Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fracture modelling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Findings on Subtask 3.1 - Bakken Rich Gas Enhanced Oil Recovery Project

Total in-place oil for the Bakken petroleum system (BPS) (which includes the Bakken and Three Forks Formations) has been estimated to be 600 billion barrels (bbl). However, BPS wells have decline rates as high as 85% over the first 3 years of their lives, and primary recovery factors typically range from 3% to 10% of original oil in place. Given the low initial recovery rates, even small incremental productivity improvements could dramatically increase technically recoverable oil in the BPS. One potential solution is enhanced oil recovery (EOR) using gas injection, such as carbon dioxide (CO2) or hydrocarbon (HC) gases. While commonly used in conventional reservoirs, CO2 EOR in unconventional tight oil reservoirs has been limited to pilot tests. EOR using rich gas (mixture of methane, ethane, and propane) has also been employed in numerous pilots in several unconventional plays and has recently been successfully applied in the Eagle Ford play. If successful, large-scale gas-based EOR in the BPS could dramatically increase oil productivity and recovery factors and extend the life of the play for decades. While CO2 may be a technically suitable working fluid for EOR in the BPS, supplies are limited and costs for using CO2 in EOR pilots are prohibitively high. Meanwhile, produced gas flaring has presented challenges for BPS operators in North Dakota. Analysis conducted by the North Dakota Pipeline Authority indicates that the current gas-gathering infrastructure in North Dakota is insufficient to accommodate all of the associated gas that is produced from the BPS. The geographically isolated location of North Dakota relative to large natural gas markets, combined with suppressed natural gas prices, has made it economically challenging for industry to invest capital in expanding gas-gathering infrastructure in the state. These circumstances led to a research program conducted by the Energy & Environmental Research Center (EERC) in partnership with Liberty Resources Management Company LLC (LR) to examine the potential to use rich gas injection for EOR and mitigate flaring. A rich gas EOR pilot test was designed and executed by LR at its Stomping Horse development area in Williams County, North Dakota. From July 2018 through May 2019, a total of 160 million standard cubic feet (MMscf) of rich produced gas was injected into the BPS using five different wells in a sequential injection strategy. LR’s Leon–Gohrick drill spacing unit (DSU) was used as the test site. Regulatory oversight was provided by the North Dakota Industrial Commission (NDIC). Technical support was provided by the EERC through a series of laboratory, modeling, and field-based activities, and additional post-pilot research activities incorporated learnings from the test, developed new laboratory data, improved fracture modeling methods, and developed machine learning and big data analytics. The results from the Stomping Horse rich gas EOR pilot activities indicate that developing an effective, economical EOR approach for the BPS will require more field tests. Another key lesson learned from the Stomping Horse tests is that detailed pre- and posttest data on reservoir conditions and fluids production are essential. Robust reservoir characterization provides information that is crucial to creating realistic geomodels and conducting valid dynamic simulations of potential EOR scenarios. A detailed understanding of the completions and production history of offset wells is also necessary for valid test result interpretations. This knowledge is essential to designing the operational parameters of injectivity tests and interpreting the results. A conformance control strategy is also essential to success. Laboratory-based examinations of rich gas interactions with reservoir fluids and rocks were conducted, with an emphasis on determining the ability to mobilize oil in the tight reservoir rocks and shales of the BPS. Injection fluid composition was shown to have a positive impact on reducing reservoir oil minimum miscibility pressure (MMP), reducing interfacial tension (IFT), and altering wettability. IFT and contact angle measurements demonstrated that wettability can be altered in the presence of rich gas, suggesting the potential to improve oil recovery. Iterative modeling of surface infrastructure and reservoir performance using data generated by the various project activities was conducted. A geologic model of the Stomping Horse area was built; history-matched oil, gas, and water production was used in simulations of various EOR scenarios. Early programmatic modeling results were used to support LR’s design and operation of the EOR pilot and to provide insight regarding optimization of future commercial-scale BPS EOR design and operations. Post-pilot modeling focused on alternative methods of understanding complex fracture networks and accelerating simulation time. These led to improved simulation run times and provide excellent history-matching results. Several of these iterative models were used as the bases for developing algorithms into machine learning and big data analytics. History matching in reservoir simulation is time-consuming and computer processing-intensive. Machine learning algorithms were created, and an automated history-matching tool was developed. A large set of synthetic reservoir simulations were created to generate well responses (oil, gas, and water production, well bottomhole pressure [BHP], and tracer or propane breakthrough) for a set of EOR operating parameters that included offset well status (open or closed), injectate (rich gas or propane), injection rate, and injection well BHP. A user interface was developed to provide real-time visualization. Machine learning-based models were developed to provide rapid forecasting of well performance given a set of user-defined EOR operating parameters. These predictive models allow the user to modify the offset well status, injection rate, and injection well BHP and rapidly forecast future production performance. The combination of real-time visualization tools with real-time forecasting tools provides a framework for real-time control—operational changes that the EOR site operator can enact (e.g., changing gas injection rates) to affect the observed performance and potentially improve the EOR outcome. There is great reason to be optimistic about the future of EOR in the Bakken. The results of the laboratory studies suggest significant potential for high rates of oil mobilization using produced field gas injection under the right conditions. The results of the lab studies, combined with rigorous statistical analysis of well production data and associated modeling efforts, confirm the notion that fluid mobility within the reservoir is controlled by fractures. As more knowledge is gained about the nature and distribution of fracture networks in the Bakken, the industry will be in a better position to predict and, ultimately, influence fluid mobility. New field tests are necessary to develop a more complete understanding of those conditions. Thoughtful and creatively engineered field tests within a well-characterized geologic setting will yield the fundamental knowledge needed to take Bakken oil production to the next level. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission’s Oil and Gas Research Program and Computer Modelling Group.

