First Principles Study on Mechanical Properties of Superhard α-Ga Boron

The mechanical properties and intrinsic hardness of the α-Ga boron phase （α-Ga-B） are studied by using the combination of first-principles calculations and a semiempirieal macroscopic hardness model. It is found that α- Ga-B is mechanically stable and possesses higher bulk/shear modulus as compared with γ-B28, a newly discovered high-pressure boron phase. The theoretical hardness of α-Ga-B is estimated to be 45 GPa, which is much higher than 38 GPa for γ-B28. The results strongly indicate that α-Ga-B is a potential superhard boron phase. To further obtain insight into the superhard nature of α-Ga-B, we simulate stress-strain curves under tensile and shear deformation. Meanwhile, the microscopic mechanism driving the tensile and shear deformation modes in α-Ga-B is discussed in detail.

A Study of the Pit-Aided Construction of Egyptian Pyramids

Pyramids,symbols of the Ancient Egyptian civilization,are visited by tourists and studied by researchers from all around the world.However,the techniques used by Ancient Egyptians to construct the pyramid,specifically,how such a tall structure could have been constructed from huge blocks of stone with the limited productive forces at the time,remains a mystery to the world.Though numerous theories,such as the use of ramps,levers,pulleys,fluid buoyancy,and cast-in-place concrete,have been proposed in academia,no consensus has been reached to date.Based on mechanical principles and the productive forces available at the time,the famous Pyramid of Khufu is used as a case study in this paper to propose a theory of pit-aided construction.The main steps include the digging of the pit,the transportation of stone blocks into the pit,the layer-by-layer construction,and the layer-by-layer filling of soil until the top of the pyramid is completed.The main idea of the pit-aided construction was to use the self-weight of the stone material to achieve the transportation of stone blocks by converting potential energy to kinetic energy,thereby avoiding the large amounts of work that must be done to elevate the huge blocks of stone.The proposed theory of pit-aided construction is consistent with the cultural custom of burial that is associated with tomb construction,namely laying the deceased to rest through burial,and is also consistent with the productive forces available in Ancient Egypt at the time.

Culm form analysis for bamboo, Phyllostachys pubescens

We investigated the culm form for one of the largest bamboo species, Phyllostachys pubescens Mazel ex Houz. in relation to the me- chanical constraint principles, i.e., elastic, stress and geometric similarity. The fine-resolution analysis of the culm taper indicated that the culm for P. pubescens consisted of three or four segments with various forms, except for the butt swell. This implied that the taper of the whole culm for P. pubescens could be expressed by neither of these principles. The regression slope between culm height and diameter at breast height on the double logarithmic coordinates was 0.629, which was significantly different from the values predicted from these principles. In conclusion, none of these mechanical constraint principles can express the culm taper and height-diameter relationship, and there may be a need for a more complicated model to express the culm form for P. pubescens.

PRINCIPLE AND TRANSMISSION TECHNOLOGY OF BERTRAND CONJUGATE SURFACES

Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.

Overall Evaluation of the Effect of Residual Stress Induced by Shot Peening in the Improvement of Fatigue Fracture Resistance for Metallic Materials

Before 1980s,the circular suspension spring in automobile subjected to torsion fatigue load,under the cyclic normal tensile stresses,the majority of fatigue fracture occurred was in normal tensile fracture mode（NTFM）and the fracture surface was under 45°diagonal.Because there exists the interaction between the residual stresses induced by shot peening and the applied cyclic normal tensile stresses in NTFM,which represents as＂stress strengthening mechanism＂,shot peening technology could be used for improving the fatigue fracture resistance（FFR）of springs.However,since 1990s up to date,in addition to regular NTFM,the fatigue fractures occurred of peened springs from time to time are in longitudinal shear fracture mode（LSFM）or transverse shear fracture mode（TSFM）with the increase of applied cyclic shear stresses,which leads to a remarkable decrease of FFR.However,LSFM/TSFM can be avoided effectively by means of shot peening treatment again on the peened springs.The phenomena have been rarely happened before.At present there are few literatures concerning this problem.Based upon the results of force analysis of a spring,there is no interaction between the residual stresses by shot peening and the applied cyclic shear stresses in shear fracture.This;means that the effect of＂stress strengthening mechanism＂for improving the FFR of LSFM/TSFM is disappeared basically.During shot peening,however,both of residual stress and cyclic plastic deformed microstructure are induced synchronously like＂twins＂in the surface layer of a spring.It has been found for the first time by means of force analysis and experimental results that the modified microstructure in the＂twins＂as a＂structure strengthening mechanism＂can improve the FFR of LSFM/TSFM.At the same time,it is;also shown that the optimum technology of shot peening strengthening must have both＂stress strengthening mechanism＂and＂structure strengthening mechanism＂simultaneously so that the FFR of both NTFM and LSFM/TSFM can be improved by shot peening.

Formation mechanism of calcium hexaluminate

To investigate the formation mechanism of calcium hexaluminate（CaAl_（12）O_（19）, CA_6）, the analytically pure alumina and calcia used as raw materials were mixed in CaO/Al_2O_3 ratio of 12.57：137.43 by mass. The raw materials were ball-milled and shaped into green specimens, and fired at 1300-1600°C. Then, the phase composition and microstructure evolution of the fired specimen were studied, and a first principle calculation was performed. The results show that in the reaction system of CaO and Al_2O_3, a small amount of CA_6 forms at 1300°C, and greater amounts are formed at 1400°C and higher temperatures. The reaction is as follows： CaO ·2Al_2O_3（CA_2） ＋ 4Al_2O_3 → CA_6. The diffusions of Ca^（2＋） in CA_2 towards Al_2O_3 and Al^（3＋） in Al_2O_3 towards CA_2 change the structures in different degrees of difficulty. Compared with the difficulty of structural change and the corresponding lattice energy change, it is deduced that the main formation mechanism is the diffusion of Ca^（2＋） in CA_2 towards Al_2O_3.

Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.