Multiaxial Stress Fields Research Articles

Advancing the understanding of short fatigue crack propagation: Leveraging ultrasonic testing device to approach rolling contact fatigue

This paper uses ultrasonic testing devices to approach the rolling contact fatigue (RCF) stress state experienced during rolling on an indented surface, in order to understand the primary cause of failures of rolling element bearings in aeronautics. It relies on testing specimens made of M50-VIM/VAR steel while inducing compressive preload. This leads to a localized multi-axial and non-proportional stress field, induced by an artificial surface defect created via electro-discharge machining (EDM). Observations reveal that the surface crack initiation occurs along the EDM beyond 108 cycles, with no shift observed from surface defects to sub-surface defects, as commonly seen in very high cycle fatigue (VHCF) regime. Our analysis suggests that the stress intensity factor range, ΔK, may govern surface initiation in the VHCF regime, particularly when the formation of fine granular area (FGA) is not feasible. Consequently, under fixed stress conditions, there exists a critical surface defect size below which short crack initiation becomes improbable. These results mirror the behavior usually observed for indentations and thereby connect ultrasonic loading with RCF. Besides, initiations of fatigue butterfly and FGA appear to be associated with VHCF tests, compression, high levels of multi-axial stresses, and the refinement of microstructure at low temperatures. These findings shed light on a potential link between fatigue butterfly and FGAs, attributed to the same underlying cause: cross-slip.

Heuristic structural optimization of two-dimensional filling materials with square-triangular supercells

Cellular filling materials are commonplace in additively manufactured parts to lower the structural weight without detriment to the mechanical properties. This technical note undergoes the heuristic optimization of a two-dimensional metamaterial with repetitive supercells derived from a square frame divided by median and diagonal lines into eight triangles. The inherent quadriaxiality of this layout is ideally suited to resist multiaxial stress fields while enabling size refinement to match the local scale of the component. A step-by-step procedure is developed which optimizes the thickness of the beams along the principal axes of the cell (sidewise and diagonal) according to a fully stressed design concept. Preliminary finite element models, including either bar or beam elements, confirm the theoretical results for a case study. Extension of the optimal approach to three-dimensional geometries is envisioned using a cubic cell that incorporates the present two-dimensional grid on each face of the cube.

Stress imaging by guided wave tomography based on analytical acoustoelastic model.

A nondestructive method ( M) for stress characterization in plate-like structures is proposed. In this method, the acoustoelastic effects (AEEs) on Lamb and shear horizontal guided waves are used to reconstruct a nonuniform multiaxial stress field. The development of M starts by deriving an analytical acoustoelastic model (An-AEM) to predict AEEs induced by a triaxial stress tensor as a function of the stress components, its orientation, the wave propagation direction, and three acoustoelastic coefficients (AECs). The AECs are independent of stress but specific to each mode. The An-AEM allows one to retrieve the three components of the stress tensor and its orientation from AEEs, assuming the stress to be uniform in the plane of the plate and through its thickness. To deal with stress that is nonuniform in the plane, the An-AEM is combined with time-of-flight straight ray tomography to enable stress field reconstruction. Numerical simulation is used to illustrate how such reconstruction can be performed. It is shown that in some cases, stress components can be reconstructed with arbitrary accuracy, and in other cases, the tensorial nature of stress renders the accuracy of its reconstruction dependent on spatial variations of the stress orientation.

Specific deformation behavior of isotactic polypropylene films under a multiaxial stress field.

The specific deformation behavior of crystalline polymer films, namely unoriented crystallized isotactic polypropylene (it PP) films, was investigated under a multiaxial stress field. Changes in the aggregation structure of the films were investigated during the bulge deformation process using in situ small-angle X-ray scattering, wide-angle X-ray diffraction (WAXD) measurements, and polarized high-speed-camera observations. The films had a thickness of approximately 10 μm. The it PP films were fixed at the hole of a plate, then bulge deformation was applied using N2 or He gas pressure, and stress-strain curves were then calculated from the applied pressure and bulge height. Yielding was observed in the stress-strain curves. Below the yield point, in situ WAXD measurements revealed that the crystal lattice expanded isotropically at the center, edge, and bottom of the bulge hole. Above the yield point, a craze started to form slightly near the center, and crazes formed in various directions with a further increase in strain, while the crystal lattice expanded uniaxially along the circumference at the edge and bottom. Crazes oriented in various directions merged and lost birefringence, indicating a change to the isotropic orientation. The different directions of the crazes indicated several directions of stress. In other words, even if multiaxial deformation is applied to a crystalline it PP film, the string-shaped crystalline polymer chain structure produces local anisotropic uniaxial stress.

