Dynamic contact strain measurement by time‐resolved stroboscopic energy dispersive synchrotron X‐ray diffraction

Recent developments of synchrotron X‐ray sources and dedicated high‐energy beamlines are now enabling strain measurements from large volumes of industrially relevant metallic materials. Such capability is allowing the validation of novel and alternative nondestructive experimental methods of strain measurement or computational models of complex deformation processes. This study describes the first dynamic contact strain measurement of a ball bearing using stroboscopic energy dispersive X‐ray diffraction. The experiment probed the dynamic contact strain in the outer raceway of a test bearing. The inner raceway of the bearing was attached to a shaft rotating at 150 revolutions per minute, and the outer raceway, where the measurements were made, was fixed in a stationary bearing housing. A triggering system was used to synchronise the data acquisition of the energy dispersive X‐ray diffraction detector with the bearing rotation. Specifically, diffraction data were acquired, stroboscopically, from the material volume within the raceway, in a known location, when the ball was positioned directly below it. A total of 20 s of accumulated diffraction signal was recorded, acquiring 2 ms of data per revolution, providing diffraction patterns of sufficient quality for the dynamic contact strain to be measured. Macromechanical stress field was calculated from the micromechanical strains measured from five lattice planes. This allowed a comparison of the experimentally measured stress field and that of finite element simulations. Good agreement was observed between the finite element results and experimental measurements indicating the applicability of this novel dynamic strain measurement technique for tribological systems.     

Overload effects on fatigue crack‐tip fields under plane stress conditions: surface and bulk analysis

The surface crack opening displacements are characterised by digital image correlation for a (thin) plane stress 316 stainless steel compact tension sample subjected to an overload event. This supports a traditional plasticity‐induced closure interpretation showing a knee in the closure response prior to overload, an absence of closure in the accelerated growth regime followed by accentuated closure in the retardation regime. By contrast, measurement of the mid‐thickness elastic strain field behind and ahead of the crack made by synchrotron X‐ray diffraction shows no evidence of significant crack face contact stresses behind the crack tip on approaching minimum loading. Rather the changes during loading and overloading can mostly be explained by a simple elastic plastic analysis using a value of the yield stress intermediate between the initial yield stress and the UTS. This shows very significant compressive reverse plastic strains ahead of the crack that start to form early during unloading. At the moment it is not clear whether this difference is because of the increasing stress intensity applied as the crack grows, or for some other reason, such as prevention of the crack faces closing mid‐thickness due to the reverse plastic zone.     

Study on contact stresses of un‐stepped rounded D‐ring under uniform squeeze rate and internal pressure by photoelastic experimental hybrid method

The stresses that occur in an un‐stepped rounded D‐ring loaded with various internal pressures and compressed to a 20% squeeze rate are analyzed using photoelastic experimental hybrid method. The analysis shows that the contact stresses on both the upper and front sides of the D‐ring increase as the applied internal pressure increases with the magnitudes of σ_X and σ_Y being considerably higher than those of τ_XY. At a pressure of zero and 20% compression, the isochromatic fringe patterns of the un‐stepped D‐ring are almost symmetrical. However, as the internal pressure applied to the D‐ring increases the isochromatic fringe patterns shift and curve smoothly towards the extrusion gap making the upper and front sides to be more stressed than the lower side. At a pressure of 1.96 MPa and above, the contact stresses on the upper side were found to be almost constant along the contact length. By supplying a fillet radius of 2.1 mm at the corners of the un‐stepped D‐ring the high stresses at the corners were reduced by up to 45%. The results from the study further demonstrated that the un‐stepped rounded D‐ring with a ratio of r/d = 0.3 to be can be an alternative choice to the O‐ring for sealing applications. Interestingly, the pressures that the un‐stepped D‐ring can withstand before extrusion are higher than those of an O‐ring.     

