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The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σθZ) and axial (σZZ) stress tensor components, stress and stress deviator tensor invariants (I1, J2, and J3), von Mises equivalent stress (σVMgrain), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter (θ‾) values were tracked for ∼ 300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σθZ, σVMgrain , and J2; by comparison, I1, J3, η, and θ‾ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

This review paper encompasses a comprehensive exploration of fatigue failure and fatigue life estimation techniques which spans from the classical methods to new and innovative approaches. The paper looks into the limitations and advancements of these techniques and highlights their respective strengths and areas for improvement. Some of the models such as artificial neural networks and genetic algorithms exhibit clear advantages in terms of processing speed, accuracy, and adaptability to diverse materials and loading scenarios. For instance, in estimating fatigue life under multiaxial loading, the stress scale factor model emerges as a viable alternative to the critical plane-based approach, as this technique offers superior efficiency under both constant and variable amplitude loadings. Additionally, optimization algorithms such as artificial neural networks and genetic algorithms show promising potential in efficiently estimating fatigue life due to their rapid computational capabilities. Despite the notable successes achieved by these techniques, none of them can be ascribed as a universal model capable of accurately estimating the fatigue life of all materials across diverse operating conditions as each of the techniques possesses its unique strengths and weaknesses, thus, necessitating the study for a better understanding of their applicability. Hence, this paper serves as a valuable compilation of various fatigue analysis techniques, targeted at paving the way towards the development of a universal model capable of handling different materials and loading conditions.

Inorganic ferroelectrics have long dominated research and applications, taking advantage of high piezoelectric performance in bulk polycrystalline ceramic forms. Molecular ferroelectrics have attracted growing interest because of their environmental friendliness, easy processing, lightweight, and good biocompatibility, while realizing the considerable piezoelectricity in their bulk polycrystalline forms remains a great challenge. Herein, for the first time, through ring enlargement, a molecular ferroelectric 1‐azabicyclo[3.2.1]octonium perrhenate ([3.2.1‐abco]ReO4) with a large piezoelectric coefficient d33 up to 118 pC/N in the polycrystalline pellet form is designed, which is higher than that of the parent 1‐azabicyclo[2.2.1]heptanium perrhenate ([2.2.1–abch]ReO4, 90 pC/N) and those of most molecular ferroelectrics in polycrystalline or even single crystal forms. The ring enlargement reduces the molecular strain for easier molecular deformation, which contributes to the higher piezoelectric response in [3.2.1‐abco]ReO4. This work opens up a new avenue for exploring high piezoelectric polycrystalline molecular ferroelectrics with great potential in piezoelectric applications. [ABSTRACT FROM AUTHOR]

Abstract Inorganic ferroelectrics have long dominated research and applications, taking advantage of high piezoelectric performance in bulk polycrystalline ceramic forms. Molecular ferroelectrics have attracted growing interest because of their environmental friendliness, easy processing, lightweight, and good biocompatibility, while realizing the considerable piezoelectricity in their bulk polycrystalline forms remains a great challenge. Herein, for the first time, through ring enlargement, a molecular ferroelectric 1‐azabicyclo[3.2.1]octonium perrhenate ([3.2.1‐abco]ReO4) with a large piezoelectric coefficient d33 up to 118 pC/N in the polycrystalline pellet form is designed, which is higher than that of the parent 1‐azabicyclo[2.2.1]heptanium perrhenate ([2.2.1–abch]ReO4, 90 pC/N) and those of most molecular ferroelectrics in polycrystalline or even single crystal forms. The ring enlargement reduces the molecular strain for easier molecular deformation, which contributes to the higher piezoelectric response in [3.2.1‐abco]ReO4. This work opens up a new avenue for exploring high piezoelectric polycrystalline molecular ferroelectrics with great potential in piezoelectric applications.

