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NASA NTRS2020

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

Cohesive elements↗

DOE OSTI2024

Vertical z-axis discontinuous carbon fibers for improved lightning strike performance of continuous fiber-reinforced polymer composites

Effective lightning strike protection for critical aerospace and wind applications requires high electrical conductivity to dissipate current efficiently. However, polymer matrix composites face a challenge due to their inherently insulating nature. While conventional carbon fiber-reinforced composites (CFRP) exhibit electrical conductivity in the planar direction, achieving through-thickness conductivity remains an ongoing challenge. In this work, we have undertaken the fabrication of CFRP interleaved with vertically oriented carbon fibers (Z-fiber) to impart higher electrical conductivity along the thickness direction. Two Z-fiber composite variations are prepared: Z-1 with a single layer of Z-fiber and Z-5 with five interleaved layers and compared with no Z-fiber layer (Z-0) composite. The composite panels were subjected to lab-scale lightning strike tests with a current magnitude of 100 kA. To emulate real-world service conditions, an aerospace-grade paint coating was applied to the composite laminates. Comparative analysis shows Z-1 reduces damage diameter to ∼22 mm compared to Z-0 (∼26 mm), while Z-5 exhibits the least damage (∼16.7 mm), confirmed by optical microscopy. Z-5 demonstrates nine times higher through-thickness electrical conductivity than Z-0, reducing electrical anisotropy substantially. Thermal-electric finite element damage modeling predicts surface damage within 6% of experimental values for both Z-0 and Z-5 composites. Flexural tests post-lightning reveal Z-5 retains 66% flexural strength and 86% modulus, significantly better than Z-0, which retains less than 40% for both properties. This study highlights the efficacy of Z-fiber composites in lightning strike protection, offering improved through-thickness conductivity and mechanical property retention.

36 MATERIALS SCIENCE↗

NASA NTRS2015

Investigation of Micro-Scale Architectural Effects on Damage of Composites

This paper presents a three-dimensional, energy based, anisotropic, stiffness reduction, progressive damage model for composite materials and composite material constituents. The model has been implemented as a user-defined constitutive model within the Abaqus finite element software package and applied to simulate the nonlinear behavior of a damaging epoxy matrix within a unidirectional composite material. Three different composite microstructures were considered as finite element repeating unit cells, with appropriate periodicity conditions applied at the boundaries. Results representing predicted transverse tensile, longitudinal shear, and transverse shear stress-strain curves are presented, along with plots of the local fields indicating the damage progression within the microstructure. It is demonstrated that the damage model functions appropriately at the matrix scale, enabling localization of the damage to simulate failure of the composite material. The influence of the repeating unit cell geometry and the effect of the directionality of the applied loading are investigated and discussed.

damage↗

DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRSDate not supplied

Critical Progressive Damage Analysis Model Features for Low-Velocity Impact on Thermoset and Thermoplastic Panels

A previous verification and validation framework evaluated the ability of various progressive damage analysis (PDA) tools to predict the mechanical response and damage state in post-buckled stiffened aerospace structures composed of fiber-reinforced thermoset composite materials. Herein, the ability of PDA tools to predict damage in thermoplastic composite materials subject to low-velocity impact (LVI) loading has been assessed. LVI tests and analyses have been conducted for similar panels, comprising thermoset or thermoplastic composite materials. Preliminary test/analysis correlations revealed that using the same combination of PDA model features and finite element model-building guidelines for the thermoset and thermoplastic LVI specimens resulted in underprediction of matrix crack lengths and delaminated area in the thermoplastic analyses despite yielding good correlations for the thermoset specimens. In this paper, the quality of the test/analysis correlations for analyses of thermoplastic LVI specimens performed with different combinations of PDA model features using the NASA CompDam material model are presented. Model features that were assessed in terms of effect on the quality of the test/analysis correlation include the representation of damageable interfaces, residual thermal stresses, and fiber damage.

