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Dynamic fracture of glass fiber-reinforced ductile polymer matrix composites and loading rate effect
Here, the dynamic fracture of S-2 glass fiber-reinforced polymer matrix composites (FRPMCs) was investigated in this study. The matrix ductility was improved by a recently developed network topology modification technique via mixing partially reacted substructures (mPRS). The composite material was manufactured and characterized by micro-CT scanning and scanning electron microscopy (SEM). Dynamic single-edge notched bending (d-SENB) experiments were performed on the composites by using a modified split-Hopkinson pressure bar. Each specimen’s fracture process was visualized by ultrafast X-ray imaging. Such in-situ radiography enabled identifying the damage initiation below 50-micron scale and inspecting its propagation through the internal structures of opaque composites, thereby accurately quantifying the composites’ mechanical properties. Furthermore, the identical d-SENB experiments were designed and the digital image correlation (DIC) was employed to monitor the stress wave propagation on the composite specimens. The force and deflection measurements were modified and correlated to the physical damage processes. Besides, quasi-static SENB experiments were conducted to identify the loading rate effects on the composites’ fracture behaviors. The force and deflection history, bending stiffness, energy dissipation, and fracture toughness at different loading rates were quantified and compared. Finally, post-fracture analysis by micro-CT scanning and SEM provided physical observations on the variation of the fracture morphology by different loading rates.
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.
Dynamic fracture processes in hydrogen embrittled iron
Mechanistic understanding of hydrogen embrittlement is critical to the transport and storage of hydrogen as a sustainable fuel. Experimental observation of dynamic fracture processes in hydrogen environments has been challenging. Here, in-situ transmission X-ray microscopy is used to image polycrystalline iron foils that are concurrently strained and electrochemically charged with hydrogen. Using this technique, voids and microcracks down to ∼30 nm in size are identified at or near the crack tip and tracked as strain is increased. We observe both hydrogen-induced transgranular failure and hydrogen-induced intergranular failure with distinct fracture processes. We find that transgranular fracture occurs through the formation of sharp branched structures at the main crack tip that are reminiscent of slip band formation. This is followed by void growth and coalescence, and interaction with secondary cracks that lead to propagation of the main crack. Intergranular fracture is found to occur through void coalescence along grain boundaries, along with significant secondary cracking near the crack tip. The crack growth rate is greater for void-mediated intergranular failure than for slip-mediated transgranular failure. Additionally, the removal of hydrogen results in recovered ductility for a crack initially propagated under hydrogen charging.
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.
Assessment of Dynamic Fracture in Ultra-High Performance Concrete Using Synchrotron X-ray Source
Ultra-high-performance concretes (UHPCs) retain higher ultimate (compressive) strengths and greater durability relative to traditional concrete materials. As a result, they are enabling construction materials for blast resistant structures, where a higher capacity for energy absorption is required. In past investigations, the strength of UHPCs was shown to retain a dependency on strain rate. Still, the failure mechanisms which govern this rate dependency have yet to be completely elucidated. In the current study, the dynamic fracture behavior of Cor-tuf UHPC was assessed, in-situ, using a Synchrotron X-ray source in phase contrast imaging (PCI) mode. Prior to testing, the material’s morphology was characterized using X-ray computed tomography (CT) and scanning electron microscopy (SEM). A polychromatic pulsed X-ray source, high-speed camera and Kolsky bar apparatus were used in tandem, to observe the transient failure modes. A pin was placed at the end of the incident bar to control the location of damage initiation, and tests were performed at a constant velocity of ~6 m/s. These test conditions were observed to yield cracks with median and/or cone like geometries. Despite the variation in the crack paths, a significant difference in peak load was not observed. The failure mode was also observed to depend on the microstructure of the concrete samples.
