Tsai-Wu Criterion

The Tsai-Wu theory defines the ply failure index as below:

$F_{i n d e x} = (\frac{1}{X_{T}} - \frac{1}{X_{C}}) σ_{1} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2} + \frac{σ_{1}^{2}}{X_{T} X_{C}} + \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + \frac{τ_{12}^{2}}{S^{2}} + 2 F_{12} σ_{1} σ_{2}$ $F_{i n d e x} = (\frac{1}{X_{T}} - \frac{1}{X_{C}}) σ_{1} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2} + \frac{σ_{1}^{2}}{X_{T} X_{C}} + \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + \frac{τ_{12}^{2}}{S^{2}} + 2 F_{12} σ_{1} σ_{2}$

Where:

$X t, X c$ $X t, X c$ are the maximum allowable stresses in the 1-direction in tension and compression,
$Y t, Y c$ $Y t, Y c$ are the maximum allowable stresses in the 2-direction in tension and compression,
$S$ $S$ is the allowable in-plane shear stress
$F_{12}$ $F_{12}$ is a factor to be determined experimentally

Syntax

TsaiWuFT(tensor,xt,xc,yt,yc,s,f12,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

Arguments

tensor: Stress table
xt: Allowable tensile stress in ply material direction 1
xc: Allowable compressive stress in ply material direction 1
yt: Allowable tensile stress in ply material direction 2
yc: Allowable compressive stress in ply material direction 2
f12: F12 experimental factor
s: Allowable in-plane shear stress
sets: Set table (D=NULL)
plies: Ply table (D=NULL)
elems: Element table (D)
parts: Part table (D)
props: Property table (D)
pool_name: Pool name (D=@current_pool)
layer_index: Layer index (D=@current_slice_index)
opt_str: This is an optional argument, which can passed if needed (D=option).

Tsai-Wu Reserve Factor

Considering the above expression for the Failure Index if we set:

$A = \frac{σ_{1}^{2}}{X_{T} X_{C}} + \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + \frac{τ_{12}^{2}}{S^{2}} + 2 F_{12} σ_{1} σ_{2}$ $A = \frac{σ_{1}^{2}}{X_{T} X_{C}} + \frac{σ_{2}^{2}}{Y_{T} Y_{C}} + \frac{τ_{12}^{2}}{S^{2}} + 2 F_{12} σ_{1} σ_{2}$

$B = (\frac{1}{X_{T}} - \frac{1}{X_{C}}) σ_{1} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2}$ $B = (\frac{1}{X_{T}} - \frac{1}{X_{C}}) σ_{1} + (\frac{1}{Y_{T}} - \frac{1}{Y_{C}}) σ_{2}$

$C = - 1$ $C = - 1$

Being $k$ $k$ a given factor of safety, then the reserve factor formula can be evaluated as below:

${RF}_{T s a i - W u} = \frac{- B \pm \sqrt{B^{2} - 4 A C}}{2 a k}$ ${RF}_{T s a i - W u} = \frac{- B \pm \sqrt{B^{2} - 4 A C}}{2 a k}$

Syntax

TsaiWuRF(tensor,xt,xc,yt,yc,s,f12,FoS,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

Arguments

tensor: Stress table
xt: Allowable tensile stress in ply material direction 1
xc: Allowable compressive stress in ply material direction 1
yt: Allowable tensile stress in ply material direction 2
yc: Allowable compressive stress in ply material direction 2
f12: F12 experimental factor
FoS: Factor of Safety (D=1.0)
s: Allowable in-plane shear stress
sets: Set table (D=NULL)
plies: Ply table (D=NULL)
elems: Element table (D)
parts: Part table (D)
props: Property table (D)
pool_name: Pool name (D=@current_pool)
layer_index: Layer index (D=@current_slice_index)
opt_str: This is an optional argument, which can passed if needed (D=option).