{"id":8732,"date":"2024-12-01T20:28:52","date_gmt":"2024-12-02T04:28:52","guid":{"rendered":"https:\/\/chansmachining.com\/pevnost-v-tahu-definice-vzorec-krivka-napeti-deformace\/"},"modified":"2024-12-17T12:53:44","modified_gmt":"2024-12-17T20:53:44","slug":"pevnost-v-tahu-definice-vzorec-krivka-napeti-deformace","status":"publish","type":"post","link":"https:\/\/chansmachining.com\/cs\/pevnost-v-tahu-definice-vzorec-krivka-napeti-deformace\/","title":{"rendered":"Pevnost v tahu: Definice, vzorec, k\u0159ivka nap\u011bt\u00ed-deformace."},"content":{"rendered":"\n

Co je to mez kluzu?<\/strong><\/h2>\n\n

Mezer pevnosti v tahu je nejv\u011bt\u0161\u00ed nap\u011bt\u00ed, kter\u00e9mu materi\u00e1l odol\u00e1, ani\u017e by do\u0161lo k jeho trval\u00e9 deformaci<\/strong>. P\u0159edstavuje okam\u017eik, kdy materi\u00e1l trvale zm\u011bn\u00ed tvar (tj. po odstran\u011bn\u00ed nap\u011bt\u00ed se ji\u017e nevr\u00e1t\u00ed do p\u016fvodn\u00edho tvaru). A\u017e do bodu kluzu je materi\u00e1l pru\u017en\u00fd a po odstran\u011bn\u00ed s\u00edly se vr\u00e1t\u00ed do p\u016fvodn\u00edho tvaru. Za touto hranic\u00ed se materi\u00e1l dost\u00e1v\u00e1 do oblasti plastick\u00e9 deformace<\/strong> a po odstran\u011bn\u00ed s\u00edly se ji\u017e nevr\u00e1t\u00ed do p\u016fvodn\u00edho stavu.<\/p>\n\n

To m\u00e1 z\u00e1sadn\u00ed v\u00fdznam pro materi\u00e1lov\u00e9 in\u017een\u00fdrstv\u00ed a navrhov\u00e1n\u00ed konstrukc\u00ed. Mez kluzu materi\u00e1lu je rozhoduj\u00edc\u00ed pro zabr\u00e1n\u011bn\u00ed deformace a selh\u00e1n\u00ed p\u0159i zat\u00ed\u017een\u00ed. V technick\u00fdch aplikac\u00edch, jako jsou stavebn\u00ed konstrukce, leteck\u00e9 konstrukce a automobilov\u00e9 in\u017een\u00fdrstv\u00ed, se mez kluzu vyu\u017e\u00edv\u00e1 k zaji\u0161t\u011bn\u00ed toho, aby sou\u010d\u00e1sti bezpe\u010dn\u011b odol\u00e1valy zat\u00ed\u017een\u00ed a nam\u00e1h\u00e1n\u00ed v pr\u016fb\u011bhu \u010dasu.<\/p>\n\n

vzorec pro mez kluzu<\/strong><\/h2>\n\n

S\u00edla p\u016fsob\u00edc\u00ed na materi\u00e1l a plocha jeho pr\u016f\u0159ezu ur\u010duj\u00ed jeho mez kluzu podle jednoduch\u00e9ho vzorce. Vyjad\u0159uje se jako.<\/p>\n

\n
\"Vzorec<\/figure><\/div>\n

Kde:<\/p>\n\n

    \n
  • –\u03c3_Y<\/strong> = mez kluzu (m\u011b\u0159eno v pascalech, Pa, nebo megapascalech, MPa)<\/li>\n\n\n\n
  • –F<\/strong> = p\u016fsob\u00edc\u00ed s\u00edla (m\u011b\u0159en\u00e1 v newtonech, N)<\/li>\n\n\n\n
  • –A<\/strong> = plocha pr\u016f\u0159ezu materi\u00e1lu (m\u011b\u0159eno v metrech \u010dtvere\u010dn\u00edch, m\u00b2)<\/li>\n<\/ul>\n\n

