Journal of Engineering Mechanics

Abstract

This paper presents a novel methodology that addresses the limited predictive capability of the existing crystal plasticity (CP) method in interfaces modeling. Our approach incorporates interfacial parameters generated from molecular dynamic (MD) simulations into the continuum-level crystal plasticity finite element analysis (CPFEA) model. To address the inherent scale mismatch between atomistic and continuum models, we employ two essential techniques—the nucleation theory and machine learning (ML) method. The nucleation theory is utilized in conjunction with the nudged elastic band (NEB) method to extrapolate the low strain-rate yield stresses from the high strain-rate MD simulation results. To overcome the length scale limitation of MD, we use a method that was recently developed by the authors—a two-step approach that utilizes MD-calculated stress–strain data to train a probabilistic ML model for predicting stress–strain behaviors at larger scale. The resulting flow parameters and extrapolated yield stresses are then integrated into the atomistic-informed interface region of the CPFEA model. This multiscale computational method that combines MD, CPFEA, nucleation theory, NEB and ML enables a grain-level large time scale crystal plasticity modeling with atomic accuracy at the interfaces, as demonstrated by carefully validating it through a bicrystal Cu model with experimental results. This validation highlights the importance of accurately describing interfaces in the modeling of material mechanical behavior. Notably, our proposed methodology is not limited to interfaces but can be applied to other microstructures requiring atomic accuracy. The method opens up new possibilities for comprehensively understanding and designing materials with complex microstructure for various engineering applications.

Practical Applications

The methodology presented in this paper offers significant practical applications for materials engineering, particularly in industries where materials are subjected to high stress and strain, such as aerospace, automotive, and structural engineering. By integrating atomistic interfacial parameters into the crystal plasticity finite element analysis (CPFEA) model, this approach allows for more accurate predictions of material behavior at the grain level, leading to better-informed decisions in material design and optimization. The ability to model interfaces with atomic accuracy means that engineers can design materials with enhanced mechanical properties, such as increased strength and ductility, by understanding and manipulating the behavior of grain boundaries. This is crucial for developing advanced materials that can withstand extreme conditions, thereby improving the safety and performance of critical components in various engineering applications. Additionally, the use of machine learning to predict stress–strain behaviors at larger scales from molecular dynamics data provides a powerful tool for scaling up the modeling process, making it more feasible and efficient for practical use. This comprehensive multiscale framework opens new avenues for innovation in material science, allowing for the design of next-generation materials with tailored properties for specific engineering challenges.

Several studies indicate that epoxy resin exhibits a very wide range of mechanical behavior, in particular its strength, as a function of stress state. Especially when epoxy resin is used as matrix material for fiber reinforced composites (FRC), this becomes relevant due to complex stress conditions in the matrix. However, the knowledge about the behavior of epoxy resin under uni, bi, and triaxial stress conditions is lacking. Therefore, the mechanical properties of a typical epoxy resin for the production of FRC were investigated given such load conditions. The determined strengths were compared with the predictions of the extended paraboloid criterion. Uniaxial tension and compression tests, torsion tests with overlaid tension and compression, and triaxial tension tests were performed. An elastoplastic material model and a nonlocal damage model were formulated to demonstrate the application of the extended paraboloid strength criterion. In particular, large plastic strains under shear stress conditions, as well as a perfectly brittle material behavior with significantly reduced strength under triaxial tension, could be shown.