Properties for Design of Composite Structures. Neil McCartney

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Properties for Design of Composite Structures - Neil McCartney

Properties for Design of Composite Structures - Neil McCartney

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V subscript text m end text end subscript over denominator left parenthesis 1 plus V subscript text f end text end subscript right parenthesis kappa subscript text m end text end subscript plus V subscript text m end text end subscript kappa subscript text T end text end subscript superscript text f end text end superscript end fraction less or equal than kappa subscript text T end text end subscript superscript text eff end text end superscript less or equal than 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 V subscript text f end text end subscript kappa subscript text T end text end subscript superscript text f end text end superscript plus V subscript text m end text end subscript kappa subscript text m end text end subscript minus fraction numerator left parenthesis kappa subscript text T end text end subscript superscript text f end text end superscript minus kappa subscript text m end text end subscript right parenthesis squared V subscript text f end text end subscript V subscript text m end text end subscript over denominator left parenthesis 1 plus V subscript text m end text end subscript right parenthesis kappa subscript text T end text end subscript superscript text f end text end superscript plus V subscript text f end text end subscript kappa subscript text m end text end subscript end fraction comma"/>(4.193)

      whenever κm≤κTf. Whenever κm≥κTf, the bounds defined by (4.193) should be reversed.

      4.10.2 Axial Young’s Modulus

      The bounds for the axial Young’s modulus are given by

      V subscript text f end text end subscript E 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 plus fraction numerator 4 left parenthesis nu subscript text A end text end subscript superscript text f end text end superscript minus nu subscript text m end text end subscript right parenthesis squared V subscript text f end text end subscript V subscript text m end text end subscript over denominator fraction numerator V subscript text m end text end subscript over denominator k subscript text T end text end subscript superscript text f end text end superscript end fraction plus fraction numerator V subscript text f end text end subscript 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 less or equal than E subscript text A end text end subscript superscript text eff end text end superscript space space space space space space space space space space space space space space space space space space space space space space space space less or equal than V subscript text f end text end subscript E 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 plus fraction numerator 4 left parenthesis nu subscript text A end text end subscript superscript text f end text end superscript minus nu subscript text m end text end subscript right parenthesis squared V subscript text f end text end subscript V subscript text m end text end subscript over denominator fraction numerator V subscript text m end text end subscript over denominator k subscript text T end text end subscript superscript text f end text end superscript end fraction plus fraction numerator V subscript text f end text end subscript over denominator k subscript text T end text end subscript superscript text m end text end superscript 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 <hr><noindex><a href=Скачать книгу

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