Weibull distribution of fiber strength Fiber strength can

Weibull distribution of fiber strength • Fiber strength can be considered as a statistical variable because it is generally characterized by a significant scattering due to the presence of material defects. • The flaw distribution along a fiber and the variability of fiber-tofiber strength within a batch of fibers is due to variations in processing and damage introduced by the handling of the fibers.

Weibull distribution of fiber strength Paper frame glue clamps fiber • Fiber strength is measured by Fiber Tension Test (FTT), which is the most straightforward method for long fibers but it has the following disadvantages: • - labor intensive • - stress concentration at fiber ends • - complicated for short gauge length cut

Weibull distribution •

Weibull distribution •

Weibull distribution <10 for brittle materials high data dispersion >40 for ductile materials low data dispersion

Effect of shape and scale parameters on the probability density <10 for brittle materials high data dispersion >40 for ductile materials low data dispersion

Weibull plot •

Weibull plot : example • i FA=i/N FA=(i-0. 4)/(N+0. 4) 1 56 0. 2 0. 1295 2 70 0. 4 0. 3138 3 75 0. 6 0. 5 4 90 0. 8 0. 6862 5 105 1 0. 8706 F=i/N is not used since it means to hypothesize a constant distribution frequency P 56 105

Weibull plot: example •

Effect of fiber size on the failure probability •

Effect of fiber size on the failure probability • The survival probability decreases with increasing V (V 3>V 2>V 1), that is with the fiber volume. If the cross-section is constant, S decreases with increasing length. V 3>V 2>V 1 V 2 V 3

Effect of fiber size on the failure risk • V 3>V 2>V 1 -V 3 -V 2 -V 1

Effect of fiber size on the failure risk •

Application example • 0 10. 9 2020

Application example • 0 10. 9 2020

Effect of fiber treatment • RCF: recycled carbon fibers • RCF 450: thermal treatment in air up to 450°C • RCFacid: HNO 3 solution at 5% for 30 minutes at 100°C • Decreasing embrittlement • Decreasing 0 reduction of strength Label 0 (Mpa) RCF 10. 9 2020 RCF 450 8. 18 1740 RCFacid 6. 82 1155

Estimation of the IFSS • sample lm (mm) lc (mm) RF(LC) (MPa) IFSS (MPa) RCF 0. 94+0. 30 1. 26+0. 40 6480 12. 9+3. 10 RCF 450 0. 81+0. 29 1. 08+0. 39 7760 18. 00+4. 74 RCFacid 0. 62+0. 09 0. 83+0. 12 7110 21. 50+2. 72

Effect of fiber size on the failure risk •

High reliability estimates •

Problem •