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At least 649 records · Page 36

Simulation of hardened cement degradation and estimation of uncertainty in predicted failure times with peridynamics

Modeling the degradation of cement-based infrastructure due to aqueous environmental conditions continues to be a challenge. In order to develop a capability to predict concrete infrastructure failure due to chemical degradation, here we created a chemomechanical model of the effects of long-term water exposure on cement paste. The model couples the mechanical static equilibrium balance with reactive–diffusive transport and incorporates fracture and failure via peridynamics (a meshless simulation method). The model includes fundamental aspects of degradation of ordinary Portland cement (OPC) paste, including the observed softening, reduced toughness, and shrinkage of the cement paste, and increased reactivity and transport with water induced degradation. This version of the model focuses on the first stage of cement paste decalcification, the dissolution of portlandite. Given unknowns in the cement paste degradation process and the cost of uncertainty quantification (UQ), we adopt a minimally complex model in two dimensions (2D) in order to perform sensitivity analysis and UQ. We calibrate the model to existing experimental data using simulations of common tests such as flexure, compression and diffusion. Then we calculate the global sensitivity and uncertainty of predicted failure times based on variation of eleven unique and fundamental material properties. We observed particularly strong sensitivities to the diffusion coefficient, the reaction rate, and the shrinkage with degradation. Also, the predicted time of first fracture is highly correlated with the time to total failure in compression, which implies fracture can indicate impending degradation induced failure; however, the distributions of the two events overlap so the lead time may be minimal. Extension of the model to include the multiple reactions that describe complete degradation, viscous relaxation, post-peak load mechanisms, and to three dimensions to explore the interactions of complex fracture patterns evoked by more realistic geometry is straightforward and ongoing.

36 MATERIALS SCIENCE↗

Modeling of fracture of protective concrete structures under impact loads

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.

36 MATERIALS SCIENCE↗

Prediction and Verification of Ductile Crack Growth from Simulated Defects in Strength Overmatched Butt Welds

Defects that develop in welds during the fabrication process are frequently manifested as embedded flaws from lack of fusion or lack of penetration. Fracture analyses of welded structures must be able to assess the effect of such defects on the structural integrity of weldments; however, the transferability of R-curves measured in laboratory specimens to defective structural welds has not been fully examined. In the current study, the fracture behavior of an overmatched butt weld containing a simulated buried, lack-of-penetration defect is studied. A specimen designed to simulate pressure vessel butt welds is considered; namely, a center crack panel specimen, of 1.25 inch by 1.25 inch cross section, loaded in tension. The stress-relieved double-V weld has a yield strength 50% higher than that of the plate material, and displays upper shelf fracture behavior at room temperature. Specimens are precracked, loaded monotonically while load-CMOD measurements are made, then stopped and heat tinted to mark the extent of ductile crack growth. These measurements are compared to predictions made using finite element analysis of the specimens using the fracture mechanics code Warp3D, which models void growth using the Gurson-Tvergaard dilitant plasticity formulation within fixed sized computational cells ahead of the crack front. Calibrating data for the finite element analyses, namely cell size and initial material porosities are obtained by matching computational predictions to experimental results from tests of welded compact tension specimens. The R-curves measured in compact tension specimens are compared to those obtained from multi-specimen weld tests, and conclusions as to the transferability of R-curves is discussed.

Nishioka, Owen S.↗

Hydro-mechanical coupled modeling of hydraulic fracturing using the mesh fragmentation technique

The inclusion of special interface elements between standard finite elements is becoming a common technique to model discontinuities in porous media using the finite element method (FEM). Recently, it was proved that high aspect ratio (HAR) elements can reproduce very satisfactorily the main features of behavior observed in a single hydraulically-induced fracture. In this paper, the mesh fragmentation technique (MFT) is proposed to extend the application of HAR elements to simulate more general problems involving the formation of hydraulic fractures in rocks by introducing this type of element in-between the standard FE of a typical mesh. The proposed framework makes use of standard FE techniques. Therefore, it is relatively easy to upgrade an existing FE program for continuous porous media to deal with evolving discontinuities. The proposed approach is verified and validated against available analytical and numerical solutions. The crack patterns predicted by the MFT are also compared with the ones observed in the laboratory. The formation of multiple fractures is also analyzed. In all cases, the proposed technique was able to properly capture the main features of rock behavior subjected to hydraulic fracturing.

