Energetic–statistical size effect simulated by SFEM with stratified sampling and crack band model

The paper presents a model that extends the stochastic finite element method to the modelling of transitional energetic–statistical size effect in unnotched quasibrittle structures of positive geometry (i.e. failing at the start of macro‐crack growth), and to the low probability tail of structural strength distribution, important for safe design. For small structures, the model captures the energetic (deterministic) part of size effect and, for large structures, it converges to Weibull statistical size effect required by the weakest‐link model of extreme value statistics. Prediction of the tail of extremely low probability such as one in a million, which needs to be known for safe design, is made feasible by the fact that the form of the cumulative distribution function (cdf) of a quasibrittle structure of any size has been established analytically in previous work. Thus, it is not necessary to turn to sophisticated methods such as importance sampling and it suffices to calibrate only the mean and variance of this cdf. Two kinds of stratified sampling of strength in a finite element code are studied. One is the Latin hypercube sampling of the strength of each element considered as an independent random variable, and the other is the Latin square design in which the strength of each element is sampled from one overall cdf of random material strength. The former is found to give a closer estimate of variance, while the latter gives a cdf with smaller scatter and a better mean for the same number of simulations. For large structures, the number of simulations required to obtain the mean size effect is greatly reduced by adopting the previously proposed method of random property blocks. Each block is assumed to have a homogeneous random material strength, the mean and variance of which are scaled down according to the block size using the weakest‐link model for a finite number of links. To check whether the theoretical cdf is followed at least up to tail beginning at the failure probability of about 0.01, a hybrid of stratified sampling and Monte Carlo simulations in the lowest probability stratum is used. With the present method, the probability distribution of strength of quasibrittle structures of positive geometry can be easily estimated for any structure size. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved prediction model for time-dependent deformations of concrete: Part 4—Temperature effects

This Part presents a refinement of the BP model for the effects of temperature on the basic creep and drying creep of concrete. The temperature effect on basic creep is introduced through two different activation energies, one for the effect of temperature increase on the rate of hydration, which causes a decrease of creep, and one for the effect of temperature increase on the rate of creep, which causes an increase of creep. The dichotomy of these two opposing temperature influences is an essential feature, required for good agreement with test data. The greatest error in basic creep is again caused by the prediction of the material parameters from concrete composition and strength. This error can be largely eliminated by conducting limited short-time basic creep tests at different temperatures. Comparisons with 13 different data sets from the literature show a satisfactory agreement, better than that achieved with previous models, while at the same time the scope of the present model is broader. The effect of temperature on the creep of drying specimens is rather different because heating causes a moisture loss from unsealed specimens. The paper presents prediction formulae which modify those for drying creep at room temperature on the basis of the activation energy concept and take into account the effect of heating on the moisture loss. Comparisons with the limited test data that exist show satisfactory agreement. No additional material parameters depending on concrete composition and strength are introduced for drying creep.     

Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: A general numerical method

The harmonic function u near point 0 from which a single singularity ray emanates is assumed to be dominated by the term r^λρ^ρU where r = distance from point 0, p = known constant and ρ = chosen function of angular spherical coordinates θ, ?, for which a partial differential equation with boundary conditions, especially those at the singularity rays, and a variational principle, are derived. Because grad U is nonsingular, a 1numerical solution is possible, using, e.g. the finite difference or finite element methods. This reduces the problem to finding λ of the smallest real part satisfying the equation Det (A_ij) = 0 where A_ij is a large matrix whose coefficients depend linearly on μ = λ(λ + 1). In general λ and A_ij are complex. Solutions can be obtained either by reduction to a standard matrix eigenvalue problem for μ, or by successive conversions to nonhomogeneous linear equation systems. Computer studies have confirmed the feasibility of the method and have shown that highly accurate results can be obtained. Solutions for cracks and notches ending at a plane or conical surface, and for cracks ending obliquely at a halfspace surface, are presented. In these cases, λ is real and the singularity is always weaker (λ > p) than on the singularity line and may even disappear (λ > 1). Furthermore, elastic stresses under a wedge-shaped rigid sliding stamp or at a corner of a crack edge, and also harmonic functions at three-sided pyramidal notches, have been analyzed. Here λ < p was found to occur. A simple analytical solution for one class of special cases has also been found and used to check some of the numerical results.     

Elastodynamic fields near running cracks by finite elements

A finite element method is developed for the computation of elastodynamic stress intensity factors at a rapidly moving crack tip. The method is restricted to bodies whose surfaces and two-material interfaces are either parallel to the direction of propagation or are sufficiently remote. The crack tip starts to move at the instant that it is struck by an incident wave. The finite element grid moves undeformed with the crack tip. The main result consists in the fact that the method of non-singular calibrated crack tip elements, in which the stress-intensity factor is determined from its statically calibrated ratio to the crack opening displacement in an adjacent node, is extended to dynamic problems with moving cracks, for both in-plane and anti-plane motions. The dependence of the calibration ratio on the crack tip velocity is established from previously developed analytical solutions for the near-tip displacement fields. Numerical results compare favorably with known analytical solutions for cracks moving in an infinite solid. The grid motion causes an apparent asymmetric additional damping matrix.     

