Complex Multiaxial Stress States Research Articles

Fatigue notch strengthening effect of nickel-based single crystal superalloys under different stress ratios

Nickel-based single crystal superalloys (Ni-SXs) are widely used in turbine blades of aircraft engines. With the increasing demand for higher temperature-bearing capacity, the introduction of film cooling holes, impingement holes, and trailing edge slots for cooling induces stress concentration, which compromises the structural integrity of the blades, generates complex multiaxial stress states, and adversely affects their operational performance. In this study, Ni-SXs, DD6, was utilized to investigate the influence of stress ratios on fatigue performance under complex stress states. Low cycle fatigue (LCF) tests were carried out at different stress ratios with stress concentration coefficient Kt = 1.0, 2.0 and 3.0. The results indicate that the notched specimens exhibit a significant fatigue notch strengthening effect under high stress ratios. The fracture surface and microstructure also indicate that under high stress ratios loading, the notches exhibit significant creep failure characteristics. This means that the main cause of fatigue notch strengthening is similar to creep notch strengthening effect. A macroscopic anisotropic constitutive model coupled with damage was developed and applied to finite element analysis of notched specimens. The results demonstrate that as the stress ratio rises, the stress relaxation effect at the notch becomes more pronounced, yet the level of damage diminishes. Additionally, a stress-equivalent model based on Bridgman stress was proposed, which effectively unifies the lifetime trends of notched and smooth specimens, predicting lifetimes within a threefold error band.

Experimental and theoretical study on high-temperature creep of VT6 titanium alloy under multi-axial loading conditions

In the framework of damage mechanics, we discuss a new mathematical model that describes the kinetics of the stress–strain state and damage accumulation during material degradation by the mechanism of long-term strength under complex multiaxial stress state. An experimental and theoretical technique is proposed for determination of material parameters and scalar constitutive functions for damaged media based on specially set experiments on laboratory specimens. The results of experimental studies and numerical simulations of short-term high-temperature creep of VT6 titanium alloy under uniaxial and multiaxial loading are presented. Numerical results are compared with the data obtained through experiments. Particular attention is paid to simulating the process of unsteady creep for complex deformation modes, accompanied by rotation of main areas of stress, strain and creep strain tensors. It is shown that the developed version of the constitutive relations of the damaged media enables us to describe the processes of unsteady creep and long-term strength of structural alloys under multiaxial stress with the accuracy sufficient for engineering calculations.

A life prediction model for rolling contact fatigue based on the improved moment of load path method

AbstractAn improved moment of load path model for rolling contact fatigue life prediction is proposed in this paper. First, the complex multiaxial stress variation of the subsurface materials under rolling contact conditions was analyzed by the finite element method. Next, the equivalent stress parameter was presented to characterize the complex stress state based on the improved moment of load path method. The key concept of the proposed method is building a new coordinate system for analyzing the load path of the complex multiaxial stress state. The efficiency of the proposed model was validated with different kinds of fatigue test results in the existing literature. The model results show a good agreement with the test data. Finally, the model was used to obtain the relationship of the Hertz stress versus fatigue life under rolling contact conditions according to the fatigue life data.

Multiaxial Fatigue Analysis of Jacket-Type Offshore Wind Turbine Based on Multi-Scale Finite Element Model.

The fatigue damage of a local joint is the key factor accounting for the structural failure of a jacket-type offshore wind turbine. Meanwhile, the structure experiences a complex multiaxial stress state under wind and wave random loading. This paper aims to develop a multi-scale modeling method for a jacket-type offshore wind turbine, in which local joints of the jacket are modeled in a detail by using solid elements, and other components are modeled via the common beam element. Considering the multiaxial stress state of the local joint, multi-axial fatigue damage analysis based on the multiaxial S-N curve is performed using equivalent Mises and Lemaitre methods. The uniaxial fatigue damage data of the jacket model calculated using the multi-scale finite element model are compared with those of the conventional beam model. The results show that the tubular joint of jacket leg and brace connections can be modeled using the multi-scale method, since the uniaxial fatigue damage degree can reach a 15% difference. The comparison of uniaxial and multiaxial fatigue results obtained using the multi-scale finite element model shows that the difference can be about 15% larger. It is suggested that the multi-scale finite element model should be used for better accuracy in the multiaxial fatigue analysis of the jacket-type offshore wind turbine under wind and wave random loading.

