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1

Zhu, Xian-Kui, and Brian N. Leis. "Application of Constraint Corrected J-R Curves to Fracture Analysis of Pipelines." Journal of Pressure Vessel Technology 128, no. 4 (2005): 581–89. http://dx.doi.org/10.1115/1.2349571.

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Fracture properties of an API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the J-R curves for the X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental J-R curves to those for actual cracked components, like flawed pipeline, constraint corrected J-R curves are developed. The two-parameter J-A2 formulation is adopted to quantify constraint effect on the crack-ti
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2

Wallin, Kim, and Anssi Laukkanen. "Improved crack growth corrections for J–R-curve testing." Engineering Fracture Mechanics 71, no. 11 (2004): 1601–14. http://dx.doi.org/10.1016/s0013-7944(03)00165-6.

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3

Saxena, Ashok, and Laurent Cretegny. "The relationship between microstructure and the J-R curve." Metallurgical and Materials Transactions A 29, no. 7 (1998): 1917–22. http://dx.doi.org/10.1007/s11661-998-0016-2.

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4

Lam, P. S., Y. J. Chao, X. K. Zhu, Y. Kim, and R. L. Sindelar. "Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks." Journal of Pressure Vessel Technology 125, no. 2 (2003): 136–43. http://dx.doi.org/10.1115/1.1564069.

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Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J
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5

Wolfenden, A., R. Herrera, and JD Landes. "A Direct J-R Curve Analysis of Fracture Toughness Tests." Journal of Testing and Evaluation 16, no. 5 (1988): 427. http://dx.doi.org/10.1520/jte11618j.

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6

Jones, R. L., J. R. Gordon, and N. V. Challenger. "A STUDY OF SPECIMEN SIZE ON J-R CURVE BEHAVIOUR." Fatigue & Fracture of Engineering Materials and Structures 14, no. 7 (1991): 777–88. http://dx.doi.org/10.1111/j.1460-2695.1991.tb00706.x.

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7

Menezes, João Teixeira Oliveira de, Juan E. Perez Ipiña, and Enrique M. Castrodeza. "Normalization method for J-R curve determination using SENT specimens." Engineering Fracture Mechanics 199 (August 2018): 658–71. http://dx.doi.org/10.1016/j.engfracmech.2018.06.033.

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8

Sahu, MK, J. Chattopadhyay, and BK Dutta. "Hybrid approach for calculation of J-R curve using R6." Engineering Fracture Mechanics 215 (June 2019): 16–35. http://dx.doi.org/10.1016/j.engfracmech.2019.04.031.

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9

Liu, Zheng, Xin Wang, and Xu Chen. "J-Resistance Curve Testing Using Modified Normalization Method for SENT Specimens." Key Engineering Materials 795 (March 2019): 367–74. http://dx.doi.org/10.4028/www.scientific.net/kem.795.367.

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A modified normalization (NM) method to determine J-R curves using clamped single edge notched tension (SENT) specimens was proposed. To validate and quantify the modified NM method, the J-R curves of X80 pipeline steel obtained by NM method are compared with those determined by the unloading compliance (UC) method for SENT specimens. The comparison shows that modified NM method is obvious better than unmodified NM method for SENT specimens. The modified NM method has great agreements with UC method, and is a valid and cost-effective tool to be applied to obtain J-R curves of API X80 steel usi
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10

Kumar, Pradeep, B. K. Dutta, J. Chattopadhyay, and R. S. Shriwastaw. "Numerical evaluation of J-R curve using small punch test data." Theoretical and Applied Fracture Mechanics 86 (December 2016): 292–300. http://dx.doi.org/10.1016/j.tafmec.2016.08.003.

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11

Wallin, Kim, M. Sokolov, and S. W. Dean. "Specimen Size Limitations in J-R Curve Testing—Standards Versus Reality." Journal of ASTM International 4, no. 9 (2007): 100978. http://dx.doi.org/10.1520/jai100978.

