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Classification of Composites• Composites: - Multiphase material w/significant proportions of ea. phase.• Matrix: - The continuous phase - Purpose is to: transfer stress to other phases protect phases from environment - Classification: MMC, CMC, PMC
From W. Funk and E. Blank, “Creep deformationof Ni3Al-Mo in-situ composites", Metall. Trans. AVol. 19(4), pp. 987-998, 1988.
--Metal: γ'(Ni3Al)-α(Mo) by eutectic solidification.
--Glass w/SiC fibers formed by glass slurry Eglass = 76GPa; ESiC = 400GPa.
From F.L. Matthews and R.L.Rawlings, Composite Materials;Engineering and Science,Reprint ed., CRC Press, BocaRaton, FL, 2000. (a) Fig. 4.22, p.145 (photo by J. Davies); (b) Fig.11.20, p. 349 (micrograph byH.S. Kim, P.S. Rodgers, andR.D. Rawlings).
Stress-strain response depends on properties of• reinforcing and matrix materials (carbon, polymer, metal, ceramic)• volume fractions of reinforcing and matrix materials• orientation of fibre reinforcement (golf club, kevlar jacket)• size and dispersion of particle reinforcement (concrete)• absolute length of fibres, etc.
Suppose a polymer matrix (E= 2.5 GPa) has 33% fibrereinforcements of glass (E = 76 GPa).
What is Elastic Modulus? 1Ec
=˜ V mEm
+˜ V
fEf
EC=EmE
f˜ V f Em +(1− ˜ V f )Ef
≈ Em
(1− ˜ V f )
Rearrange:= 3.8 GPA
* Elastic modulus of composite under isoload conditionStrongly depends on stiffness of matrix, unlike isostraincase where stiffness dominates from fibres.
Gluing together these composite layerscomposed of epoxy matrix (Em= 5 GPa)with graphite fibres (Ef= 490 GPa andVf = 0.3). Central layer is oriented 900
from other two layers.
Case I - Load is applied parallel to fibres in outer two sheets.Case II - Load is applied parallel to fibres of central sheet.
What are effective elastic moduli in the two case?• First need to know how individual sheets respond, then average.1E⊥
= 0.3490GPa+
0.75GPa→E⊥ =7.1GPa For isoload case.
E||=0.3(490GPa)+0.7(5GPa)→E||=150.5GPa For isotrain case.
Case I: Elam=(2/3)(150.5 GPa) + (1/3)(7.1 GPa) = 102.7 GPa
Case II: Elam=(1/3)(150.5 GPa) + (2/3)(7.1 GPa) = 54.9 GPa
Mechanical Response of Laminate is Complex and NOT Ideal
3 Conditions required: consider top and bottom before laminated• strain compatibility- top and bottom must have same strain when glued.• stress-strain relations - need Hooke’s Law and Poisson effect.• equilibrium - forces and torques, or twisting and bending.
Isostrain for loadalong x-dir:
Poisson Effect andDisplacements in Δ:
• When glued together displacements have to be same! • Unequal displacements not allowed!So, top gets wider (σy
Depending on placement of load and the orientation of fibresinternal to sheet and the orientation of sheets relative to oneanother, the response is then very different.
Examples of orientations of laminated sheets that providedcompressive stresses at edges of composite and also tensilestresses there. >>>> Tensile stresses lead to delamination!
The stacking of composite sheets and their angular orientationcan be used to prevent “twisting” moments but allow “bending”moments. This is very useful for airplane wings, golf club shafts(to prevent slices or hooks), tennis rackets, etc., where poweror lift comes or is not reduced from bending.
• Composites are classified according to: -- the matrix material (CMC, MMC, PMC) -- the reinforcement geometry (particles, fibers, layers).• Composites enhance matrix properties: -- MMC: enhance σy, TS, creep performance -- CMC: enhance Kc
-- PMC: enhance E, σy, TS, creep performance• Particulate-reinforced: -- Elastic modulus can be estimated. -- Properties are isotropic.• Fiber-reinforced: -- Elastic modulus and TS can be estimated along fiber dir. -- Properties can be isotropic or anisotropic.• Structural: -- Based on build-up of sandwiches in layered form.