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• A time-derivative fatigue crack growth formulation and no need for cycle counting in the presence of arbitrary loadings. • Unified methodology for high-cycle fatigue, low-cycle fatigue, and their interactions. • Demonstrated and validated with uniaxial and multiaxial random loadings. • Fatigue life prediction using crack growth analysis with explicit near-threshold modeling. A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers. [ABSTRACT FROM AUTHOR]

• A new unifying analytical approach to predict creep rupture and crack growth rates by deriving a multiscale strain-based constraint criterion. • In essence, the model links the global geometric constraint with time-dependent microstructural constraint arising from creep damage at the sub grain. • By modelling the tensile and the short-term tensile properties and long-term creep strength of the material a micro constrain based argument is developed. • The model has been validated using large data sets for 316 steels at different temperatures by considering bounds in the failure strain scatter which is substantial especially at 550 °C. • It is an ideal tool for the engineer to predict component failure using simply measured data for creep strain and tensile stress. A new failure ductility/multiscale constraint strain-based model to predict creep damage, rupture and crack growth under uniaxial and multiaxial conditions is developed for 316H Type stainless steels by linking globally uniform failure strains with a multiaxial constraint factor. The model identifies a geometric constraint and a time-dependent local constraint at the sub-grain level. Uniaxial and notched 316H steel as-received and pre-compressed data at various load levels and temperatures with substantial scatter were used to derive the appropriate constitutive equations by using the proposed empirical/mechanistic approach. Constrained hydrostatic development of creep damage at the sub-grain level is assumed to directly relate to the uniform lower-bound creep steady state region of damage development measured at the global level. Uniaxial and notched bar rupture at long terms is predicted based on the initial short-term creep or a representative tensile strength and a multiaxial constraint factor. The model is consistent with the well-known NSW remaining multiaxial ductility creep crack growth model which predicts crack growth bounds over the plane strain/stress states. This model, therefore, unifies the creep process response over the whole range of uniaxial, notched and crack growth processes which is extremely consequential to simple long term failure predictions of components at elevated temperatures. [ABSTRACT FROM AUTHOR]

Highlights • Elastic and plastic strains were out of phase for non-proportional loading. • With loading strain distribution in material differed significantly. • Substructural evolution under in phase loading resulted moslty in planar dislocations. Abstract Effect of in-phase and out of phase cyclic loading on fatigue behaviour was evaluated for 304LN stainless steel using tubular specimens. It was found that additional hardening observed for out of phase loading was a consequence of more grains participating in deformation process. Further, strains in matrix were higher and evenly distributed across grains for out of phase loadings as quantified through misorientation analysis. Disparities in misorientation studies were accounted by substructural development investigated through electron microscopy. Additionally, elastic and plastic strains were found to be out of phase with respect to total strains for out of phase loading. [ABSTRACT FROM AUTHOR]

Abstract The degradation of the superelastic properties of a commercial NiTi alloy is studied during uniaxial, biaxial and load-path-change cycling performed in-situ with synchrotron X-ray diffraction. Careful examination of the diffraction pattern during uniaxial loading shows the R-phase as a transition between the austenite and the B19′ martensite. Degradation of the superelasticity is found to depend strongly on the loading and unloading path followed, and it is discussed in terms the B19′ martensitic variant selection, the accumulation of dislocations, and the residual R-Phase and B19' martensite. Cycling biaxially leads to faster degradation than uniaxially due to a larger accumulation of dislocations. If the deformation cycle contains a load path change, dislocation accumulation increases further and more martensite is retained. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Highlights • An approach for fatigue damage prediction under multiaxial fatigue was proposed. • The critical plane approach was introduced to predict the fatigue damage. • Multiaxial stress of deck and U-rib welds in different positions was analysed. • The rotation angle of the maximum principal stress was calculated. Abstract Assessment approach for multiaxial fatigue damage of deck and U-rib weld in steel bridge decks was studied. The orthotropic steel bridge deck was modelled to analyse the multiaxial stress state of the weld under wheel load. A multiaxial fatigue loading experiment was carried out to assess the fatigue strength of deck and U-rib weld based on equivalent stress and maximum principal stress. The critical plane approach which is suitable for deck-U rib welds was also established. The assessment results were then compared to those obtained by uniaxial fatigue approach. Reasonable multiaxial fatigue principles were proposed for deck and U-rib welds in different positions. The results show that multiaxial fatigue stress is observed in the deck-U rib weld. The shear stress may exceed normal stress and become the main reason for fatigue damage, thus a multiaxial fatigue approach is necessary for fatigue damage assessment. The nominal stress approach is suggested for fatigue assessment of deck and U-rib weld between diaphragms, which leads to conservative results and is more applicable to engineering practice. The critical plane approach is suggested for fatigue assessment of deck and U-rib weld on the diaphragm considering multiaxial fatigue effects and non-proportional stress in the weld. [ABSTRACT FROM AUTHOR]

The transformation behavior of commercial superelastic NiTi material was studied during uniaxial tension and load path changes by employing a novel miniaturized biaxial stage and cruciform shaped specimens. EBSD and X-rays are used to characterize the initial and final microstructure, in situ digital image correlation at the macro and micro length-scales and in situ X-ray diffraction are used to follow the transformation characteristics. The results reveal an initial microstructure where large austenitic grains are subdivided in bands containing nanoscaled sub-grains. The link between the microstructure and strain accommodation during transformation is detailed and discussed in terms of Schmid behavior and strain path. [ABSTRACT FROM AUTHOR]

Using an Axial-Torsion testing machine, pearlitic R260 steel specimens are twisted until fracture under different axial loads. A well established framework for finite elastoplasticity with kinematic hardening is used to model the deformation of the specimens. In particular, we evaluate the ability of different kinematic hardening laws to predict the observed biaxial load versus displacement response. It is found that the combination of Armstrong–Frederick dynamic recovery and Burlet–Cailletaud radial evanescence saturation is efficient even for the large strains achieved in this study. The results are less conclusive on the appropriateness of replacing the Armstrong–Frederick with an Ohno–Wang type of kinematic hardening law. [ABSTRACT FROM AUTHOR]