04 OIL SHALES AND TAR SANDS↗

Analytical models of the strength and ductility of CNT reinforced metal matrix nano composites under elevated temperatures

Carbon nanotubes (CNTs) can greatly enhance the strength of metal matrix composites while resulting in ductility loss. This strength-ductility tradeoff dilemma always confines the development of material design and real-life applications. Here in this work, a temperature dependent strengthening analytical model is proposed for CNT reinforced metal matrix composites which considers three common strengthening mechanisms: Orowan looping effect, thermal expansion mismatch effect, and load bearing effect. The proposed model can predict composite material strength with different volume fractions of CNTs and under different temperatures. Combining the strengthening model with the stress based modified Mohr-Coulomb (sMMC) ductile fracture model, a ductility analytical model is then derived. This ductility analytical model includes the influences of temperature, multi-axial stress loading conditions, as well as the aforementioned three strengthening mechanisms. A good agreement has been achieved between literature published experimental data and analytical predictions for both composite material strength and ductility loss. The proposed two analytical models can provide a straightforward way to study the strength-ductility relationship for CNT reinforced metal matrix composites over a wide range of temperatures and different stress states, and then provide guidance on new material design and processing.

36 MATERIALS SCIENCE↗

Pressure Transient Analyses and Poroelastic Modeling of Hydraulic Fracture Dilation for Multiple Injections at the Devine Fracture Pilot Site