58 GEOSCIENCES↗

Hardening of A6111-T4 Aluminum Alloy at Large Strains and Its Effect on Sheet Forming Operations

In a number of sheet metal stamping and joining processes, the material undergoes large plastic deformation exceeding the range of plastic strain achievable in a standard tensile test prior to material plastic instability. In order to extend the range of effective strains, the multistep rolling process was employed which enabled prestraining of aluminum sheet above 2.0 of true strain. Tensile testing of rolled samples was used to identify the flow stress corresponding to the level of prestrain: By varying the prestrain level, several data points were obtained for the studied flow curve. The numerical simulation using Abaqus software for the cold rolling process of aluminum strips confirmed that majority of the strip is deformed in plane strain compression condition. Performed simulation of the LDH test determined that earlier fracture might occur if the curve obtained via rolling–tensile testing approach is used versus traditional power law approximation and Voce law approximation. The results of simulation for the multistep drawing of a cylindrical cup revealed possible wrinkling in the die entry area during redrawing stage of the process if the rolling–tensile testing flow curve is employed.

36 MATERIALS SCIENCE↗

Geomechanical modeling of distributed fiber-optic sensor measurements

Fiber-optic-based distributed acoustic sensors (DAS) are a new technology that can be deployed in a well and are continuously interrogated during operations. These sensors calculate the strain (or strain rate) at all points along the fiber and have been used extensively to monitor hydraulic stimulations. The data from these sensors indicate that they are sensitive to high-frequency signals associated with microseismicity and low-frequency signals associated with fracture growth. We have developed a set of idealized models to simulate these signals and to identify interpretation methods that may be used to estimate fracture location, geometry, and extent. We use a multiphysics code that includes rock physics, fluid flow, and elastic-wave propagation to generate synthetic DAS measurements from a set of simple models that mimic hydraulic fracturing. We then relate the signals observed in the synthetic DAS to specific features in the model such as fracture height, width, and aperture. Our results demonstrate that the synthetic DAS measurements may be used to determine field DAS measurements and to optimize the design of future sensor deployments for sensitivity to fracture attributes.

03 NATURAL GAS↗

Development, Monitoring, and Control of Fracture Thermal Energy Storage (FTES) in Crystalline Rock Formations (DEMO-FTES) (CRADA Final Report)

The DEMO-FTES project sought to demonstrate the thermal efficiency of fracture thermal energy storage (FTES) through numerical simulations, laboratory and meso-scale field tests. A detailed dimensional and scaling analysis was performed to identify key parameters and how they can be most effectively scaled to the laboratory and decameter scale. Numerical models were developed and used for three purposes: 1. Before field experiments, numerical modelling can be used to estimate fracture properties based on previous data from the EGS Collab experiment and then predict thermal hydrological behaviors of the fracture system with hot water injection/withdrawal, therefore, help to design the experiments (e.g., to decide the duration of the cycles based on the flow rate the pump can provide, and the estimated fracture properties); 2. After the field experiment, to estimate the system properties during the experiment (as the size and shape of a fracture could change over time), and understand why system performance is different than what has been predicted, i.e., to help understand the meso-scale test; and, 3. To model the lab experiments and estimate fracture properties and storage efficiency. Ultimately, the experiment and numerical models could shed light on the processes and uncertainty happening during fracture activation and help understand the scaling between lab and field test, and finally, the design and optimization of potential fracture thermal energy storage systems.

25 ENERGY STORAGE↗

Chemical-Mechanical Modeling of Subcritical-to-Critical Fracture in Geomaterials

Predicting chemical-mechanical fracture initiation and propagation in materials is a critical problem, with broad relevance to a host of geoscience applications including subsurface storage and waste disposal, geothermal energy development, and oil and gas extraction. In this project, we have developed molecular simulation and coarse- graining techniques to obtain an atomistic-level understanding of the chemical- mechanical mechanisms that control subcritical crack propagation in materials under tension and impact the fracture toughness. We have applied these techniques to the fracture of fused quartz in vacuum, in distilled water, and in two salt solutions - 1M NaC1, 1M NaOH - that form relatively acidic and basic solutions respectively. We have also established the capability to conduct double-compression double-cleavage experiments in an environmental chamber to observe material fracture in aqueous solution. Both simulations and experiments indicate that fractures propagate fastest in NaC1 solutions, slower in distilled water, and even slower in air.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Numerical Tool for the Design of Enhanced Geothermal Reservoirs based on Modeling of Thermo-Hydro-Mechanical Processes and Explicit Representation of 3D Discrete Fracture Networks

