Multiaxial Stress-strain States Research Articles

Couple analysis of DIC and FEM to quantify strain fields and crack-flank displacements in structural materials under cyclic mixed-mode I/II fracture

Mixed mode cyclic fracture under multiaxial stress-strain state is critical for the generation of appropriate damage tolerance methodologies. To this end the elaborated approach is dedicated to full range of mixed mode loading for elastic-plastic plane problem. In this study, the digital image correlation (DIC) experimental results are represented as contours as well as radial strain distributions in the local system of coordinate centered at the current crack tip position along curvilinear crack path. As a complement to the DIC measurement, finite element (FE) modelling of the displacement and strain fields around the crack tip in the compact tension shear (CTS) specimen was performed in order to reproduce experimental mixed mode loading conditions. In this study, for comparison aim we used the conventional mechanism-based strain gradient (CMSG) and classical Hutchinson–Rice–Rosengren (HRR) plasticity theories to evaluate the coupled effect of the material plastic properties and the mode mixity on the crack tip behaviour. The new material model is implemented in a commercial finite element software package ANSYS 2021R1 using a user subroutine. The intention with this work was to complement the DIC measurements as well as acquire more detailed information about the local strain ahead of the crack tip and the crack opening. From a sensitivity analysis it has been established that the DIC value depends significantly from the location along the crack direction of the pair of points selected before and behind the crack tip. As a result of the FE calculations of strain distributions, the effects of both the fracture mode and the material properties are determined.

Low-cycle fatigue assessment of offshore mooring chains under service loading

The integrity of mooring chains is essential to the safety of a range of offshore platforms. However, mooring line failures are occurring earlier than their design lives, with a high number of these failures occurring due to fatigue. Early in the fatigue life of the component fatigue initiation processes occur, where the fatigue hotspot is sensitive to the mean load and there is plastic strain accumulation from the multiaxial stress-strain responses of the material, leading to cyclic plastic damage accumulation. The traditional SN approach suggested by mooring standards does not consider these effects, and it is proposed that this lack of consideration under low-cycle fatigue conditions is the reason for the current non-conservative fatigue assessments of mooring chains. This paper aims to develop a fatigue approach based on a critical plane multiaxial fatigue criterion for mooring chains that can consider the damage-induced by the cyclic plasticity and the mean load effect, to investigate the importance of incorporating low-cycle fatigue into the mooring chain life prediction. To develop the critical plane approach, the multiaxial stress-strain states are extracted for the critical plane at the fatigue hotspot from a finite element model of a mooring chain. This is then correlated with a fatigue life prediction provided by conventional fatigue design data. It uses a simulation of an FPSO as a case study to demonstrate the importance of low cycle fatigue, which shows that the mean load effect is significant in reducing the fatigue life for mooring chain applications, while the effect of fatigue damage-induced cyclic plasticity is limited. The fatigue damage accumulation predicted by the critical plane approach is significantly higher than that of the traditional SN approach and should be accounted for in mooring line design.

New method of the estimation of the bending strength of ultrafine-grained structural ceramics for application in the conditions of multiaxial stress-strain state

A new method of mechanical testing of high-strength ultrafine-grained ceramic materials by the method of spark plasma sintering (SPS) is proposed. A promising scheme for testing cylindrical SPS-samples is the “Ball on three balls test” (B3B) scheme. The B3B test method has advantages over the standard four-point bending test method, since it is not necessary to cut standard samples from disks, cylindrical samples are aligned on a special support. In this paper, we present a methodology for processing experimental B3B test data developed using the finite element method. The finite element method for estimating the parameters allows us to consider a larger number of parameters that affect the absolute value of the maximum principal stress. The experimental data processing technique takes into account the influence of the sample size, equipment geometry, physical and mechanical properties of the material, and friction coefficient.

A novel fixture for determining the tension/compression-shear failure envelope of multidirectional composite laminates

A new approach for biaxial loading of fibre reinforced composites is presented, based on the use of a Modified Arcan Fixture (MAF). In addition to combined tension-shear loading which can be achieved using a conventional Arcan fixture, the MAF allows the application of pure compression and compression-shear loading. Digital Image Correlation is used to obtain the full-field deformations of the specimens to establish the load response and failure behaviour for a range of multiaxial stress-strain states. The approach is demonstrated on glass/epoxy prepreg laminates. For unidirectional matrix dominated laminate it is shown that the failure envelope is described accurately by Puck’s inter-fibre failure theory. For the multidirectional matrix-dominated laminate it is shown that the in-situ strength is much greater than that predicted using the unidirectional properties. The potential of the MAF for characterisation over the entire combined tension-shear and compression-shear domains using a single fixture is demonstrated.

