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Estimation of the Seismic Moment Release Rate of Mars from InSight Seismic Data

Seismicity models for Mars usually estimate the long-term average annual seismic moment rate, and also the average annual event rate. This holds for estimations based on geological evidence (Golombek et al., 1992, Golombek, 2002, Taylor et al., 2013) as well as for models based on thermal evolution and cooling of the Martian interior (Phillips, 1991, Knapmeyer et al., 2006, Plesa et al., 2018). All studies are compatible with the conclusion based on the non-observation of any unambiguous event by Viking (Anderson et al., 1977, Goins & Lazarewicz, 1979) that Martian seismicity lies somewhere between that of the Moon and that of the Earth. We developed tools to derive reasonable estimations of the annual seismic moment rate from a number of events as small as one, provided that the observed events are beyond the global completeness threshold for observable events. Numerical tests as well as evaluation of terrestrial data shows the feasibility of the approach.

Knapmeyer, Martin↗

Risk Importance Ranking of Fire Data Parameters to Enhance Fire PRA Model Realism

Fire is historically and analytically a significant contributor to nuclear power plant risk. The level of fire risk and the methods, tools and data for modeling this risk is highly debated by experts. One area of debate is the input data used in fire modeling and how to deal with this data’s high uncertainty. This report outlines initial work performed for determining the key parameters causing this uncertainty and how it propagates into nuclear power plant models. This research paves the way for the development of methods to reduce fire data uncertainty used in modeling. The Nuclear Regulatory Commission has mandated that nuclear power plants perform fire risk modeling. However, there are several issues with the current risk modeling implementation that affect the results. Approved modeling methods can be overly conservative and often do not match plant experience. Also, the data used in the modeling can have high uncertainties and is influenced by expert judgement. To evaluate input data uncertainty, researchers performed an initial review of several fire experiments done at Sandia National Laboratories. Uncertainties for fire data can come from many sources, such as experiment design constraints, environmental conditions, or other plant-specific aspects. There are many different significant and insignificant parameters driving the uncertainty. Additionally, the uncertainty of the different input data used in the fire modeling could have a significant or insignificant effect on the entire plant risk. A four-step methodology was developed to perform Integrated Probabilistic Risk Assessment Importance Ranking. A demonstration case using these steps was set up and three of the four steps were completed in fiscal year (FY) 2019 and the fourth step done FY 2020. These steps are: 1. The qualitative analysis of potential sources was conducted with the following items identified for the demonstration. • Maximum heat release rate • Time to maximum heat release rate • Duration of max heat release rate • Time to decay • Thermal conductivity of concrete • Specific heat of concrete • Density of concrete • Cable jacket thickness 2. A quantitative characterization of dominant sources of uncertainty was performed. A list of distributions and determined values of the dominant sources is shown in Appendix A. 3. A quantitative screening of the potential sources of uncertainty using Morris Elementary Effects Analysis was completed. An experimental model using the physics-based fire modeling tool Fire Dynamics Simulator was developed and coupled with the Risk Analysis Virtual Environment. The Morris analysis identified at least two parameters that can be eliminated as significant contributors (specific heat of concrete and cable jacket thickness). 4. Global importance measure (Global IM) analysis to generate a comprehensive ranking based on their influence on the plant risk. In this research, a moment-independent Global IM is used since it can address (a) uncertainty in the input parameters of the fire model, (b) uncertainty in the risk outputs, and (c) non-linearity and interactions among input parameters in the fire model, more accurately than the correlation-based and variance-based global methods. The observations from the research showed that, depending on the initial and boundary conditions of the fire scenarios, fire-induced damage could have a very small probability and could be dominated by the tail of the uncertainty distribution; hence, the accuracy of the correlation-based and variance-based methods is questionable. The moment-independent Global IM analysis in this research provides a better understanding of how experimental uncertainty data affects industry’s plant models and where improvements in that data will have the largest benefit for improving fire modeling accuracy in causing core damage. Among the five unscreened parameters obtained from the Morris EE analysis, the Global IM analysis results for the case study indicated that max heat release rate and fire location are the most important parameters. The report also outlines benefits of using a unified computational platform that integrates the underlying simulations (e.g., a fire progression model), quantitative screening (using the Morris EE method), and the Global IM analysis. A unified platform can (i) facilitate the ranking of input parameters considering multiple key fire scenarios simultaneously, rather than considering one scenario at a time, (ii) contribute to more explicit and accurate treatment of dependencies at multiple levels of Fire PRA, (iii) facilitate the sampling-based uncertainty quantification for Fire PRA, and (iv) help generating both “industry-wide” and "plant-specific" ranking of uncertainty sources in Fire PRA. Future research should be done to include additional parameters such as detection/suppression or cable fire spread. Adding a PRA software such as SAPHIRE to the RAVEN platform would help with plant model integration and improve treatment of fire-induced dependency. The I-PRA risk importance ranking methodology offered in this report can provide valuable information for efficiently (a) enhancing the realism of Fire PRA for existing plants and (b) supporting the development of Dynamic Fire PRA for advanced reactors and new plants.