Frank Leone↗

NASA NTRSDate not supplied

Critical Progressive Damage Analysis Model Features for Low-Velocity Impact on Thermoset and Thermoplastic Panels

Frank Leone↗

NASA NTRS2008

Multiscale Modeling of Damage Processes in Aluminum Alloys: Grain-Scale Mechanisms

This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework.

Hochhalter, J. D.↗

DOE OSTI2024

Development and Integration of a Stochastic Clad Damage Propagation Model into PRONGHORN-SC Subchannel Analysis Code

The failure of fuel pins in nuclear reactors is intrinsically stochastic. Typically, a combination of variation in manufacturing that affects the material characteristics and the fuel assembly dimensions, variation in operating conditions, such as local power, coolant flow rate, and irradiation induced changes in material properties lead to a large uncertainty in failure margin of the fuel pins. Failure, therefore, may occur in exceptional pins with adverse combinations of these variations. Upon a metal fuel pin (U-Pu-Zr/HT9) failure, depressurization of the fuel pin takes place by release of fission gas, liquid sodium bond, and potentially solid fuel particles or molten/eutectic fuel droplets through the hole in cladding. The effect of a fission gas jet on neighbor fuel pins and possible propagation of a clad damage during normal operation was studied experimentally in 1970s and it was found that the post-failure fission gas jet insulates the jet impingement area of the target fuel pin surface and could increase the target pin’s surface temperature by as much as 100 – 200 K during the failed pin depressurization. It was concluded that the effect should not lead to fuel pin failure propagation during normal operation. In accident scenarios of sodium and lead fast reactors such as Unprotected Loss-Of-Flow (ULOF) or Unprotected Transient Over Power (UTOP), the fuel pins can be subjected to higher clad temperatures and fuel pin pressures or fuel clad mechanical/chemical interaction where thermal creep margin becomes significantly lower compared to the normal operation conditions. Therefore, possible stochastic failure and the post-failure fission gas/fuel jet impingement could be critical in order to predict fuel pin failure propagation. Pin depressurization due to fission gas release may degrade the heat transfer by formation of a gas blanket on a neighboring pin surface, which is a local phenomenon, and by causing coolant flow deceleration and starvation, which could affect a surrounding region as well. Furthermore, the potential presence of solid fuel particles or molten fuel at the time of clad failure could boost post-failure jet induced degradation even further. The present study models the U-Pu-Zr/HT9 metal fuel pin failure and stochastic clad damage propagation by biased sampling based on a Cumulative Damage Fraction (CDF) type clad failure criterion and the normal distribution of fuel failure probability density as a function of logarithm of Cumulative Damage Fraction. In addition, the effect of post-failure fission gas jet on heat transfer degradation is modeled for the target pins. This model is called stochastic Clad Damage Propagation (CDAP). The CDAP model is now fully integrated into developmental version of PRONGHORN-SC subchannel analysis code, allowing for modeling local failures and its propagation potential. Section 2 describes the components of the CDAP models. Section 3 describes the model implementation to PRONGHORN-SC and input specifications. Section 4 describes the CDAP model validation coupled to PRONGHORN-SC.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Meso-scale modeling and damage analysis of carbon/epoxy woven fabric composite under in-plane tension and compression loadings

The mechanical properties and damage behaviors of carbon/epoxy woven fabric composite under in-plane tension and compression are studied at the meso-scale level through experiment and simulation. An efficient representative volume element (RVE) modeling method with consistent mesh, high yarn volume fraction and realistic geometry is proposed. The material constitutive laws with plasticity, tension-compression asymmetry and damage evolution are established for the three components - yarn, matrix and interface, respectively. Significantly different mechanical properties and damage evolutions are observed depending on loading conditions and initial geometry characteristics. It shows a non-linear stress-strain curve with clear transition region and intensive damage in tension, while a quasi-linear behavior up to facture is observed in compression with little damage prior to final fracture. Furthermore, compared to the constant Poisson's ratio with straining in compression, a dramatic increase in Poisson's ratio appears in tension. Simulation shows damage mechanisms including transverse damage, matrix damage and delamination, which all play critical roles in the property evolution. In particular, the rapid damage accumulation after elastic deformation destroys the strong bonds and causes the easy deformation of transverse yarns which results in the transition region and large Poisson's ratio in tension. All the mechanical behaviors and damage evolutions are well captured and explained with the current RVE model.

