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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.
The simulation of 3D hypervelocity spallation using a hydrocode PAGOSA with FLIP+MPM
n this work, a hydrocode PAGOSA with FLIP+MPM is presented and exercised to investigate the fracture in ductile material. The merit of PAGOSA with FLIP+MPM to solve the advection problem is first illustrated by a solid piston periodically moving in a sealed tube with air. Furthermore, the ability of PAGOSA with FLIP+MPM to capture the fracture in material is shown by a simple stretching fracture in ductile material. In both of two benchmark problems, the PAGOSA results and analytical solutions are also presented for comparison. Then PAGOSA with FLIP+MPM is used to model complex spall in ductile material, which is a challenging problem in engineering applications. The convergences of PAGOSA with FLIP+MPM—based on both the mesh size and the marker density—are investigated by monitoring free surface velocity. To further show the ability of PAGOSA with FLIP+MPM to predict fracture in ductile material, the numerical results are compared with the experimental results and other published numerical results. Moreover, the effect of the spall parameter in PAGOSA with FLIP+MPM on the numerical simulation is also analyzed by investigating the free surface velocity. Finally, the effects of the peak compressive stress, the tensile strain rate, and the loading rate on the spallation are further investigated. The numerical results show that PAGOSA with FLIP+MPM can improve PAGOSA's performance when applied to predicting fracture in ductile materials, and is robust enough to accurately predict spall fracture in ductile materials.
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.
High Throughput Coefficient Thermal Expansion Testing Utilizing Digital Image Correlation
Dr. Fitzgerald, a postdoc at Sandia National Laboratories, works in a materials of mechanics group characterizing material properties of ductile materials. Her presentation focuses specifically on increasing throughput of coefficient of thermal expansion (CTE) measurements with the use of optical strain measurements, called digital image correlation (DIC). Currently, the coefficient of thermal expansion is found through a time intensive process called dilatometry. There are multiple types of dilatometers. One type, a double push rod mechanical dilatometer, uses and LVDT to measure the expansion of a specimen in one direction. It uses a reference material with known properties to determine the CTE of the specimen in question. Testing about 500 samples using the double push rod mechanical dilatometer would take about 2 years if testing Monday through Friday, because the reference material needs to be at a constant temperature and heating must done slowly to ensure no thermal gradients across the rod. A second type, scissors type dilatometer, pinches a sample using a “scissor-like” appendage that also uses a LVDT to measure thermal expansion as the sample is heated. Finally, laser dilatometry, was created to provide a non-contact means to measure thermal expansion. This process greatly reduces the time required to setup a measurement but is still only able to measure one sample at a time. The time required to test 500 samples gets reduced to 3.5 weeks. Additionally, to measure expansion in different directions, multiple lasers must be used. Dr. Fitzgerald solved this conundrum by using an optical measurement technique called digital image correlation to create strain maps in multiple orientations as well as measuring multiple samples at once. Using this technique, Dr. Fitzgerald can test 500 samples, conservatively, in 2 days.
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.
Intergranular ductile failure of materials with plastically heterogeneous grains
In several precipitation hardened alloys that are susceptible to intergranular ductile failure, precipitation does not always occur uniformly throughout the microstructure, and regions close to grain boundaries may remain precipitate-free. These precipitate-free zones (PFZs) in the material microstructures result in plastically heterogeneous grains, since PFZs are expected to have lower yield strength but higher strain-hardenability compared to the precipitate containing grain interior. Experimentally, the presence of PFZs in precipitation-hardened alloys has been associated with both increase and decrease in materials’ ductility, with or without significant change in the strength. Thus, to understand and rationalize the experimental observations, we have carried out extensive microstructure-based finite element calculations of intergranular ductile failure in materials under tensile loading conditions. In the calculations, both the grain boundaries and PFZs are discretely modeled, and a wide range of the values of yield strength, strain-hardenability and width of PFZs in the material microstructures are analyzed. Our results show that the effects of PFZs on the overall mechanical response of the material strongly depend on the values of yield strength and strain-hardenability of PFZs. Here, there exists an optimum combination of the values of these two parameters that can result in the overall ductility and tensile strength of the material microstructures with PFZs being greater than the microstructures without PFZs.
