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Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials
Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.
Mitigation of spall fracture by evolving porosity
Ductile materials subject to impact loading conditions can undergo spall fracture when an incoming compressive stress wave reflects off interfaces and free surfaces as a tensile stress wave. Experimental observations suggest that in ductile materials, spall fracture is driven by the evolution of porosity. However, the presence of initial porosity in ductile materials also introduces plastic compressibility, which can attenuate the incoming compressive stress wave and, as a result, reduce the amplitude of the reflected tensile stress wave. This, in turn, can mitigate or delay spall fracture. In this work, we report on finite deformation finite element calculations that analyze the response of porous ductile materials subjected to impact loading conditions. Two sets of calculations are carried out, in the first set the material contains initial porosity values ranging from 0% to 5% while in the second set the material also undergoes stress-controlled porosity nucleation. Both sets of calculations are carried out for a wide range of imposed impact velocities. Here, our results show that porosity in ductile materials can, under certain circumstances, mitigate spall fracture by attenuating stress waves. Results correlating the effects of impact velocity, initial porosity, and porosity nucleation on spall fracture are presented and the underlying mechanisms are discussed.
Phase-field modeling of crack growth under coupled creep-fatigue
Crack growth under coupled creep-fatigue strongly influences service life of metallic components operating at high temperatures. However, there lack numerical models that enable direct simulations of crack growth and plasticity development under coupled creep-fatigue. Here, in this study, a unified phase-field model is developed for simulating crack growth under fatigue, creep, and coupled creep-fatigue. This model is able to reproduce the Paris laws for both brittle and ductile materials in pure fatigue mode, which shows that the degradation rate due to cyclic stress in ductile materials is generally larger than that in brittle materials. Fatigue simulations with different yield strengths demonstrate that plasticity facilitates crack growth in typical ductile materials. High-throughput simulations are performed under coupled creep-fatigue conditions, with varying hold-stress levels and hold-time. By analyzing crack growth rate under different hold-time, a creep-fatigue interaction term is obtained. Simulation results demonstrate that the creep-fatigue interaction is caused by smaller stress gradient and enhanced degradation rate ahead of the crack tips under coupled creep-fatigue, compared to the situation of pure fatigue. This work reveals the origin of different Paris-law exponents in brittle and ductile materials and demonstrates how the interplay between creep and fatigue affects crack growth.
Multiplexing core & sheath extrusion system development for additive manufacturing for inner-bead multi-material capability
Single-feed polymer extruders are widely used in large-format additive manufacturing (AM) systems; however, the increasing demand for multi-material functionality within a single part has driven significant innovation in this field. One approach involves robotic pick-and-place operations, while another explores mechanical switching of feed lines during extrusion. Although robotic pick-and-drop systems offer flexibility, they introduce longer layer times during material changes, which can negatively affect the structural integrity of the part. On the other hand, mechanical feed switching causes delays in material transitions, as the existing material must be flushed before the new material emerges from the nozzle. This poses particular challenges for smaller or more intricate parts. In this study we are developing a unique multiplexing extrusion system with core & sheath nozzle that combines two extruders via co-extrusion. This allows for a unique inside and outside inner-bead (i.e., within the same bead) multi-material capability. We believe that this technology will allow for combining neat and filled materials, ductile and stronger materials, and many other combinations to address the problems aforementioned above and disrupt the AM technology creating new opportunities and opening application areas.
The damage Mechanics challenge Results: Participant predictions compared with experiment
In this article, We present results from a recent exercise where participating organizations were asked to provide model-based blind predictions of damage evolution in 3D-printed geomaterial analogue test articles. Participants were provided with a range of data characterizing both the undamaged state (e.g., ultrasonic measurements) and damage evolution (e.g., 3-point bending, unconfined compression, and Brazilian testing) of the material. In this paper, we focus on comparisons between the participants’ predictions and the previously secret challenge problem experimental observations. We present valuable lessons learned for the application of numerical methods to deformation and failure in brittle-ductile materials. The exercise also enables us to identify which specific types of calibration data were of most utility to the participants in developing their predictions. Further, we identify additional data that would have been useful for participants to improve the confidence of their predictions. Consequently, this work improves our understanding of how to better characterize a material to enable more accurate prediction of damage and failure propagation in natural and engineered brittle-ductile materials.
