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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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 sigma-summation Underscript i equals 1 Overscript upper N Endscripts upper V Subscript f Superscript i Baseline left-parenthesis upper E Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline plus StartFraction 4 k Subscript upper T Superscript f left-parenthesis i right-parenthesis Baseline left-parenthesis nu Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline right-parenthesis squared mu Subscript m Baseline Over k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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"/>(4.168)

      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(4.169)

      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 sum from i equals 1 to N of V subscript text f end text end subscript superscript i E subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript alpha subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis 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 plus sum from i equals 1 to N of V subscript text f end text end subscript superscript i fraction numerator 4 nu subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript left parenthesis alpha subscript text T end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript plus nu subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript alpha subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text f end text left parenthesis i right parenthesis 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(4.170)

      4.9 Results for Two-phase Fibre-reinforced Composites

      For two-phase composites N = 1 so that, on writing Vf1=Vf=1−Vm, κAf(1)=κAf, κTf(1)=κTf, kTf(1)=kTf, μAf(1)=μAf, μtf(1)=μtf, EAf(1)=EAf, ETf(1)=ETf, νAf(1)=νAf, νtf(1)=νtf, αAf(1)=αAf and αTf(1)=αTf, the results of Section 4.8 may be written as

      kappa Subscript upper A Superscript eff Baseline equals upper V Subscript f Baseline kappa Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline kappa Subscript m Baseline comma(4.172)

      StartStartFraction 1 OverOver StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction equals StartStartFraction upper V Subscript 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 OverOver StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction comma(4.174)

      or StartFraction 1 Over k Subscript upper T Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript f Baseline plus mu Subscript m Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction comma(4.175)

      StartStartFraction nu Subscript upper A Superscript eff Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript </div> </div> </div> <hr> <div class=

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