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DOE OSTI2025

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.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Effects of HFIR neutron irradiation on fracture toughness properties of standard and Ni-doped F82H

F82H is the Japanese reference reduced-activation ferritic-martensitic (RAFM) steel for fusion blanket applications. The harsh environment of a fusion reactor, such as neutron irradiation and He/H damage, can result in significant degradation of F82H fracture toughness. Therefore, understanding the fracture toughness behavior of F82H in the fusion environment is critical to ensure the long-term safe operation of the fusion reactor. Here, we summarize seven irradiation campaigns of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) covering five variants of F82H steels, including F82H IEA, F82H Mod3, F82H doped with 1.4% natural Ni, F82H doped with 1.4% 58 Ni, and F82H doped with 1.4% 60 Ni. The irradiation temperatures covered the range from 220 °C to 530 °C and the neutron irradiation dose spanned 4 dpa to 70 dpa. The effects of neutron irradiation temperature, dose, materials composition, Ni doping, and He production on F82H fracture toughness are discussed. Our results showed that irradiation embrittlement monotonically decreased with increasing irradiation temperature until 400 °C for F82H IEA and F82H Mod3. F82H Mod3 showed better fracture toughness than F82H IEA both before and after neutron irradiation. We determined that 1.4% Ni alloying can be applied to F82H for simulating He effect in a fission reactor without jeopardizing the fracture toughness of the material. However, more studies are needed to understand the effect of high dose (>20 dpa) and He production on F82H fracture toughness.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Intrinsic and extrinsic effects on the fracture toughness of ductile metallic glasses

The potential application of metallic glasses (MGs) as structural materials demands accurate measurements of their toughness and the understanding of the underlying factors affecting it. Currently, it is challenging to precisely measure the toughness of MGs, especially ductile MGs. Measured toughness values are widely scattered, even for MGs with identical compositions. That is attributed to the combined effect of intrinsic and extrinsic factors including processing, sample geometries, and loading conditions. A fundamental understanding of the influences of these elements is thus of great significance. In the present study, molecular dynamics simulations are performed to investigate the influence of intrinsic and extrinsic effects on the fracture toughness of CuZr MGs. In particular, focused is placed on the effects of cooling rate, notch shape and size, strain rate, and temperature. The results indicate that the fracture toughness of a MG scales with the cooling rate used to prepare it. This is attributed to increased free volume content generated at high cooling rates, which enhances plastic deformation and amplifies the associated energy dissipation during plastic deformation events. Fracture toughness also increases with the strain rate, arguably due to strain rate-induced crack extension delay. Overall, the results demonstrate that the largest fracture toughness are achieved when MG samples are fabricated at high cooling rates and subjected to high strain rate deformation. In addition, results suggest that the fracture toughness decreases with increasing temperature, due to the significant decrease in strength. Here, the correlations revealed between these crucial intrinsic and extrinsic parameters and the calculated MG fracture toughness support the development of a framework to understand the root of the discrepancies in the measurement of the toughness of MGs and provide insights into the design of tough MGs for structural applications.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Investigation of Coupled Processes in Fractures and the Bordering Matrix via a Micro‐Continuum Reactive Transport Model

Abstract In multi‐mineral fractured rocks, the altered porous layer on the fracture surface resulting from preferential dissolution of the fast‐reacting minerals can have profound impacts on subsequent chemical‐physical alteration of the fractures. This study adopts the micro‐continuum approach to provide further understanding of reactive transport processes in the altered layer (AL), and mass exchanges with the bordering matrix and fracture. The modeling framework couples the Darcy‐Brinkman‐Stokes (DBS) solver in COMSOL Multiphysics and the geochemical modeling capability of CrunchFlow. Three‐dimensional steady state simulations with systematically varied chemical‐physical parameters of the AL were performed to examine the impacts of individual factors and processes. Our simulation results confirm previous observations that dissolution of the fast‐reacting mineral (i.e., calcite) is largely controlled by diffusion across the AL. We also show that dissolution of the slow‐reacting mineral (i.e., dolomite), which controls AL development and fracture enlargement, increases with surface area and has a complex dependence on different local rate‐limiting processes. In particular, advection can result in evident spatial variations in the local dissolution rates of dolomite, although it does not affect the bulk chemistry significantly. The difference in the spatial patterns between simulations with and without advection in the AL is more noticeable in the locations with smaller apertures, with up to 20% difference in local reaction rates. Therefore, it is important to include a full depiction of advection, diffusion, and reactions for accurately capturing local dynamics that control long‐term fracture evolution.

58 GEOSCIENCES↗

DOE OSTI2024

Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress

Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.