Stress Analysis and Fatigue Life Prediction of Contact Wire Located at Steady Arms in High-Speed Railway Catenary System

In an electrified railway system, the pantograph on the train roof is used to collect the electric current through a sliding contact with the contact wire (CW) of the catenary. The CW is mounted laterally in a zigzag relative to the track centerline with the help of a steady arm to ensure symmetrical wear on the pantograph’s strip, which is beneficial to slow the wear process and extend the service life. Under the pantograph’s impact, the CW around the steady arm forms a stress concentration and has been recognized as a vulnerable point in the catenary system. This article performed a uniaxial tensile test and high-cycle fatigue test to measure the mechanical properties and fatigue characteristics of Cu–Mg alloy that is used for manufacturing high-speed CW. A stress analysis method is proposed based on the combination of the pantograph–catenary interaction model and the solid CW specimen model. In the pantograph–catenary interaction simulation, the catenary is modeled using the Euler–Bernoulli beam element. The 3-D solid element is used to model the CW segment. The nodal displacements of the CW segment obtained from the pantograph–catenary interaction simulation are transferred to the CW specimen model. The stress distribution on the CW section and the entire multiaxial transient stress field are analyzed. Based on fatigue test results and stress time history data obtained by simulation, using the nominal stress method, the uniaxial fatigue and multiaxial fatigue analyses are performed to reveal the fatigue characteristics with different speed classes. The results indicate that the weakest points appear at both the wing point and the top point on a CW section. The CW’s fatigue life reduces by over 50% when the speed class is upgraded from 350 to 400 km/h.

Determination of Plastic Material Properties of Thin Metal Sheets under Electromagnetic Forming Conditions

Electromagnetic forming is a contactless high-speed forming technique. In this process force transmission is initiated by an electromagnetic field provided by a tool coil. While forming thin sheet metal, the magnetic field is present in the whole depth of the sheet metal by definition. Thus, the magnetic field generates eddy currents in the complete sheet volume. The resulting Lorenz` forces act as body forces and are used for forming. Thereby high strain rates, high temperatures and multiaxial stress fields influence the plastic material properties of the workpiece. In this study, the plastic properties were investigated under real electromagnetic forming conditions. By varying process conditions like charge energy, sheet thickness and die material, the magnetic field and thus the plastic material properties were changed. To visualize the influence of the electromagnetic field, forming experiments were carried out. The strain of the formed sheets was measured. Furthermore, the forming forces were determined by measurements during the electromagnetic forming as well as by finite element simulations. With the measured strain and the determined forming force, a model for the plastic material behavior during electromagnetic forming was evolved.

Evolution of stress fields during crack growth and arrest in a brittle-ductile CrN-Cr clamped-cantilever analysed by X-ray nanodiffraction and modelling

In order to understand the fracture resistance of nanocrystalline thin films, it is necessary to assess nanoscopic multiaxial stress fields accompanying crack growth during irreversible deformation. Here, a clamped cantilever with dimensions of 200 × 23.7 × 40 μm3 was machined by focused ion beam milling from a thin film composed of four alternating CrN and Cr layers. The cantilever was loaded to 460 mN in two steps and multiaxial strain distributions were determined by in situ cross-sectional X-ray nanodiffraction. Characterization in as-deposited state revealed the depth variation of fibre texture and residual stress across the layers. The in situ experiment indicated a strong influence of the residual stresses on the cross-sectional stress fields evolution and crack arrest capability at the CrN-Cr interface. In detail, an effective negative stress intensity of −5.9 ± 0.4 MPa m½ arose as a consequence of the residual stress state. Crack growth in the notched Cr layer occurred at a critical stress intensity of 2.8 ± 0.5 MPa m½. The results were complemented by two-dimensional numerical simulation to gain further insight into the elastic-plastic deformation evolution. The quantitative experimental and modelling results elucidate the stepwise nature of fracture advancement across the alternating brittle and ductile layers and their interfaces.

