scholarly journals A New Viscosity Constitutive Model for Generalized Newtonian Fluids Using Theory of Micropolar Continuum

2020 ◽  
pp. 120-134
Author(s):  
Muhammad Sabeel Khan
Keyword(s):  
Constitutive Model ◽  
Flow Behavior ◽  
Constitutive Relations ◽  
Shear Thickening ◽  
Blood Rheology ◽  
Newtonian Fluids ◽  
Model Parameters ◽  
Micropolar Continuum ◽  
Generalized Newtonian Fluids ◽  
Contour Plots

In this paper, a new viscosity constitutive relation for the analysis of generalized Newtonian fluids is presented and analyzed. The theory of micropolar continuum is considered for the derivation of constitutive relations where the kinematics at the macroscopic level leads to incorporate the micro-rotational effects in existing rheology of Carreau Yasuda model. It provides a more realistic approach to analyze the flow behavior of generalized Newtonian fluids. To the best of author’s knowledge such generalization of the existing rheology of Carreau-Yasuda is not present in literature. In order to show the effects of micro-rotations on the viscosity of generalized fluids, different computational experiments are performed using finite volume method (FVM). The method is implemented and validated for accuracy by comparison with existing literature in the limiting case through graphs and tables and a good agreement is achieved. It is observed that with the increase of micro-rotations the shear thinning phenomena slower down whereas the shear thickening is enhanced. Moreover, the effects of various model parameters on horizontal and vertical velocities as well as on boundary layer thickness are shown through graphs and contour plots It is worth mentioning that the proposed constitutive model can be utilized to analyze the generalized Newtonian fluids and has wider applications in blood rheology.

scholarly journals A Flow Stress Model of 300M Steel for Isothermal Tension

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 252
Author(s):  
Rongchuang Chen ◽  
Shiyang Zhang ◽  
Xianlong Liu ◽  
Fei Feng
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
Tensile Deformation ◽  
Flow Behavior ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Average Deviation ◽  
Cross Sectional ◽  
300M Steel

To investigate the effect of hot working parameters on the flow behavior of 300M steel under tension, hot uniaxial tensile tests were implemented under different temperatures (950 °C, 1000 °C, 1050 °C, 1100 °C, 1150 °C) and strain rates (0.01 s−1, 0.1 s−1, 1 s−1, 10 s−1). Compared with uniaxial compression, the tensile flow stress was 29.1% higher because dynamic recrystallization softening was less sufficient in the tensile stress state. The ultimate elongation of 300M steel increased with the decrease of temperature and the increase of strain rate. To eliminate the influence of sample necking on stress-strain relationship, both the stress and the strain were calibrated using the cross-sectional area of the neck zone. A constitutive model for tensile deformation was established based on the modified Arrhenius model, in which the model parameters (n, α, Q, ln(A)) were described as a function of strain. The average deviation was 6.81 MPa (6.23%), showing good accuracy of the constitutive model.

Linear analysis of parameters in Arrhenius model for Ti-6Al-4V at superplastic forming

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Junzhou Yang ◽  
Jianjun Wu ◽  
Qianwen Zhang ◽  
Yinxiang Ren ◽  
Han Ruolan ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Flow Behavior ◽  
Superplastic Forming ◽  
Tensile Tests ◽  
Model Parameters ◽  
Content Type ◽  
Forming Mechanism ◽  
Good Ability ◽  
Titanium Material ◽  
High Temperature Tensile

Purpose With the discussion on the linear relationship of determined material parameters, this study aims to propose a new method to analyze the deformation mechanism. Design/methodology/approach A modified constitutive model based on the hyperbolic sine Arrhenius equation has been established, which is applied to describe the flow behavior of Ti-6Al-4V alloy during the superplastic forming (SPF). Findings The modified constitutive model in this work has a good ability to describe the flow behavior for Ti-6Al-4V in SPF. Besides, a deformation map of titanium material is obtained based on the parameters. As the supplement, finite element models of high-temperature tensile tests are carried out as the application of the constitutive model. Originality/value The relationship between constitutive model parameters and forming mechanism is established, which is a new angle in rheological behavior research and constitutive model analysis.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