    Mez kluzu se obvykle ud\u00e1v\u00e1 v Pascalech (Pa) nebo Megapascalech (MPa)<\/strong>, p\u0159i\u010dem\u017e 1 MPa se rovn\u00e1 1 milionu Pascal\u016f. Tento jednoduch\u00fd vzorec n\u00e1m ukazuje, jak velk\u00e9 nap\u011bt\u00ed materi\u00e1l snese, ne\u017e se plasticky zdeformuje.<\/p>\n\n

    Pokud je nap\u0159\u00edklad ocelov\u00e1 ty\u010d o pr\u016f\u0159ezu 10 mm\u00b2 vystavena s\u00edle 1000 N, lze mez kluzu vypo\u010d\u00edtat takto:<\/p>\n

    \n
    \"Příklad<\/figure><\/div>\n

    To znamen\u00e1, \u017ee mez kluzu oceli je 100 MPa. Pokud nap\u011bt\u00ed p\u0159ekro\u010d\u00ed tuto mez, ocel se trvale deformuje.<\/p>\n\n

    Jak\u00e9 faktory ovliv\u0148uj\u00ed mez kluzu<\/strong>?<\/h2>\n\n

    Hranici kluzu materi\u00e1lu ur\u010duje \u0159ada faktor\u016f.<\/p>\n\n

    Slo\u017een\u00ed materi\u00e1lu<\/strong><\/h3>\n\n

    Hranice kluzu materi\u00e1lu je do zna\u010dn\u00e9 m\u00edry ovlivn\u011bna jeho chemick\u00fdm slo\u017een\u00edm. Nap\u0159\u00edklad ocel m\u00e1 vy\u0161\u0161\u00ed mez kluzu ne\u017e hlin\u00edk d\u00edky p\u0159\u00edtomnosti uhl\u00edku a dal\u0161\u00edch leguj\u00edc\u00edch slo\u017eek, kter\u00e9 zvy\u0161uj\u00ed jej\u00ed pevnost.<\/p>\n\n

    Teplota<\/strong><\/h3>\n\n

    S rostouc\u00ed teplotou \u010dasto kles\u00e1 mez kluzu. Kovy pou\u017e\u00edvan\u00e9 p\u0159i vysok\u00fdch teplot\u00e1ch, jako jsou motory nebo elektr\u00e1rny, se mohou p\u0159i vysok\u00fdch teplot\u00e1ch zhor\u0161ovat, p\u0159esto\u017ee p\u0159i teplot\u011b okol\u00ed vykazuj\u00ed dostate\u010dn\u00e9 vlastnosti.<\/p>\n\n

    Zpracov\u00e1n\u00ed a o\u0161et\u0159en\u00ed<\/strong><\/h3>\n\n

    Zpracov\u00e1n\u00ed za studena, tepeln\u00e9 zpracov\u00e1n\u00ed a legov\u00e1n\u00ed<\/strong> jsou procesy, kter\u00e9 mohou zv\u00fd\u0161it mez kluzu materi\u00e1lu. Nap\u0159\u00edklad ocel lze zpevnit operacemi, jako je kalen\u00ed a popou\u0161t\u011bn\u00ed<\/strong>.<\/p>\n\n

    Struktura zrna<\/strong><\/h3>\n\n

    Velikost a orientace krystalick\u00fdch zrn materi\u00e1lu m\u016f\u017ee rovn\u011b\u017e ovlivnit mez kluzu. Jemn\u011bj\u0161\u00ed zrna maj\u00ed vy\u0161\u0161\u00ed mez kluzu d\u00edky zpevn\u011bn\u00ed hranic zrn.<\/p>\n\n

    K\u0159ivka nap\u011bt\u00ed a deformace a mez kluzu<\/strong><\/h2>\n\n

    Abychom l\u00e9pe pochopili, jak funguje mez kluzu v re\u00e1ln\u00fdch podm\u00ednk\u00e1ch, pod\u00edvejme se na k\u0159ivku nap\u011bt\u00ed-deformace<\/strong>. K\u0159ivka nap\u011bt\u00ed-deformace zn\u00e1zor\u0148uje reakci materi\u00e1lu na p\u016fsob\u00edc\u00ed nap\u011bt\u00ed. Nab\u00edz\u00ed d\u016fle\u017eit\u00e9 informace o chov\u00e1n\u00ed materi\u00e1lu p\u0159i nam\u00e1h\u00e1n\u00ed, nap\u0159\u00edklad o jeho pru\u017enosti, plasticit\u011b a bodu poru\u0161en\u00ed<\/strong>.<\/p>\n\n