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12

Zhou, Z., J. D. Landes, and D. D. Huang. "J-R curve calculation with the normalization method for toughened polymers." Polymer Engineering and Science 34, no. 2 (1994): 128–34. http://dx.doi.org/10.1002/pen.760340209.

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13

Bernal, Celina R., Anibal N. Cassanelli, and Patricia M. Frontini. "A simple method for J-R curve determination in ABS polymers." Polymer Testing 14, no. 1 (1995): 85–96. http://dx.doi.org/10.1016/0142-9418(95)90616-o.

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14

Joyce, J. A., and E. M. Hackett. "Transition range drop tower J-R curve testing of A106 steel." Experimental Mechanics 29, no. 3 (1989): 274–78. http://dx.doi.org/10.1007/bf02321407.

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15

Lu, Hong Sheng, Yong He Yang, Gang Chen, Xu Chen, and Xin Wang. "Fracture Toughness of Different Locations in API X80 Pipeline Steel on Low Constraint SENT Specimens." Applied Mechanics and Materials 853 (September 2016): 251–55. http://dx.doi.org/10.4028/www.scientific.net/amm.853.251.

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With the considerable use of high-grade pipeline steel in onshore and offshore project, welded joints are recognized as the weak link in pipeline because of the non-uniform microstructural regions induced by welding heat input. At first, the microstructural of different regions in API X80 pipeline welded joints was characterized and quantified by SEM, which indicate that the pipeline steel is a typical acicular ferrite steel. In this paper we investigated the J-integral resistance curve (J-R curve) in different locations of API X80 pipeline welded joints through low constraint SENT specimens w
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16

Wohlfahrt, K. "Macbeath's Curve and the Modular Group." Glasgow Mathematical Journal 28, no. 2 (1986): 241. http://dx.doi.org/10.1017/s0017089500006583.

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On p. 244 of Glasgow Math. J.27 (1985) on the right hand side of one of the 6 equations characterizing the 4 fixed points of the involution v a sign error has occurred.The relevant equation should ready0y3y5y6=–1,or the points would not lie on the curve.Correcting the error unfortunately invalidates the model of an elliptic curve given in §6, which therefore has to be re-evaluated. First we find, in the notation of the paper,2 f (x) = ((r + 1)/(R + 2))2.
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17

Katz, Eric, and David Zureick-Brown. "The Chabauty–Coleman bound at a prime of bad reduction and Clifford bounds for geometric rank functions." Compositio Mathematica 149, no. 11 (2013): 1818–38. http://dx.doi.org/10.1112/s0010437x13007410.

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AbstractLet $X$ be a curve over a number field $K$ with genus $g\geq 2$, $\mathfrak{p}$ a prime of ${ \mathcal{O} }_{K} $ over an unramified rational prime $p\gt 2r$, $J$ the Jacobian of $X$, $r= \mathrm{rank} \hspace{0.167em} J(K)$, and $\mathscr{X}$ a regular proper model of $X$ at $\mathfrak{p}$. Suppose $r\lt g$. We prove that $\# X(K)\leq \# \mathscr{X}({ \mathbb{F} }_{\mathfrak{p}} )+ 2r$, extending the refined version of the Chabauty–Coleman bound to the case of bad reduction. The new technical insight is to isolate variants of the classical rank of a divisor on a curve which are better
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18

Wallin, K. "Low-cost J-R curve estimation based on CVN upper shelf energy." Fatigue & Fracture of Engineering Materials & Structures 24, no. 8 (2001): 537–49. http://dx.doi.org/10.1046/j.1460-2695.2001.00405.x.

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19

Asta, E. P., and E. Chomik. "Elastic-plastic fracture assessment using a J-R curve by direct method." Nuclear Engineering and Design 160, no. 1-2 (1996): 129–35. http://dx.doi.org/10.1016/0029-5493(95)01068-8.

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20

Shin, In Hwan, Chi Yong Park, Chang Sung Seok, and Jae Mean Koo. "Evaluation of Shape Parameter Effect on the J-R Curve of Curved CT Specimen Using Limit Load Method." Transactions of the Korean Society of Mechanical Engineers A 38, no. 7 (2014): 757–64. http://dx.doi.org/10.3795/ksme-a.2014.38.7.757.

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21

Pavankumar, T. V., J. Chattopadhyay, B. K. Dutta, and H. S. Kushwaha. "Transferability of specimen J–R curve to straight pipes with throughwall circumferential flaws." International Journal of Pressure Vessels and Piping 79, no. 2 (2002): 127–34. http://dx.doi.org/10.1016/s0308-0161(01)00134-x.

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22

SAHU, M. K., J. CHATTOPADHYAY, and B. K. DUTTA. "Transferability of specimen J-R curve to straight pipe with circumferential surface flaw." Fatigue & Fracture of Engineering Materials & Structures 35, no. 5 (2012): 476–87. http://dx.doi.org/10.1111/j.1460-2695.2011.01641.x.

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23

OHTSUKA, Naotake, and Yutaka MATSUMOTO. "Simple Method for the Determination of Static or Dynamic Modified J-R Curve." JSME international journal. Ser. 1, Solid mechanics, strength of materials 31, no. 4 (1988): 738–43. http://dx.doi.org/10.1299/jsmea1988.31.4_738.

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24

Zhang, Jia Ming, Kai Shu Guan, Qiong Qi Wang, Si Ning Fan, and Guo Yao Chen. "The Method to Obtain JR- Curve by Continuous Ball Indentation Method." Key Engineering Materials 795 (March 2019): 432–38. http://dx.doi.org/10.4028/www.scientific.net/kem.795.432.

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JR-curve is one of an important index to characterize the fracture properties of metal materials. It is usually determined by multi-sample unloading method and single-sample unloading compliance method recommended by standard methods; In consideration of the similarity between the continuous ball indentation method and the single-sample unloading compliance method, The JR-curve is obtained by using the empirical correlation between effective elastic modulus ED of the continuous ball indentation and the unloading compliance C for single simple in this article. The calculation conducted by the c
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25

Bai, Yong Qiang, Liang Hai Lv, Tong Wang, and Xiao Feng Zhang. "Application of the Failure Assessment Method for Cracked Pipeline." Advanced Materials Research 919-921 (April 2014): 455–59. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.455.

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A new failure assessment curve of pipeline containing crack is provided in this paper. The new failure assessment curve is based on the J integral calculation method of the effective remote stress, and it is as simple as the R6 option 2. The result of the new failure assessment curve is as accurate as the result of the curve based on strict J integral. Moreover, the new failure assessment curve could be used for any stress-strain relationship material, including Ramborg-Osgood (R-O) material and non-R-O materials under monotonic increasing loading, such as long plastic yield plateau steel. The
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26

FORZANI, LILIANA, and CARLOS TOLMASKY. "A FAMILY OF MODELS EXPLAINING THE LEVEL-SLOPE-CURVATURE EFFECT." International Journal of Theoretical and Applied Finance 06, no. 03 (2003): 239–55. http://dx.doi.org/10.1142/s021902490300192x.

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One of the most widely used methods to build yield curve models is to use principal components analysis on the correlation matrix of the innovations. R. Litterman and J. Scheinkman found that three factors are enough to explain most of the moves in the case of the US treasury curve. These factors are level, steepness and curvature. Working in the context of commodity futures, G. Cortazar and E. Schwartz found that the spectral structure of the correlation matrices is strikingly similar to those found by R. Litterman and J. Scheinkman. We observe that in both cases the correlation between two d
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27

Špirko, Vladimír, Xiangzhu Li, and Josef Paldus. "Potential energy curve of N2 revisited." Collection of Czechoslovak Chemical Communications 76, no. 4 (2011): 327–41. http://dx.doi.org/10.1135/cccc2010151.