Our team has conducted electromagnetic (EM) surveys for the past six years to monitor hydraulic-fracture behavior at the Devine Fracture Pilot Site (DFPS). The sub-horizontal orientation of a shallow hydraulic fracture at the DFPS provides uniform access to the fracture area for interrogation and data collection. Ahmadian et al. (2023) suggested a possible correlation between spatiotemporal changes in the flow rate, bottomhole pressure (BHP), and the observed surface recorded electric field at the DFPS. In this paper, we present the development of poroelastic forward models and pressure transient analyses (PTAs) to support the development of a multiphysics inverse model for these EM surveys. First, we conducted PTAs of the shut-in periods after six injections out of 10 to determine the fracture closure pressure (FCP) or the overburden pressure used in a poroelastic fracture reopening model. Second, we developed a finite-element poroelastic model throughout five injection cycles to include the effect of the cumulative injected volumes due to the previous injections on current fracture dilation in the presence of highly permeable unpropped and propped zones adjacent to the cohesive layer that models fracture reopening. Fracture reopening in this poroelastic model is based on a calibrated traction-separation response using the bottomhole pressure collected in two injection campaigns in 2020 and 2022. We used the outcomes of a previous simulation study of the primary hydraulic-fracturing stimulation to define the dimension of an unpropped fracture zone ahead of the propped fracture area. The PTAs led to FCPs consistent with those obtained using the injection data collected at the DFPS in 2020. Further, these analyses showed that at later injections, the fracture closure occurred at a later time with respect to the shut-in time, inferring the effect of cumulative injected volumes in previous injections. The simulation results show that considering the propped and unpropped fracture zones improves our poroelastic model in predicting the injection-well BHP. The numerical simulation results demonstrate a significant excess pore pressure near the fracture because of the preceding formation loadings by the previous injections. The obtained fracture dilation area and fluid pressure distribution provide a basis to improve the development of a multiphysics inverse model. Furthermore, in an iteratively coupled scheme, this pressure distribution can be introduced into EM models to render a holistic view of the causative mechanisms for the surface signal anomalies.

02 PETROLEUM↗

Fracture Mechanics—Theory, Modeling and Applications

The field of fracture mechanics was developed during the throes of World War II, and since then, it has been a very active area of research. This is a very energetic and vibrant field because fracture processes are relevant for a vast range of engineering applications spanning different temporal and length scales. Depending on the application, material fracture and fragmentation may be either a desirable feature (for example, for the purpose of hydraulic fracturing operations), or something that is to be avoided at all costs (for example, in key components of mechanical systems). In some other instances, fractures are already present and must be accommodated through novel design (for example, in the case of earthquake ruptures occurring in the Earth’s crust). Because of this wide spectra of motivation, there is a continuous need for the fracture mechanics research community to gain more insight on how fractures are created, evolve, and interact with themselves and with material microstructures. In addition, there are still many remaining questions about how fracture propagation, growth, and interaction impact overall material behavior, and how to develop accurate models to predict this behavior.

36 MATERIALS SCIENCE↗

EGS Reservoir Modeling for Developing Geothermal District Heating at Cornell University: Preprint

Cornell University is pursuing development of an enhanced geothermal system (EGS) for providing heating to its main campus in Upstate New York. A ~10,000 ft (~3 km) deep vertical observation well ("CUBO") was drilled in 2022 to characterize the subsurface using wellbore logging, borehole imaging, fluid sampling, mini-frac tests, coring and drill cutting analysis. Down-hole temperatures measured at 3 km depth are about 80 degrees C, sufficiently high for direct-use heating. The well drilled through generally low porosity and low permeability Paleozoic sedimentary formations and into metamorphic basement rock, encountered at about 9,400 ft depth. Leveraging subsurface data obtained through CUBO, we investigated technical feasibility and design requirements of a doublet well system with horizontal laterals connected to a fracture network created through hydraulic fracturing. The EGS reservoir is sized to provide a nominal heat output in the range 5 to 10 MWth of continuous heating over a 15 year-lifetime with limited thermal drawdown. We applied the Gringarten Multiple parallel fracture model, the Cornell Discrete Fracture Simulator FOXFEM and the commercial simulator ResFrac to estimate required heat transfer area and design a potential hydraulic stimulation treatment. Reservoir simulations indicate that, depending on fluid flow rate and injection temperature, 2 to 3 km2 of effective fracture heat transfer area is required to supply the target heat output of 5 to 10 MWth over 15 years.