Influence of the material anisotropy in the estimation of the yield strength with the Small Punch Test

The Small Punch Test (SPT) was developed in the 80’s as an alternative miniature test for the characterization of mechanical properties in the nuclear industry. One of the key aspects that materials must fulfill to be used with this miniature test is that of homogeneity and isotropy. The origin of the isotropy requirement comes from the fact that the estimation of mechanical properties using the SPT requires empirical correlations with standard tests, which generally show uniaxial stress fields. By contrast, the SPT shows a multiaxial stress field. There are few publications related with the influence of material anisotropy in the yield strength estimation using the SPT, and most of them are empirical studies. This research was intended to address, with a systematic finite element analysis, the influence that different anisotropy combinations could show in the yield strength estimation using the SPT. Thirty-six anisotropic hypothetical materials were evaluated with SPT simulations using the Hill’48 yield criterion. The yield strength of each material was estimated with the SPT using four correlation methods: Mao’s, CEN’s, the t/10 offset, and the optimized t/10. This study concluded that the SPT was not an appropriate test to evaluate or quantify the material anisotropy, but it was a valuable experimental test to estimate a mean yield strength of the six yielding stress components of the anisotropic material.

Phenomenological modeling of the effect of oxidation on the creep response of Ni-based single-crystal superalloys

A new constitutive equation predicting the evolution of oxide thickness is proposed and implemented in a crystal plasticity framework with a hardening-based damage density function. The oxidation model depends on the initial surface roughness as well as on the amount of accumulated plastic strain and stress triaxiality. The description for the effect of oxidation on the mechanical behavior and damage is at the flow-stress level by modifying the amplitude of the kinematic hardening. The oxidation-altered kinematic hardening can predict the effect of oxidizing environments on mechanical behavior, specifically the plastic strain rate in the secondary creep stage, and lifetime. Finally, the oxidation model is verified to predict surface roughness and oxide thickness distributions by performing a finite-element simulation on a notched specimen subjected to creep and developing a complex multiaxial stress field.

Finite element analysis of the interface defect in ceramic-metal assemblies: Alumina-Silver

The realization of a connection between a ceramic and a metal is always accompanied by the creation of a multi-axial stress field. Different physical and mechanical origins explain the genesis of stresses at the bonding interface in the ceramic and metal at the bond formation of ceramic-metal. In this study, a finite element model is developed to analyze numerically the effect of the sites of alumina grains snatches on the distribution and stresses level of the interface with the silver. The analysis has been extended to the effect of alumina grains-alumina grains interaction, alumina grains size and form.

Nanoscale evolution of stress concentrations and crack morphology in multilayered CrN coating during indentation: Experiment and simulation

The layered architecture approach allows designing mechanical and fracture properties of hard coatings. The current study investigates the performance of a multilayered CrN coating, consisted of 5 μm CrN sublayers of very similar mechanical properties and microstructure but different residual stress states, during in-situ wedge indentation. A finite element model of the indentation was developed and validated against measurements of the local multiaxial stress fields during indentation, characterized by means of X-ray nanodiffraction analysis with a spatial resolution of 500 nm. By means of numerical fracture mechanics the effect of the multilayered structure on the formation and morphology of mode II cracks is analyzed. The configurational force concept was applied to investigate the crack driving forces and crack extension angles of static cracks in different geometrical arrangements. The simulation results agree well with the experimental findings and reveal a shielding effect preventing an interface-near crack from entering the CrN layer with the higher compressive residual stresses. Furthermore, the possibility to match the numerical results with the locally resolved experiments allowed determining validated material parameters for the deformation and fracture behavior. The work revealed e.g. that a KIIC of around 1 MPa∙m1/2 is an appropriate choice for the investigated CrN coating.

