Expanding Cavity Model Combined With Johnson–Cook Constitutive Equation for the Dynamic Indentation Problem

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Kiyohiro Ito ◽  
Masayuki Arai
Keyword(s):  
Constitutive Equation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Equivalent Plastic Strain ◽  
Ductile Material ◽  
Plastic Strain Rate ◽  
Small Object ◽  
Cavity Model ◽  
Dynamic Indentation ◽  
Indentation Problem

Abstract The indentation formed on a metallic component by the high-velocity impingement of a small object can fracture the component, and this is known as foreign object damage. In this type of dynamic indentation, it is necessary to consider the effects of work hardening, strain rate hardening, and thermal softening in the impinged material. In this study, in order to consider these effects, the expanding cavity model based on a spherical formulation is modified via the Johnson–Cook constitutive equation for the dynamic indentation problem. Additionally, an equation is developed based on energy conservation and the modified expanding cavity model to predict the size of the indentation formed by an impingement of a solid sphere (EPIS). The distributions of equivalent plastic strain, equivalent plastic strain rate, temperature, and equivalent von Mises stress obtained via the expanding cavity model were in good agreement with the data obtained from the finite element analysis (FEA). Furthermore, it was demonstrated that EPIS accurately predicted the indentation size formed on various metallic materials at several impingement velocities in the range of 50–300 m/s. Consequently, EPIS can be effectively applied to an impingement problem of a hard sphere onto a sufficiently thick ductile material within 300 m/s without any help of FEA.

Prediction of Indentation Size Formed by a High-Velocity Impingement of a Solid Sphere Based on an Expanding Cavity Model

2019 ◽  
Vol 827 ◽  
pp. 355-360 ◽  
Author(s):  
Kiyohiro Ito ◽  
Masayuki Arai
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
High Velocity ◽  
Turbine Blades ◽  
Equivalent Plastic Strain ◽  
Solid Sphere ◽  
Von Mises Stress ◽  
Plastic Strain Rate ◽  
Cavity Model ◽  
Indentation Size

The fan blades and turbine blades in a jet engine are seriously damaged by high velocity impingements of various foreign objects. In this study, a prediction method of indentation size formed by a high-velocity impingement of a solid sphere (PMIS) was developed from a theoretical model based on an expanding cavity model and energy conservation before and after impingement. The Johnson-Cook constitutive equation was employed to introduce effects of work hardening, strain rate hardening and thermal softening into the cavity model. As a result, the distribution of equivalent plastic strain, equivalent plastic strain rate, temperature and equivalent von Mises stress estimated using the expanding cavity model was in good agreement with the data obtained from the finite element analysis. In addition, it has been demonstrated that PMIS can accurately predict the radius of indentation formed on various metallic materials subjected to the impingement of a solid sphere with the radii of 0.75, 1.5 and 3 mm at several impact velocities from 50 to 300 m/s.

Numerical Simulation Study of Quasi-Static Loading and Dynamic Loading for Micro Bending Forming of Copper Foil

2016 ◽  
Vol 723 ◽  
pp. 503-511
Author(s):  
Wen Hao Zhang ◽  
Qing Qian ◽  
Zong Bao Shen ◽  
You Juan Ma ◽  
Hui Xia Liu
Keyword(s):  
Numerical Simulation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Static Loading ◽  
Shock Loading ◽  
Equivalent Plastic Strain ◽  
Plastic Strain Rate ◽  
Laser Shock ◽  
Feature Size

A variety of micro forming processes has been invented, and the size effects have become a research hotspot at home and abroad. Micro bending molds with different feature sizes were designed. Quasi-static tester loading and dynamic laser shock loading with soft punch for micro bending forming was studied by numerical simulation respectively based on ANSYS implicit analysis and LS-DYNA explicit analysis. The constitutive models of workpiece are bilinear kinematic hardening model and Johnson-cook model respectively. The effects of different loading conditions and feature sizes of the die on the forming depth, equivalent plastic strain and equivalent plastic strain rate were studied. The results of numerical simulation show that, with the increasing of feature size of the mold, the forming depth under two kinds of loading conditions shows a tendency to increase. In dynamic laser shock loading, the equivalent plastic strain and equivalent plastic strain rate of the key position of the bent part would decrease with the increasing of the feature size of the die. While in quasi-static loading, the opposite law is shown. The research shows that, the flexible micro-bending processes with different loading models showed similar size effect. However, compared with quasi-static loading, in dynamic loading, the strain of forming parts is more centralized, and there is a high strain rate and better formability of the workpiece.

