Size effect on probability distribution of fatigue lifetime of quasibrittle structures

2011 ◽  
pp. 1291-1298
Author(s):  
Jia-Liang Le ◽  
Z Ba_ant
Keyword(s):  
Probability Distribution ◽  
Size Effect ◽  
Fatigue Lifetime

Preferential frequency and size effect of the Brownian force acting on a nanoparticle

2017 ◽  
Vol 828 ◽  
pp. 648-660
Author(s):  
Hanhui Jin ◽  
Ningning Liu ◽  
Xiaoke Ku ◽  
Jianren Fan
Keyword(s):  
Probability Distribution ◽  
Size Effect ◽  
Noise Spectrum ◽  
Self Similarity ◽  
Langevin Model ◽  
Gas Molecule ◽  
Spectrum Distribution ◽  
Brownian Force ◽  
Molecular Forces ◽  
New Phenomena

The Brownian motion of a nanoparticle in fluid depends on the molecular forces acting on it. Because of the small size and the high frequency, it is difficult to make experimental measurements of these forces. In the present work, Brownian forces acting on a nanoparticle are numerically investigated with the molecular dynamics method. Some new phenomena are disclosed. (i) The probability distribution shows that the Brownian forces conform to the Gaussian distribution and self-similarity of the probability distribution is also found for different $1/Kn$ numbers which are characterized with the particle radius and the mean path $\unicode[STIX]{x1D706}$ of the gas molecule $(1/Kn=R/\unicode[STIX]{x1D706})$. (ii) The frequency spectrum distribution of the Brownian force is not a white noise spectrum, which is different from the assumption commonly used in Langevin model. The preferential frequency of the Brownian force is found. (iii) The size effect relating to the Brownian forces is not monotonically varying with $1/Kn=R/\unicode[STIX]{x1D706}$ and is also found. It first increases and then decreases after it reaches the maximum value at $1/Kn\approx 250$. The variation process for $1/Kn<250$ observed in the present work has not been reported in previous research to date.

scholarly journals Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180617 ◽  
Author(s):  
Zdeněk P. Bažant
Keyword(s):  
Probability Distribution ◽  
Analytical Solution ◽  
Size Effect ◽  
Failure Probability ◽  
Transition Rate ◽  
Microelectromechanical Systems ◽  
Rate Theory ◽  
Weakest Link ◽  
Quasibrittle Materials ◽  
The Mean

The objective in materials or structure design has been to maximize the mean strength. However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10 −6 per lifetime. But this objective is not the same. Indeed, a quasibrittle material or structure with a superior mean strength can have, for the same coefficient of variation, an inferior strength at the less than 10 −6 tail. This tail is unreachable by histogram testing. So, one needs a rational theory, physically based and experimentally verified indirectly, which is feasible by size effect. Focusing on the results at the writer's home institution, this inaugural article (written three years ex post facto ) reviews recent results towards this goal, concerned with quasibrittle materials such as concretes, rocks, tough ceramics, fibre composites, bone and most materials on the micrometer scale. The theory is anchored at the atomic scale because only on that scale the failure probability is known—it is given by the frequency of breakage of bonds, governed by the activation energy barriers in the transition rate theory. An analytical way to scale it up to the macroscale representative volume element (RVE) has been found. Structures obeying the weakest-link model are considered but, for quasibrittle failures, the number of links, each corresponding to one RVE, must be considered as finite. The result is a strength probability distribution transiting from Weibullian to Gaussian, depending on the structure size. The Charles-Evans and Paris laws for subcritical crack growth under static and cyclic fatigue are also derived from the transition-rate theory. This yields a size-dependent Gauss–Weibull distribution of lifetime. Close agreement with numerous published test data is achieved. Discussed next are new results on materials with a well-defined microscale architecture, particularly biomimetic imbricated (or staggered) lamellar materials, exemplified by nacre, a material of astonishing mean strength compared to its constituents. This architecture is idealized as a diagonally pulled fishnet, which is shown to be amenable to an analytical solution of the strength probability distribution. The solution is verified by million Monte Carlo simulations for each of the fishnets of various shapes and sizes. In addition to the classical weakest-link and the fibre-bundle models, the fishnet is found to be the third strength probability model that is amenable to an analytical solution. The nacreous architecture is shown to provide an additional major (greater than 100%) strengthening at the 10 −6 failure probability tail. Finally, it is emphasized that the most important consequence of the quasibrittleness, and also the most effective way of calibrating the 10 −6 tail, is the size effect on the mean structural strength, which permeates all formulations.

Probabilistic modelling of the size effect on ductility of a C-Mn steel

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-63-Pr8-70
Author(s):  
S. Carassou ◽  
M. Soilleux ◽  
B. Marini
Keyword(s):  
Size Effect ◽  
Probabilistic Modelling ◽  
Mn Steel
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