What makes a material bendable? A thickness-dependent metric for bendability, malleability, ductility

The requirement for materials that can bend is proliferating with the growing interest in flexible electronics and devices. terms bending flexing are often used interchangeably even though usually meant to be elastic while involves plastic deformation. Materials compared a simple “bendability figure-of-merit” through fracture strain—that is, how much material bent plastically once before breaking—for given thickness of material, which similar way yield strain serves as figure-of-merit flexibility. Flexible found many new applications such healthcare, robotics, electronics. Although require repeated flexing, some only without breaking. Because underappreciated importance “single deformation” bendable materials, we distinguish flexibility (ability repeatedly) bendability fracture) formulate primary requirements into facilitate comparisons reporting. While flexibility1Peng J. Snyder G.J. A figure merit flexibility.Science. 2019; 366: 690-691Crossref PubMed Scopus (31) Google Scholar requires undergo repeatably, needs once, could accomplished plastically. All if they sufficiently thin, so metric must scaled thickness. Future applications, energy systems internet-of-things, will likely devices where trade-offs performance considered, goal this paper clearly delineate what properties make define allow compared. Currently, qualitative demonstrations flexibility,1Peng pictures being or worn, do not quantitative different rarely between single bend. Whereas stresses their impacts on well studied field mechanics, guideline experts other fields lacking. In electronics, electrically conducting intensively utilized electronic device manufacture. Thermocouples, curved displays, solar cells, example, may need during installation fabrication. Transparent oxides (TCOs),2Minami T. oxide semiconductors transparent electrodes.Semicond. Sci. Technol. 2005; 20: S35-S44Crossref (1777) Scholar,3Hosono H. How made IGZO transistor.Nat Electron. 2018; 1: 428Crossref (47) widely displays commercial when assembling under processing conditions, limitation flexural elongation (yield strain) less than 1%.4Suo Z.G. Mechanics stretchable soft machines.MRS Bull. 2012; 37: 218-225Crossref (163) Possible future wearable electronics,5Rogers J.A. Someya Huang Y. mechanics electronics.Science. 2010; 327: 1603-1607Crossref (3502) sensors, supercapacitors, batteries, thermoelectrics,6Wan C. Gu X. Dang F. Itoh Wang Sasaki Kondo M. Koga K. Yabuki et al.Flexible n-type thermoelectric by organic intercalation layered transition metal dichalcogenide TiS2.Nat. Mater. 2015; 14: 622-627Crossref (492) energy-harvesting concepts have further broadened materials. Within intensive property characterizes extent maximum deformation inducing ?y, breaking cracking ?f. (maximum divided total length) readily known most routinely measured tensile test.7Granta’s CES EduPack. Granta Material Intelligence Dataset. Design Limited 2019, (2019).Google large typically elongated called ductile, good ductility. Ductile also malleable formable deform fracturing struck hammer compression. Compressive reliable malleability. Most at high enough temperature very indefinite ductility malleability therefore bendability, metals, polymers (plastics), glasses, allows them easily formed complex shapes heated, semiconductor ceramic powders. Superplastic enhanced engineering grain boundaries nanocrystalline copper.8Lu L. Sui M.L. Lu extensibility copper room temperature.Science. 2000; 287: 1463-1466Crossref (761) During bending, ? suitable descriptor characterize point failure. Bendability simply demonstrated along radius curvature breakage. This working definition quantified related parameters. We b = 1/rb, units m?1 rb minimum fracture. (sheet wire) h (see Figure 1) is?=h2rb ?f failure occurs greatest outer surface compressive inner surface. middle layer (neutral layer) experiences no stress. Thus, depends both test geometry h.b=1rb=2h?f From expression, it clear any highly thin ? 0, analogous above definition, note demonstrating reporting recognizing limited scientific value. enters (at strain, ?f), makes (bFoM). Comparing two same thickness, higher more bendable.bFoM=?f comparison, measuring ?y), (fFOM ?y) repeatable bending1Peng (See 2).fFoM=?yTable 1The data source 2Yield strength (elastic limit), MPaYoung's modulus, GpaFlexural elongation, %Bending %LowHighLowHighLowHighLowHighElastomersNature rubber21280.00120.0021600780600780PDMS1.692.130.0002050.000215424782424782EVA9.5100.0070.009880930880930PolymersHuman hair90922.33.62.543944Paper1534240.3751.70.381.7Teflon19.721.70.40.5523.5695.425200400PE19.7290.6210.8962.1994.67200800PP20.737.20.8961.551.3354.152100600Epoxies3671.62.272.551.4123.15436Cotton fiber1003507120.8335511CeramicsSilicon1651801401800.0920.1290.090.13Soda lime Glass29.336.16674.10.040.0550.040.05MetalsGold204076810.0250.053535lead6.021213140.0430.0923060silver18930168.973.10.2590.43712Copper503401201400.0360.283650Steel25711401902100.1220.61049Conducting oxidesIGZO70013001371370.5110.949??ITO120012001161161.0341.034??Caron materialsGraphene1100001300001000105010.47613??Carbon nanotubes11000630002009501.15831.5??Carbon fiber183018505305800.3160.3490.72Diamond28002930105012100.2310.2790.230.281. broad class region carbon expected based literature values graphene, nanotube, fibers.2. listed above, including regions from chart software database (CES EduPack, ANSYS GRANTA).3. No was found. 0.7–1.3 GPa within 0.5–1%.4. IGZO, ITO, nanotube comparable elongation. Noted (?). Open table tab 1. fibers. 2. GRANTA). 3. 0.5–1%. 4. Using an Ashby ambient 2), compare various common elastomers, polymers, ceramics, carbon-based figure-of-merit, tends proportional stiffness modulus), making elastomers metals. extreme. thermoplastic flexible, approaching elastomers. Elastomers thermoset epoxy identical because cross-linked prevent molecules sliding stretching. Metals stable slip planes ceramics generally not, metals bulk not. (e.g., ITO IGZO) strong, directional bonding brittle, exceptions like Ag2S quite bendable.9Shi Chen Hao Liu R. Qiu P. Burkhardt U. Grin Room-temperature ductile inorganic semiconductor.Nat. 17: 421-426Crossref (140) increasing leads brittle extends range allowing permanent deformation, ironing clothes, styling hair, blowing glass, forming Extreme achieved superplastic increased Examples include composite Al-based Mg-based ceramics,10Kim B.N. Hiraga Morita Sakka high-strain-rate ceramic.Nature. 2001; 413: 288-291Crossref (241) strong but bendable. conclusion, suggest thickness-dependent bFoM comparing improving functional setting up criteria selection. furthermore encourage community researchers report studies simplify comparison across candidate application. acknowledge generous support AFOSR FA 9550-15-1-0377 , award 70NANB19H005 U.S. Department Commerce, National Institute Standards Technology part Center Hierarchical (CHiMaD).