RELAXATION CHARACTERISTICS G? ALFALFA STEMS Thesis for The Degree of PH D MICHIGAN STATE UNIVERSITY Glenn E. Hall 1966. W "v a: I LIBRARY I“ AlujL; L) This is to certifg that the thesis entitled RELAXATION CHARACTERISTICS OF ALFALFA STEMS presented by Glenn E. Hall has been accepted towards fulfillment of the requirements for Ph.D. Agricultural Engineering degree in W” QM Major professor/ Date 2/24/67 0-169 gran Sta 2::- U my 3337 l.'% i I ,g...‘ g (9' fir.»- v, REIAXATIGI CHARACTERISTICS OF ALFALFA STEMS By _ L \\ 9% Glenn E‘i‘nm AN ABSTRACT Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DCXITCB OF PHILCBOPHY Department of Agricultural Engineering 1966 ABSTRACT REIAXATION CHARACTERISTICS or ALFALFA sums by Glenn E. Hall The theory of viscoelastic relaxation as applied to eight percent moisture content alfalfa stems is presented. The variations of the cross-sectional areas along the stms were determined and analyzed. An end view of stem sections taken throughout one millimeter intervals was photographed and scanned with a Flying-Spot Particle Analyser to deter- une the area. Various methods for designating the cross-sectional area were used and compared. Each stem section was submitted to a relaxation test with the stress applied in a longitudinal direction. The data obtained are represented by the equation loge stress - A + B loge time, where Aisthe ordinate intercept and B is the slape of the curve. The slopes of the relaxation curves and the cross-sectional area measurements were analyzed by the spectral density method to determine the dimensional and relaxation characteristics along the alfalfa stems. The slope of the relaxation curve for the stem sections was very highly correlated with its neighboring sections up to a distance of 100 mm, which was the maximum distance included in the analysis. This indicates that the stem section selected for a relaxation test is not ii critical. The area analysis showed that it is necessary to determine the area at or within 0.75 millimeters of the point of loading if satisfactory results are to be expected since there is considerable area fluctuation along the alfalfa stem. Approved (EZLJZOA Cl=éafl1 fiaflor Professor and—Tipartment Chairman iii RELAXATION CHARACTERISTICS OF.ALEALFA STEMS By Q/(.|¥./ Q Glenn if. Hall A THESIS Submitted to ‘Michigen State University in partial fulfullment of the requirements for the degree of DOCTOR OF PHILOSOEHY Department of Agricultural Engineering 1966 VITA Date of Birth: 21 April 1931 Military Service: U. S. Am, Counter Intelligence Corps, March 1951: to March 1956 Education: Scipio-Republic High School, Republic, (1110, Graduated May 19h9 Michigan State University, 3.3., Mechanical Engineering, June 1959 Michigan State University, M.S., Agricultural Engineering, June 1960 11.8. Thesis: Conduction Drying of Shelled Corn Employment: Farming to March 1951; Research Assistant, Michigan State University June 1959 to June 1960 Instructor, 0110 Agricultural Research and Development Center, June 1960 to July 1965 Research Assistant, Michigan State University, September 1963 to February 1965 Assistant Professor, (1110 Agricultural Research and Development Center, July 1965 to present Ph.D. Oral Examination: 2 December 1966 ACKNOWEEDGMENTS I wish to express my'appreciation to the following persons for their assistance during my graduate program: Dr. Carl‘w, Hall, my Major Professor, whose guidance and encourage- ment throughout my graduate program were immensely invaluable and enjoyable; Dr. Ross D. Brazee, whose counsel, guidance, and encouragement during the theoretical and experimental portions of the investigation were greatly appreciated: Dr. Fred H. Buelow, Dr. Merle In Esmay, Dr. Carter M, Harrison, and Dr. George E. Mase, members of my graduate guidance committee, for their counsel during my graduate program; Dr. Robert E. Stewart and Dr.'William H. Johnson for encouragement and assistance toward completion of the graduate program; Mr. Roy Jordan and Mr. NCrman Hostetler for their assistance during the experimental portions of this investigation; Mr. Glenn Shiffer, Mr. Jim Cawood, and Mr. Harold Brockbank for their assistance during research performed while undertaking courses at Michigan State