This project has developed a coupled thermo-hydro-mechanical numerical modeling tool for prediction of energy production from Enhanced Geothermal Reservoirs (EGS). The tool is unique because it can explicitly represent thousands of pre-existing natural fractures. The capabilities developed in this project were built on the already existing expertise of Itasca arising from thirty years of research and development in discrete element modeling of fractured rocks. A thermal module suitable for analysis of different heat transfer mechanisms in fractured rocks percolated by fluids was developed and coupled with the already existing hydro-mechanical calculation in 3DEC, a commercial software for analysis of jointed rock based on the discrete element method (DEM). The heat transfer module simulates heat conduction, heat advection by moving fluid in rock fractures, and convective heat exchange at the fracture walls between the rock and the moving fluid. Techniques for spatial discretization of heat transfer in EGS-type problems were evaluated, and a boundary layer meshing approach was developed. Also, given the significant differences in time scale of physical processes involved, temporal integration schemes for coupled advection-diffusion processes and coupled thermal-hydro-mechanical processes were developed by taking advantage of both implicit and explicit time integration and also optimizing the coupling intervals. These improvements were necessary for modeling EGS reservoirs. Also, the DFN capacities in 3DEC were extended to include a larger number of fractures. Research was carried out on approaches to simplify the DFN so that the model can meet computational demands, while preserving thermo-hydro-mechanical characteristics of the DFN. The developed modules were coupled with the already existing capabilities of 3DEC. The results were presented as a submitted conference paper (Riahi et al., 2018a). A series of benchmark and test examples showed the developed capabilities. Finally, the developed tool was tested for a large-scale reservoir model for longer periods of injection and production. The thermal draw-down curves were generated and presented. The project successfully met all the milestones laid out in the proposal. Results demonstrated the feasibility of developing a fast and reliable software for the EGS community to use for assessment and prediction of reservoir performance. Some of its applications include assessment of stimulated volume and produced temperature and power. It can also be used for improved engineering, design and optimization of EGS reservoirs as well as other unconventional resources such as shale gas. Finally, the 3D analysis presented in this study showed that simulating EGS reservoirs with tens of thousands of fractures is feasible, and confirmed that the developed tool can serve toward meeting the goals and objectives of Geothermal Technologies Office in overcoming technical barriers associated with commercial EGS development.

15 GEOTHERMAL ENERGY↗

Fluid-structure interaction solver for transient dynamics of fracturing media

Computer implemented methods include providing a numerical simulation solid mesh comprising a plurality of solid nodes and a numerical simulation fluid mesh comprising a plurality of fluid nodes, and performing a numerical simulation with the solid mesh and fluid mesh including: determining a fluid-solid interaction between the fluid mesh and the solid mesh at a time step by (i) immersing boundaries of the solid and fluid meshes, (ii) computing current corrected fluid and solid velocities using an interaction parameter applied to an intermediate fluid-solid relative velocity, and (iii) computing a fluid-solid interaction force based on the current corrected fluid and solid velocities.

Rougier, Esteban↗

Creating Optimal Fracture Networks

The primary goal of this project is the development of a multi-physics, multi-scale simulation capability to predict the initiation, propagation and maintenance of hydraulically driven fracture networks in heterogeneous geologic materials. The development and validation of integrated code capability, GEOS, that accurately captures the phenomenology of these complex physical processes across a wide range of time-­ (~10 -6 to ~10 8 s) and length- (~10 -3 to ~10 4 m) scales is the main scientific objective of the proposed initiative. GEOS constitutes a new analytical framework incorporating the underlying physics that drives fracture development – e.g. dynamically changing fracture network topologies, fluid/solid interactions taking place along discrete interfaces, and complex matrix/fracture transport processes. Enhanced seismic observational tools and inversion methods will also be developed. This initiative has positioned LLNL to play a leading role in the development of Enhanced Geothermal Systems, unconventional gas energy resources, risk assessment associated with geologic sequestration of CO 2 and the detection of radioactive gases from clandestine nuclear tests, impacting both energy and national security.

