Changeset 185

Show
Ignore:
Timestamp:
07/08/2005 12:14:32 PM (5 years ago)
Author:
powell
Message:

Update to tube extrusion problem: added microstructure changes.

Location:
trunk/matml/transport/problems
Files:
7 modified

Legend:

Unmodified
Added
Removed

  • trunk/matml/transport/problems/chrono.html

    r179 r185  
    55of most recent modification: 
    66<ul> 
     7  <li><a href="tubextrude.pdf">Extrusion of a tube</a>, by Adam Powell 
     8    (<a href="tubextrude-solution.ps">solution</a>, 
     9    <a href="tubextrude.zip">source</a> <a href="tubextrude/">directory</a>, 
     10    <a href="tubextrude.meta">metadata</a>), last modified July 8, 2005.</li> 
    711  <li><a href="ebmeltvap2.pdf">Multicomponent evaporation II: evaporation of 
    812    alloying elements from titanium</a>, by Adam Powell 
    … …  
    176180    <a href="platedrag.meta">metadata</a>), last modified September 26, 
    177181    2004.</li> 
    178   <li><a href="tubextrude.pdf">Extrusion of a tube</a>, by Adam Powell 
    179     (<a href="tubextrude-solution.ps">solution</a>, 
    180     <a href="tubextrude.zip">source</a> <a href="tubextrude/">directory</a>, 
    181     <a href="tubextrude.meta">metadata</a>), last modified September 21, 
    182     2004.</li> 
    183182  <li><a href="polyflow.pdf">Non-Newtonian polymer flow in a channel</a>, by 
    184183    Adam Powell (<a href="polyflow-solution.ps">solution</a>, 

  • trunk/matml/transport/problems/tubextrude-solution.ps

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    … …  
    1212%+ tubextrude-solution.ps -h /home/hazelsct/.tex.pro.shift 
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     14%DVIPSSource:  TeX output 2005.07.08:1138 
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    … …  
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    16501683 

  • trunk/matml/transport/problems/tubextrude.meta

    r100 r185  
    44Title: Extrusion of a tube 
    55Author: Adam C. Powell, IV 
    6 Date: November 14, 2003 
    7 Copyright: 2002, 2003 Adam C. Powell, IV 
     6Date: May 2, 2005 
     7Copyright: 2002, 2003, 2005 Adam C. Powell, IV 
    88License: MIT Open CourseWare, http://ocw.mit.edu/OcwWeb/Global/terms-of-use.htm 
    9 Description: For flow through a seamless tube extruder, use simplifying assumptions to reduce the appropriate form of the Navier-Stokes equations as much as possible, and sketch the expected flow profile for three rheology types. 
    10 Source file: tubextrude.zip (md5sum 3cd9eaddb70e89718494a8b4fe95af7d) 
     9Description: For flow through a seamless tube extruder, use simplifying assumptions to reduce the appropriate form of the Navier-Stokes equations as much as possible, sketch the expected flow profile for three rheology types, and discuss microstructure changes during the extrusion process. 
     10Source file: tubextrude.zip (md5sum 89eaffa6421c57ccc13a0f27b12018b6) 
    1111Source directory: tubextrude 
    1212Problem source format: PDFLaTeX 
    13 Problem source file: tubextrude/tubextrude.tex (md5sum cfabd4d3a8aa349bea9d85b04a4ac157) 
     13Problem source file: tubextrude/tubextrude.tex (md5sum 1505022ee86f8d7615b91d462cd55656) 
    1414Solution source format: LaTeX 
    15 Solution source file: tubextrude/tubextrude-solution.tex (md5sum fd8225396d07c1a207e064ddd871b221) 
     15Solution source file: tubextrude/tubextrude-solution.tex (md5sum 220d33f6896eb1bea40c5ba5d37b1d39) 
    1616Problem printable format: PDF 
    17 Problem printable file: tubextrude.pdf (md5sum ad6ae799e6bfce61d5a617cf4bc6aa6d) 
     17Problem printable file: tubextrude.pdf (md5sum 959f3b963cd09b11b3e46c4abcc4d0b5) 
    1818Solution printable format: Postscript 
    19 Solution printable file: tubextrude-solution.ps (md5sum 384fbc9bf4319c8a370f33b8a3231163) 
     19Solution printable file: tubextrude-solution.ps (md5sum 0c477b743a94d7e8f77278518ebd9309) 
    2020Difficulty level: Junior 
    2121Solution time: 2 hours 
    2222Keywords: Viscous flow, Navier-Stokes, Non-Newtonian fluid, Metal, Polymer 
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  • trunk/matml/transport/problems/tubextrude/tubextrude-solution.tex

    r100 r185  
    6161      \PSbox{extruder.ps}{336pt}{135pt} 
    6262    \end{center} 
     63 
     64  \item Solid aluminum deforms significantly as it flows past the plug; the 
     65    resulting strain is likely to strengthen it quite a bit.  Stronger means 
     66    the yield stress will be high, so the center will likely flow as a solid 
     67    (uniform velocity) as in the Bingham plastic model. 
     68 
     69    Needless to say, the simple Bingham plastic model does not capture the 
     70    change in yield stress as the material flows through the extruder. 
     71 
     72  \item During extrusion, grains will be elongated in the direction of flow, 
     73    and dislocation density will rise considerably, possibly resulting in 
     74    formation of new low-angle grain boundaries.  This corresponds to stage II 
     75    or III deformation, where both the higher dislocation density and narrower 
     76    grains result in higher yield stress. 
     77 
     78    If the temperature is high enough, recrystallization could dynamically form 
     79    new grains with low defect densities, which would then be sheared along 
     80    with the rest of the material.  This would reduce the force required to 
     81    drive material through the extruder, and likely produce less strengthening 
     82    than at lower temperatures. 
    6383  \end{enumerate} 
    6484\end{enumerate} 

  • trunk/matml/transport/problems/tubextrude/tubextrude.tex

    r100 r185  
    3636    \item Bingham plastic 
    3737    \end{enumerate} 
     38 
     39  \item Briefly describe the structure and properties of the resulting extruded 
     40    tube: will the grain size be larger or smaller than before extrusion?  Will 
     41    the metal be weaker or stronger, and why? (8) 
     42 
     43  \item Based on what you know of their stress-strain behavior, which of the 
     44    above do you think will be closer to the actual behavior of an extruded 
     45    solid metal? (7) 
    3846  \end{enumerate} 
    3947\end{enumerate} 
    4048\end{document} 
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