58 GEOSCIENCES↗

DOE OSTI2020

Transient flow modeling in fractured media using graphs

In this work, we describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the O(10 4 ) speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

58 GEOSCIENCES↗

DOE OSTI2022

Adhesively-bonded Metal-CFRTP Bi-materials: Enhanced Crack Growth Resistance via Plasma and Quantified Fracture via Size Effect Method

This work investigated air plasma effect on the Mode I crack growth resistance of adhesively-bonded metal-CFRTP dissimilar joints by using aluminum alloy (AA6061) and short-carbon-fiber-reinforced polyamide 66 (CFRPA66) as an example, and the Double Cantilever Beam (DCB) fracture testing as an evaluation method. The results show that air plasma treatment can significantly improve the fracture resistance of adhesively-bonded AA6061-CFRPA66 dissimilar joints with about 140% enhanced Mode I fracture energy in maximum compared to non-treated ones. The quantified fracture energies from size effect method for both non-treated and plasma-treated cases are geometry-independent, whereas this is not true for modified beam theory causing geometry-dependent results. The foregoing improvement was confirmed from the failure surface morphology of plasma-treated specimens, showing fibers peeling off from CFRPA66 surface due to plasma-enhanced bonding between CFRPA66 and adhesive by the formation of covalent bonds at their interface. This study demonstrated air plasma as an efficient surface modification method to enhance the fracture resistance of adhesively-bonded metal-CFRTP dissimilar joints, and size effect method as a characterization method to properly quantify their fracture properties. These aspects are valuable in the area of multi-materials joining.

Plasma, Adhesive Bonding, Slow Crack Growth, fract↗

DOE OSTI2020

Value-of-Information Analysis of a Fracture Prediction Method

A core-based fracture prediction method is used to illustrate a Value of Information (VOI) decision-analysis protocol to inform completion decisions in tight-gas sandstones. The ratio of late host-rock cement to available pore volume or degradation index uses petrographic observations of cement distributions in core (including sidewall cores) to predict whether nearby but unsampled fractures (widths > 0.5 to 1 mm) are sealed (non-conductive) or open (conductive). Measurements from four sandstone plays suggest that the index correctly predicts open vs. sealed fractures with an accuracy in excess of 80%. The value added is calculated using Bayesian inference in which accuracy of the index serves as the likelihood of the prior distribution of open fractures to assess the posterior probability that data represent a useful predictor of producibility. VOI of the prediction method is more than three times the cost to acquire the data. VOI is most sensitive to play-specific geologic and cost parameters including cost to drill, expected revenue from a successful well, cost of completion, cost of acquiring data for the index, and fracture probability distributions. The approach provides a way to value acquiring fracture data and points to a need for zone-specific production data in tight-gas sandstones.

02 PETROLEUM↗

DOE OSTI2025

Geochemical Impact of Acid Spearhead and Slickwater Stimulation on Wolfcamp Shale from the Hydraulic Fracturing Test Site

The Hydraulic Fracturing Test Site 1 (HFTS-1) was a field study performed in the Wolfcamp Formation in the West Texas Permian (Midland) Basin, USA, with a focus on improving the efficiency of hydraulic fracturing. Investigating site-specific rock-fluid geochemical interactions during hydraulic fracturing is an important step to understanding the impact on formation shale porosity, permeability, and long-term shale gas production. During field operations in this region, hydraulic fracturing fluid (HFF) injection usually starts with a concentrated acid spearhead for rapid rock dissolution, followed by the injection of near-neutral pH slickwater containing chemicals and proppants. A multistep sequential injection approach was used to investigate different stages of rock-fluid interactions. The carbonate content in the host rock is important when acid spearhead is considered, as carbonate mineral dissolution is rapid and can result in porosity and permeability changes in the shale matrix. Here, in this study, we designed flow-through experiments using fractured carbonate-rich and clay-rich Wolfcamp shale cores with (1) a short-time acid soaking step and (2) a long-term slickwater flow-through step to simulate the injection method used at HFTS-1. The fluid chemistry was analyzed. A thorough mineralogical progression [e.g., Calcium (Ca) dissolution and iron (Fe) redox progression] in the cores during HFF injection was also characterized and imaged by synchrotron microprobe. Reactive transport modeling was performed based on the experimental setup. The results showed that the acid spearhead is a crucial step in creating a reaction front by mineral dissolution, especially in carbonate-rich shales. A slight layer of ferrihydrite precipitated during the slickwater flow-through period. This study provides insights into potential geochemical impact due to hydraulic fracturing operations in the Permian Basin.

