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Journal articles on the topic 'Master curves'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Gu, Linhao, Luchuan Chen, Weiguang Zhang, Haixia Ma, and Tao Ma. "Mesostructural Modeling of Dynamic Modulus and Phase Angle Master Curves of Rubber Modified Asphalt Mixture." Materials 12, no. 10 (May 22, 2019): 1667. http://dx.doi.org/10.3390/ma12101667.

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The main objective of this paper was to develop a mesostructure-based finite element model of rubber modified asphalt mixture to predict both the dynamic modulus master curve and phase angle master curve under a large frequency range. The asphalt mixture is considered as a three-phase material consisting of aggregate, asphalt mortar, and air void. The mesostructure of the asphalt mixture was digitized by a computed tomography (CT) scan and implemented into finite element software. The 2S2P1D model was used to obtain the viscoelastic information of an asphalt mortar under a large range of frequencies and temperatures. The continuous spectrum of the 2S2P1D model was converted to a discrete spectrum and characterized by the generalized Maxwell model for numerical simulation. The Prony series parameters of the generalized Maxwell model and the elastic modulus of the aggregates were inputted into the finite element analysis as material properties. The dynamic modulus tests of a rubber modified asphalt mortar and asphalt mixture were conducted under different temperatures and loading frequencies. The dynamic modulus master curve and phase angle master curve of both asphalt mortar and asphalt mixture were constructed. The frequency of the finite element simulations of the dynamic modulus tests ranged from 10−6 to 104. The dynamic modulus and phase angle of the asphalt mixture was calculated and the master curves were compared with the master curves obtained from the experimental data. Furthermore, the effect of the elastic modulus of aggregates on the master curves was analyzed. Acceptable agreement between dynamic modulus master curves obtained from experimental data and simulation results was achieved. However, large errors between phase angle master curves appeared at low frequencies. A method was proposed to improve the prediction of the phase angle master curve by adjusting the equilibrium modulus of the asphalt mortar.

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2

Zhang, Fei, Lan Wang, Chao Li, and Yongming Xing. "Predict the Phase Angle Master Curve and Study the Viscoelastic Properties of Warm Mix Crumb Rubber-Modified Asphalt Mixture." Materials 13, no. 21 (November 9, 2020): 5051. http://dx.doi.org/10.3390/ma13215051.

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To identify the most accurate approach for constructing of the dynamic modulus master curves for warm mix crumb rubber modified asphalt mixtures and assess the feasibility of predicting the phase angle master curves from the dynamic modulus ones. The SM (Sigmoidal model) and GSM (generalized sigmoidal model) were utilized to construct the dynamic modulus master curve, respectively. Subsequently, the master curve of phase angle could be predicted from the master curve of dynamic modulus in term of the K-K (Kramers–Kronig) relations. The results show that both SM and GSM can predict the dynamic modulus very well, except that the GSM shows a slightly higher correlation coefficient than SM. Therefore, it is recommended to construct the dynamic modulus master curve using GSM and obtain the corresponding phase angle master curve in term of the K-K relations. The Black space diagram and Wicket diagram were utilized to verify the predictions were consistent with the LVE (linear viscoelastic) theory. Then the master curve of storage modulus and loss modulus were also obtained. Finally, the creep compliance and relaxation modulus can be used to represent the creep and relaxation properties of warm-mix crumb rubber-modified asphalt mixtures.

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3

Bonaquist, Ramon, and Donald W. Christensen. "Practical Procedure for Developing Dynamic Modulus Master Curves for Pavement Structural Design." Transportation Research Record: Journal of the Transportation Research Board 1929, no. 1 (January 2005): 208–17. http://dx.doi.org/10.1177/0361198105192900125.

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A dynamic modulus master curve for asphalt concrete is a critical input for flexible pavement design in the mechanistic–empirical pavement design guide developed in NCHRP Project 1–37A. The recommended testing to develop the modulus master curve is presented in AASHTO Provisional Standard TP62–03, Standard Method of Test for Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures. It includes testing at least two replicate specimens at five temperatures between 14°F and 130°F (–10°C and 54.4°C) and six loading rates between 0.1 and 25 Hz. The master curve and shift factors are then developed from this database of 60 measured moduli using numerical optimization. The testing requires substantial effort, and there is much overlap in the measured data, which is not needed when numerical methods are used to perform the time–temperature shifting for the master curve. This paper presents an alternative to the testing sequence specified in AASHTO TP62–03. It requires testing at only three temperatures between 40°F and 115°F (4.4°C and 46.1°C) and four rates of loading between 0.01 and 10 Hz. An analysis of data collected using the two approaches shows that comparable master curves are obtained. This alternative testing sequence can be used in conjunction with the simple performance test system developed in NCHRP Project 9–29 to develop master curves for structural design.

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4

Pouchly, Vaclav, and Karel Maca. "Master sintering curves of two different alumina powder compacts." Processing and Application of Ceramics 3, no. 4 (2009): 177–80. http://dx.doi.org/10.2298/pac0904177p.

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Concept of Master Sintering Curve is a strong tool for optimizing sintering schedule. The sintering behaviour can be predicted, and sintering activation energy can be calculated with the help of few dilatometric measurements. In this paper an automatic procedure was used to calculate Master Sintering Curves of two different alumina compacts. The sintering activation energies were determined as 640 kJ/mol for alumina with particle size of 240 nm, respective 770 kJ/mol for alumina with particle size of 110 nm. The possibility to predict sintering behaviour with the help of Master Sintering Curve was verified. .

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5

Bertin, Jose, and Pol Vanhaecke. "The even master system and generalized Kummer surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 1 (July 1994): 131–42. http://dx.doi.org/10.1017/s030500410007242x.