97 MATHEMATICS AND COMPUTING↗

Sublaminate analysis of interlaminar fracture in composites

A simple analysis method based upon a transverse shear deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed form expressions for the interlaminar shear stresses ahead of the crack, the total energy release rate, and the energy release rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, E. A.↗

Hanford Site Composite Analysis Special Analysis: Inventory and Solid Waste Release Modeling for the LLBG Sensitivity Case - UCAQ-22-01 Inventory Discrepancies for 218-E-12B, 218-W-3A, and 218-W-3AE in the Hanford Site Composite Analysis

This environmental calculation file (ECF) documents the methodologies, assumptions, and results of four sensitivity analyses that reevaluate the representativeness of solid-waste radionuclide inventory and release rate from three solid waste sites included in the recently completed Hanford Site Composite Analysis (CA) (DOE-RL-2019-52, Composite Analysis for Low-Level Waste Disposal in the Hanford Site Central Plateau (FY 2020), Rev. 1) (hereinafter called the CA Update). Specifically, this ECF reevaluates the representativeness of the base case inventory and radionuclide waste release rates from three solid waste sites (i.e., 218-E-12B, 218-W-3A, and 218-W-3AE) and two radionuclides (i.e., carbon-14 [C-14] and technetium-99 [Tc-99]). These three waste sites and two radionuclides were identified as being the most significant contributors to groundwater contamination and dose in the CA Update for the Inner Area boundary at times periods after the compliance period. This ECF first evaluates the representativeness of the C-14 and Tc-99 inventory and second, radionuclide release rates for the three waste sites1. If the inventory and release rates assumed in the CA Update are determined to be not representative, as hypothesized in the CA Update, then this ECF evaluates the impact of more representative inventories and release rates on the transfer of radionuclides to the vadose zone. The four analyses described in this ECF are as follows: 1) 218-E-12B C-14 Inventory and Release Rate Sensitivity Case – Determine the representativeness of the C-14 inventory and associated waste release rate from the 218-E-12B waste site assumed in the CA Update. If the inventory and associated waste release are more appropriately characterized as being different from the assumptions in the CA Update, then update the predicted C-14 release rate and compare the results to the results presented in the CA Update (DOE/RL-2019-52); 2) 218-W-3A C-14 Inventory and Release Rate Sensitivity Case – Determine the representativeness of the C-14 inventory and associated waste release rate from the 218-W-3A waste site assumed in the CA Update. If the inventory and associated waste release are more appropriately characterized as being different from the assumptions in the CA Update, then update the predicted C-14 release rate and compare the results to the results presented in the CA Update (DOE/RL-2019-52); 3) 218-W-3AE Tc-99 Release Rate Sensitivity Case – Determine the representativeness of the Tc-99 inventory and associated waste release rate from the 218-W-3AE waste site assumed in the CA Update. If the inventory and associated waste release are more appropriately characterized as being different from the assumptions in the CA Update, then update the predicted Tc-99 release rate and compare the results to the results presented in the CA Update (DOE/RL-2019-52); 4) 218-W-3AE Tc-99 Release Footprint Sensitivity Case – Determine the representativeness of the Tc-99 waste area footprint for the 218-W-3AE waste site assumed in the CA Update. If the footprint of the waste is more appropriately characterized as being different from the assumptions in the CA Update, then update the predicted Tc-99 release rate and compare the results to the result presented in the CA Update (DOE/RL-2019-52).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Characterization of Mode 1 and Mode 2 delamination growth and thresholds in graphite/peek composites

