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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`R.J. REYNOLDS VAPOR COMPANY,
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`Petitioner
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`v.
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`FONTEM HOLDINGS 1 B.V.,
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`Patent Owner
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`
`
`Case IPR2016-01268
`Patent 8,365,742
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`SUPPLEMENTAL DECLARATION OF DR. ROBERT H. STURGES
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`R.J. Reynolds Vapor
`IPR2016-01268
`R.J. Reynolds Vapor v. Fontem
`Exhibit 1020-00001
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`

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`1.
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`I have been retained by the law firm of Brinks Gilson & Lione on
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`behalf of R.J. Reynolds Vapor Company (“Petitioner”) in connection with
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`IPR2016-01268. I previously provided a declaration (Ex. 1015) concerning the
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`technical subject matter relevant to the petition in IPR2016-01268 (“Petition
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`Declaration”).
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`2. My background and qualification are contained in my Petition
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`Declaration.
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`3.
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`Besides the information listed in ¶ 8 of my Petition Declaration, I
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`have also considered Patent Owner's Objections to Petitioner's Evidence (Paper
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`16).
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`4.
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`In ¶ 45 of my Petition Declaration, I explained and opined that:
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`More specifically, the porous body 27 is attached to the atomization cavity
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`wall 25. The PHOSITA would have recognized that the porous body is
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`attached to the cavity wall 25 via either a friction fit or through a bonding
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`material to prevent axial displacement of the porous body under the shear
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`forces exerted at the interface of cavity wall 25 with the porous body 27
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`when the porous body is inserted into the storage porous body 28. The shear
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`forces could be particularly significant when the porous body and the
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`solution storage body 28 are made from materials that have similar and
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`relatively high rigidity. See Ex. 1003 at 9-10 (noting that porous body 27
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`1
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`Exhibit 1020-00002
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`

