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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗
DOE OSTI2024

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗
NASA NTRS2010

Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics

The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.

Wang, John T.↗
DOE OSTI2020

Modeling the corrosion of steel casing and the damage of well cement in a borehole system

This work presents the effect of chloride-induced corrosion in an underground borehole system, specifically considering the steel casing and further damage to the surrounding cement. In the past four decades, oil well cement has been successfully used for underground construction. However, high concentrations of chloride ions gradually degrade the functionality and durability of well cement. Gasses and liquids can leak from deterioration caused by chloride ions, and thus motivate this study. The chemo-mechanical coupling diffusion model and a classical fracture mechanics model are applied. The model is validated with OPC concrete corrosion data from literature, and then applied to well cement using experimentally obtained material property data. The time when crack initiation, peak pressure, and complete fracture is reached in the model of the cement sheath provides a quantification of the expected service life of the borehole system.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗
DOE OSTI2020

Modeling Metallic Fuel using Peridynamics

Based on available modeling and simulation capabilities of peridynamics module in MOOSE framework for oxide fuel, the overall goal of this project is to further develop the peridynamics capabilities for modeling metallic fuel. It includes two major tasks: 1) develop validated scheme to handle the shape tensor singularity due to insufficient active neighbors of a material particle in the peridynamic correspondence model for fracture problems, and 2) develop failure modeling scheme including failure criterion for metallic fuels. Before the peridynamics can be applied to model metallic fuel, the formulation instability of the peridynamic correspondence model should be addressed. The PI first worked on developing new stabilization method to improve the performance of the peridynamic correspondence model and reduce the possibility of getting a singular shape tensor while applying the model for fracture problems. The new stabilization scheme uses bond-associated weight function rather than bond-associated horizon. Compared to bondassociated horizon stabilized method, this new stabilization scheme has better performance with improved prediction accuracy and reduced free surface effect. Using this newly developed stabilization, materials models from BISON can be directly used in peridynamics for metallic fuels, such as fission rate and burnup dependent creep and swell models. Publication of this work is under preparation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

A multiscale anisotropic polymer network model coupled with phase field fracture

The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. In conclusion, the results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.

42 ENGINEERING↗
DOE OSTI2022

Mechanisms for the Generation of Complex Fracture Networks: Observations From Slant Core, Analog Models, and Outcrop

We use observations of hydraulic fractures in core, outcrop attributes of natural hydraulic fractures, and analogue models, to address how hydraulic fracture networks evolve. A slant core from the Wolfcamp Formation—an unconventional shale hydrocarbon reservoir in the Permian Basin of West Texas—collected within 18 m and 30 m of two hydraulically stimulated horizontal wells, provided an opportunity to examine hydraulic fractures directly. In approximately 183 m of core, 309 calcite-sealed natural opening-mode fractures and 375 hydraulic fractures were identified. Many hydraulic fractures in the core show complex morphology, including twist-hackle segmentation, diversion, and bifurcation; these structures most commonly develop at lithological bed boundaries and mechanical heterogeneities such as natural fractures and concretions. An outcrop of bed-parallel pavements in the Cretaceous Boquillas Formation in West Texas contains opening-mode fractures that likely formed by natural hydraulic fracturing. Fracture traces provide evidence of twist-hackle segmentation, and are typically associated with bed boundaries and preexisting bed-parallel stylolites. A laboratory study of hydraulic fracturing of 33 synthetic blocks of gypsum and hydrostone revealed fracture steps, diversions, twist hackles, and multiple overlapping fractures together with information on fracture growth directions. These complexities in the fracture network were dominantly nucleated at inclusions used to simulate pre-existing fractures, and as a result of mechanical heterogeneity introduced by the wellbore and perforations. Collectively, our results show that complex fracture networks are produced in hydraulic fracturing of self-sourced reservoir strata. Mechanical stratigraphic boundaries and other heterogeneities are likely to enhance fracture network complexity through the processes of segmentation, diversion, and bifurcation. These processes create multiple fracture strands, resulting in an increased number of hydraulic fractures over those initiated, thereby increasing total fracture surface area. Our study provides insight into hydraulic fracture network propagation, and has applications for evaluation, completion, production, and fracture modeling of unconventional reservoirs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A model for discrete fracture-clay rock interaction incorporating electrostatic effects on transport

Abstract A model based on the code CrunchClay is presented for a fracture-clay matrix system that takes electrostatic effects on transport into account. The electrostatic effects on transport include those associated with the development of a diffusion potential as captured by the Nernst-Planck equation, and the formation of a diffuse layer bordering negatively charged clay particles within which partial anion exclusion occurs. The model is based on a dual continuum formulation that accounts for diffuse layer and bulk water pore space, providing a more flexible framework than is found in the classical mean electrostatic potential models. The diffuse layer model is obtained by volume averaging ion concentrations in the Poisson-Boltzmann equation, but also includes the treatment of longitudinal transport within this continuum. The calculation of transport within the bulk and diffuse layer porosity is based on a new formulation for the Nernst-Planck equation that considers averaging of diffusion coefficients and accumulation factors at grid cell interfaces. Equations for function residuals and the associated Jacobian matrix are presented such that the system of nonlinear differential-algebraic equations can be solved with Newton’s method. As an example, we consider a 2D system with a single discrete fracture within which flow and advective transport occurs that is coupled to diffusion in the clay-rich matrix. The simulation results demonstrate the lack of retardation for anions (e.g., 36 Cl − ) of the contaminant plume within the fracture flow system because they are largely excluded from the charged clay rock, while the migration of cations (e.g., 90 Sr ++ ) is more strongly attenuated. The diffusive loss of divalent cations in particular from the fracture is accentuated by their accumulation in the diffuse layer within the clay-rich matrix.

58 GEOSCIENCES↗