district heating↗

EGS Reservoir Modeling for Developing Geothermal District Heating at Cornell University

Cornell University is pursuing development of an enhanced geothermal system (EGS) for providing heating to its main campus in Upstate New York. A ~10,000 ft (~3 km) deep vertical observation well ('CUBO') was drilled in 2022 to characterize the subsurface using wellbore logging, borehole imaging, fluid sampling, mini-frac tests, coring and drill cutting analysis. Down-hole temperatures measured at 3 km depth are about 80 degrees C, sufficiently high for direct-use heating. The well drilled through generally low porosity and low permeability Paleozoic sedimentary formations and into metamorphic basement rock, encountered at about 9,400 ft depth. Leveraging subsurface data obtained through CUBO, we investigated technical feasibility and design requirements of a doublet well system with horizontal laterals connected to a fracture network created through hydraulic fracturing. The EGS reservoir is sized to provide a nominal heat output in the range 5 to 10 MWth of continuous heating over a 15 year-lifetime with limited thermal drawdown. We applied the Gringarten Multiple parallel fracture model, the Cornell Discrete Fracture Simulator FOXFEM and the commercial simulator ResFrac to estimate required heat transfer area and design a potential hydraulic stimulation treatment. Reservoir simulations indicate that, depending on fluid flow rate and injection temperature, 2 to 3 km2 of effective fracture heat transfer area is required to supply the target heat output of 5 to 10 MWth over 15 years.

district heating↗

BISON microstructure-based pulverization criterion in high burnup structure

To improve the economics of commercial nuclear power production, utilities are seeking to increase the allowable burnup limit of UO$_2$ fuel. One of the main factors that contributes to the current burnup limit of 62 GWd/MTU in commercial light water reactors (LWRs) is the risk of fine fragmentation or pulverization during a loss of coolant accident (LOCA). Pulverization primarily occurs at high burnups, especially when the high burnup structure (HBS) has formed. To allow the industry to pursue increased burnup and develop mitigation strategies, it is essential to have improved capability to predict the onset of pulverization. However, the mechanism of pulverization is not well understood, and the existing predictive capabilities implemented in the BISON fuel performance code are empirical in nature. In this report, mesoscale simulations are used to improve understanding of the formation mechanism of the HBS and how it responds during a LOCA transient, and inform development of a BISON pulverization criterion. A phase-field model was used to simulate the evolution of bubble pressure as a result of HBS formation. The simulations showed that gas atoms diffuse from grain interiors to the new grain boundaries created during HBS formation, and diffuse rapidly along these grain boundaries to reach existing bubbles. This causes an increase in bubble pressure in existing bubbles, leading to bubble growth during steady-state operation. To simulate the response of HBS bubbles to a LOCA transient, a newly developed phase-field model was used; in agreement with preliminary results from FY20, bubble size did not change significantly during the duration of the transient. A phase-field fracture model was used to study fragmentation patterns in the HBS, including using input from the phase-field model as initial conditions. Phase-field fracture simulations were used to determine a pulverization criterion for BISON. A function for the critical pressure for pulverization to occur was fit to data from the phase-field fracture simulations, and this function was implemented as a material property in BISON. For comparison, an analytical criterion for pulverization was developed and implemented within the same material property.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Predicting ductility of Mg/SiCp nanocomposite under multiaxial loading conditions based on unit cell modeling

This article presents an investigation on the ductility of Mg/SiCp under nine different multiaxial loading conditions based on a unit cell (or called representative volumetric element, RVE) finite element model. The constitutive relationship of magnesium matrix is characterized by a model combined Lode angle dependent plasticity model with the CPB06 plasticity model, which is able to describe the tension-compression asymmetry in magnesium matrix. The debonding of the matrix-particle interface and matrix fracture are considered by the modified Mohr-Coulomb (MMC) fracture model. Simulation results show that the interface debonding and subsequent matrix fracture are responsible for the ductility and fracture of nanocomposite. The computational results with parametric studies are compared and well correlated with experimental data, and it finally gives a stress-based full fracture locus of Mg/SiCp nanocomposite.

