Variational Estimates for the Elastoplastic Response of Particle-Reinforced Metal-Matrix Composites

Ductile solids reinforced by aligned elastic spheroidal inclusions, with overall transversely isotropic symmetry, are examined analytically in this paper. Estimates for the effective constitutive behavior of this class of composite materials are obtained in terms of simple optimization problems for general loading conditions, as functions of the particle stiffness, concentration and shape. In particular, explicit expressions are obtained for the yield functions of the composites. The results apply to composites with inclusion shapes ranging from continuous fibers (or needles in the limit of vanishingly small concentration), to approximately spherical, to continuous flat layers (or disks). As an example, we investigate a model composite of the type used in many structural applications, namely, 2124 Al–SiC which is made of a ductile matrix phase (Al) reinforced by hard brittle particles (SiC). The predicted stress-strain responses for these composites are compared with available experimental measurements and numerical calculations. Thus, it is shown that the constitutive model developed in this work predicts fairly accurately the uniaxial tensile experiments of Christman et al. (1989). In addition, the constitutive model is in good agreement with the periodic finite-element calculations of Tvergaard (1990) and Hom (1992), also for uniaxial loading conditions. A significant advantage of the analytical model proposed herein is that it can provide the constitutive response of composites under arbitrary loading conditions, without requiring complex numerical computations.

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An Anisotropic Constitutive Model for a Directionally Solidified Superalloy

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.340-341.901 ◽

2007 ◽

Vol 340-341 ◽

pp. 901-906 ◽

Cited By ~ 3

Author(s):

Masatsugu Yaguchi ◽

Masato Yamamoto ◽

Takashi Ogata ◽

Nobutada Ohno

Keyword(s):

Constitutive Model ◽

Inelastic Strain ◽

Transversely Isotropic ◽

Loading Conditions ◽

Directionally Solidified ◽

Creep Tests ◽

Static Recovery ◽

Calculation Results ◽

Multiaxial Creep ◽

Creep Loading

The monotonic tensile and creep deformations of a directionally solidified (DS) superalloy are investigated for several loading directions. The material exhibits remarkable anisotropy under elastic and creep loading conditions, whereas it shows isotropy under loading conditions of high strain rates. Tension-torsion creep tests are also conducted to investigate the deformation under multiaxial stress conditions. Referring to the observed behavior, a unified constitutive model, which has two features, is developed for the DS superalloy. One is a static recovery term of back stresses that is prescribed as a transversely isotropic property, which is supposed to have an effect on the deformation behavior under creep loading conditions. The other is the division of inelastic strain into two components, which represent octahedral and cubic slip system deformations, so as to describe multiaxial creep deformation. Calculation results obtained using the constitutive model are compared with the uniaxial and multiaxial experimental results to evaluate the validity of the model.

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Formulation of Inelastic Constitutive Model for Metal Matrix Composites. 1st Report, Transversely Isotropic Model .

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A ◽

10.1299/kikaia.60.1713 ◽

1994 ◽

Vol 60 (576) ◽

pp. 1713-1720

Author(s):

Masamichi Kawai

Keyword(s):

Constitutive Model ◽

Metal Matrix Composites ◽

Metal Matrix ◽

Transversely Isotropic ◽

Matrix Composites ◽

Isotropic Model

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A nonlinear strain-rate dependent constitutive model for uncured rubber materials under large deformation

Journal of Mechanics ◽

10.1093/jom/ufaa015 ◽

2020 ◽

Vol 37 ◽

pp. 118-125

Author(s):

Weihua Zhou ◽

Changqing Fang ◽

Huifeng Tan ◽

Huiyu Sun

Keyword(s):

Constitutive Model ◽

Large Deformation ◽

Mechanical Response ◽

Uniaxial Tensile ◽

Hysteresis Phenomenon ◽

Mechanical Behaviors ◽

Nonlinear Constitutive Model ◽

Rate Dependent ◽

Parallel Networks ◽

Non Gaussian

Abstract Uncured rubber possesses remarkable hyperelastic and viscoelastic properties while it undergoes large deformation; therefore, it has wide application prospects and attracts great research interests from academia and industry. In this paper, a nonlinear constitutive model with two parallel networks is developed to describe the mechanical response of uncured rubber. The constitutive model is incorporated with the Eying model to describe the hysteresis phenomenon and viscous flow criterion, and the hyperelastic properties under large deformation are captured by a non-Gaussian chain molecular network model. Based on the model, the mechanical behaviors of hyperelasticity, viscoelasticity and hysteresis under different strain rates are investigated. Furthermore, the constitutive model is employed to estimate uniaxial tensile, cyclic loading–unloading and multistep tensile relaxation mechanical behaviors of uncured rubber, and the prediction results show good agreement with the test data. The nonlinear mechanical constitutive model provides an efficient method for predicting the mechanical response of uncured rubber materials.