Uniaxial damage modelling use constituent components of the stress/strain measured data which have inherent scatter. Models developed for this purpose have also attempted to address the issues related to failure mechanisms within a multiaxial stress state context. This paper presents the multiscale approach to constraint by using the relationship between Monkman-Grant (MG) uniform failure strain and local sub-grain stress state to predict creep damage and rupture under uniaxial/multiaxial conditions. In essence, a global geometric constraint and a time-dependent local sub-grain constraint is defined with the latter controlling the failure response of the geometry. The model compliments and is in agreement with the established NSW model is also used to predict the lower/upper bound of cracking rates in crack dominated geometries. The model is employed into a finite element (FE) to assess its capability to numerically predict the rupture of plain and multiaxial notched bar specimens based on appropriate void growth models. For verification, creep constitutive properties of long term data from uniaxial and multiaxial tests on Grade 92 martensitic steels from various databases, where available, are used to establish the procedure. Given the level of scatter in the data and fabrication and testing uncertainties that cannot be accounted for in such databases, it is shown that the model is sufficiently simple and robust to be developed for use in conservatively predicting very long term failure times. [ABSTRACT FROM AUTHOR]

In order to experimentally validate concrete damage models and better characterize the concrete behavior during mixed-mode crack propagation, multiaxial tests are developed. The goal is to perform rich and discriminating tests by using state of the art techniques. The loadings are applied using a hexapod controlled by a 3D displacement system and the cracking state is analyzed via digital image correlation. To probe its consistency the experimental results are compared to numerical simulations with a nonlocal (i.e., gradient-based) damage model. The importance of using accurate boundary conditions while performing the numerical simulations is underlined. The numerical simulations are congruous to the experimental results only when full-field boundary conditions are prescribed, and only in that case it is possible to evaluate the validity or more generally the parameter sensitivity of the damage/fracture model under investigation. [ABSTRACT FROM AUTHOR]

Numerical and analytical methods for predicting uniaxial damage have largely depended on the constituent components of the stress/strain measured data which have inherent scatter. Models developed for this purpose have also attempted, with some degree of success, to address the fundamental issues of failure mechanisms within a multiaxial stress state context. This paper presents a new analytical/empirical/a postpriori unifying approach to predict creep damage and rupture under uniaxial/multiaxial and crack growth conditions by deriving a multiscale based constraint criterion. Essentially, the model links the global constraint due to geometry in a globally isotropic material with a microstructural constraint arising from creep diffusional processes occurring in a sub-grain locally anisotropic microstructure. Furthermore, it is shown that the model is consistent with the established NSW crack growth model (Nikbin et al., 1984, 1986; Tan et al., 2001) which is routinely used to determine the plane stress/strain bounds for cracking rates in fracture mechanics geometries and cracked components. The concept assumes that at very short times an initial upper shelf material tensile strength and global plasticity and power law creep control creep damage failure and sub grain multiaxial axial stress state dependent failure strain dominates the long term diffusion/dislocation controlled creep response. It is established that the material yield strength in the short term and a measure of creep failure strain at the creep secondary/tertiary transition region described at the limits by the Monkman-Grant failure strain (Monkman and Grant, 1963), are the important variables in both the uniaxial and multiaxial failure processes. For verification creep constitutive properties from long term data from uniaxial and multiaxial and crack growth tests on Grade P91/92 martensitic steels from various databases (EPRI, private communications; NIMS data base), are used to establish the procedure. [ABSTRACT FROM AUTHOR]

This study presents experimental crack growth data for naturally initiated fatigue cracks in tubular specimens of 2024-T3 aluminum alloy subjected to both uniaxial and multiaxial variable amplitude flight loading spectra. Experimental crack growth behavior is compared to predictions based on two state-of-the-art analysis codes: UniGrow and FASTRAN. UniGrow is based on the idea that residual stress distributions surrounding the crack tip are responsible for causing load sequence effects in variable amplitude crack growth, while FASTRAN attributes these effects to varying degrees of plasticity induced closure in the crack wake. For variable amplitude fatigue tests performed under pure axial nominal loading conditions, both UniGrow and FASTRAN analyses were found to produce conservative growth life predictions despite good agreement with constant amplitude crack growth data. For variable amplitude torsion and combined axial-torsion crack growth analyses, however, the conservatism in growth life predictions was found to reduce. This is attributed to multiaxial nominal stress state effects, such as T-stress and mixed-mode crack growth, which are not accounted for in either UniGrow or FASTRAN, but were observed in constant amplitude crack growth tests to increase experimental crack growth rates. Additionally, by comparing experimental crack growth lives between tests performed using full and edited versions of the same loading history, it was found that a 94% reduction in loading history length resulted in differences in experimental crack growth life of less than a factor of 5. Since cracks in this study were initiated naturally, the effect of initial crack geometry assumptions on crack growth predictions was also investigated. [ABSTRACT FROM AUTHOR]

• Effects of peak strain amplitude and strain gradient on test fatigue life studied. • Localized strain using FEA is compared with measured strain. • Fatigue life predictions using equivalent strain/critical plane based models. • Fatigue life assessment considers information at hole tip/characteristic distance. Present work is aimed at performing fatigue tests on notched C-Mn steel tubes. Tests were conducted on different sizes of notches under remote axial strain-controlled conditions. Individual effects of peak equivalent strain amplitude and strain gradient are brought out on experimental fatigue life. The localized measured strains are compared with corresponding outcome of FE analyses. Fatigue life for notched specimens was predicted based on peak equivalent strain amplitude/existing critical plane model considering stress/strain information at peak/characteristic distance locations. The characteristic distance location with critical plane model and peak equivalent strain amplitude results in improved fatigue life predictions. [ABSTRACT FROM AUTHOR]