    K\u0159ivku nap\u011bt\u00ed a deformace lze rozd\u011blit do n\u011bkolika kl\u00ed\u010dov\u00fdch oblast\u00ed.<\/p>\n\n

    Elastick\u00e1 oblast<\/strong><\/h3>\n\n

    V t\u00e9to oblasti se materi\u00e1l chov\u00e1 pru\u017en\u011b, co\u017e znamen\u00e1, \u017ee deformace je \u00fam\u011brn\u00e1 p\u016fsob\u00edc\u00edmu nap\u011bt\u00ed. Pokud je materi\u00e1l v tomto obdob\u00ed odleh\u010den, obnov\u00ed sv\u016fj p\u0159edchoz\u00ed tvar. Vztah nap\u011bt\u00ed a deformace je v t\u00e9to f\u00e1zi line\u00e1rn\u00ed a sklon t\u00e9to p\u0159\u00edmky se naz\u00fdv\u00e1 modul pru\u017enosti<\/strong> (Young\u016fv modul).<\/p>\n\n

    Bod v\u00fdnosu<\/strong><\/h3>\n\n

    To je kl\u00ed\u010dov\u00fd okam\u017eik, kdy materi\u00e1l p\u0159ech\u00e1z\u00ed z pru\u017en\u00e9 na plastickou deformaci. Po dosa\u017een\u00ed meze kluzu se materi\u00e1l za\u010dne nevratn\u011b deformovat. V tomto okam\u017eiku se ur\u010duje **m\u00edra kluzu** materi\u00e1lu. U n\u011bkter\u00fdch materi\u00e1l\u016f, jako je nap\u0159\u00edklad m\u011bkk\u00e1 ocel, se m\u016f\u017ee projevit tzv. deska meze kluzu**, kdy materi\u00e1l z\u016fst\u00e1v\u00e1 po del\u0161\u00ed dobu na ust\u00e1len\u00e9 \u00farovni nap\u011bt\u00ed, ne\u017e za\u010dne dal\u0161\u00ed deformace.<\/p>\n\n

    Plastov\u00e1 oblast<\/strong><\/h3>\n\n

    Po dosa\u017een\u00ed meze kluzu p\u0159ech\u00e1z\u00ed materi\u00e1l do plastick\u00e9 oblasti a nevratn\u011b se deformuje. Nap\u011bt\u00ed a deformace ji\u017e nejsou line\u00e1rn\u011b spojeny a materi\u00e1l vykazuje **plastickou deformaci**, kter\u00e1 se po odstran\u011bn\u00ed zat\u00ed\u017een\u00ed neobnov\u00ed.<\/p>\n\n

    Pevnost v tahu (UTS)<\/strong><\/h3>\n\n

    Jedn\u00e1 se o nejvy\u0161\u0161\u00ed nap\u011bt\u00ed, kter\u00e9 m\u016f\u017ee materi\u00e1l vydr\u017eet, ne\u017e dojde k jeho selh\u00e1n\u00ed. Po t\u00e9to f\u00e1zi materi\u00e1l obvykle za\u010dne krn\u011bt a nakonec praskne.<\/p>\n\n

    Bod zlomu<\/strong><\/h3>\n\n

    M\u00edsto, kde se materi\u00e1l l\u00e1me nebo prask\u00e1. Jedn\u00e1 se o konec k\u0159ivky nap\u011bt\u00ed a deformace.<\/p>\n\n

    Region<\/th>Popis<\/th><\/tr>
    Pru\u017en\u00e1 oblast<\/td>Line\u00e1rn\u00ed vztah; n\u00e1vrat k p\u016fvodn\u00edmu tvaru<\/td><\/tr>
    V\u00fdnosov\u00fd bod<\/td>P\u0159echod od pru\u017en\u00e9ho k plastick\u00e9mu chov\u00e1n\u00ed<\/td><\/tr>
    Plastov\u00e1 oblast<\/td>Doch\u00e1z\u00ed k trval\u00e9 deformaci<\/td><\/tr>
    Mez pevnosti v tahu<\/td>Maxim\u00e1ln\u00ed nap\u011bt\u00ed p\u0159ed selh\u00e1n\u00edm<\/td><\/tr>
    Bod zlomu<\/td>Bod, ve kter\u00e9m se materi\u00e1l zlom\u00ed<\/td><\/tr><\/tbody><\/table><\/figure>\n\n

    Jak se zkou\u0161\u00ed a m\u011b\u0159\u00ed mez kluzu?<\/strong><\/h2>\n\n

    Zkou\u0161ka tahem je nej\u010dast\u011bj\u0161\u00ed metodou stanoven\u00ed meze kluzu materi\u00e1lu. P\u0159i t\u00e9to zkou\u0161ce se na vzorek materi\u00e1lu p\u016fsob\u00ed rostouc\u00ed silou, dokud se nedeformuje. Na z\u00e1klad\u011b z\u00edskan\u00fdch \u00fadaj\u016f se vytvo\u0159\u00ed k\u0159ivka nap\u011bt\u00ed-deformace<\/strong> a vypo\u010d\u00edt\u00e1 se mez kluzu, kdy\u017e materi\u00e1l p\u0159ejde z pru\u017en\u00e9ho chov\u00e1n\u00ed do plastick\u00e9ho.<\/p>\n\n

    Mezi dal\u0161\u00ed techniky stanoven\u00ed meze kluzu pat\u0159\u00ed **zkou\u0161ky tvrdosti** (nap\u0159. tvrdost podle Brinella nebo Rockwella), kter\u00e9 mohou poskytnout p\u0159ibli\u017en\u00fd odhad meze kluzu na z\u00e1klad\u011b odolnosti materi\u00e1lu proti vtisku. Nejp\u0159esn\u011bj\u0161\u00edm a nejobl\u00edben\u011bj\u0161\u00edm p\u0159\u00edstupem z\u016fst\u00e1v\u00e1 zkou\u0161ka pevnosti v tahu.<\/p>\n\n

    Jak\u00fd v\u00fdznam m\u00e1 ve stroj\u00edrenstv\u00ed mez kluzu?<\/strong><\/h2>\n\n

    Pevnost v tahu je ve stroj\u00edrenstv\u00ed d\u016fle\u017eit\u00e1 z \u0159ady d\u016fvod\u016f.<\/p>\n\n

      \n
    • –V\u00fdb\u011br materi\u00e1lu<\/strong>: Konstrukt\u00e9\u0159i mus\u00ed vybrat materi\u00e1ly s p\u0159ijatelnou mez\u00ed kluzu pro konkr\u00e9tn\u00ed aplikace, aby byla zaji\u0161t\u011bna bezpe\u010dnost a funk\u010dnost.<\/li>\n\n\n\n
    • –Structural Integrity<\/strong>: Znalost meze kluzu umo\u017e\u0148uje in\u017een\u00fdr\u016fm navrhovat konstrukce, kter\u00e9 vydr\u017e\u00ed o\u010dek\u00e1van\u00e9 zat\u00ed\u017een\u00ed bez trval\u00fdch deformac\u00ed.<\/li>\n\n\n\n
    • –Soulad s p\u0159edpisy<\/strong>: Mnoho podnik\u016f m\u00e1 po\u017eadavky, kter\u00e9 vy\u017eaduj\u00ed, aby materi\u00e1ly m\u011bly ur\u010ditou mez kluzu, aby byla zaji\u0161t\u011bna bezpe\u010dnost a spolehlivost.<\/li>\n<\/ul>\n\n

      Pevnost v tahu u r\u016fzn\u00fdch materi\u00e1l\u016f<\/strong><\/h2>\n\n

      Mez kluzu se u jednotliv\u00fdch materi\u00e1l\u016f zna\u010dn\u011b li\u0161\u00ed a v\u00fdb\u011br vhodn\u00e9ho materi\u00e1lu pro danou aplikaci je do zna\u010dn\u00e9 m\u00edry ovlivn\u011bn mez\u00ed kluzu a v\u00fdkonem za ur\u010dit\u00fdch podm\u00ednek.<\/p>\n\n