Morphological Heterogeneity Impact of Film Solid-State Cathode on Utilization and Fracture Dynamics
Structural heterogeneity in solid-state batteries can impact material utilization and fracture mechanisms. Crystallographically oriented lithium cobalt oxide film cathodes serve as a model electrode system for exploring how void distribution contributes to stress relief and build up during cycling. Real- and reciprocal-space operando and ex situ synchrotron based experiments are utilized to understand structural changes across multiple length scales contribute to stress generation and fracture. Nanotomography uncovers a depth-dependent porosity variation in the pristine electrode and highlights preferential fracture in regions of lower porosity during delithiation. Energy-dispersive X-ray diffraction and 3D X-ray absorption near-edge spectroscopy (XANES) reveal the underutilization of cathode material in these regions. 3D XANES also confirms preferential delithiation near the sub-grain boundaries. Chemo-mechanical modeling coupled with site-specific mechanical characterization demonstrate how stress accumulation in dense regions of the electrode leads to fracture and underutilization of active material. In conclusion, our findings reveal the importance of materials design to alleviate stress in small-volume changing cathodes.
Real-Time Monitoring of Fracture Dynamics with a Contrast Agent-Assisted Electromagnetic Method
In collaboration with the Advanced Energy Consortium, our team has previously demonstrated that the placement of electrically active proppants (EAPs) in a hydraulic fracture surveyed by electromagnetic (EM) methods can enhance the imaging of the stimulated reservoir volumes during hydraulic fracturing. That work culminated in constructing a well-characterized EAP-filled fracture anomaly at the Devine field pilot site (DFPS). In subsequent laboratory studies, we observed that the electrical conductivity of our EAP correlates with changes in pressure, salinity, and flow. Thus, we postulated that the EAP could be used as an in-situ sensor for the remote monitoring of these changes in previously EAP-filled fractures. This paper presents our latest field data from the DFPS to demonstrate such correlations at an intermediate pilot scale. We conducted surface-based EM surveys during freshwater (200 ppm) and saltwater (2,500 ppm) slug injections while running surfaced-based EM surveys. Simultaneously, we measured the following: 1) bottomhole pressure and salinity in five monitoring wells; 2) injection rate using high-precision data loggers; 3) distributed acoustic sensors in four monitoring wells; and 4) tiltmeter data on the survey area. We demonstrated that injections into an EAP-filled fracture could be successfully coupled with real-time electric field measurements on the surface, leading to remote monitoring of dynamic changes within the EAP-filled fracture. Furthermore, by comparing the electrical field traces with the bottomhole pressure, flow rate, and salinity, we concluded that the observed electric field in our study is influenced by fracture dilation and flow rate. Salinity effect was observed when saltwater was injected. EM simulations solely based on assumptions of fracture conductivity changes during injection did not reproduce all of the measured electric field magnitudes. Preliminary estimates showed that including streaming potential in our geophysical model may be needed to reduce the simulation mismatch. The methods developed and demonstrated during this study will lead to a better understanding of the extent of fracture networks, formation stress states, fluid leakoff and invasion, characterizations of engineered fracture systems, and other applications where monitoring subsurface flow tracking is deemed important.
Observation and Modeling of Dynamic Fracture Behaviors of Battery Cell Under Impact Loading Using Enhanced Representative Volume Element Concept
The burgeoning electric automobile industry has increased interest in battery safety. Battery cells experience significant mechanical stress during operation, including the impact of accidents and vibrations from driving. The potential for thermal runaway reactions in battery cells raises safety concerns. Although numerous researchers have defined the dynamic behavior of battery cells and proposed numerical models to describe it, few studies have focused on the high-strain rate mechanical impact phase correlated with the onset of fracture. In this study, we describe the dynamic behavior of pouch battery cells and propose a modeling method to study their mechanical failure under impact situations. Impact tests are conducted at various velocities and heights. To overcome numerical issues commonly encountered under rapid deformation scenarios, a new finite element model is developed based on the representative volume element model. The proposed approach efficiently simulates continuous crack propagation and brittleness behavior during impact by permitting the individual behavior of the cell components. Therefore, engineers can reliably design safer electric vehicle battery cells by measuring the properties of the cell components.
Phase-field modeling and experiments of dynamic fracture in single crystal quartz
Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in α-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. In conclusion, the fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal α-quartz.
