A damage model of creep crack growth in polycrystals

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

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.

A theoretical and computational framework for studying creep crack growth

In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C ∗ -integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantity C ^ k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity ϕ 0 , which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack growth response in the limits of small and large ϕ 0 , for which analytical expression can be obtained. We also demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments.

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10(-6). The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activation-energy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size- and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.