Experimental data for damage mechanics simulation challenge
While there are many computational approaches for simulating damage in rock and other materials, few have been ground truth tested with either known experimental data or with blind data sets. Here, in this work, we present a bench-mark laboratory data set for a damage mechanics challenge to compare computational approaches on damage evolution in brittle-ductile materials. The samples were fabricated through additive manufacturing to produce repeatable specimens designed to fail in controlled ways. The failure was induced in the samples using a 3-point bending test to produce different Modes such as Mode I and mixed Modes including I-II, I-III and I-II-III Modes to generate a calibration data set and a blind challenge data set. Data collected included spatial and temporal measurements from traditional digital load–displacement sensors, 2D digital image correlation measurement to map surface deformations, 3D X-ray microscopy to ground-truth the crack-failure geometry, and laser profilometry to capture surface roughness. The data sets are available, on a data repository, to the community to advance computational models to improve our ability to predict damage in brittle-ductile materials.
A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage
Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.
History, present status, and future directions of vanadium alloys for fusion reactors
Since the need for low-activation fusion reactor materials was recognized in the mid-1980s, vanadium alloys have been researched and developed as promising candidates for blanket structural materials. Vanadium alloys are non-ferromagnetic and ductile materials and thus have advantages different from other candidates. However, since vanadium alloys are still at a premature industrial stage, research and development have been carried out not only on issues specific to fusion reactors but also on those related to industrial materials. Blankets using vanadium alloys as structural materials and liquid Li as a tritium breeder and coolant (self-cooled V/Li blankets) have unique characteristics, and research and development of issues specific to V/Li blankets have been conducted in conjunction with the development of vanadium alloys. In this paper, the progress of this research and development is reviewed, and the remaining issues are pointed out. As a result, the future direction of vanadium alloy research and development is discussed, considering recent changes in the environment surrounding fusion energy.
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.
DuctGPT: A Generative Transformer for Forward Screening of Ductile Refractory Multi-Principal Element Alloys
Designing ductile materials for extreme environments such as fusion reactors requires a deep understanding of the complex interplay between electronic structure, mechanical stability, and wide compositional space. Here, in this work, we introduce DuctGPT, a physics-informed, GPT-powered machine learning platform that enables rapid and accurate prediction of ductility across a wide range of refractory multi-principal element alloys (MPEAs). Trained on both experimental and high-fidelity computational data, DuctGPT integrates descriptors such as density of states at the Fermi level, elastic constants, and valence electron concentration to capture the fundamental mechanisms governing ductile versus brittle behavior. Using this framework, we screen over 1000 compositions in of body-centered cubic (BCC) MPEAs, including two new alloy classes, i.e., NbTa-rich (NbTa $>$ 50 at.%) NbTa-Ti-V and W-rich ($>$ 50 at.%) W-Ti-V MPEAs, to rapidly identify promising alloy compositions with enhanced ductility. Validation against experimental data confirms the model's ability to predict ductility with high fidelity and low uncertainty. By leveraging conversational AI and robust physical modeling, DuctGPT provides a blueprint for the next generation of alloy design assistants, enabling human-AI collaboration in the accelerated discovery of ductile, high-performance materials for fusion, aerospace, and advanced manufacturing.
The Toughness of Interlocking Metasurfaces
Interlocking metasurfaces (ILMs) are arrays of autogenous latching unit cells patterned across a surface. These create structural joints similar to bioinspired suture joints but patterned over a 2D surface rather than a 1D seam. This enables ILMs to be an alternative to conventional joining technologies such as bolts, welds, and adhesives. However, compared to conventional joining methods, relatively little is known of the engineering considerations for designing structural ILMs. Herein, the interfacial toughness of an archetypal ILM is examined for the first time. Under the conditions studied here, the ILM is substantially tougher than the material from which it is made, in this case, exhibiting up to a 50% increase in interfacial crack initiation energy over the solid base material, a photocured 3D‐printed polymer. Through experimental tests using in‐situ digital image correlation along with complementary computational analyses, the mechanism of toughening in the ILM structure and the origins of toughness anisotropy are revealed. The increase in toughness is associated with cross‐cell interactions, that is, load‐sharing across unit cells, which give rise to a finite process zone length with different effective material properties. In this way, ILM toughening is analogous to crack blunting in ductile materials or fiber bridging in composites; yet here, the ILM is composed of a single‐phase base material and so the architected toughening is geometric in nature and hence amenable to future topological optimization.