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`may be made from “nickel, stainless steel fiber felt, high molecule polymer
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`foam and foam ceramic,” and that solution storage body 28 “can be filled
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`with polypropylene fiber, terylene fiber, nylon fiber, or be filled with plastic
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`that are shaped by foaming, such as polyamine resin foam column or
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`polypropylene foam column; alternatively, it may be made of a column
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`formed by molding polyvinyl chloride, polypropylene, polycarbonate into a
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`stack of laminated layers.”). Ex. 1015 at ¶ 45.
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`In the Petition Declaration, I also opined that “[t]he PHOSITA would have
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`recognized that the foregoing materials can have a wide range of rigidities.” Id.
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`5.
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`The PHOSITA would have recognized the foregoing because
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`rigidities of materials were well known in the art and published in a variety of
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`resources. For example, one reliable resource that would have been available to a
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`PHOSITA with respect to the rigidity of polymer foams is the Cambridge
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`University Engineering Department's Materials Data Book, the 2003 Edition
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`(“Materials Data Book 2003”). True and correct copies of the particularly relevant
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`pages from the Materials Data Book 2003 are attached as Ex. A. The rigidity of a
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`material is defined by the Shear Modulus, G, which in turn relates to the Young's
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`modulus, E, by the formula G = E/2(1+) where  is the Poisson's ratio. As a
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`PHOSITA would have recognized, Poisson's ratio is the ratio of transverse
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`contraction strain to longitudinal extension strain in the direction of stretching
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`2
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`Exhibit 1020-00003
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`force ( = - (lateral strain)/(longitudinal strain)). Thus, rigidity generally increases
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`with the material’s Young’s modulus, E. Materials Data Book 2003 at p. 4. The
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`Young's Modulus, E, of selected materials is listed in the Materials Data Book. Id.
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`at p. 11. As noted below, for a given material the E value (and thus rigidity) can
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`vary, as shown in the following chart:
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`3
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`Exhibit 1020-00004
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`Id.
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`6.
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`The units for values of E are given in GPa (gigapascal) in the chart
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`above. It is readily apparent that range of values of E for the polymer foams in the
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`chart above is over 1,000:1. Since the rigidity of a material G is defined as G =
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`E/2(1+) and  (i.e., the material’s Poisson ratio) can vary depending on the
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`microscopic structure of the material, the range of rigidity of polymer foams is
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`even wider than 1,000:1 shown in the chart above.
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`7.
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`Another reliable resource that would have been available to a
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`PHOSITA with respect to the rigidity of polymer foams is Ashby, Materials
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`Selection in Mechanical Design, Pergamon Press, 1992 (“Ashby”). True and
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`correct copies of the particularly relevant pages from the Ashby book are attached
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`as Ex. B. The rigidity of a material is defined by the Shear Modulus, G, which in
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`turn relates to the Young’s Modulus, E, approximately represented as G ≈ 3E/8.
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`Ashby at pp. 27-29. The Young’s Modulus and specific modulus of various
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`materials are shown in the Ashby book, which are copied below. Id. at p. 28.
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`4
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`Exhibit 1020-00005
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`8.
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`The chart above shows that the range of Young’s Modulus E (hence
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`rigidity G) in GPa (gigapascal) for polymer foams is at least 30:1. Ashby also
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`discloses that E can vary from about 0.3 GPa to beyond the edges of his chart at
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`0.01 GPa. Id. at pp. 27-29. Using a conservative extrapolation of the range for
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`foams (see annotated figure below with my dashed curve showing the
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`extrapolation), it is apparent that at least another order of magnitude lower is most
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`probable. This gives a wide range of rigidity, over at least a 300:1 range, since E
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`and G, the modulus of rigidity, are linearly related.
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`5
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`Exhibit 1020-00006
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`9.
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`In ¶ 48 of my Petition Declaration, I explained and opined that:
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`By Bernouli's law, known to the PHOSITA, drawing on the mouthpiece
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`creates a substantially lower pressure around the atomizer: on the order of a
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`fraction of a pound per square inch. However, should the user blow into the
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`mouthpiece by mistake, the pressure in the space around the atomizer could
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`rise to as much [as] 2 pounds per square inch or more. Ex. 1015 at ¶ 48.
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`10. The PHOSITA would have understood that the pressure in the space
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`around the atomizer as described above could rise to as much as 2 pounds per
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`square inch or more. For example, Charbel Badr et al. “The effect of body position
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`on maximal expiratory pressure and flow,” Australian Journal of Physiotherapy,
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`6
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`Exhibit 1020-00007
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`2002, Vol. 48, pages 95 – 102 (“Badr”) investigated the effect of body position on
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`maximum expiratory pressure (MEP) and peak expiratory flow rate (PEFR). Badr
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`at Abstract. Maximum expiratory pressure (MEP) is the force (per square inch)
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`with which one can blow air out when exhaling, such as when blowing up a
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`balloon. A true and correct copy of Badr is attached hereto as Ex. C. Badr
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`discloses that for subjects with normal respiratory function, the maximum
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`expiratory pressures (MEP) in standing is 143 ± 10 cmH2O. Id. at Abstract and
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`Fig. 1A.
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`11. The PHOSITA would have understood that both cmH2O and pound
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`per square inch are pressure units, and that 1 cmH2O converts to about 0.0142
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`pound per square inch. Thus, the MEP in standing disclosed in Badr is 143 ± 10
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`cmH2O x 0.0142 pound per square inch/cmH2O = 2.03 ± 0.14 pounds per square
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`inch. Badr supports my opinion regarding the pressure in the space around the
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`atomizer should the user blow into the mouthpiece by mistake.
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`12. On pages 32-33 of my Petition Declaration, I explained and opined:
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`As illustrated in the annotated figures below, Hon ‘043 discloses a heating
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`element 26 (i.e., “heating wire”) in the path of air flowing through the run-
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`through hole in atomization cavity wall (i.e., “frame”) 25. The heating
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`element 26 of Hon ‘043 functions to “further atomize” (i.e., vaporize) liquid
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`introduced into the atomization chamber from porous body 27 via the flow
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`7
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`Exhibit 1020-00008
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`of air through the long (or short) stream ejection holes. Ex. 1003 at 9:14-16;
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`10:26-28; Fig. 6 (the pink highlighting shows the paths of the air through the
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`atomizer, the blue dashed lines show the high pressure (nearly ambient) area,
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`and the green dashed lines show the lower pressure surface). The cylindrical
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`surface of the atomizer is at a lower pressure than the flat circular end during
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`a draw, and this fact causes the air to move through the atomizer and
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`downstream towards the mouthpiece. The air stream enters the atomizer
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`from the flat, high pressure end and leaves radially through the wall 25 and
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`the lower pressure atomizer surfaces. The wall 25 would be porous itself for
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`greatest airflow.
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`Ex. 1015 at pages 32-33.
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`13. The PHOSITA would have understood that proposed paths through a
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`medium such as the ones described above must comply with the principle of least
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`8
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`Exhibit 1020-00009
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`action (commonly given to Pierre Louis Maupertuis, 1744). The principle of least
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`action dates back to the mid-1700s and is the basic principle governing the motions
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`of continuums, such as fluid flow. The true motion is one that flows like
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`streamlines taking the shortest path given the system in which it is embedded. The
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`principle of least action has been common knowledge for over 200 years, like
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`Newton's Laws of Motion, but more generalized. In brief, the Principle of Least
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`Action states that the true path of a particle (of fluid, for example) minimizes the
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`sum of the kinetic minus the potential energy. This principle is seen in streamlines
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`and many other examples of moving bodies subject to forces. In the case of the
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`flow of fluid through a porous medium, the streamlines will be smooth and subject
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`to the density of the medium, which may vary. See, for example, Feynman et al.,
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`Lectures on Physics, 6th printing, February 1977, a true and correct copy of which
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`is attached hereto as Ex. D, for a general discussion of this principle. The
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`annotated Fig. 6 on page 33 of my Petition Declaration (Ex. 1015), also copied
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`above and below, sketches such flow paths with due consideration for the
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`boundary conditions and relative porosity (resistance to fluid flow) of the media.
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`In other words, as can be seen in the figure, the airflow will enter the chamber
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`(atomization cavity 10) and flow out wherever is easiest. In any event, the airflow
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`in Hon ‘043 will pass over the heating wire as that is the only path in, and how it