This article describes a microstructural-based high cycle fatigue strength modelling approach applied to different cast Al-Si alloys used in an automotive context. Thank to different casting processes (gravity die casting and lost foam casting), associated with several heat treatment (T7 and Hot Isostatic Pressing-HIP), three alloys with very different microstructures have been obtained. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms governing these alloys under different multiaxial loading conditions, it was shown that the principal crack initiation mechanisms for the porosity-free alloy are either the formation of persistent slip bands (PSB) or the rupture and/or debonding of eutectic particles. For the porosity-containing alloys, the fatigue damage is always controlled by crack growth from pores. In order to take into account these fatigue damage mechanisms, a probabilistic model using a combination of the Dang Van and a modified LEFM criteria is proposed. The modified LEFM criterion is able to take into account the influence of the grain size on the threshold of the stress intensity factor. It is shown that for the porosity-free alloy, the predictions are good for combined tension-torsion loads with R = - 1 . However, because the crack initiation mechanisms are not the same depending on the hydrostatic stress, the predictions are non-conservative for the uniaxial and equibiaxial tension loads with R = 0.1 . For the porosity-containing alloys, the predictions are very good for the uniaxial, combined tension-torsion and equibiaxial tension loads with both R = - 1 and R = 0.1 . As observed experimentally, the proposed model can also predict a more pronounced effect of casting porosity for the uniaxial and combined tension-torsion loads, when compared to pure torsion loads. [ABSTRACT FROM AUTHOR]

The present study reports the effects of combined torsional and compressive cyclic loading on trabecular bone in order to mimic true physiological conditions and thereby provides improved data that represents clinical and real life conditions. However, only compressive behaviour is evaluated in most previous studies of bone mechanics. From the monotonic evaluation, it is observed that lower stress is needed for the onset of microcrack in the sample under torsional loading, compared to the stress needed in compression. Trabecular bone samples were subjected to a combination of torsion and compression fatigue at different stress levels during which they were compared to compressive axial fatigue. The stress levels were determined by considering the monotonic strength at 25–50% for both compressive and shear stresses. Significant decrease in fatigue lifetime is observed in between samples of pure compression fatigue and those with superpositioned torsional loading ( p <0.05). The reduction in fatigue lifetime became more evident at a high torsional stress level. In this case, the failure of the sample is said to be ‘torsional dominant’. Fatigue behaviour of bovine trabecular bone begins with plastic deformation, followed by strain accumulation and modulus reduction. As the strain rate increases, more energy dissipates and the sample finally failed. Further, the analysis of fractograph revealed something on the trabeculae by bending in sample with superpositioned torsional loading. In conclusion, torsional loading decreases the quality of the trabecular properties in terms of stiffness, life and structural integrity. It is hoped that results from this study will improve the understanding of the behaviour of trabecular bone under combined fatigue and help to develop future assessments of trabecular failure. [ABSTRACT FROM AUTHOR]

This paper describes a microstructural-based high cycle fatigue behaviour model applied to cast Al-Si alloys used in an automobile context. These materials are characterized by the presence of different microstructural heterogeneities at different scales: the aluminium matrix (DAS/SDAS and the precipitation hardening level), inclusions (Si particles and intermetallic) and casting defects (porosity). It is shown that the effects of these factors on the HCF damage mechanisms are important and can depend on the loading mode. A multiaxial fatigue test campaign has been carried out using three cast aluminium alloys, fabricated by different casting processes (gravity die casting and lost foam casting), associated with several heat treatment(T7 and Hot Isostatic Pressing-HIP). The HIP treatment is used to eliminate or minimise the porosity. The first part of the article is dedicated to the experimental characterization of the HCF damage mechanisms. With regard to the effect of the casting defects, a study of natural fatigue crack growth and artificial long crack growth is presented and subsequently used to choose an appropriate fatigue strength criterion to take into account the effect of defects, for different loading modes (tension, torsion and combined tension-torsion). Finally, a flexible modelling framework, providing the possibility of combining any two suitable criteria, which leads to the construction of a multiaxial Kitagawa-Takahashi diagram, is used. [ABSTRACT FROM AUTHOR]

A series of multiaxial ratcheting–fatigue interaction tests have been carried out on Sn–3Ag–0.5Cu lead-free solder specimens. All tests were conducted under cyclic shear strain with the constant axial stress at the room temperature with the shear strain rate of 5 × 10-3 s-1. It was found that the ratcheting strain increased with increasing axial stress and shear strain amplitude while the fatigue life decreased at the same time. The ratcheting strain rate was linear with axial stress in double logarithmic coordinate. The Ohno–Wang II constitutive model was employed to simulate the stress–strain responses. Several fatigue life prediction models were applied to predict the multiaxial ratcheting–fatigue life of the Sn–3Ag–0.5Cu lead-free solder. The Gao–Chen model which adopted the maximum shear strain and the ratcheting strain rate as the damage parameter predicted the multiaxial ratcheting fatigue life well. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this work is to model short crack growth under fretting fatigue loading conditions by considering a criterion based on linear elastic fracture mechanics quantities, which also accounts for the first non-singular terms of the asymptotic expansion, namely the T-stresses. The Modes I and II Stress Intensity Factors and the T-stresses were computed by the finite element method under plane strain hypothesis. To assess the model fretting fatigue tests were carried out using two cylindrical fretting pads, which were loaded against a flat dogbone tensile test piece, both made of a Ti–6Al–4V titanium alloy. The model was capable to correctly estimate short crack arrest and to find the threshold fretting conditions separating failure from infinite life (here defined by tests which reached one million cycles). An optimization technique was implemented to the numerical model so that it could also estimate crack path. [Copyright &y& Elsevier]

