材料成形力学 （双语教学）,Mechanics of Material Forming,The Contents of the Subject,1 Introduction (引言) 2 Stress Analysis （应力分析） 3 Strain Analysis （应变分析） 4 Yield Criteria for Ductile Metals （塑性材料的屈服准则） 5 Stress-Strain Relation （应力应变关系） 6 Stress Evaluation Approch- Slab Method （工程法） 7 Plain Strain Slip-line Field Theory（平面应变滑移线场理论） 8 Extremum Principle for a Rigid Perfectly Plastic Material（刚塑性材料的极限分析原理）,Chapter 1 Introduction,1) Elastic and plastic deformation (弹性变形和塑性变形),A) Elastic deformation,Force (small) (力),Stress-Strain: linear(线性的) Deformation: recoverable （变形） reversible,1.1 Definition and scope of the subject,B) Plastic deformation,Stress-Strain: non-linear(非线性的) Deformation: irrecoverable(不可恢复的) （变形） irreversible,2) Theory of Plasticity (塑性理论),It is concerned with the mathematical study of stress and strain in a plastically deformed body. 塑性理论主要考虑塑性变形体内应力应变的数学关系。,Object （研究对象）,Research method （研究方法）,Ductile metal materials(塑性金属材料)，independent of time.,Experimental observation,It is different from material science.,Physical explanation,3) Nature of Engineering Plasticity (工程塑性理论的特性),Practice and application （实践和应用）,To construct relation between stress and strain for metals and their alloys,To develop mathematical technique, determine stress distribution and predict plastic deformation,Features,Complex stress state Non-linear,1864. Tresca Yield criterion,1.2 Brief historical account,H.E.Tresca carried out experiments of metal forming such as punching, extrusion and compression using some metals, and measured the relation between forming load and ram displacement. He presented a series of papers to the French Academy of Sciences, first in1864. In Fig.4 the cross-section of an extruded billed made of 20 lead sheets is given. Tresca was interested in the metal flow as suggested by the title of his first paper, (On the flow of solid body subjected to high pressure), not yielding in material testing. Tresca assumed that the extrusion force P could be expressed in terms of the shear stress k , and estimated the value of k from the measured forming load of various processes. Because the values of shear stress k estimated from the forming loads dropped in a certain range, he concluded that the metal flow occurred under a constant maximum shear stress.,Saint-Venant and Lvy,1.2 Brief historical account,When Tresca presented his paper to the French Academy of Sciences, Barr de Saint-Venant (1797 1886) was the authority of mechanics in France who was elected a member of the Academy in 1868.After reading the experimental results of plastic flow by Tresca, his attention was drawn to the area of plasticity. In 1871, he wrote a paper on elastic-plastic analysis of partly plastic problems, such as twisting of rod, bending of rectangular beam and pressurizing of hollow cylinder. Saint-Venant assumed that (1) the volume of material does not change during plastic deformation, (2) the directions of principal strains coincide with those of the principal stresses (now known as total strain theory), (3) the maximum shear stress at each point is equal to a specific constant in plastic region.,1.2 Brief historical account,1.2 Brief historical account,Progress of research in yield condition,1.2 Brief historical account,1.2 Brief historical account,1920. Prandtl and Hencky. Theory of slip line field,1.2 Brief historical account,Ludwig Prandtl（1870 1953）received engineering education at the Munich TH. After graduating, he remained at the school as an assistant of A.Fppl , and carried out doctoral work on bending of circular plates. After working in the industry for a while, he was appointed as a professor of industrial mechanics of Hannover TH in 1900. There he proposed membrane analogy of torsion and boundary layer of fluid flow. In 1904 he was invited to the Institute of Mechanics in Gttingen University. Soon he began to study plasticity such as plastic buckling and bending. He was appointed the leader of the laboratory of aerodynamics, and studied wing theorem and other important works of fluid dynamics.,In 1922 Prandtl established the society of applied mathematics and mechanics, “Gesellschaft fr Angewandte Mathematik und Mechanik”, and led the area of applied mechanics. He is also famous as the teacher of many leaders in mechanics in the 20th century such as Th. von Krmn (California Institute of Technology), S.P. Timoshenko (Stanford University), A.Ndai (Westinghouse Laboratory), W. Prager (Brown University) and others.,1.2 Brief historical account,1.2 Brief historical account,1.2 Brief historical account,1.2 Brief historical account,1.2 Brief historical account,1925. Von-Karman. Slab method apply to rolling,1.2 Brief historical account,1.2 Brief historical account,1.2 Brief historical account,Chapter 1 Introduction,1 ) According to the homologous temperature TH,the homologous temperature,