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Modeling and Analysis IN THIS WEBINAR: PRESENTED BY: Orthotropic - - PowerPoint PPT Presentation

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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

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IN THIS WEBINAR:

  • Orthotropic materials and how to define them
  • Composite Laminate properties and modeling
  • Composite failure theories and postprocessing

Getting Started with Composites Modeling and Analysis

Nick Mehlig

Aerospace Stress Engineer Structural Design and Analysis nmehlig@structures.aero

PRESENTED BY:

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STRUCTURES.AERO

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

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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

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Lamina

  • Lamina: A thin layer of composite material, usually containing unidirectional

fibers or woven fibers in a fabric pattern. Also called a ply.

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Rule of Mixtures

  • The stiffness of the final material will be defined by the Fiber Volume Fraction
  • f the lamina
  • Estimations of the material properties can be made, but experimental data

should be used.

𝐹1 = 𝐹

𝑔𝑊 𝑔 + 𝐹𝑛𝑊 𝑛

1 𝐹2 = 𝑊

𝑔

𝐹

𝑔

+ 𝑊

𝑛

𝐹𝑛 1 𝐻12 = 𝑊

𝑔

𝐻𝑔 + 𝑊

𝑛

𝐻𝑛 𝑤1 = 𝑤𝑔𝑊

𝑔 + 𝑤𝑛𝑊 𝑛

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Orthotropic Material

  • 3 planes of material symmetry
  • 9 Engineering Constants

– 3 elastic moduli – 3 shear moduli – 3 poisson ratio

31 21 1 2 3 32 12 1 1 1 2 3 2 2 13 23 3 3 1 2 3 23 23 23 31 31 12 12 31 12

1 1 1 1 1 1 E E E E E E E E E G G G                                                                                                           

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Laminate Stacking Sequence

  • Plies are stacked together at different angles to create a Laminate

X Y Z

Source: http://www.composites.ugent.be/home_made_composites/what_are_composites.html

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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

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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

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Classical Lamination Theory (CLT)

  • A transformation Matrix is defined to rotate stiffnesses from one coordinate system to the other
  • A new lamina stiffness matrix, denoted 𝑅 , is defined:
  • And the stresses and strains can be written in matrix form:

𝑈 =

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Classical Lamination Theory (CLT)

  • The Laminate Stiffness Matrix, known as the ABD Matrix, is constructed by the following

relations:

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FEMAP Demo

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Laminate Offsets

𝑜 𝑜 Offset Bottom Surface = 0 Bottom of Laminate Top of Laminate

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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

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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

– Where Xt = tension allowable in “1” direction, Xc = compression – Where Yt = tension allowable in “2” direction, Yc = compression – S = Shear Allowable

  • 1 = applied stress in “1” direction
  • 2 = applied stress in “2” direction
  • 12 = applied shear stress

c t c t c t c t c

X X S Y Y X X Y Y X

2 1 2 2 12 2 2 2 1 2 1 t

1 1 1 X 1 Index Failure                               

Hoffman Failure Criteria

1.00 F ailure Index

 

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Hoffman Failure Theory

Margins of Safety using the Hoffman Theory are calculated using:

2 ; 1 ; 1 ; 1 ; 1 1 ; 1 1

11 12 2 66 22 11 2 1

F F S F Y Y F X X F Y Y F X X F

c t c t c t c t

                        

 

 

. 1 2 4 2

22 11 12 2 12 66 2 22 22 2 11 11 2 22 2 11 1 22 2 11 1

                  F F F F F F F F MS

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Structural Design and Analysis (Structures.Aero)

Structural Analysis

  • 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.

  • Specialty in composites and lightweight

structures

  • Tools used include hand analysis, HyperSizer,

Femap, NX Nastran, Fibersim, NX, Solid Edge, Simcenter 3D, LS Dyna, and LMS.

Software Sales and Support

  • Value added reseller providing software, training,

and support for products we use on a daily basis.

  • Support Femap, NX Nastran, Simcenter 3D,

Fibersim, Solid Edge, and HyperSizer.

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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
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STRUCTURES.AERO

For questions on the material covered today, please contact Nick Mehlig. For questions about pricing, or to see a demo, please contact Marty Sivic.

Questions?

Marty Sivic

Director of Sales msivic@structures.aero 724-382-5290

Nick Mehlig

Aerospace Stress Engineer nmehlig@structures.aero 703-935-2881