Axisymmetric Sample Research Articles

Strain-based criterion for uniaxial fatigue life prediction for an SBR rubber: Comparative study and development

This work proposes an engineering approach to investigate the fatigue lifetime of styrene–butadiene rubber under uniaxial loadings. Two specimen geometries are considered: axisymmetric sample AE2 and diablo sample AE42. Specimens are cycled with a sinusoidal waveform at 5 Hz for different maximum displacement values and a zero load ratio. The various damage parameters, commonly used for fatigue life calculation, are reviewed and discussed. Then fatigue models with diverse damage parameters are generated from the fatigue lives experimentally observed for specimen AE2. The efficiency of each predictive model is evaluated in terms of coefficient of determination R2. It is shown that all the studied damage parameters allow excellent fatigue-life estimations with R2 greater than 0.9. A nonlinear finite element analysis model using ABAQUS software for specimen AE42 is then set up. It is found that the model developed for specimen AE2 is appropriate to estimate the fatigue life time of AE42. Indeed, the obtained fatigue live predictions are in excellent agreement with the experimental fatigue results.

Neutron diffraction strain tomography: Demonstration and proof-of-concept.

Recently, a number of reconstruction algorithms have been presented for residual strain tomography from Bragg-edge neutron transmission measurements. In this paper, we examine whether strain tomography can also be achieved using diffraction instruments. We outline the proposed method and develop a suitable reconstruction algorithm. This technique is demonstrated in simulation, and a proof-of-concept experiment is carried out, where the strain field in an axisymmetric sample is reconstructed and validated using conventional diffraction strain scans.

The connection between supernova remnants and the Galactic magnetic field: An analysis of quasi-parallel and quasi-perpendicular cosmic-ray acceleration for the axisymmetric sample

The mechanism for acceleration of cosmic rays in supernova remnants (SNRs) is an outstanding question in the field. We model a sample of 32 axisymmetric SNRs using the quasi-perpendicular and quasi-parallel cosmic-ray-electron (CRE) acceleration cases. The axisymmetric sample is defined to include SNRs with a double-sided, bilateral morphology, and also those with a one-sided morphology where one limb is much brighter than the other. Using a coordinate transformation technique, we insert a bubble-like model SNR into a model of the Galactic magnetic field. Since radio emission of SNRs is dominated by synchrotron emission and since this emission depends on the magnetic field and CRE distribution, we are able to simulate the SNRs emission and compare this to data. We find that the quasi-perpendicular CRE acceleration case is much more consistent with the data than the quasi-parallel CRE acceleration case, with G327.6+14.6 (SN1006) being a notable exception. We propose that SN1006 may be a case where both quasi-parallel and quasi-perpendicular acceleration are simultaneously at play in a single SNR.

The connection between supernova remnants and the Galactic magnetic field: A global radio study of the axisymmetric sample

The study of supernova remnants (SNRs) is fundamental to understanding the chemical enrichment and magnetism in galaxies, including our own Milky Way. In an effort to understand the connection between the morphology of SNRs and the Galactic magnetic field (GMF), we have examined the radio images of all known SNRs in our Galaxy and compiled a large sample that have an "axisymmetric" morphology, which we define to mean SNRs with a "bilateral" or "barrel"-shaped morphology, in addition to one-sided shells. We selected the cleanest examples and model each of these at their appropriate Galactic position using two GMF models, those of Jansson & Farrar (2012a), which includes a vertical halo component, and Sun et al. (2008) that is oriented entirely parallel to the plane. Since the magnitude and relative orientation of the magnetic field changes with distance from the sun, we analyse a range of distances, from 0.5 to 10 kpc in each case. Using a physically motivated model of a SNR expanding into the ambient GMF, we find the models using Jansson & Farrar (2012a) are able to reproduce observed morphologies of many SNRs in our sample. These results strongly support the presence of an off-plane, vertical component to the GMF, and the importance of the Galactic field on SNR morphology. Our approach also provides a potential new method for determining distances to SNRs, or conversely, distances to features in the large-scale GMF if SNR distances are known.

