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A mesh size objective multiscale modeling is developed for fatigue failure prediction of long fiber-reinforced composites based on the multiscale discrete damage theory (MDDT). MDDT tracks the failure processes along discrete failure surfaces at the microscale and concurrently bridges it to continuum-based description of damage at the macroscale. The proposed approach achieves mesh-size objectivity by introducing a length scale operator which effectively adjusts the microstructure size as a function of macroscale element size; and when a non-additive fatigue damage evolution law is used to describe progressive cracking at the microscale. Temporal multiscaling is used to track long-term fatigue damage evolution with high computational efficiency. The performance of the proposed model is demonstrated by the analysis of unnotched and open-hole laminate configurations. The results indicate mesh-size objectivity even in the presence of multiple failure mechanisms including splitting, delamination and transverse matrix cracks. The interaction between splitting and transverse cracks is investigated by a parametric study, which reveals the effects of mode I and mode II dominated degradation on the failure behavior under fatigue loading.

We propose a physics-based, multiscale computational modeling framework for prediction of damage accumulation and failure in fiber-reinforced polymer composites subjected to fatigue. The proposed framework is multiscale in space and in time; and employs the principles of the mathematical homogenization theory. The spatial multiscaling is introduced to model the progressive damage accumulation at the scale of the composite constituents, and to bridge the damage information to the scale of a structural component. In order to alleviate the outstanding issues related to multiscale modeling of fracture processes (i.e., computational cost, mesh objectivity, existence of RVE), we propose the reduced order multiscale discrete damage theory (MDDT). MDDT tracks the evolution of failure at microscale at a set of potential “failure paths” and consistently bridges the failure information to the structural scale using length scale-dependent operators. The temporal multiscaling is introduced to efficiently describe the long-term evolution of damage under cyclic loading conditions, leveraging the time scale disparity between a single characteristic load cycle and the overall life of a structural component. The efficacy of the multiscale framework is demonstrated in the context of prediction of fatigue crack initiation in unnotched and open-hole specimens subjected to fatigue loading.

The effects of temperature and load on fretting fatigue induced geometrically necessary dislocation (GND) distribution in titanium alloy are studied by electron back-scattered diffraction (EBSD) in this paper. Fretting fatigue experiments under different temperature and load in TC11 titanium alloy are carried out and samples with small cracks are obtained. With Hough-based EBSD, the misorientation and GND densities induced by fretting fatigue are analyzed in both crack formation zone and crack tip. The results show that in the crack formation zone and crack tip, both temperature and load have obvious effects on the GND densities. With the increase of temperature and load, the GND densities rise significantly, which agrees with the decreasing tendency of fretting fatigue lives. The peak positions of GND density agree well with the crack formation locations, indicating the close relation between GND concentration and fretting fatigue crack formation. The relationship between GND density and distance from the crack path is studied. The results of individual GND densities on each slip system show that ‘Pyramidal ' and ‘Screw ' dislocations compose a majority of total GND density.

This manuscript presents a new reduced order computational homogenization method for failure analysis of composite materials. The proposed approach relies on the discrete representation of the fracture process at the fine scale that consistently bridges to a continuum representation of damage at the coarse scale. In order to achieve very high computational efficiency, the proposed approach builds on the ideas of the eigendeformation-based reduced order homogenization method , but tracks microscale failure evolution over a set of discrete cohesive failure surfaces. The formulation concurrently achieves mesh size objectivity and multiscale consistency by establishing analytical relationships between the microstructure size and the macroscale element size. The performance of the proposed formulation is demonstrated in the context of three-dimensional, laminated fiber reinforced composite configurations. The numerical experiments demonstrate mesh size objectivity in the presence of multiscale failure mechanisms including fiber fracture and transverse matrix cracking .

The indentation behaviours of Ni-based single crystal (NBSX) superalloy in different crystal orientations are studied by indentation tests and Electron Backscattered Diffraction (EBSD) analysis. The effects of crystal orientations on pile-up modes, dominant slip system distribution and geometrically necessary dislocation (GND) density distribution are revealed by experiments and crystal plasticity finite element (CPFE) simulation. The results and analysis of pyramid and cone indentations show that the pile-up modes produced by different azimuths are significantly different due to the off-plane displacement distribution. The differences of crystallographic slip behaviors under different crystal orientations induce different slip line and indentation symmetry patterns. EBSD observation and CPFE analysis indicate the dependence of GND density distribution on crystal orientations. The results of indentation tests, EBSD observation and CPFE simulation achieve good agreements.