Composite Analysis for Short fibres - Critical length of fibre and strength calculations
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- Опубликовано: 2 авг 2024
- This video presents analysis for obtaining short-fibre critical length and explians the concept of load transfer from matrix to the fibre.
Summary:
Short-fibre polymer composites tend to be weaker than the continuous long-fibre counterparts. However, short-fibre composites are preferred in many applications because they can be made cost-effectively by any traditional plastics manufacturing method.
For good bonding between the fibre and the matrix and for high strength of the composite, the surface area to volume ratio of the fibre should be large which means long fibres with smaller radius or flat flakes are ideal fillers for short-fibre composites.
For a given fibre/matrix interfacial shear strength and the fibre tensile strength, there is a fixed critical length of the fibre. The length of the short-fibre must be greater than the fibre critical length in order to achieve complete load transfer and high strength in the composite. Higher the fibre/matrix shear strength, smaller is the value of the fibre critical length.
Further analysis shows that the critical length of the fibre is not suffcient for good strength of the composite. The fibre length should be larger than the fibre critical length.
Thank you for making this video! It was a great help in my review of short fiber composites. If you make more videos in the future I request that you make one on strength and stiffness calculations of randomly oriented short fiber composites. Cheers from Oregon State University.
Thanks a lot for your comment and suggestion. Will definitely consider in the future.👍
Thanks for your detailed explanation!
Glad it was helpful!👍
Great video, thank you!
Thanks!👍
Thank you for this video. It was really helpful in my research.
👍
Thanks a lot for the video🙏🙏
👍👍
Great video sir. Learned the concept of critical length of the fibre
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Nice video. Thank you
welcome👍
Thank for the great video! Can someone explain equation 4.49 (32:40)? I made average strength calculations and couldn't get this exact expression.
greetings sir......This was a very nice video and very clear and simple ..... can you suggest me any reference book to study short fiber composite and calculate their stress strain analytically in randomly oriented position.....Thank you .... Keep up the work...
You may try Plastics Engineering by R J Crawford and The Mechanical Properties of solid polymers by I M Ward and J Sweeney. Thanks for the comment!
Is there any particular method to determine the shear strength for fibre-matrix interface?
Single fibre pull out test could be used. If you doing research then I would suggest an article or similar articles,
www.sciencedirect.com/science/article/pii/1359835X9500069E
Hi. Great video. I understand that the strength of long continuous fibre composites will be greater than that of short discontinuous ones. But how much of a difference will be there? For example, the difference between strengths of 2 composites, one made of a long continuous fibre of length l and another made of 2 fibres of length l/2? How will the load transfer be different? Thanks in advance.
Your question is very interesting and important. In theory, if the short fibre has length which is larger than the critical length then the short should be able to take the load similar to the long fibre. However, the short fibre composite bring other weaknesses (imperfections) just because of the presence of fibre ends. In further analysis given by Equation 4.50 in this video I have explained that for a short fibre composite to have higher strength, it must have the length of the fibre much larger than the critical length. Please watch the explanation just after Equation 4.50. Let me know if you have further question. 👍
@@engineeringmaterials-tribo5142 Thanks for your reply. I understood your explanation. But is there a way to calculate this difference? I actually have 2 laminates, each having 3 sections with different fiber lengths - top section (15mm and 42.5mm), middle section (220mm and 165mm) and bottom section (15mm and 42.5mm). The total length of both is 250mm. Using the formula mentioned, I can calculate the critical fiber length. I am interested in the load transfer between these different sections due to shear and to compare the tensile strengths of these laminates with another laminate made of just continuous fiber. Is this possible? Thanks again.
laminate 1- top 15mm, middle, 220mm, bottom 15mm;
laminate 2- top 42.5mm, middle 165mm, bottom 42.5mm
Hi
if you rewrite Equation 4.30 in terms of aspect ratio , 4.31 will be:
𝐴/𝑉=(2𝜋/𝑉)^(1∕3) [𝑎^(〖−2〗∕3)+2𝑎^(1∕3) ]
Please correct me if I am wrong .
Thanks
Yes, you are right. Thanks for this correction!👍👍
In which machine, I measure tensile test of fiber composite ? Since , UTM machine available is only measure tensile test of metal only
Please watch this video. You can use the normal UTM.
ruclips.net/video/Sm7s0ygruww/видео.html
The analysis is for a single short fibre, for a number of short fibres, what is the cumulative strength of the composite?
Cumulative effect can be brought in by considering the volume percentage of the fibre in the composite. Such analysis could be done using FEA as there are many such software.
Sir can you recheck the equation presented at the 20.21 min in the video? The equation number 4.34.
The equation is correct. Could you let me know what you meant? I have just replaced sigma f with sigma f max to represent maximum fibre stress value at the time of breakage. This will be equal to the tensile strength of the fibre. Please let me know your confusion.👍
@@engineeringmaterials-tribo5142
Sir The equation 4.34 is derived through integration of governing equation after balancing of the tensile force and increment of the same by delta f due to shearing between the matrix and fibre AT ONE END over a diameter d (2* radius ) and length delta x of fibre. So after integration we are getting the expression for critical length. My confusion is about the presence of integer 2 in denominator.
Sir kindly upload videos for calculation of critical volume fraction for ductile and brittle matrix
@@dr.mallikadatta2420 Thanks for your very relevant question.
Here, there is no integration of Equation (4.33). It is based on the maximum stress generated for the breakage of the fibre. Breakage will occur at the point where sigma f is maximum and when this stress equals the tensile strength of the fibre. The shear stress tau y is same throughout and hence there is no need for integration of Equation (4.32) either. This is total force due to shearing.
Hence, we do not have to integrate either of these two equations. We need to simply equate them as they are written. This gives us Equation (4.34). Finally, sigma y has to be made the ultimate tensile strength of the fibre.
For any failure criterion, it is the maximum stress that is taken into consideration not integration of all the stresses.
Thanks once again. 👍
How I measure shear strength of composite material. please suggest?
If you meant the shear strength between the fibre and the matrix then you can conduct fibre pull-out test.
Can you help me by providing the pdf book in which this lesson is located
pdf of the book is unfortunately not possible by me.
sir which book to follow
Engineering Materials 2 by Ashby and Jones.
Hi,
Do we have an estimation criterion for calculating the equivalent E-modulus for certain Short fiber composites with only longitudinal isotropic E-modulus available( skin orientation).
I have the temperature dependence data(isotropic).
There is no analytical estimation. You may use the finite element methods.