Trace a game-changing discovery

Trace a game-changing discovery Stephen W. Tsai Stanford University October 5, 2015

Topics Why trace? The one and only unifying constant Theory of trace simple; easy to understand C-Ply by Stanford/Chomarat bi-angle NCF Homogenization optimizable; high-speed ATL Unit circle failure criterion Trace-based sizing method power of C-Ply Conclusions

How Many Data Points? In netting analysis that is applied to pressure vessels and pipes, fiber strength is the one and only design validation calculated from burst pressure: the answer is one Carbon fibers are known to be anisotropic but we know only the longitudinal fiber stiffness and strength: the answer is one as before, plus one for stiffness With trace, laminates become universal

Dominant 11 Component in 2- & 3-D Trace-normalized stiffness: Universal [0] Q 11 * = 0.885; 1.3% 2D: Plane stress E 1 * = 0.880; 1.3% 0.880 0.735 = 1.20 = 3D/2D 2D Trace, GPa C 11 * = 0.752; 2.1% E 1 * = 0.735; 2.1% 3D: Plane strain 3D Trace, GPa

Material Selection for Weight Savings

Relative Cost of Hybrid Laminates Linear correlation with trace, but not with E x or others Trace Hybrid = v 1 Trace 1 + v 2 Trace 2 +

Black Aluminum vs Trace: 15 CFRP E x = 0.88 Trace Black aluminum vs Trace Ply stiffness E y ν x E s Unit circle X Ply strength X Y Y S (Trace) (e x, e x ) (Unit circle) (Universal) (Universal) Universal Laminates So much simpler: 4:1 5:2 15:1 15:1 15:1

Tensors and Traces for Composites Stress components σ i Strain components ε i Stiffness: Q ij, A ij, D ij, C ij, Failure criterion in stress space: F ij, F i where F ij σ i σ j + F i σ i = 1 Failure criterion in strain space: G ij, G i where G ij ε i ε j + G i ε i = 1 G ij = Q ik Q jl F kl. G i = Q ij F j 2D 3D Tr [σ] = σ 1 + σ 2 + σ 3 = pressure Tr [ε] = ε 1 + ε 2 + ε 3 = Δ volume Tr [Q] = Q 11 + Q 22 + 2Q 66 = Tr [A*] = A 11 * + A 22 * + 2A 66 * = Tr [D*] = D 11 * + D 22 * + 2D 66 * Tr [C] = C 11 + C 22 + C 33 + + 2C 66 Tr [F]= F 11 + F 22 + F 66 /2 Tr {F} = F 1 + F 2 Tr [G] = G 11 + G 22 + 2G 66 Tr {G} = G 1 + G 2

Evolution: Universal Constants [0] CFRP Ply engineering constants Plane-stress stiff matrix Trace Trace-normalized Average = Universal Trace = Q 11 + Q 22 +2Q 66

E 1 master ply, GPa 0.888; 2.1% 0.873; 2.5% CFRP tape tens 2% CFRP tape compr 0.471; 1.2% 0.472; 1.3% CFRP fabric tens CFRP fabric compr 0.423; 1.3% 2% 0.433; 1.5% GFRP fabric tens CFRP braid tens Multiple CFRP, GFRP: RT-dry, cold-dry, hot-dry, hot-wet - Good correlation No correlation GFRP fabric compr CFRP braid compr

Composition of Trace: Carbon, Kev, Glass (88, 5, 3)% (88, 6, 3)% (70, 15, 7)% Q yy Q ss Q xx Carbon/epoxy Kevlar 49/epoxy E-glass/epoxy Q xx * Q yy * Q ss * Q xy *

Universal ply: Transversely isotropic [0] Fiber Matrix In-plane PLANE STRESS Q 11 = 88% Q 22 Q 66 Fiber Matrix C 11 = 75% C 22 C 66 In-plane: 86% PLANE STRAIN Out-of-plane: 14% C 44 C 55 C 33 Transverse shear Transverse stiffness Q 22 + 2Q 66 = 12% = matrix controlled Sub-trace (out-of-plane) = C 33 + 2(C 44 + C 55 ) = 14% Trace 2D Q 11 = 88% = Fiber controlled Trace 3D Sub-trace (in-plane) = C 11 + C 22 +2C 66 = 86% 13

