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Dynamic crack growth and branching of a running crack under various biaxial loading conditions in homogeneous and heterogeneous brittle or quasi-brittle materials is investigated numerically using RFPA2D (two-dimensional rock failure process analysis)-Dynamic program which is fully parallelized with OpenMP directives on Windows. Six 2D models were set up to examine the effect of biaxial dynamic loading and heterogeneity on crack growth. The numerical simulation vividly depicts the whole evolution of crack and captured the crack path and the angles between branches. The path of crack propagation for homogenous materials is straight trajectory while for heterogeneous materials is curved. Increasing the ratio of the loading stress in x-direction to the stress in y-direction, the macroscopic angles between branches become larger. Some parasitic small cracks are also observed in simulation. For heterogeneous brittle and quasi-brittle materials coalescence of the microcracks is the mechanism of dynamic crack growth and branching. The crack tip propagation velocity is determined by material properties and independent of loading conditions.

As an improved directional solidification (DS) method, the complex directional solidification (CDS) method is used for purifying and preparing multicrystalline silicon ingot in this experiment. The induced electromagnetic field is imposed to control refining and solidification process. An integral silicon ingot with the diameter of 130 mm, the length of 130 mm and the weight of 4 kg is successfully fabricated in a self-designed CDS furnace. Metallographic analyses reveal that the direction of the most grains is parallel to the axial of silicon ingot. Analyses proved that the distribution of impurities in the cross-section is more homogeneously, the distribution in axial is improved and the effective length of silicon ingot is increased. Theoretical calculations indicate that the effect of solidified rate on the removal of impurities is limited and the impurities can be removed effectively after more than two times directional solidification process.

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