Question bank — Polymer-matrix composites — CFRP, GFRP; ply lay-up, laminate theory

False — it is stiff only along the fibres ($E_1$); across them the soft matrix sits in series and $E_2$ can be ~19× smaller, so off-axis it is limp.

It is an upper bound (iso-strain, springs in parallel); real values sit slightly below because bonding and fibre misalignment are never perfect.

False — balanced only kills tension–shear coupling; warping comes from a non-zero $B$ matrix, which needs symmetry to vanish. You need balanced and symmetric.

True — every ply at $+z$ has a mirror twin at $-z$, and $B$ weights plies by $z^2$-differences that cancel in pairs, so stretching and bending decouple.

False — carbon has far higher $E_f$ (~230 GPa vs ~70 GPa); glass wins on cost and toughness, not stiffness.

False — bending stiffness $D$ weights plies by $z^3$, so an outer ply (large $z$) dominates; a mid-plane ply barely helps resist bending.

False — above ~65–70% there is too little matrix to wet all fibres, so voids form and load transfer collapses; optimum is ~0.55–0.65.

False — the stiff fibres carry the bulk; the matrix mainly holds fibres straight, spreads load between them, and resists shear/compression.

Only its in-plane stiffness is direction-independent; through-thickness properties, strength, and fatigue behaviour stay anisotropic.

Transverse loading is iso-stress (fibre and matrix in series); use the inverse rule $1/E_2=V_f/E_f+V_m/E_m$, which gives a much smaller $E_2$.

A non-zero $B$ is a defect of design, not a bonus — it makes the panel warp under load or temperature; we deliberately zero it with symmetry.

Backwards — because $D\sim \sum \bar{Q}{z}^3$, stiff plies belong near the surfaces where $z$ (and strain $z\kappa$) is largest.

The real win is specific strength/stiffness (per kilogram); low density is what matters in flight, not raw absolute strength — see Specific strength and stiffness in aerospace materials.

They differ enormously (~19×) — parallel (add) versus series (add reciprocals) are very different averages, which is exactly why plies are anisotropic.

$[0/90]$ is not symmetric — mirrored it would read $[0/90/90/0]$; the plain two-ply stack has non-zero $B$ and warps.

One ply is strong only along its fibres; rotating plies ($0/\pm 45/90$) shares strength across every loading direction we need — see Anisotropy and crystal directions.

Bare fibres buckle in compression, can't carry shear, and one break isn't shared to neighbours; the matrix transfers load and gives integrity — see Fibre–matrix interface and load transfer.

$A$ weights plies by thickness ($z_k-z_{k-1}$), which is position-independent; $D$ weights by $z^3$, so stacking order changes bending stiffness dramatically.

Its cross-linked network gives high stiffness, creep resistance and thermal stability under load, at the cost of reprocessability — contrast in Thermoset vs thermoplastic polymers.

Each $+\theta$ ply's shear response is the mirror-opposite of its $-\theta$ partner, so their off-diagonal ($A_{16},A_{26}$) contributions cancel and pure tension gives pure stretch.

In series the softest phase dominates the total displacement, so the combined modulus is dragged down toward the matrix value — the weakest link governs.

It reduces to $E_1=E_m$ — pure matrix modulus, correctly recovering the resin-only limit.

$1/E_2\to 1/E_f$, so $E_2\to E_f$ — but this is unphysical because you cannot pack fibres with zero matrix and still bond them.

The matrix shears load back into the broken fibre over a short distance and to neighbours, so the part survives — one break is not catastrophic, unlike a bare bundle.

No in-plane coupling if it is also balanced and symmetric — the evenly spread angles make $A$ isotropic-like and $B=0$, so any in-plane direction behaves the same.

It grows too — stiffer fibres in a soft matrix widen the gap, making a single ply ever more direction-dependent and the lay-up strategy ever more essential.

Essentially zero — its $z^3$ weight vanishes at $z=0$, so mid-plane plies do almost nothing for bending resistance.