Computation of the maximum torque of a cap liner using a power‐law friction and finite element analysis

In the ‘filled closed’ containers, the cap removal torque and the sealing of the contents are two crucial criteria in the closing quality, and the consumer perceives these two parameters as constituting a guarantee of packaging integrity. This work looks at the experimental study and the finite element analysis of the maximum torque of a metal cap with a liner over a glass bottle. For studying parameters influencing the cap removal torque (twist‐off torque), several experiments and simulations were conducted in order to evaluate the maximum torque of a loose crown cap. A test bench was built to measure the torque required to slide a cap liner on the top of a glass bottle, and the result of the experiment is compared with the predicted torque given by an axisymmetric finite element (FE) analysis. Since the behaviour of the cap liner is hyperelastic, compression and friction tests were conducted to evaluate the elastic properties and the non‐linear static friction behaviour of the elastomer seal. Contact regions, material non‐linear elasticity for the liner and large displacement options are included in the FE model in order to describe the evolution of the contact area and the distribution of contact pressure as a function of the applied force. The predicted maximum torque is then calculated by a numerical integration scheme over the contact surface, using an experimental coefficient of static friction as a function of the normal pressure. The predicted torque shows good agreement with that measured through experiments, thereby making it possible to understand the influence of the liner on the cap removal torque of a glass bottle. Copyright © 2010 John Wiley & Sons, Ltd.     

An X‐FEM approach for large sliding contact along discontinuities

The extended finite element method (X‐FEM) has been developed to minimize requirements on the mesh design in a problem with a displacement discontinuity. This advantage, however, still remains limited to the small deformation hypothesis when considering sliding discontinuities. The approach presented in this paper proposes to couple X‐FEM with a Lagrangian large sliding frictionless contact algorithm. A new hybrid X‐FEM contact element was developed with a contact search algorithm allowing for an update of contacting surfaces pairing. The stability of the contact formulation is ensured by an algorithm for fulfilling Ladyzhenskaya‐Babuska‐Brezzi (LBB) condition. Several 2D simple examples are presented in this paper in order to prove its efficiency and stability. Copyright © 2008 John Wiley & Sons, Ltd.     

Hollow Pd/MOF Nanosphere with Double Shells as Multifunctional Catalyst for Hydrogenation Reaction

A new type of hollow nanostructure featured double metal‐organic frameworks shells with metal nanoparticles (MNPs) is designed and fabricated by the methods of ship in a bottle and bottle around the ship. The nanostructure material, hereinafter denoted as Void@HKUST‐1/Pd@ZIF‐8, is confirmed by the analyses of photograph, transmission electron microscopy, scanning electron microscopy, powder X‐ray diffraction, inductively coupled plasma, and N₂ sorption. It possesses various multifunctionally structural characteristics such as hollow cavity which can improve mass transfer, the adjacent of the inner HKUST‐1 shell to the void which enables the matrix of the shell to host and well disperse MNPs, and an outer ZIF‐8 shell which acts as protective layer against the leaching of MNPs and a sieve to guarantee molecular‐size selectivity. This makes the material eligible candidates for the heterogeneous catalyst. As a proof of concept, the liquid‐phase hydrogenation of olefins with different molecular sizes as a model reaction is employed. It demonstrates the efficient catalytic activity and size‐selectivity of Void@HKUST‐1/Pd@ZIF‐8.     

Crack face contact in X‐FEM using a segment‐to‐segment approach

In this study, we propose a segment‐to‐segment contact formulation (mortar‐based) that uses Lagrange's multipliers to establish the contact between crack faces when modeled with the extended finite element method (X‐FEM) in 2D problems. It is shown that, in general, inaccuracies arise when the contact is formulated following a point‐to‐point approach. This is due to the non‐linear character of the X‐FEM interpolation along the crack faces that leads to crack face interpenetration. However, the segment‐to‐segment approach optimizes the fulfilment of the contact constraints along the whole crack segment, and in practice the contact is modeled precisely. Convergence studies for mesh sequences have been performed, showing the advantages of the proposed methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of X‐Ray Imaging with Toroidally Bent Crystal