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`flows afterwards will be dictated by the principle of least action.
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`9
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`Exhibit 1020-00010
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`14. As a professor, I am aware of and knowledgeable about publications,
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`including textbooks and journal publications, used in in the fields of mechanical
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`design, mechatronics, and manufacturing, including systems that employ heat,
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`mass and fluid transfer. It is common for me and others in my industry to obtain
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`information such as journal articles and text book access from publisher web sites.
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`15. On January 24, 2017, I downloaded a copy of excerpts from the
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`Materials Data Book, Cambridge University Engineering Department, 2003
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`Edition from the Cambridge University website:
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`http://www-mdp.eng.cam.ac.uk/web/library/enginfo/cueddatabooks/materials.pdf.
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`I have used this website in the past to access information from the Materials Data
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`Book as the site provides access to the Materials Data book as well as other
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`reference materials.
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`10
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`Exhibit 1020-00011
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`16. Ex. A is a true and correct copy of excerpts from the Materials Data
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`Book, Cambridge University Engineering Department, 2003 Edition that I obtained
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`from the Cambridge University website.
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`17. Ex. B is a compilation of pages from the book Ashby, Materials
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`Selection in Mechanical Design, Pergamon Press, 1992 (“Ashby”) from my
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`personal library. Ex. B includes the title page, copyright page and pages 27-29 of
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`the Ashby book.
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`18.
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`I have examined Ex. B and it is a true and correct copy of the pages
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`from the Ashby book.
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`19. On January 24, 2017, I downloaded a copy of Charbel Badr et al.
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`“The effect of body position on maximal expiratory pressure and flow,” Australian
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`Journal of Physiotherapy, 2002, Vol. 48, pages 95 – 102 from the Australian
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`Journal of Physiotherapy website:
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`http://ajp.physiotherapy.asn.au/AJP/vol 48/2/AustJPhysiotherv48i2Badr.pdf. I
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`have used this website in the past to access information.
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`20. Ex. C is a true and correct copy of Charbel Badr et al. “The effect of
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`body position on maximal expiratory pressure and flow,” Australian Journal of
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`Physiotherapy, 2002, Vol. 48, pages 95 – 102 that I obtained from the Australian
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`Journal of Physiotherapy website.
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`11
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`Exhibit 1020-00012
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`21.
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`Ex. D is a compilation of pages from the book Feynman et a1.,
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`Lectures on Physics, 6th printing, February 1977 (“Feynman”) fi'om my personal
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`library. Ex. D includes the title page, copyright page and page 19-1 of the
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`Feynman book.
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`22.
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`I have examined EX. D and it is a true and correct copy of the pages
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`from the Feynman book.
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`23.
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`I declare under penalty of perjury under the laws of the United States
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`that the foregoing is true and correct.
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`,Executed on this 1St day of February 2017
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`
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`Dr. Robert H. Sturges
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`12
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`Exhibit 1020-00013
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`Exhibit 1020-00013
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`Materials Data Book, Cambridge Univ. Engineering Department, 2003 Ed.
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`Ex. A
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`Exhibit 1020-00014
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`Materials
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`Book
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`Data
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`2003 Edition
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`Cambridge University Engineering Department
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`Exhibit 1020-00015
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`Exhibit 1020-00015
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`PHYSICAL CONSTANTS IN SI UNITS
`
`Absolute zero of temperature
`Acceleration due to gravity, g
`Avogadro’s number,
`AN
`Base of natural logarithms, e
`Boltzmann’s constant, k
`Faraday’s constant, F
`Universal Gas constant, R
`Permeability of vacuum, µo
`Permittivity of vacuum, εo
`Planck’s constant, h
`Velocity of light in vacuum, c
`Volume of perfect gas at STP
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`
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`– 273.15 °C
`9. 807 m/s2
`6.022x1026 /kmol
`2.718
`1.381 x 10–26 kJ/K
`9.648 x 107 C/kmol
`8.3143 kJ/kmol K
`1.257 x 10–6 H/m
`8.854 x 10–12 F/m
`6.626 x 10–37 kJ/s
`2.998 x 108 m/s
`22.41 m3/kmol
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`CONVERSION OF UNITS
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`Angle, θ
`Energy, U
`Force, F
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`Length, l
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`Mass, M
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`Power, P
`Stress, σ
`Specific Heat, Cp
`Stress Intensity, K
`Temperature, T
`Thermal Conductivity, λ
`Volume, V
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`Viscosity, η
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`1 rad
`See inside back cover
`1 kgf
`1 lbf
`1 ft
`1 inch
`1 Å
`1 tonne
`1 lb
`See inside back cover
`See inside back cover
`1 cal/g.°C
`in
`1 ksi
`1 °F
`1 cal/s.cm.oC
`1 Imperial gall
`1 US gall
`1 poise
`1 lb ft.s
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`57.30 °
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`9.807 N
`4.448 N
`304.8 mm
`25.40 mm
`0.1 nm
`1000 kg
`0.454 kg
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`4.188 kJ/kg.K
`1.10 MPa m
`0.556 K
`4.18 W/m.K
`4.546 x 10–3 m3
`3.785 x 10–3 m3
`0.1 N.s/m2
`0.1517 N.s/m2
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`Exhibit 1020-00016
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`Introduction
`Sources
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`CONTENTS
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`1
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`3
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`3
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`I. FORMULAE AND DEFINITIONS
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`Stress and strain
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`Elastic moduli
`Stiffness and strength of unidirectional composites
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`Dislocations and plastic flow
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`Fast fracture
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`Statistics of fracture
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`Fatigue
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`7
`Creep
`Diffusion
`Heat flow
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`II. PHYSICAL AND MECHANICAL PROPERTIES OF MATERIALS
`Melting temperature
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`Density
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`Young’s modulus
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`Yield stress and tensile strength
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`Fracture toughness
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`Environmental resistance
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`Uniaxial tensile response of selected metals and polymers
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`III. MATERIAL PROPERTY CHARTS
`Young’s modulus versus density
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`Strength versus density
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`Young’s modulus versus strength
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`Fracture toughness versus strength
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`Maximum service temperature
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`Material price (per kg)
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`IV. PROCESS ATTRIBUTE CHARTS
`Material-process compatibility matrix (shaping)
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`Mass
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`Section thickness
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`Surface roughness
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`Dimensional tolerance
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`Economic batch size
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`4
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`5
`5
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`8
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`9
`10
`11
`12
`13
`14
`15
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`16
`17
`18
`19
`20
`21
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`22
`23
`23
`24
`24
`25
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`Exhibit 1020-00017
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`V. CLASSIFICATION AND APPLICATIONS OF ENGINEERING MATERIALS
`Metals: ferrous alloys, non-ferrous alloys
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`26
`Polymers and foams
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`27
`Composites, ceramics, glasses and natural materials
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`28
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`VI. EQUILIBRIUM (PHASE) DIAGRAMS
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`Copper – Nickel
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`Lead – Tin
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`Iron – Carbon
`Aluminium – Copper
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`Aluminium – Silicon
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`Copper – Zinc
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`Copper – Tin
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`Titanium-Aluminium
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`Silica – Alumina
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`VII. HEAT TREATMENT OF STEELS
`TTT diagrams and Jominy end-quench hardenability curves for steels
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`VIII. PHYSICAL PROPERTIES OF SELECTED ELEMENTS
`Atomic properties of selected elements
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`Oxidation properties of selected elements
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`29
`29
`30
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`31
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`Exhibit 1020-00018
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`3
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`
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`INTRODUCTION
`
`
`The data and information in this booklet have been collected for use in the Materials Courses in
`Part I of the Engineering Tripos (as well as in Part II, and the Manufacturing Engineering
`Tripos). Numerical data are presented in tabulated and graphical form, and a summary of useful
`formulae is included. A list of sources from which the data have been prepared is given below.
`Tabulated material and process data or information are from the Cambridge Engineering Selector
`(CES) software (Educational database Level 2), copyright of Granta Design Ltd, and are
`reproduced by permission; the same data source was used for the material property and process
`attribute charts.
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`It must be realised that many material properties (such as toughness) vary between wide limits
`depending on composition and previous treatment. Any final design should be based on
`manufacturers’ or suppliers’ data for the material in question, and not on the data given here.
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`
`
`
`SOURCES
`
`Cambridge Engineering Selector software (CES 4.1), 2003, Granta Design Limited, Rustat
`House, 62 Clifton Rd, Cambridge, CB1 7EG
`
` F Ashby, Materials Selection in Mechanical Design, 1999, Butterworth Heinemann
`
` F Ashby and D R H Jones, Engineering Materials, Vol. 1, 1996, Butterworth Heinemann
`
` F Ashby and D R H Jones, Engineering Materials, Vol. 2, 1998, Butterworth Heinemann
`
` Hansen, Constitution of Binary Alloys, 1958, McGraw Hill
`
` M
`
` M
`
` M
`
` M
`
` I
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` J Polmear, Light Alloys, 1995, Elsevier
`
` C
`
` J Smithells, Metals Reference Book, 6th Ed., 1984, Butterworths
`
`
`Transformation Characteristics of Nickel Steels, 1952, International Nickel
`
`
`
`Exhibit 1020-00019
`
`