Approach for the simulation of the load-deformation behaviour of hyperelastic bonded joints using strain and strain rate dependent tangent moduli

In structural glass, Structural Sealant Glazing (SSG) systems are often used to realise facades with maximum transparency. The used silicone adhesives are currently designed in accordance to the European Technical Approval Guideline 002 (ETAG 002) by a simplified two-dimensional stress calculation concept. For a more precise calculation of the adhesive stresses and deformations, finite element analyses are used. The quality of the results, however, strongly depends on the calculation concept and material model used. In this paper, a practice-oriented viscoelastic approach using strain and strain rate dependent tangent moduli within FEA is presented. Required material parameters can be determined with a simple uniaxial tension test only. The proposed model is validated with numerous FE calculations of reality-based adhesively bonded component tests with different geometric ratios that include complex multiaxial stress states. The proposed approach allows a precise prediction of the strain state- and time-dependent stress behaviour of hyperelastic silicone bonds. The prediction quality is significantly more accurate than often used linear-elastic material models or commonly available hyperelastic models.

Fatigue Crack Growth Behavior and Failure Mechanism of Nickel-Based Alloy GH4169 under Biaxial Load Based on Fatigue Test of Cruciform Specimen

Due to the complex geometry and various cyclic loads, aeroengine components are often in a multiaxial complex stress state during service. Multiaxial fatigue is a major cause of many air accidents. It is of great significance to study the fatigue failure mechanism of aeronautical materials. This paper carries out biaxial fatigue tests on cruciform specimens and uses the surface replication method to record the initiation and propagation process of crack. Based on these fatigue tests, this paper studies the multiaxial fatigue characteristics of nickel-based alloy GH4169 for aeroengines and analyzes the fatigue crack growth behavior and failure mechanism of nickel-based alloys under a complex multiaxial stress state.

An elastoplastic damage model of concrete under cyclic loading and its numerical implementation

A novel elastoplastic damage model describing the complex mechanical behaviors such as stiffness degradation and irreversible deformation of concrete under cyclic loading is constructed and the complete procedure for numerical implementation is presented. To solve the key problems including multi-axial stress states, asymmetry in tension and compression and conversion between tension and compression under cyclic loading, a series of approaches are put forward. A scalar equivalent strain based on the Hsieh-Ting-Chen strength criterion in the framework of strain space is used to convert the complex multiaxial stress state to the simple uniaxial one. Correspondingly, the equivalent strain obtained by the characteristic strength curve addresses the asymmetry in tension and compression, so that the stress–strain relationship in both uniaxial tension and uniaxial compression can be represented by the same curve, and a single damage scalar is available to characterize both tensile damage and compressive damage. To overcome the difficulty of conversion between tension and compression owing to the non-negative equivalent strain, a net equivalent strain is defined to keep the curve proceeding in the first quadrant under reverse loading. Meanwhile, a nominal damage variable is proposed to ensure that the reloading curve can return to the original stress–strain envelope. A new framework of the model with a concise mathematical form has been numerically implemented and is independent of the selection of fundamental governing equations. Typical experimental tests involving three-point bending test, mixed-mode bending test, cyclic uniaxial test, and reciprocating loading test are used for verification. The results calculated by the proposed model are all in good agreement with the tests. As a result, the correctness and reliability of the novel model are demonstrated.

A Damage Model of Concrete including Hysteretic Effect under Cyclic Loading.