02 PETROLEUM↗

Numerical study of proppant transport and settling processes in fractures

Reservoir stimulation by creating hydraulically conductive fractures is the key step for enabling enhanced geothermal systems (EGS). The effectiveness of stimulation is significantly influenced by the deposition of proppant inside induced fractures. The transportation and settling of proppant in a propagating fracture is controlled by a multitude of operational and physical parameters, including the fracturing fluid rheology, injection rate, proppant concentration, fracture length/aperture evolution, proppant size/density/shape, etc. A numerical tool that robustly and efficiently accounts for all important attributes can facilitate the design and optimization of reservoir stimulation. This study presents the novel computational tool ELK (ELectrical fracKing) developed for the numerical simulation of proppant-fluid mixture circulation in a fractured geothermal reservoir. We enriched the MOOSE-based PorousFlow module with a suite of equations to consider the fluid-proppant mixture with particle-particle/fluid interactions, which include gravitational settling, particle convection, particle hampering, and strong density and viscosity contrasts. The computational tool is validated by comparing the predicted proppant bed evolution against two different laboratory scale experiments of proppant transport in a fixed aperture channel. Further parameter studies were performed, and the modeling results show that the proppant deposition is determined by the mixing characteristics and settling of the particles from the slurry. Concentration-dependent density and viscosity lead to an inhomogeneous distribution of the proppant, particle collision, and enhanced settling at the bottom of the fractures. Preliminary coupling with dynamic fracture propagation shows promising results and will be further developed to simulate hydraulic stimulation at high fidelity.

15 GEOTHERMAL ENERGY↗

A Geo‐Structurally Based Correction Factor for Apparent Dissolution Rates in Fractured Media

Abstract Field measurements of apparent geochemical weathering reaction rates in subsurface fractured porous media are known to deviate from laboratory measurements by multiple orders of magnitude. To date, there is no geologically based explanation for this discrepancy that can be used to predict reaction rates in field systems. Proposed correction factors are typically based on ad hoc characterizations related to geochemical kinetic models. Through a series of high‐fidelity reactive transport simulations of mineral dissolution within explicit 3D discrete fracture networks, we are able to link the geo‐structural attributes with reactive transport observations. We develop a correction factor to linear transition state theory for the prediction of the apparent dissolution rate based on measurable geological properties. The modified rate law shows excellent agreement with numerical simulations, indicating that geological structure could be a primary reason for the discrepancy between laboratory and field observations of apparent dissolution rates in fractured media.

58 GEOSCIENCES↗

Three‐Phase CO 2 Flow in a Basalt Fracture Network

Abstract Geologic CO 2 sequestration in basalt reservoirs is predicated on permanent CO 2 isolation via rapid mineralization reactions. This process is supported by a substantial body of evidence, including laboratory experiments documenting rapid mineralization rates, regional storage estimates indicating large, accessible storage reservoirs, and two successful pilot‐scale studies. Nevertheless, there remains significant uncertainty in the behavior of CO 2 flow within basalt fracture networks, particularly in the context estimating physical trapping potential in early time and as CO 2 undergoes phase change. In this study, a Monte Carlo numerical model is designed to simulate a supercritical CO 2 plume infiltrating a low‐permeability flood basalt entablature. The fracture network model is based on outcrop‐scale LiDAR mapping of Columbia River Basalt, and CO 2 flow is simulated within fifty equally probable realizations of the fracture network. The spatial distribution of fracture permeability for each realization is randomly drawn from a basalt aperture distribution, and ensemble results are analyzed with e‐type estimates to compute mean and standard deviation of fluid pressure and CO 2 saturation. Results of this model after 10 years of simulation suggest that (1) CO 2 flow converges on a single dominant flow path, (2) CO 2 accumulates at fracture intersections, and (3) variability in permeability can account for a 1.6 m depth interval within which free CO 2 may change phase from supercritical fluid to subcritical liquid or gas. In the context of CO 2 sequestration in basalt, these results suggest that physical CO 2 trapping may be substantially enhanced as carbonate minerals precipitate within the basalt fracture network.