42 ENGINEERING↗

Deterministic Discrete Fracture Network (DFN) Model for the EGS Collab Project on the 4850 Level of the Sanford Underground Research Facility (SURF)

The EGS Collab is conducting hydraulic fracture stimulation and fluid circulation experiments in the Sanford Underground Research Facility (SURF) located in Lead, South Dakota. A total of eight ~60m-long subhorizontal boreholes were drilled from the 4850 Level (~1.5 km below the ground surface) into the crystalline rock of this former mine. Six of these holes are used for geophysical monitoring, one is used for hydraulic fracture stimulation, and the remaining hole was designed as a production borehole that receives water from the injection well via the induced and natural fracture system. The primary goal of creating the discrete fracture network model is to show that these modeling methods are critical for the development of enhanced geothermal systems (EGS). This includes the prediction of rock behavior during fracturing and during an extended period of water flow between the parallel injection and production boreholes. Understanding the results from the induced fracturing and flow is complicated by the presence of significant natural fractures that interact with the stimulation and/or flow pathways. The delineation and characterization of natural fractures is thus an important part of the project, and therefore a model of the Discrete Fracture Network (DFN) was developed on a deterministic basis. The DFN was populated using observations and interpretations integrated from drift (horizontal passageways that allow access in the underground) fracture mapping, analysis of core recovered from the eight boreholes, borehole televiewer logs and videos, and observations of flow between and within boreholes and in the drift. The natural fracture system is dominated by a pervasive northwest-trending, steeply dipping shear system that is identifiable in the drifts and the core. Hydraulic fracture stimulation, flow/tracer circulation tests, and geophysical monitoring revealed that the behavior of the injected water, and perhaps the growth of induced fractures, has been significantly influenced by the existing fractures identified in the DFN.

40 EE - Geothermal Technologies Office (EE-4G)↗

Accelerated Strength Testing of Thermoplastic Composites

Constant ramp strength tests on unidirectional thermoplastic composite specimens oriented in the 90 deg. direction were conducted at constant temperatures ranging from 149 C to 232 C. Ramp rates spanning 5 orders of magnitude were tested so that failures occurred in the range from 0.5 sec. to 24 hrs. (0.5 to 100,000 MPa/sec). Below 204 C, time-temperature superposition held allowing strength at longer times to be estimated from strength tests at shorter times but higher temperatures. The data indicated that a 50% drop in strength might be expected for this material when the test time is increased by 9 orders of magnitude. The shift factors derived from compliance data applied well to the strength results. To explain the link between compliance and strength, a viscoelastic fracture model was investigated. The model, which used compliance as input, was found to fit the strength data only if the critical fracture energy was allowed to vary with temperature reduced stress rate. This variation in the critical parameter severely limits its use in developing a robust time-dependent strength model. The significance of this research is therefore seen as providing both the indication that a more versatile acceleration method for strength can be developed and the evidence that such a method is needed.

Reeder, J. R.↗

Modeling CO 2 flow through faulted/fractured reservoirs using tEDFM in corner-point grids

The interest in underground CO 2 storage has increased significantly over the last decade because of the rising concern about global warming due to the growing levels of greenhouse gases in the atmosphere. Considering that CO 2 accounts for 80% of these greenhouse gases, carbon capture, utilization, and storage (CCUS) is regarded as one of the most direct approaches to achieving the net zero carbon target. Although CO 2 storage in deep saline aquifers and depleted gas reservoirs has been studied extensively, most studies use commercial simulators that model faults/fractures by simply modifying the transmissibility in the direction perpendicular to the fault surfaces. Here, this work shows that this simplistic approach ignores the accelerated flow in the directions parallel to the fault plane, leading to significantly higher leakage along the fault surface. To accurately model the flow of CO 2 in faulted reservoirs, we present the first transient embedded discrete fracture model for corner-point grids (tEDFM-CPG). By comparing the results of the tEDFM-CPG to high-resolution reference solutions, we show that this approach is accurate and efficient at predicting CO 2 flow in faulted/fractured reservoirs. Finally, this work presents the use of mixed reality (MR) to efficiently observe CO 2 gas migration in the interior of these corner-point grid systems.