University; Mrs. Doris Baum, whose typing assistance was certainly appreciated; Rose, my wife, for her constant encouragement; Christine and Melissa, my daughters, who will someday realize the implications of a graduate program; And all others who contributed to my graduate program. I also wish to express my appreciation for assistance by: Ohio Agricultural Research and Development Center for financial assistance during my leave; United States Department of Agriculture for the use of equipment during the experimental phases of this investigation. And Mbssey-Ferguson Ltd. for partial financial assistance while in attendance at Michigan State University. vi IIST OF CONTENTS Section I. II. III. IV. VI. VII. INTRODUCTION . . . . . . . . . . . A. Historical Background . . . . B. Experiments . . . . . . . . . C. Alfalfa Stem Photomicrographs VISCOELASTIC RELAXATION THEORY . . REIAXATION TIME SPECTRUM . . . . . . . . STRESS RESPONSE IN A RANDCM VISCCEIASTIC MEDIUM EXPERIMENTAL INVESTIGATION . A. Area Measurement . . . B. Relaxation Tests . . . RESULTS AND DISCUSSION . . . A. Comparison of Area Measurement Methods . . B. Methods of Analysis . . . . . . C. Area Spectral Density and Correlation . . . D. Relaxation Spectral Density and Correlation CONCLUSIONS . . . APPENDU O D O O O O O O O O 0 O RECCMMENDATIONS FOR FUTURE STUDY REFERENCES INDEX 0 O O O O O O O O O O O O 0 vii 11 15 21 23 31 3h 3h 39 ho hl be h? L8 U‘. a. J LIST OF TABLES Page Internodal distances of two alfalfa stems used for area and relaxation characteristic fluctuations ... 21 Internodal distances of alfalfa stems used for area determination comparisons .. 22 Comparison of cross-sectional area measurements.... 35 Spectral analysis program for IBM 1620 computer ... 37 Viii 10. 11. LIST OF FIGURES Photomicrograph at 77K magnification of quarter cross-section of alfalfa stem . . . . . . . . . . . . Photomicrograph at 3501 magnification of alfalfa stem eipdumia O O O O I O O C O C C O O O O O O C O O Photomicrograph at h37X magnification of longitudinal Section of alfalfa stem . . . . . . . . . . . . . . . Examples of film negatives of stem cross-sectional views as used in Flying-Spot Particle Analyzer for area measurement . . . . . . . . . . . . . . . . . . . Flying-Spot Particle Analyzer used to determine stem cross-sectional areas . . . . . . . . . . . . . . . . Block diagram of Flying-Soot Particle Analyzer film scanner 0 O O 0 O O O O D O O O O O O O C O O O . O 0 Block diagram of Flying-Spot Particle Analyzer logic Circu1t8¢aeeeoeeeeeeeaeeeeeeeee Cut-off saw used to section alfalfa stems . . . . . . Device for conducting relaxation experiments of alfalfa stem Beetion O O O O O O O O O O O O O O O O O O O O 0 Two stress relaxation curves obtained during the investigation 0 O O O O O O O O I O O O O C O C O O 0 Spectral density and correlation for alfalfa stem cross-sectional areas . . . . . . . . . . . . . . . . Spectral density and correlation of slopes of alfalfa stem relaxation curves . . . . . . . . . . . . . . . . ix =- I? 25 26 27 28 30 30 33 h2 hh I. INTRODUCTION The more information there is concerning the properties of a product the more rational becomes the design procedure for new machines and processes to utilize the product. An economical approach for new machinery design in the agricultural area would be to determine the requirements of the product before designing the machine. Prior know5 ledge of a.product's properties would save considerable time and expense in maChine development research. Product properties will assist in machine.design, but will not eliminate all empirical approaches since we cannot completely describe every situation. . Prior to conducting extensive tests concerning the physical proper- ties of forages we should have information concerning product variations within a single unit as well as between similar products. The aim of this investigation.was to determine the variation of the cross-sectional area and relaxation characteristics of alfalfa atoms as a function of position along the stem. This information will be useful to researchers inyestigating the properties of alfalfa by indicating fluctuations which are normally present and indicating the care which must be exercised if reliable