Artificial neural network potentials for mechanics and fracture dynamics of two-dimensional crystals **
Understanding the mechanics and failure of materials at the nanoscale is critical for their engineering and applications. The accurate atomistic modeling of brittle failure with crack propagation in covalent crystals requires a quantum mechanics-based description of individual bond-breaking events. Artificial neural network potentials (NNPs) have emerged to overcome the traditional, physics-based modeling tradeoff between accuracy and accessible time and length scales. Previous studies have shown successful applications of NNPs for describing the structure and dynamics of molecular systems and amorphous or liquid phases of materials. However, their application to deformation and failure processes in materials is still uncommon. In this study, we discuss the apparent limitations of NNPs for the description of deformation and fracture under loadings and propose a way to generate and select training data for their employment in simulations of deformation and fracture simulations of crystals. We applied the proposed approach to 2D crystalline graphene, utilizing the density-functional tight-binding method for more efficient and extensive data generation in place of density functional theory. Then, we explored how the data selection affects the accuracy of the developed artificial NNPs. It revealed that NNP’s reliability should not only be measured based on the total energy and atomic force comparisons for reference structures but also utilize comparisons for physical properties, e.g. stress–strain curves and geometric deformation. In sharp contrast to popular reactive bond order potentials, our optimized NNP predicts straight crack propagation in graphene along both armchair and zigzag (ZZ) lattice directions, as well as higher fracture toughness of ZZ edge direction. Our study provides significant insight into crack propagation mechanisms on atomic scales and highlights strategies for NNP developments of broader materials.
Fracture Dynamics in Silicon Anode Solid-State Batteries
Solid-state batteries (SSBs) with silicon anodes could enable improved safety and energy density compared to lithium-ion batteries. However, degradation arising from the massive volumetric changes of silicon anodes during cycling is not well understood in solid-state systems. Here, we use operando X-ray computed microtomography to reveal micro- to macro-scale chemo-mechanical degradation processes of silicon anodes in SSBs. Mud-type channel cracks driven by biaxial tensile stress form across the electrode during delithiation. We also find detrimental cracks at the silicon/ solid electrolyte interface that form due to local reaction competition between neighboring domains of different sizes. Continuum phase-field damage modeling quantifies stress-driven channel cracking and shows that the lithiated silicon stress state is critical for determining the extent of interfacial fracture. This work reveals the mechanisms that govern SSBs compared to conventional lithium-ion batteries and provides guidelines for engineering chemomechanically resilient electrodes for high-energy batteries.
Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems
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An implementation of the phase-field model based on coupled thermomechanical finite element solvers for large-strain twinning, explicit dynamic fracture and the classical Stefan problem
The implementation of a phase-field model in finite elements usually requires significant expertise and involves the development of a user element with additional degrees of freedom. An alternative implementation of the phase-field model within a thermo-mechanical finite element simulation package was presented in (Cho et al 2012 Int. J. Solids Struct. 49 1973–1992), where the phase-field variable is treated as the temperature degree of freedom. However, this approach has only been used for small strain phase-field modelling of martensitic transformations and quasistatic phase-field modelling of fracture. Here, we present a phase-field finite element implementation via the temperature degree of freedom for several additional cases from the literature: (i) the large-strain phase-field description of deformation twinning presented in (Clayton and Knap 2011 Physica D 240 841–858), (ii) phase-field description of brittle fracture with inertial effects based on the theory from (Molnár and Gravouil 2017, Finite Elem. Anal. Des. 130 27–38) and (Miehe et al 2010 Int. J. Numer. Methods Eng. 83 1273–1311) and (iii) the classical Stefan problem of solidification presented in (Mackenzie and Robertson 2002 J. Comput. Phys. 181 526–544). The last problem involves the temperature and phase-field variables as unknowns.
Predicting Pervasive Dynamic Fracture of PMMA Under Compressive Loadings - Response to CFRAC 2025 Fracture Benchmark
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Dynamic Fracture Network Evolution: Monitoring and Characterizing using a Geomechanically Constrained Time-Lapsed Windowed Microseismic Imaging
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