Universal Properties in Filler-Loaded Rubbers

1994 ◽  
Vol 67 (1) ◽  
pp. 1-16 ◽  
Author(s):  
H. G. Kilian ◽  
M. Strauss ◽  
W. Hamm
Keyword(s):  
Power Law ◽  
Filler Particle ◽  
Simple Extension ◽  
Stress Strain ◽  
Normal Forces ◽  
Matrix Interactions ◽  
Universal Properties ◽  
Filler Particles ◽  
Bridge Distribution ◽  
Interfacial Slippage

Abstract Stress-strain cycles in filler loaded rubbers can be described with the aid of the van der Waals-network model. Reinforcement comes about by drawing pairs of filler particles apart. Reinforcement is observed because the intrinsic strain within the rubber bridge which is located between the filler particles exceeds the macroscopic strain very much, so much that interfacial slippage is enforced. The rubbery intra-cluster bridge distribution is represented by three dominant filler particle distances. One of them describes direct filler-to-filler (FF-) contacts, the critical strength of which is different from the filler-to-matrix (FM-) contacts of the filler-to-filler chains which are located on the whole surface of the filler particles. Formation of clusters is described by a power law. Stress-strain experiments are described with the aid of this model for different filler-matrix combinations (NR, SBR, carbon blacks, silica). Many universal features are observed: The intra-cluster rubber bridges display the same mean thickness when being related to the radius of the primary filler particles. The exponent in the power law is always identical. The deformation mechanisms, including irreversible slippage, do not to depend on the type of strain (simple extension, uniaxial compression). Yet, the Einstein-Smallwood effect turns out to be anisotrop so far as quasipermanent filler-to-matrix interactions seem to be determined by normal forces in the particles surfaces only. Different filler and matrix combinations display different strengths of the FF- and FM-contacts independent of the type of strain.

Volterra dislocations in power law elastic materials

1991 ◽  
Vol 432 (1884) ◽  
pp. 77-91 ◽  
Keyword(s):  
Integral Equations ◽  
Power Law ◽  
Elastic Materials ◽  
Displacement Fields ◽  
Nonlinear Integral Equations ◽  
Stress Strain ◽  
Incompressible Medium ◽  
Softening Parameter

The solution for a Volterra dislocation, with edge and screw components, is given for an incompressible medium with a power law hardening or softening stress-strain law. The form of the stress, strain and displacement fields is identified with angular variations satisfying nonlinear integral equations. Results are presented for various values of the hardening (or softening) parameter.

scholarly journals Investigation of the Mechanical Properties of St. Lawrence River Ice

1971 ◽  
Vol 8 (2) ◽  
pp. 163-169 ◽  
Author(s):  
L. W. Gold ◽  
A. S. Krausz
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Yield Stress ◽  
Power Law ◽  
River Ice ◽  
Stress Strain ◽  
Strain Behavior ◽  
Brittle Transition ◽  
Ductile To Brittle Transition ◽  
St Lawrence River

Observations are reported on the stress–strain behavior at −9.5 ± 0.5 °C of four types of ice obtained from the St. Lawrence River. The ice was subject to nominal rates of strain covering the range 2.1 × 10−5 min−1 to 5.8 × 10−2 min−1. A ductile-to-brittle transition was observed for strain rate of about 10−2 min−1. In the ductile range the four types had an upper yield stress that increased with strain rate according to a power law.

Departures of the Elastic Behavior of Rubbers in Simple Extension from the Kinetic Theory

1955 ◽  
Vol 28 (1) ◽  
pp. 24-35 ◽  
Author(s):  
S. M. Gumbrell ◽  
L. Mullins ◽  
R. S. Rivlin
Keyword(s):  
Kinetic Theory ◽  
Volume Fraction ◽  
Single Parameter ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Strain Behavior

Abstract It is shown that the equilibrium stress-strain behavior of highly swollen rubber vulcanizates in simple extension agrees with the predictions of the kinetic theory. The departures from these predictions which are found in dry or lightly swollen rubbers have been investigated, and it is shown that they can be described in terms of a single parameter C2. The magnitude of this parameter is large in dry rubbers, and decreases to zero at high degrees of swelling ; this decrease occurs linearly with decrease in the volume fraction of rubber. The value of C2 is found to be independent of the nature of the rubber polymer, of the degree of vulcanization, and of the nature of the swelling liquid. The possible significance of this parameter is discussed in light of these observations.