Highlights: [•] The multiaxial elastic–plastic stress–strain model for notched components is developed. [•] The model is used for elastic–plastic stress–strain analysis based linear-elastic FE results. [•] The model is validated against the experimental data of SAE 1070 steel notched bar. [•] The model can be employed to perform fatigue life estimation for notched components. [ABSTRACT FROM AUTHOR]

Abstract: A multiaxial fatigue damage model for fibre reinforced polymer composite materials is presented. The model combines (i) fatigue-induced fibre strength and modulus degradation, (ii) irrecoverable cyclic strain effects and (iii) inter-fibre fatigue. The inter-fibre fatigue aspect is based on a fatigue-modified version of the Puck multiaxial failure criterion for static failure. The model is implemented in a user material finite element subroutine and calibrated against fatigue test data for unidirectional glass fibre epoxy. A programme of uniaxial fatigue tests on quasi-isotropic glass fibre epoxy laminates is presented for validation of the novel fatigue damage methodology. The latter is successfully validated across a range of stress levels. [Copyright &y& Elsevier]

Abstract: Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range – cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude loadings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented. [Copyright &y& Elsevier]

Abstract: The objective of this work is to develop a simple multiaxial version of a rainflow algorithm that allows the proper calculation of multiaxial fatigue damage induced by non-proportional load histories. One of the issues in such algorithm involves a complementary problem, how to properly quantify equivalent stress or strain ranges and mean components associated with each rainflow-counted cycle. A traditional way to estimate such ranges is to use enclosing surface methods, which search for convex enclosures like balls or prisms, of the entire history path in stress or strain diagrams. To treat these two intrinsically related problems, this work is divided into two parts. Part I deals with how to compute equivalent stress or strain ranges in multiaxial NP histories using enclosing surface methods. The available methods are first reviewed, and new enclosing surface models are proposed, based on Deperrois’ idea of longest chords. Then, these methods are compared using results from more than 3×106 Monte Carlo simulations of random and especially chosen path topologies in two to five-dimensional stress or strain diagrams. Moreover, a new simpler but powerful approach to evaluate equivalent stress and strain ranges in NP histories is presented, called the Moment Of Inertia (MOI) method. The MOI method is not based on enclosing surfaces, it assumes instead that the path contour in the stress or strain diagram is analogous to a homogeneous wire with a unit mass. The center of mass of such wire gives then the mean component of the path, while the moments of inertia of the wire can be used to obtain the equivalent stress or strain ranges. Experimental results for 15 different multiaxial histories prove the effectiveness of the MOI method to predict the associated fatigue lives, when compared to the existing enclosing surface methods. Part II of this paper presents a multiaxial rainflow counting algorithm that allows the MOI and enclosing surface methods to be generalized to non-periodic NP histories and to periodic NP histories formed by complex blocks with multiple cycles each. [Copyright &y& Elsevier]

Abstract: This paper describes the methodology developed by Decathlon, through its MKniX Engineering Center, to master the fatigue design of welded aluminium-alloy bicycle frame. The objective is to optimize the design prior to the standard testing by calculating the fatigue reliability of the bicycle frame. The fatigue assessment method is based on the Dang Van multiaxial fatigue criterion combined with a unique S-N design curve independent of the geometry of the welded structure and the loading mode. The design stress is defined through a linear elastic finite element analysis using a specific thin shell meshing method. [Copyright &y& Elsevier]

Abstract: A new equivalent stress amplitude expression has been developed for the assessment of fatigue life in components under multiaxial loading. The expression was generated by incorporating non-linear/plastic stress–strain relation into a mechanical energy calculation, and then applying the calculation to the distortion energy theory for a cyclic loading case. Therefore, the new uniaxial equivalent stress expression determines an appropriate stress amplitude value for multiaxial cyclic loading. The purpose of the equivalent stress value is to determine multiaxial fatigue failure using an energy-based fatigue life prediction criterion. The governing understanding behind the criterion states that the physical damage quantity for failure is equal to the accumulated strain energy in a monotonic fracture, which is also equal to the accumulated strain energy during fatigue failure. Using the new equivalent stress amplitude expression and the energy-based life prediction method, a comparison is made between prediction results and multiaxial empirical data. The multiaxial data was acquired by a vibration-based biaxial bending fatigue test and a torsion fatigue test with an assumed axial misalignment. The results of the comparison provide encouragement regarding the capability of the newly developed equivalent stress amplitude expression for fatigue life prediction. [Copyright &y& Elsevier]

Abstract: Dielectric elastomers are increasingly used for so called electro-active polymer actuators, sensors and generators. The materials are typically shaped as thin membranes loaded with an electric field in thickness direction. To increase the electromechanical performance, the membranes are pre-stretched with an in-plane area stretch up to 36. These large deformations may lead to rupture and thus impair the mechanical integrity of the devices. This work reports about a systematic investigation of the multiaxial deformation and mechanical failure characteristics of the acrylic elastomer membrane VHB 4910. Different tensile plane stress configurations were experimentally investigated using a large number of samples. Uniaxial and pure-shear tensile tests as well as membrane inflation tests were performed. Results of ultimate stretch, critical stress and stored deformation energy are reported along with stress–stretch relations for the three different kinematic configurations. The critical value of the maximum principal stretch at failure is found to be in the range of 9 and to be relatively independent of the imposed state of deformation. This is attributed to local failure initiating at stress rising features at the edges of the membranes. Stress concentrations at notches or load introduction regions were observed to dominate the mechanical failure behavior of VHB 4910. The present data are used to investigate the predictive capabilities of different nonlinear constitutive models previously proposed for VHB 4910. Limitations of the applicability of these models are shown for very large deformations and uniaxial stress states. A new set of parameters is determined for a simple Yeoh-model formulation to overcome these limitations. [Copyright &y& Elsevier]