`

`4
`
`
`
`I. FORMULAE AND DEFINITIONS
`
`
`
`STRESS AND STRAIN
`
`
`=ε
`n
`
`o
`
`
`
`l −
`l
`
`l
`o
`
`
`
`
`
`
`
`l
`o
`l
`
`
`
`
`
`lnε
`=
`t
`
`tσ = true stress
`nσ = nominal stress
`tε = true strain
`nε = nominal strain
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`n =σ
`
`F
`oA
`
`
`
`
`
`AF
`
`t =σ
`
`F = normal component of force
`oA = initial area
`
`
`A = current area
`
`
`ol = initial length
`
`
`l = current length
`
`
`
`Poisson’s ratio,
`−=ν
`
`strain
`lateral
`strain
`
`allongitudin
`
`
`
`
`
` curve = initial slope of
` nn εσ −
`
`
`
` curve.
`
`
`Young’s modulus E = initial slope of
` tt εσ −
`
`Yield stress
`yσ is the nominal stress at the limit of elasticity in a tensile test.
`
`Tensile strength
`tsσ is the nominal stress at maximum load in a tensile test.
`
`Tensile ductility
`fε is the nominal plastic strain at failure in a tensile test. The gauge length of
`the specimen should also be quoted.
`
`
`
`
`
`
`ELASTIC MODULI
`
`
`K
`
`=
`
`E
`)21(3
`ν−
`
`
`
`G
`
`=
`
`E
` )1(2 ν+
`
`
`31
`
`≈ν
`
`E
`
`
`
`83
`
`G
`
`≈
`
`
`
`K ≈
`
`E
`
`
`
`For polycrystalline solids, as a rough guide,
`
`Poisson’s Ratio
`
` Shear Modulus
`
` Bulk Modulus
`
`
`These approximations break down for rubber and porous solids.
`
`
`
`Exhibit 1020-00020
`
`

