scholarly journals Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates

Polymers ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 988 ◽  
Author(s):  
Francesca Carleo ◽  
Ettore Barbieri ◽  
Roly Whear ◽  
James Busfield
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Low Cycle Fatigue ◽  
Constitutive Models ◽  
Strain Range ◽  
Operating Conditions ◽  
Strain Rates ◽  
Strain And Strain Rate ◽  
Wide Range ◽  
Dynamic Strains

Modelling the viscoelastic behavior of rubber for use in component design remains a challenge. Most of the literature does not consider the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). Previous studies have either focused on the behaviour at small strains and small strain rates or in fast loading conditions that result in low cycle fatigue or tearing phenomena. There is a lack of understanding of the dynamic response of natural rubber suspension components when used in real vehicle applications. This paper presents a review of popular viscoelastic nonlinear constitutive models and their ability to model the mechanical behaviour of typical elastomer materials such as Natural Rubber (NR) incorporating different PHR (Parts per Hundred Rubber, XX) of carbon black. The range of strain and strain rate are typical for the materials used in rubber suspensions when operating in severe service operating conditions, such as over rough terrain or over pot-holes. The cyclic strain is applied at different amplitudes and different strain rates in this medium strain range. Despite the availability of many models in the literature, our study reports that none of the existing models can fit the data satisfactorily over a wide range of conditions.

Material Characterization of Rubber Vulcanizates under Dynamic Conditions Appropriate for Tire Modeling

1991 ◽  
Vol 19 (2) ◽  
pp. 79-99 ◽  
Author(s):  
D. G. Young
Keyword(s):  
Finite Element ◽  
High Performance ◽  
Fatigue Testing ◽  
Nonlinear Models ◽  
Pure Shear ◽  
Strain Range ◽  
Operating Conditions ◽  
Simple Extension ◽  
Strain Rates ◽  
Wide Range

Abstract Material property data used in finite element and other models for tire applications have often been obtained under static or low strain rate conditions at room temperature. In the latter case Williams-Landel-Ferry (WLF) shifts are assumed in order to relate the data to strain rates and temperatures typical of actual tire operation. However, such shifts may not always be appropriate for the highly loaded, diverse elastomer blends used in tires today unless one wishes to go to the trouble of generating the WLF constant for each compound. Data are presented to show that one can directly and easily obtain high quality stress or strain energy density results over wide ranges of strain rates, strain levels, and temperature using techniques developed for fatigue characterization. Thus, material properties can be obtained as a by-product of fatigue testing with little added work, or they can be obtained straightforwardly and quickly if fatigue testing is not required. These data are generated in a dynamic, pulsed loading mode which is especially relevant for those modeling applications which deal with the rolling tire. Results from a high performance tire tread, a sidewall, and an innerliner are presented to illustrate the wide range of compounds that can be accommodated. The primary mode of deformation employed is pure shear. Also, limited data from static simple extension and pulsed simple extension tests are shown for comparison. The pulsed pure shear and simple extension data, obtained over a wide strain range, are an excellent source of basic information on a given compound to fit empirical models, generate Mooney-Rivlin constant, or define material constants for more generalized nonlinear models such as Ogden, Peng, or Peng-Landel. The latter material models are now becoming available in commercial finite element codes to allow studies of tire deformations, rolling resistance, and failure properties under realistic operating conditions.

A Procedure for Low Cycle Fatigue Life Prediction for Various Temperatures and Strain Rates

1990 ◽  
Vol 112 (4) ◽  
pp. 422-428 ◽  
Author(s):  
Ange Zhang ◽  
T. Bui-Quoc ◽  
R. Gomuc
Keyword(s):  
Fatigue Life ◽  
Strain Rate ◽  
Life Prediction ◽  
Low Cycle Fatigue ◽  
Low Frequency ◽  
Strain Range ◽  
Strain Rates ◽  
Total Strain Range ◽  
Wide Range ◽  
Experimental Values

This paper describes a procedure that permits the calculation of the fatigue life over a wide range of temperatures and strain rates. The isothermal fatigue life is expressed in terms of the total strain range by an equation previously obtained from a continuous damage concept. Additional new terms are introduced to take into account the effect of the temperature and of the strain rate. For a given material, a multiple regression analysis is carried out using some experimental results in order to evaluate the material constants involved. Once these constants are known, the life prediction can be made for other specified values of temperature and strain rate. The approach is applied to available data obtained from several stainless steels (AISI 304, 316, 348, and some SUS materials) under several combinations of temperatures and strain rates. The deviation of the calculated lives from the experimental values is reasonably acceptable. The extension of the proposed procedure to cases of cycling with a very low frequency, usually involving hold times, is examined and discussed.