Abstract: An innovative procedure is presented here for determining the minimum low cycle fatigue (LCF) life of turbine disk bores under multiaxial states of stress. The procedure statistically combines multiaxial data from spin pit tests with the data from uniaxial LCF tests. The connecting link between the two data sets is a new probability density function which can be derived from the uniaxial data and subsequently applied to the probability of failure calculated for a set of mini disks. The overall objective was to establish which of the criteria, principal stress-based versus effective stress-based, is valid for life estimation of the turbine disk bores made of DP-718. The minidisks, designed to simulate the same biaxial stress ratio as in an actual turbine disk bore, were tested at 589K by cycling between 5000 and 52,000rpm in a spin pit. The testing was interrupted to check for fatigue crack initiation in the bore by means of a proprietary vibration monitor. Only one of the disks showed a valid crack initiation. The initiation life is defined as the number of cycles required to initiate a crack of 381μm (0.015in.) depth, and was derived experimentally through subsequent striation counting. The approach established principal stress range with its associated stress ratio as the proper lifing parameter for DP-718 mini disks. Fractographic observations of similarity in the crack initiation modes observed for the alloy support the methodology. [Copyright &y& Elsevier]

Abstract: When an anisotropic material is subject to creep conditions and a complex state of stress, an anisotropic creep damage behavior is observed. Previous research has focused on the anisotropic creep damage behavior of isotropic materials but few constitutive models have been developed for anisotropic creeping solids. This paper describes the development of a new anisotropic tertiary creep damage constitutive model for anisotropic materials. An advanced tensorial damage formulation is implemented which includes both material orientation relative to loading and the degree of creep damage anisotropy in the model. A variation of the Norton-power law for secondary creep is implemented which includes the Hill’s anisotropic analogy. Experiments are conducted on the directionally-solidified bucket material DS GTD-111. The constitutive model is implemented in a user programmable feature (UPF) in ANSYS FEA software. The ability of the constitutive model to regress to the Kachanov-Rabotnov isotropic tertiary creep damage model is demonstrated through comparison with uniaxial experiments. A parametric study of both material orientation and stress rotation are conducted. Results indicate that creep deformation is modeled accurately; however an improved damage evolution law may be necessary. [Copyright &y& Elsevier]

Abstract: Fatigue life formulas are still based on phenomenological models which adopt simple relations directly from experiments for different loading conditions and use fitted material parameters. The combination of enormous complexity of fatigue damage processes and simple, macro appearance of the formulas (usually power laws), are the source of Generic Fatigue Models (GFM). GFMs rely on minimal, but coherent, micro-details which are independent of the specific micro structure. Such a model has been developed, connecting analytically the S-N power law and endurance stress in terms of statistical strength distributions of material microelements and their neighbors. This paper describes two types of generalizations of the basic GFM: a.) Two level (H-L and L-H) loading, in which a history dependent micro-damage evolution law is proposed, and b.) Multiaxial fatigue response by a simple 2D truss. Emphasize is on minimal parameters and capability of analytical predictions, in which every “material constant” has a physical or micro-geometrical meaning. The theoretical generalizations are compared with experimental data from the literature and show that the predictions are coherent with main experimental features. [Copyright &y& Elsevier]

Abstract: Thin-walled tubular specimens were employed to study the cyclic deformation of extruded AZ61A magnesium alloy. Experiments were conducted under fully reversed strain-controlled tension–compression, torsion, and combined axial–torsion in ambient air. Mechanical twinning was found to significantly influence the inelastic deformation of the material. Cyclic hardening was observed at all the strain amplitudes under investigation. For tension–compression at strain amplitudes higher than 0.5%, the stress–strain hysteresis loop was asymmetric with a positive mean stress. This was associated with mechanical twinning in the compression phase and detwinning in the subsequent tension phase. Under cyclic torsion, the stress–strain hysteresis loops were symmetric although mechanical twinning was observed at high shear strain amplitudes. When the material was subjected to combined axial–torsion loading, the alternative occurrence of twinning and detwinning processes under axial stress resulted in asymmetric shear stress–shear strain hysteresis loops. Nonproportional hardening was not observed due to limited number of slip systems and the formation of mechanical twins. Microstructures after the stabilization of cyclic deformation were observed and the dominant mechanisms governing cyclic deformation were discussed. Existing cyclic plasticity models were discussed in light of their capabilities for modeling the observed cyclic deformation of the magnesium alloy. [Copyright &y& Elsevier]

Abstract: To assemble tubular structures such as pipelines, risers, , threaded couplings can be used. In service these couplings are often subjected to dynamic loads, and to maintain a secure connection, they are generally preloaded. The combination of preload and external dynamic loads results in a multiaxial stress distribution over the connection, where the coupling’s threads act as stress raisers, initiating fatigue cracks. In this study the fatigue life of the standard API Line Pipe coupling and two modified coupling configurations is determined experimentally. This way the influence of the coupling’s global geometry on the connection’s fatigue life is studied. Threaded pipe samples with a nominal size of are tested on a four-point bending fatigue test setup to obtain S-N curves. Both modified coupling configurations exhibit a fatigue life improvement. In the final part of this paper, these experimental observations are explained by a combination of a damage evolution law and a finite element model. [Copyright &y& Elsevier]

Abstract: Some mechanical components are subjected to thermo-mechanical fatigue, which occurs when both thermal and mechanical loads vary with time. Due to the complexity of the components geometry, stresses and strains field becomes multiaxial, worsening the fatigue resistance. In this paper several damage models are applied and compared on a case study, an automotive exhaust manifold simulacrum replying the material and the geometrical features of the commercial component. A complete thermo-structural FE analysis has been run and results have been post-processed by means of a numerical code implementing several multiaxial damage models available in literature and based both on a critical plane approach (Kandil-Brown-Miller, Fatemi-Socie) and strain-based models (Von Mises, ASME Code and Sonsino-Grubisic). The model calibration has been carried out by means of literature experimental data referred to commercial exhaust manifolds of similar geometry and material. [Copyright &y& Elsevier]