42 ENGINEERING↗

NASA NTRS1984

An elastic failure model of indentation damage

A mechanistically consistent model for indentation damage based on elastic failure at tensile or shear overloads, is proposed. The model accommodates arbitrary crack orientation, stress relaxation, reduction and recovery of stiffness due to crack opening and closure, and interfacial friction due to backward sliding of closed cracks. This elastic failure model was implemented by an axisymmetric finite element program which was used to simulate progressive damage in a silicon nitride plate indented by a tungsten carbide sphere. The predicted damage patterns and the permanent impression matched those observed experimentally. The validation of this elastic failure model shows that the plastic deformation postulated by others is not necessary to replicate the indentation damage of brittle structural ceramics.

Liaw, B. M.↗

NASA NTRS2016

Modeling Fatigue Damage Onset and Progression in Composites Using an Element-Based Virtual Crack Closure Technique Combined With the Floating Node Method

A new methodology is proposed to model the onset and propagation of matrix cracks and delaminations in carbon-epoxy composites subject to fatigue loading. An extended interface element, based on the Floating Node Method, is developed to represent delaminations and matrix cracks explicitly in a mesh independent fashion. Crack propagation is determined using an element-based Virtual Crack Closure Technique approach to determine mixed-mode energy release rates, and the Paris-Law relationship to obtain crack growth rate. Crack onset is determined using a stressbased onset criterion coupled with a stress vs. cycle curve and Palmgren-Miner rule to account for fatigue damage accumulation. The approach is implemented in Abaqus/Standard® via the user subroutine functionality. Verification exercises are performed to assess the accuracy and correct implementation of the approach. Finally, it was demonstrated that this approach captured the differences in failure morphology in fatigue for two laminates of identical stiffness, but with layups containing θdeg plies that were either stacked in a single group, or distributed through the laminate thickness.

De Carvalho, Nelson V.↗

DOE OSTI2023

Continuum Damage Mechanics Modeling of High-Temperature Flaw Propagation: Application to Creep Crack Growth In 316H Standardized Specimens and Nuclear Reactor Components

Predicting creep crack growth (CCG) of flaws found during operation in high-temperature alloy components is essential for assessing the remaining lifetime of those components. While defect assessment procedures are available for this purpose in design codes, these are limited in their range of applicability. This study assesses the application of a local damage-based finite-element methodology as a more general technique for the prediction of CCG at high temperatures on a variety of structural configurations. Numerical results for stainless steel 316H, which are validated against experimental data, show the promise of this approach. This integration of continuum damage mechanics (CDM) based methodologies, together with adequate inelastic models, into assessment procedures can therefore inform the characterization of CCG under complex operating conditions, while avoiding excessive conservatism. This article shows that such modeling frameworks can be calibrated to experimental data and used to demonstrate that the degree of tri-axiality ahead of a growing creep crack affects its rate of growth. The framework is also successfully employed in characterizing CCG in a realistic reactor pressure vessel geometry under an arbitrary loading condition. These results are particularly relevant to the nuclear power industry for defect assessment and inspections as part of codified practices of structural components with flaws in high-temperature reactors.