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Recently generated ground state potential energy curves (PECs) for the nitrogen molecule, as obtained with the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR-CCSD), and its version corrected for the secondary triples RMR-CCSD(T), using cc-pVXZ basis sets with X = D, T, and Q, as well as the extrapolated complete basis set (cbs) limit (X. Li and J. Paldus: J. Chem. Phys. 2008, 129, 054104), are compared with both the highly accurate theoretical configuration interaction PEC of Gdanitz (Chem. Phys. Lett. 1998, 283, 253) and analytic PECs obtained by fittin
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28

Kaneta, Hitoshi, and Tatsuya Maruta. "An elementary proof and an extension of Thas' theorem on k-arcs." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 3 (1989): 459–62. http://dx.doi.org/10.1017/s0305004100077823.

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Let q be the finite field of q elements. Denote by Sr q the projective space of dimension r over q. In Sr,q, where r ≥ 2, a k-arc is defined (see [4]) as a set of k points such that no j + 2 lie in a Sj,q, for j = 1,2,…, r−1. (For a k-arc with k > r, this last condition holds for all j when it holds for j = r−1.) A rational curve Cn of order n in Sr,q, is the set
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29

Hang, Ma, Wang Zheng, and Zhu Liang. "The measurement of J-R curves and J-integral values at crack initiations for metallic materials with three curve method of single specimen." International Journal of Fracture 68, no. 1 (1994): 45–54. http://dx.doi.org/10.1007/bf00032325.

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30

Wainstein, J., P. M. Frontini, and A. N. Cassanelli. "J-R curve determination using the load separation parameter S method for ductile polymers." Polymer Testing 23, no. 5 (2004): 591–98. http://dx.doi.org/10.1016/j.polymertesting.2003.10.010.

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31

Zhu, X.-K., BN Leis, and SW Dean. "Constraint Corrected J-R- Curve and Its Application to Fracture Assessment for X80 Pipelines." Journal of ASTM International 3, no. 6 (2006): 13209. http://dx.doi.org/10.1520/jai13209.

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32

Huang, Yifan, and Wenxing Zhou. "Effective Thickness of Side-Grooved Clamped SE(T) Specimens for J-R Curve Testing." Journal of Testing and Evaluation 45, no. 2 (2016): 20150274. http://dx.doi.org/10.1520/jte20150274.

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33

Kumar, Sachin, I. V. Singh, and B. K. Mishra. "XFEM simulation of stable crack growth using J–R curve under finite strain plasticity." International Journal of Mechanics and Materials in Design 10, no. 2 (2014): 165–77. http://dx.doi.org/10.1007/s10999-014-9238-1.

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34

Shin, In Hwan, Kyoung Soo Lee, and Chang Sung Seok. "J-R Curve Assessment for Austenitic Stainless Steel (SA312 Tp304L) Pipes with a Butt-Welding Joint Using 4-Point Bending Tests." Transactions of the Korean Society of Mechanical Engineers - A 42, no. 11 (2018): 967–73. http://dx.doi.org/10.3795/ksme-a.2018.42.11.967.

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35

HAYASHI, CHUICHIRO, MIWA HAYASHI, MINORI SAWADA, and SAYAKA YAMADA. "MINIMAL UNKNOTTING SEQUENCES OF REIDEMEISTER MOVES CONTAINING UNMATCHED RII MOVES." Journal of Knot Theory and Its Ramifications 21, no. 10 (2012): 1250099. http://dx.doi.org/10.1142/s021821651250099x.

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Arnold introduced invariants J+, J- and St for generic planar curves. It is known that both J+/2 + St and J-/2 + St are invariants for generic spherical curves. Applying these invariants to underlying curves of knot diagrams, we can obtain lower bounds for the number of Reidemeister moves required for unknotting. J- /2 + St works well to count the minimum number of unmatched RII moves. However, it works only up to a factor of two for RI moves. Let w denote the writhe for a knot diagram. We show that J-/2 + St ± w/2 also gives sharp counts for the number of required RI moves, and demonstrate th
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36

Venegas, José G., R. Scott Harris, and Brett A. Simon. "A comprehensive equation for the pulmonary pressure-volume curve." Journal of Applied Physiology 84, no. 1 (1998): 389–95. http://dx.doi.org/10.1152/jappl.1998.84.1.389.