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AbstractIn this paper we study a generalized Kummer surface associated to the Jacobian of those complex algebraic curves of genus two which admit an automorphism of order three. Such a curve can always be written as y2 = x6 + 2kx3 + 1 and k2 ╪ 1 is the modular parameter. The automorphism extends linearly to an automorphism of the Jacobian and we show that this extension has a 94 invariant configuration, i.e. it has 9 fixed points and 9 invariant theta curves, each of these curves contains 4 fixed points and 4 invariant curves pass through each fixed point. The quotient of the Jacobian by this automorphism has 9 singular points of type A2 and the 94 configuration descends to a 94 configuration of points and lines, reminiscent to the well-known 166 configuration on the Kummer surface. Our ‘generalized Kummer surface’ embeds in ℙ4 and is a complete intersection of a quadric and a cubic hypersurface. Equations for these hypersurfaces are computed and take a very symmetric form in well-chosen coordinates. This computation is done by using an integrable system, the ‘even master system’.

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6

SOLATIFAR, Nader, Amir KAVUSSI, Mojtaba ABBASGHORBANI, and Henrikas SIVILEVIČIUS. "Application of FWD data in developing dynamic modulus master curves of in-service asphalt layers." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 23, no. 5 (May 24, 2017): 661–71. http://dx.doi.org/10.3846/13923730.2017.1292948.

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This paper presents a simple method to determine dynamic modulus master curve of asphalt layers by conducting Falling Weight Deflectometer (FWD) for use in mechanistic-empirical rehabilitation. Ten new and rehabilitated in-service asphalt pavements with different physical characteristics were selected in Khuzestan and Kerman provinces in south of Iran. FWD testing was conducted on these pavements and core samples were taken. Witczak prediction model was used to predict dynamic modulus master curves from mix volumetric properties as well as the bitumen viscosity characteristics. Adjustments were made using FWD results and the in-situ dynamic modulus master curves were obtained. In order to evaluate the efficiency of the proposed method, the results were compared with those obtained by using the developed procedure of the state-of-the-practice, Mechanistic-Empirical Pavement Design Guide (MEPDG). Results showed the proposed method has several advantages over MEPDG including: (1) simplicity in directly constructing in-situ dynamic modulus master curve; (2) developing in-situ master curve in the same trend with the main predicted one; (3) covering the large differences between in-situ and predicted master curve in high frequencies; and (4) the value obtained for the in-situ dynamic modulus is the same as the value measured by the FWD for a corresponding frequency.

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7

Zou, Guilian, Xiaoning Zhang, Jian Xu, and Fengxia Chi. "Morphology of Asphalt Mixture Rheological Master Curves." Journal of Materials in Civil Engineering 22, no. 8 (August 2010): 806–10. http://dx.doi.org/10.1061/(asce)mt.1943-5533.0000024.

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8

Lambrigger, Markus. "Avrami Master Curves for Isothermal Polymer Crystallization." Polymer Journal 29, no. 2 (February 1997): 188–89. http://dx.doi.org/10.1295/polymj.29.188.

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9

Kapnistos, M., and D. Vlassopoulos. "Rheological Master Curves of Crystallizing Polymer Mixtures." Applied Rheology 16, no. 3 (June 1, 2006): 132–35. http://dx.doi.org/10.1515/arh-2006-0008.

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Abstract We present a simple methodology for extending linear viscoelastic measurements of crystallizing polymers to the high-frequency regime, where usually crystallization kinetics represents an obstacle. The idea is to perform rapid quenches, below the melting temperature (which corresponds to the high-frequency region), account for the thermal equilibration and the very slow early stages of crystallization, and perform the measurements before really crystallization sets in, in the “quasi-equilibrium” state. Albeit tedious, when properly done, this method works remarkably well, as demonstrated for a particular polybutadiene mixture, and opens the route for obtaining rheological master curves in a wide variety of crystallizing polymers.

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10

Rojas, Jose I., Jorge Nicolás, and Daniel Crespo. "Study on Mechanical Relaxations of 7075 (Al–Zn–Mg) and 2024 (Al–Cu–Mg) Alloys by Application of the Time-Temperature Superposition Principle." Advances in Materials Science and Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/2602953.

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The viscoelastic response of commercial Al–Zn–Mg and Al–Cu–Mg alloys was measured with a dynamic-mechanical analyzer (DMA) as a function of the temperature (from 30 to 425°C) and the loading frequency (from 0.01 to 150 Hz). The time-temperature superposition (TTS) principle has proven to be useful in studying mechanical relaxations and obtaining master curves for amorphous materials. In this work, the TTS principle is applied to the measured viscoelastic data (i.e., the storage and loss moduli) to obtain the corresponding master curves and to analyze the mechanical relaxations responsible for the viscoelastic behavior of the studied alloys. For the storage modulus it was possible to identify a master curve for a low-temperature region (from room temperature to 150°C) and, for the storage and loss moduli, another master curve for a high-temperature region (from 320 to 375°C). These temperature regions are coincidental with the stable intervals where no phase transformations occur. The different temperature dependencies of the shift factors for the identified master curves, manifested by different values of the activation energy in the Arrhenius expressions for the shift factor, are due to the occurrence of microstructural changes and variations in the relaxation mechanisms between the mentioned temperature regions.

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11

Yu, Tao, Hui Zhang, Jiang Feng Sheng, and Yi Xi Liu. "Lifetime Prediction of Nitrile Butadiene Rubber Used for O-Ring Sealing." Applied Mechanics and Materials 423-426 (September 2013): 326–30. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.326.

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This work predicts the service life of nitrile butadiene rubbers used for O-ring sealing. The principle of time-temperature equivalence was adopted to shift the thermal ageing behaviors of rubbers and construct a master curve by superposition. The lifetime of rubbers were estimated from the master curves.

