Fractal Approval To 3D Printed Graphene/SiC Composites And Instability Of The Printing Process

The 3D printing technology uses a digital model to harness a high viscous paste to print layer by layer three-dimensional objects with various shapes.It needs neither traditional mechanical processing nor complex mold design,the printed object’s shape and its inner structure can be precisely controlled by the computer,so as to greatly reduce production costs and improve production efficiency.3D-printed graphene/SiC composites have many advantages in low density,high electrical conductivity,excellent electrical conductivity,good mechanical properties,good thermodynamic properties,and good energy storage properties,and can be widely used in aerospace,transportation,advanced materials,semiconductors,energy storage,industrial design,etc.The 3D printing technology can be considered as one of the most important inventions in the 21 st century.According to much experiment observation,this dissertation applies modern mathematics,especially the fractal theory and the fractional calculus,to study the complex experimental phenomena through physical laws from slurry preparation,instability of the printing process and the main key factors affecting the performance of printed products,in order to control the printing process and to predict the product’s performance.This dissertation starts from the geometric structure of graphene,whose Steiner minimum tree structure endows it with unique electrical,heat conduction and mechanical properties.Moreover,fractal geometry,which is the basic characteristic of graphene,is proposed,and the graphene’s performance is closely related to its fractal dimensions.In particular,a theoretical model is proposed to calculate graphene’s resistance,and it is verified experimentally.When preparing graphene/SiC paste,it is often found that graphene has agglomeration.In order to explain the agglomeration mechanism,this dissertation introduces the basic concept of the geometric potential theory,and proposes the basic concepts for the zero-dimensional agglomeration,the one-dimensional agglomeration and the two-dimensional agglomeration.Furthermore,the Casimir effect is adopted for graphene dispersion.The rheological properties of graphene/SiC paste are the most critical parameters for 3D printing technology,which not only affect the printability,but also affect the morphology and properties of the products.In order to describe the rheological properties of graphene/SiC paste,a fractal rheological model is proposed,and the key parameters affecting the rheological properties of graphene/SiC paste are analyzed and verified experimentally.In order to explain liquid migration of the graphene/SiC paste and the discontinuous printing process,the variational theory is harnessed to establish a governing equation,which can elucidate the effects of receiving distance,nozzle diameter and printing speed on the printing process and printed products.The motion stability is proposed,and it shows that a higher printing speed sees a more stable printing process.However,the faster the printing speed is,the shorter the solvent evaporation time is,and the printed products are not solidified completely,and easy to be deformed.To overcome this problem,an approximate formula for calculating the optimal printing speed is proposed.If the printed object is received before complete solvent evaporation,it is easy to adhere to the receiver,thus making the printed object deformed.In order to solve this technical problem,a flexible receiver is proposed in this dissertation.The experimental results show that the flexible receiver can meet the requirements of high printing precision.In order to elaborate the mechanical properties of graphene/SiC composites,an improved Hall-Petch effect is proposed in this dissertation,which is suitable for studying the effects of graphene content on the mechanical properties.The effect of graphene distribution on the electrical properties of graphene/SiC composites is proved by simple experiments,and the conductivity formula of graphene/SiC composites is derived by fractal theory.Finally,the Steiner minimum tree structure of graphene is used to illustrate the thermal conductivity of graphene/SiC composites.According to the spinning and web characteristics of spiders,this dissertation also puts forward a preliminary idea of bionic printing.According to the bubble spinning technology,an improvement scheme of printing process is put forward.