Composite materials often fail by delamination. The onset and growth of delamination in AS4/PEEK, a tough thermoplastic matrix composite, was characterized for mode 1 and mode 2 loadings, using the Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) test specimens. Delamination growth per fatigue cycle, da/dN, was related to strain energy release rate, G, by means of a power law. However, the exponents of these power laws were too large for them to be adequately used as a life prediction tool. A small error in the estimated applied loads could lead to large errors in the delamination growth rates. Hence strain energy release rate thresholds, G sub th, below which no delamination would occur were also measured. Mode 1 and 2 threshold G values for no delamination growth were found by monitoring the number of cycles to delamination onset in the DCB and ENF specimens. The maximum applied G for which no delamination growth had occurred until at least 1,000,000 cycles was considered the threshold strain energy release rate. Comments are given on how testing effects, facial interference or delamination front damage, may invalidate the experimental determination of the constants in the expression.

Martin, Roderick H.↗

Characterization of Mode I and Mode II delamination growth and thresholds in AS4/PEEK composites

Composite materials often fail by delamination. The onset and growth of delamination in AS4/PEEK, a tough thermoplastic matrix composite, was characterized for mode 1 and mode 2 loadings, using the Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) test specimens. Delamination growth per fatigue cycle, da/dN, was related to strain energy release rate, G, by means of a power law. However, the exponents of these power laws were too large for them to be adequately used as a life prediction tool. A small error in the estimated applied loads could lead to large errors in the delamination growth rates. Hence strain energy release rate thresholds, G sub th, below which no delamination would occur were also measured. Mode 1 and 2 threshold G values for no delamination growth were found by monitoring the number of cycles to delamination onset in the DCB and ENF specimens. The maximum applied G for which no delamination growth had occurred until at least 1,000,000 cycles was considered the threshold strain energy release rate. Comments are given on how testing effects, facial interference or delamination front damage, may invalidate the experimental determination of the constants in the expression.

Martin, Roderick H.↗

A New Approach to Model Delamination Growth in Fatigue Using the Virtual Crack Closure Technique Without Re-Meshing

A modeling approach is proposed to simulate delamination propagation in fatigue that combines the Virtual Crack Closure Technique (VCCT) with a progressive nodal release strategy. The progressive nodal release alleviates the artificial stress concentrations found when using the VCCT with instantaneous release to model 3D delamination without re-meshing. This enables crack shapes that do not conform to the underlying mesh to be readily simulated. The progressive release is formulated such that no artificial growth or healing occurs as a result of a change in loading conditions. Furthermore, expressions for calculating energy release rates at partially released nodes are proposed and applied to arbitrarily shaped delamination fronts. The shape of the delamination front is considered explicitly in the energy release rate calculations, and is determined by considering the normalized crack positions associated with the partial nodal release. Contrary to previous implementations, the local delamination propagation direction is not assumed to follow mesh lines, but instead is computed as part of the iterative procedure proposed to determine the maximum energy release along the crack front. The results obtained suggest the approach can accurately simulate Mode I, Mixed Mode I/II and Mode II fatigue delamination growth and be used to simulate growth of arbitrarily shaped cracks that do not conform to the underlying mesh.

