Inhomogeneous Behavior Research Articles

Comparison of degradation behaviour and osseointegration of the two magnesium scaffolds, LAE442 and La2, in vivo

Porous magnesium implants have been investigated for some time for their orthopaedic applicability as resorbable bone substitutes. The objective of this study was to evaluate the in vivo degradation behaviour and osseointegration of open-pored scaffolds made of the two magnesium alloys, LAE442 (n = 40) and Mg-La2 (n = 40). Cylindrical magnesium scaffolds (diameter 4 mm, length 5 mm) with defined interconnecting pore structure were produced by investment casting and coated with MgF2. Commercially available porous ß-tricalcium phosphate scaffolds (TCP, n = 40) of the same dimensions served as control. The scaffolds were inserted in the cancellous part of the greater trochanter of both femurs in rabbits and evaluated over a period of 36 weeks using regular clinical, radiological and in vivo µCT examinations. No clinical adverse reactions were observed in any of the scaffolds. The X-ray and µCT image evaluation of La2 showed fast and inhomogeneous degradation behaviour with increased gas formation and a rapid loss of scaffold structure and shape from week 12 on. In comparison, the LAE442 scaffolds showed a slow, homogeneous degradation with low but continuous gas production over the entire study period. Furthermore, LAE442 scaffolds showed comparatively better osseointegration with more trabecular contacts than La2 scaffolds and retained their original scaffold structure. Although the TCP control group demonstrated the best osseointegration, it showed overly-rapid degradation. Based on the results of this study, the LAE422 scaffolds have promising properties for further investigations in weight-bearing bone defects.

Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

We consider a queuing network with single-server nodes and heterogeneous customers. The number of customers, which can obtain service simultaneously, is restricted. Customers that cannot be admitted to the network upon arrival make repeated attempts to obtain service. The service time at the nodes is exponentially distributed. After service completion at a node, the serviced customer can transit to another node or leave the network forever. The main features of the model are the mutual dependence of processes of customer arrivals and retrials and the impatience and non-persistence of customers. Dynamics of the network are described by a multidimensional Markov chain with infinite state space, state inhomogeneous behavior and special structure of the infinitesimal generator. The explicit form of the generator is derived. An effective algorithm for computing the stationary distribution of this chain is recommended. The expressions for computation of the key performance measures of the network are given. Numerical results illustrating the importance of the account of the mentioned features of the model are presented. The model can be useful for capacity planning, performance evaluation and optimization of various wireless telecommunication networks, transportation and manufacturing systems.

Penalized I-spline monotone regression estimation

We propose a penalized regression spline estimator for monotone regression. To construct the estimator, we adopt the I-splines with the total variation penalty. The I-splines lend themselves to the monotonicity because of the simpler form of restrictions, and the total variation penalty induces a data-driven knot selection scheme. A coordinate descent algorithm is developed for the estimator. If the number of complexity parameter candidates sufficiently increases, the algorithm considers all possible monotone linear spline fits to the given data. The pruning process of the algorithm not only provides numerical stability, but also implements the data-driven knot selection. We also compute the maximum candidate of the complexity parameter to facilitate complexity parameter selection. Extensive numerical studies show that the proposed estimator captures spatially inhomogeneous behaviors of data, such as sudden jumps.

Double tricrystal nucleation behavior in Pb-free BGA solder joints

The orientations of tin grains in a solder joint have a significant influence on its inhomogeneous deformation behavior under thermomechanical fatigue (TMF). In this paper, the tin orientations in as-solidified BGA joints were observed in detail by electron backscattering diffraction (EBSD). Double twinning of tin in the process of solidification was observed in the Sn-based solder joints. Although the morphologies of these twinned microstructures differed (beachball or intertwined), four orientations of tin grains, with each twin grain sharing a corporate [100] or [010] axis, were observed and analyzed in these systems. The results showed that the difference in orientation between the two groups of double tricrystals was in the range of 80° to 90°. The accurate misorientations were calculated to be 79.1°, 82.9° and 86.5°, corresponding to 57.2° and 62.8°. In a joint comprising 9 grains, there were 3 groups of double tricrystals. A joint comprising two grains, involving 55–65° tricrystal misorientations and a corporate [100] rotation axis, was practically a tricrystal. The joints exhibiting 4–9 grains with misorientations close to 60° (with a [100] or [010] axis) and 85° were composed of 1–3 groups of double tricrystals.