Gierzynski, Alec O.↗

Characterization of unsaturated hydraulic conductivity in fractured media using the multistep outflow method - 15461

The multistep outflow method is routinely used to characterize the unsaturated hydraulic conductivity of soils. The technique involves placing a soil sample in a pressure plate apparatus, subjecting the sample to multiple gas pressures in discrete steps through time, and measuring the transient volume of pore fluid extracted. Unsaturated hydraulic property values are estimated through inverse modeling of the experimental conditions. In this study the multistep outflow concept was applied to micro-cracked cementitious materials to assess the efficacy of the technique for these materials. The cementitious materials tested were salt-waste simulant grout samples artificially damaged through oven-drying. Compared to typical soils, fractured media exhibit higher saturated conductivity and lower air-entry pressure, and the volume of fluid extractable from fractures is much lower than soil porosity. To accommodate these material differences the standard test apparatus was modified to incorporate a higher conductivity ceramic pressure plate, a high-precision digital balance for logging outflow mass, a low volume (diameter) effluent line, multiple in-line high-precision gas regulators, and a high-precision low-range pressure gauge. Testing to date indicates that the modified apparatus can provide a viable means to measure the unsaturated hydraulic properties of micro-fractured cementitious materials. However the accuracy/uniqueness of inverse modeling is limited by the inherent characteristics of fractured media: high saturated conductivity, low air-entry pressure, and strong non-linearities. Hydraulic property results in the form of van Genuchten / Mualem curves are presented for three fractured grout specimens. DOE Performance Assessments often involve cementitious barriers and/or waste forms that are predicted or assumed to degrade over time due to various mechanisms such as carbonation-influenced reinforcing steel corrosion, external sulfate attack, differential settlement, and seismic activity. Physical degradation typically takes the form of small-scale cracking / fracturing, and the affected materials reside in unsaturated hydrogeologic zones. In these cases, unsaturated hydraulic properties are needed for fractured cementitious materials to simulate moisture movement and contaminant transport within and around the facility. The outflow extraction method, as implemented in the present study, provides a suitable method for estimating these material properties. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Development of a Modified Embedded Atom Force Field for Zirconium Nitride Using Multi-Objective Evolutionary Optimization

Zirconium nitride (ZrN) exhibits exceptional mechanical, chemical, and electrical properties, which make it attractive for a wide range of technological applications, including wear-resistant coatings, protection from corrosion, cutting/shaping tools, and nuclear breeder reactors. Despite its broad usability, an atomic scale understanding of the superior performance of ZrN, and its response to external stimuli, for example, temperature, applied strain, and so on, is not well understood. This is mainly due to the lack of interatomic potential models that accurately describe the interactions between Zr and N atoms. To address this challenge, we develop a modified embedded atom method (MEAM) interatomic potential for the Zr–N binary system by training against formation enthalpies, lattice parameters, elastic properties, and surface energies of ZrN (and, in some cases, also Zr3N4) obtained from density functional theory (DFT) calculations. The best set of MEAM parameters are determined by employing a multiobjective global optimization scheme driven by genetic algorithms. Our newly developed MEAM potential accurately reproduces structure, thermodynamics, energetic ordering of polymorphs, as well as elastic and surface properties of Zr–N compounds, in excellent agreement with DFT calculations and experiments. As a representative application, we employed molecular dynamics simulations based on this MEAM potential to investigate the atomic scale mechanisms underlying fracture of bulk and nanopillar ZrN under applied uniaxial strains, as well as the impact of strain rate on their mechanical behavior. These simulations indicate that bulk ZrN undergoes brittle fracture irrespective of the strain rate, while ZrN nanopillars show quasi-plasticity owing to amorphization at the crack front. The MEAM potential for Zr–N developed in this work is an invaluable tool to investigate atomic-scale mechanisms underlying the response of ZrN to external stimuli (e.g, temperature, pressure etc.), as well as other interesting phenomena such as precipitation.

