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Properties for Design of Composite Structures. Neil McCartney

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Properties for Design of Composite Structures - Neil McCartney

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end fraction plus fraction numerator 1 over denominator mu subscript text T end text end subscript superscript text f end text end superscript end fraction end fraction comma"/>(4.194)

      which are valid only if μTf≥μm, and the bounds are reversed if μTf≤μm.

      4.10.3 Axial Poisson’s Ratio

      The bounds for the axial Poisson’s ratio are given by

      which are valid only if (νAf−νm)(kTf−kTm)(μtf−μm)≥0, and the bounds are reversed if (νAf−νm)(kTf−kTm)(μtf−μm)≤0.

      4.10.4 Transverse Bulk Modulus

      The bounds for the transverse bulk modulus are given by

      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 StartStartFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction less-than-or-equal-to StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction less-than-or-equal-to 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 StartStartFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction EndEndFraction comma(4.196)

      which are valid only if μtf≤μm, and the bounds are reversed if μtf≥μm.

      4.10.5 Transverse Shear Modulus

      The bounds for transverse shear modulus are given by

      StartLayout 1st Row upper V Subscript f Baseline mu Subscript t Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartStartFraction left-parenthesis mu Subscript t Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver upper V Subscript m Baseline mu Subscript t Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus 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 EndEndFraction less-than-or-equal-to mu Subscript t Superscript eff Baseline 2nd Row less-than-or-equal-to upper V Subscript f Baseline mu Subscript t Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartStartFraction left-parenthesis mu Subscript t Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver upper V Subscript m Baseline mu Subscript t Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus StartFraction k Subscript upper T Superscript f Baseline mu Subscript t Superscript f Baseline Over k Subscript upper T Superscript f Baseline plus 2 mu Subscript t Superscript f Baseline EndFraction EndEndFraction comma EndLayout(4.197)

      which are valid only if

StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript f Baseline EndFraction less-than-or-equal-to StartFraction 1 Over mu Subscript m Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript m Baseline EndFraction period

      The bounds are reversed if

StartFraction 1 Over mu Subscript t Superscript f Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript f Baseline EndFraction greater-than-or-equal-to StartFraction 1 Over mu Subscript m Baseline EndFraction plus StartFraction 2 Over k Subscript upper T Superscript m Baseline EndFraction period

      4.10.6 Axial Shear Modulus

      The bounds for the axial shear modulus are given by

      upper V Subscript f Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline <noindex><p style= Скачать книгу


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