clastic rock↗

DOE OSTI2025

Fracture Network Quantification during CO2 Injection

This is the presentation prepared for the ARMA 2025 (59th US Rock Mechanics/Geomechanics Symposium) Conference held in Santa Fe, New Mexico, June 8-11, 2025. Accurate mapping and quantification of these networks are essential to ensure the integrity of CO2 storage reservoirs, understand and reduce potential leakage, and maintain long-term environmental safety. This study presents a novel machine learning-driven approach, integrated with geomechanical analysis, to quantify fracture networks and assess their spatial distribution during CO2 injection. This paper combines microseismic monitoring data with principles of hydraulic diffusivity and geomechanical analysis to characterize reservoir scale fracture network. The novelty of our approach lies in its capacity to assimilate time-dependent pressure data and microseismicity into a cohesive framework, which not only identifies microseismic triggering fronts but also tracks fracture distribution during active injection. Besides, leveraging image log data and analysis our approach also provides another angle of the insights to solidate the fracture networks understanding and geomechanical impacts. Key results from our study include the detection of over 100 distinct fracture clusters across the injection site, with fracture orientations strongly correlated with the prevailing in-situ stress field.

CO2 storage and sequestration↗

DOE OSTI2024

A multiphysics coupling framework for exascale simulation of fracture evolution in subsurface energy applications

Predicting the evolution of fractured media is challenging due to coupled thermal, hydrological, chemical and mechanical processes that occur over a broad range of spatial scales, from the microscopic pore scale to field scale. We present a software framework and scientific workflow that couples the pore scale flow and reactive transport simulator Chombo-Crunch with the field scale geomechanics solver in GEOS to simulate fracture evolution in subsurface fluid-rock systems. This new multiphysics coupling capability comprises several novel features. An HDF5 data schema for coupling fracture positions between the two codes is employed and leverages the coarse resolution of the GEOS mechanics solver which limits the size of data coupled, and is, thus, not taxed by data resulting from the high resolution pore scale Chombo-Crunch solver. The coupling framework requires tracking of both before and after coarse nodal positions in GEOS as well as the resolved embedded boundary in Chombo-Crunch. We accomplished this by developing an approach to geometry generation that tracks the fracture interface between the two different methodologies. The GEOS quadrilateral mesh is converted to triangles which are organized into bins and an accessible tree structure; the nodes are then mapped to the Chombo representation using a continuous signed distance function that determines locations inside, on and outside of the fracture boundary. The GEOS positions are retained in memory on the Chombo-Crunch side of the coupling. The time stepping cadence for coupled multiphysics processes of flow, transport, reactions and mechanics is stable and demonstrates temporal reach to experimental time scales. The approach is validated by demonstration of 9 days of simulated time of a core flood experiment with fracture aperture evolution due to invasion of carbonated brine in wellbore-cement and sandstone. We also demonstrate usage of exascale computing resources by simulating a high resolution version of the validation problem on OLCF Frontier.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Simulating Fracture Sealing by Granular LCM Particles in Geothermal Drilling

Lost circulation occurs when the returned fluid is less than what is pumped into the well due to loss of fluid to pores or fractures. A lost-circulation event is a common occurrence in a geothermal well. Typical geothermal reservoirs are often under-pressured and have larger fracture apertures. A severe lost-circulation event is costly and may lead to stuck pipe, well instability, and well abandonment. One typical treatment is adding lost-circulation materials (LCMs) to seal fractures. Conventional LCMs fail to properly seal fractures because their mechanical limit is exceeded at elevated temperatures. In this paper, parametric studies in numerical simulations are conducted to better understand different thermal effects on the sealing mechanisms of LCMs. The computational fluid dynamics (CFDs) and the discrete element method (DEM) are coupled to accurately capture the true physics of sealing by granular materials. Due to computational limits, the traditional Eulerian–Eulerian approach treats solid particles as a group of continuum matter. With the advance of modern computational power, particle bridging is achievable with DEM to track individual particles by modeling their interactive forces between each other. Particle–fluid interactions can be modeled by coupling CFD algorithms. Fracture sealing capability is investigated by studying the effect of four individual properties including fluid viscosity, particle size, friction coefficient, and Young’s modulus. It is found that thermally degraded properties lead to inefficient fracture sealing.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

A New Modeling Framework for Multi-Scale Simulation of Hydraulic Fracturing and Production from Unconventional Reservoirs