Metal (Cu,Al)/CNT Composite Wires for Energy Efficient Motors
This report summarizes the main results of research project on Metal/CNT nanocomposites conducted at University of Central Florida (UCF). It should be noted that the project was budgeted for three years, but the budget period 3 was unfortunately not funded and conducted in COVID19 pandemic years due to many reasons. The demonstration plan on the small motors was also removed according to the discussion with the DOE program manager. All research activities were focused on the (Cu,Al)/CNT material development and wire extrusion. Existing methods to fabricate Metal/CNTs were usually suffering from agglomeration of CNTs due to their density and stiffness differences. A new method is studied by the UCF research team, where CNTs are surface treated firstly, then coated with pure metals (i.e., Al, Cu, and Nickle). The metal encapsulation on CNT is expected to significantly improve the interfacial bonding between CNTs and the intimated metal matrices. The coated CNT powders were used to make sample materials through sintering, then a customized wire extrusion process was employed to fabricate wires. Measurement of material property improvements in mechanical strength, thermal conductivity, and electrical conductivity were conducted on both cylinder samples and extruded wires. In addition to the sintering process, casting on metal coated CNT powder was also investigated. The best results we achieved are summarized as follows. (1) The measured thermal conductivity of Al/CNT composite made with Ni-encapsulated CNTs and pure Al powders is about 85% better than that of pure aluminum fabricated. The measured electrical conductivity of fabricated Al/CNT is about 14-20% better than that of pure aluminum. (2) The measured electrical conductivity of Cu/CNT is about 14.5% better than that of pure copper fabricated. (3) The mechanical strengths of both Cu/CNT and Al/CNT (with about 1% wt. CNTs) are 70% better than pure metals although losing some material ductility. (4) Two-stage wire extrusion at high temperatures were designed and successfully conducted to fabricate wires of Metal/CNTs.
Results of FY 2023 Alloy 617 and Alloy 709 High-Temperature Crack-Growth Testing
This report summarizes the work performed at Idaho National Laboratory under the “Creep, fatigue and creep-fatigue crack growth tests” task of the “Long-Term VHTR Material Qualification – INL” work package. Work was performed this year to validate the crack growth monitoring setup used with the test frames against both continuous crack length monitoring using an optical camera, as well as post-mortem analysis of marker bands on the fracture surface. Delays prevented the use of a gauge to measure load-line displacement for early tests, and so the creep-fatigue crack growth setup was evaluated using the actuator displacement for a load-line displacement setup. While not ideal, this allowed examination of the shortcomings with the current software setup that was originally designed for performing stress corrosion crack growth rate studies. The method for data collection was modified to link the crack growth monitoring software with Instron’s Wave Matrix software. Once the load-line displacement gauge arrived, the crack growth equipment was successfully modified to permit continuous monitoring of both load-line displacement and crack length. This is critical for creep-fatigue and creep crack growth rate studies for ductile material, as it permits the C* and Ct analyses. Test results are shown for Alloy 617 fatigue and creep-fatigue (without the gauge for load-line displacement measurements), as well as creep-fatigue of Alloy 709, which was performed with the completed test setup, allowing for crack length and load-line displacement monitoring.
Final report on assessment of molten salt corrosion testing of unirradiated and ion irradiated advanced manufactured high entropy alloys
Generation IV reactors and future fusion reactor designs have led to more demanding materials performance requirements due to their increased operating temperatures, corrosive coolants, and increased radiation doses compared to the current light-water reactor fleet. Among the innovative nuclear technologies under development, molten salt reactors stand out for their potential to offer superior fuel utilization, intrinsic safety characteristics, and economic viability. Of the proposed Generation IV designs, the gas fast reactor operates at 450 to 850°C and the molten salt reactor operates at 565 to 850°C, with the molten salt reactor design needing molten salt corrosion resistant materials [1, 2]. These increased temperatures and more extreme corrosion environments necessitate higher material performance, such as creep strength, radiation-tolerant microstructures, corrosion resistance, and high-temperature tensile properties. Hastelloy-N, a nickel-based alloy with additions of molybdenum and chromium, has been successfully employed to contain molten fluoride salt at temperatures up to 705°C. However, Hastelloy-N becomes embrittled upon neutron irradiation, primarily due to the accumulation of helium produced by (n,a) transmutation reactions. Furthermore, the corrosive nature of molten fluoride and chloride salts presents a formidable challenge, as these salts can react with and dissolve alloying elements such as Cr, Mo, and Fe, leading to selective leaching, loss of protective oxide layers, and accelerated degradation. High entropy alloys (HEAs) and refractory high entropy alloys (RHEAs) have emerged as a prominent area of interest, due to their ability to