| Metal material has been widely used in many fields such as aerospace,automobile manufactory and mechanical design.Microscopically,a rolled metal sheet is an aggregate of numerous tiny crystallities separated by grain boundaries,and single crystal is composed of atom arranged as some periodic regularities.The metal usually is anisotropic for the difference on sight,shape,direction density and boundary distribution of grains.The mechanical and physical properties are determined by the inherent property of crystal and material micro-structure.early in1965,Roe and Bunge put forward the famous ODF(Orientation Distribution Function),by which the micro structural information of metal materials such as the crystal orientation and direction can be well described.According to the symmetrical feature of the crystals,the physical and mechanical properties of materials in different crystal directions can be derived based on statistics principle.During pressing,rolling and forming process,the grains vary with the crystal size and shape,and they also have preferred to some directions which results in different macroscopic physical and mechanical properties.Microscopically,when material rotates,it must meet symmetry.Hence,by means of total rotation function considering micro-structure,the physical and mechanical properties of elasticity and plasticity under different direction are studied in this thesis.Related scholars have obtained many achievements on the relation between macroscopic physical and mechanical properties and texture coefficient in direction n.But these is from the fitting formula by experimental results,not by theory.Based on the microscopic and macroscopic symmetry,group theory,tensor analysis,this thesis gives the general expression of total rotation function,which is also validated by laboratory tests.These total rotation functions not only take into account micro-structure information,but also describe the physical and mechanical properties in any spatial direction.With the application of the general expression of total rotation function to describe the properties of single crystal and polycrystal,the total rotation functionsconcluding micro-structure information for aggregate of cubic crystallites,triangular crystallites and hexagonal crystallites are established.As well,both the macroscopic physical properties(piezoelectric constants and dielectric constant)and macroscopic elastic properties(elastic modulus,flexibility and elastic strain energy and so on)are studied by the total rotation function in this papers.The research lay a theoretical foundation for preparation and formation of metal materials.Hosford yield function suffering from the restriction that the three principal stresses must be coaxial with the orthotropy of materials such as rolling direction(RD),transverse direction(TD)and normal direction(ND),the general Hosford yield function in any stress state is set up by total rotation function.Then we give the computational expressions of determining all elastic and plastic parameters only via the experimental data of uniaxial tension test.Compared to the existing yield functions,the proposed general Hosford yield function has many advantages.For example,firstly,it is suitable for analyzing the problem that the principal stress is inconsistent with the axis of materials orthotropy.secondly it can be used to explain the phenomenon that the six and eight earring developed during deep drawing process.Finally,it is convenient to utilize for concluding the micro-structure information in the total rotation function.In a word,the new general Hosford yield function can be widely used in the field of sheet forming processes.Finally,based on the rotation location function concluding micro-structure information,the plastic mechanical properties of metal sheet about micro-structure are studied in this paper.The plastic anisotropy index for q-value,r-value and yield stress for the cubic crystal and Hexagonal crystal sheet metal under the different angle are derived from the general Hosford yield function on any stress state concluding texture coefficients.And the theory formulas,which consider the orientation and texture coefficients,can be verified by some experiments results.The related research shows that the previous yield functions can be used to well describe only one of the plastic anisotropy index of q-value,r-value and yield stress,but they are difficult to illustrate all the index simultaneously.if the total rotation function are expressed in their Taylor expansion to higher-order tensors,experimental results agree better with the plastic anisotropy index of q-value,r-value and yield stressobtained from the general Hosford yield function for weakly-textured metal sheets concluding the micro-structure information in any stress state.And the general Hosford yield function concluding more than six-order plastic parameters can well describe the plastic forming and plastic yield of sheet simultaneously.Hence,the theoretical results can be widely used in the study of plastic mechanical properties of sheet metal. |
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