`

`
`
`5
`
`
`
`STIFFNESS AND STRENGTH OF UNIDIRECTIONAL COMPOSITES
`
`
`E
`
`=
`
`II
`
`EV
`f
`
`+
`
`f
`
`(
`
`1
`
`−
`
`E)V
`f
`
`
`
`m
`
`1
`−
`
`
`
` 
`
`1
`
`f
`
`V
`−
`E
`
`m
`
`
`
`+
`
`ff
`
`EV
` 
`
`E
`
`⊥
`
`=
`
`σ
`ts
`
`=
`
`V
`
`f
`
`f
`σ
`f
`
`(
`
`1
`
`−
`
`m
`)V
`σ
`f
`y
`
`
`
`
`+
`
`IIE = composite modulus parallel to fibres (upper bound)
`⊥E = composite modulus transverse to fibres (lower bound)
`fV = volume fraction of fibres
`fE = Young’s modulus of fibres
`mE
`= Young’s modulus of matrix
`tsσ = tensile strength of composite parallel to fibres
`σ = fracture strength of fibres
`
`ff
`
`my
`
`σ = yield stress of matrix
`
`
`
`
`
`
`21
`
`y =τ
`
`DISLOCATIONS AND PLASTIC FLOW
`
`The force per unit length F on a dislocation, of Burger’s vector b , due to a remote shear stress
`
` bF τ=
`. The shear stress
`τ, is
`yτ required to move a dislocation on a single slip plane is
`Tc
`2
` where T = line tension (about
`bG , where G is the shear modulus)
`
`Lb
`L = inter-obstacle distance
`2≈c
`c = constant (
`for strong obstacles,
`
`2<c
`
` for weak obstacles)
`
`
`
`
`The shear yield stress k of a polycrystalline solid is related to the shear stress
`yτ required to
`3≈
`k
`.
`move a dislocation on a single slip plane:
`τ2
`y
`
`yσ of a polycrystalline solid is approximately
`The uniaxial yield stress
`is the shear yield stress.
`
`Hardness H (in MPa) is given approximately by:
`
`2=σ
`y
`
`k
`
`, where k
`
`.
`
`H σ3≈
`y
`g/H
`
`HV =
`
`, where g is the acceleration due
`
`Vickers Hardness HV is given in kgf/mm2, i.e.
`to gravity.
`
`
`
`
`
`Exhibit 1020-00021
`
`

`

`6
`
`
`
`
`
`FAST FRACTURE
`
`K
`
`Y
`a
`πσ=
`
`
`
`
`The stress intensity factor, K :
`
`ICK
`Fast fracture occurs when
`
`In plane strain, the relationship between stress intensity factor K and strain energy release rate
`G is:
`
`
`
`
`
`K =
`
`K
`
`=
`
`EG
`2
`1 ν
`−
`
`≈
`
`GE
`
`2
`.≈ν
`10
` (as
`
`)
`
`Plane strain fracture toughness and toughness are thus related by:
`
`K
`
`IC
`
`=
`
`GE
`IC
`2
`1
`
`−ν
`
`≈
`
`GE
`
`IC
`
`
`
`
`
`2I
`
`C f
`
`1≈Y
`
`
`
`“Process zone size” at crack tip given approximately by:
`
`r
`
`p
`
`=
`
`K
`2
`σπ
`ICG ) are only valid when conditions for linear elastic fracture mechanics
`ICK (and
`Note that
`apply (typically the crack length and specimen dimensions must be at least 50 times the process
`zone size).
`In the above:
`σ = remote tensile stress
`a = crack length
`Y = dimensionless constant dependent on geometry; typically
`ICK
`= plane strain fracture toughness;
`ICG = critical strain energy release rate, or toughness;
`E = Young’s modulus
`ν = Poisson’s ratio
`fσ = failure strength
`
`P
`s
`
`=
`
`1
`e
`
`=
`
`
`
`370.
`
`
`
`
`
`STATISTICS OF FRACTURE
`
`
`
`
`
`
`
`V
`o
`
`Vd
`
`m
`
`
`
`
`
`σσ
`
`o
`
`
`
`
`
`−
`
`V
`
`∫
`
`
`
`
`
`Weibull distribution,
`
`P
`s
`
`(V)
`
`=
`
`exp
`
`
`
`
`
`
`
`
`
`VV
`
`o
`
`m
`
`
`
`
`
`σσ
`
`
`
`
`
`−
`
`
`
`o
`
`sP = survival probability of component
`V = volume of component
`σ = tensile stress on component
`oV = volume of test sample
`oσ = reference failure stress for volume oV , which gives
`m = Weibull modulus
`
`For constant stress:
`
`P
`s
`
`(V)
`
`=
`
`exp
`
`
`
`Exhibit 1020-00022
`
`

