On the heat flux from the moon's interior o potoke tepla iz nedr luny
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Krotikov, V. D.↗
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Reformulating a Gurson-based dynamic damage model and demonstrating improved predictive power and numerical robustness
The original Tepla (TEnsile PLAsticity) ductile damage model, based on the Gurson yield surface, has long been used to model damage evolution and material failure under dynamic loading. Unfortunately, Tepla suffered from mesh sensitivity, numerical instability, and limited predictive capability. Here, we theoretically reformulate Tepla to address these issues. We especially focus on the prediction of porosity, which is the key state variable used for modeling ductile damage, as compared to more easily measured surface velocities, which are at best an indirect measure of damage. Key model changes include separating the viscosity during volumetric void growth from underlying shear strength behavior and switching to an iterative bisection solver. The new Tepla is then calibrated on incipient spall experiments on half-hard copper and tantalum, which demonstrate its ability to simultaneously fit the model to recovered porosity distributions and measured surface velocities, a stringent test. Improved numerical behavior, such as greatly reduced mesh sensitivity, is also shown in those simulations. Finally, the new Tepla model is applied to several high-explosive loaded, sweeping wave experiments, showing the ability of the model to predict behavior on tests with significantly different loading conditions and histories than the calibration data.
36 MATERIALS SCIENCE↗
Effect of surface defects on damage and failure of dynamically driven cylindrical shells
Here, in this work, expanding cylinder experiments are performed using a gas gun on the aluminum 6061 alloy to understand the dynamic deformation and failure behavior of this material in the presence of surface defects in the form of scratches. The experiments are then modeled with the modified Tepla (for tensile plasticity) model, which is equipped with the damage yield function of Gurson [“Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media,” (1977)] and Tvergaard and Needleman [Acta Metall. 32(1), 157–169 (1984)], over-stress viscosity [F. Addessio and J. Johnson, J. Appl. Phys. 74(3), 1640–1648 (1993)], and the underlying viscoplastic model of Preston et al. [J. Appl. Phys. 93(1), 211–220 (2003)] (Preston–Tonks–Wallace model) for the dense material. The Tepla model parameters were calibrated using the Bayesian approach against experimentally measured free-surface velocity data obtained from plate impact experiments on the aluminum 6061 alloy. The evolution of radial expansion and shapes of the deformed cylinder from the simulations on a pristine cylinder wall and a cylinder wall with a longitudinal surface defect shows excellent agreement with the corresponding experimental results. Finally, the role of surface defect size and cylinder wall geometry on the dynamic strength of the cylinder wall was also investigated through a series of simulations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Effect of macroscopic surface defects on dynamic damage: An experimental and numerical study
This study examines the impact of macroscopic surface defects on the dynamic ductile damage behavior of polycrystalline metals using plate-impact experiments. Defects of various shapes (flat, round, and point) were manufactured on the free or impact surfaces of annealed copper specimens. The experiments were diagnosed with photon Doppler velocimetry measurements and soft recovery techniques. The experimental results revealed that defect shape and location significantly affect velocity–time profiles and void distribution. In order to understand the dynamics of shock propagation and corresponding ductile damage evolution within the target specimens, the impact experiments were modeled with a calibrated Tepla model, a dynamic ductile damage model for polycrystalline metals [Nguyen et al., Int. J. Solids Struct. 329, 113833 (2026)]. Overall, our resulting simulated velocity showed good agreement with measured velocity, and our simulated porosity distributions qualitatively matched experimental data. Based on our simulation results, defects on the free surface were found to distort rarefaction waves and therefore the corresponding spall planes. On the other hand, defects on the impact surface generated a delayed shock when the flyer plate and the defected target area were in contact, leading to distortion of the spall plane. The distortion of the spall plane resulted in a non-uniform distribution of voids within the defected specimens. Lastly, we examined the role of local work hardening due to the defect manufacturing process on the velocity and porosity distribution, using Tepla simulations with a simplified representation of local hardening. This investigation highlights the importance of defect geometry, location, and local hardening associated with defect generation in dynamic ductile damage processes.
36 MATERIALS SCIENCE↗
Machine learning based approach to predict ductile damage model parameters for polycrystalline metals
Damage models for ductile materials typically need to be parameterized, often with the appropriate parameters changing for a given material depending on the loading conditions. This can make parameterizing these models computationally expensive, since an inverse problem must be solved for each loading condition. Using standard inverse modeling techniques typically requires hundreds or thousands of high-fidelity computer simulations to estimate the optimal parameters. Additionally, the time of a human expert is required to set up the inverse model. Machine learning has recently emerged as an alternative approach to inverse modeling in these settings, where the machine learning model is trained in an offline manner and new parameters can be quickly generated on the fly, after training is complete. Here, this work utilizes such a workflow to enable the rapid parameterization of a ductile damage model called TEPLA with a machine learning inverse model. The machine learning model can efficiently estimate the model parameters much faster, as compared to previously employed methods, such as Bayesian calibration. The results demonstrate good accuracy on a synthetic test dataset and is validated against experimental data.
36 MATERIALS SCIENCE↗
LEAD - LEArning Damage
LEAD is a suite of scripts to enable rapid estimation of model parameters for damage models for ductile materials using machine learning. In its current version, the only supported damage model is TEPLA, though others are planned. The data we train on are comprised of free surface velocity data as well as porosity data. Some details about our method can be found in the preprint LA-UR-23-20468 (arxiv.org/abs/2301.07790)
Blaschke, Daniel↗
The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta
A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.
36 MATERIALS SCIENCE↗