Filler Metal Mixing Behaviour of 10 mm Thick Stainless Steel Butt-Joint Welds Produced with Laser-Arc Hybrid and Laser Cold-Wire Processes

In thick section laser welding, filler metal addition is usually required to improve joint fit-up tolerances or to control the chemical composition of the weld metal. With deep and narrow welds produced using an over-alloyed filler metal, it may be challenging to ensure that the filler metal and its elements are homogeneously mixed and evenly distributed throughout the fusion zone. Inhomogeneous filler metal mixing can cause unfavourable changes to weld metal chemistry and microstructure. Filler metal mixing behaviour in laser-arc hybrid and laser cold-wire welding is studied in this work. Welding tests were conducted on 10 mm thick butt-welded joints of AISI 316L austenitic stainless steel. An overmatching type 2205 duplex stainless steel filler wire was used to obtain a composition contrast between the base metal and filler metal. Energy dispersive spectroscopy (EDS) with chromium as the trace element was used for element mapping and stepwise characterization of the weld cross-section samples. Optical metallography was used to observe possible inhomogeneous filler metal mixing behaviour like local acute changes in macro- and microstructural features. The results showed a clear difference in filler metal mixing between the weld surface part (upper half) of the weld and the weld root part (lower half) in 10 mm thick welded cross-sections for closed root gap of I-groove welds or when the gap was only 0.4 mm. In narrow I-groove preparations, inhomogeneous mixing phenomena were more pronounced in laser cold-wire welds than in laser-arc hybrid welds. In both welding processes, a combination of trailing wire feeding and the use of a wider groove enabled filler metal to be introduced deeper into the bottom of the groove and improved mixing in the root portion of the welds.

Multiscale computational scheme for semi-analytical modeling of the point contact of inhomogeneous materials

Semi-analytical models (SAMs) have been developed to analyze contact problems efficiently, including those of inhomogeneous materials, based on the equivalent inclusion method. However, understanding the behavior of microscopic inhomogeneities requires SAMs of even higher efficiency. This study builds a new semi-analytical model for high-speed simulations of contacts of materials containing distributed particles of sizes orders of magnitude smaller than that of the contact radius. The domain decomposition method is applied to construct a two-level mesh set to implement multiscale computation. The macroscopic mesh uses homogenized elements that ensure a high computing efficiency in obtaining the contact pressure distribution as a boundary condition, whereas the material microstructures are modeled using the microscopic mesh, and thus the microscopic stress and strain are obtained. New influence coefficients are derived for eigenstress and eigenstrain calculations in both mesh levels and are used to calculate the eigenstress and equivalent eigenstrains. The new model is implemented to investigate the effects of particle clustering on the contact performances of composites.

Correlation between quenching rate, mechanical properties and microstructure in thick sections of Al[sbnd]Mg[sbnd]Si([sbnd]Cu) alloys

Thermal treatment is key for the mechanical behavior of 6000 series aluminum alloys. Numerous studies have therefore been devoted to the impact of aging treatment parameters like time and temperature. However the influence of quenching rate is rather poorly documented while it could be of primary interest for applications requiring thick sections. Using a series of AlMgSi(Cu) specimens quenched in various fluids, we propose to monitor and describe the quench properly and study the impact of the quenching rate on the microstructure and mechanical properties obtained after aging. Acknowledging the critical quench rate to be about 10 °C s−1, quenching was performed in various quenching fluids (water, air and oil) on 10 cm side 6061 alloy cubes. The quench rate was evaluated by thermocouples placed at several locations and by numerical modeling. For each temper, the microstructure and mechanical behavior has been studied at local and macro scales to highlight some correlations. The combination of transmission electron microscopy imaging and related image analysis, chemical and crystallographic mapping, microhardness maps and tensile tests has pointed out many microstructural differences at nanoscale and inhomogeneous mechanical behavior we strived to explain and correlate.