INVESTIGATING THE INFLUENCE OF ENVIRONMENTAL CONDITIONING ON EPOXY RESINS AT QUASISTATIC AND HIGH STRAIN RATES FOR MATERIAL OPERATING LIMIT

2021 ◽  
Author(s):  
SAGAR M. DOSHI, SAGAR M. DOSHI, ◽  
NITHINKUMAR MANOHARAN ◽  
BAZLE Z. (GAMA) HAQUE, ◽  
JOSEPH DEITZEL ◽  
JOHN W. GILLESPIE, JR.
Keyword(s):  
Mechanical Properties ◽  
Epoxy Resin ◽  
Yield Stress ◽  
High Strain ◽  
Operating Conditions ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Wide Range ◽  
Environmental Aging

Epoxy resin-based composite panels used for armors may be subjected to a wide range of operating temperatures (-55°C to 76°C) and high strain rates on the order of 103-104 s-1. Over the life cycle, various environmental factors also affect the resin properties and hence influence the performance of the composites. Therefore, it is critical to determine the stress-strain behavior of the epoxy resin over a wide range of strain rates and temperatures for accurate multi-scale modeling of composites and to investigate the influence of environmental aging on the resin properties. Additionally, the characterization of key mechanical properties such as yield stress, modulus, and energy absorption (i.e. area under the stress-strain curve) at varying temperatures and moisture can provide critical data to calculate the material operating limits. In this study, we characterize mechanical properties of neat epoxy resin, SC-15 (currently used in structural armor) and RDL-RDC using uniaxial compression testing. RDL-RDC, developed by Huntsman Corporation, has a glass transition temperature of ~ 120°C, compared to ~ 85°C of SC-15. A split Hopkinson pressure bar is used for high strain rate testing. Quasistatic testing is conducted using a screw-driven testing machine (Instron 4484) at 10-3 s-1 and 10-1 s-1 strain rates and varying temperatures. The yield stress is fit to a modified Eyring model over the varying strain rates at room temperature. For rapid investigation of resistance to environmental aging, accelerated aging tests are conducted by immersing the specimens in 100°C water for 48 hours. Specimens are conditioned in an environmental chamber at 76 °C and 88% RH until they reach equilibrium. Tests are then conducted at five different temperatures from 0°C to 95°C, and key mechanical properties are then plotted vs. temperature. The results presented are an important step towards developing a methodology to identify environmental operating conditions for composite ground vehicle applications.

Comparative studies of the constitutive models for tungsten heavy alloy (95W-3.5Ni-1.5Fe) at high strain rates

2021 ◽  
pp. 095440622110451
Author(s):  
Xiuwen Lai ◽  
Zhanjiang Wang ◽  
Na Qin
Keyword(s):  
Threshold Stress ◽  
Dynamic Compression ◽  
Constitutive Models ◽  
Heavy Alloy ◽  
Tungsten Heavy Alloy ◽  
Strain Rates ◽  
Stress Model ◽  
Static Compression ◽  
Mechanical Threshold ◽  
Wide Range

The plastic behaviors’ description of a tungsten heavy alloy (95W-3.5Ni-1.5Fe) at temperatures of 298–773 K and strain rates of 0.001–11,000 s−1 is systematically studied based on four constitutive models, that is, Zerilli-Armstrong model, modified Zerilli-Armstrong model, Mechanical Threshold Stress model, and modified Mechanical Threshold Stress model. The quasi-static compression experiments using an electronic universal testing machine and the dynamic compression experiments using a split Hopkinson pressure bar apparatus are employed to obtain the true stress–strain curves at a total of three temperatures (298 K, 573 K, and 773 K) and a wide range of strain rates (0.001–11,000 s−1). The parameters of the four constitutive models are obtained by the above fundamental experimental data and Grey Wolf Optimizer. The correlation coefficient and average absolute relative error are used to evaluate the predicted performance of these models. Modified Mechanical Threshold Stress model is found to have the highest predicted performance in describing the flow stress of the 95W-3.5Ni-1.5Fe alloy. Eventually, two compression experiments whose loading conditions are not in the fundamental experiments are conducted to validate the four models.

scholarly journals A Comparative Study on Johnson Cook, Modified Zerilli–Armstrong, and Arrhenius-Type Constitutive Models to Predict Compression Flow Behavior of SnSbCu Alloy

Materials ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1726 ◽  
Author(s):  
Tongyang Li ◽  
Bin Zhao ◽  
Xiqun Lu ◽  
Hanzhang Xu ◽  
Dequan Zou
Keyword(s):  
Experimental Data ◽  
Flow Behavior ◽  
Constitutive Models ◽  
Strain Range ◽  
Type Model ◽  
Strain Rates ◽  
Compression Tests ◽  
Predictive Values ◽  
Specific Strain ◽  
Optimum Model