E x in GPa E x of [0] E 1 in GPa E 1 of [π/4] E x /Trace E 1 /Trace Trace in GPa Trace in GPa 0.880, cv = 1.33% 0.337, cv = 0.10%

Ascending 2D and 3D Trace: CFRP 2D/3D trace, GPa

Dominant 11 Component in 2- & 3-D Trace-normalized stiffness: Universal [π/3],[π/4], E 1 * = E 2 * = 0.336; 0.1% Q 11 * = 0.371; 0.1% 2D: Plane stress 0.336 0.281 = 1.20 = 3D/2D Q 66 * = 0.129; 0.1% A 11 * = A 22 * = 0.323; 0.5% 2D Trace, GPa E 6 * = 0.129; 0.1% 0.129 0.107 = 1.20 = 3D/2D E 1 * = E 2 * = 0.281; 0.4% A 66 * = 0.107; 0.1% A 33 *= 0.057; 0.5% 3D: Plane strain E 6 * = 0.107; 0.1% A 44 * = A 55 * = 0.020; 0.2% E 3 * = 0.053; 0.5% 3D Trace, GPa

Components: 2D Universal Laminates Universal laminate stiffness [0/90] [Quasi-iso] [0/±45] [0/±45/0] 2D Trace, GPa 2D Trace, GPa T700 C-Ply 55 AS4/MTM45 T700/2510 T4708/MR60H T650/epoxy AS4/3501 T700 C-Ply 64 T300/F934 T800S/3900 IM7/8552 T800/Cytec IM7/MTM45 T300/5208 15 Individual CFRP IM7/977-3 IM6/epoxy T700 C-Ply 55 AS4/MTM45 T700/2510 T4708/MR60H T650/epoxy AS4/3501 T700 C-Ply 64 T300/F934 T800S/3900 IM7/8552 T800/Cytec IM7/MTM45 T300/5208 15 Individual CFRP IM7/977-3 IM6/epoxy

Universal Laminate Constants Generated from classical laminated plate theory, and universal [0] derived from average of 15 CFRP Universal laminates Universal [0] [0/90] [π/4] [0 7 /±45/90] [0/±45 4 /90] [0/±45] [0/±45/0] [0/±30] [0/±30/0] [±12.5] E 1 * E 2 * E 6 * ν 21 Trace

Components: 3D Universal Laminates C 33 * = 0.057 C 33 * = 0.057 C 33 * = 0.057 In-plane: 0.86 Out-plane: 0.14 C 55 * = 0.021 C 44 * = 0.021 C 66 * = 0.026 C 22 * = 0.41 C 11 = C 22 = 0.405 C 11 * = 0.41 C 55 * = 0.021 C 44 * = 0.021 C 66 * = 0.11 C 22 * = 0.32 C 11 * = 0.32 C 55 * = 0.022 C 44 * = 0.019 C 66 * = 0.14 C 22 * = 0.18 C 11 * = 0.41 [0/90] [π/3], [π/4], [0/±45] 3D Trace, GPa

Components: 3D Universal Laminates C 33 * = 0.057 C 33 * = 0.057 C 33 * = 0.057 In-plane: 0.86 Out-plane: 0.14 C 55 * = 0.024 C 44 * = 0.017 C 66 * = 0.059 C 22 * = 0.16 C 11 * = 0.58 C 11 = C 22 = 0.405 C 55 * = 0.020 C 44 * = 0.020 C 66 * = 0.16 C 22 * = 0.27 C 55 * = 0.025 C 44 * = 0.016 C 66 * = 0.087 C 22 * = 0.083 C 11 * = 0.604 C 11 * = 0.27 [0 7 /±45/90] [0/±45 4 /90] [0 2 /±30] 3D Trace, GPa

