Papers by Author: Elena Lyamina

Abstract: Gradient theories of plasticity play an important role in the description of inelastic behavior of materials. Usually, these theories involve space derivatives of stress or strain. On the other hand, conventional theories of plasticity can be divided into two groups, flow and deformation theories. Each of these groups has its own area of applications. The main conceptual difference between the theories belonging to the different groups is that the primary kinematics variables in deformation theories are displacements (or strains) whereas in flow theories velocities (or strain rates). Therefore, it is of interest to propose a gradient theory of plasticity involving space derivatives of a measure of strain rate (strain-rate gradient theory of plasticity) and to compare qualitative behavior of solutions for the strain-rate gradient theory of plasticity and an existing strain gradient theory of plasticity. One possible strain-rate gradient theory of plasticity is proposed in the present paper. The equivalent strain rate (second invariant of the strain rate tensor) is used as a measure of strain rate. The Laplacian operator is adopted to introduce the gradient term. An analytic solution for expansion of a hollow sphere is given for two strain-rate gradient theories of plasticity and one strain gradient theory. Comparison of the solutions shows that some qualitative features of the solutions for the strain-rate gradient theories are in better agreement with general physical expectations than those for the strain gradient theory.

Abstract: A layer of intensive plastic deformation often appears in the vicinity of frictional interfaces in metal forming processes. The paper presents a study to reveal a possible effect of intensive plastic deformation in such a layer on ductile fracture. To this end, an upsetting test of special design is used to move the site of ductile fracture initiation to the friction surface independently of the effect of intensive plastic deformation on the occurrence of ductile fracture. Experimental results obtained are compared to the theoretical prediction based on a conventional empirical ductile fracture criterion. It is shown that there is some deviation of the fracture conditions predicted theoretically from the experimental results.

Abstract: The paper reviews several theoretical and experimental methods for the assessment of ductile fracture criteria and for their application to the fracture prediction in metal forming processes. In particular, distinguished features of two widely used ductile fracture criteria are demonstrated in the case of free surface fracture. Conventional empirical ductile fracture criteria are not compatible with behaviour of plastic solutions in the vicinity of maximum friction surfaces. An approach to overcome this difficulty is discussed. Finally, a theoretical/experimental method to reveal a possible effect of geometric singularities on the applicability of ductile fracture criteria is reviewed.

Abstract: Conventional ductile fracture criteria are not applicable in the vicinity of maximum friction surfaces for several rigid plastic material models because the equivalent strain rate (second invariant of the strain rate tensor) approaches infinity near such surfaces. In the present paper, a non-local ductile fracture criterion generalizing the modified Cockroft-Latham ductile fracture criterion is proposed to overcome this difficulty with the use of conventional local ductile fracture criteria. The final form of the new ductile fracture criterion involves the strain rate intensity factor which is the coefficient of the principal singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. When the velocity field is not singular, the new ductile fracture criterion reduces to the modified Cockroft-Latham criterion. The strain rate intensity factor cannot be found by means of commercial finite element packages since the corresponding velocity field is singular. In the present paper, the new fracture criterion is illustrated with the use of an approximate semi-analytical solution for plane strain drawing. It is shown that the prediction is in qualitative agreement with physical expectations.

Abstract: The paper concerns with an effect of plastic anisotropy on the load required to deform hollow cylinders between two parallel, rough dies. It is assumed that the material obeys Hill’s quadratic yield criterion and its associated flow rule. The friction stress is supposed to be proportional to the corresponding shear yield stress, including the maximum friction law as a special case. The kinematically admissible velocity field is chosen such that the stress field following from the associated flow rule satisfies the boundary condition at the plane of symmetry. Moreover, this velocity field is singular in the vicinity of the friction surface. Therefore, in the case of the maximum friction law the friction law is satisfied, again if the associated flow rule is combined with the velocity field. A significant effect of plastic anisotropy on the limit load is illustrated.

Abstract: The flow behavior and ductility of the Aluminium alloy 5A06 was investigated in the tensile test at the elevated temperatures from 20oC to 300oC and strain rates range of 0.0006s-1 0.06s-1. The influences of strain, strain rate and temperature to elongation strain at fracture , percentage elongation , tensile strength , strain hardening exponent and strain rate sensitive exponent were researched on the basis of experimental stress-strain curves, showing 5A06 is a temperature sensitive alloy. Warm/hot hydromechanical processing of cylindrical cup deep drawing was simulated. It is demonstrated that the differential temperature mode with cool punch and heated die can enhance the forming limit significantly compared with the constant temperature mode of all tools in the same temperature.

Abstract: The quality of surface of the product of metal forming processes depends on physical processes in the vicinity of frictional interfaces between the material and tool. It is well known that material properties in a narrow layer in the vicinity of such interfaces are usually quite different from the properties in the bulk. It is therefore necessary to develop a special approach to account for this feature of the distribution of material properties. A possible approach is proposed in the present paper. It is based on the concept of strain rate intensity factor.