Indentation and hydride orientation in Zr-2.5%Nb pressure tube material

In this study, indentations were made on Zr-2.5%Nb pressure tube material to induce multi-axial stress field. An I-shaped punch mark was indented on the Pressure tube material with predefined punch load. Later material was charged with 50 wppm of hydrogen. The samples near the punch mark were metallographically examined for hydrides orientation. It was observed that hydrides exhibited preferentially circumferential orientation far away from the indent to mixed orientation containing both circumferential and radial hydrides near the indent. This is probably as a result of stress field generated by indentation. Extent of radial hydride formation was observed to be varying with indentation load.

Effect of stress gradient and quadrant averaging on fretting fatigue crack initiation angle and life

Abstract Fretting fatigue involves multiaxial stress field due to presence of contact between two bodies. Near the contact edge, high stress gradient may be present depending on load and geometrical conditions. To account for high stress gradient or singular results, a regularization method may be required for better prediction of crack initiation angle and life. In the present work, conventional point and volume averaging methods are compared with a proposed quadrant averaging method to predict crack initiation angle and life. It is found that quadrant method produce more realistic results for initial crack orientation than other methods. Two multiaxial critical plane damage parameters, McDiarmid (MD) and Fatemi Socie (FS) are employed for this purpose. In addition, the influence of stress averaging on crack initiation life is analysed for two different geometries. It is observed that critical radius for stress averaging depends on stress gradient or rate of decay of damage parameter under the surface of the contact.

Analysis of Multiaxial Near-Surface Residual Stress Fields by Energy- and Angle-Dispersive X-ray Diffraction: Semi- Versus Nondestructive Techniques

Abstract Under laboratory conditions while applying angle-dispersive X-ray diffraction, the information depth in steel is usually restricted to less than 10 μm. Access to residual stresses induced by mechanical, chemical, or both types of surface treatment in deeper regions requires either the application of the layer removal method or an analysis with highly penetrating X rays and synchrotron radiation, respectively. Successive layer removal yields the actual residual stress depth profiles σij(z) up to any depth below the surface, but this is time consuming and semidestructive. High-energy X-ray diffraction performed in the energy-dispersive mode avoids these drawbacks, but it provides only the Laplace stresses, σij(τ), which have to be transformed back into the real space in order to obtain the actual stress-depth profile σij(z). Using an example of a uniaxially ground steel specimen, it is shown that the layer removal method and the energy-dispersive diffraction method for X-ray stress analysis when performed in reflection geometry yield comparable results in the case of the in-plane stress components σ11 and σ22. However, significant differences were observed concerning the out-of-plane stresses, which can be attributed to the boundary conditions that the σi3 components must satisfy at the free surface. It is demonstrated that stress redistribution at the newly generated surfaces after successive layer removal leads to an underestimation of the shear stresses σ13. The analysis of the out-of-plane normal stress component σ33 is shown to require nondestructive measurements.

Predicting fretting fatigue in engineering design

The progress in fretting fatigue understanding and predictability is reviewed, with engineering applications in mind. While industrial assessments often relies on simple empirical parameters, research in fretting fatigue should allow the design engineer to improve confidence in the fretting fatigue analysis.Fretting fatigue cracks often form in multiaxial stress fields with severe gradients under the contact area, and are inherently difficult to predict.By describing the fretting stress gradients using comparisons with the mechanical fields surrounding cracks and notches, crack nucleation threshold conditions and finite life can efficiently be determined. Also, non-local stress intensity multipliers provide promising tools for the industrial finite element analysis, often involving complex geometries and loading conditions.The use of multiaxial fatigue criteria to determine fretting fatigue nucleation life is also reviewed. Researchers have shown that critical plane calculations with some stress-averaging method can predict fretting fatigue crack initiation. However, the frictional interface causes non-proportional loading paths, and the application of critical plane methods is not straight forward.

Experimental and micromechanical modeling of fracture toughness: MWCNT-reinforced polypropylene/glass fiber hybrid composites

In this study, polypropylene-based nano and hybrid composites are prepared with 20 wt% glass fiber and multiwalled carbon nanotubes (MWCNTs) ranging up to 5 wt%. The multiaxial stress fields developed during external loading of composites cause crack propagation by various fracture mechanisms. Among the nanocomposites, it is observed that the critical stress intensity factor (KI) is highest for the one prepared at 3 wt% loading of MWCNTs. The synergistic effect of multiscale fillers in hybrid composite with MWCNT content of 3 wt% results in superior fracture toughness properties as evidenced by 16.6% increase in KI with respect to neat PP. Analytical expressions that take into account the fracture mechanisms like particle debonding and matrix yielding are employed to estimate the composite crack resistance and then compared with experimentally obtained fracture toughness properties. The fracture toughness properties are found to be dependent on composition of fillers, matrix yield strain, and debonding strain of the composites.

