrided and ground variant were examined. The specimens were tested with stress ratios R = –1 and 0. Depending on the nitrogen content cyclic loading evokes compressive residual stresses at the specimens' surfaces, caused by elastic‐plastic deformation. Specimens of the ground variant show additionally a decrease of the residual austenite content when cycled. The induced compressive residual stresses are substantially responsible for high endurance limits at both stress ratios and are the key for understanding the beneficial effect of carbonitriding in this regard.     

Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity,non‐zero mean stresses,and critical distance/plane

This paper deals with the formulation and experimental validation of a novel fatigue lifetime estimation technique suitable for assessing the extent of damage in notched metallic materials subjected to in‐service proportional/nonproportional constant/variable amplitude multiaxial load histories. The methodology being formulated makes use of the Modified Manson‐Coffin Curve Method, the Shear Strain–Maximum Variance Method, and the elasto‐plastic Theory of Critical Distances, with the latter theory being applied in the form of the Point Method. The accuracy and reliability of our novel fatigue lifetime estimation technique were checked against a large number of experimental results we generated by testing, under proportional/nonproportional constant/variable amplitude axial‐torsional loading, V‐notched cylindrical specimens made of unalloyed medium‐carbon steel En8 (080M40). Specific experimental trials were run to investigate also the effect of non‐zero mean stresses as well as of different frequencies between the axial and torsional stress/strain components. This systematic validation exercise allowed us to demonstrate that our novel multiaxial fatigue assessment methodology is remarkably accurate, with the estimates falling within an error factor of 2. By modelling the cyclic elasto‐plastic behaviour of metals explicitly, the design methodology being formulated and validated in the present paper offers a complete solution to the problem of estimating multiaxial fatigue lifetime of notched metallic materials, with this holding true independently of sharpness of the stress/strain raiser and complexity of the load history.     

A study of fatigue crack growth with changing loading direction

Round compact specimens made of 1070 steel were experimentally tested under cyclic loading for crack growth. The specimen was first subjected to Mode I loading. After the crack reached a certain length, the external loading direction was changed 50° from the original loading direction. Right after the change of the loading direction, the specimen experienced the combined Mode I/II loading condition. Following a short transient period, the fatigue crack was found to grow in the direction approximately perpendicular to the external loading direction, indicating the recovery of Mode I cracking. A recently developed approach was used to predict the cracking behavior of the specimens. Detailed elastic-plastic stress analysis was conducted using the finite element (FE) method. Both crack growth rate and cracking direction were predicted by employing a critical plane multiaxial fatigue criterion based on the stress-strain response outputted from the FE analysis. The predictions made by using the approach were in excellent agreement with the experimental observations in terms of both crack growth rate and cracking direction. The material constants used in the approach were obtained from testing smooth specimens for crack initiation.     

Micromechanical interactions in a superduplex stainless steel subjected to low cycle fatigue loading

Micromechanical interactions in an austenitic‐ferritic SAF 2507 steel under lowcycle fatigue loading was studied by experiment and simulation. Neutron diffraction measurements of residual lattice strains were made on specimens unloaded from different cyclic deformation stages, namely cyclic hardening, softening and saturation. With self‐consistent modelling, the micromechanical behaviour of the constituent phases was studied for the first loading cycle. The evolution of the residual lattice strain distributions with cyclic loading and the development of phase stresses have been analysed with respect to the initial residual stress field and the different mechanical properties of the constituent phases.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Deformation behaviour,short crack growth and fatigue livesunder multiaxial nonproportional loading

Experimental results of a research project on short crack growth under multiaxial nonproportional loading are presented. Fatigue lives, crack growth curves and the deformation behaviour of hollow tube specimens and notched specimens were investigated under combined tension and torsion loading. The results served as basis for the development of a cyclic plasticity model [Döring R, Hoffmeyer J, Vormwald M, Seeger T. A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading. In: Comput Mater Sci. 28(3–4);2003:587–96; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Constitutive modelling of nonproportional hardening, cyclic hardening and ratchetting. In: Proceedings of the seventh international conference on biaxial/multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 291–6; Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004.] and a short crack model [Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Fatigue lifetime prediction based on a short crack growth model for multiaxial nonproportional loading. In: Proceedings of the seventh international conference on biaxial and multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 253–8].Stress–strain paths including nonproportional hardening and experimental fatigue lives of the unnotched specimens under different loading cases are discussed and compared with calculations. Load-time-sequences were in-phase, 45° and 90° out-of-phase loading with constant and variable amplitudes, torsion without and with superimposed static normal stress, and strain paths like box, butterfly, diamond and cross path. For the notched specimens fatigue lives under 0° and 90° out-of-phase loading are compared with calculations based on finite element results and the short crack model. During some tests the initiation, growth and orientation of short cracks was studied using the plastic replica technique.     

A hardness law for inelastic deformation

Certain formulations of elastic-viscoplastic constitutive equations lead to inelastic deformations being governed by a functional relation between the plastic deformation rate and the stress. A parameter that appears in certain forms of this equation can be interpreted as an internal variable measure of the overall resistance of the material to plastic flow. In this paper, it is taken to be a second order tensor and designated the “hardness stress.” A procedure for calculating changes in the hardness stress parameter for general multiaxial loading histories is proposed in this paper. These evolutionary equations lead to induced plastic anisotropy. Stress-strain relations that would be predicted by this procedure appear to be consistent with experimental results for various multiaxial loading histories including proportional and non-proportional cyclic loading.     

A 3D full‐field study of cracks in a nuclear graphite under mode I and mode II cyclic dwell loading conditions

Three‐dimensional (3D) full‐field deformation around crack tips in a nuclear graphite has been studied under mode I and mode II cyclic dwell loading conditions using digital volume correlation (DVC) and integrated finite element (FE) analysis. A cracked Brazilian disk specimen of Gilsocarbon graphite was tested at selected loading angles to achieve mode I and mode II cyclic dwell loading conditions. Integrated FE analysis was carried out with the 3D displacement fields measured by DVC injected into the FE model, from which the crack driving force J‐integral was obtained using a damaged plasticity material model. The evolution of near‐tip strains and the J‐integral during the cyclic dwell loading was examined. Under cyclic dwell, residual strain accumulation was observed for the first time. The results shed some light on the effect of dwell time on the 3D crack deformation and crack driving force in Gilsocarbon under cyclic mode I and II loading conditions.     

Kurzrisswachstum bei mehrachsig nichtproportionaler Beanspruchung

Short fatigue crack growth under multiaxial nonproportional loading Initiation and short fatigue crack growth have been investigated under nonproportional cyclic loading. A critical plane approach based on fracture mechanics is used for modelling the fatigue process. A Paris‐type crack growth law, formulated using the effective cyclic J‐integral as crack driving force parameter, is integrated to give crack growth curves. Crack opening stresses and strains are calculated with approximation equations. Jiang's plasticity model is used to predict the stress‐strain path. The good agreement between model and real damage evolution is shown comparing experimentally determined crack growth curves, crack orientations, and life curves.