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12

Gong, Yu-Seok, Dowan Kim, and Sungho Mun. "Estimation of the Dynamic Moduli of Viscoelastic Asphalt Mixtures Using the Extended Kalman Filter Algorithm." Advances in Civil Engineering 2018 (December 10, 2018): 1–8. http://dx.doi.org/10.1155/2018/3089085.

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Here, we develop a model predicting the dynamic moduli of hot-mix asphalt/concrete using the extended Kalman filter (EKF) algorithm and draw frequency-domain master curves. Discrete dynamic moduli were obtained via impact resonance tests (IRTs) on linear viscoelastic (LVE) asphalt at 20, 30, 35, 40, and 50°C. Typically, viscoelastic characteristics have been used to derive asphalt dynamic moduli; compressive frequency sweep tests at different frequencies (Hz) and temperatures are employed to this end. We compared IRT-derived viscoelastic master curves obtained via compressive frequency sweep testing to those derived using the EKF algorithm, which employs a nonlinear sigmoidal curve and a Taylor series to explore the viscoelastic function. The model reduced errors at both low and high frequencies by correcting the coefficients of the master curve. Furthermore, the predictive model effectively estimated dynamic moduli at various frequencies, and also root-mean-square errors (RMSEs) which, together with the mean percentage errors (MPEs), were used to compare predictions.

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13

Nega, Ainalem, Behzad Ghadimi, and Hamid Nikraz. "Developing Master Curves, Binder Viscosity and Predicting Dynamic Modulus of Polymer-Modified Asphalt Mixtures." International Journal of Engineering and Technology 7, no. 3 (June 2015): 190–97. http://dx.doi.org/10.7763/ijet.2015.v7.790.

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14

Seo, Boh Wi, and Jae Hoon Kim. "Estimation of Master Curves of Relaxation Modulus and Tensile Properties for Solid Propellant." Advanced Materials Research 871 (December 2013): 247–52. http://dx.doi.org/10.4028/www.scientific.net/amr.871.247.

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The stress relaxation modulus E(t) is one of the most important properties of viscoelastic materials such as solid propellant, and it is used to define the viscoelastic behavior based on the influence of time and temperature. In this paper, stress relaxation tests are conducted under constant strain 2% for 600 seconds in the range of temperature 60°C to-60°C and tensile tests are performed for solid propellants under constant cross head rate 5 mm/min in the same temperatures as stress relaxation tests. Based on the results, time-temperature shift factors are obtainedby shifting the relaxation modulus curves horizontally and the master curve of relaxation modulus is generated. The master curve of relaxation modulus according to classical method and Williams-Landel-Ferry (WLF) method are discussed. Also, the master curve of tensile properties are drawn using predetermined shift factor and the results are discussed.

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15

Liu, Jiefeng, Xianhao Fan, Yiyi Zhang, Hanbo Zheng, Huilu Yao, Chaohai Zhang, Yubo Zhang, and Dajian Li. "A Novel Universal Approach for Temperature Correction on Frequency Domain Spectroscopy Curve of Transformer Polymer Insulation." Polymers 11, no. 7 (July 2, 2019): 1126. http://dx.doi.org/10.3390/polym11071126.

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It is a fact that the frequency domain spectroscopy (FDS) curve at different temperatures can be corrected by the shift factor (αT) extracted from the master curve. However, the αT and master curve reported by previous works are distinctive due to the difference in the construction algorithm. Therefore, it is of great significance to report a universal approach for extracting αT. In this work, the unaged oil-immersed pressboards with different moisture content (mc%) are firstly prepared and selected as the research specimen. Then, the αT of FDS curves on the above pressboard is extracted based upon the master curve technique. The influence mechanism under the various test temperature (T) and mc% is therefore analyzed so as to establish a universal model for predicting the αT. The present findings reveal that the αT value extracted from FDS curves is both temperature-dependent and moisture-dependent. In addition, the predicted αT is not only suitable for temperature correction on FDS curve of same type pressboard with different insulation conditions (moisture contents and aging degrees), but also maintains considerable accuracy when applied to different types of pressboard. Therefore, the obtained conclusions will provide a universal method for temperature correction on FDS curve of transformer polymer insulation.

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16

Iwadate, T., Y. Tanaka, and H. Takemata. "Prediction of Fracture Toughness KIC Transition Curves of Pressure Vessel Steels From Charpy V-Notch Impact Test Results." Journal of Pressure Vessel Technology 116, no. 4 (November 1, 1994): 353–58. http://dx.doi.org/10.1115/1.2929601.

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A single and generalized prediction method of fracture toughness KIC transition curves of pressure vessel steels has been greatly desired by engineers in the petro-chemical and nuclear power industries, especially from the viewpoint of life extension of reactor pressure vessels. In this paper, the toughness degradation of Cr-Mo steels during long-term service was examined and the two prediction methods of fracture toughness KIC transition curves were studied using the data of 54 heats. 1) The toughness degradation of 2 1/4Cr-1Mo steels levels off within around 50,000 h service. 2) The FATT versus J-factor (=(Si+Mn)(P+Sn)×104) and/or X (=(10P+5Sb+4Sn+As)x10−2) relationships to estimate the maximum embrittlement of Cr-Mo steels were obtained. 3) A master curve method developed by authors et al.; that is, the method using a KIC/KIC−US versus excess temperature master curve of each material was presented for 2 1/4Cr-1Mo, 1 1/4Cr-1/2Mo, 1Cr and 1/2Mo chemical pressure vessel steels and ASTM A508 C1.1, A508 C1.2, A508 C1.3 and A533 Gr.B C1.1 nuclear pressure vessel steels, where KIC−US is the upper-shelf fracture toughness and excess temperature is test temperature minus FATT. 4) A generalized prediction method to predict the KIC transition curves of any low-alloy steels was developed. This method consists of KIC/KIC−US versus T–T0 master curve and temperature shift ΔT between fracture toughness and CVN impact transition curves versus yield strength relationship, where To is the temperature showing 50 percent KIC−US of the material. 5) The KIC transition curves predicted using both methods showed a good agreement with the lower bound of measured KJC values obtained from JC tests.