We investigate the combined effects of surface diffraction and total internal reflection (TIR) in the design of 3-dimensional materials exhibiting distinct structural colour on various facets. We employ mechanical wrinkling to introduce surface diffraction gratings (from the nano to the micron scales) on one face of an elastomeric rectangular parallelepiped-shaped slab and explore the roles, in the perceived colours, of wrinkling pattern, wavelength, the directionality of incident light and observation angles. We propose a simple model that satisfactorily accounts for all experimental observations. Employing polydimethylsiloxane (PDMS), which readily swells in the presence of various liquids and gases, we demonstrate that such multifaceted colours can respond to their environment. By coupling a right angle triangular prism with a surface grating, we demonstrate the straightforward fabrication of a so-called GRISM (GRating + prISM). Finally, using a range of examples, we outline possibilities for a predictive material design using multi-axial wrinkling patterns and more complex polyhedra. [ABSTRACT FROM AUTHOR]

This paper investigates the fatigue behavior of S135 high-strength drill pipe steel under tension–torsion multiaxial loading. Based on the concept of critical plane during fatigue, the fatigue model under the combined loading of tension–torsion is established. The proposed model is validated, and the predicted results are in good agreement with the experimental testing results. The maximum relative errors between the estimation and the experiment are mostly within the range of factor two to three for proportional, and 90° non-proportional tension–torsion loading. Meanwhile, the failure mechanism is also discussed through fracture analysis. [ABSTRACT FROM AUTHOR]

The isothermal planar‐biaxial fatigue behavior was studied for two different disk batches of nickel‐base superalloy Inconel 718 using cruciform specimens at 400°C and 630°C under equi‐biaxial and shear loading. Additionally, non‐proportional tests were performed. The planar‐biaxial test results were compared with uniaxial reference tests using the von Mises equivalent strain hypothesis, a shear strain parameter of the critical plane, and a modified crack‐opening‐displacement strain range approach. Additionally, the crack initiation mechanism was analyzed. Using a modified crack‐opening‐displacement strain range approach, the low‐cycle fatigue lifetimes of the proportional planar‐biaxial tests (i.e., lifetimes up to 40,000 cycles) were described within a scatter band of two. Thus, it was better than using the equivalent strain of von Mises or a shear strain parameter. The fatigue crack initiation took place at oxidized primary carbides at the surface. The crack paths were presented. Highlights: IN718 showed cyclic softening and final stabilization, also for planar‐biaxial loading.A modified COD strain range approach showed a good correlation in the LCF regime.Crack initiation occurred on the surface at oxidized primary carbides in the gauge area.The crack paths were monitored for the different planar‐biaxial loading conditions. [ABSTRACT FROM AUTHOR]

Much progress has been witnessed in exploring host–guest type ferroelectrics represented by ammonium‐crown ether compounds. However, the major obstacles in expanding their promising applications in nonvolatile memory elements, capacitors, and sensors are relatively low Curie temperature (Tc) and uniaxial attribute. Herein, by screening different organic cations and inorganic anions to assemble with 18‐crown‐6 molecule, it is found that a new ammonium‐crown ether inclusion ferroelectric 1, [(ATHTP)(18‐crown‐6)]BF4 (ATHTP = protonated 4‐aminotetrahydrothiopyran), undergoing a ferroelectric phase transition at a much higher Tc of 392 K which is comparable to BaTiO3 (Tc = 393 K). Notably, the distinct symmetry breaking, that is, 4/mmmFmm2, leads to a biaxial ferroelectric with four equivalent directions of polarization. Such high Tc and multiaxial nature are rare in existing crown ether‐based ferroelectrics. This work can help the exploration of high‐Tc multiaxial ferroelectrics toward further device applications. [ABSTRACT FROM AUTHOR]

