consider a bone plate made of a unidirectional fibrous campsite. what fiber and

Question

consider a bone plate made of a unidirectional fibrous campsite. what fiber and matrix material are suitable in view of the need for bio-compatibility? assume the 50% fibers by volume and determine the young's Modulus in the longitudinal direction. compare with a metal implant?


this is the link for the book if you need it question(8.3 in the book)
http://books.google.com/books?id=bb68wb0R_EAC&pg=PA222&lpg=PA222&dq=calculate+the+shear+modulus+of+dental+composites&source=bl&ots=TA2F6wIJMM&sig=D9tdqkoPdKs2Efog_mpC_JI6DpA&hl=en&ei=dr2wTv-VJO3gsQKKr7HSAQ&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=calculate%20the%20shear%20modulus%20of%20dental%20composites&f=false

Explanation / Answer

Given Data A composie matix is given. Volume occupied by fibre is 50% of total volume Solution: let Af and Am be area of cross-section of fibre part and matrix part respectively. let Ef and Em be young modulus of fibre material and matrix material respectively. Assuming that length of fibre and matrix part is same in longitudinal direction. Load carried by fibre and matrix should add up to the total load. P = Pf + Pm     .....(1) As the shape of plate remains same, deflection of fibre material and matrix material has to be same. This is a compatibility requirement. f = m =     ....(2) deflection of each material under a uniaxial load is given as f = ( Pf L / Af Ef ) ..............(3) m = ( Pm L / Am Em ) ...........(4) Let E be effective modulus of this composite plate and A be total crosss-section of plate , then = (P L / A E) ...................(5) using 2,3 and 5 ...we get Pf = ( Af Ef P)/ (A E). ..................(6) using 2,4 and 5 ...we get Pm= ( Am Em P)/ (A E). ..................(7) using 6 , 7 in 1 and re rarranging terms E = (AmEm + AfEf) /( Af +Am) ....(8) As lengths are same in longitudinal dircetion, volume percentage boils down to area of cross-section percentage Af = 0.50 A = 0.50 ( Af +Am) Am = 0.50 A = 0.50 ( Af +Am) Using these equations in 8 , we get E = (Em + Ef) / 2. Comparing it with metal, u need to divide it with metal modulus. f = ( Pf L / Af Ef ) ..............(3) m = ( Pm L / Am Em ) ...........(4) Let E be effective modulus of this composite plate and A be total crosss-section of plate , then = (P L / A E) ...................(5) using 2,3 and 5 ...we get Pf = ( Af Ef P)/ (A E). ..................(6) using 2,4 and 5 ...we get Pm= ( Am Em P)/ (A E). ..................(7) using 6 , 7 in 1 and re rarranging terms E = (AmEm + AfEf) /( Af +Am) ....(8) As lengths are same in longitudinal dircetion, volume percentage boils down to area of cross-section percentage Af = 0.50 A = 0.50 ( Af +Am) Am = 0.50 A = 0.50 ( Af +Am) Using these equations in 8 , we get E = (Em + Ef) / 2. Comparing it with metal, u need to divide it with metal modulus. using 2,4 and 5 ...we get Pm= ( Am Em P)/ (A E). ..................(7) using 6 , 7 in 1 and re rarranging terms E = (AmEm + AfEf) /( Af +Am) ....(8) As lengths are same in longitudinal dircetion, volume percentage boils down to area of cross-section percentage Af = 0.50 A = 0.50 ( Af +Am) Am = 0.50 A = 0.50 ( Af +Am) Using these equations in 8 , we get E = (Em + Ef) / 2. Comparing it with metal, u need to divide it with metal modulus.

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