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Order of singularity at the tip of a fiber

This question is puzzling me for some time now. As we know that for a crack in a infinite homogeneous body the singularity at the tip in inverse square root. On top of that we are fairly comfortable with the derivation of stress fields at the crack- tip. My question is: Let's say I have composite with only one or more fibers (steel or polymeric cord for example), what is the stress field at the tip of the fiber. Is this something I can find in a pape. If somebody can direct me in the right direction I will really appreciate.

Thanks in advance 

 Best RegardsNj


L. Roy Xu's picture

Dear NJ,


You can read David Body’s classical paper in J of Applied Mechanics (Vol.38, pp.377-386, 1971) to determine the stress singularity order of dissimilar materials such as a fiber and a matrix. You may check my recent post on nanofiber composites and one recent paper (Xu and Sengupta, JNN, 2006) to get further details.  I also have several photos showing the stress/fringe concentration due to the theoretical stress singularity at the fiber/matrix end, from model fiber push-out experiments (Xu et al, JCM, 2005)

I really appreciate your direction on the reading materials, I will come back to you on that. With your expertise in this field can you comment little bit on the effect of fiber diameter on the stress field around the tip.

Also, I really want to read the applied mechanics paper right now, but can't get a copy right away. I was wondering, if its not a botheration, if you can send me a copy of it if you have with you at jniteshATgmailDOTcom



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