results are to be obtained. A. Historical Background , Alfalfa is an herbaceous perennial legume that may live 15 to 20 years or more unless destroyed by insects or disease. The most commonly cultivated species is Medicago sativa, which includes the purple-flowered vernal alfalfa variety. -1- The name alfalfa, which comes from the Arabic language, means best fodder. It is generally called lucerne in Europe and is believed to . have originated in sauthwestern Asia. Alfalfa was first cultivated in Iran, then.Arabia and the Mediterranean countries, and finally carried to the New“Wbrld. The first recorded attempt to raise alfalfa in the Uhited States was in Georgia in 1736. Its introduction into California from Chile in about 1850 started a rapid expansion in alfalfa acreage. The alfalfa plant varies from two to three feet in height and has 20 or more erect stems that continue to grow'from the crown branch as the older stems are harvested. Many short branches may grow’from each atom and the oblong leaves, arranged alternately on the atom, are pinnately trifoliate. The root system.consists of an almost straight taproot--sometimes growing to a depth of 25 to 3D feet--frcm which side branches extend short distances. The fruit of alfalfa is a spirally", twisted pod containing the small seeds. Further information concerning alfalfa cultivation can be found in Martin and Leonard (19h?) and Hayward (1938). B. Experiments There are two types of rheological experiment for obtaining visco- elastic properties: transient and dynamic. Included in the transient tests are relaxation, creep, and constant strain rate experiments._ The dynamic tests include steady-state sinusoidal and non-sinusoidal, and impeot eXperiments. The alfalfa stem sections used in this investigation behaved as viscoelastic material, rather than viscoplastio, because the dtmensional characteristics of the stem sections were the same before and after the stress loading cycle. If plastic deformation did occur it was not possible to observe the dimensional changes after stress removal with the use of the microscope. C. Alfalfa Stem Photomicrographs A photomicrograph, at 77X magnification, of a quarter cross-section of an alfalfa stem is shown in Figure l. The various parts of the stem are labeled on the photomicrograph. As the stem matures an interfascicular cambium develops, and a cambical cylinder develops which produces a continuous zone of lignified xylem. Some of the smaller parenchymatous (thin-walled) cells on the inner face of the bundles may become lignified. The stem is also rein- forced by a layer of collenchyma (thick-walled cells): the four corners of the stem are reinforced with several layers of collenchyma. The parenchymatous cells of the pith may disintegrate or become ruptured so that the mature stem becomes hollow. This is in evidence in the large open area of the pith shown in Figure 1. Figure 2 is a photomicrograph of alfalfa stem epidermis at 3SOX magnification. The long dimension of the epidermal cells, (a), is parallel to the longitudinal direction of the stem. A stoma is shown at (b). Figure 3 is a photomicrograph of a longitudinal section of alfalfa stem, at h37X magnification, showing the spiral tracheal tube, (a), and pitted tracheid, (b). Additional details on the structure of alfalfa are given by Wilson and Loomis (1962), Wilson (1913), and Hayward (1938). -),_ _ 35¢ , Pericyclic W‘Q, “. fibers . Q Xfflem’p ' 2." Cam iumm qh‘i 39m” '54, 31‘. I F‘I‘H‘hju'mw . Figure 1. Photomicrograph at 77K magnification of onwrter cross—section of alfalfa stem >—.... ’ iv p‘.m.\- ‘ 1 - , . -'m .“-- ‘ ' ' “3 i \: f4“- ..1 w, _ , . n ‘5 fijgure ?. Photomicrograph at 350x magnification of ‘ ' alfalfa stem epidermis WESLEMESwu ~. . > . ‘ ‘ L'W'i':"‘ 3" '- "~, ~.”1,/ 'gl'f ; H. ~~ 11" Figure 3. Photomicrograph at h37X magnification of longitudinal section of alfalfa stem an?! ! 'P' ~.K$».!'..b "-. ‘0' ‘V .... 