We developed a focusing imager with a toroidally bent crystal imager. The imager can be used in X‐ray imaging of laser fusion experiments. This article discusses the focusing properties of toroidally bent crystal in Bragg geometry. Simulations of spatial resolution for toroidally bent crystals with different conditions including source size and detector position were done using the ray‐tracing method. The applicable conditions for optimized two‐dimensional (2D) imaging of X‐ray source are proposed. Toroidally bent crystal of mica with curvature radius 290 mm in the meridional plane and 190 mm in the sagittal plane is used as imaging element in the experiments. The high‐quality visible 2D X‐ray image was obtained with the imaging plate due to the high collection efficiency of the bent crystal imaging system. It is demonstrated that the toroidally bent mica crystal could be used in X‐ray imaging. By analyzing the image information of the sagittal direction, we find out that the toroidal crystal imager has spatial resolution about 34 µm.     

Improved implementation and robustness study of the X‐FEM for stress analysis around cracks

Numerical crack propagation schemes were augmented in an elegant manner by the X‐FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X‐FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a ‘topological’ enrichment (only the elements touching the front are enriched). We suggest a ‘geometrical’ enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X‐FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that ‘off the shelf’ iterative solver packages can be used and perform as well on X‐FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X‐FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental and numerical rolling contact fatigue study on the 32CrMoV13 steel

The aim of this work is to study pure rolling contact fatigue in 32CrMoV13 quenching and tempering steel. The study involves both experimental and numerical work. The influence of the roughness and the residual stresses on the mechanisms and zones of cracking were studied. The results show a rapid reduction in roughness during the first minute of test but even so there will be specimen deterioration. The residual stress profile after rolling contact tests have high compression values in the surface and at a depth of approximately 240 μm, which is related with the Hertzian maximal shear stress. The numerical simulation of the Hertzian loading was used both to determine the elastic shakedown of the material and to apply a high‐cycle multiaxial fatigue criterion. The three‐dimensional finite element analysis used in the numerical calculation includes elastic‐linear kinematic hardening plastic material and allows the introduction of an initial residual stress state. Taking into account the elastoplastic load induced by the Hertz pressure, low‐cycle fatigue tests were used to characterize the mechanical properties of the material. In order to validate the numerical simulation, the results of the calculation after elastic shakedown were compared with the values measured by X‐ray diffraction after rolling contact tests. The results showed a reasonable agreement between calculated and measured stresses. The Dang Van high‐cycle multiaxial fatigue criterion showed a good relationship with the experimental findings.     

Synchrotron‐Based Micro‐CT and Refraction‐Enhanced Micro‐CT for Non‐Destructive Materials Characterisation

X‐ray computed tomography is an important tool for non‐destructively evaluating the 3‐D microstructure of modern materials. To resolve material structures in the micrometer range and below, high brilliance synchrotron radiation has to be used. The Federal Institute for Materials Research and Testing (BAM) has built up an imaging setup for micro‐tomography and ‐radiography (BAMline) at the Berliner storage ring for synchrotron radiation (BESSY). In computed tomography, the contrast at interfaces within heterogeneous materials can be strongly amplified by effects related to X‐ray refraction. Such effects are especially useful for materials of low absorption or mixed phases showing similar X‐ray absorption properties that produce low contrast. The technique is based on ultra‐small‐angle scattering by microstructural elements causing phase‐related effects, such as refraction and total reflection. The extraordinary contrast of inner surfaces is far beyond absorption effects. Crack orientation and fibre/matrix debonding in plastics, polymers, ceramics and metal‐matrix‐composites after cyclic loading and hydro‐thermal aging can be visualized. In most cases, the investigated inner surface and interface structures correlate to mechanical properties. The technique is an alternative to other attempts on raising the spatial resolution of CT machines.     