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17

Hsueh, Chun-Hway, and Pedro Miranda. "Master curves for Hertzian indentation on coating/substrate systems." Journal of Materials Research 19, no. 1 (January 2004): 94–100. http://dx.doi.org/10.1557/jmr.2004.19.1.94.

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An analytical model was developed to derive an approximate closed-form solution for indenter displacement when a rigid spherical indenter is pressed onto a coating/substrate system. Finite element analyses were also performed to verify the analytical solution. The results showed that the solution could be obtained from the analytical expression for Hertzian indentation on a homogeneous semi-infinite elastic medium multiplied by a modification term. This modification term is a function of two ratios: (i) Young’s modulus ratio between the coating and the substrate and (ii) the ratio between the coating thickness and the contact radius. Based on this modification term, master curves for Hertzian indentation on coating/substrate systems were plotted.

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18

Steller, Ryszard, and Jacek Iwko. "Shear Stress‐Dependent Viscosity Master Curves for Practical Applications." Polymer Engineering & Science 60, no. 1 (October 18, 2019): 44–54. http://dx.doi.org/10.1002/pen.25257.

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19

Zanzotto, L., and J. Stastna. "Dynamic master curves from the stretched exponential relaxation modulus." Journal of Polymer Science Part B: Polymer Physics 35, no. 8 (June 1997): 1225–32. http://dx.doi.org/10.1002/(sici)1099-0488(199706)35:8<1225::aid-polb8>3.0.co;2-s.

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20

Asgharzadeh, Seyed Mohammad, Nader Tabatabaee, Koorosh Naderi, and Manfred Partl. "An empirical model for modified bituminous binder master curves." Materials and Structures 46, no. 9 (December 4, 2012): 1459–71. http://dx.doi.org/10.1617/s11527-012-9988-x.

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21

Mizumura, Kazumasa. "Analyses of Flow Mechanism Based on Master Recession Curves." Journal of Hydrologic Engineering 10, no. 6 (November 2005): 468–76. http://dx.doi.org/10.1061/(asce)1084-0699(2005)10:6(468).

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22

Robertson, I. M., and G. B. Schaffer. "Refinement of Master Densification Curves for Sintering of Titanium." Metallurgical and Materials Transactions A 41, no. 11 (July 2, 2010): 2949–58. http://dx.doi.org/10.1007/s11661-010-0290-7.

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23

Lambrigger, Markus. "Non-isothermal polymer crystallization kinetics and Avrami master curves." Polymer Engineering & Science 38, no. 4 (April 1998): 610–15. http://dx.doi.org/10.1002/pen.10225.

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24

Wang, Teng, Jun Tao Lin, Ling Pang, Min Lei, Kim Jenkins, and Shao Peng Wu. "Study on the Viscoelastic Performance of Asphalt Mixture Based on Dynamic Modulus." Advanced Materials Research 753-755 (August 2013): 728–33. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.728.

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The fitting models of dynamic modulus of asphalt mixtures were studied in this paper. UTM dynamic modulus tests were adopted to determine the dynamic modulus of two asphalt (A, B) mixtures. Then, the WLF equation and Arrhenius formula, based on the time-temperature equivalence principle, were used to get the shift factors and master curves of asphalt mixtures. Combined with Sigmoidal model and CAM model, it was founded that the Arrhenius formula was more suitable to get the master curves of asphalt mixtures. What is more, the CAM model was more suitable to fit master curves of both asphalt mixtures.

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25

De, S., J. A. M. Kuipers, E. A. J. F. Peters, and J. T. Padding. "Viscoelastic flow past mono- and bidisperse random arrays of cylinders: flow resistance, topology and normal stress distribution." Soft Matter 13, no. 48 (2017): 9138–46. http://dx.doi.org/10.1039/c7sm01818e.

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Different flow resistance curves for viscoelastic flows through random arrangements of cylinders collapse to a single master curve when plotted against a Deborah number based on the square root of the permeability as characteristic length scale.

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26

Lambrigger, Markus. "Polymer crystallization kinetics, master quotients, master curves and Nakamura-Ozawa-equations of iPP and PTFE." Polymer Engineering and Science 44, no. 12 (2004): 2194–202. http://dx.doi.org/10.1002/pen.20247.

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27

Álvarez-Vázquez, Adrián, Alfonso Fernández-Canteli, Enrique Castillo Ron, Pelayo Fernández Fernández, Miguel Muñiz-Calvente, and María Jesús Lamela Rey. "A Novel Approach to Describe the Time–Temperature Conversion among Relaxation Curves of Viscoelastic Materials." Materials 13, no. 8 (April 11, 2020): 1809. http://dx.doi.org/10.3390/ma13081809.

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Time and temperature, besides pressure in a lesser extent, represent the most significant variables influencing the rheological behavior of viscoelastic materials. These magnitudes are each other related through the well-known Time–Temperature Superposition (TTS) principle, which allows the master curve referred to relaxation (or creep) behavior to be derived as a material characteristic. In this work, a novel conversion law to interrelate relaxation curves at different temperatures is proposed by assuming they to be represented by statistical cumulative distribution functions of the normal or Gumbel family. The first alternative responds to physical considerations while the latter implies the fulfillment of extreme value conditions. Both distributions are used to illustrate the suitability of the model when applied to reliable derivation of the master curve of Polyvinil–Butyral (PVB) from data of experimental programs. The new approach allows not only the TTS shift factors to be estimated by a unique step, but the whole family of viscoelastic master curves to be determined for the material at any temperature. This represents a significant advance in the characterization of viscoelastic materials and, consequently, in the application of the TTS principle to practical design of viscoelastic components.