The flow behavior of the SnSbCu alloy is studied experimentally by the compression tests in the range of the strain rates from 0.0001 to 0.1 s−1 and temperature from 293 to 413 K. Based on the experimental data, three constitutive models including the Johnson–Cook (J–C), modified Zerilli–Armstrong (Z–A), and Arrhenius-type (A-type) models are compared to find out an optimum model to describe the flow behavior of the SnSbCu alloy. The results show that the J–C model could predict the flow behavior of the SnSbCu alloy accurately only at some specific strain rates and temperature near the reference values. The modified Z–A and A-type constitutive models can give better fitting results than the J–C model. While, at high strains, the predictive values of the modified Z–A model have larger errors than those at low strains, which means this model has limitations at high strains. By comparison, the A-type model could predict the experimental results accurately at the whole strain range, which indicates that it is a more suitable choice to describe the flow behavior of the SnSbCu alloy in the focused range of strain rates and temperatures. The work is beneficial to solve the tribological problem of the bearing of the marine engine by integrating the accurate constitutive model into the corresponding numerical model.

QUANTIFICATION OF THE CONTRIBUTION OF FILLER CHARACTERISTICS TO NATURAL RUBBER REINFORCEMENT USING PRINCIPAL COMPONENT ANALYSIS

2018 ◽  
Vol 91 (1) ◽  
pp. 79-96 ◽  
Author(s):  
Cindy S. Barrera ◽  
Alfred B. O. Soboyejo ◽  
Katrina Cornish
Keyword(s):  
Principal Component Analysis ◽  
Carbon Black ◽  
Natural Rubber ◽  
Polymer Composites ◽  
Principal Component ◽  
Component Analysis ◽  
Specific Product ◽  
Industrial Residues ◽  
Explanatory Variables ◽  
Wide Range

ABSTRACT Practical statistical models were developed to quantify individual contributions from characteristics of conventional and non-conventional fillers and predict resulting mechanical properties of both hevea and guayule natural rubber composites. Carbon black N330 and four different agro-industrial residues, namely, eggshells, carbon fly ash, processing tomato peels, and guayule bagasse, were used in this study. Filler characteristics were used as explanatory variables in multiple linear regression analyses. Principal component analysis was used to evaluate correlations among explanatory variables based on their correlation matrices and to transform them into a new set of independent variables, which were then used to generate reliable regression models. Surface area, dispersive component of surface energy, carbon black, and waste-derived filler loading were found to have almost equal importance in the prediction of composite properties. However, models developed for ultimate elongation poorly explained variability, indicating the dependence of this property on other variables. Agro-industrial residues could potentially serve as more sustainable fillers for polymer composites than conventional fillers. This new modeling approach for polymer composites allows the performance of a wide range of different waste-derived fillers to be predicted with minimum laboratory work, facilitating the optimization of compound recipes to address specific product requirements.

scholarly journals Dynamic Mechanical Characteristics and Constitutive Modeling of Rail Steel over a Wide Range of Temperatures and Strain Rates

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Peijie Liu ◽  
Yanming Quan ◽  
Guo Ding
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Split Hopkinson Pressure Bar ◽  
Rail Steel ◽  
Strain Rates ◽  
Dynamic Mechanical ◽  
Flow Response ◽  
Strain And Strain Rate ◽  
Average Absolute Relative Error ◽  
Wide Range

Rail steel plays an indispensable role in the safety and stability of the railway system. Therefore, a suitable constitutive model is quite significant to understand the mechanical behavior of this material. Here, the compressive mechanical behavior of heat-treated U71Mn rail steel over a wide range of strain rates (0.001 s−1–10000 s−1) and temperatures (20°C–800°C) was systematically investigated via uniaxial quasistatic and dynamic tests. The split Hopkinson pressure bar (SHPB) apparatus was utilized to perform dynamic mechanical tests. The effects of temperature, strain, and strain rate on the dynamic compressive characteristics of U71Mn were discussed, respectively. The results indicate that the flow response of U71Mn is both temperature-sensitive and strain rate-sensitive. However, the influence of temperature on the flow response is more remarkable than that of strain rate. On the basis of the experimental data, the original and modified Johnson-Cook (JC) models of the studied material were established, respectively. Using correlation coefficient and average absolute relative error parameters, it is revealed that better agreement between the experimental and predicted stress is reached by the modified JC model, which demonstrates that the modified one can characterize the mechanical behavior of the studied material preferably.