Experimental investigation of the acoustic anisotropy field in the sample with a stress concentrator

The behavior of acoustic anisotropy and the longitudinal wave velocity in the case of multiaxial stress-strain state of the plate under inelastic deformation has been studied experimentally. The plate had a stress concentrator in the form of the central hole. The results for several deformation levels, and the results of finite element analysis of active stresses were presented. The qualitative agreement between the calculated stress fields and the distribution fields of acoustic anisotropy was revealed. It was found that the absolute magnitude maximum of acoustic anisotropy fell on the areas with the biggest stresses near the concentrator. It was supposed that the non-uniform distribution of acoustic anisotropy in the material testified to a possible stress concentration at the corresponding points.

True stress and shakedown analysis of pressure vessel under repeated internal pressure

This study aims to investigate the true stress and the plastic shakedown behavior of a cyclically loaded pressure vessel. To serve this study, an experimental platform has been built up, which comprised of a self-made thin-wall cylinder pressure vessel, a water pressure loading system to simulate the actual working loading condition, and strain gauge sets for strain measurement. A number of experiments have been done by cyclically loading and unloading the vessel at different strain levels of plastic deformation to shakedown state in different experiments respectively. The relationship between plastic strain and shakedown range has therefore been obtained. The true stress-strain constitutive model of the vessel under large deformation condition has also been derived. The experiments lead to three observations: (1) the strain hardening technology can effectively reduce the residual stress of stainless steel pressure vessel. (2) The shakedown range is less than 2000 μe for a total strain under 4%, and yet the shakedown range increases fast to more than 3000 μe for a total strain higher than 6%. (3) It is also found that the true stress-strain constitutive model given in this paper describes the multi-axial stress-strain state of pressure vessels, and validates the engineering practicability of conventional uniaxial tensile shakedown constitutive curve.

Multiaxial Fatigue Damage Prediction and Life Estimation of a Centrifugal Impeller for a Turboshaft Engine

The rotating gas turbine engine component such as centrifugal compressor is subjected to various static and dynamic loads during service. These service loads introduce multiaxial stress-strain states and inflict severe structural damage and hence reduce compressor efficiency and service life. In many cases, the service loads are non-proportional which introduces additional cyclic hardening depending on the loading path and the material used (Wu et al., Int J Fatigue 59:170–175, 2014). Studies have revealed that fatigue life is drastically reduced as a result of this additional cyclic hardening phenomenon. In recent decades, numerous multiaxial fatigue damage theories (which are strain based) have been developed taking into account the factors influencing fatigue like operating temperature, anisotropy, microstructure, nature of loading (proportional or non-proportional), and environmental effects. In general, these theories envisage crack nucleation and propagation to take place at a critical plane, but differ from one another the way critical planes are defined and damage parameters are proposed. To estimate the fatigue life under the multiaxial loading conditions, these theories relate multiaxial stress-strain components to uniaxial fatigue properties obtained from test data. But, it is observed that most of these theories are limited in application to a particular material or loading conditions. No general consensus is available on the best available fatigue damage theory for a particular application. Further, literature shows that most of these theories are applied and compared on tubular and notched test specimens under proportional and non-proportional loading conditions. Literatures are seldom available which compares these theories at the application level and validate through experiments. The objective of this paper is to estimate the low-cycle fatigue life of a centrifugal impeller used in a gas turbine application using different multiaxial fatigue damage models in the literature and propose a methodology which closely fits the experimental results. For applications such as gas turbine engines, the margin of safety (with respect to 0.2% PS) varies in the range of 1.05 to 1.15 (Stephens et al. in Metal fatigue in engineering. Wiley, New York, 2001). For this, it is extremely important to estimate the life and damage mechanism affecting the life of the components accurately to ensure the flight safety, reliability, and total service life of the gas turbine engine. The centrifugal impeller was designed for a pressure ratio of 3.2 and maximum rotational speed of 52,500 rpm. The titanium alloy Ti6Al4V was chosen as the possible material for the impeller as it has high strength and stiffness to weight ratio and is widely used in aerospace application (Wu et al., Int J Fatigue 44(12):14–20, 2012). The entire analysis can be divided into three main modules. Firstly, the stress and strain history on the centrifugal impeller was determined under actual operating condition. Finite element structural analysis packages were used for this purpose. Secondly, the stress-strain histories obtained from FE analysis were post-processed using several multiaxial fatigue damage models like Maximum von Mises strain model (Kalluri and Bonacuse in In-Phase and Out-of-Phase Axial-Torsional Fatigue Behavior of Haynes 188 at 760 °C. NASA Technical Report 1991, 91-C-046, 1991), which is based on the equivalent strain and the Smith-Watson-Topper (SWT) model (Shamsaei and McKelvey, Int J Fatigue 59:170–175, 2014), Kandil-Brown-Miller (KBM) model (Kandil et al., Met Struct 280:203–210, 1988), Fatemi and Socie (FS) model (Fatemi and Socie, Fatigue Fract Eng Mater 11(3):149–166, 1987), which are based on the critical plane approach to obtain the fatigue life. Finally, a prototype of the centrifugal impeller was made and tested at our sophisticated cyclic spin test facility to validate the Low-Cycle Fatigue life.

