Fatigue modeling of materials with complex microstructures Hai Qing ⇑ , Leon Mishnaevsky Jr. Materials Research Division, Risø National Laboratory for Sustainable Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark article info Article history: Received 4 November 2010 Accepted 16 December 2010 Available online 22 January 2011 Keywords: Fatigue Finite element analysis Multiscale modeling Micromechanics Hierarchical materials Wood abstract A new approach and method of the analysis of microstructure-lifetime relationships of materials with complex structures is presented. The micromechanical multiscale computational analysis of damage evo- lution in materials with complex hierarchical microstructures is combined with the phenomenological model of fatigue damage growth. As a result, the fatigue lifetime of materials with complex structures can be determined as a function of the parameters of their structures. As an example, the fatigue lifetimes of wood modeled as a cellular material with multilayered, fiber reinforced walls were determined for dif- ferent parameters of wood microstructures. In so doing, 3D hierarchical finite element models of soft- wood, and a computational technique, including the repeating restart and model change procedures, have been employed to model the fatigue response of latewood. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Fatigue lifetime is one of the major parameters, influencing the reliability and service properties of materials and parts of ma- chines. The control of microstructures of materials represents an important potential source of the enhancement of lifetime and reli- ability of parts and machines. Recently, hierarchical materials started to attract a growing interest of scientists. The reasons for this lie both in the possibility of control microstructure at several scale levels and in the unusu- ally high strength of natural hierarchical biomaterials, which sug- gest the idea of biomimicking. For the optimal design and optimization of hierarchical materials with view on the higher life- time, mathematical models studying the combined effect of micro- structural and cyclic loading effects are necessary. Complex multiscale computational models of hierarchical materials should be combined with fatigue analysis to analyze the microstructure- lifetime relationships, and, ultimately, to design materials with high lifetime and fatigue damage resistance. There exist a number of methods to model fatigue strength of materials and the material behavior under cyclic loading: phenom- enological (residual stiffness, or strength models), progressive damage models (e.g., continuum damage mechanics based, proba- bilistic, stochastic, etc.), fatigue failure criteria and fatigue laws based models, fracture mechanics based fatigue models, homoge- nization and dislocation analysis based models, micromechanical models, etc. (See the reviews in [1–3]). Still, the problem of carrying out computational simulations of long term fatigue of materials with complex, hierarchical struc- tures taking into account the microstructure parameters, has not been solved yet. The computational modeling of hierarchical heterogeneous materials with complex structures is quite challenging even for elastic static problems, and approaches the limits of computational capacity for non-linear problems with evolving microstructures (e.g., damage). On the other side, the problem of simulation of dam- age evolution under long term cyclic loading, taking into account the real damage mechanisms, is also very challenging, and also ap- proaches the limits of computational capacity of contemporary computers. Thus, the development of computational models which take into account both the complex microstructures and the fatigue damage mechanisms can not be realized in straightforward way, by running complex numerical models subject to long term loadings, but require some new solutions. In this paper, we develop a numerical–analytical model which allows to investigate the combined effect of microstructures and fa- tigue damage on the lifetime of materials. We combine the micro- mechanical multiscale models of damage evolution in materials with complex microstructures with the phenomenological model of fatigue damage growth. As a result, one can determine the fatigue lifetime of materials with complex structures as a function of the parameters of their structures. The simulations are carried out for the wood, which is consid- ered as a gradient cellular material with multilayered, composite- structured cell walls [4]. While many micromechanical models have been developed to study the elastic properties of wood (see review [4]), the studies of wood failure, especially fatigue failure, are very limited, and mostly focused on experimental tests 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.12.022 ⇑ Corresponding author. E-mail addresses: qingh07@yahoo.com (H. Qing), lemi@risoe.dtu.dk (L. Mis- hnaevsky Jr). Computational Materials Science 50 (2011) 1644–1650 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci