Strength and Lifetime Distributions of Unidirectional Fiber Composites in Tension |
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Page 7
... Weibull - Poisson statis- tics . Thus , the strengths of individual fiber elements of small length 8 are indepen- б dent and identically distributed ( i.i.d. ) random variables that follow the Weibull distribution F ( o ) = 1 - exp ...
... Weibull - Poisson statis- tics . Thus , the strengths of individual fiber elements of small length 8 are indepen- б dent and identically distributed ( i.i.d. ) random variables that follow the Weibull distribution F ( o ) = 1 - exp ...
Page 7
... Weibull distribution called the power - law distribution if 0 ≤ σ ≤ 08 , Fp ( 0 ) = 1 if σs < σ . ( 1.2 ) Clearly as o0 , F ( o ) ~ F , ( o ) . Compared to the Weibull distribution Eq . ( 1.1 ) , however , F , ( o ) limits the maximum ...
... Weibull distribution called the power - law distribution if 0 ≤ σ ≤ 08 , Fp ( 0 ) = 1 if σs < σ . ( 1.2 ) Clearly as o0 , F ( o ) ~ F , ( o ) . Compared to the Weibull distribution Eq . ( 1.1 ) , however , F , ( o ) limits the maximum ...
Page 22
... distribution , Ŵ ( o ) , for composite sizes n = 225 , 625 and 900 appears to converge onto one master distribution ... Weibull distribution , Eq . ( 1.1 ) . The former reduces the strength of all fibers stronger than σs to exactly σs ...
... distribution , Ŵ ( o ) , for composite sizes n = 225 , 625 and 900 appears to converge onto one master distribution ... Weibull distribution , Eq . ( 1.1 ) . The former reduces the strength of all fibers stronger than σs to exactly σs ...
Contents
Strength Distributions and Size Effects for 2D and 3D Composites | 7 |
3 | 17 |
Bibliography | 66 |
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Common terms and phrases
1D HLLS 2D array 2D HVLLS 8-bundle applied load approximation asymptotic B₁ B₂ Beyerlein broken fibers characteristic distribution function cluster edge cluster growth model cluster of breaks composite failure composite lifetime Composite Materials composite strength convergence critical cluster decreases dispersed failure mode elastic matrix empirical weakest link equal load sharing failure configurations failure process fiber adjacent fiber arrays fiber breaks fiber direction fiber load fiber strength fibers to fail Figure Gaussian intact fibers l₁ lifetime distribution load sharing bundle load-sharing model log-normal log(nC lower tail matrix Monte Carlo simulations n₁ neighbors normal distribution normalized number of fibers overload length periodic boundary conditions Phoenix planar plane plotted power law probability of failure r-cluster random variables Section shear shear-lag single break standard representative random strength distribution stress concentration ahead sub-bundle tensile transverse unit cell viscoelastic weak-linked Weibull distribution Weibull fibers ρβ