A laminate, such as [0/±45/90]ₛ, stacked from plies whose fiber directions are divided at equal angles. The in-plane Young's modulus is nearly equal in all directions, but the through-thickness direction remains weak.
Japanese name: 疑似等方積層
Quasi-isotropic laminate appears in 1 practice question across 1 topic, including Composite materials.
Field: Composite materials
When unidirectional plies are stacked in equal numbers in n directions (n ≥ 3) at equal intervals of 180°/n, the in-plane stiffness becomes independent of direction. For n = 3 the minimum set is [0/60/−60], and for n = 4 it is [0/45/−45/90]. Calculating with classical laminate theory for carbon fiber/epoxy with E₁ = 140 GPa, E₂ = 10 GPa, G₁₂ = 5 GPa and ν₁₂ = 0.3, both [0/±45/90]ₛ and [0/60/−60]ₛ give a Young's modulus of about 54 GPa in every direction. For [0/90]ₛ, by contrast, the modulus is about 75 GPa at 0° but falls to about 18 GPa at 45°.
The in-plane Young's modulus of a quasi-isotropic laminate is about 40% of the fiber-direction value of the unidirectional material. In the example above it is about 54 GPa against 140 GPa: the laminate can take loads from any direction, but the stiffness in any particular direction drops considerably. Even so, with high-performance carbon fibers, a modulus close to that of aluminum alloys (about 70 GPa) is obtained at about 60% of the density. For members with a clear load direction, it is more rational to add 0° plies to raise stiffness and strength in that direction; making everything quasi-isotropic is not always the answer.
Even when the in-plane extensional stiffness is isotropic, the material does not truly become isotropic. Bending stiffness changes with the stacking order, and because the orientation of the outer plies dominates, the bending stiffness differs with direction. Strength also varies somewhat with direction, and interlaminar stresses concentrate at ply edges and around holes. Moreover, through-thickness stiffness and strength are carried by the resin and remain far lower than in-plane values. Stacking symmetrically about the midplane (the subscript s) is done to prevent coupling between extension and bending, which would make the plate warp or twist on cooling or under load.
In aircraft structures, load directions vary from place to place and unexpected loads also occur, so quasi-isotropic or near-quasi-isotropic laminates are often used as a baseline. Design conventions include placing at least about 10% of the plies in each of the 0°, ±45° and 90° directions, not stacking many plies of the same orientation in a row, and using equal numbers of +45° and −45° plies (balanced laminates). Thick blocks of plies with the same orientation produce large shear stresses between plies, making resin cracking and delamination more likely. Around bolt holes, the proportion of ±45° plies is sometimes increased to ease stress concentration.
Answer: C. The Young's moduli in the 0° and 90° directions are nearly equal, but in the 45° direction in-plane shear dominates and the modulus is lower
In [0/90]ₛ, loading in the 0° direction is carried along the fibers of the 0° plies and loading in the 90° direction along the fibers of the 90° plies, so the moduli in the two directions are nearly equal. Loaded at 45°, however, the fibers of every ply are 45° off the load direction, and the deformation becomes mainly in-plane shear supported by the resin, so the modulus drops considerably. To approach in-plane isotropy, ±45° plies are added to make a quasi-isotropic layup such as [0/±45/90]ₛ. Saying the 45° direction is the same overlooks this point. In the 90° direction the fibers of the 90° plies carry the load, so the modulus is not that of the resin alone. Note that in any layup the through-thickness direction is supported by the resin, so susceptibility to delamination remains.
The bracket lists the ply orientations of one half of the laminate from the outside inward; ±45 means 2 plies at +45° and −45°, and the subscript s means the sequence is mirrored about the midplane. The full laminate is the 8 plies [0/45/−45/90/90/−45/45/0].
It is found by classical laminate theory, which transforms the stiffness of each ply according to its angle using the 4 elastic constants of the unidirectional material and averages over the thickness. For carbon fiber/epoxy it is often about 40% of the unidirectional fiber-direction value.
No. The through-thickness direction is carried by the resin and remains weak, and delamination can start from impacts, ply edges and holes. Choosing the stacking sequence carefully can make it less likely.
To approach in-plane isotropy, ±45° plies are added to make a quasi-isotropic layup such as [0/±45/90]ₛ.
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