scholarly journals Theoretical predictions of dynamic necking formability of ductile metallic sheets with evolving plastic anisotropy and tension-compression asymmetry

2021 ◽  
Author(s):  
Murlidhar Anil Kumar ◽  
Komi Espoir N'souglo ◽  
navab hosseini ◽  
Nicolas Jacques ◽  
Jose Rodriguez-Martinez
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Plastic Anisotropy ◽  
Theoretical Models ◽  
Unit Cell ◽  
Forming Limit ◽  
Plastic Behavior ◽  
Zone Model ◽  
Wide Range ◽  
The Stability

In this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion [10] which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation [37]. From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. [32] –which investigated materials with yielding described by the orthotropic criterion of Hill [19]– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s−1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations

scholarly journals A three-pronged approach to predict the effect of plastic orthotropy on the formability of thin sheets subjected to dynamic biaxial stretching

2020 ◽  
Author(s):  
Jose Rodriguez-Martinez ◽  
Komi Espoir N'souglo ◽  
Nicolas Jacques
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Zone Model ◽  
Strain Rates ◽  
Biaxial Stretching ◽  
Loading Paths ◽  
Finite Element Calculations ◽  
The Stability

In this paper, we have investigated the effect of material orthotropy on the formability of metallic sheets subjectedto dynamic biaxial stretching. For that purpose, we have devised an original three-pronged methodology which includes a linear stability analysis, a nonlinear two-zone model and ?finite element calculations. We have studied 5 different materials whose mechanical behavior is described with an elastic isotropic, plastic anisotropic constitutive model with yielding based on Hill (1948) criterion. The linear stability analysis and the nonlinear two-zone model are extensions of the formulations developed by Zaera et al. (2015) and Jacques (2020), respectively, to consider Hill (1948) plasticity. The ?finite element calculations are performed with ABAQUS/Explicit (2016) using the unit-cell model developed by Rodriguez-Martinez et al. (2017), which includes a sinusoidal spatial imperfection to favor necking localization. The predictions of the stability analysis and the two-zone model are systematically compared against the ?finite element results --which are considered as the reference approach to validate the theoretical models-- for loading paths ranging from plane strain stretching to equibiaxial stretching, and for different strain rates ranging from 100 s-1 to 50000 s-1. The stability analysis and the two-zone model yield the same overall trends obtained with the ?finite element simulations for the 5 materials investigated, and for most of the strain rates and loading paths the agreement for the necking strains is also quantitative. Notably, the differences between the ?finite element results and the two-zone model rarely go beyond 5%. Altogether, the results presented in this work provide new insights into the mechanisms which control dynamic formability of anisotropic metallic sheets.

Influence of a localized plastic layer on embankment stability

1977 ◽  
Vol 14 (4) ◽  
pp. 524-530 ◽  
Author(s):  
C. D. Thompson ◽  
J. J. Emery
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Clayey Soil ◽  
Plastic Material ◽  
Plastic Layer ◽  
Natural Soil ◽  
General Terms ◽  
Clayey Silt ◽  
The Stability ◽  
Embankment Stability

Conventional stability analyses of a 47 ft (14.3 m) high embankment constructed of clayey silt fill indicated a satisfactory design with 2:1 slopes. However, cracking of the fill and movements of the embankment occurred when its height reached 32 ft (9.8 m). Investigation revealed that, in general terms, the geotechnical profile employed for the stability analysis was satisfactory. There was a localized layer of firm clayey soil at the interface between the fill and natural soil, which coincided with the observed cracks and the zone of high pore pressure.Construction scheduling was critical, and an initial wedge analysis showed that a 17 ft (5.2 m) high berm would ensure adequate safety during completion of the fill. A detailed investigation followed to determine the actual deformation mechanism responsible for the cracking. This included plane strain finite element runs using estimated moduli values. It was concluded that the cracking was caused by ‘spreading’ of plastic material at or near the base of the embankment. This case history illustrates that localized layers of weaker soil can be critical even when construction has been carefully controlled.

Stability and Response of Rotors Supported on Active Magnetic Bearings

1993 ◽  
Author(s):  
K. Ramesh ◽  
R. G. Kirk
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Transfer Matrix ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Finite Element Program ◽  
Element Program ◽  
Matrix Codes ◽  
The Stability

Abstract A PC-based program has been developed which is capable of performing stability analysis and response calculations of rotor-bearing systems. The paper discusses the modeling of rotors supported on active magnetic bearings (AMB) and highlights the advantages in the modeling using the finite element method, over the transfer matrix method. An 8-stage centrifugal compressor supported on AMB was chosen for the case study. The results for the stability analysis, obtained using the finite element program was compared with those obtained by the well established transfer matrix codes. The results of unbalance response, including the effects of sensor non collocation are presented and this demonstrates how an AMB supported rotor can experience a synchronous instability for selected sensor locations and balance distributions.

scholarly journals Theoretical stability analysis of mixed finite element model of shale-gas flow with geomechanical effect

2020 ◽  
Vol 75 ◽  
pp. 33
Author(s):  
Mohamed F. El-Amin ◽  
Jisheng Kou ◽  
Shuyu Sun
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Shale Gas ◽  
Gas Flow ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Model ◽  
Mathematical Proofs ◽  
The Stability ◽  
Shale Gas Transport

In this work, we introduce a theoretical foundation of the stability analysis of the mixed finite element solution to the problem of shale-gas transport in fractured porous media with geomechanical effects. The differential system was solved numerically by the Mixed Finite Element Method (MFEM). The results include seven lemmas and a theorem with rigorous mathematical proofs. The stability analysis presents the boundedness condition of the MFE solution.