3"." - or b \. \ The cellular structure of the alfalfa stem consists of cross-linked and linear polymers which affect both the physical and chemical proper- ties. I'rom this it would be expected that alfalfa stuns would behave in a manner similar to other viscoelastic polymers, and that mathematical techniques employed to define the behavior of other polymers could be applied to alfalfa stems. II. VISCCELASTIC REIAXATION THEORY Consider two neighboring points of a stress-free continuous medium and denote their separation by the infinitesimal vector _6_ = if), + 3’6, 56,. When the medium is subjected to a stress, the two points will be dis- placed from their initial positions by a and r +»A£, with point 1 dis— placed by r_ and point 2 displaced by r + Ag. Since g and A; approach zero together, we expand A3 to obtain, component-wise, (AS); " (ar‘/BX)5,‘ + (arm/BY)51 + (arm/az)623 (1) (As), ' (513/5305: + (51" /BY)5y 1" (51‘ flz)5z; (2) All); 3 (Br; /5X)6x + (5r: /BY)6y + (art/Pa )619 (3) or, in vector form, A: - é . V30 (1“) Following the approach of Fitts (1962), separate V; into its symmetric and antisymmetric parts, v3 ' g + (V:)a, (5) where (V£)a is antisymmetric, and the symmetric part 5 represents the strain on the medium. The antisymmetric part may be written (Vr)a ' -%*Z x a) X E, (6) where y is the unit dyadic (second-order tensor) defined as "(:1 I i + Q; + k . (7) Since ' (V x r) s O (8) Id -7- -8- for any vector, the dyadic (V£)a,is divergenceless and represents a pure rotation of the medium. Hence, it does not contribute to the strain and will hereafter be omitted. Next assume that the medium is 33322- elastic, with stress and strain both functions of time. The stress and strain are related by the equation g(t) - Q 3 fit) (9) where g is a fourth-order tensor which transforms : under the indicated operation into a new (stress) dyadic, g. If the Y6 component of the 3 strain tensor experiences a unit step change at time t-O, then “Y6 - O for t<0, 3Y6 . 1 for t>0. (10) The response of the GB stress component to the unit step change in the Y6 strain component is denoted by KGB,Y6(t)’ and this response, under the relaxation test of viscoelasticity, is a time function which is zero for t<0. Owing to the symmetry of g, a change in ‘ya is accompanied by an equal change in e If KoB,y6 is defined as one-half the sum of the 6v responses ‘Y6 and céy, then KGB,Y5 is symmetric in Y and 6. Also, it must be symmetric in a and 6 since KoB,Y6 gives the o8 stress component, which is known to be symmetric. As a consequence of these symmetries for o and a tensors. Kw,yé(t) 8 KBG,Y5(t) ’ KOfi,6Y(t) -"- KBU’5Y(t)' (11) These qtantities are the components of a fourth-order tensor £(t), as in Eq. (9), which in general would have 81 components in three-dimensional space but, due to the symmetries expressed in Eq. (11), has instead only 36 independent components. Assuming the unit-strain response to be invariant under translation of the time origin, ;(_(t-s) may be regarded as the response to a unit step in g occuring at time s. When the temperature and other quantities which might affect the form of §(t) are constant or change slowly as compared with stress-strain changes in the medium, then this assumption will be valid. Upon assuming that the stresses may be compounded in a linear manner, the change done (t) in the (:6 component of the stress tensor g(t) due to unit steps dc at time s in the Y6 component of the strain _e_(s) Y6 may be written as doaa(t) - ézxafiméfi'wdcvsh)‘ (12) To find the stress on the medium at time t integrate Eq. (12) to obtain t t 003(13)‘ f sagas) = JP SEKs,y,] ' Hana/axe + Buox/Bxe) , (17) where "a is the a component of u, the center-of—mass velocity. Hence, g is the symmetrical part of V1_1_. III. REIAXATION TIME SPECTRUM This section embodies an extension of the relaxation stress response theory as discussed in Section II. As a first step pertinent theory as outlined by Ferry (1961) is reviewed. Any experimentally observed stress relaxation curve which decreases monotonically can, in principle, be fitted with any desired degree of accuracy to a series of exponential terms of sufficient number, each with its own relaxation time. If the number of terms or elements in the defin- ing medal is increased without limit, the result is a continuous spectrum in which each infinitesimal contribution to rigL y Edf is associated with relaxation times lying between T and T+dT. According to Ferry (1961) a logarithmic time scale is more convenient and the continuous relaxation spectrum is defined