Directional Young’s modulus of single-crystal and cold-rolled titanium from ab initio calculations: Preferred crystal orientation due to cold rolling

Titanium is a strong, corrosion resistant metal with low mass density, making it ideal for various purposes, including aviation and medical applications. In the present work, the elastic properties of titanium have been investigated using the first principles Exact Muffin-Tin Orbitals method. The focus of our study is the anisotropic elasticity of single-crystal and cold-rolled titanium. Both types of titanium are used in industrial applications because of their special mechanical properties compared to randomly ordered polycrystalline alloys. Single crystals have better creep resistance compared to polycrystalline metals, while cold-rolled ones, on the other hand, possess more strength. Here cold-rolled titanium is investigated for the first time using ab initio calculations. Single-crystal results are obtained directly from first principles total energy calculations, whereas the elasticity of the cold-rolled structure is estimated from the single-crystal data. The elasticity of cold-rolled titanium has previously been investigated only experimentally, and thus the present computational approach provides new insight and valuable complementary information, not only for cold-rolled titanium, but also for more complex structures. Our results are found to be in good agreement with experimental findings and therefore serve as a starting point for investigating the elasticity of titanium alloys, which, using our method, can be accomplished as easily as the pure titanium case.     

Mechanical Properties and Flow Behavior of Polymers for Enhanced Oil Recovery

The mechanical properties and flow behavior in porous media of three different polymer systems including a hydrophobically modified acrylamide-based copolymer (HMSPAM), a partially hydrolyzed polyacrylamide (HPAM), and a polysaccharide (xanthan gum) were evaluated to establish their functional differentiation as mobility control agents in enhanced oil recovery (EOR). The rheological properties of the polymers were described by the power-law model to investigate their non-Newtonian behavior. The first normal stress difference (N₁) and Weissenberg number (W_e) were also used to compare their elastic properties. The experimental results showed that, at comparable shear viscosity, HMSPAM exhibited significant elasticity compared to HPAM and xanthan gum. Shear resistance tests indicated that all of the polymers experienced an extra stress when converging into a capillary tube due to the “entrance effect.” Xanthan gum was the most mechanically stable polymer. Moreover, HMSPAM showed the superior reformability which was quantified by the regained viscosity with relaxation time. This could be explained by the rapid re-association of the hydrophobic interactions. Sandpack flood tests indicated that HMSPAM rendered extremely high mobility control ability during polymer flooding suggesting its potential in EOR. However, this polymer also experienced significant retention within the porous media (potential injectivity and plugging problems), which may be attributed to the formation of bulky associative polymer networks. In this work, UV spectrometry was employed to monitor the concentration of the produced polymer solutions and quantify the polymer retention within porous media. This analytical approach offers great reliability and simplicity. It was concluded that the use of a particular polymer system depends on the oil reservoir conditions and the target EOR application.     

Harnack Inequalities and Discrete—Continuous Error Estimates for a Chain of Atoms with Two—Body Interactions

We consider deformations in ℝ³ of an infinite linear chain of atoms where each atom interacts with all others through a two-body potential. We compute the effect of an external force applied to the chain. At equilibrium, the positions of the particles satisfy an Euler–Lagrange equation. For large classes of potentials, we prove that every solution is well approximated by the solution of a continuous model when applied forces and displacements of the atoms are small. We establish an error estimate between the discrete and the continuous solution based on a Harnack lemma of independent interest. Finally we apply our results to some Lennard-Jones potentials.     

基于AVR单片机的万能材料试验机控制系统

采用AVR单片机AT90S8515作为控制核心,通过步进电机带动丝杠运动,利用光栅编码器、高精度力传感器、2个引伸计分别测量了位移、力及试件横、纵变形,在老式电子万能材料实验机上建立了新型计算机控制系统,可方便测定弹性模量和泊松比.     

利用近红外光谱技术预测粗皮桉木材弹性模量

采用近红外光谱分析技术,对粗皮桉木材弹性模量进行了快速预测研究.使用快速傅里叶变换(FFT)分析法和常规力学测试方法测定了粗皮桉木材无疵小试样的弹性模量,并用近红外光谱仪采集试样径切面和弦切面的近红外漫反射光谱,对原始光谱进行二阶导数预处理,并选择410～2 480 nm光谱段建立回归模型.以2/3的试样作为校正集建立弹性模量的偏最小二乘法校正模型,以1/3/的试样作为预测集对模型进行验证.结果表明,粗皮桉木材的弹性模量与近红外光谱之间有较好的相关性,纵向弹性模量和抗弯弹性模量的预测模型的相关系数分别为0.93和0.81,相对分析误差分别为2.70和1.71.利用近红外光谱分析方法可以实现对粗皮桉木材无疵小试样弹性模量的快速预测.     

Theories of surface elasticity for nanoscale objects

The emergence of nanotechnology has driven recent interest in systems having surface atoms as a significant fraction of all atoms present, in particular nano-sheets (ultra-thin slabs), nano-wires, and nano-particles. In these systems, the bulk (i.e. non-surface region or interior) is typically strained in response to the stress of the surface. This elastic strain of the bulk in turn changes the surface lattice constants. Since the bulk and the surface are coupled, the problem must be solved self-consistently. Solving this problem requires a quantitative model of the surface elastic properties which are different from the bulk. In this paper we consider various models that have been proposed for surface elasticity. Our goal is to elucidate the relationship between two contrasting approaches: (1) the Shuttleworth equation which defines a surface stress based on the strain derivative of the surface energy and (2) the Gurtin-Murdoch (GM) theory which considers the surface layer as a membrane with residual strain and with elastic constants different from the bulk. The GM theory is analogous to the 2-D Frenkel-Kontorova (FK) model and can be used to obtain quantitative parameters for the FK model. We present an embedded atom method calculation of the surface elastic constants of Cu(1 1 1) using the GM theory with the surface represented by a membrane one atomic layer thick. This quantitative approach describes the elastic properties of surfaces in a physically appealing way. Just as the bulk elastic constants provide direct information regarding the stress/strain relationship in a bulk material, the surface elastic constants provide similar information for a surface monolayer. This theory will allow elasticity analysis and atomistic calculations of properties of nano-scale objects.     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

Ab initio calculation of phonons in bulk HfC and the HfC(001)(1 × 1) surface

Structural, elastic and dynamical properties of the rock-salt HfC have been studied by employing an ab initio pseudopotential method and a linear response scheme, within the generalised gradient approximation. In addition to achieving good agreement with experimental measurements of the phonon dispersion results along the symmetry direction Γ-X, we have presented accurate dispersion results along several other directions in the Brillouin zone. Sharp features in the phonon density of states are ascertained and their origin discussed. This is followed by investigations of the structural, electronic and phonon properties of the HfC(001) surface. The agreement between our surface phonon spectrum and experimental measurements is very good. By analysing the atomic displacement patterns of the zone-centre and zone-edge phonon modes we have determined the energy locations and polarisation characteristics of Fuchs–Kliewer, Wallis, Lucas and Rayleigh modes.