[0/25] Flip over Unique NCF at Chomarat Shallow angles, wide range ply thicknesses with high quality from tow spreading, noninvasive stitching, hybrid, [-25/0] [20 ϕ 30]

Wide-range GSM to Meet Requirement 160 120 80 40 0 Laminate thickness in mil

Thick-thin Combinations of C-Ply Thin [0]; thick [ϕ] Thin [0]; thin [ϕ] Thick [0]; thin [ϕ] [ϕ] or [-ϕ] [ϕ] or [-ϕ] [ϕ] or [-ϕ] [ϕ] or [-ϕ] [0] [0] [0] Black Alum C-Ply laminates [0] [0/±45/90] [0/±ϕ] [0/±ϕ/90] [0/±ϕ/±ψ/90] 1-axis 4-axis 1-axis 2-axis 2-axis

Layup: 4-axis [0] thk vs 2-axis [0/45] thn/thk [0] [90] [45] [-45] Jim Hecht of MAG More exact estimate: 2.7X faster for thin ply; 5.4X for thick ply 4-axis Unitape layup Time, min 2-axis [0/45] thin-ply layup Laminate length, m

High Speed Layup of Thick-thin C-Ply Starting C-Ply 1-axis layup 1:0 5X 2-axis layup 2:1 3X 2-axis layup 1:1 2X [0/ϕ 2 ] - Thin-Thick (33/67/0) 150 gsm High shear [0/±ϕ] 2 = [π/3] 2 for ϕ = 60 (33/67/0) [(0/±ϕ) 2 /(±ψ/90)] 2 Ψ = 90 - ϕ (22/67/11) [0/±ϕ/±ψ/90] 2 = [π/6] 2 for ϕ = 30 (17/66/17) [0/ϕ] - Thin-Thin (50/50/0) 150 gsm Regular [0 2 /±ϕ] (50/50/0) [(0 2 /±ϕ) 2 /±ψ 2 /90 2 ] Ψ = 90 - ϕ (33/50/17) [0 2 /±ϕ/±ψ/90 2 ] = [π/4] 2 for ϕ = 45 (25/50/25) [0 2 /ϕ] - Thick-Thin (67/33/0) 150 gsm Low shear [0 4 /±ϕ] (67/33/0) [(0 4 /±ϕ) 2 /±ψ/90 4 ] Ψ = 90 - ϕ (44/33/22) [0 4 /±ϕ/±ψ/90 4 ] Ψ = 90 - ϕ (33/33/33) 27

Universal Stiffness Components: C-Ply Universal laminate stiffness E 1 * 1:0 2:1 1:1 [0/±ϕ] 2 [0/ϕ 2 ]; [0/-ϕ 2 ] Thin-thick High shear [0/±30] [0/±45] E 1 * 1:0 2:1 1:1 E 6 * [π/3] = 0.13 [0 2 /±ϕ] [0/ϕ]; [0/-ϕ] Thin-thin Regular A;sk [0/±30/0] [0/±45/0] [π/6] [π/3] = 0.34 [π/4] E 1 * 1:0 2:1 1:1 E 6 * [0 4 /±ϕ] [0 2 /ϕ]; [0 2 /-ϕ] Thick-thin Low shear Off-axis angle ϕ

[0 5 /±45 3 ] (45/55/0) Black Aluminum Design: Bricky Cannot be optimized; manufacturing nightmare E 1 * = 0.45 E 6 * = 0.14 0.466 0.138 0.268 0.187 E 1 * = 0.22 E 6 * = 0.20 E 1 * = 0.28 E 6 * = 0.16 [0/±45 2 ] 0.277 [0/±45 2 /90] (20/80/0) 0.161 (17/66/17)

C-Ply: Black Aluminum Replacement E 1 * [0/±ϕ] 2 [0/ϕ 2 ]; [0/-ϕ 2 ] Thin-thick High shear 1:0 [0/±35] [0/±45] Trace-normalized stiffness 2:1 1:1 E 6 * Layup ratio 0.45 [0 5 /±45 3 ] 0.14 [0/±45 2 ] 0.22 0.20 0.28 0.16 [0/±45 2 /90] Off-axis angle Off-axis angle