Hematite carries magnetic signals of interest in tectonic, paleoclimatic, paleomagnetic, and planetary studies. First‐order reversal curve (FORC) diagrams have become an important tool for assessing the domain state of, and magnetostatic interactions among, magnetic particles in such studies. We present here FORC diagrams for diverse hematite samples, which provide a catalog for comparison with other studies and explain key features observed for hematite. Ridge‐type signatures typical of uniaxial single‐domain particle assemblages and "kidney‐shaped" FORC signatures, and combinations of these responses, occur commonly in natural and synthetic hematite. Asymmetric features that arise from the triaxial basal plane anisotropy of hematite contribute to vertical spreading in kidney‐shaped FORC distributions and are intrinsic responses even for magnetostatically noninteracting particles. The dominant FORC distribution type in a sample (ridge, kidney‐shaped, or mixture) depends on the balance between uniaxial/triaxial switching. The identified signals explain magnetization switching and anisotropy features that are intrinsic to the magnetic properties of hematite and other materials with multiaxial magnetic anisotropy. Plain Language Summary: First‐order reversal curve (FORC) diagrams have become a standard method for identifying the domain state of magnetic materials. It has recently been demonstrated that the magnetic anisotropy type can also be identified using FORC diagrams. The magnetic domain state and anisotropy type of a magnetic mineral control the fidelity of recording of magnetic information, so identifying these features is fundamental to paleomagnetic, rock magnetic, and environmental magnetic studies. Hematite is a naturally abundant magnetic mineral that is encountered commonly in such studies, so it is important to have extensive FORC reference data for this mineral. We present the most comprehensive available FORC study of diverse natural and synthetic hematite samples, including numerical simulation results, to seek to explain key domain state and anisotropy signals for hematite. Key Points: FORC diagrams are presented for diverse natural and synthetic hematite samples to demonstrate domain state and anisotropy signaturesKidney‐shaped FORC distributions are indicative of multiaxial anisotropy and central ridge‐type distributions reflect uniaxial anisotropyThe dominant FORC distribution type depends on the balance between uniaxial and triaxial switching mechanisms [ABSTRACT FROM AUTHOR]

Objective: Classification systems and their practical implications have become increasingly important in child and adolescent psychiatry. This paper presents the evolution and practical applications of a multiaxial classification system for children and adolescents presenting to mental health services. Included are some worked examples demonstrating both the complexity of many presentations and how broadening the use of the multiaxial system can help in identifying appropriate interventions. Conclusions: Classification systems in child and adolescent psychiatry have largely remained uniaxial in nature. A multiaxial system encapsulates the broader biopsychosocial aspects of the presenting child or adolescent, and orders complex data in a concise manner. This approach can be used to concisely communicate with other treating clinicians, and assist with case reviews, formulation and teaching. [ABSTRACT FROM AUTHOR]

In this paper, the relationship between the tearing energy and the far-field cracking energy density (CED) is evaluated for an embedded penny-shaped flaw in a 3D elastomer body under a range of loading modes. A 3D finite element model of the system is used to develop a computational-based fracture mechanics approach which is used to evaluate the tearing energy at the crack in different multiaxial loading states. By analysing the tearing energy's relationship to the far-field CED, the proportionality parameter in the CED formulation is found to be a function of stretch and biaxiality. Using a definition of biaxiality that gives a unique value for each loading mode, the proportionality parameter becomes a linear function of stretch and biaxiality. Tearing energies predicted through the resulting equation show excellent agreement to those calculated computationally. [ABSTRACT FROM AUTHOR]

Durability is an essential feature of most elastomer products, directly linked to safety and to perceptions of brand quality. Product designers must therefore consider the impact on product durability of typical and abusive end-user loading scenarios. This can be accomplished using critical plane analysis (CPA). CPA starts by acknowledging that a small crack precursor might exist at any point in a part, and in any orientation, and that the potential development of all crack precursors must be evaluated. The analysis produces a full accounting of which location and orientation maximizes crack growth (or, equivalently, minimizes fatigue life) at each point, the energy release rate history experienced, and of course the worst-case fatigue life across all possible orientations. This review provides an account of the development of the method over the last two decades and the validation case that has accumulated. This review also suggests directions for further development of the method. [ABSTRACT FROM AUTHOR]