Cone bit bearing seal failure analysis based on the finite element analysis

Failure analysis of cone bit bearing seals is important in reducing production cost and preventing in-service component failure. However, a generally accepted criterion for their failure has not yet been established because of complexities in both their material properties and the environment. In this study, a two-dimensional axisymmetric finite element analysis (FEA) numerical model was established. FEA software was developed based on the Mooney–Rivlin constitutive model of the rubber material, and the penalty function contact algorithm. The distributions of stress, strain and contact pressure were analyzed to establish their effect on failure. The locations and causes of the failure and preventive measures were determined by comparison with an actual failure case. It was found that stress concentration and uneven pressure distribution occur at the seal. Rubber rings are highly and unequally compressed. Metal ring structure mainly determines sealing performance. To reduce the occurrence of failure, the structure must be improved by: designing an appropriate angle-tapered metal ring end face structure instead of a plane to change the trend in pressure distribution, increasing the contact area of the metal ring end face to reduce contact pressure and make the contact pressure distribution more uniform to reduce sealing surface wear, reducing the radial thickness to reduce the compression of the rubber ring, and improving back support structures to reduce the stress concentration. Results from the study can prevent and minimize risk for future failures to increase bit life and reduce drilling costs.     

DEM calibration of cohesive material in the ring shear test by applying a genetic algorithm framework

This research demonstrates capturing different stress states and history dependency in a cohesive bulk material by DEM simulations. An automated calibration procedure, based on the Non-dominated Sorting Genetic Algorithm, is applied. It searches for the appropriate simulation parameters of an Elasto-Plastic Adhesive contact model such that its response is best fitted to the shear stress measured in experiments. Using this calibration procedure, the optimal set of DEM input parameters are successfully found to reproduce the measured shear stresses of the cohesive coal sample in two different pre-consolidation levels. The calibrated simulation resembles the stress history dependent values of shear stress, bulk density and wall friction. Through the case study of the ring shear tester, this research demonstrates the robustness and accuracy of the calibration framework using multi-objective optimization on multi-variable calibration problems irrespective of the chosen contact model.     

Large deformation analysis of contact in degenerate shell elements

A new formulation is presented for the analysis of contact in degenerate shell elements. This formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces, and the problem is formulated in terms of Variational Inequalities (VI). Large deformations and rotations are accounted for by invoking the appropriate stress and strain measures. The solution of the variational inequality is obtained using Lagrange multipliers. This guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique. © 1998 John Wiley & Sons, Ltd.     

Effect of cyclic hardening on fatigue performance of slide burnished components made of low‐alloy medium carbon steel

The slide burnishing process causes cyclic loading of the surface being treated, which provokes cyclic hardening. Using a forced‐controlled indentation test, the sixth “loading‐unloading” cycle was stabilised. The effect of the number of passes and the cyclic loading coefficient (CLC) on the fatigue performance of slide burnished specimens was investigated. Rotating bending fatigue tests were conducted using nine groups of hourglass shaped specimens, which were slide burnished through a different number of passes and CLC values. A stabilised cycle of the surface layer achieved with six passes, lead to largest fatigue limit, whereas the CLC exerted negligible influence on the fatigue performance. The observed phenomenon was explained through different residual stress relaxation rates, due to the rotating bending load, as well as with the obtained surface layer microstructure. The residual stress relaxation was investigated through rotating bending fatigue tests, using cylindrical fatigue specimens, followed by X‐ray stress analysis.     

Implicit boundary method for analysis using uniform B‐spline basis and structured grid

Several analysis techniques such as extended finite element method (X‐FEM) have been developed recently, which use structured grid for the analysis. Implicit boundary method uses implicit equations of the boundary to apply boundary conditions in X‐FEM framework using structured grids. Solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary. In this paper, this method is applied for analysis using uniform B‐spline basis defined over a structured grid. Solution structures that are C¹ or C² continuous throughout the analysis domain can be constructed using B‐spline basis functions. As a structured grid does not conform to the geometry of the analysis domain, the boundaries of the analysis domain are defined independently using equations of the boundary curves/surfaces. Compared with conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B‐spline elements. The results are compared with analytical solutions as well as with traditional finite element solutions. Convergence studies for several examples show that B‐spline elements provide accurate solutions with fewer elements and nodes compared with traditional FEM. They also provide continuous stress and strain in the analysis domain, thus eliminating the need for smoothing stress/strain results. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling arbitrary crack propagation in coupled shell/solid structures with X‐FEM