This paper describes a new modeling framework for microscopic to reservoir-scale simulations of hydraulic fracturing and production. The approach builds upon a fusion of two existing high-performance simulators for reservoir-scale behavior: the GEOS code for hydromechanical evolution during stimulation and the TOUGH+ code for multi-phase flow during production. The reservoir-scale simulations are informed by experimental and modeling studies at the laboratory scale to incorporate important micro-scale mechanical processes and chemical reactions occurring within the fractures, the shale matrix, and at the fracture-fluid interfaces. These processes include, among others, changes in stimulated fracture permeability as a result of proppant behavior rearrangement or embedment, or mineral scale precipitation within pores and microfractures, at µm to cm scales. In our new modeling framework, such micro-scale testing and modeling provides upscaled hydromechanical parameters for the reservoir scale models. We are currently testing the new modeling framework using field data and core samples from the Hydraulic Fracturing Field Test (HFTS), a recent field-based joint research experiment with intense monitoring of hydraulic fracturing and shale production in the Wolfcamp Formation in the Permian Basin (USA). Below, we present our approach coupling the reservoir simulators GEOS and TOUGH+ informed by upscaled parameters from micro-scale experiments and modeling. We provide a brief overview of the HFTS and the available field data, and then discuss the ongoing application of our new workflow to the HFTS data set.

58 GEOSCIENCES↗

DOE OSTI2025

Fracture Network Quantification during CO2 Injection

This is the conference paper accompanying an oral presentation at the ARMA 2025 (59th US Rock Mechanics/Geomechanics Symposium) Conference held in Santa Fe, New Mexico, June 8-11, 2025. Accurate mapping and quantification of these networks are essential to ensure the integrity of CO2 storage reservoirs, understand and reduce potential leakage, and maintain long-term environmental safety. This study presents a novel machine learning-driven approach, integrated with geomechanical analysis, to quantify fracture networks and assess their spatial distribution during CO2 injection. This paper combines microseismic monitoring data with principles of hydraulic diffusivity and geomechanical analysis to characterize reservoir scale fracture network. The novelty of our approach lies in its capacity to assimilate time-dependent pressure data and microseismicity into a cohesive framework, which not only identifies microseismic triggering fronts but also tracks fracture distribution during active injection. Besides, leveraging image log data and analysis our approach also provides another angle of the insights to solidate the fracture networks understanding and geomechanical impacts. Key results from our study include the detection of over 100 distinct fracture clusters across the injection site, with fracture orientations strongly correlated with the prevailing in-situ stress field.

CO2 storage and sequestration↗

DOE OSTI2022

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗

DOE OSTI2021

Characterizing Reactive Transport Behavior in a Three-Dimensional Discrete Fracture Network

While several studies have linked network and in-fracture scale properties to conservative transport behavior in subsurface fractured media, studies on reactive transport cases remain relatively underdeveloped. In this study, we explore the behavior of an irreversible kinetic reaction during the interaction of two solute plumes, one consisting of species A and the other species B. When the plumes converge, these species react kinetically to form a new species C via A+B→kC. This reactive system is studied using a three-dimensional discrete fracture network (DFN) model coupled with reactive Lagrangian particle tracking. We find that the interplay of network topology and chemical properties of the reactive solutes controls reactive transport processes. The network topology drives species A and B together, and the chemical properties dictate whether and how quickly a reaction occurs. Results demonstrate that reactions are most likely to occur in high-velocity fractures that make up the network backbone. The interplay between species’ chemical properties and transport is characterized by a non-dimensional Damköhler (Da) number. We show that the spatial distribution of reactions is sensitive to Da, which subsequently influences late-time tailing behavior in outlet breakthrough time distributions. The results of this study provide initial insights into how an irreversible reaction occurs during transport in a fracture network, using a methodology that can be applied to study reactive transport in a wide range of fractured media environments and contexts.

58 GEOSCIENCES↗

DOE OSTI2020

Grain Boundary and Lattice Fracture Toughness of UO 2 Measured Using Small-Scale Mechanics

Small-scale mechanical testing has been used to isolate the properties of individual grain boundaries and regions of the lattice in undoped UO 2 polycrystals. Notched microcantilever specimens were prepared by focused ion beam milling and tested in bending. Fracture toughness values were calculated from finite element analysis of the sample geometry at fracture load using the J-integral method. Lattice and grain boundary fracture toughness values of 1.17 ± 0.16 MPa m 1/2 and 1.08 ± 0.08 MPa m 1/2 , respectively, were obtained. The similarity between the lattice and grain boundary fracture toughness values is consistent with the preference for transgranular room-temperature fracture in UO 2 . The grain boundary and lattice fracture toughness values also agree well with the toughness of dense polycrystals, which suggests that microstructural-scale toughening mechanisms are limited in such samples.

36 MATERIALS SCIENCE↗