`

`
`
`Basquin’s Law (high cycle fatigue):
`
`7
`
`
`
`FATIGUE
`
`
`N f =ασ∆
`
`1C
`
`
`
`
`
`Coffin-Manson Law (low cycle fatigue):
`
`
`=β
`N f
`
`Goodman’s Rule. For the same fatigue life, a stress range σ∆ operating with a mean stress mσ ,
`oσ∆ and zero mean stress, according to the relationship:
`is equivalent to a stress range
`
`
`2C
`
`
`
`p
`ε∆ l
`
`
`
`
`
`
`
`
`
`σ
`m
`1
`
`σ∆σ∆
`−
`=
`o σ
`ts
`
`Miner’s Rule for cumulative damage (for i loading blocks, each of constant stress amplitude and
`iN cycles):
`duration
`
`
`i
`
`Paris’ crack growth law:
`
`
`
`
`ad
`Nd
`
`nK
`A
`∆=
`
`
`
`
`
`In the above:
`σ∆ = stress range;
`=lpε∆
` plastic strain range;
`K∆ = tensile stress intensity range;
`N = cycles;
`fN = cycles to failure;
`,
`=n,A,C,C,
` constants;
`1βα
`2
`a = crack length;
`tsσ = tensile strength.
`
`
`
`CREEP
`
`)RT/Q(
`−
`
`A n
`expσ
`
`
`
`
`
`ε&
`ss
`
`=
`
`Power law creep:
`
`
` = steady-state strain-rate
`ssε&
`Q = activation energy (kJ/kmol)
`R = universal gas constant
`T = absolute temperature
`n,A
` = constants
`
`
`
`
`
`NN
`
`∑ fi
`
`i
`
`1=
`
`
`
`Exhibit 1020-00023
`
`

`

`
`
`8
`
`
`
`
`Diffusion coefficient:
`
`D
`
`=
`
`D
`
`o
`
`exp
`
`DIFFUSION
`)RT/Q(
`
`−
`
`
`
`2 x
`∂∂
`
`C
`2
`
`=
`
`D
`
`tC
`∂∂
`
`
`
`dCD
`dx
`
` and
`
`J = diffusive flux
`
`D = diffusion coefficient (m2/s)
`oD = pre-exponential factor (m2/s)
`Q = activation energy (kJ/kmol)
`
`Fick’s diffusion equations:
`
`J
`
`−=
`
`C = concentration
`x = distance
`t
` = time
`
`
`
`
`
`
`
`
`HEAT FLOW
`dT
`dx
`
`q λ−=
`
`
`
`
`
`λ = thermal conductivity (W/m.K)
`a = thermal diffusivity (m2/s)
`
`Steady-state 1D heat flow (Fourier’s Law):
`
`2 x
`∂∂
`
`T
`2
`
`=
`
`a
`
`tT
`∂∂
`
`Transient 1D heat flow:
`
`T = temperature (K)
`
`
`
`q = heat flux per second, per unit area (W/m2.s)
`
`
`For many 1D problems of diffusion and heat flow, the solution for concentration or temperature
`depends on the error function, erf :
`
`
`)t,x(C
`
`=
`
`f
`
`erf
`
`2
`
` or
`
`)t,x(T
`
`=
`
`f
`
`erf
`
`x
`ta
`
`2
`
`
`
`
` 
`
`, with the corresponding
`
`tD
`ta
`.
`
` 
`
`
`
`and
`
`
`
`d
`dX
`
`[
`
`erf
`
`)]X(
`
`=
`
`2
`π
`
`exp
`
`(
`
`−
`
`X
`
`)2
`
`
`
`
`x ≈
`A characteristic diffusion distance in all problems is given by
`x ≈
`characteristic heat flow distance in thermal problems being
`The error function, and its first derivative, are:
`X
`2
`0
`
`
` 
`
`x
`tD
`
` 
`
`
`
`
`
`erf
`
`)X(
`
`=
`
`exp
`
`(
`
`−
`
`2
`
`y
`
`) dy
`
`∫π
`
`
`The error function integral has no closed form solution – values are given in the Table below.
`
`
`X
`(X
`
`)
`
`
`
`X
`(X
`)
`
`
`
`erf
`
`
`erf
`
`0
`0
`
`0.9
`0.80
`
`0.1
`0.11
`
`1.0
`0.84
`
`0.2
`0.22
`
`1.1
`0.88
`
`0.3
`0.33
`
`1.2
`0.91
`
`0.4
`0.43
`
`1.3
`0.93
`
`0.5
`0.52
`
`1.4
`0.95
`
`0.6
`0.60
`
`1.5
`0.97
`
`0.7
`0.68
`
`∞
`1.0
`
`0.8
`0.74
`
`
`
`
`
`
`Exhibit 1020-00024
`
`