In this paper, the extended finite element method (X‐FEM) formulation for the modeling of arbitrary crack propagation in coupled shell/solid structures is developed based on the large deformation continuum‐based (CB) shell theory. The main features of the new method are as follows: (1) different kinematic equations are derived for different fibers in CB shell elements, including the fibers enriched by shifted jump function or crack tip functions and the fibers cut into two segments by the crack surface or connecting with solid elements. So the crack tip can locate inside the element, and the crack surface is not necessarily perpendicular to the middle surface. (2) The enhanced CB shell element is developed to realize the seamless transition of crack propagation between shell and solid structures. (3) A revised interaction integral is used to calculate the stress intensity factor (SIF) for shells, which avoids that the auxiliary fields for cracks in Mindlin–Reissner plates cannot satisfy exactly the equilibrium equations. Several numerical examples, including the calculation of SIF for the cracked plate under uniform bending and crack propagation between solid and shell structures are presented to demonstrate the performance of the developed method. Copyright © 2015 John Wiley & Sons, Ltd.     

金属半球壳压缩力学性能实验和模拟研究

金属空心球结构是一种新型的多孔金属材料,对金属半球壳压缩力学性能的研究是研究整体材料力学性能的基础。通过一系列准静态压缩实验,研究了金属半球壳受刚性球、刚性平板及三种不同截面积的刚性圆柱压缩下的变形形貌及屈服极限、弹性模量等力学性能,分析了球壳受不同压头压缩时的变形规律。通过建立与实验对应的数值模型,对金属半球壳进行了压缩数值模拟,分析了其力学性能。研究表明:金属半球壳的屈服极限和弹性模量均与平面压头的截面积无关,屈曲应力则随刚性圆柱形压头截面积增大而增大,半球壳压缩吸能性能随压头面积减小而降低。     

3D Nanoprinted Plastic Kinoform X‐Ray Optics

High‐performance focusing of X‐rays requires the realization of very challenging 3D geometries with nanoscale features, sub‐millimeter‐scale apertures, and high aspect ratios. A particularly difficult structure is the profile of an ideal zone plate called a kinoform, which is manufactured in nonideal approximated patterns, nonetheless requires complicated multistep fabrication processes. Here, 3D fabrication of high‐performance kinoforms with unprecedented aspect ratios out of low‐loss plastics using femtosecond two‐photon 3D nanoprinting is presented. A thorough characterization of the 3D‐printed kinoforms using direct soft X‐ray imaging and ptychography demonstrates superior performance with an efficiency reaching up to 20%. An extended concept is proposed for on‐chip integration of various X‐ray optics toward high‐fidelity control of X‐ray wavefronts and ultimate efficiencies even for harder X‐rays. Initial results establish new, advanced focusing optics for both synchrotron and laboratory sources for a large variety of X‐ray techniques and applications ranging from materials science to medicine.     

Real‐Time Tracking of Superparamagnetic Nanoparticle Self‐Assembly

The spontaneous self‐assembly process of superparamagnetic nanoparticles in a fast‐drying colloidal drop is observed in real time. The grazing‐incidence small‐angle X‐ray scattering (GISAXS) technique is employed for an in situ tracking of the reciprocal space, with a 3 ms delay time between subsequent frames delivered by a new generation of X‐ray cameras. A focused synchrotron beam and sophisticated sample oscillations make it possible to relate the dynamic reciprocal to direct space features and to localize the self‐assembly. In particular, no nanoparticle ordering is found inside the evaporating drop and near‐surface region down to a drop thickness of 90 µm. Scanning through the shrinking drop‐contact line indicates the start of self‐assembly near the drop three‐phase interface, in accord with theoretical predictions. The results obtained have direct implications for establishing the self‐assembly process as a routine technological step in the preparation of new nanostructures.