• 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]

Stress/strain measured data which have inherent scatter are used to develop predictive models in creep failure assessment under uniaxial and multiaxial conditions. Models developed for this purpose also need to address the multiaxial stress state effect when creep damage dominates. A unifying approach to predict creep damage and rupture under uniaxial/multiaxial and crack growth conditions is presented in this paper by deriving a multiscale based constraint criterion. The model identifies global constraint due to geometry and a microstructural time-dependent constraint arising from local creep diffusional processes occurring at the sub grain level. The concept assumes that at very short times the initial upper shelf material tensile strength and global plasticity controls the creep damage failure and at long term diffusion/dislocation control creep response develop local constraint depending on the time-dependent anisotropic microstructural conditions. Using creep data for two different steels, P91 and 316H at different temperatures 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, are the important variables in both the uniaxial and multiaxial failure processes. It is also shown that the model is consistent with the established NSW crack growth model which bounds the plane stress/strain cracking rates in fracture mechanics geometries and cracked components. [ABSTRACT FROM AUTHOR]

Real mechanical assemblies favor the initiation and propagation of fatigue cracks due to stress concentration phenomena arising from the geometrical features such as notches, corners, holes, welding toes, etc. Classical fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue strength reduction factor, which is experimentally expensive and lacks physical scene. In the present paper, a simple and meaningful methodology is proposed to assess notched components against multiaxial fatigue. In this method, by precisely defining a finite-size volume surrounding the fatigue crack initiation site (notch tip), over which the strain energy is averaged, the morphological effect on the process zone is fully addressed. Such a method takes into account the effect of combination of different modes (I, II, III) and the load ratio. In order to implement it for components with a sharp or blunt notch, it is enough to analyze a linear elastic finite element model and to know only the properties of materials obtained from simple uniaxial tests. New relationships for determining an effective (tensile-type) stress and fatigue strength reduction factors are derived for notched specimens. The accuracy of the proposed model is validated by experimental data available in the literature, related to tubular specimens weakened with sharp/blunt notches under combined bending-torsion loading. Such a situation widely appears in equipment used for various branches of industry such as piping, automotive, power plant, drilling, etc. [ABSTRACT FROM AUTHOR]

The compressive strength of concrete under biaxial dynamic compression The compressive strength of two concretes under biaxial dynamic compressive stress was investigated. A biaxial split Hopkinson bar was used, that applied the dynamic load to the test specimen in the form of two load waves perpendicular to each other. For reference, the static compressive strengths under biaxial load with different stress ratios of the two load axes were determined in a triaxial testing machine. The results indicate a partially superposition of the two strength‐increasing effects of multi‐axial compressive stress and increased strain rate. In particular, clear differences can be seen in the fracture and crack pattern for the different load types. [ABSTRACT FROM AUTHOR]

Important components such as gears, rollers, or bearings operate in rolling‐sliding contact loading conditions. Determination of their fatigue lives remains a challenging task due to complex states of stress and strain in the contact region, as well as complex contact conditions such as variable loading amplitude and complex geometry of contact. A mathematical model of rolling‐sliding line contact combined with a multiaxial fatigue life calculation model based on the Fatemi‐Socie critical plane crack initiation criterion is proposed. The developed model was applied to gears' teeth in mesh and compared with fatigue lives of gears reported in the literature. Good agreement was determined confirming the validity of the proposed model. A further advantage is obtaining locations of initiated cracks and the orientation of critical plane(s), which can subsequently be used for the estimation of crack shapes in initial phases of their growth and the damage type that they can be expected to develop into. [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]

