Trace a game-changing discovery Stephen W. Tsai Stanford - - PowerPoint PPT Presentation

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

E1* = 0.880; 1.3% Q11* = 0.885; 1.3% C11* = 0.752; 2.1% E1* = 0.735; 2.1%

0.735 = 1.20 3D Trace, GPa

2D: Plane stress 3D: Plane strain

0.880 = 3D/2D

Trace-normalized stiffness: Universal [0]

2D Trace, GPa

Material Selection for Weight Savings

Relative Cost of Hybrid Laminates

TraceHybrid = v1Trace1 + v2Trace2 + …

Linear correlation with trace, but not with Ex or others

Black Aluminum vs Trace: 15 CFRP

Ex Ey νx Es X X’ Y Y’ S Ply stiffness Ply strength Black aluminum vs Trace Unit circle Universal Laminates

= 0.88 Trace

(Unit circle) (Universal) (Trace) (ex, ex’) (Universal) 4:1 5:2 15:1 15:1 15:1 So much simpler:

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

• Stress components σi
• Strain components εi
• Stiffness: Qij, Aij, Dij, Cij,…
• Failure criterion in stress

space: Fij, Fi where Fijσiσj + Fiσi = 1

• Failure criterion in strain

space: Gij, Gi where Gijεiεj + Giεi = 1 Gij = QikQjlFkl. Gi = QijFj Tr [σ] = σ1 + σ2 + σ3 = pressure Tr [ε] = ε1 + ε2 + ε3 = Δ volume Tr [Q] = Q11 + Q22 + 2Q66 = Tr [A*] = A11* + A22* + 2A66* = Tr [D*] = D11* + D22* + 2D66* Tr [C] = C11 + C22 + C33 +…+ 2C66 Tr [F]= F11 + F22 + F66/2 Tr {F} = F1 + F2 Tr [G] = G11 + G22 + 2G66 Tr {G} = G1 + G2

Tensors and Traces for Composites

2D 3D

Evolution: Universal Constants [0] CFRP

Average = Universal Ply engineering constants Plane-stress stiff matrix Trace-normalized Trace Trace = Q11 + Q22 +2Q66

CFRP tape tens CFRP tape compr CFRP fabric tens CFRP fabric compr GFRP fabric tens GFRP fabric compr CFRP braid tens CFRP braid compr

0.888; 2.1% 0.873; 2.5% 0.471; 1.2% 0.472; 1.3% 0.423; 1.3% 0.433; 1.5%

E1° master ply, GPa Good correlation No correlation Multiple CFRP, GFRP: RT-dry, cold-dry, hot-dry, hot-wet -

2% 2%

Composition of Trace: Carbon, Kev, Glass

Carbon/epoxy Kevlar 49/epoxy E-glass/epoxy Qxx Qyy Qss (88, 5, 3)% (88, 6, 3)% (70, 15, 7)%

Qxx* Qyy* Qss* Qxy*

C11 C22 C66 C44 C55 C33 Q11 = 88% = Fiber controlled Q22 + 2Q66 = 12% = matrix controlled Sub-trace (in-plane) = C11 + C22 +2C66 = 86% Sub-trace (out-of-plane) = C33 + 2(C44 + C55) = 14% Fiber

Trace 2D Trace 3D

Matrix

Universal ply: Transversely isotropic [0]

Q11 Q22 Q66 Fiber Matrix Out-of-plane: 14% Transverse shear Transverse stiffness = 88% = 75% In-plane

PLANE STRESS

13

In-plane: 86%

PLANE STRAIN

Ex in GPa Trace in GPa Ex/Trace E1° in GPa Trace in GPa E1°/Trace

0.880, cv = 1.33% 0.337, cv = 0.10% E1° of [π/4] Ex of [0]

Ascending 2D and 3D Trace: CFRP

2D/3D trace, GPa

Dominant “11” Component in 2- & 3-D

E1* = 0.880; 1.3% Q11* = 0.885; 1.3% C11* = 0.752; 2.1% E1* = 0.735; 2.1%

0.735 = 1.20 3D Trace, GPa

2D: Plane stress 3D: Plane strain

0.880 = 3D/2D

Trace-normalized stiffness: Universal [0]

2D Trace, GPa

Dominant “11” Component in 2- & 3-D

3D Trace, GPa

Trace-normalized stiffness: Universal [π/3],[π/4], …

2D Trace, GPa

A11* = A22* = 0.323; 0.5% A66* = 0.107; 0.1% A44* = A55* = 0.020; 0.2% E1* = E2* = 0.281; 0.4% E3* = 0.053; 0.5%

3D: Plane strain

A33*= 0.057; 0.5% E6* = 0.107; 0.1%

0.107 = 1.20 0.129 = 3D/2D

E1* = E2* = 0.336; 0.1% E6* = 0.129; 0.1%

0.281 = 1.20 = 3D/2D 0.336

Q11* = 0.371; 0.1% Q66* = 0.129; 0.1%

2D: Plane stress

Components: 2D Universal Laminates

Universal laminate stiffness

[0/90] [Quasi-iso] [0/±45/0] [0/±45]