A framework and a performance assessment for serverless MapReduce on AWS Lambda

MapReduce is one of the most widely used programming models for analysing large-scale datasets, i.e. Big Data. In recent years, serverless computing and, in particular, Functions as a Service (FaaS) has surged as an execution model in which no explicit management of servers (e.g. virtual machines) is performed by the user. Instead, the Cloud provider dynamically allocates resources to the function invocations and fine-grained billing is introduced depending on the execution time and allocated memory, as exemplified by AWS Lambda. In this article, a high-performant serverless architecture has been created to execute MapReduce jobs on AWS Lambda using Amazon S3 as the storage backend. In addition, a thorough assessment has been carried out to study the suitability of AWS Lambda as a platform for the execution of High Throughput Computing jobs. The results indicate that AWS Lambda provides a convenient computing platform for general-purpose applications that fit within the constraints of the service (15 min of maximum execution time, 3008 MB of RAM and 512 MB of disk space) but it exhibits an inhomogeneous performance behaviour that may jeopardise adoption for tightly coupled computing jobs.

Inhomogeneous Warm Deformation Behavior and Its Effect on the Deformability of an Fe-6.5PctSi Alloy with Ce Doping

The inhomogeneous deformation behavior generated by deformability differences between soft and hard phases is a critical factor that influences the deformation and processability of materials. For Fe-6.5pctSi alloys with coexisting disordered and ordered phases, this work studied warm (300 °C to 500 °C) tensile deformation property differences and mechanisms for non-Ce-doped and 0.02 wt pct Ce-doped alloys. The warm deformation behavior was analyzed according to the stress and strain partitioning of the two-phase alloy by establishing a two-phase (A2 disordered phase + B2/D03 ordered phase) system model based on the structural characteristics of the alloy. The results show that the plastic deformation is mainly attributed to the A2 disordered phase, and the existence of a hard and ordered phase leads to local and inhomogeneous deformation behavior, which decreases the uniform plastic elongation and deformability of the alloy. Ce doping improves the warm deformation homogeneity and deformability by reducing the size and amount of the B2 ordered phase, which improves the warm rolling deformation and increases subsequent cold rolling deformability. Cold rolling with a total thickness reduction greater than 63 pct was achieved after the Ce-doped hot-rolled specimen with a 2 mm thickness was warm rolled to an 82.5 pct reduction, and the warm-rolled and cold-rolled sheets had good surface integrity and no obvious cracking.

Characterization of non-uniform Ni/4H-SiC Schottky diodes for improved responsivity in high-temperature sensing

The development of high-temperature sensors (up to 450 °C), based on SiC Schottky diodes, which are able to work in harsh conditions, requires using high-barrier Schottky contacts, such as nickel silicide. It is well known that post metallization annealing, targeting silicide formation, leads to Schottky barrier height (SBH) non-uniformity on the contact surface. On the other hand, sensor performances are intimately tied to the value and stability of SBH. This paper discusses solutions for assessing temperature sensing performances of inhomogeneous SiC Schottky diodes, particularly targeting high-temperature, harsh industrial applications where conventional solutions are unreliable. Microphysical investigations and electrical measurements are carried out on Ni/4H-SiC Schottky diodes with varying levels of non-uniformity. Devices are characterized using SEM and EDX analyses, together with electrical parameter evaluation techniques. It is demonstrated that, despite highly inhomogeneous electrical behavior, SiC-Schottky diodes exhibit stable sensitivity (up to 2.33 mV/°C) with excellent linearity (R2 > 99.9%) over wide temperature (up to 450 °C) and bias ranges (at least 100 nA–10 µA).