achieve tailored chemical compositions for specific applications. Unlike conventional alloys, HEAs are characterized by having multiple principal elements in equimolar or near equimolar ratios, leading to an unconventional alloying strategy [3]. This alloying strategy is believed to promote unique properties, such as single-phase stabilization of chemically compatible elements, lattice distortion effects due to atomic radius differences, and proposed sluggish diffusion effects. For extreme-environment applications, RHEAs have garnered much research interest because of the possibility of creating relatively ductile materials that can operate in extremely high-temperature environments, beyond the operating temperatures where other Ni-based superalloys begin to lose strength [4-6]. Idaho National Laboratory (INL) initiated a joint international effort with the Czech Republic to explore the feasibility of manufacturing HEAs for high-temperature nuclear applications using advanced manufacturing. This effort was funded at INL by the United States Department of Energy's Office of Nuclear Energy under the Advanced Reactor Technologies and Advanced Materials and Manufacturing Technologies (AMMT) Program. The HEAs were specifically designed for the corrosive and irradiation environments experienced in gas-cooled fast reactors, molten salt reactors, and fusion power. These alloys have been manufactured by multiple processes to determine the impact of manufacturing processes on the performance of the alloys in corrosive and irradiation environments. Preliminary molten salt corrosion testing showed that equimolar MoNbTiV and MoNbTi alloys exhibit exceptional performance, with arc-melted variants demonstrating only minimal degradation after 1000 hours of exposure to molten chloride salt at 700°C. Conversely, Nb2TiVZr2 showed significant molten salt corrosion susceptibility and microstructural instability during high-temperature molten salt exposures, and was, therefore deemed unfit for molten salt reactor applications. The MoNbTiV, MoNbTi, and Nb2TiVZr2 alloys were further evaluated through ion irradiation experiments conducted at the Michigan Ion Beam Laboratory at the University of Michigan. The microstructural stability and the evolution of irradiation-induced defects were characterized to assess the irradiation resistance of each of these alloys.
Unveiling the Fatigue Behavior of 2D Hybrid Organic–Inorganic Perovskites: Insights for Long-Term Durability
2D hybrid organic–inorganic perovskites (HOIPs) are commonly found under subcritical cyclic stresses and suffer from fatigue issues during device operation. However, their fatigue properties remain unknown. Here, the fatigue behavior of (C 4 H 9 -NH 3 ) 2 (CH 3 NH 3 ) 2 Pb 3 I 10 , the archetype 2D HOIP, is systematically investigated by atomic force microscopy (AFM). It is found that 2D HOIPs are much more fatigue resilient than polymers and can survive over 1 billion cycles. 2D HOIPs tend to exhibit brittle failure at high mean stress levels, but behave as ductile materials at low mean stress levels. These results suggest the presence of a plastic deformation mechanism in these ionic 2D HOIPs at low mean stress levels, which may contribute to the long fatigue lifetime, but is inhibited at higher mean stresses. The stiffness and strength of 2D HOIPs are gradually weakened under subcritical loading, potentially as a result of stress-induced defect nucleation and accumulation. The cyclic loading component can further accelerate this process. The fatigue lifetime of 2D HOIPs can be extended by reducing the mean stress, stress amplitude, or increasing the thickness. These results can provide indispensable insights into designing and engineering 2D HOIPs and other hybrid organic–inorganic materials for long-term mechanical durability.
Tuning the Mechanical Properties of Crosslinked Copolymers via Sequence and Solvent‐Selective Swelling for Vat Photopolymerization
Block copolymers (BCPs) offer distinct advantages for vat photopolymerization by enabling mechanically programmable network structures through microphase-separated morphologies that can be kinetically trapped during curing, yielding properties unattainable in homogeneous resins. However, the respective roles of repeat-unit sequence and solvent environment, together with their interplay in directing network formation and mechanical performance, remain unclear. Here, we synthesize a series of CO 2 -based polycarbonate copolymers comprising a crosslinkable glassy poly(vinyl cyclohexene carbonate) (PVCHC, A block) and a non-crosslinkable soft poly(propylene carbonate) (PPC, B block). The polymer sequence is systematically varied (ABA, BAB, and statistical), and solvent choice controls block-selective swelling to jointly control gelation behavior, microphase morphology, and mechanical response through changes in the accessibility and local environment of photocrosslinkable vinyl groups during network formation, as revealed by photorheology and small angle x-ray scattering. By tuning polymer sequence and curing solvent, we transform nominally identical formulations from brittle to highly ductile materials, achieving a three-orders-of-magnitude range in toughness (0.003 to 9.1 MJ m −3 ). These results establish clear structure–processing–property relationships and identify polymer sequence and selective solvation as powerful strategies for programming both printability and performance of block copolymer resins for additive manufacturing.
Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture
ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.