Mathematical law of size effect on the flexural property of ceramics

Brittle materials generally exhibit size effects, and the mechanical properties of these materials degrade significantly with an increase in size. However, the mathematical law governing the attenuation degree of mechanical properties with the increase in size is still unknown. In this study, maximum loads of differently sized ceramic test strips were subjected to three point bending tests under two working conditions of equal spans and span amplifications, respectively. Subsequently, the theoretical maximum loads of materials were calculated using the finite element method (FEM). By calculating the difference between the calculated values and the actual maximum loads, the attenuation of mechanical properties of ceramic samples were observed. The results show that the theoretical mechanical properties and the performance attenuation caused by the size effect tend to increase according to the following equation: y=ax³+bx²+cx+d. Therefore, mechanical properties and performance attenuation of any sample exhibiting a size within the experimental range can be predicted by a mathematical law, which was obtained through mechanical tests results of four samples with different sizes. The obtained mathematical law holds great significance for predicting the mechanical properties of materials under size effects.     

Dielectric breakdown behavior of ferroelectric ceramics: The role of pores

Dielectric breakdown is a fundamental issue for ferroelectric ceramics. In this work, a phase-field method is introduced to study the breakdown behavior of ferroelectric ceramics with pores randomly distributed. Effects of the position and the size of pores on the breakdown behavior are analyzed. Results indicate that the position of pores, for example in grains or at grain boundaries, has a significant influence on the breakdown strength of ferroelectric ceramics. The nominal breakdown strength of ferroelectric ceramics with 2 % pores at grain boundaries is almost 50 % higher than 2 % pores in grains. Further, for ferroelectric ceramics with a certain porosity, the smaller the pore size, the higher the breakdown strength. As the nominal pore size decreases from 2.5 to 1, the nominal breakdown strength is enhanced from 0.73 to 1.16. Such results agree well with the widely accepted Gerson-Marshall model and previously published experimental observations.     

A new linearly constrained minimum variance beamformer for reconstructing EEG sparse sources

Brain source imaging based on EEG aims to reconstruct the neural activities producing the scalp potentials. This includes solving the forward and inverse problems. The aim of the inverse problem is to estimate the activity of the brain sources based on the measured data and leadfield matrix computed in the forward step. Spatial filtering, also known as beamforming, is an inverse method that reconstructs the time course of the source at a particular location by weighting and linearly combining the sensor data. In this paper, we considered a temporal assumption related to the time course of the source, namely sparsity, in the Linearly Constrained Minimum Variance (LCMV) beamformer. This assumption sounds reasonable since not all brain sources are active all the time such as epileptic spikes and also some experimental protocols such as electrical stimulations of a peripheral nerve can be sparse in time. Developing the sparse beamformer is done by incorporating L1-norm regularization of the beamformer output in the relevant cost function while obtaining the filter weights. We called this new beamformer SParse LCMV (SP-LCMV). We compared the performance of the SP-LCMV with that of LCMV for both superficial and deep sources with different amplitudes using synthetic EEG signals. Also, we compared them in localization and reconstruction of sources underlying electric median nerve stimulation. Results show that the proposed sparse beamformer can enhance reconstruction of sparse sources especially in the case of sources with high amplitude spikes.     

具有自动装卸搬运机器人的制造单元建模与分析

针对具有自动装卸搬运机器人的制造单元，着重考虑其双重资源约束的特点，提出了该系统的有限缓冲开排队网的建模方法。根据工件的加工、装卸与搬运等工艺流程，定义该系统的排队网模型的各种状态，基于连续时间马尔可夫链，采用精确解法对该模型进行分析求解，获得系统一系列的稳态性能指标。为了验证排队网建模方法的有效性，建立其对应的仿真模型，分别采用排队网模型的数值计算与仿真模型的仿真统计2种方法求出系统的性能指标进行对比，并基于排队网模型对该制造单元的系统性能进行分析，为该类制造单元的资源配置优化和设施布局优化等问题提供重要的理论支撑。     

Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

Age-dependent size effect and fracture characteristics of ultra-high performance concrete