Understanding the Elastic, Plastic, and Damage Features in Fracturing of Self-reinforced Thermoplastic Composites via Non-destructive Digital Imaging Correlation
This work demonstrated the utilization of non-destructive Digital Imaging Correlation (DIC) method to characterize the elastic, plastic, and damage features during the Mode I intra-laminar fracturing process of self-reinforced thermoplastic composites by using a self-reinforced polypropylene (PP) composite as an example. The DIC results clearly showed the development of huge plastic zone (PZ) and non-negligible Fracture Process Zone (FPZ) in front of the notch tip during the fracturing process, and the geometries and sizes of the foregoing zones at the peak load were further quantified. Such an interesting fracturing behavior of self-reinforced thermoplastic composites is way different from brittle materials (e.g., glass, acrylic, etc.), ductile materials (e.g., aluminum, steel, etc.), and even quasi-brittle materials (e.g., concrete, nanoparticle-reinforced composites, tough ceramics, wood, cement, carbon/glass fiber-reinforced polymers, etc.). Thus, understanding the elastic, plastic, and damage features is the first step before better characterizing the material fracture properties of self-reinforced thermoplastic composites through new analytical methods and computational modeling. These efforts are of utmost importance for wide applications of self-reinforced thermoplastic composites in various engineering fields in the future.
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.
Toughening materials: enhancing resistance to fracture
It has been said that ‘God invented plasticity, but the Devil invented fracture!’ Both mechanisms represent the two prime modes of structural failure, respectively, plastic collapse and the rupture/breaking of a component, but the concept of developing materials with enhanced resistance to fracture can be difficult. This is because fracture resistance invariably involves a compromise—between strength and ductility, between strength and toughness—fundamentally leading to a ‘conflict’ between nano-/micro-structural damage and the mechanisms of toughening. Here, we examine the two major classes of such toughening: (i) intrinsic toughening, which occurs ahead of a crack tip and is motivated by plasticity—this is the principal mode of fracture resistance in ductile materials, and (ii) extrinsic toughening, which occurs at, or in the wake of, a crack tip and is associated with crack-tip shielding—this is generally the sole mode of fracture resistance in brittle materials. We briefly examine how these distinct mechanistic processes have been used to toughen synthetic materials—intrinsically in gradient materials and in multiple principal-element metallic alloys with the example of metallic glasses and high-entropy alloys, and extrinsically in ceramics with the example of ceramic-matrix composites—in comparison to Nature which has been especially adept in creating biological/natural materials which are toughened by one or both mechanistic classes, despite often consisting of constituents with meagre mechanical properties. The success of Nature has been driven by its ability to cultivate the development of materials with multiple length-scale hierarchical structures that display ingenious gradients and structural adaptability, a philosophy which we need to emulate and more importantly learn to synthesize to make structural materials of the future with unprecedented combinations of mechanical properties.
Falling particle impact erosion testing for particle based CSP systems
CSP systems are currently being examined as an effective method for using solar energy to generate electricity. While much of this research has been conducted using molten salt as the heat transfer medium, in recent years, solid particles have been posited as a cheaper and more energy efficient heat transfer medium for use in CSP systems. Many researchers have looked into the effectiveness of solid particles as a heat transfer medium. However, a concern with the use of particles is that the falling particles will impact various components within the CSP system, such as the hopper, the heat exchanger, and the insulating material, resulting in surface erosion and damage. With repeated impacts from falling particles, material from the surfaces under impact is removed. The degree of erosion depends on whether the substrate is made of brittle or ductile material. Furthermore, factors such as particle shape, size, hardness, concentration, impact angle, particle velocity, and substrate hardness will contribute to the erosion process and determine how much and how quickly erosion will takes place in a system. Three types of erosion will be observed simultaneously: impact erosion from particle impact on receiver, particle storage, and heat exchanger walls, abrasion erosion from particle sliding motion along walls, and attrition erosion as the particles breakdown from particle-to-particle contact and particle-to-wall interactions. It is imperative to understand each of these erosions individually for a more comprehensive understanding and prediction of CSP system durability. In this work, we developed an experimental test setup capable of measuring impact erosion at conditions relevant to 1MW CSP plant. Subsequently, Impact erosion measurements were performed for three different candidate substrate materials at low particle velocities using HSP 40/70 ceramic particles.