Studies on the Fracture Mechanism and Kinetics of Randomly Oriented Surface Semielliptic Cracks at the Multiaxial Stress–strain State with Deformation Criteria of Nonlinear Fracture Mechanics

Functional relations are proposed to determine a stress–strain state along randomly oriented low-cycle surface semielliptic cracks considering 3D anisotropy of physicomechanical properties of the material that provide refined estimation of strength and residual life of NPP equipment with deformation fracture criteria and numerical methods based on experimental data.

Procedures for Multiaxial Creep-Fatigue Verifications of Nuclear Components

Nuclear high heat flux components (HHFCs) experience large thermal gradients and high heat flux variations, which induce severe thermal cyclic loadings. The most critical design issue for these components is their endurance strength under the required number of thermal cycles.The aim of this work is to provide procedures to perform the multiaxial creep-fatigue life assessment of HHFCs. Since the existing design codes present limitations due to simplifying assumptions concerning procedures for the multiaxial fatigue verification considering interactive effects of creep-fatigue and local stress and temperature conditions, better accurate verification methods and rules are developed starting from the available scientific literature and experimental data. The new verification methods identify the shape of the most damaging hysteresis loop considering plasticity and creep strains in both tensile and compressive conditions.The developed procedures are used to post-process the thermomechanical results of finite element (FE) analyses. They foresee the calculation of the creep-fatigue damage in each node and for each cyclic loading of the analyzed FE model by using the fatigue curve corresponding to the shape of the local hysteresis loop. Furthermore, the most fatigued elements are bounded and the causes of damage are identified to improve the local design. The fatigue damage is evaluated considering the effects of local conditions: temperature, multiaxial stress-strain state, strain intensity range, effect of local mean stresses, material shakedown, accumulated damage for multiple cyclic loads, combined effect of creep-fatigue, hold periods, and neutron flux.The developed procedures are successfully verified by comparing the results with experimental data for different levels of mean stress.This paper presents a description of the procedures and design rules focusing on the innovative aspects. The new procedures have been developed in the framework of the activities for the design, manufacturing, and procurement of the ITER neutral beam injector, and they are applied for creep-fatigue verifications of the in-vessel HHFCs.

Basic propositions of damage mechanics as a basis for justifying the strength and service life of nuclear power systems

The paper addresses the problem of providing a long-term (up to 60 years) strength reliability of engineering facilities operated under developing damage accumulation. Basic propositions of damage mechanics for derivation of coupled equations descriptive of elastoplastic deformation and fatigue damage accumulation in structural elements of nuclear power systems are given as a tool to assess their expended and residual life from actual operation history. The mathematical model is based on macroscopic variables that integrally characterize the mesoscale structural changes of material under deformation and damage accumulation. The degree of bulk isotropic fatigue damaging is estimated using a macroscopic parameter (0 which is an internal state parameter interpreted as the relative volume fraction of defects in a given material zone. The assessment of fatigue damage accumulation in danger zones of nuclear power systems from actual history of their thermal force loading is based on simulation of the main physical stages of damage accumulation: nucleation and development of micro defects and their coalescence into a fatigue macrocrack. The energy approach used to simulate the damage accumulation allows one to take into account the main peculiarities of elastoplastic deformation in danger zones of structural elements of nuclear power systems under complex nonstationary thermomechanical loading: pronounced localization of damage accumulation due to a high load gradient and design- and process-dependent stress concentration; multiaxial stress-strain states; rotation of principal planes of stress and strain tensors; and nonlinear damage accumulation under changes of loading modes.