The damage estimation for a structure under random loading is a challenge in fatigue assessment, especially when the loading is multiaxial. The comparison of the effect of different spectra on fatigue damage is essential when the structure can be subjected to different types of loadings. Therefore, in the present paper, the expected fatigue damage produced on metallic structures by combined bending and torsion stationary proportional and nonproportional loading is evaluated varying the shape of spectra of the normal and shear stress tensor components. [ABSTRACT FROM AUTHOR]

In this study, a miniaturized cruciform-shaped sample geometry which allows reaching high plastic strain under equibiaxial loading with reduced thickness at the test section is presented. The thinning method results in excellent surface quality that can be used for electron backscatter diffraction (EBSD) and high-resolution digital image correlation (HRDIC) investigations. The new cruciform geometry is used to study the slip activity in metastable austenitic stainless steel 304 during uniaxial and equibiaxial deformation using HRDIC. The results are discussed with respect to the Schmid law and the effect of multiple slip activity on the nucleation of martensitic transformations. [ABSTRACT FROM AUTHOR]

Utilizing molecular dynamics (MD) integration model we have investigated some of the relevant physical processes caused by different loading paths at the atomic level in Cu and Al monocrystal specimen. Interactions among the atoms in the bulk are modeled with the standard realistic Embedded Atom Method (EAM) potentials. MD simulation gives us the detailed information about non-equilibrium dynamics including crystal structure defects, vacancies and dislocations. In particular, we have obtained result that indicate increase in the total energy of the crystal during loading (especially cyclic) that provides us direct quantitative evidence of the metal weakening. For the basic response, we have deformed copper and aluminum single crystal according to the simple loading path and a series of multiaxial loading-paths including cyclic repetition. We compute equivalent stress-strain diagrams as well as dislocation total length vs time graphs to describe signatures of the anisotropic response of the crystal

Most of the prior studies on the prediction of fatigue lives have been limited to uniaxial loading cases, whereas real world loading scenarios are often multiaxial, and the prediction of fatigue life based upon uniaxial fatigue properties may lead to inaccurate results. A detailed exploration of multiaxial fatigue under constant amplitude loading scenarios for a range of metal alloys has been performed in this study, and a new methodology for the accurate prediction of fatigue damage is proposed. A wide variety of uniaxial, torsional, proportional and non-proportional load-paths has been used to simulate complex, real-world loading scenarios. Test data have been analyzed and a critical-plane based fatigue damage parameter has been developed. This fatigue damage parameter contains stress and strain terms, as well as a term consisting of the maximum value of the product of normal and shear stresses on the critical plane. The shear-dominant crack initiation phenomenon and the combined effect of shear and tensile stresses on micro-crack propagation have been modeled in this work. The proposed formulation eliminates many of the shortcomings of the earlier developed critical-plane fatigue damage models. It is mathematically simple with substantially fewer material dependent constants, and provides design engineers with a tool to predict the fatigue life of machine parts with minimal computational effort. This life prediction methodology is intended for a wide variety of LCF and HCF loadings on machine parts made of metals including advanced alloys

This study concerns the multiaxial static and fatigue strength properties. Short-glass-fibre-reinforced phenolic-resin composites (SGP) molded by injection and compression processes were subjected to tensiontorsion combined static and fatigue tests at room temperature under various test conditions. Tension – torsion combined static strength well agreed with Tsai-Hill failure criteria without depending on processes. Relationships between the maximum principal stress, σp1, max, and the number of fracture cycles, Nf, were approximately linear in the whole range of up to 106 cycles. For a unified evaluation of multiaxial fatigue life for SGP, non-dimensional effective stress, σ*, defined by modifying Tsai-Hill failure criteria was applied. The slopes of σ*- Nf curves according to Baskin’s law were almost identical to the injection (n = 26.3) and compression (n = 26.2). We finally confirmed that the multiaxial fatigue life of SFRP could be predicted by using σ* with a unique Wöhler curve without relying on molding processes