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Venegas, José G., R. Scott Harris, and Brett A. Simon.A comprehensive equation for the pulmonary pressure-volume curve. J. Appl. Physiol. 84(1): 389–395, 1998.—Quantification of pulmonary pressure-volume (P-V) curves is often limited to calculation of specific compliance at a given pressure or the recoil pressure (P) at a given volume (V). These parameters can be substantially different depending on the arbitrary pressure or volume used in the comparison and may lead to erroneous conclusions. We evaluated a sigmoidal equation of the form, V = a + b[1 +[Formula: see text]]−1, for its ability to
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37

Gui, Le Le, Tong Xu, Bin An Shou, Han Kui Wang, and Jing Xiang. "Estimation of Fracture Toughness JIC by Miniature Specimen Hydraulic Bulge Test." Materials Science Forum 898 (June 2017): 753–57. http://dx.doi.org/10.4028/www.scientific.net/msf.898.753.

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The fracture toughness tests and a new miniature specimen technology named hydraulic bulge test (HBT) of 3Cr1Mo1/4V at four service time were carried out. Four J-R resistance curves by single-specimen method with one inch CT specimens were obtained to compute the JIC. Different definitions of equivalent fracture strain according to the section morphologies of HBT testing specimens were compared, and fracture energy of miniature specimens with three different thicknesses (0.4mm, 0.5mm and 0.6mm) were also calculated. Results showed that the typical HBT load-deflection curve can be divided into
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38

EL-Bagory, Tarek M. A. A., Hossam E. M. Sallam, and Maher Y. A. Younan. "Effect of strain rate, thickness, welding on the J–R curve for polyethylene pipe materials." Theoretical and Applied Fracture Mechanics 74 (December 2014): 164–80. http://dx.doi.org/10.1016/j.tafmec.2014.09.008.

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39

Gordon, J. R., and R. L. Jones. "THE EFFECT OF SPECIMEN SIZE ON THE J R-CURVE BEHAVIOUR OF A TITANIUM ALLOY." Fatigue & Fracture of Engineering Materials and Structures 12, no. 4 (1989): 295–308. http://dx.doi.org/10.1111/j.1460-2695.1989.tb00538.x.

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40

PAVANKUMAR, T. V., J. CHATTOPADHYAY, B. K. DUTTA, and H. S. KUSHWAHA. "On the transfer of specimen J-R curve to piping components with throughwall circumferential flaw." Fatigue Fracture of Engineering Materials and Structures 28, no. 9 (2005): 779–94. http://dx.doi.org/10.1111/j.1460-2695.2005.00916.x.

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41

Kobayashi, H., T. Kusumoto, and H. Nakazawa. "The cyclic J-R curve and upper-limit characteristic of fatigue-crack growth in steel." International Journal of Pressure Vessels and Piping 52, no. 3 (1992): 337–56. http://dx.doi.org/10.1016/0308-0161(92)90090-3.

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42

Şen, Zekai. "Discussion of “Continuous Hydrologic Models and Curve Numbers: A Path Forward” by S. J. Lamont, R. N. Eli, and J. J. Fletcher." Journal of Hydrologic Engineering 15, no. 4 (2010): 325–26. http://dx.doi.org/10.1061/(asce)he.1943-5584.0000034.

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43

Dagbasi, M., and C. E. Turner. "Fully plastic ductile tearing of HY130 steel—an analysis by J, COD, energy rate and crack opening angle." Journal of Strain Analysis for Engineering Design 30, no. 4 (1995): 257–69. http://dx.doi.org/10.1243/03093247v304257.