• The torsional and coupled torsion-tension/compression behaviors of magnesium alloy solid rod are systematically investigated through experiments and the crystal plasticity model. • Torsional behavior and the resultant Swift effect depend strongly on the texture. • The axial stress would affect the twinning activities drastically in different loadings. • The difference between shears and torsion is attributed to the significant bulk stress caused by the strong interaction between the cylindrical elements. Extensive attention has been paid to magnesium (Mg) alloys considering their potential as lightweight structural materials. However, it is still challenging to process and manufacture Mg materials that carry high strength and good ductility. This issue mainly arises from a lack of understanding toward the anisotropic mechanical behavior of Mg alloys in response to large deformation in a multiaxial stress state, which is unavoidably in existence under various material processing routes. In this regard, we seek to understand the torsional and coupled torsion-tension/compression behaviors of a magnesium alloy subject to large-strain deformation. The elastic viscoplastic self-consistent (EVPSC) model, which incorporates the twinning-detwinning (TDT) scheme and takes a torsion-specific finite element (TFE) approach, was employed to illuminate the inhomogeneous and multiaxial features of the torsional deformation in the AZ31 Mg alloy subjected to free/fixed-end torsion and coupled torsion-tension/compression. Experimental validation was conducted by characterizing the mechanical responses of the torsional specimens under the loading paths of free-end torsion and coupled torsion-tension. Our model successfully captures the Swift effect along with the shear texture, which is hardly predicted by conventional constitutive models. In addition, our model reveals that twinning is nearly equally active under free-/fixed-end torsion, while twinning under coupled torsion-tension and torsion-compression is promoted and suppressed, respectively. The comparison between the simple shear and pure torsion by simulation demonstrates that the significant bulk stress existing within the torsional rod is ascribed to the strong interaction between the cylindrical elements in the EVPSC model. As a final thought, we believe that the TFE-EVPSC-TDT model not only highlights the inhomogeneous and multiaxial features underlying the torsional and coupled torsion-tension/compression behaviors of the Mg alloy solid rod, but more significantly, can be used as a numerical tool for designing/tuning gradient twinning structures that may lead to optimized properties of Mg alloys. [ABSTRACT FROM AUTHOR]

• The novel model using a grain (GR)/grain boundary (GB) scale mesh in the cracking region of a Compact Tension geometry simulates crack growth rates under different microstructural anomalies and variabilities such as voids and precipitates and grain shapes. • In this model micro-cracks can randomly initiate and grow under a micro-triaxial stress state at positions where accumulated creep damage reaches critical values. • A detailed sensitivity analysis of GB/GR/size/distortion/strength and void/precipitate density and distribution simulations is used to identify the likely reasons for cracking rates, crack branching and data scatter in creep test. • This approach can be extended to predict long term creep cracking failures in components. Over the years numerous of materials based experimental research programmes have focused on understanding the high temperature failure mechanisms and their relation to the microstructure of engineering alloys. These microstructures are complex in nature and are being continuously developed to improve creep/fatigue and oxidation strength of components at elevated temperatures. Furthermore, with the advent of additive manufacturing (AM) even more diverse microstructures which can contain voids, interstitial Titanium Aluminides (Ti-Al) and grain distortions have evolved at the sub-grain level affecting the creep strength of the alloys. Since measurements of detailed sub-grain properties are difficult to obtain and are likely to contain large levels of scatter a modelling procedure for a meso-scale model in multiaxial creep to identify creep damage is needed. The model using a grain (GR)/grain boundary (GB) scale mesh in the cracking region of a Compact Tension geometry simulates crack growth rates under different microstructural anomalies and variabilities such as voids and precipitates and grain shapes. In this model micro-cracks can randomly initiate and grow under a micro-triaxial stress state at positions where accumulated creep damage reaches critical values. A detailed sensitivity analysis of GB/GR/size/distortion/strength and void/precipitate density and distribution simulations is used to identify the likely reasons for cracking rates, crack branching and data scatter in creep test. Available high temperature material and mechanical properties from a representative Ti-Al intermetallic alloy are used to validate the model. The present analysis sets out the modelling approach and points the way to more complex microstructures which could contain a multiplicity of phases and sub-grain particles. The development of such models is likely to be the preferred approach to predict virtual creep crack growth in both welding and new additive manufacturing processes. [ABSTRACT FROM AUTHOR]

Abstract: A new multiaxial high-cycle fatigue initiation life prediction model for railroad wheels is proposed in this paper. A general fatigue damage analysis methodology for complex mechanical components is developed and applied to the wheel/rail rolling contact fatigue problem. A 3-D elasto-plastic finite element model is used for stress analysis. A submodeling technique is used to achieve both computational efficiency and accuracy. Then the fatigue damage in the wheel is evaluated numerically using the stress history during one revolution of the wheel rotation. The effects of wheel diameter, vertical loading, material hardness, and material fatigue properties on fatigue crack initiation life are investigated using the proposed model. [Copyright &y& Elsevier]

Abstract: A facility has been developed capable of high strain rate material characterization in multiaxial flexure. Using this novel equipment, a formulation of a glass filled nylon composite (Ultramid B3WG6 BGVW) has been tested in biaxial flexure at a variety of strain rates. For the material tested, the flexural modulus was shown to have no significant dependence on the rate of application of load. The measured modulus was found to be over a range of –. A FE model was created and found to have an excellent correlation over the entire range of strain rate. The capabilities and limitations of the experimental facility are discussed. [Copyright &y& Elsevier]