Influence of material inhomogeneity and non-linear mechanical behavior of the material on delamination in multilayered beams

The delamination fracture in four-point bending beams made of adhesively bonded lengthwise vertical layers is studied assuming that each layer exhibits smooth material inhomogeneity along the width and length of the layer. The study aims at determining the strain energy release rate with applying the Ramberg-Osgood equation for modeling the non-linear mechanical behavior of the material in each layer. Cosine laws are used to describe the continuous variation of the modulus of elasticity in width and length directions of layers. Beams made of an arbitrary number of vertical layers which have individual widths and material properties are considered. Besides, the delamination crack is located arbitrary between layers, i.e. the two crack arms have different widths. The J-integral is applied for verification of the non-linear solution to the strain energy release rate derived in the present paper. The solution is used to investigate the influence of material inhomogeneity in width and length directions of layers, the crack location along the beam width, the non-linear mechanical behavior of the material and the crack length on the delamination fracture behavior. The approach developed is expected to be useful in structural design of multilayered inhomogeneous beams with considering the delamination fracture behavior.

Anisotropy and strain rate effects on the failure behavior of TWIP steel: A multiscale experimental study

The effect of anisotropy and strain rate on the work hardening and fracture behavior of high manganese twinning induced plasticity (TWIP) steel was investigated. Uni-axial tensile tests in conjunction with digital image correlation were carried out to study the local deformation behavior and failure initiation. The influence of adiabatic heating on the mechanical behavior was studied by performing quasi-static and dynamic tensile tests with synchronous temperature and strain measurements. Interrupted micro tensile test samples were analyzed in the scanning electron microscope combined with the electron backscatter diffraction measurements to study the evolution of microstructure, twinning, and micro-cracking mechanisms. TWIP steel showed high strength of ≥1100 MPa in combination with excellent ductility of ≥45%, but slight variation in yield strength and elongation values was observed when tested along rolling, transverse and shear (45∘) directions. The material exhibited excellent energy absorption capacity of above 55 kJ/kg at different strain rates. The serrations on the σ–ε curves was the main characteristic behavior of TWIP steel observed under quasi-static loading, which start to disappear with increasing ε˙ and vanishes completely under dynamic loading. Serrated flow behavior was caused due to dynamic strain aging (DSA), which include the dynamic interaction of solute atoms with dislocations and the Mn-C short-range ordering. The plastic instability caused due to DSA has led to inhomogeneous behavior in the form of nucleation and propagation of shear bands during deformation known as Portevin-Le Chatelier (PLC) effect. Temperature rise due to adiabatic heating at high ε˙ has led to increase of SFE, thereby resulting in a change of twinning behavior or the promotion of dislocation glide. Failure at macro-level occurred at the intersection of two shear bands close to the edge of the specimen with the negligible amount of strain localization. At the micro-level, cracks originated mainly at grain boundaries (GB) and triple junctions due to increased stress concentration caused by the intercepting deformation twins and the slip band extrusions at GB. Intergranular crack initiation and propagation instances were evident in the microstructure along with the rapid nucleation of minute voids. Even though few micro-cracks have appeared at lower strains, their growth was rather limited. Thus, TWIP steel exhibited enhanced resistance to damage resulting in superior ductility.

Phase field simulation of microstructural evolution and thermomigration-induced phase segregation in Cu/Sn58Bi/Cu interconnects under isothermal aging and temperature gradient

Sn-Bi based alloys are widely used as thermal interfacial materials, solders in electronic packaging, thermal fuse and low temperature resistant performance electronic components. However, the inherent tendency of microstructure coarsening and phase segregation in Sn-Bi alloys under thermal loading can easily lead to the inhomogeneous mechanical and thermal response behavior, which can promote crack initiation and expansion near the interface between two major phases (i.e., Bi-rich and Sn-rich phases), and this has brought about serious reliability concern for the above applications and thus attracted increasing attention in recent years. In this study, a phase field model is developed to simulate the microstructural evolution and phase segregation behavior of the eutectic Sn58Bi solder in a line-type Cu/Sn58Bi/Cu interconnect under the condition of isothermal aging and temperature gradient respectively. Results show that the Bi-rich phase and Sn-rich phase distribute inhomogeneously in the Sn58Bi alloy matrix of the solder interconnect during thermal aging; the large size Bi-rich phase particles grow up at the expense of the small size ones, and the value of coarsening exponent n is 0.17. Under temperature gradient, Bi atoms migrate along the direction of the heat flux, and consequently a Bi-rich phase segregation layer forms on the cold end, while a Sn-rich phase area is left on the hot end. The relationship between the temperature gradient distribution and the microstructural characteristics is well revealed. Moreover, the phase segregation under temperature gradient induces the decrease of thermal conductivity, which in turn deteriorates the heat transfer performance of solder interconnects. In addition, comparing the coarsening behavior of the Bi-rich phase under temperature gradient with that during isothermal aging, it is clear that the temperature gradient leads to faster coarsening of the Bi-rich phase, and there is a linear relationship between the mean equivalent radius of the Bi-rich phase and nondimensional time. Finally, the study of thermomigration kinetics of the Bi-rich phase shows that the thickness of the Bi-rich phase segregation layer increases almost linearly with nondimensional time, which is consistent with the theoretical analysis.

