Lab Work: Determining the Fracture Toughness of Wood

Transcription

1 CHEM-C105: ood nd ood Products Lb ork: Determining the Frcture Toughness of ood 1 Introduction In essence, frcture mechnics provides mesure of the toughness of mteril by considering the conditions under which pre-existing shrp crck or crck-like defect, which might ultimtely led to filure, begins to propgte (Mrtin, 1996) Both energy nd force bsed filure criteri hve been developed for mterils exhibiting brittle or qusi-brittle behviour (Knott, 1973; Prton, 199) These re collectively known s liner elstic frcture mechnics (LEFM) Primrily developed for metls (BSI, 1991, ASTM, 1991), LEFM hs nonetheless been pplied, with vrying degrees of success to non-metllic mterils including wood nd synthetic PMCs (Ashby et l, 1980; Ptton-Mllory & Crmer, 1987; illims, 1981; Stnzl-Tschegg, et l, 1994, 1995, 1996) s well s to other biologicl mterils (Lucs et l, 1991, 1995, 1997) 11 Liner-Elstic Frcture Mechnics Frcture mechnics evolved from the erly work of Griffith (190), in which the thermodynmics of the frcture process in nerly perfectly liner-elstic mteril (glss) contining shrp crck ws considered Griffith derived n expression for frcture stress s function of crck length nd work of frcture (tken to be the work required to crete new crck surfces) It ws shown tht, for crck of length contined in n infinite body, with stress pplied norml to the plne of the crck, the following reltionship exists between frcture stress, F, crck length nd work of frcture (Eqution 1): F S E 1/ (1) here: E is Young s modulus S is the work of frcture ( S is the surfce energy) This work ws lter extended to encompss mterils which were cpble of energy dissiption through plstic flow, s well s the cretion of new surfces In this pproch, the S term is supplemented by other, irreversible, contributions to the energy bsorbed in the vicinity of the crck-tip A new term (Eqution ) ws subsequently introduced to replce work of frcture, known s the energy relese rte, G, defined s (Anderson, 1995): G d d () here is potentil energy is crck re Mrk Hughes, 15 th Mrch 016

2 Thus G is mesure of the rte of chnge of potentil energy with respect to crck re For the exmple noted bove, it cn be shown tht G E For frcture to occur, G must exceed criticl vlue, G C, the criticl energy relese rte, or frcture toughness In the bove noted exmple, it cn be shown tht the reltionship between frcture stress nd G C is (Anderson, 1995): F GC E 1/ (3) An equivlent, force-bsed, pproch considers the stress field in the vicinity of the crck-tip It my be shown tht constnt K, the stress intensity fctor (units of MN m -3/ ) chrcterises the crck-tip stress conditions Furthermore, it cn be shown tht G nd K re relted s follows (Anderson, 1995): G K E (in plne stress) (4) G K 1 v E (in plne strin) (5) here: v is Poisson s rtio It my be shown tht the stress distribution in mteril hed of crck in loded homogeneous, isotropic nd idelly liner-elstic body tkes the generl form (Prton, 199): K f + (6) 1/ z here z is the distnce from the crck tip,, the ngulr displcement bout the plne of the crck The stress intensity fctor chrcterises the intensity of the stress field hed of the crck (Knott, 1973) The stress field in the vicinity of the crck-tip therefore differs only by constnt (depending upon the mode of the crck surfce displcement), K, which encompsses the externl lod nd geometry of the body A criticl vlue of K K C defines the onset of crck growth nd provides force bsed frcture criterion The criticl stress intensity fctor K C, is lso referred to s frcture toughness Under opening mode, plne strin conditions, plne strin frcture toughness ( K IC ) cn be regrded s mteril prmeter, provided stringent vlidity criteri re met (see eg BSI, 1991; ASTM, 1991) For rnge of specimen configurtions nd loding schemes, stndrd solutions for the determintion of the stress intensity fctor ( K ) re vilble nd generlly tke the form K l pp Y, where pp is the nominl pplied stress, l the crck length nd Y is dimensionless constnt, known s the K-clibrtion The K-clibrtion depends upon the rtio of crck length to specimen thickness, b K-clibrtions usully tke the form of polynomil, thus (Prton, 199): 3 Y c c c c (7) Mrk Hughes, 15 th Mrch 016

3 here: l b It is therefore possible to determine the frcture toughness of mteril, if the remote stress t crck initition cn be determined, if the globl behviour of the mteril is liner-elstic, nd if the specimen geometry nd loding fll within certin bounds These vlidity criteri re set out in the stndrds (eg BSI, 1991; ASTM, 1991) Frcture mechnics hve been pplied to wood nd is the subject of much reserch interest s well s prcticl ppliction In this prcticl work, we will im to mesure the criticl stress intensity fctor under plne strin conditions (KIC) - or plne strin frcture toughness of wood where the crck propgtion direction is either prllel or perpendiculr to the grin direction In this work consider the following points: 1 ht do you notice bout how the crcks propgte? How does the crck propgtion direction influence the vlue of KIC? 3 How do the vlues tht you hve obtined compre with the vlues found by other workers? 4 How do the vlues tht you hve found compre with other mterils? 5 ht cn you conclude bout the toughness of wood? 6 ht do you think bout the vlidity of using LEFM in wood frcture? Methods You will be given rnge of specimens tht hve been previously been pre-crcked using first bnd sw to crete the strter notch, which is then shrpened using rzor blde The design of the specimen is show in Fig 1 Figure 1: Schemtic representtion of test specimen The crcks re oriented differently, following the following the convention shown in Fig : Mrk Hughes, 15 th Mrch 016

