Morphology Evolution and Probability Characteristic of γ' Phase in Single Crystal Superalloy during Creep Rafting

Ni-based single crystal (SC) superalloys are widely applied in the turbine blades of advanced aero-engine due to their excellent heat resistance. Rafting is a major degradation mode of SC under creep damage. In this study, the morphology evolution and probability characteristic of shape parameters are investigated for cuboidal γ´ phase during creep rafting. Three groups of SC creep tests are carried out at 850 °C and 600 Mpa along [001] direction. Scanning electron microscope (SEM) is used to observe the microstructure of SC at four different creep times including 0 h, 8 h, 16 h and 64 h. In addition, an image processing program is developed to identify the length (normal to uniaxial stress) and width (parallel to the stress) of each γ´ phase. Two interesting findings of this investigation can be summarized as: 1) During the N-type rafting of SC, the vertical matrix channel widths are gradually decreased, and the γ phases near the vertex of the cuboidal γ´ phases disappear 2) The length, width of γ´ phases both obey lognormal distributions during creep rafting, and the standard deviations change slightly for the width, but increase significantly for the length. These above findings are of significance to multi-scale probability modeling for creep deformation and fracture.

Reliability Study on Bolt Support Systems of Coal Roadway under Group Failure Modes Based on Maximal Entropy Principle

Currently, there are several failure modes in the blot structure of coal roadway. Existing reliability analysis method of blot support structure of coal roadway does not consider the relevance existing among these methods, thus reducing reliability of the blot structure. In order to fix this defect, we put forward the group failure mode of coal roadway bolt structure analysis method taking the relevance issue into consideration. At the same time, we analyze the probability characteristic of blot structure parameters based on the maximum entropy principle; through the normal distribution curve express the coal - rock characterization of cohesion and the friction angle. The Monte Carlo simulation method calculates reliability of the model with the matlab. The results show that the maximum entropy can effectively reflect the probability characteristic of variables in coal roadway bolt structure. Furthermore, Group failure modes allow for the relevance among existing failure modes in the same group, thus in the general, providing more scientific and accurate responses evaluating the overall reliability of the system. Under the group failure modes, the results of reliability are larger than those under traditional reliability analysis method with same conditions.

Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic is proved. Interpretation of objects in the equations is given.

Uncertainty of One-Dimensional Consolidation of Multi-Layered Soft Clay Soils

The measured coefficient of consolidation can have a substantial degree of variation even in a uniform clay layer. The probability characteristic values for such parameters as consolidation coefficient and compression modulus are analyzed from local engineering data. This paper, through a probabilistic analysis, examines the variability of one-dimensional consolidation solutions. The multilayer models are evaluated. Then the Monte Carlo method is used to develop solutions for one dimensional consolidation. It identified the influence of the parameter uncertainty on the probability characteristic of the consolidation degree. The uncertainty of consolidation coefficient has a great impact on the probabilistic characteristics of the consolidation degree, but for compression modulus it is opposite true. It proposed a simplification analysis method that considers only the uncertainty of consolidation coefficient without consideration of the uncertainty of compression modulus, and its erroneous precision can meet the engineering requirements.