25 ENERGY STORAGE↗

Fracture Behavior Considerations for the TRISO Particle Matrix

To assess whether matrix fracture would result in an unacceptable loss of containment or confinement in TRISO fuel particles, it is crucial to evaluate the micro-tensile strength, fracture toughness, and irradiation effects on matrix materials. Current data must be comprehensive and validated for modeling fractures under various conditions. Relevant material properties surrounding matrix fracture will be discussed during the presentation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Delamination Modeling of Composites for Improved Crash Analysis

Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.

Fleming, David C.↗

Delamination Modeling of Composites for Improved Crash Analysis

Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.

Fleming, David C.↗

Vulnerable window of yield strength for swelling-driven fracture of phase-transforming battery materials

Abstract Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith’s criterion. Here, we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and propagation during lithiation of Si nanopillars. Our computational results reveal that fracture occurs within a “vulnerable window” inside the two-dimensional parameter space of yield strength and fracture energy and highlight the importance of taking into account the surface localization of plastic deformation to accurately predict the magnitude of tensile stresses at the onset of fracture. They further demonstrate how the increased robustness of hollow nanopillars can be understood as a direct effect of anode geometry on the size of this vulnerable window. Those insights provide an improved theoretical basis for designing next-generation mechanically stable phase-transforming battery materials undergoing large volume changes.

25 ENERGY STORAGE↗

Interpretation of Hydraulic Fractures Based on Microseismic Response in the Marcellus Shale, Monongalia County, West Virginia, USA: Implications for Shale Gas Production

Summary Hydraulic fracturing is critical for extracting shale gas in the subsurface. The treatment technique of multistage hydraulic fracturing is widely used to maximize production. In multistage hydraulic fracturing, not all pumping stages make the same contribution for production, although the designed stimulation process is almost same in every pumping stage. In this study, we characterize the microseismic responses of hydraulic fracturing. Significant variations of microseismic characteristics are observed among the different pumping stages. Pre-existing natural fractures are examined along the horizontal well in selected stages. Combined with the Mohr’s circle analysis, results of the fracture study show that induced hydraulic fractures can be captured by pre-existing natural fractures. Induced hydraulic fractures are simulated by the unconventional fracture model (UFM), and the result reveals that the stress-shadow effect diverts the direction of hydraulic fractures. The diverted hydraulic fracture affects the development of the hydraulic fracture network, which has influence on production. The treatment of two-step pumping is investigated by application of hydraulic diffusivity. Hydraulic fracturing performance and production could be optimized by the treatment of two-step pumping in a single stage. The second pumping creates new fractures and fills the fractures with additional proppants to maintain production for a long duration.

Energy & Fuels↗

Micro-mechanical analysis of damage growth and fracture in discontinuous fiber reinforced metal matrix composites

An experimental verification is presented for a new two parameter fracture model based on the equivalent remote biaxial stresses (ERBS). A detailed comparison is made between the new theory and the constant K(sub IC) approach of linear elastic fracture mechanics (LEFM). Fracture is predicted through a failure curve representing the change in a variable fracture toughness K(sub IC) with the ERBS ratio B(sub E). The nonsingular term (T) in the series expansion of the near crack-tip transverse stress is included in the model. Experimental results for polymethyl methacrylate (PPMA) show that the theory can account for the effects of geometry on fracture toughness as well as indicate the initiation of crack branching. It is shown that the new criterion predicts failure for PMMA with a 95 percent confidence zone which is nearly three times smaller than that of the LEFM K(sub IC) approach.

Goree, James G.↗