`

`
`
`
`
`(Data courtesy of Granta Design Ltd)
`n/a: not applicable (materials decompose, rather than melt)
`(*) glass transition (softening) temperature
` For full names and acronyms of polymers – see Section V.
`
`Polymer Foams
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
` 1
`
`Thermoset Epoxies
`
`
`
`
`
`
`
`
`
`
`
`
`
`171
`157
`171
`177
`177
`177
`
`
`
` 123
` 105
` 160
` 110
`– 15
`– 8
` 165
` 80
`– 15
` 199
` 205
` 56
` 77
` 107
` 128
`– 73
`– 23
`– 43
`– 63
`– 78
`– 23
`– 63
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`n/a
`n/a
`n/a
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`
`
`
`
`
`
`
`67
`67
`67
`112
`112
`112
`
`
`
`107
`75
`120
`74
`– 25
`– 18
`85
`68
`– 25
`143
`142
`44
`27
`– 9
`88
`– 123
`– 73
`– 48
`– 78
`– 83
`– 73
`– 73
`
`
`
`Rigid Polymer Foam (HD) (*)
`Rigid Polymer Foam (MD) (*)
`Rigid Polymer Foam (LD) (*)
`Flexible Polymer Foam (MD) (*)
`Flexible Polymer Foam (LD) (*)
`Flexible Polymer Foam (VLD) (*)
`
`
`
`Polyester
`Phenolics
`
`Teflon (PTFE)
`PVC
`Polyurethane Thermoplastics (tpPU) (*)
`Polystyrene (PS) (*)
`Polypropylene (PP) (*)
`Acetal (POM) (*)
`Acrylic (PMMA) (*)
`PET (*)
`Polyethylene (PE) (*)
`PEEK (*)
`Polycarbonate (PC) (*)
`Nylons (PA) (*)
`Ionomer (I) (*)
`Cellulose Polymers (CA) (*)
`
`Silicone Elastomers (*)
`Polyurethane Elastomers (elPU) (*)
`Neoprene (CR) (*)
`Natural Rubber (NR) (*)
`Isoprene (IR) (*)
`EVA (*)
`
`
`
`
`
`Tm (oC)
`
`9
`
`
`
`
`
`
`
`
`
`Polymers 1
`
`
`
`
`
`Elastomer Butyl Rubber (*)
`
`
`
`
`
`
`
`
`
`Thermoplastic ABS (*)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`102
`102
`127
`102
`102
`
`
`
`2920
`2496
`2500
`1412
`2507
`2507
`2096
`1427
`1227
`1227
`592
`1557
`1647
`602
`
`627
`
`
`
`492
`1682
`1466
`649
`328
`1082
`677
`1450
`1529
`1526
`1514
`1478
`1250
`
`
`
`
`
`
`
`
`
`
`
`temperature, above which the mechanical properties rapidly fall. Melting temperatures of selected elements are given in section VIII.
`All data are for melting points at atmospheric pressure. For polymers (and glasses) the data indicate the glass transition (softening)
`
`II.1 MELTING (or SOFTENING) TEMPERATURE, Tm
`
`II. PHYSICAL AND MECHANICAL PROPERTIES OF MATERIALS
`
`Tm (oC)
`
`
`
`
`
`
`
`Metals
`
`Ferrous Cast Irons
`
`
`
`
`
`
`
`
`
`
`
`Tungsten Carbide
`Silicon Nitride
`Silicon Carbide
`Silicon
`Boron Carbide
`Aluminium Nitride
`
`
`
`Soda-Lime Glass (*)
`Silica Glass (*)
`Glass Ceramic (*)
`Borosilicate Glass (*)
`
`Zinc Alloys
`Titanium Alloys
`Nickel Alloys
`Magnesium Alloys
`Lead Alloys
`Copper Alloys
`
`
`
`Stone
`Concrete, typical
`
`Porous Brick
`
`Glasses
`
`
`
`
`
`
`
`
`
`
`
`Ceramics
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`n/a
`n/a
`-
`
`-
`-
`-
`-
`-
`
`
`
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`
`
`
`
`
`77
`77
`107
`77
`77
`
`
`
`375
`1477
`1435
`447
`322
`982
`475
`1375
`1382
`1480
`1380
`1289
`1130
`
`
`
`2827
`2388
`2152
`1407
`2372
`2397
`2004
`1227
`927
`927
`442
`957
`563
`450
`
`525
`
`
`
`
`
`Wood, typical (Transverse) (*)
`Wood, typical (Longitudinal) (*)
`Leather (*)
`Cork (*)
`Bamboo (*)
`
`
`
`GFRP
`Polymer CFRP
`
`Metal Aluminium/Silicon Carbide
`
`Natural
`
`
`
`
`
`
`
`
`
`
`
`
`
`Composites
`
`
`
`
`
`
`
`
`
`
`
`
`
`Technical Alumina
`
`Non-ferrous Aluminium Alloys
`Stainless Steels
`Low Alloy Steels
`Low Carbon Steels
`Medium Carbon Steels
`High Carbon Steels
`
`Exhibit 1020-00025
`
`