An Experimental Study on the Effect of Prior Plastic Straining on Creep Behavior of 304 Stainless Steel

1993 ◽  
Vol 115 (2) ◽  
pp. 200-203 ◽  
Author(s):  
Z. Xia ◽  
F. Ellyin
Keyword(s):  
Stainless Steel ◽  
Plastic Strain ◽  
Strain Rate ◽  
Creep Behavior ◽  
Test Procedure ◽  
Constant Strain Rate ◽  
304 Stainless Steel ◽  
Creep Model ◽  
Plastic Strain Rate ◽  
Creep Tests

Constant strain-rate plastic straining followed by creep tests were conducted to investigate the effect of prior plastic straining on the subsequent creep behavior of 304 stainless steel at room temperature. The effects of plastic strain and plastic strain-rate were delineated by a specially designed test procedure, and it is found that both factors have a strong influence on the subsequent creep deformation. A creep model combining the two factors is then developed. The predictions of the model are in good agreement with the test results.

An Assessment of the Method Used to Determine Activation Parameters in L12 Alloys

1998 ◽  
Vol 552 ◽  
Author(s):  
B. Matterstock ◽  
G. Saada ◽  
J. Bonneville ◽  
J. L Martin
Keyword(s):  
Mechanical Properties ◽  
Theoretical Analysis ◽  
Plastic Strain ◽  
Strain Rate ◽  
Characteristic Time ◽  
Constant Strain Rate ◽  
Activation Parameters ◽  
Plastic Strain Rate ◽  
Clear Indication ◽  
Load Relaxation

ABSTRACTThe characterisation of dislocation mechanisms in connection with macroscopic mechanical properties are usually performed through transient tests, such as strain-rate jumps, load relaxations or creep experiments. The present paper includes a careful and complete theoretical analysis of the relaxation and the creep kinetics. We experimentally show that the plastic strain-rate is continuous at the transition between constant strain-rate conditions and both load relaxation and creep test. The product of the plastic strain-rate at the onset of the transient test () with the characteristic time (tk) of the transient is found to be independent of , as theoretically expected. This is a clear indication that the assumptions underlying the theoretical analysis are relevant.

Calculation of Material Flow in Orthogonal Cutting by Using Streamline Model

2009 ◽  
Vol 407-408 ◽  
pp. 490-493 ◽  
Author(s):  
Xue Feng Bi ◽  
Gautier List ◽  
Yong Xian Liu
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Line Shape ◽  
Material Flow ◽  
General Equation ◽  
Flow Line ◽  
Orthogonal Cutting ◽  
Plastic Strain Rate ◽  
Complex Variation ◽  
Streamline Method

The streamline method was used to investigate the plastic strain rate in machining. The streamline function presented in this paper is a general equation with three parameters controlling the complex variation of flow line shape. Velocity and deformation field were obtained by streamline analysis. The validation of this model was conducted by comparing with other experimental results published. It shows that the streamline model presented in the paper can be applied to the evaluation of strain rate in machining.

scholarly journals How to Realize Volume Conservation During Finite Plastic Deformation

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Heling Wang ◽  
Dong-Jie Jiang ◽  
Li-Yuan Zhang ◽  
Bin Liu
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Strain Rate ◽  
Strain Rate Tensor ◽  
Cauchy Stress ◽  
Volume Conservation ◽  
Tangential Stiffness ◽  
Manufacture Process ◽  
Universal Approach

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

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