Characterization of material property variation across an inertia friction welded CrMoV steel component using the inverse analysis of nanoindentation data

In this study, a new application of the inverse analysis of the depth-sensing indentation technique based on the optimization theory has been satisfactorily demonstrated. The novel approach for determining the mechanical properties from experimental nanoindentation curves has been applied in order to generate the elastic–plastic stress–strain curves of three phases located across the joint of a like-to-like inertia friction weld of a CrMoV steel, i.e. the parent phase of tempered martensite and two child phases formed during the IFW process, martensite in the quenched and over-tempered condition. The inverse analysis carried out in this study consists of an optimization algorithm implemented in MATLAB, which compares an experimental nanoindentation curve with a predicted indentation curve generated by a 3D finite element model developed using the ABAQUS software; the optimization algorithm modifies the predicted curve by changing the material properties until the best fit to the experimental nanoindentation curve is found. The optimized parameters (mechanical properties) have been used to generate the stress–strain relationships in the elastic–plastic regime that can be used to simulate numerically the effects of the variation in material properties arising from phase transformations occurring across the joint during the IFW process of a CrMoV steel.The proposed inverse analysis was capable of fitting experimental load–depth (P–h) curves produced with a Nanoindentation Nanotest NTX unit from three characteristic regions located across the joint where the above mentioned phases are known to exist. The capability of the inverse analysis to build the stress–strain relationship in the elastic–plastic regime using the optimized mechanical properties of the parent metal has been validated using experimental data extracted from the compressive test of an axisymmetric sample of tempered martensite [1]. According to previous experimental studies, the presence of martensite in the quenched and over-tempered condition formed during the IFW of shaft sections of CrMoV steel are responsible of the 1.52:1 harder and 0.75:1 softer regions, compared to the region where the tempered martensite is located [2–4]. These ratios are in very good agreement with the optimized magnitudes of yield stress provided by the inverse analysis, that is, 1.54:1 for the quenched martensite and 0.68:1 for the over-tempered martensite, compared to the optimized value of yield stress of the tempered martensite. Moreover, a relative difference of less than 1.5% between the experimental and predicted maximum depth (hmax) supports the capability of the method for extracting the elastic–plastic mechanical properties defining each of the indented regions.

Visualizing shear bands in 3-D using axisymmetric sample: An experimental study

In this study a qualitative description of the occurrence of shear bands produced by a sudden impact on an axisymmetric specimen made of medium carbon steel 0.45% C is given. A simple experiment was developed aimed at producing a pinch shear stress in the front side of the test sample in order to visualize shear bands in 3-D. Curve fitting using MATLAB was employed based on the points taken from the images of the front section of the test sample. The predictions of the curve fitting suggests a hyperbolic section leading to the conclusion that within the sample there is a double cone region of material where the shear band region is located on its outer surface. The formation of the shear band is explained by the fact that the interaction of the stress wave front with the free surface of the test sample produces reflection waves that attenuate the incoming stress wave inwards leading to a stress gradient in the plane of the front side of the specimen that causes shear localization. Also, the progressively increasing cross sectional area of the test sample causes the expansion of the wave front, which also results in a stress gradient in the normal direction of the front side of the specimen. So the formation of shear bands depends not only on the impact momentum and strain rates but also on the sample’s geometry.

Neutron Strain Tomography using the Radon Transform

Determining bulk residual elastic strains is a topic of critical importance for predictive modelling and materials testing. Although there are numerous approaches to obtaining this information the process is often time-consuming and frequentlyinvolves destructive sectioning of the sample. This paper presents the latest developments in Bragg-edge neutron strain tomography which offers a rapid, non-destructive means of determining residual elastic strains in polycrystalline materials with high spatial resolution.Neutron strain tomography utilises the fact that the energy-resolved transmission spectrum of thermal neutrons froma polycrystalline sample displays well-defined, sudden jumps in intensity known as ‘Bragg-edges’, which reveal information about the average residual elastic strain throughout the sample volume. By measuring the spatially resolved transmission spectrum for a number of different sample orientations it is possible to recover the underlying three-dimensional residual elastic strain profile. This process is analogous to conventional absorption tomography where a three-dimensional map of the sample density is recovered from a lower order two-dimensional set of integral absorption measurements. Using the newly developed microchannel plate TimePixneutron detectorin time-of-flight experiments, elastic strains can in principle be recovered with 10 um spatial resolution. The current work demonstrates a model-free method for direct inversion of the average strain profiles obtained from Bragg-edge measurements using results from linear elasticity theory and the Radon transform, which is the basis for absorption tomography reconstructions. We demonstrate this method in simulation on an axisymmetric sample with analytic strain profile before applying it to a ‘real-world’ sample where the results are validated against conventional neutron diffraction and hole drilling measurements.