2D Trace, GPa 2D Trace, GPa 15 Individual CFRP

IM6/epoxy T700 C-Ply 55 IM7/8552 IM7/977-3 T300/5208 T800/Cytec AS4/MTM45 T650/epoxy T300/F934 T700/2510 T4708/MR60H AS4/3501 T700 C-Ply 64 T800S/3900

15 Individual CFRP

IM6/epoxy T700 C-Ply 55 IM7/8552 IM7/977-3 T300/5208 T800/Cytec AS4/MTM45 T650/epoxy T300/F934 T700/2510 T4708/MR60H AS4/3501 T700 C-Ply 64 T800S/3900 IM7/MTM45 IM7/MTM45

Universal Laminate Constants

Universal [0] [0/90] [π/4] [07/±45/90] [0/±454/90] [0/±45] [0/±45/0] [0/±30] [0/±30/0] [±12.5] E1* E2* E6* ν21

Generated from classical laminated plate theory, and universal [0] derived from average of 15 CFRP

Trace Universal laminates

C11 = C22 = 0.405

C11* = 0.41

[π/3], [π/4], … [0/90]

In-plane: 0.86 Out-plane: 0.14

[0/±45]

C22* = 0.41 C11* = 0.32 C22* = 0.32 C11* = 0.41 C22* = 0.18 C66* = 0.14 C66* = 0.11 C66* = 0.026 C44* = 0.021 C55* = 0.021 C33* = 0.057 C44* = 0.021 C55* = 0.021 C33* = 0.057 C44* = 0.019 C55* = 0.022 C33* = 0.057

3D Trace, GPa

Components: 3D Universal Laminates

C11 = C22 = 0.405 In-plane: 0.86 Out-plane: 0.14

C44* = 0.017 C55* = 0.024 C33* = 0.057 C44* = 0.020 C55* = 0.020 C33* = 0.057 C44* = 0.016 C55* = 0.025 C33* = 0.057

3D Trace, GPa

C11* = 0.58 C22* = 0.16 C66* = 0.059

[07/±45/90] [0/±454/90]

C11* = 0.27 C22* = 0.27 C66* = 0.16

[02/±30]

C11* = 0.604 C22* = 0.083 C66* = 0.087

Components: 3D Universal Laminates

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

Unique NCF at Chomarat

[0/25] Flip

• ver

[-25/0]

Shallow angles, wide range ply thicknesses with high quality from tow spreading, noninvasive stitching, hybrid, …

[20 ≤ ϕ ≤ 30]

Wide-range GSM to Meet Requirement

160 120 80 40 Laminate thickness in mil

[0] [ϕ] or [-ϕ]

Thin [0]; thick [ϕ] Thin [0]; thin [ϕ] Thick [0]; thin [ϕ]

[ϕ] or [-ϕ] [0] [ϕ] or [-ϕ] [0] [ϕ] or [-ϕ]

[0] [0/±45/90] [0/±ϕ] [0/±ϕ/90] [0/±ϕ/±ψ/90] 1-axis 4-axis 1-axis 2-axis 2-axis

C-Ply laminates Thick-thin Combinations of C-Ply Black Alum

Layup: 4-axis [0]thk vs 2-axis [0/45]thn/thk

Laminate length, m Time, min

2-axis [0/45] thin-ply layup 4-axis Unitape layup

Jim Hecht of MAG

More exact estimate: 2.7X faster for thin ply; 5.4X for thick ply

[0] [90] [45] [-45]

Starting C-Ply 1-axis layup 1:0 2-axis layup 2:1 2-axis layup 1:1 [0/ϕ2] - Thin-Thick (33/67/0) – 150 gsm [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 [02/±ϕ] (50/50/0) [(02/±ϕ)2/±ψ2/902] Ψ = 90 - ϕ (33/50/17) [02/±ϕ/±ψ/902] = [π/4]2 for ϕ = 45 (25/50/25) [02/ϕ] - Thick-Thin (67/33/0) – 150 gsm [04/±ϕ] (67/33/0) [(04/±ϕ)2/±ψ/904] Ψ = 90 - ϕ (44/33/22) [04/±ϕ/±ψ/904] Ψ = 90 - ϕ (33/33/33)

High Speed Layup of Thick-thin C-Ply

27

High shear Low shear Regular 5X 3X 2X

A;sk

1:0 1:0 1:0 2:1 2:1 2:1 1:1 1:1 1:1

E1* E1* E1* E6*

[π/3] = 0.13

E6* [02/±ϕ] [0/ϕ]; [0/-ϕ] Thin-thin Regular [0/±ϕ]2 [0/ϕ2]; [0/-ϕ2] Thin-thick High shear [04/±ϕ] [02/ϕ]; [02/-ϕ] Thick-thin Low shear