A Class of Rate-Independent Lower-Order Gradient Plasticity Theories: Implementation and Application to Disc Torsion Problem.

As the characteristic scale of products and production processes decreases, the plasticity phenomena observed start to deviate from those evidenced at the macroscale. The current research aims at investigating this gap using a lower-order gradient enhanced approach both using phenomenological continuum level as well as crystal plasticity models. In the phenomenological approach, a physically based hardening model relates the flow stress to the density of dislocations where it is assumed that the sources of immobile dislocations are both statistically stored (SSDs) as well as geometrically necessary dislocations (GNDs). In the crystal plasticity model, the evolution of the critical resolved shear stress is also defined based on the total number of dislocations. The GNDs are similarly incorporated in the hardening based on projecting the plastic strain gradients through the Burgers tensor on slip systems. A rate-independent formulation is considered that eliminates any artificial inhomogeneous hardening behavior due to numerical stabilization. The behavior of both models is compared in simulations focusing on the effect of structurally imposed gradients versus the inherent gradients arising in crystal plasticity simulations.

Staff optimization for time-dependent acute patient flow

The emergency department is a key element of acute patient flow, but due to high demand and an alternating rate of arriving patients, the department is often challenged by insufficient capacity. Proper allocation of resources to match demand is, therefore, a vital task for many emergency departments.Constrained by targets on patient waiting time, we consider the problem of minimizing the total amount of staff-resources allocated to an emergency department. We test a matheuristic approach to this problem, accounting for both patient flow and staff scheduling restrictions. Using a continuous-time Markov chain, patient flow is modeled as a time-dependent queueing network where inhomogeneous behavior is evaluated using the uniformization method. Based on this modeling approach, we recursively evaluate and allocate staff to the system using integer linear programming until the waiting time targets are respected in all queues of the network. By comparing to discrete-event simulations of the associated system, we show that this approach is adequate for both modeling and optimizing the patient flow. In addition, we demonstrate robustness to the service time distribution and the associated system with multiple classes of patients.

Inhomogeneities in the light curves of gamma-ray bursts afterglow

We discuss the inhomogeneous behavior of gamma-ray burst afterglow light curves in optic. We use well-sampled light curves based on mostly our own observations to find and identify deviations (inhomogeneities) from broken power law. By the inhomogeneous behavior we mean flashes, bumps, slow deviations from power law (wiggles) in a light curve. In particular we report parameters of broken power law, describe phenomenology, compare optical light curves with X-ray ones and classify the inhomogeneities. We show that the duration of the inhomogeneities correlates with their peak time relative to gamma-ray burst (GRB) trigger and the correlation is the same for all types of inhomogeneities.

In Situ Local Measurement of Austenite Mechanical Stability and Transformation Behavior in Third-Generation Advanced High-Strength Steels

