MT-1620 al.2002 Notes Graphite/epoxy has a negative C.t.E. in the fiber direction so it contracts when heated Implication: by laying up plies with various orientation can achieve a structure with a C.T.E. equal to zero in a desired direction C.T.E. of a structure depends on c t.e. and elastic constants of the parts 2 examples E=E CTE=5 1) total a of C.T.E. =2 structure E=0(perfectly compliant E=E CTE=5 total a of CTE=2 structure E=∞( perfectly rigid 2 Paul A Lagace @2001 Unit 9-p. 11
MIT - 16.20 Fall, 2002 Notes: • Graphite/epoxy has a negative C.T.E. in the fiber direction so it contracts when heated Implication: by laying up plies with various orientation can achieve a structure with a C.T.E. equal to zero in a desired direction • C.T.E. of a structure depends on C.T.E. and elastic constants of the parts E = E E = 0 (perfectly compliant) 1 C.T.E. = 5 2 examples 1) total α of C.T.E. = 2 structure = 5 E = E1 C.T.E. = 5 2) total α of C.T.E. = 2 structure E = ∞ (perfectly rigid) = 2 Paul A. Lagace © 2001 Unit 9 - p. 11
MT-1620 al.2002 a=at=cte is a function of temperature(see MIL HDBK 5 for metals). Can be large difference Implication: a zero C T E structure may not truly be attainable since it may be C T.E. at T, but not at T2 Sources of temperature differential ( heating ambient environment (engine, polar environment, earth shadow, tropics, etc aerodynamic heating radiation(black-body) Constant AT ( with respect to spatial locations) In many cases, we are interested in a case where AT (from some reference temperature)is constant through-the-thickness, etc thin structures structures in ambient environment for long periods of time Relatively easy problem to solve. Use equations of elasticity · equilibrium stress-strain Paul A Lagace @2001 Unit 9-p. 12
MIT - 16.20 Fall, 2002 • α = α(T) ⇒ C.T.E. is a function of temperature (see MIL HDBK 5 for metals). Can be large difference. Implication: a zero C.T.E. structure may not truly be attainable since it may be C.T.E. at T1 but not at T2 ! --> Sources of temperature differential (heating) • ambient environment (engine, polar environment, earth shadow, tropics, etc.) • aerodynamic heating • radiation (black-body) --> Constant ∆T (with respect to spatial locations) In many cases, we are interested in a case where ∆T (from some reference temperature) is constant through-the-thickness, etc. • thin structures • structures in ambient environment for long periods of time Relatively easy problem to solve. Use: • equations of elasticity • equilibrium • stress-strain Paul A. Lagace © 2001 Unit 9 - p. 12
MT-1620 al.2002 Example 1-2-material bar Total deformation is zero but there will be nonzero total strain in the aluminum and steel . stress is constant throughout match deformations Example 2-truss -- use equilibrium for forces in each member match displacements at each node Paul A Lagace @2001 Unit 9-p. 13
MIT - 16.20 Fall, 2002 Example 1 - 2-material bar Total deformation is zero, but there will be nonzero total strain in the aluminum and steel --> stress is constant throughout --> match deformations Example 2 - Truss --> use equilibrium for forces in each member --> match displacements at each node Paul A. Lagace © 2001 Unit 9 - p. 13