Upper bound of the limit load for a tensile cylinder with a soft welded (soldered) joint containing a crack

The limit load is one of the main characteristics in estimating the performance of different structures, in particular, structures with soft welded (soldered) joints. In some cases, the difference between the yield strengths of the main material and the joint material is so great that plastic strain is localized in a thin joint. With some features of such strain distribution taken into account, an upper bound of the limit load of a tensile axisymmetric sample with a crack in a welded (soldered) joint is obtained.

Measurement and Calculation of Residual Stress in Axi-Symmetric Glass Sample Using Structural Relaxation Theory

Consistent model including structural relaxation is necessary for correct glass stress calculation in numerical computations of glass forming processes. Calculation of glass relaxation phenomena is often done by combining independent empirical formula on stress relaxation (for a simple temperature regime) and independent model of time-temperature dependence on Tool fictive temperature, Tf. Another approach was developed and verified here. Tool-Narayanaswamy and Moynihan/Mazurin relaxation model was adopted. Relaxation was obtained not from empirical model, but from calculated time-temperature dependence of Tool fictive temperature (Tf), dynamic viscosity, heat capacity and coefficient of thermal expansion. Heat conduction in a glass probe of known temperature history, structural relaxation and stress calculation were used in one computation scheme using Matlab. The stress of glass probe was measured using polarized light (Senarmont method). Rather high stress computation accuracy was obtained in comparison to stress experimental results. The applied model approach is being to be extended for application in commercial finite element codes for modeling of glass forming processes.

An attempt to improve the evaluation of mechanical material properties from the Axisymmetric Tensile Test

AbstractThis paper deals with new analytical modeling of the classical tensile test with an axisymmetric sample and determining the yield stress of elasto‐plastic materials under the neck formation. Known for many years, classical Bridgman and Siebel‐Davidenkov‐Spiridonova's formulas provide certain errors, especially visible in the case of weakly hardening or ideal‐plastic materials. Accurate numerical simulations of the process allowed verification of the analytical results. Based on the numerical simulations, some modifications of the analytical models and their derivation have been proposed which enabled the elimination of the two most questionable classic assumptions. Comparison of new results with well‐known formulas shows that some progress is reached for small plastic deformations; however, for greater strain level further improvement is still advisable.

Finite element simulation of the effect of surface roughness on nanoindentation of thin films with spherical indenters

The effect of the surface roughness on nanoindentation results was investigated instancing a series of CrN thin films deposited by unbalanced magnetron sputtering. The arithmetic roughness (Ra) of the films ranged between 2 and 10 nm and was measured by atomic force microscopy. The measured surface topography was incorporated into a finite element model, which allowed simulating the indentation of an axisymmetric sample by a rigid spherical indenter. For the applied conditions it was found that plastic deformation could be neglected and thus purely elastic material behavior was assumed. For roughness values of Ra ≈ 2, 5, and 10 nm, 100 indents each were simulated. Subsequently, the software Elastica and the approach by Oliver and Pharr were used to evaluate Young's modulus of the CrN thin films from the simulated load-displacement curves. Under the applied conditions, the increasing roughness causes a reduction of the contact area and leads to an underestimation of Young's modulus. The mean Young's modulus of all simulated indents on the rough surfaces lies 5–14% below the Young's modulus determined for a perfectly smooth surface. This deviation seems to be independent of Ra, although the data scatter increases significantly with increasing roughness. Additionally, an influence of the lateral extension of the surface texture on the data scatter was observed which is not accounted for in roughness measures such as Ra.

Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material's local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length was 870–890 μm with deformation imposed through a Split-Hopkinson Pressure Bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. The deformation behavior of tantalum tophat samples is modeled through direct polycrystal simulations. An embedded Voronoï-tessellated two-dimensional microstructure is used to represent the material within the shear zone of the sample. A thermo-mechanically coupled elasto-viscoplastic single crystal model is presented and used to represent the response of the grains within the aggregate shear zone. In the shoulder regions away from the shear zone where strain levels remain on the order of 0.05, the material is represented by an isotropic J 2 flow theory based upon the elasto-viscoplastic Mechanical Threshold Stress (MTS) model for flow strength. The top surface stress versus displacement results were compared to those of the experiments and over-all the simulated stress magnitude is over-predicted. It is believed that the reason for this is that the simulations are two-dimensional. A region within the numerical shear zone was isolated for statistical examination. The vonMises stress state within this isolated shear zone region suggests an approximate normal distribution with a factor of two difference between the minimum and maximum points in the distribution. The equivalent plastic strain distribution within this same region has values ranging between 0.4 and 1.5 and is not symmetric. Other material state distributions are also given. The crystallographic texture within this isolated shear zone is also compared to the experimental texture and found to match reasonably well considering the simulations are two-dimensional.

An experimental and numerical study of the localization behavior of tantalum and stainless steel

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic–plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material’s local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length is 870–890 μm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8–25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 × 10 4 s −1 in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the shear section. The numerical results for stainless steel suggest that melting temperature was reached throughout the shear band shortly after peak load. Due to sample geometry, the stress state in the shear zone was not pure shear; a significant normal stress relative to the shear zone basis line was developed.

Transport of neutral solute in articular cartilage: effects of loading and particle size

We investigate the influence that matrix structure, size of diffusing molecules and type and intensity of mechanical loading have on the transport of neutral solutes in articular cartilage. Although this type of investigation has been performed in the past, earlier researchers assumed a constant diffusion coefficient. By contrast, our diffusion coefficient depends on the local deformation of the matrix, and thus varies both in space and in time during an experiment. We derive a three-dimensional formulation of the problem based on mixture theory and utilize the commercial finite-element code ABAQUS to study it numerically. We also make use of the Cohen–Turnbull–Yasuda model to correlate the decrease of the diffusion coefficient with the increase in tortuosity, owing to the presence of the matrix. Under appropriate circumstances, the equations derived here reduce to the classical convection/diffusion equation and the equations of the biphasic cartilage model. Even though we chose axisymmetric sample geometry for the present calculations, the model can easily be applied to irregular three-dimensional samples. Our results reinforce and refine previously published studies. The neutral solute's rate of diffusion is reduced under static compression, due to the strain dependence of the diffusion coefficient; an increase in static compression leads to a decrease in the rate of transport of solutes of all sizes. Dynamic loading, on the other hand, augments solute transport due to convection, depending on particle size. The transport of small molecular size solute is moderately enhanced, but only within the surface layer; however, the rate of transport of large molecule solute is greatly increased, even in the deep layer of the cartilage.

Non-contact property measurements of liquid and supercooled ceramics with a hybrid electrostatic-aerodynamic levitation furnace

The use of a hybrid pressurized electrostatic-aerodynamic levitation furnace and procedures developed by the Japan Aerospace Exploration Agency overcame the contamination problems associated with the processing of ceramics under extreme temperature conditions. This made possible property measurements over wide temperature ranges, above the melting point as well as in the supercooled region. In this study, samples of various ceramics were levitated and their densities were found as a function of temperature by extracting the area from images of a UV backlit axi-symmetric sample of known mass. In addition, the work function of each molten material was estimated using the Richardson–Dushman equation.

Une approche non destructive pour l'identification de contraintes de contact

This note presents a nondestructive method for the identification of contact stresses between a rigid punch and an elastic half-space from measurements of normal displacements and tangential strains on the traction-free part of the surface. Numerical results obtained on axisymmetric sample problems validate the identification method, even in the presence of imperfect data and when the contact zone is not exactly known a priori.