N V De Carvalho↗

Quantification of Energy Release in Composite Structures

Energy release rate is usually suggested as a quantifier for assessing structural damage tolerance. Computational prediction of energy release rate is based on composite mechanics with micro-stress level damage assessment, finite element structural analysis and damage progression tracking modules. This report examines several issues associated with energy release rates in composite structures as follows: Chapter I demonstrates computational simulation of an adhesively bonded composite joint and validates the computed energy release rates by comparison with acoustic emission signals in the overall sense. Chapter II investigates the effect of crack plane orientation with respect to fiber direction on the energy release rates. Chapter III quantifies the effects of contiguous constraint plies on the residual stiffness of a 90 deg ply subjected to transverse tensile fractures. Chapter IV compares ICAN and ICAN/JAVA solutions of composites. Chapter V examines the effects of composite structural geometry and boundary conditions on damage progression characteristics.

Minnetyan, Levon↗

Quantification of Energy Release in Composite Structures

Energy release rate is usually suggested as a quantifier for assessing structural damage tolerance. Computational prediction of energy release rate is based on composite mechanics with micro-stress level damage assessment, finite element structural analysis and damage progression tracking modules. This report examines several issues associated with energy release rates in composite structures as follows: Chapter I demonstrates computational simulation of an adhesively bonded composite joint and validates the computed energy release rates by comparison with acoustic emission signals in the overall sense. Chapter II investigates the effect of crack plane orientation with respect to fiber direction on the energy release rates. Chapter III quantifies the effects of contiguous constraint plies on the residual stiffness of a 90 ply subjected to transverse tensile fractures. Chapter IV compares ICAN and ICAN/JAVA solutions of composites. Chapter V examines the effects of composite structural geometry and boundary conditions on damage progression characteristics.

Minnetyan, Levon↗

Analysis of Composite Skin-Stiffener Debond Specimens Using Volume Elements and a Shell/3D Modeling Technique

The debonding of a skin/stringer specimen subjected to tension was studied using three-dimensional volume element modeling and computational fracture mechanics. Mixed mode strain energy release rates were calculated from finite element results using the virtual crack closure technique. The simulations revealed an increase in total energy release rate in the immediate vicinity of the free edges of the specimen. Correlation of the computed mixed-mode strain energy release rates along the delamination front contour with a two-dimensional mixed-mode interlaminar fracture criterion suggested that in spite of peak total energy release rates at the free edge the delamination would not advance at the edges first. The qualitative prediction of the shape of the delamination front was confirmed by X-ray photographs of a specimen taken during testing. The good correlation between prediction based on analysis and experiment demonstrated the efficiency of a mixed-mode failure analysis for the investigation of skin/stiffener separation due to delamination in the adherents. The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to three-point bending is also demonstrated. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to capture the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D simulations were in good agreement with results obtained from full solid models. The good correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents.

Krueger, Ronald↗

Matrix resin effects in composite delamination - Mode I fracture aspects

A number of thermoset, toughened thermoset, and thermoplastic resin matrix systems were characterized for Mode I critical strain energy release rates, and their composites were tested for interlaminar critical strain energy release rates using the double cantilever beam method. A clear correlation is found between the two sets of data. With brittle resins, the interlaminar critical strain energy release rates are somewhat larger than the neat resin values due to a full transfer of the neat resin toughness to the composite and toughening mechanisms associated with crack growth. With tougher matrices, the higher critical strain energy release rates are only partially transferred to the composites, presumably because the fibers restrict the crack-tip deformation zones.

Hunston, Donald L.↗

Separation of crack extension modes in orthotropic delamination models

In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.

Beuth, Jack L.↗

Sublaminate analysis of interlaminar fracture in composites. I - Analytical model

A simple analysis method based on a transverse shear-deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed-form expressions for the interlaminar shear stresses ahead of the crack, the total strain-energy release rate, and the strain-energy release-rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite-element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically.

