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.

Modelling of Damage Evolution in the Vicinity of Frictional Interfaces in Metal Forming

2012 ◽  
Vol 579 ◽  
pp. 124-133
Author(s):  
Elena Lyamina ◽  
Sergei Alexandrov ◽  
Yeau Ren Jeng ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Rate ◽  
Ductile Fracture ◽  
Fracture Criterion ◽  
Equivalent Strain ◽  
Ductile Fracture Criterion ◽  
Equivalent Strain Rate ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity ◽  
Friction Surfaces

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.

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.

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.

Developing the concept of the strain rate intensity factor in plasticity theory

2003 ◽  
Vol 48 (3) ◽  
pp. 131-133 ◽  
Author(s):  
S. E. Aleksandrov ◽  
R. V. Goldshtein ◽  
E. A. Lyamina
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Plasticity Theory ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity

On the Prediction of the Strain Rate Intensity Factor in Metal Forming Processes

2008 ◽  
Author(s):  
Elena Lyamina
Keyword(s):  
Intensity Factor ◽  
Strain Rate ◽  
Closed Form ◽  
Upper Bound ◽  
Approximate Solutions ◽  
Closed Form Solutions ◽  
Perfectly Plastic ◽  
Strain Rate Intensity Factor ◽  
Rate Intensity ◽  
Strain Rate Intensity

The strain rate intensity factor is the coefficient of the principal singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Such singular behaviour occurs in the case of several rigid plastic models (rigid perfectly plastic solids, the double-shearing model, the double slip and rotation model, some of viscoplastic models). Since it is only possible to introduce the strain rate intensity factor for singular velocity fields, it is obvious that standard finite element codes cannot be used to calculate it. The currently available distributions of the strain rate intensity factor have been found from closed form solutions or with the use of simple approximate solutions (for instance upper bound solutions). Closed form solutions are available for boundary value problems with simple geometry (flow through infinite rough channels, compression of infinite layers between rough plates and so on) and, therefore, are mostly of academic interest. Simple approximate solutions can predict general tendencies in the distribution of the strain rate intensity factor but cannot predict its distribution with a sufficient accuracy for industrial applications. For, the strain rate intensity factor reflects a very local effect inherent in the velocity field whereas simple approximate methods, such as the upper bound method, estimate global parameters, such as the limit load. The purpose of the present research is to propose a special numerical technique for calculating the strain rate intensity factor in the case of plane strain deformation of rigid perfectly plastic materials and to verify it by means of comparison with an analytical solution. The technique is based on the method of Riemann.

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