The Constitutive Model for High Temperature Flow Behavior of SiC/6168Al Composite

2015 ◽  
Vol 1089 ◽  
pp. 37-41
Author(s):  
Jiang Wang ◽  
Sheng Li Guo ◽  
Sheng Pu Liu ◽  
Cheng Liu ◽  
Qi Fei Zheng
Keyword(s):  
Constitutive Model ◽  
Hot Deformation ◽  
Flow Behavior ◽  
Type Equation ◽  
Strain Rate Range ◽  
Compression Tests ◽  
Stress Strain ◽  
Hollomon Parameter ◽  
Proposed Model ◽  
Relationship Of

The hot deformation behavior of SiC/6168Al composite was studied by means of hot compression tests in the temperature range of 300-450 °C and strain rate range of 0.01-10 s-1. The constitutive model was developed to predict the stress-strain curves of this composite during hot deformation. This model was established by considering the effect of the strain on material constants calculated by using the Zenter-Hollomon parameter in the hyperbolic Arrhenius-type equation. It was found that the relationship of n, α, Q, lnA and ε could be expressed by a five-order polynomial. The stress-strain curves obtained by this model showed a good agreement with experimental results. The proposed model can accurately describe the hot flow behavior of SiC/6168Al composite, and can be used to numerically analyze the hot forming processes.

Constitutive Modeling for Elevated Temperature Flow Behavior of ZHMn34-2-2-1 Manganese Brass

2017 ◽  
Vol 872 ◽  
pp. 30-37
Author(s):  
Meng Han Wang ◽  
Kang Wei ◽  
Xiao Juan Li
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Flow Behavior ◽  
Peak Stress ◽  
Strain Rates ◽  
Hollomon Parameter ◽  
Prediction Ability ◽  
Absolute Relative Error ◽  
Deformation Behaviors ◽  
State Stress

The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures (923K-1073K) and strain rates (0.01s-1-10s-1). The true stress-strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. A revised constitutive model coupling flow stress with strain, strain rate and deformation temperature is established with the material constants expressed by polynomial fitting of strain. Moreover, better prediction ability of the constitutive model is achieved by implementation of a simple approach for modified the Zener-Hollomon parameter considering the compensation of strain rate and temperature increment. By comparing the predicted and experimented values, the correlation coefficient and mean absolute relative error are 0.997 and 2.363%, respectively. The quantitative statistical results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.

Study on Multi-Axial Mechanical Properties of a Polyurethane Foam and Experimental Verification

2011 ◽  
Vol 311-313 ◽  
pp. 301-308
Author(s):  
Shou Hong Han ◽  
Zhen Hua Lu ◽  
Yong Jin Liu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Polyurethane Foam ◽  
Axial Compression ◽  
Axial Loading ◽  
Hydrostatic Compression ◽  
Model Parameters ◽  
Loading Conditions ◽  
Three Point Bending ◽  
Pu Foam

In order to investigate the multi-axial mechanical properties of a kind of PU (polyurethane) foam, some experiments in different loading conditions including uni-axial tension, uni-axial compression, hydrostatic compression and three-point bending were conducted. It is shown that the hydrostatic component influences yield behavior of PU foam, the yield strength and degree of strain hardening in hydrostatic compression exceed those for uni-axial compression. In terms of the differential hardening constitutive model, the evolution of PU foam yield surface and plastic hardening laws were fitted from experimental data. A finite element method was applied to analyze the quasi-static responses of the PU foam sandwich beam subjected to three-point bending, and good agreement was observed between experimental load-displacement responses and computational predictions, which validated the multi-axial loading methods and stress-strain constitutive model parameters. Moreover, effects of two foam models applied to uni-axial loading and multi-axial loading conditions were analyzed and compared with three-point bending tests and simulations. It is found that the multi-axial constitutive model can bring more accurate prediction whose parameters are obtained from the tests above mentioned.

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