Discussion on relationship between minimal energy and curve shapes

Energy minimization has been widely used for constructing curve and surface in the fields such as computer-aided geometric design, computer graphics. However, our testing examples show that energy minimization does not optimize the shape of the curve sometimes. This paper studies the relationship between minimizing strain energy and curve shapes, the study is carried out by constructing a cubic Hermite curve with satisfactory shape. The cubic Hermite curve interpolates the positions and tangent vectors of two given endpoints. Computer simulation technique has become one of the methods of scientific discovery, the study process is carried out by numerical computation and computer simulation technique. Our result shows that： （1） cubic Hermite curves cannot be constructed by solely minimizing the strain energy; （2） by adoption of a local minimum value of the strain energy, the shapes of cubic Hermite curves could be determined for about 60 percent of all cases, some of which have unsatisfactory shapes, however. Based on strain energy model and analysis, a new model is presented for constructing cubic Hermite curves with satisfactory shapes, which is a modification of strain energy model. The new model uses an explicit formula to compute the magnitudes of the two tangent vectors, and has the properties： （1） it is easy to compute; （2） it makes the cubic Hermite curves have satisfactory shapes while holding the good property of minimizing strain energy for some cases in curve construction. The comparison of the new model with the minimum strain energy model is included.

Establishment Method of Shape Standard Curve Based on Stepwise Optimization and Its Compensation Models

There are very few researches on the shape standard curve currently,and they merely remain on the level of description of the general concept and production experiences,lacking of the in-depth theoretical analysis,and the concrete principle,method and steps for determining the shape standard curve are not put forward,therefore,they are not applicable in industrial production.This is the weakest spot in the research on the basic shape theory.In this paper,the basic shape standard curve and the transverse distribution curve of the exit thickness are attained with stepwise optimization,which is based on the theoretical calculation method of the shape standard curve of strip mills proposed by authors.By calculating the shape discrimination model and the shape forecast model separately,the simultaneous iterative calculation by the previous method is avoided,and the speed and stability of calculation are improved.The compensation models of the transverse temperature difference of the strip,the shape detection roller deflection and the shape of the strip coil are established,respectively,meantime,the basic shape standard curves are compensated,and the relatively perfect theoretical establishment method of the shape standard curve is formed.The simulation and calculation are done on a 1 220 mm five-stand cold strip tandem mill.The simulation and calculation result shows that the principle,method and steps for determining the shape standard curve are correct and feasible,and the correctness of theoretical analysis and calculation is verified.This paper proposes an idea and a method for the establishment of the shape standard curve in the rolling processes of cold strip mills,which develop the theory and model of the shape standard curve and improve the quality and efficiency of the shape control in the rolling processes of cold strip mills.

Formation Mechanism of Curved Martensite Structures in Cu-based Shape Memory Alloys

The curved martensite structures have been observed in CuZnAI-based shape memory alloys by both transmission electron microscope and optical microscope. It was found that the curved martensite structures observed in as-solution treated, as-aged and as-trained alloys usually occurred around dislocation tangles or precipitate, at the plate boundary or grain boundary, and when the growing plates collided with each other or alternate mutually.

Innovation in the Computing System of Straightening Force

Currently in China, the computing system of the straightening force of the six-rollers straightening machine generally follows the traditional computing system. The force status of the traditional computing system for the straightening force deviates far away from the actual force status of the roller system in the six-rollers straightening machine. In the traditional system, the computing model of the straightening force of the six-roller straightening machine was based on the roller shape of hyperbola, which led to the length of the contacting line between the tube and the straightening roller to be excessively short, i.e., only 0.1~）.2 of the length of the roller. Thus the constructed computing system has relatively large difference from the actual measured result. To solve the above problems, flattening straightening and bend straightening are analyzed on the basis of materials mechanics and bend beam theory, the roll er shape using the envelope method of A.I4.~e：mKoB is generated, and a new computing system for straightening force in six-rollers straightening machine is built. The roller shape of the straightening roller, on which the new computing system for the straightening force is based, is designed according to the envelope method under the condition of ideally full contacting between the tube and the roller body of the straightening roller, therefore the new computing model accords with the practical status of straightening force. According to the comparison of the new computing system with finite element method and the actual measured result of straightening force, it has been proved that the computation accuracy of the new computing system for straightening force satisfies the practical requirements of engineering. New six-rollers straightening machines are designed and manufactured according to the new calculation system, and the new machines not only have higher precision and quality, but also have adopted the force sensor and computer and combined with the new computing system for straightening force to realize the fully automatic adjustment of the straightening machine. The new six rollers straightening machine have obtained notable economical and social benefits.

CREEP BEHAVIOR MODELING OF UDIMET 720Li SUPERALLOY

Constant load creep tests on isothermally forged Udimet 720Li, an advanced superalloy for gas turbine disc application, were run in the stress/temperature field 900-450MPa/650-700 ℃ producing rupture times in the 20-5000h range. The creep curves have shown a predominant accelerating creep stage, that has been described by the following equation: where ε min depends on stress and temperature, while parameter C depends mainly on stress. A strain dependent damage, defined by the parameter C, causes the accelerating creep stage at stresses lower than 750MPa, whilst its contribution to the creep strain acceleration is less important at higher stresses. The model rationalizes the different behaviors at high and low stress and has been validated with variable stress and temperature creep behavior.

Evaluation of the cracking and aging susceptibility of asphalt mixtures using viscoelastic properties and master curve parameters

Aging can significantly affect the performance of asphalt mixtures, causing increase in stiffness, reduction in relaxation capability and increase in cracking susceptibility. It is also well known that fundamental viscoelastic properties are used for design and modelling of asphalt mixtures and pavement structures to addressing rutting, fatigue and thermal cracking concerns. The objective of this paper is to study how the viscoelastic properties of asphalt mixture change over time, and evaluate and identify the cracking and aging susceptibility of asphalt mixtures with different mix variables during material selection and mixture design. Ten mixtures are evaluated using different laboratory conditioning protocols to simulate a range of aging levels in the field. The complex modulus test is then conducted on the lab aged mixtures to measure the viscoelastic properties in order to construct the dynamic modulus and phase angle master curves. The mixture Glover-Rowe(G-Rm) parameter and the shape parameters of the dynamic modulus and phase angle master curves, including inflection point frequency(-β/γ), difference between the glassy modulus and the inflection point modulus(γ), peak value of phase angle(a) and the horizontal position(frequency) of the peak phase angle value(c), are determined and evaluated for the mixtures with different aging conditions and mix variables. The study indicates the ability of the G-Rmparameter and all the master curve shape parameters to capture the effect of different aging conditions on linear viscoelastic mixture properties, as well as the cracking and aging susceptibility of asphalt mixtures.