Shear Bands in Glassy Amorphous Polymers
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1 Shear Bands in Glassy Amorphous Polymers Shear banding in tension or compression. Neck formation via shear bands (a) (b) (c) (d) Stress Image removed due to copyright restrictions. Please see Fig. 12a and 15a in Shin, E., et al. The Brittle-to-Ductile Transition in Microlayer Composites. Journal of Applied Polymer Science 47 (1993): Strain Figure by MIT OCW. MicroShear Bands
2 Strain Rate Dependence Yield stress increases as strain rate increases Yield stress increases as strain rate increases ε eff (s -1 ) Effective stress (MPo) x x x x Effective strain 125 C 0.6 Figure by MIT OCW.
3 Temperature Dependence Modulus and Yield Stress increase with decreasing T Stress N/mm O 0 O Cellulose Acetate 25 O O 50 O 65 O Extension Figure by MIT OCW.
4 Molecular Theories of Localized Flow in Glassy Polymers Eyring Theory of Viscous Flow υ o = B e ΔG* / kt Apply shear stress σ υ f = B e (ΔG*.5σAx)/kT υ f = υ o e (σax)/2kt υ b = υ o e (σax)/2kt strain rate dε /dt is proportional to υ f υ b de /dt = υ o e (σax)/2kt υ o e (σax)/2kt = K sinh σv 2kT where V = Ax = Activation volume
5 Pressure Dependence of Yield Stress P = 1/3 (sum of 3 principal stresses) Strain rate 7 x 10-3 sec 25 C ENGINEERING STRESS, MPa MPa 828 MPa 552 MPa 276 MPa 138 MPa ENGINEERING STRESS, MPa MPa MPa MPa MPa atm MPa 80 1 atm ENGINEERING STRAIN (a) ENGINEERING STRAIN (b) Polycarbonate Figure by MIT OCW.
6 Crazes in Amorphous Glassy Polymers Crazing in tension only, not in compression. Crack Craze Image removed due to copyright restrictions. (a) (b) (c) Crack-craze (craze breakdown) Figure by MIT OCW. Crazes extending across PC tensile specimen
7 Designs: 12-Connected Stretch Dominated Structures Octo-Truss Structure Inverse FR-D IL Structure (Red Curves) (Blue Curves) Images removed due to copyright restrictions. Please see: Fig. 3 in Maldovan, Martin, et al. "Sub-Micrometer Scale Periodic Porous Cellular Surfaces: Microframes Produced by Holographic Interference Lithography." Advanced Materials 19 (2007):
8 Experimental Realization and FEM (linear) of P Microframe 6-connected Single P Tubular P Images removed due to copyright restrictions. Please see: Fig. 4 in Maldovan, Martin, et al. "Sub-Micrometer Scale Periodic Porous Cellular Surfaces: Microframes Produced by Holographic Interference Lithography." Advanced Materials 19 (2007): Single P (0.21 to 0.79) Tubular P (solid line), Single P (Dots)
9 3D Microframe with 200 nm feature size - Large Strain Deformation Images removed due to copyright restrictions. Please see Fig. 1c, d, e in Jang, J.H., Ullal, C.K., Choi, T., LeMieux, M.C., Tsukruk, V.V., Thomas, E.L. 3D Polymer Microframes that Exploit Length-Scale Dependent Mechanical Behavior. Advanced Materials 18 (2006): L/D ~ 3.2 for struts ~ 2.3 for posts Density ~ 0.3 gm/cm 3
10 Large Strain Deformation Modes of Microframe Images removed due to copyright restrictions. Please see Fig. 2b, c, 3b, c in Jang, J.H., Ullal, C.K., Choi, T., LeMieux, M.C., Tsukruk, V.V., Thomas, E.L. 3D Polymer Microframes that Exploit Length-Scale Dependent Mechanical Behavior. Advanced Materials 18 (2006):
11 Mechanical Properties of SU8 1. SU-8: negative photoresist; used in MEMS applications. Tensile test results of 130 μm SU-8 film: Bulk Image removed due to copyright restrictions. Please see Fig. 2 in Feng, Ru, and Farris, Richard J. Influence of Processing Conditions on the Thermal and Mechanical Properties of SU8 Negative Photoresist Coatings. Journal of Micromechanics and Microengineering 13 (2003): Feng & Farris (2003) 2. Abnormal mechanical behavior observed in SU-8 Microframe NanoFrame Image removed due to copyright restrictions. Please see Fig. 3b in Jang, J.H., Ullal, C.K., Choi, T., LeMieux, M.C., Tsukruk, V.V., Thomas, E.L. 3D Polymer Microframes that Exploit Length-Scale Dependent Mechanical Behavior. Advanced Materials 18 (2006): Ji-Hyun Jang et al. (2006)
12 Fabrication of SU-8 fibers using photolithography 1. Spin-coat SU-8 on Si substrates. (SU : 25 μm, SU : 2 μm, and SU : 0.5 μm) 2. Soft bake: 65 o C, 1 min; 95 o C3 min. 3. Exposure: λ=365 nm; total dose: 270 mj/cm 2. (A mask is an array of windows having a length of 1 mm and variable line widths of 25 μm, 2 μm, and 1 μm.) 4. Post-exposure bake: 65 o C, 1 min; 95 o C, 1 min. 5. Develop. 6. Hard bake: 180 o C5 min. Cross-sectional SEM images of the fibers: 27 μm Images of SU8 fibers removed due to copyright restrictions. 24 μm 20 μm 1.65 μm 1.6 μm 1 μm 0.5 μm Diameter: 25 μm 1.8 μm 0.7 μm
13 Get Simple: Tensile Behavior of SU8 Fibers 2 μm 10 mm Spin coat SU-8 on silicon substrates Soft bake: 65 o C, 1 min; 95 o C3 min. Exposure: λ: 365 nm; total dose: 270 mj/cm 2. Develop: SU-8 developer (from Microchem Corporation). Post-exposure bake: 65 o C, 1 min; 95 o C, 1 min. Hard bake: 180 o C5 min. Image of experimental apparatus removed due to copyright restrictions. Cardboard template & fiber a) Engineering Stress (MP μm SU-8 thin film 25 μm SU-8 fiber 1.8 μm SU-8 fiber 0.7 μm SU-8 fiber Strain (mm/mm) 0.9
14 Tensile Test Results of SU-8 fibers Without hard-baking With hard-baking (180 o C, 5 min ) Stress-strain curves removed due to copyright restrictions.