as EdlnT with relaxation times whose logarithms lie between 1n? and 1n? + dlnv. For the continuous spectrums we have K(t) - Fe + f He't/Tdun‘f), (18) -m which.may be taken as the mathematical definition of H without the need of mechanical models language. The constant K8 is added to allow for a discrete contribution with 7:”. The value of Ke is zero for uncross- linked polymers. The function H is multiplied by the intensity functicn ert/i which goes from zero 7:0 to 1 as'rapproaches infinity. This is approximated by a step function going from zero to one at T=t. Therefore 1((t) =~ KG + (Imam), (19) x. 1!) t -11- -12- and H(T) =- - dK(t)/d(ln t)|’o (20) -'r 01' H(‘r=t) a -dK(t)/d(1n t) (21) In terms of stress, c(t) a cK(t), where s is constant strain during the relaxation experiment. Substituting into Eq. (21) we obtain H('r-t) = -(l/c)dc(t)/d(1n t). (22) According to Perry and Williams (1952), if H(1') is of the form H('r )-kw"' with o(t) - a j‘ He't/rd(ln'r), then m o(t) - I k'r"e‘t/Td(1n 'r) - kc] 7"e't/Td'r/T =- k 'r"'"? 't/7 a}; e d1. Letting x - VT and dr - -tdx/xa, then 0(t) . kc J" (t/x)“"'1e"‘(tdx/x3) O Q -- ket" 'Jd'le"dx 1; c(t) - ksl"(m)t", m > o, (23) where 1(m) is the gamma function. Insorting Eq. (23) into EL. (22) yields H('r=t) = H('r) = kI‘(m + 1)T"', 11'! error by a factor of l"(m +1). But the second approximation may be -13- written H(T-t) - -[1/T(m + 1)] (1/6) [d0(t)/a(1n t)]. (2h) Letting M(m) - [1/T(m +1)] (25) and Kim - (l/e)c(t), (26) and noting that dK,(t)/d(1n t) - K1 (t) d[1n K,(t)]/d(1n t) (27) so that H(‘r) = {-M(m)K1 (t)[d1n K,(t)/d(1n t):}t"r (28) Based on these procedures by Ferry (1961) and Ferry'and Williams (1952), it is hypothesized that the relationship existing between stress and time for the alfalfa stem sections can be expressed as In c(t) - m ln t - m In to + 1n co, (29) which can be changed to the form In [c(t)/cb] - -m 1n (t/to) (30) and -m - 1n reeves/1n (mo). (31) From Eq. (29). a(t)/c'o (t/to)", (32) letting ks - coto' , I c(t) .- kct‘“ (33) and H('r=t) - -(l/s)do(t)/d(ln t) . [-(l/e)ketdt"/dt]t.1_ - 1cm" (3h) -1h- c(t) =- e JPHa't/Tdfln 1') - c I km"e"t/Td(1n 1‘) - kem ‘ 'r"'1e't/Td'r - ksmt" P x'"e"dx o o - kcmT(m)t" - ksI"(m + l)t"II (35) and, after attaching the factor [l/I'(m + 1)] to H(1') for a second approxi- mation, INT-t) = {l/Nm + 1)] (1/6) da(t)/d(1n t). (36) If so - tO - 1, Eq. (29) reduces to . 0(t) - t' (37) which is actually of the form cont) - 9"") (38) since the stress and slope are functions of position and time, and posi- tion, respectively. IV. STRESS RESPONSE IN A RANDCM VISCGELASTIC MEDIUM The stress response is now considered as an homogeneous random func- tign 2! position in a viscoelastic medium whose microstructure consists of grains, cells, or fibers of random sizes, lengths, diameters, or strength prOperties. Such structures could be generated, e.g., by growth processes of various kinds, biological materials being typical. It is implied that the physical parameter fluctuations can be described by distributions or correlations in the statistical sense. The random func- tion describing the fluctuating stress response may be linearly separated into a uniform mean component and fluctuating component. Interest will center on the fluctuating component. Assume that raw data are available from a series of viscoelastic experiments with a particular random medium. Further, suppose that these data have teen investigated, removing trends and periodicities of interest, and it is now desired to study the residual aperiodic fluctuations. A 1articu1ar point to be investigated here is whether the random data are statistically homogeneous throughout the medium. This could be done in a preliminary way by observing whether statistical parameters or distribu- tions persistently change in magnitude or form in various regions of the medium. It seems appropriate to sketch this theory by starting with simple alterations of Eqs. (1b) and (15), viz., t g(X.t) j“ he, t-s) : gene, (39) -15- -15- 01' t g(X.t) = get) : .e__(0) + j get, t-s) : é(s)ds (ho) +0 where now spatial dependence of the stress response prevails. The eighth- order correlation tensor is written ":0 (as, so) = (§(xi, t)§(se. t)>. (bl) The fluctuations in viscoelastic