42 ENGINEERING↗

DOE OSTI2021

Spent Nuclear Fuel Mechanical Loads in the General Package Drop Scenario

The US Department of Energy Spent Fuel and Waste Science and Technology program is performing research to determine the mechanical loading conditions applied to spent nuclear fuel (SNF) during normal conditions of transportation to inform mechanical tests of SNF and close an important knowledge gap related to the practical disposition of SNF in the US. A recent multi-national collaborative test campaign measured SNF assembly impact response to the 30 cm horizontal package drop scenario, which is a common regulatory basis test of SNF package design. Researchers at Pacific Northwest National Laboratory (PNNL) are using the test data to validate explicit finite element models to calculate the mechanical loads and structural response of spent nuclear fuel assemblies in the as-tested 30 cm horizontal package drop scenario. Once the as-tested package drop model is validated, the next step is to apply the model to the general 30 cm drop scenario, which includes all impact angles, all fuel assembly types, and all burnup conditions. PNNL is developing a damage model that will incorporate the results of finite element parametric studies to establish trends in SNF mechanical loading to various input parameters, like impact orientation and burnup. The damage model will have the capability to estimate mechanical loads for any single set of input parameters, but it will first be used to describe the upper bounds of potential SNF loading in the 30 cm drop scenario. This paper describes PNNL’s progress toward developing the general solution to the problem of spent nuclear fuel mechanical loads in the 30 cm package drop scenario and it describes the next steps in closing the knowledge gap.

Klymyshyn, Nicholas A.↗

NASA NTRS1991

A continuum model for damage evolution in laminated composites

The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.

Lo, D. C.↗

NASA NTRS2014

Damage Simulation in Non-Crimp Fabric Composite Plates Subjected to Impact Loads

Progressive failure analysis (PFA) of non-crimp fabric (NCF) composite laminates subjected to low velocity impact loads was performed using the COmplete STress Reduction (COSTR) damage model implemented through VUMAT and UMAT41 user subroutines in the frame works of the commercial finite element programs ABAQUS/Explicit and LS-DYNA, respectively. To validate the model, low velocity experiments were conducted and detailed correlations between the predictions and measurements for both intra-laminar and inter-laminar failures were made. The developed material and damage model predicts the peak impact load and duration very close with the experimental results. Also, the simulation results of delamination damage between the ply interfaces, in-plane matrix damages and fiber damages were all in good agreement with the measurements from the non-destructive evaluation data.

Satyanarayana, Arunkumar↗

NASA NTRS2006

Simulation of Delamination Under High Cycle Fatigue in Composite Materials Using Cohesive Models

A new thermodynamically consistent damage model is proposed for the simulation of high-cycle fatigue crack growth. The basis for the formulation is an interfacial degradation law that links Fracture Mechanics and Damage Mechanics to relate the evolution of the damage variable, d, with the crack growth rate da/dN. The damage state is a function of the loading conditions (R and (Delta)G) as well as the experimentally-determined crack growth rates for the material. The formulation ensures that the experimental results can be reproduced by the analysis without the need of additional adjustment parameters.

Camanho, Pedro P.↗

NASA NTRS1983

Mathematical modeling of damage in unidirectional composites

Extending the work of Goree and Gross (1979), solutions are given for a two-dimensional region of unidirectional fibers embedded in an elastic matrix whose initial flaw may take the form of a transverse notch, a rectangular cutout, or a circular hole. Subsequent flaw-induced damage is generated by remote stresses acting parallel to the fibers. For the case of such ductile matrix composites as boron/aluminum, present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Little difference is found for the three types of initial damage considered. In all cases, the presence of additional damage changes the nature of stress distribution through the unbroken fibers.

Goree, J. G.↗

DOE OSTI2021

Modeling Lithium Diffusion in Battery Cathodes Considering Chemo-Mechanically Induced Damage

This talk will present a 3D, continuum-level damage model for simulating Lithium diffusion within generated Li_{x}Ni_{0.5}Mn_{0.3}Co_{0.2} (NMC 532) secondary cathode particles. The primary motivation of the particle-level model is to inform cathode-particle design and determine charging profiles that reduce cathode fracture. The model considers NMC 532 secondary particles containing an agglomeration of anisotropic, randomly oriented grains. The model predicts that secondary-particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. The model predicts that small secondary-particles with large grains develop significantly less damage than larger secondary particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first high-rate cycles. This chemo-mechanical “damage saturation” effect indicates that initial secondary-particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced.

47 OTHER INSTRUMENTATION↗