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A continuum damage mechanics (CDM) based Wilshire model for creep deformation, damage, and rupture prediction
In this report, a new constitutive model is derived that combines the Wilshire equations with continuum damage mechanics (CDM) to enable the long-term prediction of creep deformation, damage, and rupture. The Wilshire equations have been demonstrated to accurately extrapolate the stress-rupture, minimum-creep-strain-rate, and time-to-strain of various alloys across decade of life. Recently, the time-to-creep-strain equation has been rearranged to predict creep deformation curves; however, the resulting equation is difficult to calibrate and does not track damage. The CDM-based Sinh constitutive model accurately predicts creep deformation, damage, and stress-rupture for a variety of alloys; however, it lacks an explicit description of stress and temperature co-dependence which limits interpolation and extrapolation ability. In this study, the Wilshire and the CDM-based Sinh equations are combined to create the “WCS” model. The WCS model combines the best features of each model while eliminating their deficiencies. Experimental data for alloy P91 is gathered and the WCS model is calibrated to the data. The WCS model accurately predicts the stress rupture, minimum-creep-strain-rate, creep deformation, and damage of alloy P91 across the experimental stress and temperature range as well as consistency in parametric simulations.
A model for predicting damage dependent damping in laminated composites
A constitutive model has been developed for predicting the dynamic properties of composite beams which accounts for the influence of microstructural damage. The model assumes the damage state to be fixed. The model can account for both the damping increase and stiffness loss due to microstructural damage. Damage dependent material constants obtained from a baseline data set can be used to predict damping changes for several composite layups. The validity of the model has been verified by comparing the experimental results to model predictions for crossply laminates with a variety of stacking sequences.
Meshfree Methods for Modeling Chemo-Mechanical Cathode Cracking in Li-Ion Batteries
Through repeated charging and discharging, the electrodes of a Li-ion battery experience cyclic loading causing swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries. Chemo-mechanical models are simulated mainly by two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a chemo-mechanical crack propagation model that achieves both intermediate accuracy and computational time between a CDM and CZM. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.
A procedure for utilization of a damage-dependent constitutive model for laminated composites
Described here is the procedure for utilizing a damage constitutive model to predict progressive damage growth in laminated composites. In this model, the effects of the internal damage are represented by strain-like second order tensorial damage variables and enter the analysis through damage dependent ply level and laminate level constitutive equations. The growth of matrix cracks due to fatigue loading is predicted by an experimentally based damage evolutionary relationship. This model is incorporated into a computer code called FLAMSTR. This code is capable of predicting the constitutive response and matrix crack damage accumulation in fatigue loaded laminated composites. The structure and usage of FLAMSTR are presented along with sample input and output files to assist the code user. As an example problem, an analysis of crossply laminates subjected to two stage fatigue loading was conducted and the resulting damage accumulation and stress redistribution were examined to determine the effect of variations in fatigue load amplitude applied during the first stage of the load history. It was found that the model predicts a significant loading history effect on damage evolution.
A study of material damping in large space structures
A constitutive model was developed for predicting damping as a function of damage in continuous fiber reinforced laminated composites. The damage model is a continuum formulation, and uses internal state variables to quantify damage and its subsequent effect on material response. The model is sensitive to the stacking sequence of the laminate. Given appropriate baseline data from unidirectional material, and damping as a function of damage in one crossply laminate, damage can be predicted as a function of damage in other crossply laminates. Agreement between theory and experiment was quite good. A micromechanics model was also developed for examining the influence of damage on damping. This model explicitly includes crack surfaces. The model provides reasonable predictions of bending stiffness as a function of damage. Damping predictions are not in agreement with the experiment. This is thought to be a result of dissipation mechanisms such as friction, which are not presently included in the analysis.
