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.

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.

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.

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

Evaluation of prediction error resulting from using average state variables in the calibration of ductile fracture criterion

2017 ◽  
Vol 27 (8) ◽  
pp. 1231-1251 ◽  
Author(s):  
Xincun Zhuang ◽  
Yehui Meng ◽  
Zhen Zhao
Keyword(s):  
Ductile Fracture ◽  
Prediction Error ◽  
Fracture Criterion ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Equivalent Strain ◽  
State Variables ◽  
Ductile Fracture Criterion ◽  
Series Of Experiments ◽  
Relationship Of

In order to evaluate the prediction error resulting from using average state variables in the calibration procedure of the ductile fracture criterion, a series of experiments and corresponding simulations were performed to extract the evolution of fracture-related state variables such as stress triaxiality (η), Lode parameter, and equivalent strain to fracture at the fracture initiation points. The average stress triaxiality, average Lode parameter, and equivalent strain to fracture were used to calibrate the Lou-Huh (L-H) ductile fracture criterion. The average induced prediction error was evaluated by comparing the accumulated damage value, which was computed with the calibrated L-H ductile fracture criterion at the fracture initiation point, with the critical threshold value. Comparisons based on a series of experiments covering a wide range of values for stress triaxiality indicated the existence of an average induced prediction error for the compression tests, and demonstrated that different values of embedded-constants C1 and C2 of L-H ductile fracture criterion resulted in entirely different average induced prediction errors. Thus, a parameter study was performed to investigate the influences of C1, C2, the relationship of η and equivalent plastic strain ([Formula: see text]), and the internal function of the integral formula on the average induced relative error. The influence of the relationship of [Formula: see text] could be represented by the influence of the exponent a, the intercept for the stress triaxiality, and the allocation of equivalent strain for the segmented function. Among these influence factors, the value of C2, the value of the exponent a, and the value of the negative intercept for stress triaxiality contributed significantly to an increase in relative error.

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