Weld start and end points are fatigue failure sensitive locations. Their fatigue behaviour especially in thin sheet structures under multiaxial load conditions is not sufficiently explored so far. Therefore, a research project was initiated to increase the knowledge concerning this topic, which is of special interest in the automotive industry. In the present study, fatigue tests on welded joints were conducted. In the numerical part of the study, notch stresses were calculated with an idealised weld end model. A numerical method which combines the geometrical and statistical size effect to an integrated approach was used, in order to consider the size effects

Fatigue cracking of longerons manufactured from Al-alloy AVT-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. Complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress R-ratio near to zero. Calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. It is not above the designed equivalent stress level. Crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages

Multiaxial high cycle fatigue is a topic that concerns nearly all industrial domains. In recent years, a great deal of recommendations how to address problems with multiaxial fatigue life time estimation have been made and a huge progress in the field has been achieved. Until now, however, no universal criterion for multiaxial fatigue has been proposed. Addressing this situation, this paper offers a design of a new multiaxial criterion for high cycle fatigue. This criterion is based on critical plane search. Damage parameter consists of a combination of normal and shear stresses on a critical plane (which is a plane with maximal shear stress amplitude). Material parameters used in proposed criterion are obtained from torsion and axial S-N curves. Proposed criterion correctly calculates life time for boundary loading condition (pure torsion and pure axial loading). Application of proposed model is demonstrated on biaxial loading and the results are verified with testing program using specimens made from S355 steel. Fatigue material parameters for proposed criterion and multiple sets of data for different combination of axial and torsional loading have been obtained during the experiment.

This study compares both uniaxial and multiaxial variable amplitude experimental crack growth data for naturally initiated fatigue cracks in tubular specimens of 2024-T3 aluminum alloy to predictions based on two state-of-the-art analysis codes: UniGrow and FASTRAN. For variable amplitude fatigue tests performed under pure axial nominal loading conditions, both UniGrow and FASTRAN analyses were found to produce mostly 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 was 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 found in constant amplitude fatigue tests to increase experimental crack growth rates. Since cracks in this study were initiated naturally, different initial crack geometry assumptions were also investigated in the analyses.

Fatigue cracking of longerons manufactured from Al-alloy AVT-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. Complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress R-ratio near to zero. Calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. It is not above the designed equivalent stress level. Crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages.

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 mechanical properties of bone are fundamental to the ability of our skeletons to support movement and to provide protection to our vital organs. As such, deterioration in mechanical behavior with aging and/or diseases such as osteoporosis and diabetes can have profound consequences for individuals' quality of life. This article reviews current knowledge of the basic mechanical behavior of bone at length scales ranging from hundreds of nanometers to tens of centimeters. We present the basic tenets of bone mechanics and connect them to some of the arcs of research that have brought the field to recent advances. We also discuss cortical bone, trabecular bone, and whole bones, as well as multiple aspects of material behavior, including elasticity, yield, fracture, fatigue, and damage. We describe the roles of bone quantity (e.g., density, porosity) and bone quality (e.g., cross-linking, protein composition), along with several avenues of future research. [ABSTRACT FROM AUTHOR]

The planar dynamic response of a cantilever metallic beam structure under combined harmonic base excitations (consisting of in-plane transverse and rotation about the out-of-plane transverse axis) was investigated experimentally. The important effect of the phase angle between the two simultaneous biaxial excitations on the beam tip displacement was demonstrated. The experiments were performed using a unique six degree-of-freedom (6-DoF) electrodynamic shaker with high control accuracy. The results showed that the beam tip displacement at the first flexural mode was amplified when the phase angle between the rotational and translational base excitations was increased. The beam nonlinear stiffness, on the other hand, simultaneously: (i) decreased due to fatigue damage accumulation, and (ii) increased due to an increase in the phase angle. The results were compared to the uniaxial excitation technique, where the principle of superposition was applied (mathematical addition of the structural response for each uniaxial excitation). The principle of superposition was shown to overestimate the structural response for low phase angles. Thus, the application of the superposition vibration testing as a substitute for multiaxial vibration testing may lead to over-conservatism and erroneous dynamic and reliability predictions. [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]