[π/6] [π/3] = 0.34 [π/4]

Off-axis angle ϕ Universal laminate stiffness

[0/±30] [0/±45] [0/±30/0] [0/±45/0]

Universal Stiffness Components: C-Ply

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

(45/55/0) (20/80/0) (17/66/17)

0.466 0.138 0.268 0.187 0.277 0.161

[05/±453] [0/±452] [0/±452/90]

E1* = 0.45 E6* = 0.14 E1* = 0.22 E6* = 0.20 E1* = 0.28 E6* = 0.16

Black Aluminum Design: Bricky

Cannot be optimized; manufacturing nightmare

C-Ply: Black Aluminum Replacement

1:0 2:1 1:1

[0/±ϕ]2 [0/ϕ2]; [0/-ϕ2] Thin-thick High shear

E1* E6*

[0/±35] [0/±45]

0.45 0.14 0.28 0.16 Trace-normalized stiffness Off-axis angle Off-axis angle Layup ratio 0.22 0.20

[05/±453] [0/±452] [0/±452/90]

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

T700/2510; Em* = 0.15:

Fiber dominated omni envelope

σ2° σ1°

Unit circle in stress for IM7/977-3 [π/4] only Unit circle One unit circle in strain for all CFRP, all ply angles Unit circle

Evoluation: Unit Circle Failure Envelope

Safety Factor R; Failure Index k

Hard [π/4] Soft Soft [π/4] Hard 64% 74% 78%

Universal Stress-Strain Curves for CFRP

Trace-normalized X’

ε1°/ex

Trace-normalized X

ε1°/ex’

Metal* Metal*

Metal*: Specific stiffness of Al, Ti and Fe (normalized by density) As-built As-built

Comparison Unit Circle vs WWFE Data

Unit circle

Data: WWFE

Ply-by-Ply vs Homogenized Plate

RFPF R(i)

Runit circ

E1° = 1/a11*, E2° = 1/a22*, . . . from trace Unit circle: ex and ex’ Homogeneous anisotropic plate: one R Ply-by-ply R(i) of a laminated anisotropic or orthotropic plate

R = strength ratio = safety factor

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

Direct Weight and Layup Rate Method

Universal virtual laminates Boundary-value problem Unit circle: failure index k(p) Tapered thickness: k(p)

max

Layup/zone selection Stiffness correction Material ranking Multiple load Weight/Layup rate

Uniax tens Uniax comp

Material selection

Essential ply properties

k-based Taper

Examples of 1- and 2-axis Layup

1-axis 1:0 layup: Homogenized, single ply drop 2-axis: 1 to 1 ratio 2-axis 2-axis 2:1 layup: Homogenized, single ply drop 2-axis 2-axis 1:1 layup: Homogenized, single ply drop

Examples of Transition between Layups

2-axis 2-axis

2-axis layup Transition 2 or 1-axis layups Transition from 2:2 to 2:0; 50% axial

2-axis

Transition from 3:3 to 4:2; 50% axial Transition from 2:1 to 2:0; 67% axial

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

Ply sequence

[02/90] [0] [0/90] [0] [0/90/02/902] [02/90]

A;sk

1:0 1:0 1:0 2:1 2:1 2:1 1:1 1:1 1:1

E1* E1* E1* E6*

[π/3] = 0.13

E6* [02/±ϕ] [0/ϕ]; [0/-ϕ] Thin-thin Regular [0/±ϕ]2 [0/ϕ2]; [0/-ϕ2] Thin-thick High shear [04/±ϕ] [02/ϕ]; [02/-ϕ] Thick-thin Low shear

[π/6] [π/3] = 0.34 [π/4]

Off-axis angle ϕ Universal laminate stiffness

[0/±30] [0/±45] [0/±30/0] [0/±45/0]

Cases Investigated

2- and 3-zone Layup

Weight Reduction and Layup Speed

Weight Aluminum C-Ply layup 4-axis layup 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

Linear = Wt/speed Wt2/speed Wt/speed2

C-Ply

Material Selection for Weight Savings

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

Traditional building blocks Trace-based: just like metals

Coupons from pristine laminates

Traditional vs Trace-based Pyramids

Reduce coupons to one [0] and uniaxial tests Unleash choices of laminates (not just 4), and Include processing defects in as-built coupons

Composite components

As-built: with defects As-designed: pristine Need one and only one universal ply data from [0] for each CFRP

Black Aluminum vs Trace: 15 CFRP

Ex Ey νx Es X X’ Y Y’ S Ply stiffness Ply strength Black aluminum vs Trace Unit circle Universal Laminates

= 0.88 Trace

(Unit circle) (Universal) (Trace) (ex, ex’) (Universal) 4:1 5:2 15:1 15:1 15:1 So much simpler:

Relative Cost of Hybrid Laminates

TraceHybrid = v1Trace1 + v2Trace2 + …

Linear correlation with trace, but not with Ex or others

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