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28

Yanyo, L. C., and F. N. Kelley. "Effect of Network Chain Length on the Tearing Energy Master Curves of Poly(Dimethyldiphenyl Siloxane)." Rubber Chemistry and Technology 61, no. 1 (March 1, 1988): 100–118. http://dx.doi.org/10.5254/1.3536169.

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Abstract Five different molecular weights of vinyl-terminated poly(dimethyldiphenyl siloxane) were endlinked with tetrakis(dimethylsiloxy)silane to produce networks of various crosslink densities. A hydrosilation endlinking reaction was chosen, since this method provides the advantage of easily controlling the network chain length and network morphology. Tear energies were determined using a modified trouser-tear test piece at several rates and temperatures. All of the tear energy data for each crosslink density could be shifted to a single master curve with the same WLF coefficients, C1=6 and C2=108 K. The threshold tear energy of PDMDPS is different from unsubstituted PDMS because the average molecular weight per backbone atom and density are increased by the presence of phenyl groups. Each of the tear-energy master curves of PDMDPS shift to a single curve with Mc1/2, except in regions near the glass transition. Deviations of the curves are observed to coincide with increases in the crack-tip diameter with increasing molecular weight between crosslinks. In the lower transition region of the tear-energy master curve, the loss function is determined by the hysteresis of the material. Near the glass transition, the effect of the strain energy and strain-energy distribution, as well as the hysteresis, must be considered. Deviations of the master curves with crosslink density can also be explained from the changes in the loss function for each curve due to the differences in strain and strain distribution for different crack-tip diameters which were visually evident. Andrews' representation of the loss function of the tear energy is known to be dependent on hysteresis, strain energy, and the strain-energy distribution near the crack tip. Modifying his relation, the tear energy was shown to increase with hysteresis as long as the strain energy and strain-energy distribution remained constant. The strain energy distribution was also shown to increase directly with the molecular weight between crosslinks of the network.

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29

Bódai, Gábor, and Tibor Goda. "On the Relation between Stress Relaxation and Constant Strain Rate Tensile Behavior for Linear Viscoelastic Materials; An Engineering Approach." Materials Science Forum 729 (November 2012): 314–19. http://dx.doi.org/10.4028/www.scientific.net/msf.729.314.

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The present paper, as a first step summarizes briefly the master curve construction methods applying the stress relaxation and DMTA based approach. Then, authors make recommendation to increase the covered time (frequency) domain of relaxation modulus master curve coming from standard tensile tests-performed at wide temperature range-by utilizing the time-temperature superposition principle. The proposed approach is used for natural rubber, whose tensile tests, for the sake of simplicity, are replaced by calculated engineering stress-strain curves. All in all, the proposed method gives fast and reliable way for engineers to identify the parameters of spring-dashpot models.

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30

Wunde, Matthias, and Manfred Klüppel. "VISCOELASTIC RESPONSE DURING CRACK PROPAGATION OF UNFILLED AND FILLED SBR." Rubber Chemistry and Technology 91, no. 4 (October 1, 2018): 668–82. http://dx.doi.org/10.5254/rct.18.81537.

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ABSTRACT The crack propagation behavior of unfilled and filled styrene–butadiene rubber (SBR) in steady and dynamic tearing was investigated using tensile tests on trousers samples and tear fatigue measurements on single edge notched tension (SENT) samples, respectively. For the unfilled sample, both types of measurements indicated that the tearing energy is dominated by the viscoelastic response of the polymer. This was demonstrated by the creation of crack growth master curves using the horizontal shift factors obtained from mastering the complex modulus. The tearing energy increased with increasing crack velocity and decreasing temperature as required by the time-temperature superposition principle. The crack growth master curves followed a power law with the same exponent for steady and dynamic tearing. This exponent agrees fairly well with the exponent predicted by linear viscoelastic crack propagation theory. For steady tearing at high crack propagation rates, systematic deviations from the master curves appeared, which were attributed to flash temperature effects. For the filled SBR, which contained 50 phr carbon black, only dynamic tearing was found to be dominated by the viscoelastic response of the polymer. For steady tearing, filler networking seemed to alter crack propagation rates significantly, so that the viscoelastic fingerprint was no longer visible. For the filled sample, additional measurements with a high preload were conducted. It was demonstrated that a single master curve can be constructed, only if the (static) preload contribution is neglected and the dynamic contribution of the energy density is used for the evaluation of the tearing energy. This master curve showed two distinct slopes at high and low crack velocities. It is argued that the higher slope at low crack speeds is relevant for lifetime predictions based on the integration of the Paris–Erdogan power law. Under conditions in which the viscoelastic crack propagation holds, very slow crack growth rates can be explored at reasonable testing times by measurements at elevated temperatures.

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31

Stacer, R. G., E. D. von Meerwall, and F. N. Kelley. "Time-Dependent Tearing of Carbon Black-Filled and Strain Crystallizing Vulcanizates." Rubber Chemistry and Technology 58, no. 5 (November 1, 1985): 913–23. http://dx.doi.org/10.5254/1.3536103.