        \n
      1. Kovy<\/strong>: Kovy s vysokou mez\u00ed kluzu, jako je ocel, titan a hlin\u00edk<\/strong>, jsou \u0161iroce pou\u017e\u00edv\u00e1ny. Nap\u0159:\n
          \n
        • –Ocel<\/strong> se m\u016f\u017ee pohybovat od 250 MPa u m\u011bkk\u00e9 oceli a\u017e po v\u00edce ne\u017e 2000 MPa u slitin vysokopevnostn\u00edch ocel\u00ed.<\/li>\n\n\n\n
        • –Titan<\/strong> se vyzna\u010duje vysok\u00fdm pom\u011brem pevnosti a hmotnosti, jeho mez kluzu je zhruba 900 MPa.<\/li>\n\n\n\n
        • –Hlin\u00edkov\u00e9<\/strong> slitiny maj\u00ed mnohem ni\u017e\u0161\u00ed mez kluzu (asi 150 MPa), ale jsou v\u00fdhodn\u00e9 v situac\u00edch, kdy je d\u016fle\u017eit\u00e1 hmotnost.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Polymery<\/strong>: Materi\u00e1ly jako plasty a pry\u017ee<\/strong> maj\u00ed mnohem ni\u017e\u0161\u00ed meze kluzu ne\u017e kovy. Pro r\u016fzn\u00e1 pou\u017eit\u00ed jsou nicm\u00e9n\u011b d\u00edky sv\u00e9 p\u0159izp\u016fsobivosti a toleranci k prom\u011bnliv\u00fdm vliv\u016fm prost\u0159ed\u00ed ide\u00e1ln\u00ed. Nap\u0159\u00edklad **polykarbon\u00e1t** m\u00e1 mez kluzu p\u0159ibli\u017en\u011b 60 MPa, zat\u00edmco **PVC** m\u016f\u017ee m\u00edt a\u017e 50 MPa.<\/li>\n\n\n\n
        • Kompozity<\/strong>: Kompozity z uhl\u00edkov\u00fdch a sklen\u011bn\u00fdch vl\u00e1ken<\/strong> jsou sice lehk\u00e9, ale maj\u00ed vysokou mez kluzu. Zejm\u00e9na kompozity z uhl\u00edkov\u00fdch vl\u00e1ken mohou dosahovat meze kluzu vy\u0161\u0161\u00ed ne\u017e 1000 MPa, co\u017e je p\u0159edur\u010duje k pou\u017eit\u00ed ve vysoce v\u00fdkonn\u00fdch a kosmick\u00fdch vozidlech.<\/li>\n<\/ol>\n\n

          Jak\u00e9 jsou aplikace meze kluzu<\/h2>\n\n

          V mnoha r\u016fzn\u00fdch technick\u00fdch oborech je mez kluzu materi\u00e1l\u016f z\u00e1sadn\u00ed pro zaji\u0161t\u011bn\u00ed jejich p\u0159edpokl\u00e1dan\u00e9 funk\u010dnosti bez poruch.<\/p>\n\n

          Stavebn\u00ed in\u017een\u00fdrstv\u00ed<\/strong><\/h3>\n\n

          V\u00fdb\u011br materi\u00e1l\u016f pro konstruk\u010dn\u00ed prvky, jako jsou nosn\u00edky, sloupy a v\u00fdztu\u017ee, z\u00e1vis\u00ed do zna\u010dn\u00e9 m\u00edry na mezi kluzu. Konstruk\u010dn\u00ed ocel a \u017eelezobeton<\/strong> jsou navr\u017eeny tak, aby odolaly velk\u00e9mu zat\u00ed\u017een\u00ed a nap\u011bt\u00ed bez trval\u00e9 deformace.<\/p>\n\n

