Molecular-dynamics of a 2D Model of the Shape Memory Effect

This work investigates the thermodynamic properties of a qualitative atomistic model for austenite–martensite transitions. The model, still in 2D, employs Lennard-Jones potentials for the determination of the atomic interactions. By use of two atom species it is possible to identify three stable lattice structures in 2D, interpreted as austenite and two variants of martensite. The model is described in the first part of the work [6] in detail. The present work studies the thermodynamic properties of the model concerning a small, 2-dimensional test assembly consisting of 41 atoms. The phase stability is investigated by exploitation of the condition of minimal free energy. The free energy is calculated from the thermal equation of state, which is measured in numerical tensile tests. In the second part of this work a chain of eleven 41-atom assemblies is investigated. The chain is interpreted as an idealized larger body, where the individual crystallites represent crystallographic layers allowing for the creation of micro structure. By use of tensile tests at various temperature conditions we sketch how such chain may exhibit quasi-plasticity, pseudo-elasticity and the shape memory effect.     

Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves.We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.     

无人机捷联航姿系统磁航向误差分析

为进一步提高某型飞机捷联航姿系统的磁航向精度,分析了该系统中姿态角误差对磁航向精度的影响,详细推导了磁航向角的误差公式。结合某型飞机的特点,对误差公式做了进一步简化分析,结论表明磁航向角的误差大小主要由姿态角误差的平方和决定。采用试飞数据进行仿真,结果验证了误差公式及分析结论的正确性。     

反射焦散线实验中斜入射光对应力强度因子测试精度的影响

本文用空间解析几何方法,推导了在一般非平行斜入射光条件下,裂纹体表面所形成的反射焦散线和初始曲线的方程.分析了倾斜入射光造成的焦散线畸变,给出了这种畸变造成的裂端应力强度因子测量误差的解析表达式.     

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.     

Microstructure morphology transitions at mesoscopic epitaxial surfaces

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.     

Internal loops in pseudoelastic behaviour of Ti-Ni shape memory alloys: Experiment and modelling

The stress-strain isothermal hysteresis loops due to the incomplete martensitic transformation are analysed for Ti-Ni shape memory alloys. Experiments show the existence of two distinct yield lines for phase transition; one for the forward transformation austenitemartensite (AM), the other for the reverse transformation MA. The tensile behaviour of single crystals with only one yield line (AM) [1] can be considered as an ideal case. An extension of a thermodynamic model for pseudoelasticity [2] allows these two yield lines to be taken into account.

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Sommario Per leghe Ti-Ni con memoria di forma vengono analizzati i cicli di isteresi isotermici tensione-deformazione prodotti da una incompleta trasformazione martensitica. Gli esperimenti mostrano l'esistenza di due distinte linee di snervamento per la transizione di fase, una verso la trasformazione austenitemartensite (AM), l'altra per la trasformazione inversa MA. Il comportamento a trazione di un singolo cristallo con una sola linea di snervamento (AM) [1], può essere considerato un caso ideale. L'estensione ad un modello termodinamico pseudo-elastico [2] consente di analizzare queste due linee di snervamento.

     

Holomorphic Flows on Simply Connected Regions Have No Limit Cycles

The dynamical system or flow = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.     

CO2 will probably not help to save Venice from the sea

It has been proposed to rise Venice by injecting CO₂ into an aquifer lying 600–800 m below its lagoon. It is shown that because of the prevailing ambient conditions in the aquifer phase change of CO₂ cannot be avoided. The ensuing change of specific volume and compressibility will inhibit a uniform uplift pattern which is needed to avoid cracks in historical buildings. Further, both liquid and gaseous CO₂ produce capillary effects at the contact surface with water in the voids of the reservoir rock and this affects its mechanical response. Hence further non homogeneity in the uplift pattern will be produced. This prevents the use of CO₂ in the proposed conditions.     

Bubble clustering and trapping in large vortices. Part 1: Triggered bubbly jets investigated by phase-averaging

The characteristics of large coherent structures in turbulent, periodically-excited, as well as naturally-developing bubbly jets are investigated, and interactions between bubbles and large-scale vortices are studied quantitatively.