4 Figure : Crck propgtion directions in wood Procedure: 1 Lbel ech specimen nd identify the crck propgtion system in ech smple Mesure the dimensions of the smple You cn ssume tht the crck depth = -15mm 3 ith the help of the techer/instructor, plce ech smple in turn on the loding device nd test the smple to destruction Tke creful note of the test set up the distnce between the supports (spn), cross-hed (loding) speed, etc, etc If you re ble, tke photogrph for lter reference (lso note things like the equipment used, mke model, the test environment etc, s these should be included in the Mterils nd methods section of your report) 4 ht we re interested in is the lod t which the crck first strts to dvnce As it is wood, nd reltively dry wood, you will probbly be ble to her the wood begin to crck (listen out for this!) However, there is nother wy to detect when the crck begins to dvnce If you exmine the lod-deformtion curve, you will most probbly notice sudden drop in the force reding t certin points These points re known s pop-ins in the lod-deformtion curve nd re n indiction of sudden crck dvnce To enble you to see these pop-ins more clerly, if you tke the second derivtive of the lod-time curve, you will see sudden Mrk Hughes, 15 th Mrch 016

5 Mrk Hughes, 15 th Mrch 016 pek ppering ith digitl dt cpture, it is possible to perform numericl differentition on these dt in progrms such s Origin or Excel Once you hve identified the pop-in point, you then will know the lod t crck initition This is necessry in order to clculte the criticl vlue of K 5 ASTM nd other stndrds developed for mesuring the frcture toughness of metls, give the K-clibrtions for specific specimen geometries nd loding configurtions Using the expression given in Eqution 8, nd the K-clibrtion given in Eqution 9, clculte the criticl vlue of K t crck initition 15 B f S P* K (8) = f (9) here P* is the force t crck initition S is the spn is the crck length is the thickness of the specimen B is the width of the specimen

6 Instructions on report writing: 1 rite the report s pir (or group of three) The rw dt from the test will be sent vi MyCourses 3 Anlyse the dt s per these instructions 4 A simplified reporting method is pplied in these ssignments Prepre slide show with PowerPoint Note tht there will be no seminr Just return the slides to Mrk electroniclly 5 The report should cover the following issues (the following slides, one or severl in ech topic): Introduction Bckground Objective of present study b Mterils nd methods Equipment nd mterils used Methods c Results Anlysis of the results (include the steps tht you took to nlyse the dt) Observtions Py ttention to presenttion nd clrity Cler figures nd tbles d Discussion nd conclusions ht do the results men? Justifictions for nlysis Comprison to relted literture (compre your results with those of others) Conclusions (ht do you conclude from your study) e Literture reference list -3 literture references Dedline for submission: Fridy 1 st April Further hints If you hve ccess to cmer, tke some photos of the set up nd the smples nd the frcture Observe nd record! I will mke vilble key reference which you cn refer to for more informtion There is much further literture in books nd in scientific rticles (you cn serch these using eg SciFinder Scholr 007 or the Science Cittion Index (found in Nelli)) Further reding: JE Gordon, The New Science of Strong Mterils JM Dinwoodie, Timber, Its Nture nd Behviour (Section 77) Mrk Hughes, 15 th Mrch 016

7 References: Anderson, TL, (1995) Frcture Mechnics: Fundmentls nd Applictions Second Edition CRC Press Inc, Boc Rton Ashby, MF, Esterling, KE, Hrrysson, R nd Miti, SK (1985) The Frcture Toughness of oods Proc R Soc Lond A, 398: ASTM Designtion: E (1991) Stndrd Test Method for Plne-Strin Frcture Toughness of Metllic Mterils ASTM, Phildelphi, USA BS 7448: Prt 1 (1991) Determintion of Plne Strin Frcture Toughness (KIc), Criticl Crck Tip Opening Displcement (CTOD) nd Criticl J Frcture Toughness Vlues for Metllic Mterils under Displcement Controlled Monotonic Loding t Qusi Sttic Rtes British Stndrds Institution, London Griffith, AA (190) The Phenomenon of Rupture nd Flow in Solids Phil Trns R Soc Lond A, 1: Knott, JF (1973) Fundmentls of Frcture Mechnics Butterworths, London Lucs, P, Choong, MF, Tn, HT, Turner, IM nd Berrick, AJ (1991) The Frcture Toughness of the Lef of the Dicotyledon Clophyllum inophyllum L (Guttifere) Phil Trns R Soc Lond B, 334: Lucs, P, Drvell, B, Lee, KD, Yuen, TDB nd Choong, MF (1995) The Toughness of Plnt Cell lls Phil Trns R Soc Lond B, 348: Lucs, P, Tn, HT nd Cheng, PY, (1997) The Toughness of Secondry Cell ll nd oody Tissue Phil Trns R Soc Lond B, Mrtin, J (1996) Mterils for Engineering Inst of Mterils, London Prton, VZ (199) Frcture Mechnics: From Theory to Prctice Gordon nd Brech, Phildelphi Ptton-Mllory, M nd Crmer, SM (1987) Frcture Mechnics: A Tool For Predicting ood Component Strength Forest Products Journl, 37(7/8): Stnzl-Tschegg, SE, Tschegg, EK nd Teischinger, A (1994) Frcture Energy of Spruce ood fter Different Drying Procedures ood nd Fiber Science, 6(4): Stnzl-Tschegg, SE, Tn, DM nd Tschegg, EK (1995) New Splitting Method for ood Frcture Chrcteriztion ood Sci Technol, 9: Stnzl-Tschegg, SE, Tn, DM nd Tschegg, EK (1996) Mode II Frcture Tests on Spruce ood Mokuzi Gkkishi, 4(7), illims, JG (1981) Frcture Mechnics of Non-Metllic Mterils Phil Trns R Soc Lond A, 99: 59-7 Mrk Hughes, 15 th Mrch 016