Armanios, Erian A.↗

Spherically expanding flame in silane–hydrogen–nitrous oxide–argon mixtures

The effect of silane addition on the laminar flame speed ($S^0_u$) of flames propagating in hydrogen–nitrous oxide–argon mixtures has been investigated experimentally for the first time using the spherically expanding flame technique in a constant volume combustion chamber. Replacing hydrogen by silane and maintaining the equivalence ratio constant, much higher flame speeds, explosion peak pressures, and pressure rise coefficients were measured. A previously developed detailed reaction model has been updated based on ab initio thermodynamic properties calculations and collision limit violation analysis. The improved reaction model demonstrates encouraging performance in predicting the flame speed, with a mean absolute error below 11%. To explain the effect of silane addition on the flame dynamics, a number of parameters have been calculated including OH and H rate of production, heat release rate per reaction, and sensitivity coefficient on . The dynamics of freely propagating flames in SiH 4 –H 2 –N 2 O–Ar mixtures is essentially controlled by reactions of the H–O–N chemical system: N 2 O+H=N 2 +OH, OH+H 2 =H 2 O+H, and N 2 O(+M)=N 2 +O(+M). Whereas silane addition does not influence much the rate of production of OH, it significantly modifies that of H with a number of pyrolytic chemical pathways of silicon hydrides, such as SiH+H 2 =SiH 2 +H and Si+H 2 =SiH+H, which act as sink of H atom as they proceed in the backward direction. The reactions forming SiO(s) and SiO 2 (s), such as SiO+OH=SiO 2 (s)+H and 2SiO=2SiO(s), are exothermic and significantly contribute to the temperature increase. The adiabatic, constant pressure flame temperature for mixture containing silane is significantly higher, up to several 100’s K. The increase of induced by silane addition seems to be mostly related to the large increase of the flame temperature which leads to higher energy release rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Laser Confocal Microscopy Uncertainty Quantification Study

At Los Alamos National Laboratory (LANL), the Storage Safety and Engineering (SSE) team completes annual surveillance on a subset of in-use interim nuclear material storage containers in fulfilment of requirements outlined in DOE Manual M 441.1-1. The containers are selected through several methods, such as subject matter expert judgement, random selection, and trending items. Following these selections, the SSE team has the capacity to complete surveillance on 15-20 containers each fiscal year, composed of a combination of SAVY-4000 and Hagan storage containers. Through previous work, the stainless-steel components of the containers have been identified as life limiting components, with an emphasis on the thin-walled bodies. The team is focused on understanding the extent of general and pitting corrosion, due to observations of extensive corrosion from stored contents and bag-out-bag degradation. Quantifying corrosion effects on the thin-walled stainless steel container bodies, and understanding potential impacts to the respective design release rates and design qualification release rates is paramount to the team. To date, destructive examination (DE) has proven to be the most insightful method for developing an understanding on the extent of corrosion on used containers. To standardize this process, the SSE team developed a destructive examination guide for analyzing stainless steel components of the containers. Corroded containers of interest are identified during surveillance activities and set aside for sectioning and characterization. Following sectioning, a major step in the DE workflow is the utilization of laser confocal microscopy for scanning corroded samples of interest and extracting data on pits, such as count, depth, and equivalent diameter. Adhering to the techniques outlined in the DE guide, analysis has been completed on two Hagans and one SAVY-4000 container, with the maximum pit depth recorded as 139.1 ± 22.82 μm on a 17.5 year old Hagan. The findings from the completed destructive examinations will be utilized to support lifetime extension efforts of the SAVY-4000 as the team can better estimate corrosion rates and effects over time based on stored contents and age. Due to the implications of observing extreme pit depths that approach the nominal container body thickness of .0299 inches (0.759 mm) or minimum container thickness of 0.236” (0.6 mm), high confidence in the LCM measurements is desired. Through testing outlined in, it was concluded that the total error ascribed to the 20x objective when conducting large image mapping on the Keyence VK-X3050 laser confocal microscope (LCM) relative to a 50x objective (reference) is 16.4% (± 8.73%). For shallow features on the order of pristine SAVY surface defects (i.e. 5 μm), this uncertainty is appropriate. However, this conservative estimate of total error poses a fundamental concern for pit depths that approach the thickness of the measured samples. That is, with the measurement uncertainty currently employed on all measurements, the LCM would be unable to resolve if a pit with a depth of 515 μm is through wall. Standard step height samples were procured and used in the present study to assess the resolution and repeatability of height measurements. Understanding the resolution and repeatability of height measurements was the first focus of the team as it relates directly to pit depth, which is of primary concern. Calibration gratings were procured to evaluate the resolution and repeatability of measurements in the X and Y axes of the LCM stage. The results of the depth uncertainty study were conducted first and presented in the subsequent sections. The planar uncertainty study is appended to the depth study with conclusions from both summarized at the end of the report.