Enhancing Lithium-Ion Battery Aging Simulations: Coupling a High-Resolution, 3D, Grain-Scale Electromechanical Model to a Single-Particle Model
One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. Unfortunately, this requires simulation of thousands of charge/discharge cycles, which can be rather time consuming depending on the fidelity of the simulation. The purpose of this talk is to discuss a new modeling framework that couples a high-resolution, continuous damage model (CDM) to a single particle model (SPM) resulting in a good combination of speed and fidelity. In previous work, a 3D, continuum-level chemo-mechanical model was developed to investigate cracking within a single cathode particle comprised of hundreds to thousands of randomly oriented grains. The CDM predicted that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains were misaligned, they expanded different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicted that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicted most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicated that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. This led to a need for simulating fatigue-like mechanism that degrade the battery over longer time scales. In order to reach the time scales, need to resolve fatigue-like degradation, the CDM needs to be complemented by a faster model. Therefore, recent efforts have been focused on using results from the CDM to inform parameters within the SPM. These parameters are homogenization factors that are associated with diffusion, particle radius, and/or exchange current density. By coupling the CDM to the SPM, the aging simulation is broken up into two domains: short-term and long-term degradation. The short-term degradation occurs over a single cycle and is handled by the CDM due of its high fidelity, but relatively expensive computational cost. Such mechanism include break-in crack caused by mismatches in grain orientation. The long-term degradation occurs over tens of cycles and is handled by the SPM due it's computational efficiency. Most of the fatigue-like mechanism fall into this category. The eventual goal of this modeling framework is to upscale to a psudo-2D model allowing for full electrode simulation, which are informed by high-fidelity grain-scale simulations.
Quantification of Error Associated with Using Misaligned Meshes in Continuum Damage Mechanics Material Models for Matrix Crack Growth Predictions in Composites
The ability of a material model to capture in-plane matrix mode I and mode II crack growth is an essential component for modeling ply level damage evolution in composite structures. Previous studies using a continuum damage mechanics (CDM) approach have shown success in satisfying benchmark solutions for mode I and II crack growth. However, success was shown using a fiber-aligned meshing strategy, which encourages matrix cracks to propagate in a single band of elements, along the fiber direction. Generating a fiber-aligned mesh becomes a highly involved process for laminates including off-axis (non 0° or 90°) plies. The objective of this study is to quantify the effect of non-fiber aligned mesh discretization on predictions of in-plane matrix crack propagation. The approach taken incrementally varies the mesh orientation angle relative to the fiber orientation; more specifically, misaligned meshes are used to quantify the effect of element angle orientation relative to the initial crack orientation on the energy released during matrix crack propagation simulations using a CDM method. CDM solutions obtained with the misaligned meshes are evaluated against known benchmarks for mode I and II matrix crack growth. The CDM solutions reveal a near-polynomial trend of increased predicted failure stress with increased mesh misalignment angle; hence implying a potential relationship between element orientation angle and apparent fracture toughness.
Structural analysis demonstration of constitutive and life models
The overall objective of this program is to demonstrate the applicability of NASA-developed advanced constitutive and life damage models for calculating cyclic structural response and crack initiation in selected components of reusable space propulsion systems. The computer model resulting from this program will enable the user to produce an accurate life prediction of hot gas path, life limiting components of propulsion systems such as the space shuttle main engine (SSME). Previously developed computer models addressing constitutive modeling and life damage will be combined in an advanced finite element analysis to generate a sophisticated baseline life prediction program. A material data base will be established for the constitutive and life models parametrically involving temperature, strain range, strain rate, mean strain/stress, and dwell time. The verified computer program will be used to accomplish the life predictions of three SSME critical components as evidence of the model functionality.
A Dual Spring Modeling Approach for Static and Fatigue Failure Assessments of Carbon/Epoxy Composite Sub-Elements
A dual spring model is developed for the static and fatigue damage predictions of laminates interface in composite structures. Stress concentrations can be induced by the defects formed in the fabrication or service process. A conventional S-N based fatigue damage model may not be accurate to predict the fatigue life of a structure with high stress concentration. With the dual spring model, static delamination failure can be simulated using springs of cohesive type material model while fatigue delamination development can be predicted using linear springs, where the crack driving force is computed based on virtual crack closure technique (VCCT). A Paris law type fatigue growth law with its mode mixity is applied for fatigue crack growth prediction. After verified using benchmark examples, including Double Cantilever Beam (DCB), End-Notched Flexure (ENF) and Mix-Mode Bending (MMB), the proposed dual spring model is applied in the static and fatigue damage prediction of NASA/Boeing sub-elements and UTC sub-elements.