`

`
`
`
`
`1 For full names and acronyms of polymers – see Section V
`
`(Data courtesy of Granta Design Ltd).
`
`Thermoset Epoxies
`
`Polymer Foams
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`1.4
`1.32
`1.4
`2.2
`1.58
`1.24
`1.05
`0.91
`1.43
`1.22
`1.4
`0.96
`1.32
`1.21
`1.14
`0.96
`1.3
`1.21
`1.8
`1.25
`1.25
`0.93
`0.94
`0.955
`0.92
`
`0.47
`0.165
`0.07
`0.115
`0.07
`0.035
`
`
`
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`
`
`
`
`
`
`
`0.17
`0.078
`0.036
`0.07
`0.038
`0.016
`
`1.04
`1.24
`1.11
`2.14
`1.3
`1.12
`1.04
`0.89
`1.39
`1.16
`1.29
`0.939
`1.3
`1.14
`1.12
`0.93
`0.98
`1.01
`1.3
`1.02
`1.23
`0.92
`0.93
`0.945
`0.9
`
`
`
`
`
`Rigid Polymer Foam (HD)
`Rigid Polymer Foam (MD)
`Rigid Polymer Foam (LD)
`Flexble Polymer Foam (MD)
`Flexble Polymer Foam (LD)
`Flexble Polymer Foam (VLD)
`
`
`
`Polyester
`Phenolics
`
`Teflon (PTFE)
`PVC
`Polyurethane Thermoplastics (tpPU)
`Polystyrene (PS)
`Polypropylene (PP)
`Acetal (POM)
`Acrylic (PMMA)
`PET
`Polyethylene (PE)
`PEEK
`Polycarbonate (PC)
`Nylons (PA)
`Ionomer (I)
`Cellulose Polymers (CA)
`
`Silicone Elastomers
`Polyurethane Elastomers (elPU)
`Neoprene (CR)
`Natural Rubber (NR)
`Isoprene (IR)
`EVA
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`ρ (Mg/m3)
`
`
`
`
`
`
`
`
`
`Polymers 1
`
`
`
`II.2 DENSITY, ρ
`
`Elastomer Butyl Rubber
`
`
`
`
`
`
`
`
`
`
`
`
`
`Thermoplastic ABS
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`1.97
`1.6
`2.9
`
`0.8
`0.8
`1.05
`0.24
`0.8
`
`
`
`
`
`15.9
`3.29
`3.21
`2.35
`2.55
`3.33
`3.98
`3
`2.6
`2.1
`2.49
`2.22
`2.8
`2.3
`
`7
`4.8
`8.95
`1.95
`11.4
`8.94
`2.9
`8.1
`7.9
`7.9
`7.9
`7.9
`7.25
`
`
`
`
`
`
`
`
`
`
`
`-
`-
`-
`
`-
`-
`-
`-
`-
`
`
`
`
`
`-
`-
`-
`-
`-
`-
`-
`
`
`
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`
`1.75
`1.5
`2.66
`
`0.6
`0.6
`0.81
`0.12
`0.6
`
`
`
`
`
`15.3
`3
`3
`2.3
`2.35
`3.26
`3.5
`2.5
`2.2
`1.9
`2.44
`2.17
`2.2
`2.2
`
`4.95
`4.4
`8.83
`1.74
`10
`8.93
`2.5
`7.6
`7.8
`7.8
`7.8
`7.8
`7.05
`
`
`
`ρ (Mg/m3)
`
`
`
`Wood, typical (Transverse)
`Wood, typical (Longitudinal)
`Leather
`Cork
`Bamboo
`
`
`
`GFRP
`Polymer CFRP
`
`Metal Aluminium/Silicon Carbide
`
`Natural
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Composites
`
`
`
`
`
`
`
`
`
`
`
`
`
`Tungsten Carbide
`Silicon Nitride
`Silicon Carbide
`Silicon
`Boron Carbide
`Aluminium Nitride
`
`
`
`Soda-Lime Glass
`Silica Glass
`Glass Ceramic
`Borosilicate Glass
`
`Zinc Alloys
`Titanium Alloys
`Nickel Alloys
`Magnesium Alloys
`Lead Alloys
`Copper Alloys
`
`
`
`Ferrous Cast Irons
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Metals
`
`
`
`10
`
`Non-ferrous Aluminium Alloys
`Stainless Steels
`Low Alloy Steels
`Low Carbon Steels
`Medium Carbon Steels
`High Carbon Steels
`
`Stone
`Concrete, typical
`
`Porous Brick
`
`Glasses
`
`
`
`
`
`
`
`
`
`
`
`Ceramics
`
`
`
`
`
`
`
`
`
`
`
`
`
`Technical Alumina
`
`Exhibit 1020-00026
`
`

`

`
`
`
`
`(Data courtesy of Granta Design Ltd)
`1 For full names and acronyms of polymers – see Section V
`
`.
`
`
`
`Polymer Foams
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Thermoset Epoxies
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`4.41
`4.83
`3.075
`0.552
`4.14
`2.07
`3.34
`1.55
`5
`3.8
`4.14
`0.896
`4.2
`2.44
`3.2
`0.424
`2
`2.9
`0.02
`0.003
`0.002
`0.0025
`0.004
`0.04
`0.002
`
`0.48
`0.2
`0.08
`0.012
`0.003
`0.001
`
`
`
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`
`-
`-
`-
`-
`-
`-
`
`
`
`2.07
`2.76
`2.35
`0.4
`2.14
`1.31
`2.28
`0.896
`2.5
`2.24
`2.76
`0.621
`3.5
`2
`2.62
`0.2
`1.6
`1.1
`0.005
`0.002
`0.0007
`0.0015
`0.0014
`0.01
`0.001
`
`0.2
`0.08
`0.023
`0.004
`0.001
`0.0003
`
`
`
`Rigid Polymer Foam (HD)
`Rigid Polymer Foam