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A Flow Stress Model of 300M Steel for Isothermal Tension

Materials ◽

10.3390/ma14020252 ◽

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.311-313.301 ◽

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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Damage of Short-Fiber-Reinforced Metal Matrix Composites Considering Cooling and Thermal Cycling

Journal of Engineering Materials and Technology ◽

10.1115/1.482788 ◽

1999 ◽

Vol 122 (2) ◽

pp. 203-208 ◽

Cited By ~ 20

Author(s):

Chuwei Zhou ◽

Wei Yang ◽

Daining Fang

Keyword(s):

Thermal Cycling ◽

Metal Matrix Composites ◽

Stress Drop ◽

Metal Matrix ◽

Failure Modes ◽

Short Fiber ◽

Uniaxial Tensile ◽

Matrix Composites ◽

Fiber Reinforced ◽

Matrix Damage

Mechanical properties and damage evolution of short-fiber-reinforced metal matrix composites (MMC) are studied under a micromechanics model accounting for the history of cooling and thermal cycling. A cohesive interface is formulated in conjunction with the Gurson-Tvergaard matrix damage model. Attention is focused on the residual stresses and damages by the thermal mismatch. Substantial stress drop in the uniaxial tensile response is found for a computational cell that experienced a cooling process. The stress drop is caused by debonding along the fiber ends. Subsequent thermal cycling lowers the debonding stress and the debonding strain. Micromechanics analysis reveals three failure modes. When the thermal histories are ignored, the cell fails by matrix damage outside the fiber ends. With the incorporation of cooling, the cell fails by fiber end debonding and the subsequent transverse matrix damage. When thermal cycling is also included, the cell fails by jagged debonding around the fiber tops followed by necking instability of matrix ligaments. [S0094-4289(00)01202-0]

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EFFECTS OF TANGENT OPERATORS ON PREDICTION ACCURACY OF MESO-MECHANICAL CONSTITUTIVE MODEL OF ELASTO-PLASTIC COMPOSITES

International Journal of Computational Methods ◽

10.1142/s0219876213500643 ◽

2014 ◽

Vol 11 (04) ◽

pp. 1350064

Author(s):

S. J. GUO ◽

G. Z. KANG ◽

J. ZHANG ◽

Q. H. KAN

Keyword(s):

Constitutive Model ◽

Error Analysis ◽

Metal Matrix Composites ◽

Metal Matrix ◽

Prediction Accuracy ◽

Strain Difference ◽

Accurate Prediction ◽

Matrix Composites ◽

Load Increment ◽

Plastic Composites

With a newly developed homogenization cyclic constitutive model of particle reinforced metal matrix composites [Guo et al. (2011)], the effects of tangent operators, i.e., continuum and algorithmic tangent operators [defined by Doghri and Ouaar (2003)] on the accuracy of the developed meso-mechanical constitutive model to predict the monotonic tensile and uniaxial ratchetting deformations of SiC P /6061 Al composites were investigated in this work. The predictions were obtained by the developed model with the choices of different tangent operators and various magnitudes of load increments. Comparison of prediction accuracy and necessary error analysis on the results obtained by different tangent operators were conducted. It is shown that: the stress or strain difference in each load increment and produced by using different tangent operators will accumulate step by step; accurate prediction should be obtained by employing a load increment small enough, especially when the algorithmic tangent operator is used in predicting the uniaxial ratchetting of the composites.

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Actuation of fluidic flexible matrix composites in structural media

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x11428676 ◽

2011 ◽

Vol 23 (3) ◽

pp. 269-278 ◽

Cited By ~ 6

Author(s):

Bin Zhu ◽

Christopher D Rahn ◽

Charles E Bakis

Keyword(s):

Matrix Material ◽

Unit Cell ◽

Analytical Models ◽

Thin Wall ◽

Matrix Composites ◽

Soft Matrix ◽

Structural Applications ◽

Order Of Magnitude ◽

Flexible Matrix Composite ◽

Free Strain

Fluidic flexible matrix composite (F2MC) tubes have been shown to provide actuation and stiffness change in applications that require isolated tubes or multiple tubes embedded in a soft matrix. Structural applications often require stiff and strong composites, however, so this article addresses the actuation performance of F2MC tubes embedded in structural media. Two analytical models are developed based on Lekhnitskii’s solutions for a homogeneous orthotropic cylinder with axial force and pressure loading. These unit cell models are cylindrical and bilayer with the inner layer being a thick-walled F2MC tube and the outer layer representing the surrounding rigid composite and are composed of either homogeneous epoxy or a second FMC layer made with stiffer matrix material. The models are validated using ABAQUS. Free strain and blocked force are calculated for a variety of unit cell designs. The analytical results show that actuation performance is generally reduced compared to that of an isolated F2MC tube due to the radial and longitudinal constraints imposed by the surrounding structural medium. The free strain is generally two orders of magnitude smaller for an F2MC tube in structural media, requiring higher actuation pressures for bilayer F2MC structures. The blocking force of F2MC in either epoxy or composite is roughly an order of magnitude smaller than that of an isolated F2MC tube. The analysis shows a great degree of tailorability in actuation properties, so that the F2MC tube can be designed to minimize these differences. Higher actuation performance is achieved, for example, with a thick-walled F2MC tube, as opposed to the thin wall that maximizes performance in an isolated F2MC tube.

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