36 MATERIALS SCIENCE↗

DECOVALEX-2023: Task A Final Report

Task A, also known as HGFrac, examines the fracturing processes that may occur in the Callovo-Oxfordian claystone (COx) in the context of the high-level (HLW) and intermediate-level long-lived (ILW-LL) radioactive waste repository in France. Understanding these processes and improving numerical models to reproduce them will aid in the design, optimization, and safety of the repository. Heat and gas fracturing are studied in two independent subtasks following a stepwise approach: laboratory tests/benchmark exercises, in-situ experiment, and finally, an application case. The in-situ heater experiment aimed to thermally induce a hydraulic fracture; temperature and pore pressure were monitored to detect any evidence of fracturing. The in-situ gas injection experiment aimed to study the effect of the stress orientation and gas injection kinetics on the gas fracturing process. The occurrence of fracturing was monitored by gas pressure measured in the injection interval. In both experiments, the excavation-induced fracture network around the heater/injection boreholes played an important role in the reduction of the compressive stress state, leading to both a tensile and shear failure response of the COx. During the first two years of the project, the research teams working on each task developed and/or proposed numerical approaches for reproducing the occurrence of fracturing in the in-situ experiments. The failure criteria were defined by reproducing the measurements from laboratory extension tests for the heat fracturing subtask. In the gas fracturing subtask, their approaches were used for simulating several benchmark exercises, and an inter-comparison between models was carried out. In both tasks, the developed approaches were compared with a simplified approach considering poro-elasticity for the mechanical behaviour of the COx. Most of the developed approaches are based on a continuous medium that takes into account variations in hydraulic properties due to mechanical degradation, such as plastic deformation or damage. Other approaches implicitly modelled weak planes or embedded discontinuities to reproduce fracture propagation. The potential for fracture initiation was also studied through of a discrete approach. In the second half of the project, the research teams mainly focused on interpretative modelling of two in-situ experiments and a blind prediction exercise to test their respective approaches. The models developed by the research teams were also applied at the repository scale to evaluate fracture initiation in a case study under vi unfavourable conditions, particularly in terms of spacing between High-Level Waste cells. The results showed that the poro-elasticity approach could be an efficient tool for understanding the main processes occurring in the COx. One example is the explicit representation of the excavation-induced fracture network around the boreholes, which yielded acceptable results compared to the measurement data. However, advanced approaches were needed to evaluate the potential increase of the excavation-induced fracture network extend and better understand fracture initiation. The stress analyses carried out by the teams revealed that hydraulic boundary conditions had a strong impact on fracture initiation in the heater experiment. Furthermore, in most cases, the results required higher pore pressure increments to reach fracturing than those measured in the experiment. This implies that the measurements may have been biased by the packer’s capacity to fully isolate the piezometric chambers, leading to lower pressures. On the contrary, there was no agreement on the fracturing mode, as some reported either shear or tensile fracturing, while others reported a combination of the two modes. In the case of gas fracturing, the research teams were limited to the comparison of a single point, which complicated their task. Nonetheless, the numerical results were able to reproduce the measurements and capture processes such as longitudinal gas flow through the excavation-induced fracture network, as suggested by some evidence in the observation piezometric chambers. The numerical models also agreed with the measurements in the sense of higher probability of developing along the injection borehole than radially towards the sound rock. The approaches developed by the research teams showed that they are capable of analysing and reproducing fracture initiation in the COx. However, areas of future work should focus on the fracture propagation and fracture aperture, which were out of the scope of this task. To this end, additional data must be gathered for the parameter characterisation and validation of the numerical models. Nonetheless, various approaches showed promising results as they were able to reproduce fracture development under certain conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Importance of corners in fracture of highly crosslinked polymeric adhesives

In this study, very large molecular dynamics simulations with open ends between two solid adherends have been performed treating tensile deformation of coarse-grained, highly crosslinked polymer networks modeling epoxy systems. The open boundary and the presence of corners dramatically alter the fracture behavior. In contrast to systems with periodic boundaries, the failure strain decreases with increasing system size until a critical size is reached. This decrease greatly reduces the difference in the crack initiation strains between simulation and experiment. In the open geometry, the sides of the polymer network contract inward forming wedge shaped corners. The stress and strain are concentrated in the corners where the shear component is present and large. The nonuniformity of the strain results in accumulation of bond breaking in the corners and crack initiation there. Lastly, t the corner strain is system size dependent, which results in a system size dependence of the failure strain.

36 MATERIALS SCIENCE↗