Creep rupture of brittle matrix composites reinforced with time dependent fibers: Scalings and Monte Carlo simulations

Ibnabdeljalil, M.; Phoenix, S. Leigh

doi:10.1016/0022-5096(95)00008-7

Cited by 38 publications

(19 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lifetime statistics was first studied for fibrous materials (Coleman, 1957(Coleman, , 1958 and later for fiber composites (Phoenix, 1978a;Tierney, 1983;Ibnabdeljalil and Phoenix, 1995;Mahesh and Phoenix, 2004). These models were derived by assuming the infinite weakest-link model for a single fiber, which is questionable because experimentally observed strength histograms of single fibers consistently showed deviations from the classical Weibull distribution (Schwartz, 1987;Wanger et al, 1984;Schwartz et al, 1986), and the size effect was not checked.…”

Section: Lifetime Statisticsmentioning

confidence: 99%

See 1 more Smart Citation

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Bažant

Bazant

2011

Journal of the Mechanics and Physics of Solids

161

134

View full text Add to dashboard Cite

Section: Lifetime Statisticsmentioning

confidence: 99%

“…When k is very small, the foregoing transformation can be approximated by the logarithmic transformation for the region of l that is near some prescribed lifetime l 0 (Ibnabdeljalil and Phoenix, 1995):…”

Section: Distribution Of Structural Lifetimementioning

confidence: 99%

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Bažant

Bazant

2011

Journal of the Mechanics and Physics of Solids

161

134

View full text Add to dashboard Cite

“…The Weibull distribution is often used in applications of reliability to model time-to-failure to predict the properties of composite materials such as residual strength, fatigue life, ultimate strength, and creep rupture [11][12][13][14] . The lognormal and normal distributions have also been used to model lifetime and material properties that degrade over time [15][16][17] . The formulation of the lognormal distribution is a simple exponential function of a normal random variable and therefore its probabilities are easier to evaluate when compared to those of the Weibull distribution.…”

Section: Staistical Distributionsmentioning

confidence: 99%

Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin

Simsiriwong

Sullivan

Hilton

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

6
0
3
0

View full text Add to dashboard Cite

The objective of this study is to formulate the statistical distribution functions for the viscoelastic creep compliance of a vinyl ester polymer. Short-term tensile creep/creep recovery experiments are conducted at two stress levels and at three temperatures below the glass transition temperature. Strain measurements in the longitudinal and transverse directions are measured simultaneously using the digital image correlation technique. The creep compliance functions are obtained using the generalized 3-D viscoelastic constitutive equation with a Prony series representation. Weibull and lognormal distributions are considered for the probability distribution of the creep functions. This effort involves an analytical study based on experimental results for representing the data scatter in polymer composites. Such a study has not been found in the literature. Nomenclature ε ii (t)= sampled strain at t σ jj (t) = sampled stress at t C 0 iijj = elastic compliance C n iijj = Prony series coefficient C iijj (t) = creep compliance at t τ n = retardation time N pr = length of Prony series (1≤ n ≤ Npr) t 1 = time when load reaches steady state (t 1 > 0) H(t) = Heaviside step function t m * = the m th experimental time sample β = Weibull shape parameter α = Weibull scale parameter μ = Lognormal mean parameter σ = Lognormal standard deviation parameter 2 N 0 = number of sample size D no = Kolmogorov-Smirnov maximum deviation λ = Significance level ν ij (t) = Poisson's ratio at t

show abstract

“…When fibers break, the load on the cross section is redistributed. The simulation method is also used to predict the lifetime of composites with broken fibers [66,67]. A number of experimental and theoretical studies have been conducted on the creep of composites.…”

Section: Creep Limit Statementioning
confidence: 99%

Reliability Analysis of Composite Structures and Materials
Mahadevan¹
2004
Engineering Design Reliability Handbook
0
0
0
0
View full text Add to dashboard Cite

From the perspective of strength limit states, composite laminate failure may be considered in two major stages, first-ply failure (FPF) and last-ply failure (LPF). The first-ply failure usually corresponds to the commencement of matrix cracking failure; structural ultimate failure or last-ply failure consists of a series of the ply-level component failures, such as matrix cracking, delamination, and fiber breakage, from the first one to the last one. Well-known methods such as the first-order reliability method (FORM), second-order reliability method (SORM), or Monte Carlo simulation can be combined with finite element analysis to compute the component failure probability. The branch-and-bound method can then be employed to search for the significant system failure sequences. When each component failure occurs, the structural stiffness is modified to account for this damage, and the damaged structure is reanalyzed. This proceeds until system failure occurs. Based on the identified significant failure sequences, the system failure probability is determined by means of bounding techniques. In the composite structure, multiple sequences are found to be highly correlated, leading to efficient approximations in the failure probability computation. Section 44.2 to Section 44.4 present these methods and illustrate them with simple examples, with a practical application for a composite aircraft wing presented in Section 44.4.5.The characteristics of fatigue-damage growth in composite materials are different from those of damage growth in homogeneous materials. Continuum damage mechanics concepts have been used to evaluate the degradation of composite materials under cyclic loading. Damage-accumulation models that capture the unique characteristics of composite materials are presented in Section 44.5. The predictions from the models are compared with experimental data.Fatigue leads to delamination in several laminated composite applications, affected by anisotropic material properties of various plies, ply thicknesses and orientations, loads, and boundary conditions. The limit state can be formulated in terms of the strain energy release rate computed based on the virtual crack-closure technique. The critical value of the strain energy release rate, obtained from test data, is seen to be a random function of life of the structure. Once the delamination initiation probability is estimated, the propagation life until system failure is estimated through the exploration of multiple paths through the branch-and-bound enumeration technique. The analysis is then repeated for multiple initiation sites, and the overall probability of failure is computed through the union of the multiple initiation/growth events. These techniques are presented and illustrated in Section 44.6 using a practical applicationfatigue-delamination analysis of a helicopter rotor component.Composite materials are particularly attractive for high-temperature applications, as in engine components. Therefore, creep reliability models for high-temperature comp...

show abstract

Creep rupture of brittle matrix composites reinforced with time dependent fibers: Scalings and Monte Carlo simulations

Cited by 38 publications

References 20 publications

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Statistical Analysis of Viscoelastic Creep Compliance of Vinyl Ester Resin

Reliability Analysis of Composite Structures and Materials

Contact Info

Product

Resources

About