On The Adequate Representation Of Velocity Fields In A Narrow Layer Near Maximum Friction Surfaces

2007 ◽  
Author(s):  
Sergei Alexandrov ◽  
Gow-Yi Tzou ◽  
Teng Hui Chen
Keyword(s):  
Velocity Fields ◽  
Maximum Friction ◽  
Narrow Layer ◽  
Adequate Representation ◽  
Friction Surfaces

The Strain Rate Intensity Factor and its Applications: A Review

2009 ◽  
Vol 623 ◽  
pp. 1-20 ◽  
Author(s):  
Sergei Alexandrov
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Material Properties ◽  
Velocity Fields ◽  
Rigid Plastic ◽  
Maximum Friction ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity ◽  
Friction Surfaces

The present paper concerns with the concept of the strain rate intensity factor in rigid plastic solids. The strain rate intensity factor is the coefficient of the principal singular term in the expansion of the equivalent strain rate in a series in the vicinity of maximum friction surfaces. Such singular velocity fields appear in solutions based on several rigid plastic models. Because of this singularity in the velocity field, many conventional evolution equations for material properties are not compatible with such rigid plastic solutions. On the other hand, qualitative behaviour of the singular rigid plastic solutions in the vicinity of maximum friction surfaces is in agreement with a number of experimental results. Therefore, the primary objective of research in this direction is to develop an approach to relate parameters of the singular velocity fields and parameters characterizing material properties. The approaches proposed in previous works are based on the strain rate intensity factor. In the case of analytical and semi-analytical solutions the strain rate intensity factor can be found by means of an asymptotic analysis of the solutions. A number of such solutions obtained by inverse methods are reviewed in the present paper and the strain rate intensity factor is found. An effect of process parameters on its magnitude is shown and discussed.

Comparison of Double-Shearing and Coaxial Models for Pressure-Dependent Plastic Flow at Frictional Boundaries

2003 ◽  
Vol 70 (2) ◽  
pp. 212-219 ◽  
Author(s):  
S. Alexandrov
Keyword(s):  
Channel Flow ◽  
Friction Surface ◽  
Qualitative Difference ◽  
Strain Rate Tensor ◽  
Parallel Plates ◽  
Maximum Friction ◽  
Classical Plasticity ◽  
Pressure Independent ◽  
Pressure Dependent Plasticity ◽  
Friction Surfaces

The qualitative difference in solution behavior in the vicinity of maximum friction surfaces is demonstrated for two distinct models of pressure-dependent plasticity (the double-shearing and coaxial models) using closed-form solutions for planar flow through an infinite wedge-shaped channel and plane-strain compression of an infinite block between parallel plates. Singular velocity fields (some components of the strain rate tensor approach infinity at the friction surface) occur in the solutions based on the double-shearing model. This is similar to behavior in the vicinity of maximum friction surfaces in classical plasticity of pressure-independent materials. A singular velocity field is also obtained in the solution based on the coaxial model for the problem of channel flow; but, in contrast to the double-shearing model and classical plasticity, sticking must occur at this friction surface. For the problem of compression of a material obeying the coaxial model, no solution based on conventional assumptions exists with the maximum friction law. This is quite different from both the corresponding solution based on the double-shearing model and the channel flow solution based on the coaxial model.

Effect of Plastic Anisotropy on the Strain Rate Intensity Factor: A Simple Analytic Solution

2014 ◽  
Vol 626 ◽  
pp. 240-245
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Hguyen Minh Tuan ◽  
Natalia Kalenova
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Analytic Solution ◽  
Equivalent Strain ◽  
Maximum Friction ◽  
Equivalent Strain Rate ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity ◽  
Friction Surfaces

Solutions for many rigid/plastic models are singular in the vicinity of maximum friction surfaces. In particular, the magnitude of the equivalent strain rate near such surfaces is controlled by the strain rate intensity factor. This factor is the coefficient of the leading singular term is a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since the equivalent strain rate has a great effect of material properties, it is of important to reveal the dependence of the strain rate intensity factor on parameters characterizing material models. In the present paper, quite a general model of anisotropic plasticity under plane strain conditions is adopted. Then, using an analytic solution for instantaneous compression of a layer of plastic material between two parallel plates the effect of the shape of the yield locus on the asymptotic behavior of the equivalent strain rate in the vicinity of the friction surface is demonstrated.

An Effect of Plastic Anisotropy on the Strain Rate Intensity Factor

2010 ◽  
Author(s):  
Sergei Alexandrov
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Plastic Anisotropy ◽  
Rigid Plastic ◽  
Maximum Friction ◽  
Perfectly Plastic ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity ◽  
Friction Surfaces

The strain rate intensity factor in the theory of rigid perfectly plastic isotropic materials is the coefficient of the principal singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. This coefficient can be used to predict the evolution of material properties in a narrow layer in the vicinity of surfaces where the friction stress is high. Usually, conventional evolution equations are not compatible with the plasticity equations near maximum friction surfaces. It is therefore of interest to extend the theories based on the strain rate intensity factor to more general models than the rigid perfectly plastic isotropic solids. The present paper deals with plane strain deformation of rigid plastic anisotropic material. It is shown by means of a simple analytic solution that the velocity field is singular in the vicinity of maximum friction surfaces. Thus the strain rate intensity factor can be introduced for such materials. An effect of plastic anisotropy on its value is demonstrated. In addition, it is shown that rigid plastic solutions for anisotropic materials can exhibit various types of singularity in the vicinity of maximum friction surfaces, in contrast to isotropic materials where one type only is possible. Nevertheless, in most cases the type of singularity is same for isotropic and anisotropic materials.

An Approach to Predicting Evolution of Material Properties Near Surfaces With High Friction in Metal Forming

2005 ◽  
Author(s):  
S. Alexandrov
Keyword(s):  
Strain Rate ◽  
Material Properties ◽  
Evolution Equations ◽  
Plastic Material ◽  
Equivalent Strain ◽  
Maximum Friction ◽  
Perfectly Plastic ◽  
Equivalent Strain Rate ◽  
Strain Rate Intensity ◽  
Friction Surfaces

In the case of rigid/perfectly plastic material, the velocity fields in the vicinity of maximum friction surfaces must be describable by nondifferentiable functions. In particular, the equivalent strain rate follows an inverse square root rule near such surfaces and, therefore, approaches infinity at the surface. Because the equivalent strain rate is involved in many evolution equations for material properties, its behavior near the maximum friction surfaces should lead to high gradients in the material properties near the surface, which is confirmed by experiment. To quantitatively describe the evolution of material properties in the vicinity of surfaces with high friction, the concept of strain rate intensity factor can be adopted.

scholarly journals An Accurate Upper Bound Solution for Plane Strain Extrusion through a Wedge-Shaped Die

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sergei Alexandrov ◽  
Yusof Mustafa ◽  
Yeong-Maw Hwang ◽  
Elena Lyamina
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Friction Stress ◽  
Velocity Fields ◽  
Singular Behavior ◽  
Shear Yield Stress ◽  
Bound Solution ◽  
Shear Yield ◽  
Friction Surfaces ◽  
Very High

An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high.

Ductile Fracture in Metal Forming: A Review of Selected Issues

2012 ◽  
Vol 528 ◽  
pp. 1-11 ◽  
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina
Keyword(s):  
Free Surface ◽  
Ductile Fracture ◽  
Experimental Method ◽  
Metal Forming ◽  
Experimental Methods ◽  
Fracture Criteria ◽  
Surface Fracture ◽  
Maximum Friction ◽  
Ductile Fracture Criteria ◽  
Friction Surfaces

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.

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