Getting Started with Composites Modeling and Analysis IN THIS WEBINAR: PRESENTED BY: • Orthotropic materials and how to define them Nick Mehlig • Composite Laminate properties and modeling Aerospace Stress Engineer • Composite failure theories and postprocessing Structural Design and Analysis nmehlig@structures.aero 5/22/2012 Page 1
What is a Composite Material? • Composite Material – a material made from two or more distinct materials with differing properties that are combined to produce a new material with unique properties 5/22/2012 STRUCTURES .AERO Page 2
Lamina • Lamina: A thin layer of composite material, usually containing unidirectional fibers or woven fibers in a fabric pattern. Also called a ply. • Unidirectional plies have fibers in the Longitudinal (1) direction • Fabric plies have fibers in both the Longitudinal (1) and Transverse (2) Unidirectional Woven Fabric 5/22/2012 STRUCTURES .AERO Page 3
Lamina • Lamina: A thin layer of composite material, usually containing unidirectional fibers or woven fibers in a fabric pattern. Also called a ply. 5/22/2012 STRUCTURES .AERO Page 4
Rule of Mixtures • The stiffness of the final material will be defined by the Fiber Volume Fraction of the lamina • Estimations of the material properties can be made, but experimental data should be used. 1 = 𝑊 + 𝑊 1 = 𝑊 + 𝑊 𝑔 𝑔 𝑛 𝑛 𝐹 1 = 𝐹 𝑔 𝑊 𝑔 + 𝐹 𝑛 𝑊 𝑤 1 = 𝑤 𝑔 𝑊 𝑔 + 𝑤 𝑛 𝑊 𝑛 𝑛 𝐹 2 𝐹 𝐹 𝑛 𝐻 12 𝐻 𝑔 𝐻 𝑛 𝑔 5/22/2012 STRUCTURES .AERO Page 5
Orthotropic Material • 3 planes of material symmetry • 9 Engineering Constants 1 21 31 0 0 0 – 3 elastic moduli E E E 1 2 3 1 – 3 shear moduli 12 32 0 0 0 E E E 1 1 2 3 1 – 3 poisson ratio 1 2 2 13 23 0 0 0 E E E 3 1 2 3 3 1 23 23 0 0 0 0 0 G 31 23 31 1 12 12 0 0 0 0 0 G 31 1 0 0 0 0 0 G 12 5/22/2012 STRUCTURES .AERO Page 6
Laminate Stacking Sequence • Plies are stacked together at different angles to create a Laminate Z Y X Source: http://www.composites.ugent.be/home_made_composites/what_are_composites.html 5/22/2012 STRUCTURES .AERO Page 7
Composite Laminate • A laminate is made of multiple lamina stacked together and held together by a Matrix • Terminology: – Balanced equal number of + and – plies of the same angle – Symmetric the plies in the laminate are a mirror image about the midplane – Quasi-Isotropic Laminate has isotropic behavior in-plane 5/22/2012 STRUCTURES .AERO Page 8
Classical Lamination Theory (CLT) • Classical Lamination Theory (CLT) – CLT is the method used to calculate the ABD (stiffness) Matrix of the composite laminate – Each Lamina contains a “Reduced Stiffness Matrix” , Q 5/22/2012 STRUCTURES .AERO Page 9
Classical Lamination Theory (CLT) • A transformation Matrix is defined to rotate stiffnesses from one coordinate system to the other 𝑈 = • A new lamina stiffness matrix, denoted 𝑅 , is defined: • And the stresses and strains can be written in matrix form: 5/22/2012 STRUCTURES .AERO Page 10
Classical Lamination Theory (CLT) • The Laminate Stiffness Matrix, known as the ABD Matrix, is constructed by the following relations: 5/22/2012 STRUCTURES .AERO Page 11
FEMAP Demo 5/22/2012 Page 12
Laminate Offsets Bottom of Laminate Offset Bottom Surface = 0 Top of Laminate 𝑜 𝑜 5/22/2012 STRUCTURES .AERO Page 13
Failure Theories • Ply-by- ply failure theories predict a “Failure Index (FI)” for each ply – A failure index greater than or equal to 1.0 signifies a ply failure • Examples of ply-by-ply failure theories: – Max Stress/Strain – Tsai-Hill – Tsai-Wu – Hoffman Source: http://www.montana.edu/dcairns/documents/composites/The%20Ts ai-Wu%20Failure%20Criterion.pdf 5/22/2012 STRUCTURES .AERO Page 14
Hoffman Failure Theory • The Hoffman Failure Criterion combines the stresses in a lamina (a single ply of a composite laminate) to predict failure • A Failure Index is calculated and can be displayed • Failure Index does not represent failure mode or percentage of failure 2 2 2 1 1 1 1 1 2 12 1 2 Failure Index 1 2 2 X X Y Y X X Y Y S X X t c t c t c t c t c Hoffman – Where X t = tension allowable in “1” direction, X c = compression Failure Criteria – Where Y t = tension allowable in “2” direction, Y c = compression F ailure Index – S = Shear Allowable • 1 = applied stress in “1” direction • 2 = applied stress in “2” direction • 12 = applied shear stress 1.00 5/22/2012 STRUCTURES .AERO Page 15
Hoffman Failure Theory Margins of Safety using the Hoffman Theory are calculated using: 1 1 1 1 1 1 1 F 11 ; ; ; ; ; F F F F F F 1 2 11 22 66 12 2 X X Y Y X X Y Y S 2 t c t c t c t c 2 MS 1 . 0 2 2 2 2 F F F F 4 F F F 2 F 1 11 2 22 1 11 2 22 11 11 22 22 66 12 12 11 22 5/22/2012 STRUCTURES .AERO Page 16
Structural Design and Analysis (Structures.Aero) Structural Analysis Software Sales and Support • Team of stress engineers that help our clients design lightweight and load efficient structures. • We service aerospace companies and other industries that require high level analysis. • Value added reseller providing software, training, • Specialty in composites and lightweight and support for products we use on a daily structures basis. • Tools used include hand analysis, HyperSizer, • Support Femap, NX Nastran, Simcenter 3D, Femap, NX Nastran, Fibersim, NX, Solid Edge, Fibersim, Solid Edge, and HyperSizer. Simcenter 3D, LS Dyna, and LMS. 5/22/2012 STRUCTURES .AERO Page 17
CAMX Tradeshow • December 12-14 at the Orange County Convention Center – Orlando, FL • Largest event for composites and advanced materials • SDA will be at Booth U84 • Want a free pass to walk the show? Email Marty Sivic at msivic@structures.aero 5/22/2012 STRUCTURES .AERO Page 18
Questions ? For questions on the material covered For questions about pricing, or to see a today, please contact Nick Mehlig. demo, please contact Marty Sivic . Nick Mehlig Marty Sivic Aerospace Stress Engineer Director of Sales nmehlig@structures.aero msivic@structures.aero 703-935-2881 724-382-5290 5/22/2012 STRUCTURES .AERO Page 19
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