This manuscript presents a multiscale stochastic failure modeling approach for fiber reinforced composites. A homogenization based reduced-order multiscale computational model is employed to predict the progressive damage accumulation and failure in the composite. Uncertainty in the composite response is modeled at the scale of the microstructure by considering the constituent material (i.e., matrix and fiber) parameters governing the evolution of damage as random variables. Through the use of the multiscale model, randomness at the constituent scale is propagated to the scale of the composite laminate. The probability distributions of the underlying material parameters are calibrated from unidirectional composite experiments using a Bayesian statistical approach. The calibrated multiscale model is exercised to predict the ultimate tensile strength of quasi-isotropic openhole composite specimens at various loading rates. The effect of random spatial distribution of constituent material properties on the composite response is investigated.

This paper presents the results from the authors' participation in the Air Force Research Laboratory's Damage Tolerance Design Principles Program. The Eigendeformation-based reduced order homogenization method was employed to predict the mechanical response of a suite of open hole and unnotched IM7/977-3 composite laminates under static tension and compression. Damage accumulation, effective stiffness, and ultimate strength blind predictions are included in addition to the results of the recalibration study. In blind predictions, the proposed multiscale model produced predictions with an average error of 13.1% compared to the experiments for static ultimate strength and 13.6% for stiffness. After recalibration, the average prediction error was improved to 8.7% for static ultimate strength and 4.4% for stiffness. Details of the blind predictions and the recalibration are discussed.

This manuscript investigates the use of Bayesian statistical methods for calibration and uncertainty quantification in rate-dependent damage modeling of composite materials. The epistemic and aleatory uncertainties inherent in the model prediction due to model parameter uncertainty, model form error, solution approximations, and measurement errors are investigated. Gaussian process surrogate models are developed to replace expensive finite element models in the analysis. A viscous damage model is employed with a solution algorithm designed for implementation within a commercial finite element software package (Abaqus). Experimental results from a suite of monotonic load tests conducted on unidirectional glass fiber reinforced epoxy composite samples at multiple strain rates and strain orientations are used to quantify the uncertainty in the prediction of the composite response within a Bayesian framework.

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This manuscript presents the blind prediction of fatigue life performance in three laminated carbon fiber reinforced polymer composite layups using a reduced-order space-time homogenization model. To bridge the spatial scales, the modeling approach relies on the Eigendeformation-based reduced order homogenization method. To bridge the time scales associated with a single load cycle and the overall life of the composite, a homogenization-based accelerated multiple-time-scale integrator with adaptive time stepping capability is employed. The proposed multiscale modeling approach was used to predict the evolution of composite stiffness and progressive damage accumulation as a function of loading cycles, as well as residual strength after fatigue in tension and compression, for three layups ([0,45,90,−45]2 s, [30,60,90,−60,−30]2 s, and [60,0,−60]3 s). Following blind prediction, the experimental data from the blind prediction specimens were employed to better understand the failure mechanisms and recalibrate the model. This study was performed as a part of the Air Force Research Laboratory's “Damage Tolerant Design Principles” Program.

1 This manuscript provides a combined computational-experimental investigation of the 2 interaction of damage mechanisms in carbon fiber reinforced polymer (CFRP) laminated 3 composites subjected to fatigue loading. The investigations particularly focus on [60,0,-4 60] 3S laminates, whose behavior demonstrates strong interactions between the relevant dam-5 age modes. Numerical investigations are performed using a spatio-temporal computational 6 homogenization-based multiscale life prediction model. The computational approach relies on 7 a model order reduction methodology to develop a meso-model that can capture the relevant 8 failure mechanisms in a computationally efficient manner. The model was calibrated using a 9 suite of experimental data from the static and fatigue response of simple laminates made of the 10 same constituents. The calibrated model along with experimental observations from acoustic 11 emission and X-ray computed tomography were employed to understand the relative roles of 12 delamination and splitting, and their interactions in controlling fatigue failure processes in 13 CFRPs. 14 The state of damage in laminated composite structures subjected to fatigue loading has a sig-18 nificant effect on the remaining life and the residual strength. Early works on fatigue modeling 19focused on identification of damage markers or characteristic states of damage that correlate 20 well with the prediction metrics such as life, residual strength or residual stiffness (e.g., [25]). 21While this approach provides accurate predictions for some laminate layups and geometries, 22 damage markers may significantly differ from one laminate configuration to another, and there-23 fore the approach does not generalize to arbitrary laminate configurations. The difficulty is 24 largely due to the interactions between various damage mechanisms that depend on the consti-25 tutive and failure properties of the composite constituents, laminate stacking, ply thicknesses, 26 loading profile, and structural geometry. In the context of carbon fiber reinforced polymers 27 (CFRPs) subjected to tension-tension fatigue, understanding and modeling of the interactions 28 between the transverse matrix cracks, longitudinal splits, fiber fracture and delaminations are 29 critical to achieving reliable predictive capability when subjected to cyclic loading. 30 Damage mechanisms and their evolution under fatigue loading conditions of notched and 31 unnotched specimens have been traditionally investigated separately. While the damage mech-32 anisms in both types of specimens are typically the same, damage in unnotched specimens orig-33 inates at edge singularities, whereas stress concentrations at the notch tip initiates damage in 34 notched specimens. Mohandesi and Majidi [17] investigated the fatigue damage mechanisms of 35 quasi-isotropic unnotched specimens. Off-axis matrix cracking and delamination between 90 36 degree and 45 degree plies at the exterior edges of the specimens constituted the initial dam-37 age. The propagation of d...

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