A Constitutive Equation Including Compressibility Effects

1987 ◽  
Vol 31 (6) ◽  
pp. 425-438 ◽  
Author(s):  
Wen‐Chien Ko ◽  
Donald C. Bogue
Keyword(s):  
Constitutive Equation ◽  
Compressibility Effects

A New Constitutive Equation to Represent Drilling Fluids

2018 ◽  
Author(s):  
Tainan Gabardo ◽  
Cezar Otaviano Ribeiro Negrao
Keyword(s):  
Constitutive Equation ◽  
Drilling Fluids

Fiber symmetry

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Composite Materials ◽  
Constitutive Equation ◽  
Transversely Isotropic ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced Materials

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

scholarly journals Hot Deformation Behavior and Processing Maps of a New Ti-6Al-2Nb-2Zr-0.4B Titanium Alloy

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2456
Author(s):  
Zhijun Yang ◽  
Weixin Yu ◽  
Shaoting Lang ◽  
Junyi Wei ◽  
Guanglong Wang ◽  
...  
Keyword(s):  
Titanium Alloy ◽  
Flow Stress ◽  
Constitutive Equation ◽  
Deformation Mechanism ◽  
Power Dissipation ◽  
Hot Deformation ◽  
Dissipation Rate ◽  
Dynamic Recovery ◽  
Processing Maps ◽  
Temperature Range

The hot deformation behaviors of a new Ti-6Al-2Nb-2Zr-0.4B titanium alloy in the strain rate range 0.01–10.0 s−1 and temperature range 850–1060 °C were evaluated using hot compressing testing on a Gleeble-3800 simulator at 60% of deformation degree. The flow stress characteristics of the alloy were analyzed according to the true stress–strain curve. The constitutive equation was established to describe the change of deformation temperature and flow stress with strain rate. The thermal deformation activation energy Q was equal to 551.7 kJ/mol. The constitutive equation was ε ˙=e54.41[sinh (0.01σ)]2.35exp(−551.7/RT). On the basis of the dynamic material model and the instability criterion, the processing maps were established at the strain of 0.5. The experimental results revealed that in the (α + β) region deformation, the power dissipation rate reached 53% in the range of 0.01–0.05 s−1 and temperature range of 920–980 °C, and the deformation mechanism was dynamic recovery. In the β region deformation, the power dissipation rate reached 48% in the range of 0.01–0.1 s−1 and temperature range of 1010–1040 °C, and the deformation mechanism involved dynamic recovery and dynamic recrystallization.

The influence of strain rate on the cavitation time and deformation of an underwater impulsively rectangular plate

2021 ◽  
pp. 030932472110208
Author(s):  
Habib Ramezannejad Azarboni ◽  
Abolfazl Darvizeh
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Rectangular Plate ◽  
Total Pressure ◽  
Elastoplastic Deformation ◽  
Underwater Explosion ◽  
Strain Rate Effect ◽  
Linear Solution ◽  
Explosion Load ◽  
Explosive Forming

The effect of strain rate on the cavitation time and elastoplastic deformation of steel rectangular plate subjected to underwater explosion load is analytically and numerically investigated in this study. At the cavitation time, the total pressure of the explosion is eliminated so that the cavitation time plays a significant role in the elastoplastic deformation of underwater explosive forming of plate. Taking into account the strain rate effect, the Cowper-Symond constitutive equation of mild steel is employed. Exact linear solution using the Eigen function and numerical linear and nonlinear solution using finite difference method (FDM) of dynamic response of impulsively plate is obtained. Implementing the linear work hardening, the stress, strain, displacement, and velocity in any steps of loading are calculated. The time of cavitation can be recognized in elastic or plastic regimes by applying the Cowper-Symond constitutive equation. Considering the strain rate influence, the effects of charge mass and standoff are investigated to occur of cavitation and time dependent deflection and velocity of a rectangular plate.

scholarly journals The Effect of α-Al(MnCr)Si Dispersoids on Activation Energy and Workability of Al-Mg-Si-Cu Alloys during Hot Deformation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xiaoguo Wang ◽  
Jian Qin ◽  
Hiromi Nagaumi ◽  
Ruirui Wu ◽  
Qiushu Li
Keyword(s):  
Activation Energy ◽  
Aluminum Alloys ◽  
Constitutive Equation ◽  
Hot Deformation ◽  
Flow Instability ◽  
Void Formation ◽  
Activation Energies ◽  
Compression Tests ◽  
Softening Mechanism ◽  
Dynamic Softening

The hot deformation behaviors of homogenized direct-chill (DC) casting 6061 aluminum alloys and Mn/Cr-containing aluminum alloys denoted as WQ1 were studied systematically by uniaxial compression tests at various deformation temperatures and strain rates. Hot deformation behavior of WQ1 alloy was remarkably changed compared to that of 6061 alloy with the presence of α-Al(MnCr)Si dispersoids. The hyperbolic-sine constitutive equation was employed to determine the materials constants and activation energies of both studied alloys. The evolution of the activation energies of two alloys was investigated on a revised Sellars’ constitutive equation. The processing maps and activation energy maps of both alloys were also constructed to reveal deformation stable domains and optimize deformation parameters, respectively. Under the influence of α dispersoids, WQ1 alloy presented a higher activation energy, around 40 kJ/mol greater than 6061 alloy’s at the same deformation conditions. Dynamic recrystallization (DRX) is main dynamic softening mechanism in safe processing domain of 6061 alloy, while dynamic recovery (DRV) was main dynamic softening mechanism in WQ1 alloy due to pinning effect of α-Al(MnCr)Si dispersoids. α dispersoids can not only resist DRX but also increase power required for deformation of WQ1 alloy. The microstructure analysis revealed that the flow instability was attributed to the void formation and intermetallic cracking during hot deformation of both alloys.

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