Effect of CO2 on porous concrete

Through the action of CO₂ and moisture, 11 Å-tobermorite of porous concrete is decomposed into vaterite, calcite and SiO₂-gel. Due to pseudo-morphosis, the morphology of the crystals of the cementing phase undergoes no substantial change. The lowest compressive strengths were obtained after 30 days storage in 30 and 10% CO₂. The compressive strengths drop after 1 year of storage was less than 10%. As regards shrinkage of porous concrete, the main influence is exerted by CO₂, and only in the second place by the humidity of the environment. Porous concrete exposed to air (0.03% CO₂) at r.h. of 50, 75 and 100% expanded slightly in one year.     

Crack band theory for fracture of concrete

A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.     

Solution‐Based Processing of Optoelectronically Active Indium Selenide

Layered indium selenide (InSe) presents unique properties for high‐performance electronic and optoelectronic device applications. However, efforts to process InSe using traditional liquid phase exfoliation methods based on surfactant‐assisted aqueous dispersions or organic solvents with high boiling points compromise electronic properties due to residual surface contamination and chemical degradation. Here, these limitations are overcome by utilizing a surfactant‐free, low boiling point, deoxygenated cosolvent system. The resulting InSe flakes and thin films possess minimal processing residues and are structurally and chemically pristine. When employed in photodetectors, individual InSe nanosheets exhibit a maximum photoresponsivity of ≈5 × 10⁷ A W^?1, which is the highest value of any solution‐processed monolithic semiconductor to date. Furthermore, the surfactant‐free cosolvent system not only stabilizes InSe dispersions but is also amenable to the assembly of electronically percolating InSe flake arrays without posttreatment, which enables the realization of ultrahigh performance thin‐film photodetectors. This surfactant‐free, deoxygenated cosolvent approach can be generalized to other layered materials, thereby presenting additional opportunities for solution‐processed thin‐film electronic and optoelectronic technologies.     

Composition driven (Ba,Ca)(Zr,Ti)O3 lead-free ceramics with large quality factor and energy harvesting characteristics

A comprehensive study on energy harvesting characteristics as well as electro-mechanical properties of lead-free (1−x)(BaZr_0.2Ti_0.8)O₃—x(Ba_0.7Ca_0.3Ti)O₃ ceramics were systematically carried out. Raman and Rietveld analyses show a formation of rhombohedral-orthorhombic-tetragonal (R-O-T) phase boundary region between 4/6 BZT/BCT and 6/4 BZT/BCT compositional range. Raman modes shift toward lower frequencies with increased Zr/Ca stoichiometric ratio attributed to asymmetric Ti-O phonon vibrations, which caused local disorder, widening of energy band and reduced Curie temperature. The large mechanical quality factor Q_m = 556 is related to the hardening effect and significantly high energy conversion efficiency η = 96% was discovered for 3/7 BZT/BCT composition. Largely, the noblest electro-mechanical properties were retrieved for 5/5 BZT/BCT ceramics, in which d₃₃ = 500 pC/N (from quasi-static d₃₃ meter), d₃₃ = 540 pm/V (from field-dependent d₃₃ curves) indicating that the both methods are analogous with a deviation of 8%. The outstanding energy harvesting characteristics such as voltage constant g₃₃ = 27 × 10⁻³ Vm/N, transduction coefficient d₃₃ × g₃₃ = 13 301 × 10⁻¹⁵ m²/N, figure of merit under off-resonance conditions FOM_off = 12.1 × 10⁻¹⁰ m²/N and fairly large η of 94% were attained again for 5/5 BZT/BCT ceramics. These outstanding characteristics were ascribed to the R-O-T phase boundary region that comprises a low energy barrier, consequently facilitated easy polarization rotation and triggered an increased electro-mechanical conversion. These characteristics outperform other lead-free and even most commercially available lead-based ceramics, and thus suitable for sensors, actuators, resonators, and energy harvesting applications.     

Transient Thermal Stress Calculation of a Shell and Tube Condenser with Fixed Tubesheet

The present article deals with transient thermal stress calculation on a safety horizontal shell and tube condenser. This condenser is used in a power plant for cooling of hot steam diverted from the turbine in the case of its emergency shutdown. The standard stress calculation was provided according to the EN 13445 standard in steady regime. As consistent with this calculation, an expansion joint must be used on the shell. The main aim of this article is to describe a detailed calculation of the transient temperature field on the shell and tubes, using finite element method analysis, and longitudinal thermal stresses on the shell and tubes during the start-up process. Transient analyses are useable for more accurate EN 13445 calculation and, furthermore, for fatigue calculation.