The Solution of Lateral Heat Loss Problem Using Collocation Method with Cubic B-Splines Finite Element

2011 ◽  
Vol 110-116 ◽  
pp. 3184-3190
Author(s):  
Necdet Bildik ◽  
Duygu Dönmez Demir
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Heat Loss ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
B Splines ◽  
Stability Method ◽  
The Stability ◽  
Lateral Heat

This paper deals with the solutions of lateral heat loss equation by using collocation method with cubic B-splines finite elements. The stability analysis of this method is investigated by considering Fourier stability method. The comparison of the numerical solutions obtained by using this method with the analytic solutions is given by the tables and the figure.

Multiscale Finite Element Modeling of Alumina Ceramics Undergoing Laser-Assisted Machining

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Xiangyang Dong ◽  
Yung C. Shin
Keyword(s):  
Finite Element ◽  
High Temperatures ◽  
Cutting Forces ◽  
Cohesive Zone Model ◽  
Multiscale Approach ◽  
Zone Model ◽  
Alumina Ceramics ◽  
Weight Percentage ◽  
Laser Assisted Machining ◽  
Wide Range

Alumina ceramics, due to their excellent properties of high hardness, corrosion resistance, and low thermal expansion coefficient, are important industrial materials with a wide range of applications, but these materials also present difficulty in machining with low material removal rates and high tool wear. This study is concerned with laser-assisted machining (LAM) of high weight percentage of alumina ceramics to improve the machinability by a single point cutting tool while reducing the cutting forces. A multiscale model is developed for simulating the machining of alumina ceramics. In the polycrystalline form, the properties of alumina ceramics are strongly related to the glass interface existing in their microstructure, particularly at high temperatures. The interface is characterized by a cohesive zone model (CZM) with the traction–separation law while the alumina grains are modeled as continuum elements with isotropic properties separated by the interface. Bulk deformation and brittle failure are considered for the alumina grains. Molecular dynamics (MD) simulations are carried out to obtain the atomistic structures and parameterize traction–separation laws for the interfaces of different compositions of alumina ceramics at high temperatures. The generated parameterized traction–separation laws are then incorporated into a finite element model in Abaqus to simulate the intergranular cracks. For validation purposes, simulated results of the multiscale approach are compared with the experimental measurements of the cutting forces. The model is successful in predicting cutting forces with respect to the different weight percentage and composition of alumina ceramics at high temperatures in LAM processes.

Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals

2000 ◽  
Vol 123 (4) ◽  
pp. 409-416 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Plastic Behavior ◽  
Computational Results ◽  
Sheet Metals ◽  
Element Analysis ◽  
The Matrix

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

Finite Element Analysis for the Stiffness and the Buckling of Corrugated Tubes in Heat Exchanger

2012 ◽  
Vol 468-471 ◽  
pp. 1675-1680 ◽  
Author(s):  
Xiao Jing Wang ◽  
Zhi Min Wang ◽  
Nian Wang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stability Analysis ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
External Pressure ◽  
Element Analysis ◽  
Value Analysis ◽  
Compressive Pressure ◽  
The Stability

Corrugated tubes in a heat exchanger are analyzed by using the FEA methods. And the formula how to compute single wave’s rigidity is obtained. Besides, methods of analyzing the stability of corrugated tubes under internal compressive pressure and external pressure are proposed which include characteristic value analysis and non-linear stability analysis, thus providing theory basis for the stability research of heat exchangers.

Stability Analysis about the Impact of Soft Rock to the Underground Cavern Group

2013 ◽  
Vol 706-708 ◽  
pp. 560-564
Author(s):  
Yi Huan Zhu ◽  
Guo Jian Shao ◽  
Zhi Gao Dong
Keyword(s):  
Finite Element ◽  
Rock Mass ◽  
Stability Analysis ◽  
Soft Rock ◽  
Element Model ◽  
Underground Excavation ◽  
Power Station ◽  
Excavation Process ◽  
The Stability ◽  
The Impact

Soft rock is frequently encountered in underground excavation process. It is difficult to excavate and support in soft rock mass which has low strength, large deformation and needs much time to be out of shape but little time to be self-stabilized. Based on a large underground power station, finite element model analysis was carried out to simulate the excavation process and the results of displacement, stress and plasticity area were compared between supported and unsupported conditions to evaluate the stability of the rock mass.

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