36 MATERIALS SCIENCE↗

Fatigue Life Methodology for Bonded Composite Skin/Stringer Configurations

A methodology is presented for determining the fatigue life of composite structures based on fatigue characterization data and geometric nonlinear finite element (FE) analyses. To demonstrate the approach, predicted results were compared to fatigue tests performed on specimens which represented a tapered composite flange bonded onto a composite skin. In a first step, tension tests were performed to evaluate the debonding mechanisms between the flange and the skin. In a second step, a 2D FE model was developed to analyze the tests. To predict matrix cracking onset, the relationship between the tension load and the maximum principal stresses transverse to the fiber direction was determined through FE analysis. Transverse tension fatigue life data were used to -enerate an onset fatigue life P-N curve for matrix cracking. The resulting prediction was in good agreement with data from the fatigue tests. In a third step, a fracture mechanics approach based on FE analysis was used to determine the relationship between the tension load and the critical energy release rate. Mixed mode energy release rate fatigue life data were used to create a fatigue life onset G-N curve for delamination. The resulting prediction was in good agreement with data from the fatigue tests. Further, the prediction curve for cumulative life to failure was generated from the previous onset fatigue life curves. The results showed that the methodology offers a significant potential to Predict cumulative fatigue life of composite structures.

Krueger, Ronald↗

Incorporating civilian radioxenon background estimates in anomaly detection

A nuclear explosion screening exercise in 2023 (Maurer et al., 2023) found challenges with discerning anomalous radioxenon activity concentrations relative to elevated background concentrations. Research has continued into methods to detect anomalous radioxenon concentrations by comparing samples to estimates of atmospheric radioxenon background concentrations caused by releases at nuclear reactors or medical isotope production facilities. A new approach estimates the sample concentrations using time-varying radioxenon release rates obtained using optimization techniques that constrain the facility release rates to plausible amounts based on historical data or facility knowledge. The purpose of the optimization is to determine whether any combination of plausible release rates from emitting facilities can explain a series of radioxenon measurements at one or more sampling stations. A case study uses radioxenon data collected at three locations in western Europe for a month in 2021 and considers releases from 77 locations. Fewer samples are identified as being anomalous using a simplistic flagging rule than from an application of the current International Monitoring System (IMS) activity concentration-level rule.

Environmental sciences↗

Analysis of interface crack branching

A solution is presented for the problem of a finite length crack branching off the interface between two bonded dissimilar isotropic materials. Results are presented in terms of the ratio of the energy release rate of a branched interface crack to the energy release rate of a straight interface crack with the same total length. It is found that this ratio reaches a maximum when the interface crack branches into the softer material. Longer branches tend to have smaller maximum energy release rate ratio angles indicating that all else being equal, a branch crack will tend to turn back parallel to the interface as it grows.

Ballarini, R.↗