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Abstract 1. Unstable tearing can be minimized and tear-tip diameter held reasonably constant for carbon black-filled and strain-crystallizing vulcanizates using a constrained trouser tear testpiece first suggested by Gent and Henry. In the absence of these complicating features, the tear energy has been shown to be thermo-rheologically simple, readily lending itself to time-temperature superposition over a broad range of temperatures and rates. 2. Shift factors used to superpose tear energy data at different temperatures for both filled and unfilled SBR also superposed small deformation stress-relaxation data. This result did not hold for the NR formulations tested, indicating that the temperature dependency of the principal viscoelastic process is different for these properties. Evidence of this was observed in the thermal expansion coefficient, a, derived from the WLF coefficients, which increased by a factor of 10 for tear energy data. It is concluded that even with the tear path constrained, strain-induced crystallization still occurs near the tear tip for the NR formulations. 3. Temperature-reduced tear energy master curves for both filled and unfilled vulcanizates showed the same general tear behavior when referenced to Tg. At high rates or low temperatures, the master curves coincide, approaching a characteristic tear energy of approximately 50 kJ/m2, regardless of formulation. Only at lower rates did the different nature of the rubbers become apparent. All the master curves showed evidence of a tear energy plateau between −15 and −10 decades in rate, with the NR compounds showing the lowest slopes in this region. 4. Addition of filler increases the tear energy by approximately 20–40% over most of the master curves. This supports a previous conclusion of Gent and Henry that the major effect of reinforcing filler is to dissipate energy over a larger volume of material without significantly increasing inherent strength. Addition of filler also tended to mask the plateau in the tear energy master curve and decrease both the free volume at Tg and the thermal expansion coefficient of the material.

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32

Tatami, Junichi, Y. Suzuki, Toru Wakihara, Takeshi Meguro, and Katsutoshi Komeya. "Control of Shrinkage during Sintering of Alumina Ceramics Based on Master Sintering Curve Theory." Key Engineering Materials 317-318 (August 2006): 11–14. http://dx.doi.org/10.4028/www.scientific.net/kem.317-318.11.

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The Master Sintering Curve (MSC) is quite useful for analyzing the shrinkage behavior of ceramics. It is possible to compare shrinkage behavior using MSCs that are obtained from different firing profiles. In this study, shrinkage behavior during sintering of green bodies of several kinds of Al2O3 based ceramics were evaluated, using an electric furnace equipped with a dilatometer to be controlled based on the MSC theory. Although all of the samples shrank monotonically, shrinkage behavior depended on the additive and heating rate. The MSC theory was applied to analyze shrinkage behavior. As a result, a different MSC could be obtained in Al2O3 with and without the addition of MgO. In the pure Al2O3, a single MSC could be obtained from shrinkage curves by firing at a heating rate of 7.5-20oC/min, though the shrinkage curve at a heating rate of 3-5oC/min did not correspond with the MSC. In contrast, shrinkage curves at heating rate of 5-20oC/min were converged in the case of the MgO doped Al2O3 to obtain a unique MSC independent of firing profile. Apparent activation energy for sintering was estimated as 555 kJ/mol in the pure Al2O3 and 880 kJ/mol in the MgO doped Al2O3. The firing profile to obtain a requested sintering shrinkage curve was predicted from the resultant MSC. A comparison between the predicted and the experimental shrinkage curves, showed good consistency, thus confirming that it is possible to control shrinkage behavior using the MSC.

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Zhou, Song, and Xiaodi Wu. "Fatigue life prediction of composite laminates by fatigue master curves." Journal of Materials Research and Technology 8, no. 6 (November 2019): 6094–105. http://dx.doi.org/10.1016/j.jmrt.2019.10.003.

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Thiel, B. L. "Gas Amplification Master Curves for Low Vacuum and Environmental SEM." Microscopy and Microanalysis 10, S02 (August 2004): 128–29. http://dx.doi.org/10.1017/s1431927604884605.

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35

Marković, Smilja, and Dragan Uskoković. "The master sintering curves for BaTi0.975Sn0.025O3/BaTi0.85Sn0.15O3 functionally graded materials." Journal of the European Ceramic Society 29, no. 11 (August 2009): 2309–16. http://dx.doi.org/10.1016/j.jeurceramsoc.2009.01.027.

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Reichert, Thomas, Wolfgang Böhme, and Johannes Tlatlik. "Modified Shape of Dynamic Master Curves due to Adiabatic Effects." Procedia Structural Integrity 2 (2016): 1652–59. http://dx.doi.org/10.1016/j.prostr.2016.06.209.

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Pittenger, Bede, Sergey Osechinskiy, Thomas Mueller, and Dalia Yablon. "Measuring Viscoelastic Master Curves at the Nanoscale in Polymer Composites." Microscopy and Microanalysis 26, S2 (July 30, 2020): 1958–60. http://dx.doi.org/10.1017/s1431927620019947.

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38

Thridandapani, R. R., D. C. Folz, and D. E. Clark. "Development of a microwave dilatometer for generating master sintering curves." Measurement Science and Technology 22, no. 10 (September 2, 2011): 105706. http://dx.doi.org/10.1088/0957-0233/22/10/105706.

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Liang, Ji-Zhao, Lei Zhong, and Kejian Wang. "Analysis of melt spinning master-curves of low density polyethylene." Journal of Applied Polymer Science 125, no. 3 (January 20, 2012): 2202–6. http://dx.doi.org/10.1002/app.36421.

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40

Flämig, M., M. Hofmann, and E. A. Rössler. "Field-cycling NMR relaxometry: the benefit of constructing master curves." Molecular Physics 117, no. 7-8 (September 16, 2018): 877–87. http://dx.doi.org/10.1080/00268976.2018.1517906.

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41

Mazaheri, Mehdi, A. Simchi, M. Dourandish, and F. Golestani-Fard. "Master sintering curves of a nanoscale 3Y-TZP powder compacts." Ceramics International 35, no. 2 (March 2009): 547–54. http://dx.doi.org/10.1016/j.ceramint.2008.01.008.

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Khandaker, Md Shahriar K., Daniel M. Dudek, Eric P. Beers, and David A. Dillard. "Expression, crosslinking, and developing modulus master curves of recombinant resilin." Journal of the Mechanical Behavior of Biomedical Materials 69 (May 2017): 385–94. http://dx.doi.org/10.1016/j.jmbbm.2017.01.009.