Austenite mechanical stability, i.e., retained austenite volume fraction (RAVF) variation with strain, and transformation behavior were investigated for two third-generation advanced high-strength steels (3GAHSS) under quasi-static uniaxial tension: a 1200 grade, two-phase medium Mn (10 wt pct) TRIP steel, and a 980 grade, three-phase TRIP steel produced with a quenching and partitioning heat treatment. The medium Mn (10 wt pct) TRIP steel deforms inhomogeneously via propagative instabilities (Luders and Portevin Le Châtelier-like bands), while the 980 grade TRIP steel deforms homogenously up to necking. The dramatically different deformation behaviors of these steels required the development of a new in situ experimental technique that couples volumetric synchrotron X-ray diffraction measurement of RAVF with surface strain measurement using stereo digital image correlation over the beam impingement area. Measurement results with the new technique are compared to those from a more conventional approach wherein strains are measured over the entire gage region, while RAVF measurement is the same as that in the new technique. A determination is made as to the appropriateness of the different measurement techniques in measuring the transformation behaviors for steels with homogeneous and inhomogeneous deformation behaviors. Extension of the new in situ technique to the measurement of austenite transformation under different deformation modes and to higher strain rates is discussed.

Modelling gas‐liquid mass transfer in a two‐phase jet flow

ABSTRACTThe efficiency and selectivity of chemical reactions are influenced by the mixing characteristic of the reactor. Existing models for reactor precalculation are often based on mean values, e.g. for the energy dissipation rate or the volumetric mass transfer coefficient, and assume a homogeneous mass transfer behaviour. As a result, process optimization by avoiding mass transfer limitations is not efficient, due to the missing knowledge of local limitations.Jet reactors typically provide inhomogeneous mixing and mass transfer behaviour, where the highest rates occur in the jet vicinity. Hence, the mass transfer processes in the jet flow, which cannot be properly characterized in gas‐liquid two‐phase flow, dominate the reactor performance. Experimental results concerning the volumetric mass transfer coefficient in the jet vicinity of the Jetzone‐Loopreactor are discussed, and a model approach for describing the phenomenon is presented. It is shown that the mass transfer rates strongly depend on the hydrodynamics of the loop flow. The model is adapted to the loop flow determining mechanisms, the drag coefficient, and the density difference between the circulation and the jet flow.

Coupled simulation of ferrite recrystallization in a dual-phase steel considering deformation heterogeneity at mesoscale

Microstructure-based numerical modeling of ferrite recrystallization in a cold-rolled dual-phase (DP) steel during continuous annealing has been performed by considering the deformation heterogeneity with a coupled simulation method. The plastic deformation inside the two-phase structures is firstly simulated using the crystal plasticity finite element method (CPFEM) at the grain scale with the initial grain structures and crystallographic orientations inputted from EBSD maps based on a digital material representation algorithm. The predicted local stored deformation energy is then incorporated into the cellular automaton model as the driving force for subsequent ferrite recrystallization nucleation and growth. The simulations demonstrate inhomogeneous microstructural behaviors of ferrite recrystallization owing to the microstructural deformation heterogeneity inherited from the deformed multi-phase structures. Reliable predictions regarding the recrystallization kinetics, grain size distribution and microstructure morphology can be made compared with the experimental results. The influence of annealing temperatures and heating rates is also obtained by the simulation approach.

Composition and Impedance Heterogeneity in Oxide Electrode Cross‐Sections Detected by Raman Spectroscopy

AbstractLithium‐bearing layered transition metal oxides are the materials of choice for positive electrodes in high energy lithium‐ion cells being developed for electric vehicle applications. During electrochemical cycling, the loss of mobile lithium‐ions due to undesirable side reactions and an increase in cell resistance leads to a decline in the energy and power performance of the cells. This performance loss is often nonuniform across multiple cells, especially for those cycled at high voltages or high C‐rates. This nonuniformity results from inhomogeneous behavior in the battery electrodes, which can lead to localized areas that deteriorate faster than the neighboring regions. Raman spectroscopy is among the many techniques that are used to probe inhomogeneity in electrode behavior. Typically, Raman spectroscopy measurements on lithium‐ion cell electrodes are conducted in the top‐down mode, and at‐best produce an incomplete, surface biased account of electrode behavior. In contrast, micro‐Raman measurements conducted on ion‐milled electrode cross‐sections provide information from regions that span the full thickness of the electrode. Here, Raman spectroscopy data from pristine, aged, and relithiated/aged positive electrodes are reported. The spectral differences between oxide particles near the top‐surface and particles deeper into the aged electrodes clearly indicate compositional heterogeneities that arise during cell aging.