Fatigue damage is a parameter which plays an important role in lifetime and reliability predictions of randomly loaded structures. In this paper, four different forms of the Miner linear accumulation damage rule are examined. They are used to compare observed experimental damage and the results of numerical simulations for both uniaxial and multiaxial fatigue. First, critical fatigue damage values for all forms of the Miner accumulation damage rule are calculated for uniaxial cases. Based on the results presented in this paper, it has been established that for high strength materials the critical damage value is around 0.3. These results are then applied to the multiaxial cases. The multiaxiality is taken into account using either the signed von Mises or critical plane method. Finally, the fatigue fracture surface has been calculated and compared to the experimental pattern of fatigue fracture. The results show that the fatigue fracture surface determined by the numerical simulation is comparable to the fatigue fracture observed experimentally. [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]

En este trabajo se presenta una metodología para evaluar la recuperación elástica o springback de chapa de acero inoxidable AISI 304 DDQ basada en la realización de ensayos bajo tensión. A diferencia de los estudios existentes en la literatura, los ensayos realizados son efectuados en condiciones multiaxiales típicas de los procesos de embutición de chapa. Esto afecta fundamentalmente a las tensiones involucradas en el proceso así como al estado de endurecimiento que experimenta el material. La evaluación del springback se ha efectuado en dos áreas diferentes. En la zona de doblado se ha evaluado a partir del factor de recuperación definido como la razón entre el radio de doblado y el radio con el que queda finalmente el material. La zona de doblado y desdoblado se ha evaluado en base a la inversa del radio de curvatura de la chapa en dicha zona y teniendo en cuenta una longitud de arco en función de la relación de deformación practicada en el material. Los resultados encontrados permiten establecer que dentro del rango de valores de ángulo y de radio de doblado experimentados, el springback es independiente de la relación de embutición o de deformación practicada en el material. El radio de doblado tiene poca influencia en el rango de radios ensayados, siendo el ángulo de doblado la variable más significativa. Los resultados obtenidos son contrastados con los medidos en copas embutidas, encontrando un alto grado de concordancia.

• 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]

Fatigue cracking of longerons manufactured from Al-alloy AVT-1 for helicopter in-service rotor-blades was considered and crack growth period and equivalent of tensile stress for different blade sections were estimated. Complicated case of in-service blades multiaxial cyclically bending-rotating and tension can be considered based on introduced earlier master curve constructed for aluminum alloys in the simple case of uniaxial tension with stress R-ratio near to zero. Calculated equivalent tensile stress was compared for different blade sections and it was shown that in-service blades experienced not principle difference in this value in the crack growth direction by the investigated sections. It is not above the designed equivalent stress level. Crack growth period estimation in longerons based on fatigue striation spacing or meso-beach-marks measurements has shown that monitoring system introduced designer in longerons can be effectively used for in-time crack detecting independently on the failed section when can appeared because of various type of material faults or in-service damages. [ABSTRACT FROM AUTHOR]

Most of the prior studies on the prediction of fatigue lives have been limited to uniaxial loading cases, whereas real world loading scenarios are often multiaxial, and the prediction of fatigue life based upon uniaxial fatigue properties may lead to inaccurate results. A detailed exploration of multiaxial fatigue under constant amplitude loading scenarios for a range of metal alloys has been performed in this study, and a new methodology for the accurate prediction of fatigue damage is proposed. A wide variety of uniaxial, torsional, proportional and non-proportional load-paths has been used to simulate complex, real-world loading scenarios. Test data have been analyzed and a critical-plane based fatigue damage parameter has been developed. This fatigue damage parameter contains stress and strain terms, as well as a term consisting of the maximum value of the product of normal and shear stresses on the critical plane. The shear-dominant crack initiation phenomenon and the combined effect of shear and tensile stresses on micro-crack propagation have been modeled in this work. The proposed formulation eliminates many of the shortcomings of the earlier developed critical-plane fatigue damage models. It is mathematically simple with substantially fewer material dependent constants, and provides design engineers with a tool to predict the fatigue life of machine parts with minimal computational effort. This life prediction methodology is intended for a wide variety of LCF and HCF loadings on machine parts made of metals including advanced alloys. [ABSTRACT FROM AUTHOR]