A novel damage model for concrete has been developed, which can reflect the complex hysteresis phenomena of concrete under cyclic loading, as well as other nonlinear behaviors such as stress softening, stiffness degradation, and irreversible deformation. The model cleverly transforms the complex multiaxial stress state into a uniaxial state by equivalent strain, with few computational parameters and simple mathematical expression. The uniaxial tensile and compressive stress–strain curves matching the actual characteristics are used to accommodate the high asymmetry of concrete in tension and compression, respectively. Meanwhile, an unloading path and a reloading path that can reflect the hysteresis effect under cyclic loading of concrete are established, in which the adopted expressions for the loading and unloading characteristic points do not depend on the shape of the curve. The proposed model has a concise form that can be easily implemented and also shows strong generality and flexibility. Finally, the reliability and correctness of the model are verified by comparing the numerical results with the three-point bending beam test, cyclic loading test, and a seismic damage simulation of the Koyna gravity dam.

A complemented multiaxial creep constitutive model for materials with different properties in tension and compression

A complemented multiaxial creep constitutive model is proposed in this paper. The model is able to describe the different creep behaviors in tension and compression under a complex multiaxial stress state. To improve the convergence and adaptability for large-scale structures in engineering, a complemented constitutive model is established by complementing the shear part of the creep constitutive matrixes in principal space through a limitation process. The finite element method and forward Euler method are used to establish the numerical calculation framework. Efficient solution procedures are also proposed and implemented. Room temperature creep experiments of titanium alloy Ti–6Al–3Nb–2Zr–1Mo are performed. It is found that titanium alloy has different creep properties in tension and compression. The numerical results show that the proposed creep constitutive model and numerical calculation framework are in good agreement with the experimental results. The response of each specific creep strain component under a complex stress multiaxial state can be accurately calculated, and the different properties of the creep response in tension and compression in different directions are reflected.

Material model calibration against axial-torsion-pressure experiments accounting for the non-uniform stress distribution

The need to calibrate material models towards complex multiaxial stress states has received much attention in the last decades. Such stress states are often obtained by axial, torsion and pressure experiments on tubular test bars. These experiments are typically simulated by considering the behavior in a single material point, using the thin-walled assumption of uniform stresses and strains. In this paper, a new simulation methodology that does not rely on the thin-walled assumption has been developed. The accuracy improvements are compared with experimental uncertainties for tubular test bars. Compared to using ABAQUS for equivalent simulations, a speed increase of 100–200 times was found. This simulation methodology has been implemented in an open source software material calibration software called matmodfit. The calibration of material parameters is first demonstrated for cyclic ratcheting axial-torsion experiments using thin-walled test bars. Thereafter, calibration of material parameters from experiments on solid test bars subjected to very large shear deformation under axial compression is performed. This demonstrates a key advantage with the proposed method: Thick-walled or even solid test bars can be modeled without loss of simulation accuracy at a low computational cost.

Computational framework for multiaxial fatigue life prediction of compressor discs considering notch effects

Aero engine components like compressor discs normally operate under harsh conditions like complex multiaxial stress states. Notch effect is often critical for structural integrity assessment in virtue of complex structure and discontinuities. According to the notch effect under cyclic loadings, a computational framework for multiaxial fatigue analysis of compressor discs is established by coupling finite element (FE) simulation of stress gradient with Fatemi-Socie (FS) criterion. Specifically, a notch support extension method accounting for stress gradient effect is elaborated through elasto-plastic FE analysis, which can be determined for fatigue life prediction of arbitrary shaped components. Experimental fatigue data for smooth and notched specimens of TC4 and GH4169 alloys demonstrated the appropriateness of the proposed computational approach. The applicability and performance of the prediction model to a compressor blade-disc attachment subjected to field spectra is presented. Results show that testing effect can be significantly reduced by using this framework with acceptable prediction accuracy.

Simulation of Fatigue Crack Growth in Weld Joint of Thin Structures Using Characteristic Tensor

It is known that fatigue life of welded structures, such as automotive and ship structures, is greatly influenced by welding residual stress. In case of real structures, the orientation of the stresses produced by static load and that produced by repeated load and that of welding residual stress are generally different from each other and they form a highly complex multi axial stress states. On the other hand, the fatigue behaviour has been mostly studied for uniaxial stress state without residual stress. The crack growth rate is related to the stress intensity factor range ΔK such as in the Paris Low [1]. To predict the fatigue behaviour of real welded structures, the three dimensional stresses produced by static load, repeated load and welding must be rationally correlated with a scalar value ΔK. The author proposes a Characteristic Tensor which characterizes the singular stress field at crack tip and its invariant parameters, such as principal values or invariants which has similar form as strain energy density, are used to compute ΔK in a consistent manner. Its potential usefulness is demonstrated through simple examples.