From S-N to the Paris Law with a New Mixed-Mode Cohesive Fatigue Model
The relationship between fatigue life and fatigue crack propagation rate is explored with a new cohesive damage model. The parameters of the model are obtained from idealizations of S-N diagrams used in engineering design. The model is based on the hypothesis that both stable tearing damage and damage due to cyclic loading are representations of a density of microcracks and, therefore, a single damage variable can describe the state of damage. This assumption implies that the quasi-static cohesive law that describes tearing is also the envelope of the fatigue damage. Fatigue damage within the cohesive envelope is assumed to accumulate at a rate that depends on the displacement jumps. The fatigue model was implemented as a UMAT subroutine for Abaqus cohesive elements by adding fatigue damage accumulation to a cohesive model based on the Turon mixed-mode cohesive laws. The analyses were conducted using a simplified cyclic loading procedure in which the maximum applied load is kept constant and the computational expense of cycling the load is avoided. The predicted propagation rates in mode I and mixed mode were compared to experimental results for IM7/8552 graphite/epoxy tape. Several aspects of the results were investigated, including the effect of R-curves, the stress ratio R, and the difference between displacement control and force control.
Numerical modeling and experimental validation of low velocity impact of woven GFRP/CFRP composites
Low-velocity impact of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composite laminates was studied experimentally and numerically. Hybrid laminates containing blocked layers of GFRP/CFRP/GFRP with all plies oriented at 0° were investigated. Relatively high impact energies were used to obtain full perforation of the laminate in a low-velocity impact setup. Numerical simulations were carried out using the in-house transient dynamics finite element code, Sierra/SM, developed at Sandia National Laboratories. A three-dimensional continuum damage model was used to describe the response of a woven composite ply. Two methods for handling delamination were considered and compared: (1) cohesive zone modeling and (2) continuum damage mechanics. The reduced model size achieved by omission of the cohesive zone elements produced acceptable results at reduced computational cost. Further, the comparison between different modeling techniques can be used to inform modeling decisions relevant to low velocity impact scenarios. The modeling was validated by comparing with the experimental results and showed good agreement in terms of predicted damage mechanisms and impactor velocity and force histories.
LET analyses of biological damage during solar particle events
The effects of nuclear reactions on integral low-linear-energy-transfer (LET) protons spectra are studied, behind typical levels of spacecraft and body shielding, for the historically largest flares using the high-energy transport code BRYNTRN in conjunction with several biological damage models. The cellular track model of Katz provides an accurate description of cellular damage from heavy ion exposure. The track model is applied with BRYNTRN to provide a LET decomposition of survival and transformation rates for solar proton events. In addition, a fluence-based risk coefficient formalism is used to estimate Harderian gland-tumor induction in rodents and cataractogenesis in rabbits from solar flares, and a LET analysis is used to assess the relative contribution from target fragments on these biological endpoints.
Relating Measured Component Damage to Assessed Component Reliability in Reliability Integrity Management (RIM)
There is currently no widely agreed detailed general method for licensing a novel plant incorporating novel materials (or materials being deployed in novel environments); in many such situations, there are no directly applicable engineering code cases for decision-makers (including regulators) to rely on. It may be possible to develop an approach to licensing such a plant that is based on the Reliability and Integrity Management (RIM) approach delineated in ASME BPVC Section XI Division 2. NRC Regulatory Guide 1.246, Rev.0, endorses, with conditions, the subject portion of the ASME Code. But that portion of the ASME code is written at a very high level, and there are fundamental technical challenges associated with applying it literally to licensing a real plant. In the RIM approach, applicants need to do the following (among other things): • Allocate target reliabilities to structures, systems, and components (SSCs) that collectively support the top-level plant safety and availability objectives; • Understand failure modes of those SSCs, and the degradation mechanisms that could lead to those failure modes; • Develop and propose a program of surveillances that will identify degradation prior to failure of SSCs; • Provide a means of reporting results, taking actions for anomalous or undesirable conditions, and give the regulator assurance of continued safe operations. Applying RIM in a specific case will call for advances in the state of practice of relating physical observables to functional reliability of certain component types. Except where a given level of damage corresponds to a failed (or nearly failed) state, it is not practical to establish a precise quantitative relationship between physical observables and reliability. This paper focuses on managing risk of passive component failures based on observable damage parameters. A simple approach to cumulative damage modeling will be illustrated with a view to possible use in RIM applications.
