Constitutive Relation of Yunjialing Anthracite Under Medium Strain Rate

2007 ◽  
Vol 17 (1) ◽  
pp. 126-132 ◽  
Author(s):  
Wen-jiao GAO ◽  
Ren-liang SHAN ◽  
Gong-cheng WANG ◽  
Rui-qiang CHENG
Keyword(s):  
Strain Rate ◽  
Constitutive Relation ◽  
Medium Strain Rate

scholarly journals Dynamic constitutive relation of 5083P-O aluminium alloy and its influence on energy-absorbing structure

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880733
Author(s):  
Yue Feng ◽  
Shoune Xiao ◽  
Bing Yang ◽  
Tao Zhu ◽  
Guangwu Yang ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Aluminium Alloy ◽  
Constitutive Relation ◽  
High Strain ◽  
Deformation Mode ◽  
Strain Rates ◽  
Strengthening Effect ◽  
Element Simulation ◽  
Energy Absorbing

Dynamic and quasi-static tensile tests of 5083P-O aluminium alloy were carried out using RPL100 electronic creep/fatigue testing machine and the split Hopkinson tension bar, respectively. The dynamic constitutive relation of the material at high strain rates was studied, and the constitutive model in accordance with Cowper–Symonds form was established. At the same time, a method to describe the constitutive relation of material using the strain rate interpolation method which is included in LS-DYNA software was proposed. The advantages and accuracy of this method were verified by comparing the results of the finite element simulation with the fitting results of the Cowper-Symonds model. The influence of material strain rate effect on squeezing force, energy absorption and deformation mode of the squeezing energy-absorbing structure based on the constitutive models of 5083P-O were studied by means of finite element simulation. The results show that when the strain rate of the structure deformation is low, the material strain rate strengthening effect has little influence on the structure. However, with the increase of the strain rate, the strengthening effect of the material will improve the squeezing force and the energy absorption of the structure, and will also influence the deformation mode, that is, the decrease of the deformation with high strain rates while the increase of the deformation with low strain rates.

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

scholarly journals A Modified Fractional Maxwell Numerical Model for Constitutive Equation of Mn-Cu Damping Alloy

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2020
Author(s):  
Baoquan Mao ◽  
Rui Zhu ◽  
Zhiqian Wang ◽  
Yuying Yang ◽  
Xiaoping Han ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Maxwell Model ◽  
Nonlinear Viscoelastic ◽  
Fractional Maxwell Model ◽  
Hysteretic Characteristics ◽  
Nonlinear Elastic

To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

scholarly journals Experimental Study on the Tensile Properties of Rock-Mortar Interface under Different Strain Rates

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Nan Wu ◽  
Zhende Zhu ◽  
Zhilei He
Keyword(s):  
Experimental Study ◽  
Tensile Strength ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Crack Width ◽  
Axial Stress ◽  
Downward Trend ◽  
Crack Model ◽  
Strain Rates ◽  
Softening Function

In this paper, an experimental study was carried out on a rock-mortar interface specimen under three different strain rates (10−6, 10−5, and 10−4  s−1) using the MTS322 electrohydraulic servo loading system, and a new constitutive relation function of fictitious crack model (FCM) according to the axial-stress-crack-width curves of the rock-mortar interface is established, because the traditional nonlinear softening function easily distorts, shakes, and so cannot describe the damage-evolution process of the rock-mortar interface accurately. Through the use of a precise servo actuator system and three extensometers measured axial-stress-crack-width curves, it is shown that the rock-mortar interface is very sensitive to the strain rate. The tensile strength increases with strain rate, the crack width decreases at the same time, and the axial-stress-crack-width curves gradually evolve from a concave-downward trend to a linear decreasing trend. At the same time, the new constitutive relation function can reflect the tensile strength, crack width, and the downward trend of the rock-mortar interface more accurately.

Singular Fields in Plane-Strain Penetration

1991 ◽  
Vol 58 (4) ◽  
pp. 910-915 ◽  
Author(s):  
David Durban ◽  
Omri Rand
Keyword(s):  
Boundary Layer ◽  
Strain Rate ◽  
Plane Strain ◽  
Constitutive Relation ◽  
Solid Material ◽  
Material Behavior ◽  
Wall Friction ◽  
Friction Factors ◽  
Hardening Parameter ◽  
Strain Rate Hardening

Local singular fields are investigated in the vicinity of the vertex of a sharp wedge that penetrates a viscous solid. Material behavior is modeled by the usual powerlaw constitutive relation. Wall friction is accounted for by imposing friction factors along the walls of the wedge. The case of a Newtonian fluid is investigated analytically, and sample numerical results are presented for nonlinear strain rate hardening. It is shown that the exponent of strain rate singularity increases as the wedge becomes sharper and smoother. Increasing the hardening parameter also results in a stronger strain rate singularity. High levels of wall friction induce an intensive shear boundary layer near the wall.

Research on Dynamic Constitutive Relation of Materials Taking Account of Damage Evolution and Fracture Law for High Speed Cutting

2011 ◽  
Vol 188 ◽  
pp. 224-229
Author(s):  
J.Q. Li ◽  
Tao Tao Dong ◽  
Min Jie Wang
Keyword(s):  
Shear Band ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Damage Evolution ◽  
High Speed ◽  
Adiabatic Shear Band ◽  
Adiabatic Shear ◽  
Damage Effect ◽  
Serrated Chip ◽  
Softening Effect

The adiabatic shear, which may produce serrated chip, usually occurs for a large number of materials in high speed machining. Adiabatic shear band is an important damage model for metals under high-velocity deformation process. The damage evolution of micro-voids in adiabatic shear bands resulted in material fracture finally. Now the thermal softening effect, the strain rate harding effect and the strain harding effect have been discussed extensively in literature, but there is very little research on its damage effect. Based on the experiments of predecessors, this paper presents a new damage evolution equation that is dependent on strain, strain rate and is suitable for the description of voids damage evolution in adiabatic shear band. The corresponding rate-dependent constitutive relation taking account of damage evolution and temperature are proposed. The predicted results are in good agreement with the experiment datum.

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