Yield surfaces for solid foams: A review on experimental characterization and modeling

Solid foams are a very important class of lightweight materials with energy absorption properties for application in automotive and aerospace industry. In such applications, foams are subjected not only to uniaxial but in most cases to very complex multiaxial stress states. Hence, yield surfaces are needed for the reliable prediction of the failure behavior by simulations under multiaxial loading. As multiaxial loading of cellular solids is a very challenging task, in literature, yield surfaces are usually based mainly on simulation results not validated by real experimental data sets. The present contribution starts with a review of the theory of yield surfaces and numerical models. It gives a deep insight into the state of the art on the experimental assessment of yield surfaces for solid foams. Finally, a yield surface and its post‐yield surfaces are determined exemplarily for open‐cell aluminum foams by using a multitude of experimental methods.

Modeling fatigue behavior of slewing rings in crane structures. Identification of influencing parameters on local stresses and fatigue damage calculations

In the case of Crane industry sector, with high requirements of security and performance, slewing rings are important parts of equipment and manufacturers need to guarantee their mechanical strength and durability. Since more than ten years, on demand of industrial groups, CETIM is working on slewing rings in the fields of tests, design and calculations.For the last couple of years, extensive work has been done to develop a calculation methodology giving access to forces in balls of rings. These forces, used as input of local non-linear finite element models including contact definition, allow stress state calculations in tracks of rings. Fatigue analysis is then conducted based on appropriate criteria taking into account the complex multiaxial stress state and the gradient of material properties due to the surface treatment of the tracks (induction hardened parts). Parametric calculations have been made in order to estimate the influence of some parameters such as contact angle of the balls, geometric conformity, mechanical clearance and depth of treated material. Results allow identifying most important parameters and show how these parameters influence the damage location on the slewing rings, with good correlation with physical observations on damaged components. A synthesis of this long term work is presented in this paper.

Microstructural characterisation and experimental determination of a multiaxial yield surface for open-cell aluminium foams

Metal foams are bio-inspired microheterogeneous materials, which exhibit a strong structure-property relationship. Their global mechanical properties depend strongly on the local micromechanical properties of the struts and on the pore geometry of the foams. A solid micromechanical and macromechanical understanding of the yield behaviour of the foams under realistic complex stress states is essential in order to be able to design components made of foams. However, up to now, experimental yield surface data for foams are very limited.The present contribution deals with the structural characterisation of open-cell aluminium foams of different pore sizes by X-ray computed tomography (CT). The strut geometry e.g. regarding cross-sectional shape and the mass distribution along the struts is evaluated from the CT data. Yield surfaces for 10, 20 and 30ppi foams are experimentally probed by performing uniaxial tensile and compression tests, pure torsion as well as combined compression-torsion and tension-torsion tests. This results in one of the most comprehensive experimental data sets in the literature ever reported for open-cell aluminium foams. The shape of the yield surface and its degree of asymmetry were connected to the geometric data from the structural characterisation. It provides a deeper understanding of aluminium foams under complex multiaxial stress states.

Modeling of Ductile Failure in High Strength Steel

Ductile fracture is an important field in dynamic materials research. The simulation of ductile failure by means of numerical codes requires accurate material models that are validated with data obtained from precise high-rate mechanical testing. In this work, a high strength quenched and tempered steel is studied over a wide range of strain rates using different test methods to achieve a range of stress states with numerical computations being used to determine the precise stress and strain rate states for the multiaxial GISSMO model. The consideration of stress state, not only in tensile triaxiality 0.33 and above but also in shear, tension/shear and compression/shear, will lead to greater accuracy in failure predictions for a wide range of applications involving complex multiaxial stress states, particularly for thick and high strength materials.