1008 Ti-Ni形状記憶合金円筒の引張-ねじり挙動(S03-2 形状記憶合金の特性と応用技術(2),21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

This paper describes experimental results for stress - strain behavior of Ti-Ni shape memory alloys in the super elastic regime. Cylindrical hollow test pieces were loaded and unloaded by the strain control in the multi-axial (axial-shear) strain space under the proportional loading condition. Test results showed the complicated stress-strain behavior of the material under multi-axial stress-strain states.

Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading

ABSTRACTThis paper is concerned with an experimental and numerical study of the fatigue behaviour of tubular AlMgSi welded specimens subjected to biaxial loading. In‐phase torsion–bending fatigue tests under constant amplitude loading were performed in a standard servo‐hydraulic machine with a suitable gripping system. Some tests in pure rotating bending with and without steady torsion were also performed. The influence of stress ratio R and bending–torsion stress ratio were analysed. Correlation of the fatigue lives was done using the distortion energy hypothesis (DEH), based on the local stresses and strains. The applicability of the local strain approach method to the prediction of the fatigue life of the welded tubular specimens was also investigated. Static torsion has only a slight detrimental influence on fatigue strength. The DEH (von Mises criterion) based on local stresses in the weld toes was shown to satisfactorily correlate fatigue lives for in‐phase multiaxial stress–strain states. The stress–strain field intensity predictions were shown to have less scatter and are in better agreement with the experimental results than the equivalent strain energy density approach.

Fatigue-life predictions including the effects of hold time and multiaxial loads on crack-coalescence behavior

Two aspects of crack-coalescence behavior are reported. The first concerns a regime frequently referred to in the literature as creep-fatigue interactions but which in this paper is essentially a time-dependent, fatigue-failure process. The second relates to crack coalescence under a wide range of different multiaxial stress-strain states. In the framework of the first approach, a fatigue-crack growth model is derived based on experimental observations during high-temperature, high-strain, reversed-bend, hold-time tests on AISI 316 stainless steel. Essential features of these tests are the compressive and the tensile 60-min hold periods on different surfaces, which induce, respectively, transgranular-short and intergranular-long cracks. The latter, more damaging cracks involve the coalescence of numerous short cracks to form a dominant Stage II crack that leads to failure. Then, in the framework of the second approach, the crack-coalescence model is advanced to predict the fatigue lifetimes for multiaxial, variable amplitude, proportional loading of a medium carbon steel commonly used to manufacture engineering components. It is shown that under high strain fatigue conditions the models used for the calculations of lifetime must necessarily involve crack-coalescence behavior if unsafe lifetime predictions are to be avoided.

Problem of the strength of pump casings

1. Analysis of the investigations carried out to icrease greatly the reliability of operation of the pump casing indicates that the problems which must be solved in this case are complicated and have a number of various aspects. 2. Since the highly stressed casing have a complicated form, to evaluate their strength, it is necessary to introduce the methods of calculating the multiaxial stress-strain state into calculations of the strength of these casing in practice. 3. The results show that it is convenient to normalize the local stresses in the pump casing and carry out variant calculations n the stresses by FEM to select the optimum design in respect of both static and fatigue strength. 4. The amount of information on the characteristics of the materials of the pump casings is at present completely insufficient for objective selection of the material and, in particular for carrying out elastoplastic calculations and also calculations concerned with the propagation of resultant cracks. These calculations are essential for determining the residual working life.

A new method for low cycle fatigue life analysis at high temperature

High temperature low cycle fatigue analysis is a problem of general concern in engineering. In this paper, which deals with prediction of high temperature low cycle fatigue (LCF) life at the edge of the leakage hole of an aero-turbine disk, the LCF tests have been carried out at 300°C for cylindrical specimens with and without circumferential notch. A new parameter, local equivalent strain energy density (LESED), was suggested. It can be used to describe and predict the high temperature LCF life of notched specimens which are in the multiaxial stress-strain state. Various mechanics parameters including LESED at the notch root of specimens have been calculated using an elastic-plastic finite element program. Comparing the LCF life curves obtained with different methods, it is evident that the LESED method can be used effectively not only for describing the LCF behavior of the notched specimens but also for predicting the LCF life of the notched specimens from the LCF life curves of the smooth specimens.