scholarly journals An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2161
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Marina Rynkovskaya
Keyword(s):  
Strain Rate ◽  
Hollow Cylinder ◽  
Yield Criterion ◽  
Tube Hydroforming ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Equivalent Strain Rate ◽  
Pressure Independent

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

A Semi-Analytical 3-D Solution for Bending Under Tension

2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Bending Under Tension ◽  
Associated Flow Rule

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

scholarly journals An An Analysis of Strain Rate Distribution Using Streamline Model and A Quick Stop Device in Metal Cutting

2019 ◽  
Vol 22 (2) ◽  
pp. 136-142
Author(s):  
Osama Ali Kadhim ◽  
Fathi A. Alshamma
Keyword(s):  
Strain Rate ◽  
Chip Formation ◽  
Metal Cutting ◽  
Equivalent Strain ◽  
Element Analysis ◽  
Rate Distribution ◽  
Equivalent Strain Rate ◽  
Cumulative Plastic Strain ◽  
Cutting Speeds ◽  
Strain Rate Distribution

In this paper, a quick stop device technique and the streamline model were employed to study the chip formation in metal cutting. The behavior of chip deformation at the primary shear zone was described by this model. Orthogonal test of turning process over a workpiece of the 6061-T6 aluminum alloy at different cutting speeds was carried out. The results of the equivalent strain rate and cumulative plastic strain were used to describe the complexity of chip formation. Finite element analysis by ABAQUS/explicit package was also employed to verify the streamline model. Some behavior of formation and strain rate distribution differs from the experimental results, but the overall trend and maximum results are approximately close. In addition, the quick stop device technique is described in detail. Which could be used in other kinds of studies, such as the metallurgical observation.

scholarly journals Continuum modelling and simulation of granular flows through their many phases

2015 ◽  
Vol 779 ◽  
pp. 483-513 ◽  
Author(s):  
Sachith Dunatunga ◽  
Ken Kamrin
Keyword(s):  
Granular Media ◽  
Yield Criterion ◽  
Granular Flows ◽  
Material Point ◽  
Large Strains ◽  
Flow Rule ◽  
Flow Process ◽  
Viscoplastic Solid ◽  
Free Media ◽  
Nonlinear Deformations

We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure-sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the ${\it\mu}(I)$ inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A material point method (MPM) procedure is written for the simulation of this model and many demonstrations are provided in different geometries, which highlight the ability of the numerical model to handle transitions through dense and disconnected states. By using the MPM framework, extremely large strains and nonlinear deformations, which are common in granular flows, are representable. The method is verified numerically and its physical predictions are validated against many known experimental phenomena, such as Beverloo’s scaling in silo flows, jointed power-law scaling of the run-out distance in granular-column-collapse problems, and various known behaviours in inclined chute flows.

The Research and Optimization of a 6061 Aluminum Rectangular Tube Extrusion Using Porthole Dies According to the Parameter of Split Ratio

2012 ◽  
Vol 268-270 ◽  
pp. 391-395
Author(s):  
Shu Mei Lou ◽  
Guo Liang Xing ◽  
Sheng Xue Qin ◽  
Lin Jing Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain Rate ◽  
Equivalent Strain ◽  
Tube Extrusion ◽  
Split Ratio ◽  
Die Structure ◽  
Rectangular Tube ◽  
Equivalent Strain Rate ◽  
Deform 3D

Extrusions of a 6061 aluminum rectangular tube using porthole dies with three assigned different split ratios were simulated by the software DEFORM-3D based on Finite element method. The distributions of stress, equivalent strain rate, temperature, velocity of the deformation materials and the mold stress during the three extrusion processes were obtained, respectively. By analyzing the distributions of those fields, the most reasonable split ratio is selected and then the die structure is modified.

scholarly journals A Method for Determining the Workability Diagram by Varying Friction Conditions in the Upsetting of a Cylinder between Flat Dies