A crack arrest methodology based on Bazant’s parameter to fretting fatigue

There are several short crack methodologies available in the literature to estimate crack arrest under fretting loading conditions. Some of them claim that the most appropriate threshold stress intensity factor curve for short crack behaviour is better described by the El-Haddad curve, others assume that the approximation of the threshold curve by two straight lines in the Kitagawa-Takahashi diagram (in logarithm scale) would be a simpler and adequate threshold. Despite the non-proportional multiaxial stress field under the contact, the crack driving force in such methodologies has either been computed considering just mode I or mixed mode (I and II). The aim of this work is to conduct a review of these short crack arrest models and to propose a new and more conclusive approach. Plain fretting and fretting fatigue data available in the literature for AISI 1034, Al4%Cu and Ti-6Al-4V were considered to validate the analysis. The results showed that the accuracy of the short crack arrest methodology is strongly dependent of the threshold stress intensity factor curve considered and that the introduction of the Bazant’s parameter in the analysis is preferred to obtain more sensible estimates. It was also observed that the introduction of the mode II for the computation of an effective stress intensity factor did not significantly improve the results for the data here assessed.

A tribo-dynamic contact fatigue model for spur gear pairs

This study proposes a contact fatigue model for spur gears operating under the high speed condition where the dynamic behavior is evident. Realizing the tight relationship between the gear dynamics and the gear tribology, a six degree-of-freedom discrete dynamics model and a mixed elastohydrodynamic lubrication model for spur gears are bridged through an iterative numerical scheme to determine the surface normal pressure and tangential shear under the tribo-dynamic condition, where the gear dynamics and the gear tribology interact. The resultant multi-axial stress fields (from these surface tractions) on and below the surface are then used to assess the fatigue damage. A comparison between the tribo-dynamic and quasi-static life predictions is performed to demonstrate the important role of the gear tribo-dynamics in the fatigue damage. The impacts of the input torque, surface roughness and lubricant temperature on the gear contact fatigue under the tribo-dynamic condition are also investigated.

Determination of residual stress in a microtextured α titanium component using high-energy synchrotron X-rays

A shrink-fit sample is manufactured with a Ti-8Al-1Mo-1V alloy to introduce a multiaxial residual stress field in the disk of the sample. A set of strain and orientation pole figures are measured at various locations across the disk using synchrotron high-energy X-ray diffraction. Two approaches—the traditional [Formula: see text] method and the bi-scale optimization method—are taken to determine the stresses in the disk based on the measured strain and orientation pole figures, to explore the range of solutions that are possible for the stress field within the disk. While the stress components computed using the [Formula: see text] method and the bi-scale optimization method have similar trends, their magnitudes are significantly different. It is suspected that the local texture variation in the material is the cause of this discrepancy.

Stress gradient effects in surface initiated rolling contact fatigue of rails and wheels

The paper investigates gradient effects, which relate to how highly stressed regions should be dealt with in fatigue design analyses. In particular stress gradients in rolling contact are investigated with a focus on differences in response between full and partial slip conditions. To this end the multiaxial state of stress beneath a wheel–rail contact featuring full or partial slip is quantified using a multiaxial equivalent stress criterion. A comparative study shows that the significant differences in peak interfacial shear stress magnitudes between full and partial slip conditions are significantly reduced when translated to equivalent stress magnitudes. An innovative procedure to quantify the gradient effects by comparing the multiaxial contact stress field to uniaxial conditions is developed and employed. For the studied cases stress gradients beneath the frictional contact were found to be similar to stress gradients outside a uniaxially loaded large plate featuring a small hole with a radius in the order of 0.5–0.7mm. The study concludes that the use of local magnitudes of interfacial shear stress in the analysis of surface initiated rolling contact fatigue under partial slip conditions is conservative. The analysis framework established in the current study can be used to estimate the level of conservativeness.