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43

Ashtiani, Milad Zokaei, Walaa S. Mogawer, and Alexander J. Austerman. "A Mechanical Approach to Quantify Blending of Aged Binder from Recycled Materials in New Hot Mix Asphalt Mixtures." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 28 (August 20, 2018): 107–18. http://dx.doi.org/10.1177/0361198118787634.

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In the paving industry, there is increased interest in using recycled materials like recycled asphalt shingles (RAS) and reclaimed asphalt pavements (RAP) due to the valuable asphalt binder contained within them. The major concern with using these materials is that the binder they contain is highly aged, which could lead to reduced mixture durability. Therefore, a method is needed to quantify the extent to which the aged binders from these materials blend with virgin binder when producing mixtures in order to understand better their effects on mixture performance. In this study, a new approach to quantify the amount of blending that occurs between aged RAS and RAP binders and a virgin binder was developed. Asphalt binders were extracted and recovered from RAS and RAP stockpiles and blended with a PG64-28 virgin binder in varying proportions. The master curves of these mixtures were constructed at 20°C. Asphalt mixtures containing different proportions of the same RAS and RAP stockpiles were then designed and the dynamic moduli of the mixtures were measured to construct mixture master curves at 20°C. The binder master curves for each blending proportion were then substituted into a locally calibrated Hirsch model to predict the mixture master curves. Comparison of the measured and predicted mixture master curves suggested that the aged binder from RAS and RAP blends with the virgin binder less than 40% and 60%, respectively. Cracking tests were also conducted to validate the proposed degrees of blending from a mixture mechanical performance point of view.

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44

Latuamury, Bokiraiya Okky, Lydia Riekie Parera, and Husein Marasabessy. "Characterizing River Baseflow Recession Using Linear Reservoir Model in Alang Watershed, Central Java, Indonesia." Indonesian Journal of Geography 52, no. 1 (April 28, 2020): 15. http://dx.doi.org/10.22146/ijg.43565.

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Alang is a sub-watershed emptying into the Gajah Mungkur Reservoir in Wonogiri, Central Java Indonesia, with an area of 51.01 km2 and lithology composed of Baturetno Formation and Wonosari Formation. Baseflow is a major component of river flow during the dry season. Hence, the characterization of its recession becomes necessary, and it can be performed with innovation in baseflow hydrological modeling, that is, the recession curve. This study was designed to describe the distinctive features of baseflow recession using a linear reservoir model, which is depicted in individual and master recession curves. The baseflow recession in AlangSubwatershed was represented by a combination of varying initial recession discharge (Q0), α, and recession constants (Krb). The individual recession curves were typified by Q0=0.19-9.11, α= 0.089-0.243, and Krb=0.7843-0.9148. As for the master recession curve, it had Q0=9.99, α=0.085, and Krb=0.928. These results signify a sloping recession curve, meaning that the water storage and aquifer characteristics that store and transmit water in Alang Subwatershed are in good condition.

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45

Gomez Isidro, Sully, and Viviana Lucía Gómez-Ríos. "Baseflow analysis using master recession curves and numerical algorithms in mountain basins: Suratá's river and Oro's river (Santander, Colombia)." DYNA 83, no. 196 (April 20, 2016): 213–22. http://dx.doi.org/10.15446/dyna.v83n196.53222.

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<p>The interaction between groundwater inflow and outflow is complex in streams connected from aquifers located in fractured rock media. The recession curves of hydrographs provide information about these hydrogeological processes and they are useful to assess an insight in the storage-discharge relationship in subsurface reservoirs. In this study, the physic base and the nonlinearity relationship of storagedischarge were analyzed through a mathematical expression which describe a master recession curve. Four numerical algorithms were applied to estimate the baseflow of the Suratá's River basin and the high Oro's River basin, Santander-Colombia. In both cases, master recession curves showed the nonlinearity relationship in storage-discharge. Furthermore, the exponent values and the proportionality constants give additional information about the aquifers in contact to the river and the special scale of recharges that may occur in these aquifers.</p>

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Abdollahi, Seyed Farhad, Mehdi Farrokhi, and Nader Tabatabaee. "Development of a Computer Program for Calculation of the Alpha Parameter in the Linear Amplitude Sweep Test and Comparison with Rheological Parameters." Transportation Research Record: Journal of the Transportation Research Board 2674, no. 7 (June 12, 2020): 284–98. http://dx.doi.org/10.1177/0361198120922042.

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Characterizing and modeling the fatigue performance of an asphalt binder is important when designing asphalt mixtures which can resist premature fatigue failure. Performance grading (PG) standards include the fatigue factor ( G*.sinδ) to evaluate the fatigue resistance of asphalt binders. This criterion seems to be inaccurate, especially when applied to modified asphalt binders. American Association of State Highway and Transportation Officials (AASHTO) TP 101 has been designed to evaluate the fatigue resistance of asphalt binders using Schapery’s work potential theory. The damage evolution rate ( α parameter) is the key element of this method and is calculated from the rheological properties of the undamaged asphalt binder using the slope of the relaxation modulus versus the time on the log-log scale. Owing to the difficulties of conducting the relaxation test, the relaxation modulus is usually obtained using conversion methods. However, AASHTO TP 101 uses a simplified indirect method to calculate α. The present study developed a computer program called RheoSUT with which to construct relaxation master curves using different methods. The relaxation master curves of 27 asphalt binders were evaluated for estimation of the value of α. The results indicated that AASHTO TP 101 yields higher values of α. The results of the sensitivity analysis show that overestimation of α will result in up to about 200% error in the estimation of the fatigue life ( Nf). It is also shown that binder aging and styrene-butadiene-styrene (SBS) modification directly affected the rheological parameters and relaxation master curves. Finally, it is recommended to use the relaxation-master curved based methods of calculation of α instead of the storage-modulus based ones.