15 Summary of SU8 Tensile Test Results Material Toughness Kevlar Polycarbonat e 25 μm SU-8 fiber 1.8 μm SU-8 fiber 0.7 μm SU-8 fiber Toughness (MPa) 120 ± ± ± ± 3.3 Modulus Plot of Young s modulus against fiber diameter removed due to copyright restrictions. SU-8 film
16 Micromechanics of Tensile Deformation Microscopic response under tension Actual Sample Images of simulated deformation and stress-strain curve removed due to copyright restrictions. Model Lessons Learned Red indicates material deforming Image removed due to copyright restrictions. Blue indicates material not deforming Please see Fig. 3b in Jang, J.H., Ullal, C.K., Choi, T., LeMieux, M.C., Tsukruk, V.V., Thomas, E.L. 3D Polymer Microframes that Exploit Length-Scale Dependent Mechanical Behavior. Advanced Materials 18 (2006): Small scale of epoxy makes it deformable Micro-frame geometry creates multiple deformation domains which spread the deformation through the structure
17 Stress-Strain Behavior of Polygranular Isotropic Samples of 4 Microdomain Types 3 DG Stress (MPa) 2 1 LAM CYL SPH Strain Figure by MIT OCW.
18 Roll-Casting of Block Copolymers Concept of roll-casting Set-up of roll-caster X-Ray Diffraction Pattern and TEM Micrograph Image removed due to copyright restrictions. Please see Fig. 2 and 9 in Honeker, Christian C., and Thomas, Edwin L. Impact of Morphological Orientation in Determining Mechanical Properties in Triblock Copolymer Systems. Chemistry of Materials 8 (1996): ABA Triblock Copolymer (Doped with Conjugated Polymer) with Cylindrical Morphology Comercially available SIS block copolymer (M n = 101,000 PDI = 1.05) Films of block copolymers with nearly single crystal structure Film Dimensions: 0.04mm Thick and 6 x 16 cm 2 in area
19 Deformation of Lamellar Morphology cont d Material: Dexco Vector 4461-D triblock copolymer styrene-butadiene-styrene ( ) Roll-cast from 40% solution in toluene Image removed due to copyright restrictions. Please see Fig. 1 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000):
20 Deformation of Lamellar Microdomain Morphology Image removed due to copyright restrictions. Please see Fig. 4 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000): SAXS TEM Roll cast lamellar BCP
21 Stress-strain Curves for Oriented Lamellar Films Anisotropy Image removed due to copyright restrictions. Please see Fig. 2 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000):
22 Perpendicular Deformation of Lamellae In Situ SAXS X12B, NSLS, Brookhaven N.L. At 20 o C Image removed due to copyright restrictions. Please see Fig. 5 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000):
23 Kinking Pattern Image removed due to copyright restrictions. Please see Fig. 8 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000):
24 Model: The Lamellae Rotate in an Affine Relation to the Macroscopic Elongation Image removed due to copyright restrictions. Please see Fig. 17 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000): Macroscopic measurement of elongation: SAXS measurement of lamellar spacings: and rotation angle: Incompressibility: ad o = constant Affine rotation: λ = L/L o = d + /d o Affine Rotation Model Predictions: d(λ) = constant = d o => λ = 1/cosα λ = L/L o d o and d(λ) α
25 In Situ SAXS Deformation X12B, NSLS, Brookhaven N.L. Test/confirm: d o = 27nm, maintained throughout deformation d at 600% strain (λ=5) is 25nm SAXS - microscopic Image removed due to copyright restrictions. Please see Fig. 18 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000): /cosα = λ Macroscopic
26 Parallel Deformation of Lamellae (Note: very similar to cylinder parallel deformation) Image removed due to copyright restrictions. Please see Fig. 17 and 16 in Cohen, Yachin, et al. Deformation of Oriented Lamellar Block Copolymer Films. Macromolecules 33 (2000):
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