Abstract: Since bone-mass-based measurements have demonstrated limited success in predicting age-related increase in fracture incidence, recent emphasis has been placed on quantification of bone quality. Specifically, material parameters such as strength, stiffness, and toughness have been quantified to characterize bone quality through mechanical testing. This study is the first one to report multiaxial failure characteristics of bone (quality) by conducting fatigue tests on human cortical bone specimens under physiologically relevant loading involving simultaneous application of axial and torsional loading to produce previously reported in vivo shear/normal stress ratios. Our results show that, compared to uniaxial tests, multiaxial fatigue tests show up to a 20-fold reduction in the fatigue life of human cortical bone. More significantly, the susceptibility of mixed-mode failure increases bone fragility in aging human bone. Furthermore, since the magnitude of mixed-mode loading varies with physiological activities, results of this study also suggest that a reduction in the activities involving significant mixed-mode loading may lower the overall fracture incidence among older individuals. [Copyright &y& Elsevier]

Abstract: An experimental study was conducted on the inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading. Thin-walled tubular specimens were used and small strain gages were bonded on the specimen surface to characterize the local deformation. The controlled loading paths included cyclic tension–compression, cyclic torsion, proportional axial-torsion, 90°-out-of-phase axial-torsion, and fully reversed torsion with a constant axial stress. The maximum stress in each experiment was lower than the lower yield stress of the material. It was found that the cyclic plastic deformation within the gage section of the specimen under multiaxial stress state followed the three-stage process that was observed from uniaxial loading, namely, incubation, propagation, and saturation. The plastic deformation was significantly inhomogeneous during the propagation stage, and the inhomogeneity continued through the saturation stage. The duration of each stage and the saturated strains were dependent on the cyclic stress amplitude and the loading path. Multiaxial stress state reduced the incubation stage. With identical equivalent stress magnitude, the nonproportional loading path resulted in the shortest incubation and propagation stages, and the saturated equivalent plastic strain magnitude was the smallest. Although the deformation over the gage section was inhomogeneous, the plastic deformation in a given local area was found to be practically isotropic. [Copyright &y& Elsevier]

Abstract: This study examined the engineering and true axial stress–strain behavior of smooth cylindrical and shallow and deep notched cylindrical test specimens, under applied axial tensile loading using non-contacting methods, of both conventional and highly crosslinked ultra-high molecular weight polyethylenes (UHMWPEs). The smooth specimens experienced a uniaxial stress state, while the notched specimens experienced a triaxial stress state in the vicinity of the notch. Materials were all prepared from a single batch of medical grade GUR 1050 resin (Ticona, Bayport, TX). The two conventional UHMWPEs were as-received (virgin) and gamma radiation sterilized at 30kGy in a nitrogen atmosphere (radiation sterilized). The two highly crosslinked UHMWPEs were each irradiated at 100kGy and then post-processed with one of either of the two thermal treatments: annealing, which was done below the melt transition temperature (Tm), at 110°C for two hours (110°C-annealed), and remelting, which was done above Tm, at 150°C (150°C-remelted). All of the materials showed notch strengthening; that is, a significant elevation of axial yield properties (both engineering and true) for the shallow and deep notched conditions. Axial ultimate properties (engineering and true) were significantly decreased for the notched conditions compared with the smooth condition. Hardening ratios (both true and engineering), which are defined in this work as the ratio of ultimate stress or strain to yield stress or strain, were also found to significantly decrease with notching. The extent of change was dependent on the UHMWPE material. The micromechanism of fracture differed between the smooth and notched conditions. This study suggests that notches inherent in the design of UHMWPE joint replacement components (posts, undercuts, grooves) will have different notch sensitivities depending on the UHMWPE formulation. [Copyright &y& Elsevier]

Fatigue fractures of cortical bone involve combined axial–torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0° and 90° phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures. [Copyright &y& Elsevier]

Given the previous complete-potential structure framework [see Int. J. Plasticity 10(3) (1994) 263], together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation), see [Int. J. of Plasticity 17(10) (2001) 1305], a detailed viscoelastoplastic multimechanism characterization of a specific hardening functional form of the model is presented and discussed. TIMETAL 21S is the material of choice as a comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. are available at various temperatures. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model particularly with regard to the notion of hardening saturation as well as the interaction of multiplicity of dissipative (reversible/irreversible) mechanisms. [Copyright &y& Elsevier]

Non-proportional multiaxial fatigue tests of tubular specimens were performed under purely alternating strain-controlled loading. Different loading paths with different phase shifts were applied. With increasing phase shift at the same equivalent load, the lifetime was found to increase. For lifetime prediction a model based on the Manson–Coffin law was developed. By including the hydrostatic loading part, it was possible to compare the results of the multiaxial fatigue tests with uniaxially ascertained results. To obtain more information about the microcrack behaviour under multiaxial non-proportional loading, sonic emission studies and fractographic analyses were performed. The results suggest a discontinuous microcrack propagation. Motivated by the good agreement between these observations and some microcrack propagation models known from literature, a simplified model was proposed for micro and short crack propagation. This model which is based on the J-integral range ΔJ yields a quite good agreement between the experimentally observed and the calculated lifetimes. [Copyright &y& Elsevier]

A reliable design of industrial parts against high-cycle multiaxial fatigue requires a fatigue criterion capable of predicting both the stress gradient and the load-type effects. These effects are very important in the transfer of fatigue data from specimen to component. By using the concept of volume influencing fatigue crack initiation proposed by Palin-Luc and Lasserre with an energy based approach, a new criterion is presented. Based on the strain-work density given to the material, this proposal is usable whatever the constant amplitude loading is: in and out-of-phase combined loadings, with or without mean stress. Its predictions are compared both with a total of 38 experiments on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron) and with the predictions of local criteria (Crossland, Dang Van, Papadopoulos and Morel). The comparison shows that the predictions of the volumetric proposal are very good and less scattered than those of the local approaches, especially for loadings with mean stresses or under non-proportional loadings. [Copyright &y& Elsevier]