Correlation of Large Longitudinal Deformations with Different Strain Histories

1967 ◽  
Vol 40 (2) ◽  
pp. 506-516 ◽  
Author(s):  
L. J. Zapas ◽  
T. Craft
Keyword(s):  
Stress Relaxation ◽  
Single Step ◽  
Strain History ◽  
Simple Extension ◽  
Stress Strain ◽  
Fluid Equation ◽  
Elastic Fluid ◽  
Strain Behavior ◽  
Elastomeric Materials ◽  
Single Integral

Abstract In 1963 Bernstein, Kearsley, and Zapas1 presented a theory of an elastic fluid which gave the correct stress-relaxation response for a large variety of elastomeric materials, including vulcanized rubbers. A principle attractiveness of this theory is its relative simplicity; with a single integral in time, it describes the stress-strain behavior for all types of deformation histories. In the case of simple extension, it predicts the behavior in any uniaxial strain history from the results of single step stress-relaxation experiments which cover the same range of extension and time. We designed a series of experiments to check the validity of this theory and found, as is shown in this paper, excellent agreement with experiment in all cases. We are aware that experiments cannot prove a theory. From our results, however, we feel strongly that a single integral expression with a nonlinear integrand such as the BKZ elastic fluid equation is sufficient to describe the stress-strain behavior of elastomeric materials.

scholarly journals REGULARITIES OF THE LINING STRESS-STRAIN STATE DURING OF THE PYLON METRO STATION CONSTRUCTION

2021 ◽  
pp. 19-27
Author(s):  
D. O. BANNIKOV ◽  
V. P. KUPRII ◽  
D. YU. VOTCHENKO
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Finite Elements ◽  
Strain State ◽  
Finite Element Models ◽  
Bending Moments ◽  
Stress Strain ◽  
Normal Forces ◽  
Stress Strain State ◽  
Station Structure

Purpose. Perform numerical analysis of the station structure. Take into account in the process of mathematical modeling the process of construction of station tunnels of a three-vaulted station. Obtain the regularities of the stress-strain state of the linings, which is influenced by the processes of soil excavation and lining construction. Methodology. To achieve this goal, a series of numerical calculations of models of the deep contour interval metro pylon station was performed. Three finite-element models have been developed, which reflect the stages of construction of a three-vaulted pylon station. Numerical analysis was performed on the basis of the finite element method, implemented in the calculation complex Lira for Windows. Modeling of the stress-strain state of the station tunnel linings and the soil massif was performed using rectangular, universal quadrangular and triangular finite elements, which take into account the special properties of the soil massif. Station tunnel linings are modeled by means of rod finite elements. Findings. Isofields of the stress-strain state in finite-element models reflecting the stages of construction are obtained. The vertical displacements and horizontal stresses that are characteristic of a three-vaulted pylon station are analyzed. The analysis of horizontal stresses proved that at the stage of opening of the middle tunnel the scheme of pylon operation is rather disadvantageous. The analysis of bending moments and normal forces was also carried out and the asymmetry of their distribution was noted. Originality. Based on the obtained patterns of distribution of stress-strain state and force factors, it is proved that numerical analysis of the station structure during construction is necessary to take measures to prevent or reduce deformation of frames that are in unfavorable conditions. Practical value. In the course of research, the regularities of changes in stresses, displacements, bending moments and normal forces in the models of the pylon station, which reflect the sequence of its construction, were obtained.

scholarly journals Pseudo-Ductility, Morphology and Fractography Resulting from the Synergistic Effect of CaCO3 and Bentonite in HDPE Polymer Nano Composite

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3333
Author(s):  
Tauseef Ahmed ◽  
Hamdan H. Ya ◽  
Rehan Khan ◽  
Abdul Munir Hidayat Syah Lubis ◽  
Shuhaimi Mahadzir
Keyword(s):  
Synergistic Effect ◽  
Filler Particle ◽  
Stress Transfer ◽  
Polymeric Materials ◽  
High Strength ◽  
Type I ◽  
Nano Composite ◽  
Rigid Particles ◽  
Rigid Filler ◽  
Filler Particles

Polymeric materials such as High density polyethylene(HDPE) are ductile in nature, having very low strength. In order to improve strength by non-treated rigid fillers, polymeric materials become extremely brittle. Therefore, this work focuses on achieving pseudo-ductility (high strength and ductility) by using a combination of rigid filler particles (CaCO3 and bentonite) instead of a single non-treated rigid filler particle. The results of all tensile-tested (D638 type i) samples signify that the microstructural features and surface properties of rigid nano fillers can render the required pseudo-ductility. The maximum value of tensile strength achieved is 120% of the virgin HDPE, and the value of elongation is retained by 100%. Furthermore, the morphological and fractographic analysis revealed that surfactants are not always going to obtain polymer–filler bonding, but the synergistic effect of filler particles can carry out sufficient bonding for stress transfer. Moreover, pseudo-ductility was achieved by a combination of rigid fillers (bentonite and CaCO3) when the content of bentonite dominated as compared to CaCO3. Thus, the achievement of pseudo-ductility by the synergistic effect of rigid particles is the significance of this study. Secondly, this combination of filler particles acted as an alternative for the application of surfactant and compatibilizer so that adverse effect on mechanical properties can be avoided.

