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    Mechanics of Composite Materials

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    1. A glass/epoxy laminate with a fiber orientation of 30 degrees is subjected to a shear stress t_xy (or tau_xy) which can be positive or negative.

    a) Determine the maximum positive and negative shear stresses that can be applied to the laminate using Tsai-Hill failure criterion.
    b) Determine the reserve factors for t_xy = + 10 MPa and for t_xy = - 10 MPa. Note that the reserve factor is given by R = 1/Fl.

    DATA: Ultimate strength values for glass/epoxy are:

    sigma hat_1T = 1000 MPa
    sigma hat_2T = 40 MPa
    tau hat_12 = 80 MPa
    sigma hat_1C = -800 MPa
    sigma hat_2C = - 120 MPa

    FORMULAE: Tsai-Hill failure criterion is given by:

    Fl = [(sigma_1)/(sigma hat_1)]^2 - (sigma_1 * (sigma_2)/(sigma hat_1)^2 + [(sigma_2)/(sigma hat_2)]^2 + [(t_12)/(t hat_12)]^2 <= 1,

    where sigma hat indicates the ultimate strength value given in the data.

    2. Compute the burst pressure of a carbon/epoxy cylindrical vessel with a diameter of d = 250 mm and a wall thickness of t = 2.5 mm by:
    a) Using the Tsai-Hill criterion
    b) Using the maximum stress criterion

    The cylindrical section of the pressure vessel is constructed by winding fibers in the circumferential direction

    Data: Ultimate strength values for carbon/epoxy are:

    sigma hat_1T = 1826 MPa
    sigma hat_2T = 19 MPa
    tau hat_12 = 75 MPa
    sigma hat_1C = -1134 MPa
    sigma hat_2C = - 131 MPa

    Formulae: For cylindrical pressure vessels:
    Circumferential stresses: sigma_c = pd /2t (16)
    Axial stresses: sigma_a = pd /4t (17)

    Tsai-Hill failure criterion is given by:

    Fl^2 = [(sigma_1)/(sigma hat_1)]^2 - (sigma_1)(sigma_2)/(sigma_ hat_1)^2 + [(sigma_2)/(sigma hat_2)]^2 + [(tau_12)/(tau hat_12)]^2 <= 1.

    where sigma hat indicates the ultimate strength value given in the data.

    Maximum stress criteria are given by:

    sigma_1 <= sigma hat_1
    sigma_2 <= sigma hat_2
    t_12 <= t hat_12

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    https://brainmass.com/engineering/manufacturing-engineering/mechanics-composite-materials-41533

    Solution Preview

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    Problem 1: (Question 4)

    A glass epoxy/lamina with a fiber orientation of 30 is subjected to a shear stress xy which can be positive or negative.
    a) Determine the maximum positive and negative shear stresses that can be applied to this lamina using Tsai-Hill failure criterion.
    b) Determine the reserve factors for xy = 10 Mpa and xy = -10 Mpa

    Note that the reserve factor is given by R = 1/Fl.

    Data: Ultimate strength values for glass/epoxy are:

    Formulae: Tsai-Hill failure criterion is given by:

    where indicates the ultimate strength value given in the data.

    Solution:
    Since the ultimate properties of material are given with respect to the main directions (along the fibers and transversally), we need to find out the actual stresses in a frame reference oriented accordingly:

    By rotating a reference frame in a 2D stress state by angle (), the new values of stresses are given by:
    ( 1)
    ( 2)
    ( 3)
    In our problem, the normal stresses are missing, so ...

    Solution Summary

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