Structural steel–glass facade panels with multi-side bonding – Nonlinear stress–strain behaviour under complex loading situations

Today in practice, finite element analyses (FEA) are used to design modern structural steel–glass facade panels showing multi-side bonded joints with a complex geometry, because no reliable analytical methods are available for calculating such occurring complex multi-axial stress states. However, experiences show great deviations between experimental and numerical results, which may lead on the one hand to significant over-dimensioning, but on the other hand – more critical – to unexpected cases of damages.For applications of facade panels with multi-side bonding, mainly hyper-elastic adhesives are used. The aim of this work is to show the possibilities existing hyper-elastic material models provide for specific steel–glass components and where and under which circumstances these in many FE programs given material models fit best the true behaviour observed in large-scale component tests.To this end, three testing levels have been introduced to investigate the adhesives within multi-side bonding. Small-scale tests have been performed to characterise the adhesives and to determine the material model for subsequent FEA. After that component tests with two different loading situations have been performed to investigate both a complex and a simpler stress state within the adhesive. This paper focuses on both component tests and evaluates the results from these tests. For thin glass thicknesses (here 6mm) the FEA with hyper-elastic material models provide results in very good compliance with the experimental results. When increasing the glass thickness (here 10 and 15mm) the influences of the non-linear adhesive characteristic to the total structural behaviour decreases, which leads to rather high deviations from the experimental results.

Development of a Multiaxial Fatigue Damage Model for High Strength Alloys Using a Critical Plane Methodology

The prediction of fatigue life for metallic components subjected to complex multiaxial stress states is a challenging aspect in design. Equivalent-stress approaches often work reasonably well for uniaxial and proportional load paths; however, the analysis of nonproportional load paths brings forth complexities, such as the identification of cycles, definition of mean stresses, and phase shifts, that the equivalent-stress approaches have difficulties in modeling. Shear-stress based critical-plane approaches, which consider the orientation of the plane on which the crack is assumed to nucleate, have shown better success in correlating experimental results for a broader variety of load paths than equivalent-stress models. However, while the interpretation of the ancillary stress terms in a critical-plane parameter is generally straightforward within proportional loadings, there is often ambiguity in the definition when the loading is nonproportional. In this study, a thorough examination of the variables responsible for crack nucleation is presented in the context of the critical-plane methodology. Uniaxial and multiaxial fatigue data from Ti–6Al–4V and three other alloys, namely, Rene’104, Rene’88DT, and Direct Age 718, are used as the basis for the evaluation. The experimental fatigue data include axial, torsional, proportional, and a variety of nonproportional tension/torsion load paths. Specific attention is given to the effects of torsional mean stresses, the definition of the critical plane, and the interpretation of normal stress terms on the critical plane within nonproportional load paths. A new modification to a critical-plane parameter is presented, which provides a good correlation of experimental fatigue data.

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.

A three‐dimensional model describing stress‐temperature induced solid phase transformations: solution algorithm and boundary value problems

AbstractAn always increasing knowledge on material properties as well as a progressively more sophisticated production technology make shape memory alloys (SMA) extremely interesting for the industrial world. At the same time, SMA devices are typically characterized by complex multi‐axial stress states as well as non‐homogeneous and non‐isothermal conditions both in space and time.This aspect suggests the finite element method as a useful tool to help and improve application design and realization. With this aim, we focus on a three‐dimensional macroscopic thermo‐mechanical model able to reproduce the most significant SMA features (Int. J. Numer. Methods Eng. 2002; 55: 1255–1264), proposing a simple modification of such a model. However, the suggested modification allows the development of a time‐discrete solution algorithm, which is more effective and robust than the one previously discussed in the literature.We verify the computational tool ability to simulate realistic mechanical boundary value problems with prescribed temperature dependence, studying three SMA applications: a spring actuator, a self‐expanding stent, a coupling device for vacuum tightness. The effectiveness of the model to solve thermo‐mechanical coupled problems will be discussed in a forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd.