i am trying to find Lc by using fibre pull out test for different embedded length of fibre. Bt during fibre pullout many of my fibres break and not pull out.
you can use Kelly-Tyson formulae but you will require teh strength of your fibre, its geometry and the IFSS. If you have problem of fibre breakage, i should advise you to reduce your embedded length to reduce the interfacial force.
More contact area means more shear stress at the interface which increases the tension forces inside the fibre (based on equilibrium equations). Theoretically, the fibre tends to fail if the maximum tensile stress reaches the fibre strength but there would be a critical length in which no fibre breakage happens. The maximum embedded length for which your fibre breaks, is called critical length. It would be better if you could show your experimental setup.