          Automobilov\u00fd a leteck\u00fd pr\u016fmysl<\/strong><\/h3>\n\n

          P\u0159i navrhov\u00e1n\u00ed sou\u010d\u00e1st\u00ed letadel, motor\u016f a r\u00e1m\u016f automobil\u016f je nutn\u00e1 pevnost v tahu, proto\u017ee jsou pro n\u011b typick\u00e1 velk\u00e1 zat\u00ed\u017een\u00ed a mo\u017en\u00e9 n\u00e1razy. Pro tato pou\u017eit\u00ed se \u010dasto vol\u00ed vysokopevnostn\u00ed ocel, titan a uhl\u00edkov\u00e1 vl\u00e1kna<\/strong>.<\/p>\n\n

          V\u00fdroba a elektronika<\/strong><\/h3>\n\n

          Materi\u00e1ly s vhodnou mez\u00ed kluzu se pou\u017e\u00edvaj\u00ed ve v\u00fdrob\u011b k v\u00fdrob\u011b n\u00e1stroj\u016f, za\u0159\u00edzen\u00ed a mikroelektroniky. Zat\u00edmco **chirurgick\u00e9 n\u00e1stroje** nebo **sou\u010d\u00e1sti letadel**<\/strong> pot\u0159ebuj\u00ed materi\u00e1ly s v\u00fdrazn\u011b vy\u0161\u0161\u00ed pevnost\u00ed, sou\u010d\u00e1sti **smartphon\u016f** nebo **laptop\u016f**<\/strong> mohou b\u00fdt vytvo\u0159eny z kov\u016f se sn\u00ed\u017eenou mez\u00ed kluzu.<\/p>\n\n

          Z\u00e1v\u011br<\/h2>\n\n

          In\u017een\u00fd\u0159i a konstrukt\u00e9\u0159i, kte\u0159\u00ed pracuj\u00ed s r\u016fzn\u00fdmi materi\u00e1ly, mus\u00ed pochopit meze kluzu. Ta ur\u010duje, jak velk\u00e9mu nam\u00e1h\u00e1n\u00ed materi\u00e1l odol\u00e1, ne\u017e dojde k jeho nevratn\u00e9 deformaci, a zaji\u0161\u0165uje tak technickou bezpe\u010dnost a funk\u010dnost. Vzorce a k\u0159ivky nap\u011bt\u00ed a deformace pom\u00e1haj\u00ed odborn\u00edk\u016fm p\u0159i v\u00fdb\u011bru materi\u00e1l\u016f a zaji\u0161\u0165uj\u00ed integritu konstrukce.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Navrhov\u00e1n\u00ed konstrukc\u00ed, stroj\u016f a p\u0159edm\u011bt\u016f denn\u00ed pot\u0159eby vy\u017eaduje znalost pevnosti materi\u00e1l\u016f. Pevnost v tahu je pro in\u017een\u00fdry a materi\u00e1lov\u00e9 v\u011bdce kl\u00ed\u010dovou vlastnost\u00ed. Pevnost v tahu m\u00e1 z\u00e1sadn\u00ed v\u00fdznam pro bezpe\u010dnost, \u017eivotnost a v\u00fdkonnost materi\u00e1lu p\u0159i nam\u00e1h\u00e1n\u00ed. Tato str\u00e1nka pojedn\u00e1v\u00e1 o meze pevnosti, o tom, jak se vypo\u010d\u00edt\u00e1v\u00e1, o jej\u00ed vazb\u011b na k\u0159ivku nap\u011bt\u00ed-deformace a o tom, jak ovliv\u0148uje v\u00fdb\u011br materi\u00e1lu pro r\u016fzn\u00e9 aplikace.<\/p>\n","protected":false},"author":1,"featured_media":8653,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-8732","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized-cs"],"yoast_head":"\nPevnost v tahu: Definice, vzorec, k\u0159ivka nap\u011bt\u00ed-deformace. - ChansMachining<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/chansmachining.com\/cs\/pevnost-v-tahu-definice-vzorec-krivka-napeti-deformace\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pevnost v tahu: Definice, vzorec, k\u0159ivka nap\u011bt\u00ed-deformace. - ChansMachining\" \/>\n<meta property=\"og:description\" content=\"Navrhov\u00e1n\u00ed konstrukc\u00ed, stroj\u016f a p\u0159edm\u011bt\u016f denn\u00ed pot\u0159eby vy\u017eaduje znalost pevnosti materi\u00e1l\u016f. 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