properties, mainly relaxation characteristics, are important random fluctuations of position. These variations are partially described by a distribution function F[§(x,t)]. The distribution function could, ideally, be estimated on the basis of experimental data. Knowing the distribution function, moments could be calculated, (5(x,t)_§(x,t) §(5’t))order n - f [§(s,t)§(x,t) gen») dFC§(2.C.t)J. (1.2) order n work by Beran (1965), using a similar approach for heterogeneous materials, was discovered after this portion of the theoretical background had been developed. Ideally, information would be available on the distribution mall components of _I_(__(x,t) which would yield the form of If§(_x,t)]. But in physical problems it will be necessary to be content with considerably less. A complete description of the system could be given if the ideal situation existed. Instead approximate descriptions are available on limited information. It may be more profitable to make less detailed descriptions of more systems. The statistical-mathematical model based on less detail may be the most useful one available from the infinite number of models available. -17- Wiener (1956) has discussed modeling of physical systems on the basis of imprecise, but extensive information. An important point which he discusses is that highly precise measurements in some cases are not the best technique. The more extensive, less precise measurements may yield more real information and understanding of the actual system. Blackman and Tukey (1958) also discuss the trouble that may be encountered by the investigator who attempts to apply overprecise measurements to problems in physical research. Now, letting X represent a particular time t, Eq. (38) becomes am) - x' M as) and, for different locations on the stem, x1 and x9 a(x o(x1,}\) ’ A 1) (M4) and WM) ' XI (1") (1.5) It is also assumed that at least wide sense statistical homogeneity pre- veils. The autocorrelation of stress fluctuations, according to Papoulis (1965) is defined by the formula E - Roo(£1’§3’)‘) - Ekxt(l‘)/\£(£')> . E(,3(3-;)";(52 )) (’46) where E denotes the expectation and R is correlation of data. If x; - x + A and xh - x, then E\:Q:X,)\)> ‘ RGO(A’A) ' RO(A,X) a'x + A) + a x . Eb. ‘ -( )) (h?) -13- From Eq. ([13), gfx) = ln g(x,A)/ln X. (he) Hence, the autocorrelation of slope is E*r_rg(X;)r_r_1(x2)> - R. new) = saw = (1/(1n A)‘)E<1n gemnn gem» ~ <1/<1n 02>E<1n g\)]1nC0(X227\)] X fr; cafgbcl ,X)g_€x3,>\),l]dol do; (51) . [l/(ln majmn g(x + A,x)1n grow». (52) Dividing Eq. (52) by R.(0.K). ' n-A R,(A,l) XEI 1n g(x,x)1n g x + An.) ' i-l _ fOPA=l,2 .00 M n—A R.(0.A) 531 (In {)3 ’" (53) -19- which corresponds to the equation used to determine the autocorrelation in the spectral analysis routine, which will be discussed later. Since the spectral density fT(w), of a process x(t) is the Fourier transform.of the autocorrelation, ° 1 rT(w) -f e' “Rom, (Sh) ..O and since R(-l) . R(l),fT(w) is a real function. Using the Fourier inver- sion formula R0.) . (1/2n)f fI(w)eiw)‘dw. (55) which yields, with x - 0, MO) = <1/2n) J:fT(w)dw - Ex> - when”) 2 o (96) therefore fT(w) is non-negative. If x(t) is real, then R(l) is real and even, and fT(w) is also even and Eq. (5b) and (55) can be written 1"”) fit 30.) cos ml d). (57) and an) . (1/2n)f are») cos col dw (58) In this investigation the interest is mainly in the first and second moments, @512» =,F 5291:) dP[§_ “I _§_(51,t)§(zz.t) dFC§(a333 _) 95308.0 0.00.. 0h _ 1 .oo mesmwe )— >Jt 3m H 23.20 2.353 oz< caeecwzuo good :2: data” 352.8 3533 —) > _ ”300$ 0..¢2>0 us a 1|— o c» was 45.95 h! 22 2:5 _ ~85» , .2283?! 5:334 _ «9.29. 294523 _ 79832... 9: ONO->1—Ucahua 02‘ 02.!!(4. ”CU.E.J&!¢. _ 33533 I oza onus» — ‘— 20:83.3 . .1 Eu 3E... 2.3 2252.3 3.8 3.8 ZOFONJug ggu U03» IOhOtm ......s. r _ _ Ognugh CU. 24.58408; 00354.8( _4 — — >41...“ ghlchoxc rite g‘hdgts. x mpfisoaeo oamoa aeshamc< oaofipamm uoamnmCfihHm mo Seawewp xooam .90 opsmfim COFOUJUO SPCCUZUO cahzaoo gh‘tflluo \ 88.5 2.3 29:88 was... 02.38... _V 25...:- 8.58:3: 43.2.. 33.58 0. ..o. a: .8811 8:53- 4838., 34.8.. 42.2.8 8:58 . 8.5.5. , 88.. .82.. 8...: IDUSO X.Ih‘. a 552. .. m Inner a. M m m x 2.08: 8.... Sheena.“ l c L a 9:. 