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47

Lee, Yong-Shin, Sang-Jun Lee, Sangmok Lee, Eung-Zu Kim, and Duck Jae Yoon. "Development of a Master Sintering Curve for Al-Mg Alloy." Advances in Materials Science and Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/5607386.

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A new master sintering curve (MSC) is proposed for Al-Mg alloy in order to effectively design the pressure-assisted sintering process. In this work, hot pressing experiments of Al-Mg alloy powders are performed. The changes of relative density during hot pressing are measured for the various heating rates of 5°C/min, 10°C/min, and 20°C/min at the fixed pressure of 50 MPa. A work of sintering, designated as Θ, is introduced and defined as Θ(t,T)=∫0t1/Texp-Q/RTdt. A work of sintering, Θ, could be interpreted as a measure for the amount of sintering work. The MSC in this work defines the relation between the apparent density and a work of sintering, Θ. Since the measurement of an apparent activation energy, Q, is very difficult, the correct value of Q is obtained numerically using a mean residual square method. Then, the master sintering curves for sintering of Al-Mg alloy powders are proposed for the sintering temperatures of 400°C and 500°C through scaling procedures. It is expected that the master sintering curves proposed in this work could help an engineer to design pressure-assisted sintering process for Al-Mg alloy.

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48

Yoon, K. K., W. A. Van Der Sluys, and K. Hour. "Effect of Loading Rate on Fracture Toughness of Pressure Vessel Steels." Journal of Pressure Vessel Technology 122, no. 2 (March 7, 2000): 125–29. http://dx.doi.org/10.1115/1.556176.

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The master curve method has recently been developed to determine fracture toughness in the brittle-to-ductile transition range. This method was successfully applied to numerous fracture toughness data sets of pressure vessel steels. Joyce (Joyce, J. A., 1997, “On the Utilization of High Rate Charpy Test Results and the Master Curve to Obtain Accurate Lower Bound Toughness Predictions in the Ductile-to-Brittle Transition, Small Specimen Test Techniques,” Small Specimens Test Technique, ASTM STP 1329, W. R. Corwin, S. T. Rosinski, and E. Van Walle, eds., ASTM, West Conshohocken, PA) applied this method to high loading rate fracture toughness data for SA-515 steel and showed the applicability of this approach to dynamic fracture toughness data. In order to investigate the shift in fracture toughness from static to dynamic data, B&W Owners Group tested five weld materials typically used in reactor vessel fabrication in both static and dynamic loading. The results were analyzed using ASTM Standard E 1921 (ASTM, 1998, Standard E 1921-97, “Standard Test Method for the Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range,” 1998 Annual Book of ASTM Standards, 03.01, American Society for Testing and Materials, West Conshohocken, PA). This paper presents the data and the resulting reference temperature shifts in the master curves from static to high loading rate fracture toughness data. This shift in the toughness curve with the loading rate selected in this test program and from the literature is compared with the shift between KIc and KIa curves in ASME Boiler and Pressure Vessel Code. In addition, data from the B&W Owners Group test of IAEA JRQ material and dynamic fracture toughness data from the Pressure Vessel Research Council (PVRC) database (Van Der Sluys, W. A., Yoon, K. K., Killian, D. E., and Hall, J. B., 1998, “Fracture Toughness of Ferritic Steels and ASTM Reference Temperature T0,” BAW-2318, Framatome Technologies. Lynchburg, VA) are also presented. It is concluded that the master curve shift due to loading rate can be addressed with the shift between the current ASME Code KIc and KIa curves. [S0094-9930(00)01302-0]

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Yang, Fuqian, Lingling Peng, and Kenji Okazaki. "Localized Deformation of Equal Channel Angular Extruded Aluminum." Materials Science Forum 475-479 (January 2005): 425–28. http://dx.doi.org/10.4028/www.scientific.net/msf.475-479.425.

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The localized deformation behavior of annealed Al and Al severely deformed by ECAE process was determined by using microindentation test. Using the method proposed by Tabor, the indentation stress-strain curves of annealed Al and as-ECAE deformed Al were constructed, which display similar work-hardening behavior. For annealed Al, the altitude of the indentation stressstrain curves is a function of the indenter size. A master curve then is constructed, which displays different work-hardening behavior. For the ECAE deformed Al, the indentation stress-strain curves are independent of the indenter size, suggesting that the microstructure inside the as-ECAE deformed Al is different from the annealed Al.

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Latuamury, Bokiraiya, Hendrik S. E. Aponno, and Miranda H. Hadijah. "KAJIAN KEBERLANJUTAN ALIRAN DASAR SUNGAI MELALUI ANALISIS KURVA RESESI HIDROGRAF PADA DAS KEDUANG KABUPATEN WONOGIRI PROVINSI JAWA TENGAH." JURNAL HUTAN PULAU-PULAU KECIL 1, no. 3 (March 1, 2017): 222. http://dx.doi.org/10.30598/jhppk.2017.1.3.222.

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The streamflow hydrograph recession curve notes that behavior of the relationship between the aquifer structure and dependencies with the groundwater outflow towards river basin channel. The recession behavior of river basin hydrographs will investigate to understand the hydrology processes of the river basin in the future. This research was conducted with the aim: to analyze the characteristics of the baseflow recession based on the parameters and coefficients of the recession, and the shape of the individual recession curve and the master recession curves both manually and through the processing of genetic algorithms using a linear reservoir model of hydrooffice software package recession curve (RC) 4.0. The results of the visualization of the recession curve shape of the watershed of the research shows there is a very interesting trend in the watershed storage process.The characteristics of the baseflow recession to research watershed with the recession curve slope describe the baseflow recession conditions, especially excellent water storage. The river basin of Keduang have the form of a relatively sloping recession curves, both individual and master recession curve with relatively high recession constant ranged between 0,80 – 0,90 have baseflow recession characteristic is excellent, i.e. the watershed water storage which is the higher volume of water storage.

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