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.

Ductile Fracture Modeling of DH36 Grade Steels

2018 ◽  
Author(s):  
Burak Can Cerik ◽  
Sung-Ju Park ◽  
Joonmo Choung
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Fracture Surface ◽  
Ductile Fracture ◽  
Stress Triaxiality ◽  
Local Stress ◽  
Fracture Initiation ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Element Analysis

A Hosford-Coulomb type ductile fracture surface was developed for DH36 grade steels. The fracture experiments reported in the literature, which consist of tests with notched tensile specimens, tensile specimens with a central hole, shear specimen and disc specimens for punch specimens, were utilized in a detailed finite element analysis of each experiment to evaluate the evolution of local stress and strain fields and identify plasticity and fracture response of DH36. The developed plasticity model consists of a von Mises yield surface, an associated flow rule and a combined Swift-Voce type isotropic hardening rule. The loading paths to fracture initiation were determined in terms of stress triaxiality and normalized Lode angle parameter histories. Finally, the Hosford-Coulomb fracture surface was calibrated using the finite element analysis results and adapting a linear damage accumulation law.

Descriptions of Reversed Yielding in Internally Pressurized Tubes

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Woncheol Jeong ◽  
Kwansoo Chung
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Kinematic Hardening ◽  
Material Model ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Law ◽  
Solving Equations ◽  
Associated Flow Rule ◽  
Reversed Deformation

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

Plastic Instability of Cylindrical Shells With Rigid End Closures

1963 ◽  
Vol 30 (3) ◽  
pp. 401-409 ◽  
Author(s):  
Martin A. Salmon
Keyword(s):  
Yield Criterion ◽  
Spherical Shape ◽  
Plastic Instability ◽  
Maximum Pressure ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Modulus ◽  
Pressure Maximum ◽  
Three Stages ◽  
Associated Flow Rule

Solutions are obtained for the large plastic deformations of a cylindrical membrane with rigid end closures subjected to an internal pressure loading. A plastic linearly hardening material obeying Tresca’s yield criterion and the associated flow rule is considered. It is found that, in general, a shell passes through three stages of deformation, finally assuming a spherical shape. The instability pressure (maximum pressure) may be reached in any of the stages depending on the length/diameter ratio of the shell and the hardening modulus of the material. Although numerical integration is required to obtain solutions for shells in the first stages of deformation, the solution in the final stage is given in closed form.

Experimental and Numerical Study of Ductile Fracture Initiation in Aluminum 6061-T6

2015 ◽  
Author(s):  
W. Rekik ◽  
O. Ancelet ◽  
C. Gardin
Keyword(s):  
Numerical Simulation ◽  
Ductile Fracture ◽  
Void Growth ◽  
Numerical Study ◽  
Micromechanical Model ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Compact Tension ◽  
Growth Ratio ◽  
Ductile Fracture Initiation

This work deals with the characterization of ductile damage in Aluminum 6061-T6 alloy. In this paper we discuss the stress triaxiality effect on the initiation and the evolution of damage through a sequence of tensile tests conducted on round specimens with different rate of trixialities and tearing tests on precracked Compact Tension specimens. Scattering of ductility and toughness values was highlighted between the three characteristic directions studied in this topic. Based on the experimental results, numerical simulation has been performed in order to analyze and predict ductile fracture initiation of this aluminum alloy by simulating void growth according to the Rice-Tracey micromechanical model. The numerical simulation was conducted in two steps: first the critical void growth ratio (R / R0)c was evaluated for tensile cylindrical specimens with different degrees of triaxiality and then used to analyze crack growth initiation on Compact Tension specimen. Due to the Al-6061-T6 highly sensitivity to triaxiality, a necessary adaptation of the Rice-Tracey model’s coefficient was made.

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.

Assessment of Gurson-Tveergard-Needleman Model Under High Stress Triaxiality

2016 ◽  
Author(s):  
Jiru Zhong ◽  
Tong Xu ◽  
Kaishu Guan
Keyword(s):  
Ductile Fracture ◽  
Volume Fraction ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Tensile Specimen ◽  
Void Volume Fraction ◽  
Model Parameters ◽  
Gtn Model ◽  
Notched Specimens ◽  
Critical Void

The Gurson-Tveergard-Needleman (GTN) model has been widely used to describe ductile fracture. In this paper, a series of tensile tests were carried out on notched specimens to assess the GTN model. The GTN model parameters were calibrated from a smooth tensile specimen by a hybrid particle swarm optimization, and the reliability of the calibrated parameters was verified by the profile of the smooth tensile specimen. The calibrated parameters were used to predict the ductile fracture of notched specimens. A comparison of fracture initiation sites between simulations and experiments indicates that the GTN model has a good performance on predicting fracture initiation site but fails at predicting fracture moment. The assessment of the transformability of the GTN model parameters was performed by comparing the load-displacement curves between simulations and experiments. It is observed that the GTN model parameters are material constant, except the critical void volume fraction fc. The influence of stress triaxiality on the critical void volume fraction fc is also discussed.

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.

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