Properties for Design of Composite Structures. Neil McCartney

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Название Properties for Design of Composite Structures
Автор произведения Neil McCartney
Жанр Техническая литература
Серия
Издательство Техническая литература
Год выпуска 0
isbn 9781118789780
Properties for Design of Composite Structures - Neil McCartney
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eff Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction equals StartStartFraction upper V Subscript f Baseline nu Subscript upper A Superscript f Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction plus StartStartFraction upper V Subscript m Baseline nu Subscript m Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction comma"/>(4.176)

      StartFraction 1 Over mu Subscript upper A Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over mu Subscript upper A Superscript f Baseline plus mu Subscript m Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over mu Subscript m Baseline plus mu Subscript m Baseline EndFraction comma(4.177)

      StartFraction 1 Over mu Subscript t Superscript eff Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over mu Subscript t Superscript f Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over mu Subscript m Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction with mu Subscript m Superscript asterisk Baseline equals StartFraction k Subscript upper T Superscript m Baseline mu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus 2 mu Subscript m Baseline EndFraction comma(4.178)

      upper E Subscript upper A Superscript eff Baseline plus StartFraction 4 k Subscript upper T Superscript eff Baseline left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared mu Subscript m Baseline Over k Subscript upper T Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals upper V Subscript f Baseline left-parenthesis upper E Subscript upper A Superscript f Baseline plus StartFraction 4 k Subscript upper T Superscript f Baseline left-parenthesis nu Subscript upper A Superscript f Baseline right-parenthesis squared mu Subscript m Baseline Over k Subscript upper T Superscript f Baseline plus mu Subscript m Baseline EndFraction right-parenthesis plus upper V Subscript m Baseline left-parenthesis upper E Subscript m Baseline plus StartFraction 4 k Subscript upper T Superscript m Baseline nu Subscript m Superscript 2 Baseline mu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction right-parenthesis comma(4.179)

      StartFraction 1 Over upper E Subscript upper T Superscript eff Baseline EndFraction equals StartFraction 1 Over 4 mu Subscript t Superscript eff Baseline EndFraction plus StartFraction 1 Over 4 k Subscript upper T Superscript eff Baseline EndFraction plus StartFraction left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared Over upper E Subscript upper A Superscript eff Baseline EndFraction comma StartFraction nu Subscript t Superscript eff Baseline Over upper E Subscript upper T Superscript eff Baseline EndFraction equals StartFraction 1 Over 4 mu Subscript t Superscript eff Baseline EndFraction minus StartFraction 1 Over 4 k Subscript upper T Superscript eff Baseline EndFraction minus StartFraction 4 left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared Over upper E Subscript upper A Superscript eff Baseline EndFraction comma(4.180)

      table attributes columnalign left end attributes row cell E subscript text A end text end subscript superscript text eff end text end superscript alpha subscript text A end text end subscript superscript text eff end text end superscript plus fraction numerator 4 nu subscript text A end text end subscript superscript text eff end text end superscript left parenthesis alpha subscript text T end text end subscript superscript text eff end text end superscript plus nu subscript text A end text end subscript superscript text eff end text end superscript alpha subscript text A end text end subscript superscript text eff end text end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text eff end text end superscript end fraction plus 1 over mu subscript text m end text end subscript end fraction equals V subscript text f end text end subscript E subscript text A end text end subscript superscript text f end text end superscript alpha subscript text A end text end subscript superscript text f end text end superscript plus V subscript text m end text end subscript E subscript text m end text end subscript alpha subscript text m end text end subscript end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus V subscript text f end text end subscript fraction numerator 4 nu subscript text A end text end subscript superscript text f end text end superscript left parenthesis alpha subscript text T end text end subscript superscript text f end text end superscript plus nu subscript text A end text end subscript superscript text f end text end superscript alpha subscript text A end text end subscript superscript text f end text end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text f end text end superscript end fraction plus 1 over mu subscript text m end text end subscript end fraction plus V subscript text m end text end subscript fraction numerator 4 nu subscript text m end text end subscript left parenthesis alpha subscript text m end text end subscript plus nu subscript text m end text end subscript alpha subscript text m end text end subscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text m end text end superscript end fraction plus 1 over mu subscript text m end text end subscript end fraction comma end cell end table (4.181)

      These results (4.173)–(4.182) can also be written in the form of a mixtures estimate plus a correction term as follows

      StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript m Baseline EndFraction minus StartFraction lamda Over 2 EndFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline </div> </div> </div> <hr> <div class=

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