23.. u L m 3.5.088 5.3.58 m m M #898»... l Q. Q 1|.lll m m u m m 82.3 v c .38... .28.: ..o. 28.8.. 8:58 .8 S. 8 8. on . _ 8 a u . - :88 w _ .33... 2... 2892a 92 :58 5.288. .880 ErLrL 30.2.1 85:28 2.18.8 Rats; 26.588 89> 88...“: 8:58 up: 89> , .58.. 2.58.. 3 22.52.58 I ... .282... _H :38 :88»... 828.5.» _H < _ . _. A 8....- 34.3.. 2.58.. 8.83.: -29- measured with the Flying-Spot Particle Analyzer (FSPA) with the 100 percent transmission base taken as the light transmitted through the area between frames which had not been exposed to light prior to film development. The background film density was maintained constant by using an exposure meter adapted to the microscope to determine the proper exposure settings on the 35 mm camera for each and every cross-sectional stem area photographed. The area data were automatically punched on standard computer input cards for use in the spectrum analysis of the area data and subsequent stress calculations for the relaxation experiments. The stem sections were prepared by cutting the stem on a high-speed cut-off sew shown in Figure 7. The air-powered saw, with a one-inch diameter 70-tooth blade, turned at approximately 65,000 rpm. A set-screw adjustment permitted cutting a consistent section length of 0.75 mm. The saw blade cut was 0.25 mm thick resulting in area measurements taken at intervals of one mm. The stem sections were photographed on 35 mm high- contrast c0py film immediately after sectioning and were maintained in order of cutting throughout the experiment. The orientation of the sec- tions was maintained to assure that the photographs were taken at one mm intervals along the stem. In an attempt to compare cro;s-sectional areas of alfalfa stems obtained by several methods, areas were determined with a.micrometer "diameter" measurement, a microscope "diameter" measurement, and the FSPA area measurement. Ten stems similar to the two used for the area spectrum work and relaxation tests were selected and measured at the midpoint between nodes with a micrometer to determine the distance between opposite flat -30- Figure 7. Cut-off saw used to section alfalfa stems Figure 8. Device for Conducting relaxation experiments of alfalfa stem sections -31- sides._ A cross-section was then removed at the midpoint between nodes and measured under the microscope to determine the distance between opposite flat sides, apposite corners, and wall thickness. The section was then photographed and scanned on the FSPA to determine its area. B. Relaxation Tests Afer the area measurements were determined, the individual stem sections were submitted to relaxation tests. Supplementary tests, which were conducted to deve10p the equipment, were run with a standard four- inch micrometer as the main support member. Further tests indicated the need for strengthening the main support member and the device shown in Figure 8 evolved and was used for all relaxation tests. A relaxation test was conducted by placing the stem section vert- cally on the load cell of the relaxation test stand. A piece of brass shim.stock was placed on tap of the specimen and firmly held to prevent twisting of the specimen as the load was applied. The load was applied to the section manually by turning the micrometer screw down onto the shim stock and alfalfa stem section until the desired load was applied as registered on a recording cscillograph chart via the load cell. A stress of 3,000 grams per square millimeter (gsmm) was applied to each section. Approximately 6,000 gsmm were required to collapse the section. The deflection required to achieve a stress of 3,000 gsmm was held con- stant during the ZOO-second relaxation test. The 3,000 gsm stress level was selected to assure that the complete set of relaxation tests could be conducted at a common stress. -32- Tests conducted by placing the stem section horizontally on the load cell, with the stem sides collapsed, yielded stress relaxation curve slopes that were twice those of stems tested vertically. As a result of this, all subsequent tests were conducted with the stem sec- tion placed vertically on the load cell since this was the direction that exhibited the greater, or limiting, strength if the stems were under compression. Figure 9 shows two of the relaxation curves obtained. The load exerted on the alfalfa stem section was monitored by the, differential transformer load cell which transmitted an electrical sig- nal to the recorder where the signal was amplified and recorded. A curve reader coupled to a card punch was used to read points on the curves and punch the data on card for further analysis on an IBM 1620 computer. -33.. BECKMAN INSTRUMENTS INC, omen clvmlou m ran. an. 