Tailoring anisotropic thermal conductivity by varying filler particle organization in nickel-polydimethylsiloxane composites

2019 ◽  
Vol 53 (18) ◽  
pp. 2569-2577
Author(s):  
Peiying J Tsai ◽  
Souvik Pal ◽  
Suvojit Ghosh ◽  
Ishwar K Puri
Keyword(s):  
Thermal Conductivity ◽  
Additive Manufacturing ◽  
Volume Fraction ◽  
Filler Particle ◽  
Material Design ◽  
Interparticle Spacing ◽  
Element Analysis ◽  
Anisotropic Thermal Conductivity ◽  
Transverse Conductivity ◽  
Filler Particles

Anisotropic properties can be imparted to composite materials by arranging filler particles along specific directions inside the polymer matrix. These anisotropic patterns can be produced through dynamic field-assisted assembly of the filler particles during additive manufacturing. Using finite element analysis, we explore how chainlike arrangements of nickel particles embedded in a polydimethylsiloxane matrix modify bulk thermal conductivities in the axial and transverse directions. The axial conductivity increases up to nine times of the matrix conductivity with increasing filler volume fraction. While the axial conductivity decreases with increasing interparticle spacing, the transverse conductivity is uninfluenced. When particles within a chain are arranged in a zigzag pattern, increasing the interparticle zigzag angle decreases axial conductivity but increases transverse conductivity. As that angle increases to ∼55 º, the axial conductivity approaches a minimum, while the transverse conductivity approaches its maximum. An empirical model that includes effects of interparticle spacing and zigzag angle to predict the anisotropic thermal conductivity of a composite containing particle chains is presented. These results are relevant for the material design of particulate-reinforced polymer composites for advanced field-assisted additive manufacturing strategies.

The Resolution of Elastomer Blend Properties by Stress-Strain Modelling. An Extension of the Model to Carbon-Black-Loaded Elastomers

1990 ◽  
Vol 63 (5) ◽  
pp. 779-791 ◽  
Author(s):  
R. F. Bauer ◽  
A. H. Crossland
Keyword(s):  
Carbon Black ◽  
Full Range ◽  
Filler Particle ◽  
Particle Surface ◽  
Practical Method ◽  
Particulate Phase ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Relationship ◽  
Elastomer Blend

Abstract The unique stress-strain behavior of a carbon-black-loaded elastomer is due to the presence of a rigid, particulate phase, but also to the interaction of the elastomer chains with the filler. It is postulated that this interaction takes the form of adsorption on the filler-particle surface, which results in trapped entanglements. Upon deformation, the trapped chains are aligned parallel to the axis of stress. Thus, a practical stress-strain relationship could be developed which is capable to model the stress-strain behavior of compounds over the full range of extensions up to break. The analysis of a highly prestrained carbon-black-loaded NR compound in which the entanglement effect had been mechanically destroyed, demonstrated that the “sea-island” (SIP) coupling arrangement is most suitable for accounting for the interaction effect of the elastomer and carbon black. For moderately prestrained carbon-black-loaded NR and BR compounds a good fit of theory to experiment is obtained for a combination of the SIP coupling arrangement and the specially derived stress-strain relationship. Thus, a practical method is available for describing the deformation of carbon-black-loaded elastomers and for the modelling of carbon-black-loaded elastomer blends.

A novel phenomenological constitutive model for Ti-6Al-4V at high temperature conditions and quasi-static strain rates

2021 ◽  
pp. 095441002098599
Author(s):  
Mohammad Mahdi Ashrafian ◽  
Seyed Ali Hosseini Kordkheili
Keyword(s):  
High Temperature ◽  
Constitutive Model ◽  
Power Law ◽  
Phenomenological Approach ◽  
Strain Rates ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Strain Behavior ◽  
Temperature Conditions ◽  
Cook Model

Phenomenological constitutive modeling of Ti-6Al-4V at temperatures between 923 and 1023 K under 0.0005–0.05 s−1 quasi-static rates is studied based on a phenomenological approach. For this purpose, the Johnson–Cook constitutive model is revisited. At low temperature conditions under moderate to high strain rates, the material’s stress–strain curves are the most similar to power-law function. Contrary to this, at high temperature conditions under low to moderate strain rates, the saturation-type function well describes the stress–strain curves. On the other hand, it is illustrated that the Johnson–Cook constitutive model is feeble to predict the material’s behavior correctly. Accordingly, in this study, a viscoplastic temperature-dependent constitutive model is developed. The strain rate hardening as well as thermal softening of the developed model is the same as the Johnson–Cook model. But a temperature-dependent strain hardening function is proposed in which both the saturation-type and power-law hardening behaviors of the material are implemented. In comparison with the Johnson–Cook model, the new constitutive model’s fidelity in capturing the titanium behavior is depicted. At last, by considering an Arrhenius-type phenomenological constitutive model, it is noted that the developed constitutive model has the best correctness in predicting the Ti-6Al-4V stress–strain behavior at high temperature conditions under quasi-static rates.

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