A New Method For Calculating The Stress Field Of Rigid Plastic Materials And Its Application In Forging Of Large Forgings

Rigid plastic material is one of the most important and widely used material models in plastic mechanics.The three positive strain components in the mechanical equation are linearly correlated,and the relationship between stress component and strain component is missing in the constitutive equation.The calculation of stress field can only be solved according to the stress,so many existing methods of calculating stress field in solid mechanics cannot be applied,which makes the method of calculating stress field of rigid plastic materials very deficient,which not only affects the development of plastic mechanics,but also affects the application of plastic mechanics.Large forgings play a very important role in the construction of major equipment and national defense equipment,and the defects of large forgings can be eliminated or improved by forging to provide high quality blanks for the equipment manufacturing industry.Plastic mechanics is its important theoretical basis,and rigid plastic materials are the material models for forging calculations of large forgings.In view of the lack of the method of calculating stress field of rigid plastic materials in plastic mechanics,as well as the difficulty of solving the stress field of large forgings and the lack of theoretical development,the following research work was carried out in this paper:（1）Based on the concept of static equilibrium stress field,the expansion second variational principle of rigid-plastic material with static equilibrium stress field as a self-variable function was established and named.It was proved strictly by functional variational theory and method.The variational principle adds new content to plastic mechanics,the innovation and significance are as follows:1)A new variational principle has been established;2)A new method for calculating the stress field of rigid plastic materials which has the advantages of low difficulty in initial stress field design and easy application;3)The method established an energy functional with more application advantages,with fewer autofunctions and easier application;4)The calculation results are more accurate,and the yield condition is constrained in the expression of the functional.When the functional variation takes a stationary value,the yield condition is strictly satisfied;5)To construct a new finite element method based on stress solving,both theoretical support and feasibility of implementation are provided.（2）The general procedure for solving the stress field using the expansion second variational principle of rigid-plastic material was established.The general calculation method is provided for the application of the expansion second variational principle of rigid-plastic material.（3）The analytical expression of the real stress field in the upsetting billet of large ingot is obtained for the first time by using the expansion second variational principle of rigid-plastic material and calculation steps.The analytical formula shows that:1)After the side surface has a drum shape,the absolute value of the two sidesσ_z is higher than that of the middle drum shape section,and the difference is proportional to the drum shape coefficient K and inversely proportional to the height h;2)After a drum shape is generated on the side surface,tangential stressσ_θis generated on it,and a maximum value is obtained at the maximum of the drum shape,and the maximum value is proportional to the drum shape coefficient K;3)The drum shape of the side surface is a sufficient condition for the tangential stress generated at each point on it,and the end friction only affects its size.（4）The surface cracking on the upsetting side of large ingot is common in forging production and causes huge economic losses.According to the deformation and crack characteristics before cracking,it belongs to ductile fracture.The commonalities and particularities between it and conventional ductile fracture were analyzed.Based on the widely used theory of critical expansion ratio of ductile fracture,the stress field analytical formula for large ingot upsetting was used to calculate the equivalent strain,equivalent stress,hydrostatic stress and triaxial degree of stress on the side surface of ingot for the first time.The analytical formula for the mechanical conditions of large ingot upsetting side surface cracking was obtained.The analytical formula shows that:1)when the billet side surface is cylindrical,the upsetting hole expansion ratio _GV at each point is equal,the crack location depends on the distribution of the critical hole expansion ratio V_{G C},and the crack expands at the minimum critical hole expansion ratio V_GC;2)When the billet side surface is a drum curved surface,the upsetting hole expansion ratio V_Gon the side surface is the maximum at the edge of the maximum drum section.When the critical cavity expansion ratio V_GC is uniformly distributed on it,the cracking is at the edge of the maximum drum section.When the critical hole expansion ratio V_GC is unevenly distributed,the location of the crack depends on the distribution of the critical hole expansion ratio V_{G C}.Due to the occurrence of cracks at the equal position of _GV and V_GC,there may be multiple simultaneous cracks,namely dispersed cracks.（5）In order to verify the theoretical research,the laboratory upsetting test of Mn18Cr18N ring steel specimen was carried out.In order to make up for the huge difference in size between the laboratory specimen and the large ingot,comparisons were made with the forging production example.The laboratory test results showed that the relative compression of the crack on the side surface of the specimen and the location of the crack are close to the theoretical calculation value in Chapter 4.The test result of the upsetting load is close to that of the theoretical calculation,with a maximum difference of about 17.5%.The comparison between the forging production example and the theoretical calculation value in Chapter 4 showed that the two are consistent in the crack location,which indicated that the analytical formula of the mechanical conditions of the surface cracking of the upsetting side of the large ingot is correct,and also indirectly verified the analytical formula of the stress field inside the upsetting billet during the upsetting process of the large ingot is correct.