'I Figure 9. Two stress relaxation curves obtained during the investigation VI. RESULTS AND DISCUSSION A. Comparison of Area Measurement Methods The comparison of cross-sectional area measurements made by several methods is given in Table 3. The Flying-Spot Particle Analyzer (ESPA) measurement was determined as previously described. The microscope measurement was made by measuring the distance across Opposite sides of the alfalfa stem at their midpoints and measuring the wall thickness of the stem section. These measurements were made on the stem while it was in position for photography as utilized in the FSPA method. The micro- scope measurements were made with a micrometer scale in the microscope ocular. Prior to stem sectioning for the FSPA and microscope measurements, a micrometer was used to measure across opposite sides of the alfalfa stem at the location of the section to be removed. Distances A and B were the longer and shorter distances across the stem sides. AxB would assume that the stem is a rectangle A units long and B units wide; "Ag/h and nBz/h assumes a round stem configuration with a diameter of A and B respectively; and n(A+B)2/16 assumes a round stem configuration with a diameter of (A+B)/2. None of the micrometer measurements took into consideration the fact the stem was hollow. The section designation used in Table 3 indicates the stem number, from three to twelve corresponding to Table 2 internodal distances, followed by the two numbers which designate the two nodes between which the section was measured. -35- Table 3. Comparison of cross-sectional area measurements Cross-sectional area, mm? Micro Micrometer . Section FSPA scope AxB nA§7h Egg/L n(A+B)5/l6 101 0.817 0.78 1.86 2.28 0.98 1.58 112 0.711 0.97 2.18 2.86 1.02 1.98 123 0.358 0.78 1.98 1.65 1.82 1.58 138 0.218 0.62 1.68 1.82 1.22 1.32 185 0.830 0.59 3.87 1.82 1.22 1.32 156 0.215 0.68 1.55 ,1.27 1.17 1.22 167 0.289 0.63 1.88 h 1.22 1.12 1.17 178 0.899 0.58 1.82 1.22 1.02 1.12 189 0.263 0.88 1.01 0.81 0.77 0.79 201 0.850 1.05 1.61 1.32 1.22 1.27 212 0.878 0.96 2.36 1.98 1.75 1.85 223 0.883 1.11 2.21 1.75 1.71 1.73 238 0.575 0.85 1.98 1.65 1.82 1.58 285 0.577 0.88 2.03 1.75 1.82 1.59 256 0.837 0.71 1.88 1.58 1.37 1.86 267 0.505 0.50 1.33 1.07 1.02 1.05 278 0.321 0.38 1.30 1.22 0.85 1.03 289 0.351 0.29 0.86 0.70 0.65 0.68 301 0.715 1.18 1.82 1.27 0.98 1.13 312 0.788 1.08 1.68 1.37 1.22 1.30 323 0.766 0.99 2.13 1.95 1.80 1.68 338 0.916 1.39 2.72 2.38 1.95 2.15 385 1.086 1.07 2.52 2.01 1.95 1.98 356 0.725 1.08 1.92 1.58 1.88 1.51 367 0.618 0.79 1.86 1.16 1.12 1.18 378 0.602 0.85 1.55 1.32 1.12 1.22 389 0.521 0.62 1.81 1.30 0.98 1.12 812 0.928 1.65 2.29 1.83 1.77 1.80 823 0.818 1.52 2.56 2.01 2.01 2.01 838 0.751 1.86 2.68 2.15 2.07 2.11 885 0.885 1.88 2.77 2.21 2.15 2.18 856 0.798 1.21 2.55 2.15 1.89 2.02 867 0.725 1.27 2.32 1.89 1.77 1.83 878 0.792 0.92 1.88 1.88 1.83 1.86 889 0.855 0.67 1.52 1.22 1.17 1.19 501 1.150 1.78 2.56 2.07 1.95 2.01 512 0.907 1.59 2.77 2.21 2.18 2.18 523 0.780 1.59 2.98 2.89 2.21 2.35 538 1.100 1.51 3.12 2.89 2.82 2.85 585 1.011 1.68 2.98 2.35 2.28 2.32 556 0.881 1.38 2.32 1.89 1.77 1.82 567 0.959 1.50 2.88 2.09 1.82 1.96 578 0.763 1.06 2.80 2.01 1.77 1.89 589 0.915 1.02 2.13 1.77 1.59 1.68 (Table No. 3 Continued) 601 612 623 638 685 656 667 678 689 712 723 738 785 756 767 778 789 812 823 838 885 856 867 878 889 901 912 923 938 956 967 978 989 1012 1023 1038 1085 1056 1067 1078 1089 1.025 0.862 0.793 0.619 0.807 0.559 0.367 0.868 0.899 1.281 1.075 1.068 0.898 0.983 0.788 0.780 0.571 0.635 0.683 0.612 0.577 0.378 0.279 0.179 0.303 0.891 0.868 0.873 0.876 1.007 0.838 0.615 0.805 0.318 0.822 0.619 0.879 0.508 0.790 0.585 0.580 0.750 1.60 1.16 0.91 1.09 0.95 1.18 0.82 0.88 0.69 1.86 1.67 1.62 1.38 1.03 0.89 0.85 0.85 812323 9999????. 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