Weld start and end points are fatigue failure sensitive locations. Their fatigue behaviour especially in thin sheet structures under multiaxial load conditions is not sufficiently explored so far. Therefore, a research project was initiated to increase the knowledge concerning this topic, which is of special interest in the automotive industry. In the present study, fatigue tests on welded joints were conducted. In the numerical part of the study, notch stresses were calculated with an idealised weld end model. A numerical method which combines the geometrical and statistical size effect to an integrated approach was used, in order to consider the size effects. [ABSTRACT FROM AUTHOR]

This study concerns the multiaxial static and fatigue strength properties. Short-glass-fibre-reinforced phenolic-resin composites (SGP) molded by injection and compression processes were subjected to tensiontorsion combined static and fatigue tests at room temperature under various test conditions. Tension - torsion combined static strength well agreed with Tsai-Hill failure criteria without depending on processes. Relationships between the maximum principal stress, σp1, max, and the number of fracture cycles, Nf, were approximately linear in the whole range of up to 106 cycles. For a unified evaluation of multiaxial fatigue life for SGP, non-dimensional effective stress, σ*, defined by modifying Tsai-Hill failure criteria was applied. The slopes of σ*- Nf curves according to Baskin's law were almost identical to the injection (n = 26.3) and compression (n = 26.2). We finally confirmed that the multiaxial fatigue life of SFRP could be predicted by using σ* with a unique Wöhler curve without relying on molding processes. [ABSTRACT FROM AUTHOR]

Random vibration excitation is a common cause of failure, especially if natural dynamics is excited. The high-cycle vibration-fatigue analysis typically requires the structural dynamics analysis, the response analysis and the fatigue analysis. The material parameters (S–N curve) are obtained at uniaxial stress state. However, in real structures the stress state is rarely uniaxial and the direct application of the S–N curve is difficult. The stress tensor is reduced to a more manageable representation using a multiaxial criterion. In this study, maximum normal stress, maximum shear stress, maximum normal-and-shear stress, C–S criterion, Projection-by- Projection and the Preumont and Piéfort criterion for multiaxial stress state are compared theoretically and experimentally. The crack location and the time-to-failure were compared. The time-to-failure was found relatively accurate with all multiaxial criteria; however, the crack-location estimation was found not to be accurate enough for either of the compared criteria. The study proves the applicability of the vibration-fatigue analysis procedure on real vibrating structures with rich structural dynamics. Random vibration excitation is a common cause of failure, especially if natural dynamics is excited. The high-cycle vibration-fatigue analysis typically requires the structural dynamics analysis, the response analysis and the fatigue analysis. The material parameters (S–N curve) are obtained at uniaxial stress state. However, in real structures the stress state is rarely uniaxial and the direct application of the S–N curve is difficult. The stress tensor is reduced to a more manageable representation using a multiaxial criterion. In this study, maximum normal stress, maximum shear stress, maximum normaland-shear stress, C–S criterion, Projection-by-Projection and the Preumont and Piéfort criterion for multiaxial stress state are compared theoretically and experimentally. The crack location and the time-to-failure were compared. The time-to-failure was found relatively accurate with all multiaxial criteria; however, the crack-location estimation was found not to be accurate enough for either of the compared criteria. The study proves the applicability of the vibration-fatigue analysis procedure on real vibrating structures with rich structural dynamics. [ABSTRACT FROM AUTHOR]