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The dependence of J-R curves on size of test piece is examined for fully plastic deep notch bend (DNB) tests on HY130 steel, taken to large amounts of ductile crack growth (60 per cent of the ligament) for a range of initial widths at 20 mm thick and one geometrically similar size, 50 mm thick. The object is to understand the cause of the widely different patterns of behaviour that have been reported in the literature, even within the DNB type of configuration. In the present tests, the proportion of shear lip is the same for the geometrically similar pair but the J-R curve for the 50 mm thick
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44

Ghafari, Sepehr, and Fereidoon Moghadas Nejad. "R-Curve Characterization of Crumb Rubber Modified Asphalt Mixtures Incorporating Warm Mix Additive at Low Temperatures." Key Engineering Materials 894 (July 27, 2021): 109–14. http://dx.doi.org/10.4028/www.scientific.net/kem.894.109.

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In a previous research by authors, a methodology was developed to derive J-R curves for Hot Mix Asphalt (HMA) mixtures using an elastic-plastic approach where a comprehensive understanding of crack propagation regime could be achieved. In this research, the effect of crumb rubber modification of HMA binder is studied in terms of R-curves and crack propagation at low temperatures. Mode I Single edge notched beam (SE(B)) fracture tests were conducted in temperature levels of 0 °C, -10 °C, and -20 °C. PG58-22 and PG64-22 binders were used in the fabrication of HMA samples. Modified specimens cons
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45

Chattopadhyay, J., B. K. Dutta та H. S. Kushwaha. "Derivation of ‘γ’ parameter from limit load expression of cracked component to evaluate J–R curve". International Journal of Pressure Vessels and Piping 78, № 6 (2001): 401–27. http://dx.doi.org/10.1016/s0308-0161(01)00053-9.

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46

Chowdhury, Tamshuk, S. Sivaprasad, H. N. Bar, S. Tarafder, and N. R. Bandyopadhyay. "Comparative assessment of cyclic J-R curve determination by different methods in a pressure vessel steel." Journal of Nuclear Materials 472 (April 2016): 55–64. http://dx.doi.org/10.1016/j.jnucmat.2016.01.030.

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47

Qian, Xudong, Yang Zhang, and Yoo Sang Choo. "A load–deformation formulation with fracture representation based on the J–R curve for tubular joints." Engineering Failure Analysis 33 (October 2013): 347–66. http://dx.doi.org/10.1016/j.engfailanal.2013.06.004.

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48

MORISHITA, Shinichiro, Koichi KASABA, and Tatsuya SUGITANI. "Considerations for R-curve and critical J-integral obtained from a round bar with circumferential crack." Proceedings of the Materials and Mechanics Conference 2019 (2019): OS1713. http://dx.doi.org/10.1299/jsmemm.2019.os1713.

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49

Wang, Zhirui, and Jirong Zhang. "Short fatigue crack growth and J-R curve behavior of particulate Al2O3-reinforced Al(2014) alloy." Materials Science and Engineering: A 171, no. 1-2 (1993): 85–94. http://dx.doi.org/10.1016/0921-5093(93)90395-u.

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50

FORZANI, LILIANA, and CARLOS F. TOLMASKY. "ON THE SPECTRAL DECOMPOSITION OF EMPIRICAL CORRELATION MATRICES." Journal of Knot Theory and Its Ramifications 10, no. 08 (2001): 1201–13. http://dx.doi.org/10.1142/s0218216501001396.

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One of the most widely used methods to build yield curve models is to use principal components analysis on the correlation matrix of the innovations. R. Litterman and J. Scheinkman found that three factors are enough to explain most of the moves in the case of the US treasury curve. These factors are level, steepness and curvature. Working in the context of commodity futures, G. Cortazar and E. Schwartz found that the spectral structure of the correlation matrices is strikingly similar to those found by R. Litterman and J. Scheinkman. We observe that in both cases the correlation between two d
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