This paper presents an investigation of the age-dependent size effect and fracture characteristics of ultra-high performance concrete (UHPC). The study is based on a unique set of experimental data connecting aging tests for two curing protocols of one size and size effect tests of one age. Both aging and size effect studies are performed on notched three-point bending tests. Experimental data are augmented by state-of-the-art simulations employing a recently developed discrete early-age computational framework. The framework is constructed by coupling a hygro-thermo-chemical (HTC) model and the Lattice Discrete Particle Model (LDPM) through a set of aging functions. The HTC component allows taking into account variable curing conditions and predicts the maturity of concrete. The mechanical component, LDPM, simulates the failure behavior of concrete at the length scale of major heterogeneities. After careful calibration and validation, the mesoscale HTC-LDPM model is uniquely posed to perform predictive simulations. The ultimate flexural strengths from experiments and simulations are analyzed by the cohesive size effect curves (CSEC) method, and the classical size effect law (SEL). The fracture energies obtained by LDPM, CSEC, SEL, and cohesive crack analyses are compared, and an aging formulation for fracture properties is proposed. Based on experiments, simulations, and size-effect analyses, the age-dependence of size effect and the robustness of analytical-size effect methods are evaluated.     

Tunable electrocaloric and energy storage behavior in the Ce,Mn hybrid doped BaTiO3 ceramics

The electrocaloric effect and energy storage property are tuned in the Ba_1-xCe_xTi_0.99Mn_0.01O₃ ceramics prepared by the solid state reaction method. The ceramics with lower Ce content (x?=?0.005, 0.015) show a better ΔT and ΔT/ΔE response. The ceramics with higher Ce content (x?=?0.030, 0.040, 0.045) represent the broader ΔT peaks (50?K–60?K), and the higher energy storage density and efficiency. The largest electrocaloric response (ΔT_max?=?1.22?K, ΔT/ΔE?=?0.41?K mm/kV) is found in the Ba_0.995Ce_0.005Ti_0.99Mn_0.01O₃ ceramics, which is comparable or even higher than that of the most isovalent substituting BaTiO₃-based ceramics reported before. The maximum energy storage density 0.11?J/cm³ (E?=?30?kV/cm) is obtained for the Ba_0.970Ce_0.030Ti_0.99Mn_0.01O₃ ceramics, with high efficiency of 65–88% over a wide temperature range of 72?K. This work may open more opportunities to design high electrocalaric and energy storage performance lead-free systems from the viewpoint of the heterovalent and size mismatch substitution.     

Statistics of ceramic strength: Use ordinary Weibull distribution function or Weibull statistical fracture theory?

“Weibull statistics” for strength distribution analysis refers to either the ordinary Weibull distribution function or the Weibull statistical fracture theory. The ordinary Weibull distribution function is an empirical distribution function on an equal footing with other type of classical empirical distributions such as normal and log-normal distributions for fitting the statistical data of various random variables nonexclusive to materials strength. It has no explicit physical meaning and cannot be used for size scaling and prediction of strength. The Weibull statistical fracture theory is a weakest-link statistical fracture model for a solid with the strength distribution of an elemental volume being described by the ordinary Weibull distribution function. It has the capability of size scaling and prediction of strength for specimens with different geometries and different loading modes. The three-parameter Weibull statistical fracture theory in uniaxial flexure of prismatic beams is reformulated and validated by both numerical and real strength experiments of different ceramics.     

“Size effect” in the fatigue behavior of Friction Stir Welded plates

Comparative fatigue tests were carried out on Friction Stir Welded specimens of a 2195-T8 aluminum–lithium alloy that differed significantly in width. The width of the larger specimens was over thirteen times greater than that of the small specimens. Fatigue results showed a clear “size effect”, i.e. fatigue life of large specimens was about 40% of the corresponding value of small specimens. The Equivalent Initial Flaw Size methodology was adopted to correlate the two sets of results. Fatigue crack initiation life was disregarded with respect to crack propagation life, and fatigue life was evaluated only as propagation of a small pre-existing defect. Following this methodology, test results of small specimens were used to evaluate the initial equivalent flaw contained in each specimen. It was assumed that this data followed a normal distribution. The equivalent initial flaw in larger specimens was evaluated by simple geometrical considerations. A very good assessment of mean fatigue life and scatter in the fatigue results of large specimens was obtained by simulating the propagation of these defects. Calculations were carried out by taking also welding residual stresses into account, but the results demonstrated that this effect was not significant.