Evoluation: Unit Circle Failure Envelope T700/2510; E m * = 0.15: Fiber dominated omni envelope One unit circle in strain for all CFRP, all ply angles σ 2 Unit circle Unit circle σ 1 Unit circle in stress for IM7/977-3 [π/4] only

Safety Factor R; Failure Index k

Universal Stress-Strain Curves for CFRP ε 1 /e x Trace-normalized X As-built 74% Hard [π/4] Metal* Soft ε 1 /e x Soft Metal* [π/4] 64% 78% As-built Hard Trace-normalized X Metal*: Specific stiffness of Al, Ti and Fe (normalized by density)

Comparison Unit Circle vs WWFE Data Unit circle Data: WWFE

Ply-by-Ply vs Homogenized Plate Ply-by-ply R (i) of a laminated anisotropic or orthotropic plate R FPF R (i) R = strength ratio = safety factor Runit circ E Homogeneous anisotropic plate: one R 1 = 1/a 11 *, E 2 = 1/a 22 *,... from trace Unit circle: e x and e x

Direct Weight and Layup Rate Method Universal virtual laminates Boundary-value problem Unit circle: failure index k (p) Multiple load Essential ply properties Uniax tens Uniax comp Tapered thickness: k (p) max Layup/zone selection Weight/Layup rate Stiffness correction Material selection Material ranking

k-based Taper

Examples of 1- and 2-axis Layup 1-axis 1:0 layup: Homogenized, single ply drop 2-axis 2-axis: 2:1 layup: 1 to Homogenized, 1 ratio 2-axis single ply drop 2-axis 2-axis 1:1 layup: Homogenized, single ply drop

Examples of Transition between Layups Ply sequence 1 2 1 2 1 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 1 1 [0 2 /90] [0] 2-axis [0/90] [0] 2-axis [0/90/0 2 /90 2 ] [0 2 /90] 2-axis Transition from 2:1 to 2:0; 67% axial Transition from 2:2 to 2:0; 50% axial Transition from 3:3 to 4:2; 50% axial 2-axis layup Transition 2 or 1-axis layups

Cases Investigated Universal laminate stiffness E 1 * 1:0 2:1 1:1 [0/±ϕ] 2 [0/ϕ 2 ]; [0/-ϕ 2 ] Thin-thick High shear [0/±30] [0/±45] E 1 * 1:0 2:1 1:1 E 6 * [π/3] = 0.13 [0 2 /±ϕ] [0/ϕ]; [0/-ϕ] Thin-thin Regular A;sk [0/±30/0] [0/±45/0] [π/6] [π/3] = 0.34 [π/4] E 1 * 1:0 2:1 1:1 E 6 * [0 4 /±ϕ] [0 2 /ϕ]; [0 2 /-ϕ] Thick-thin Low shear Off-axis angle ϕ

2- and 3-zone Layup

Weight Reduction and Layup Speed Aluminum C-Ply layup 4-axis layup Weight Aluminum Black Al C-Ply

Cost Reduction: Weight/speed of C-Ply Ranking insensitive among values of exponents Distinct regions between black aluminum and C-Ply Black aluminum: by unitape C-Ply Linear = Wt/speed Wt 2 /speed Wt/speed 2

Material Selection for Weight Savings

Traditional vs Trace-based Pyramids Traditional building blocks Trace-based: just like metals Composite components Coupons from pristine laminates As-designed: pristine As-built: with defects Need one and only one universal ply data from [0] for each CFRP Reduce coupons to one [0] and uniaxial tests Unleash choices of laminates (not just 4), and Include processing defects in as-built coupons

Relative Cost of Hybrid Laminates Linear correlation with trace, but not with E x or others Trace Hybrid = v 1 Trace 1 + v 2 Trace 2 +

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