In this paper, a multiaxial generalization of the viscoplastic “mechanical equation of state” (MEOS) by Gittus is proposed that preserves the physical soundness of the theory. The concept of forward and backward mobility of dislocations is generalized to a concept of directional mobility by splitting the mobile dislocation density in an isotropic and a tensorial part, similar to the approach used in the Bodner unified viscoplastic model. It is shown that the formulation is equivalent to the original MEOS in the case of uniaxial loadings. The approach is easily applied to any uniaxial viscoplastic material model. [Copyright &y& Elsevier]

• We propose a model for deformation-induced damage and failure of annulus fibrosus. • We introduce the structural arrangement of collagen network at different scales. • We account for the chemically-induced volumetric effects on damage and failure. • We perform simulations under different multiaxial loading histories. This article presents a multiscale model to predict deformation-induced damage and failure of human annulus fibrosus under multiaxial loading. In the modeling approach, formulated within the framework of nonlinear continuum mechanics, the hierarchical structure of the soft tissue is considered from the nano-sized collagen fibrils to the micro-sized oriented collagen fibers. At the macroscale, the multi-layered lamellar/inter-lamellar organization of the soft tissue is introduced by considering the effective interactions between adjacent layers. The stochastic process of progressive damage events operating at different scales of the solid phase is introduced for the extracellular matrix and the network of nano-sized fibrils/micro-sized fibers. The damage is made anisotropic due to lamellar oriented collagen fibers and special orientation distribution of the inter-fibrillar and inter-lamellar network of fibrils. The chemical-induced volumetric strain is also considered in our modeling approach to take into account the osmolarity effects along with the anisotropic time-dependent transversal deformations. The capacity of the model is discussed using a few available stretching datasets till failure along circumferential and radial directions. Model predictions under tilted stretching, biaxial stretching and shearing are also presented to illustrate further the efficiencies of our modeling approach. This work shows for the first time the directional effects on annulus mechanics and failure in relation to external loading mode, structure features, damage events and hydration. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel approach to estimate fatigue life of notched components is proposed. • The critical point position is determined using the Line Method by Taylor. • The fatigue life is assessed through a critical-plane based criterion. • The approach is validated by means of experimental tests on V-notched specimens. • A quite good estimation of the fatigue lives for the experimental data is achieved. It is well known that combination of multiaxial cyclic loading and geometrical discontinuities (such as notches and holes) frequently occurs in engineering practice, and different methods are available in the literature for multiaxial notch fatigue analysis. In such a context, a new analytical approach is here proposed in order to assess the fatigue lifetime of notched components. Such an approach consists in the joint application of (i) the multiaxial high-cycle fatigue criterion by Carpinteri et al. (formulated in terms of stresses on the critical plane) and (ii) the Critical Distance Theory by Taylor (in the form of the Line Method). In order to evaluate the accuracy of the proposed approach, experimental data, recently published in the literature and related to severely notched specimens under uniaxial and multiaxial fatigue loading, are examined, being the specimens made of Ti-6Al-4 V, material attracting significant interest by leading industries, such as the biomedical one. [ABSTRACT FROM AUTHOR]

• A procedure for fatigue life assessment of fillet-welded joints is proposed. • The procedure exploits a multiaxial fatigue criterion for complex random loading. • Experimental data related to a T-joint are used to validate the novel procedure. • Such a T-joint is the weakest link of an arm sprayer used in agriculture. • The crack nucleation location on the weld toe is numerically evaluated. In the present paper, a novel procedure for fatigue resistance assessment of fillet-welded joints under complex random loading is proposed. It consists of two consecutive steps: (1) computation of the stress tensor at the verification point; (2) evaluation of damage and, consequently, fatigue life. The procedure exploits the multiaxial critical plane-based criterion by Carpinteri et al. for random loading. A case study, represented by a mechanical component of an arm sprayer used in agriculture, is examined in order to assess such a procedure. A comparison between experimental and numerical results in terms of crack nucleation location is performed. [ABSTRACT FROM AUTHOR]

• Cycle counting is ill-defined for non-proportional multiaxial fatigue. • A new cycle counting paradigm is proposed. • The new paradigm is backwards compatible with conventional cycle counting. • And also introduces incremental, continuous tracing of cycle characteristics. The article examines a universal method to count cycles in the context of non-proportional, multiaxial fatigue. It is independent of the damage criterion used to predict the lifetime curve, and provides the same number of cycles as when using the classic counting methods for proportional loading cases. It is shown that, at any point on the loading path, an immediate estimation of the current fractional cycle count, mean and amplitude values can be computed. This enables to describe lifetime as a function of these variables, and also to apply the method to fatigue problems with variable amplitude and frequency. [ABSTRACT FROM AUTHOR]

• A new approach to predict the creep rupture life with substantial scatter data was presented. • The Kachanov's Continuum Damage Model (CDM) and strain-based exponential relation models have been evaluated. • The approach is relatively simple yet reliable to be employed for high temperature creep rupture assessment. The extension of the available stress-based predictive models from uniaxial to multiaxial feature is uncertain due to the difficulty to justify the model transferability to the cases which involves complex deformation and fracture mechanisms. This paper presents a new approach to predict the creep rupture life of Grade 92 steel under multiaxial stress state as the case of notched bar samples using Kachanov's Continuum Damage Mechanics (CDM) model. Combining the CDM model with the concept of Hayhurst's representative stress and accounting two extreme conditions; fully dislocation-controlled and diffusion-controlled creep mechanisms provide the bounds for short- and long-term rupture data of notched bar up to 10,000 h. Although the CDM is scientifically relevant and fundamental in their approach, it is generally complex and contains too many variables. Therefore, it needs proper measurements or numerically intensive to make the model acceptable for industrial applications. Alternatively, the recent developed strain-based exponential-type predictive model which links globally uniform failure strain with a multiaxial constraint factor was employed with the intention to reduce the large number of CDM parameters. The approach is relatively simple yet reliable to be used for high temperature creep rupture assessment. [ABSTRACT FROM AUTHOR]