Modeling of Carbon Black Filled Natural Rubber Vulcanizates by the Standard Triboelastic Solid

1999 ◽  
Vol 72 (4) ◽  
pp. 673-683 ◽  
Author(s):  
V. A. Coveney ◽  
D. E. Johnson
Keyword(s):  
Mathematical Modeling ◽  
Carbon Black ◽  
Natural Rubber ◽  
Dynamic Behavior ◽  
Low Frequency ◽  
Specific Reference ◽  
Published Data ◽  
General Terms ◽  
Wide Range ◽  
Natural Rubber Vulcanizates

Abstract Mathematical modeling of the dynamic behavior of vulcanizates is reviewed with the emphasis on carbon black filled natural rubber (NR). The 3 constant standard triboelastic solid (STS) model and its behavior are described, in general terms and with specific reference to low frequency shear data for a wide range of filled NR vulcanizates. Good general agreement is found between model and experiment for the data obtained at strain amplitudes down to 0.01; there is also acceptably good correlation between carbon black loading and values of STS constants. For previously published data down to very low strain amplitudes (1×10−4), agreement is much less satisfactory.

Isothermal Fatigue Responses and Constitutive Modeling of Haynes 230

2012 ◽  
Author(s):  
Paul Ryan Barrett ◽  
Mamballykalathil Menon ◽  
Tasnim Hassan
Keyword(s):  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Strain Range ◽  
Thermal Recovery ◽  
Material Behavior ◽  
Accurate Estimation ◽  
Experimental Database ◽  
Macroscopic Models ◽  
Physically Based

Constitutive models are an integral part of a lifing system because it allows for accurate estimation of stresses and strains at failure locations of interest. Constitutive models can be properly defined in a material subroutine of a finite element code. The computational capabilities of today are far higher, allowing for more comprehensive models that can provide more accurate results. Macroscopic models that are physically based, phenomenological models characterize the material behavior on a larger scale that provides invaluable insights even at such length scales which are compatible for industrial application. A unified viscoplastic model based on nonlinear kinematic hardening (Chaboche type) with several added features such as nonproportionality, multiaxiality, strain range dependence, and thermal recovery is being implemented in ANSYS through the User Programmable Features. The simulation capability of the model will be experimentally validated on a nickel based superalloy, HA230. The experimental database encompasses a broad set of low cycle fatigue, symmetric, uniaxial strain-controlled loading histories which include isothermal with and without hold times, with and without a mean strain, at temperatures ranging from 75°F to 1800°F. Simulations from the modified model compared to the experimental responses will be presented to demonstrate the strengths and weaknesses.

Dynamic Fracture of Natural Rubber3

2007 ◽  
Vol 35 (4) ◽  
pp. 252-275 ◽  
Author(s):  
Ali A. Al-Quraishi ◽  
Michelle S. Hoo Fatt
Keyword(s):  
Finite Element ◽  
Carbon Black ◽  
Natural Rubber ◽  
Strain Rate ◽  
Fracture Energy ◽  
Dynamic Fracture ◽  
High Strain ◽  
Field Strain ◽  
Far Field ◽  
Strain Rates

Abstract This paper illustrates how the fracture energy of a tensile strip made of unfilled and 25 phr carbon black-filled natural rubber varies with far-field strain rate in the range 0.01–71 s−1. Quasistatic and dynamic fracture tests were performed at room temperature with an electromechanical INSTRON machine, a servo-hydraulic MTS machine, and Charpy tensile apparatus, respectively. It was found that the fracture energy of the unfilled natural rubber did not vary significantly over the range of sample strain rate, but there was significant variation in the fracture energy of the 25 phr carbon black-filled natural rubber from 0.01 to 71 s−1 sample strain rate. The fracture energy of the 25 phr carbon black-filled natural rubber at a sample strain rate of 0.1 s−1 was about three times greater than it was at the 10 s−1 sample strain rate. While the carbon black fillers increased the fracture energy of natural rubber by about 200% at quasistatic sample strain rates (0.01–0.1 s−1) and at 71 s−1, the carbon black fillers did nothing to improve the fracture energy of natural rubber at sample strain rates between 5 and 29 s−1. In this strain rate range, the fracture energy of 25 phr carbon black-filled natural rubber was almost the same as that in the unfilled natural rubber. The variation in the fracture energy with far-field strain rate was due to changes in the material behavior of natural rubber at high strain rates. Finite element analysis using a high-strain-rate constitutive equation for the 25 phr carbon black rubber specimen was used to calculate the fracture energy of the specimen at a sample strain rate of 55 s−1, and good agreement was found between the test and finite element results.

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