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1411
Author(s):  
Dejan Movrin ◽  
Mladomir Milutinovic ◽  
Marko Vilotic ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Ductile Fracture ◽  
Yield Criterion ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Medium Carbon Steel ◽  
New Method ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Workability Diagram

This paper aims to develop a method for determining the workability diagram by varying frictional conditions in the cylinder upsetting test. The method is based on a known theoretical relationship between the average stress triaxiality ratio and in-surface strains if the initiation of fracture occurs at a traction-free surface. This relationship is valid for any rigid/plastic strain hardening material obeying the Mises-type yield criterion and its associated flow rule, which shows the wide applicability of the method. The experimental input to the method is the strain path at the site of fracture initiation. Neither experimental nor numerical determination of stress components is required at this site, though the general ductile fracture criterion involves the linear and quadratic invariants of the stress tensor. The friction law’s formulation is neither required, though the friction stress is the agent for varying the state of stress and strain at the site of ductile fracture initiation. The upsetting tests are carried out on normalized medium-carbon steel C45E, for which the workability diagram is available from the literature. Comparison of the latter and the diagram found using the new method shows that the new method is reliable for determining a certain portion of the workability diagram.

scholarly journals In Situ Stress Effects on Smooth Blasting: Model Test and Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Renshu Yang ◽  
Shizheng Fang ◽  
Aiyun Yang ◽  
Huanzhen Xie ◽  
Liyun Yang
Keyword(s):  
Strain Rate ◽  
Confining Pressure ◽  
Equivalent Strain ◽  
In Situ Stress ◽  
Image Correlation ◽  
Propagation Mechanism ◽  
Equivalent Strain Rate ◽  
Ground Stress ◽  
Smooth Blasting

Most of the roadway excavation is completed by the drilling and blasting method. With the increase of buried depth, the existence of ground stress will generate a significant impact on the rock blasting, especially on the smooth blasting. In this study, self-made homogeneous similar materials and digital image correlation methods were used to determine influence of ground stress on the smooth blasting under uniform explosive charge parameters and various in situ stress conditions. The results show that the crack outline after blasting changes from zigzag to straight in shape, and multifractal calculation results of the rupture section between blastholes show that the fracture surface becomes flatter as ground stress increases, which is conducive to roadway formation. The strain and equivalent strain rate obviously decrease as the distance between the blasthole and measuring points increases. The same trend occurs as the confining pressure goes up. Meanwhile, a postexplosion acoustic wave test indicates that confining pressure inhibits damage of the retained rock, which is consistent with strain and equivalent strain rate results. Finally, we discussed the crack propagation mechanism of rock in smooth blasting.

Chip Prediction in Finite Element Modeling of the Chip Formation Process during Cutting Ti-6Al-4V Alloy

2011 ◽  
Vol 418-420 ◽  
pp. 1148-1153
Author(s):  
Yu Gang Ye
Keyword(s):  
Finite Element ◽  
Titanium Alloy ◽  
Strain Rate ◽  
Equivalent Stress ◽  
Cutting Speed ◽  
Chip Thickness ◽  
Equivalent Strain ◽  
Forming Process ◽  
Serrated Chip ◽  
Equivalent Strain Rate

Based on the theory of adiabatic shearing, the forming process of a serrated chip during cutting Ti-6Al-4V titanium alloy was analyzed by comparing the results of the finite element (FE) calculations with the cutting experiments. The results show that the equivalent stress, equivalent strain and equivalent strain rate within a ribbon chip varied a little, but they varied a lot within a serrated chip. Moreover, the effect of cutting speed on equivalent strain rate is greater than on the equivalent stress and equivalent strain within a serrated chip. It can also be found from the results that there are small gaps between the simulation results and experimental results for the chip thickness and sawtooth height, while there is a big gap for saw-tooth pitch. This means that the simulation model has its limitations for accurate simulation of micro-geometric shape of a chip during cutting the Ti-6Al-4V titanium alloy, and further research remains to be done.

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