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.     

POD-assisted strategies for structural topology optimization

We propose a new numerical tool for structural optimization design. To cut down the computational burden typical of the Solid Isotropic Material with Penalization (SIMP) method, we apply Proper Orthogonal Decomposition on SIMP snapshots computed on a fixed grid to construct a rough structure (predictor) which becomes the input of a SIMP procedure performed on an anisotropic adapted mesh (corrector). The benefit of the proposed design tool is to deliver smooth and sharp layouts which require a contained computational effort before moving to the 3D printing production phase.     

Application of the sampling moiré method to shallow open-channel flows with circular roughness elements

This research presents an application of the sampling moiré method, a novel technique originally developed for measuring slight deformation of a static object such as a plate, to fluctuating free water surface in rough open channel flows. The method was used to capture the two-dimensional water surface deformation at a high sampling rate by dyeing the color of water white. The target flow was a very shallow subcritical flow with a depth of 1.5 times the height of the roughness. As a result, a series of instantaneous water surface profiles with non-uniform rough planes were successfully measured at a sampling rate of 100 Hz.It has become clear that the effect of dispersive gravity waves traveling on the water surface is greater than that of non-dispersive waves driven by the turbulence, and that this feature becomes more pronounced as the Froude number increases in such shallow flow conditions. Furthermore, it was experimentally and theoretically verified that the intensity of water surface fluctuation increases with the square of the Froude number. The decomposition of surface fluctuations due to gravity waves and subsurface turbulence using the wavenumber frequency spectrum revealed that the effects of subsurface turbulence are about 20%. This is much less than the contribution from gravity waves in very shallow flows as in this experiment.     

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.     

Combined size and shape optimization of structures with a new meta-heuristic algorithm

In this study, a new meta-heuristic algorithm called teaching-learning-based optimization (TLBO) is used for the size and shape optimization of structures. The TLBO algorithm is based on the effect of the influence of a teacher on the output of learners in a class. The cross-sectional areas of the bar element and the nodal coordinates of the structural system are the design variables for size and shape optimization, respectively. Displacement, allowable stress and the Euler buckling stress are taken as the constraint for the problem considered. Some truss structures are designed by using this new algorithm to show the efficiency of the TLBO algorithm. The results obtained from this study are compared with those reported in the literature. It is concluded that the TLBO algorithm presented in this study can be effectively used in combined size and shape optimization of the structures.     

INDIANA: An interactive system for assisting database exploration

We propose INDIANA, a system conceived to support a novel paradigm of database exploration. INDIANA assists the users who are interested in gaining insights about a database though an interactive and incremental process, like a conversation that does not happen in natural language. During this process, the system iteratively provides the user with some features of the data that might be “interesting” from the statistical viewpoint, receiving some feedbacks that are later used by the system to refine the features provided to the user in the next step. A key ability of INDIANA is to assist “data enthusiastic” users (i.e., inexperienced or casual users) in the exploration of transactional databases in an interactive way. For this purpose, we develop a number of novel, statistically-grounded algorithms to support the interactive exploration of the database. We report an in-depth experimental evaluation to show that the proposed system guarantees a very good trade-off between accuracy and scalability, and a user study that supports the claim that the system is effective in real-world database-exploration tasks.