A microstructure-based modeling approach to predict the mechanical properties of Zr alloy with hydride precipitates
In nuclear reactors, hydrides can form in fuel cladding due to hydrogen absorption in ZIrcaloy and cause embrittlement. This work presents a microstructure-based finite element model to predict the stress-strain response of Zircaloy containing hydrides. Quantitative microstructural details extracted from scanning electron microscopy (SEM) images were used to generate heterogeneous microstructures including the morphology and spatial distribution of hydrides. The constitutive material model for zircaloy in this study is based on crystal plasticity theory which considers the hexagonal close-packed (HCP) atomic structure of Zircaloy material. The hydrides were modeled as brittle material along with a damage model. Hydride formation inside the zircoloy matrix results in residual stress. This phenomenon is also captured in this model. A parametric study has been conducted to understand the effect of volume fraction, orientation, and lamellae thickness of the hydride phase on the mechanical properties of the overall material.
Equivalent electron fluence for solar proton damage in GaAs shallow junction cells
The short-circuit current reduction in GaAs shallow junction heteroface solar cells was calculated according to a simplified solar cell damage model in which the nonuniformity of the damage as a function of penetration depth is treated explicitly. Although the equivalent electron fluence was not uniquely defined for low-energy monoenergetic proton exposure, an equivalent electron fluence is found for proton spectra characteristic of the space environment. The equivalent electron fluence ratio was calculated for a typical large solar flare event for which the proton spectrum is PHI(sub p)(E) = A/E(p/sq. cm) where E is in MeV. The equivalent fluence ratio is a function of the cover glass shield thickness or the corresponding cutoff energy E(sub c). In terms of the cutoff energy, the equivalent 1 MeV electron fluence ratio is r(sub p)(E sub c) = 10(9)/E(sub c)(1.8) where E(sub c) is in units of KeV.
Matrix Fatigue Cracking Mechanisms of Alpha(2) TMC for Hypersonic Applications
The objective of this work was to understand matrix cracking mechanisms in a unidirectional alpha(sub 2) TMC in possible hypersonic applications. A (0)(sub 8) SCS-6/Ti-24Al-11Nb (at. percent) TMC was first subjected to a variety of simple isothermal and nonisothermal fatigue cycles to evaluate the damage mechanisms in simple conditions. A modified ascent mission cycle test was then performed to evaluate the combined effects of loading modes. This cycle mixes mechanical cycling at 150 and 483 C, sustained loads, and a slow thermal cycle to 815 C. At low cyclic stresses and strains more common in hypersonic applications, environment-assisted surface cracking limited fatigue resistance. This damage mechanism was most acute for out-of-phase nonisothermal cycles having extended cycle periods and the ascent mission cycle. A simple linear fraction damage model was employed to help understand this damage mechanism. Time-dependent environmental damage was found to strongly influence out-of-phase and mission life, with mechanical cycling damage due to the combination of external loading and CTE mismatch stresses playing a smaller role. The mechanical cycling and sustained loads in the mission cycle also had a smaller role.
Tailoring ductile-phase toughened tungsten hierarchical microstructures for plasma-facing materials
Biological materials, such as bones, nacre, etc., have been found to show attractive and unique combinations of stiffness, strength and fracture toughness. Research has been conducted in various engineering areas to mimic the naturally hierarchical microstructures or nanostructures of these materials to produce materials with optimum stiffness, high strength and fracture toughness for their intended structural applications. In the same objective, this work applies a multiscale microstructural approach recently developed to investigate the deformation and fracture behavior of ductile phase toughened tungsten (W) materials such as tungsten-nickel/iron (W-Ni/Fe) composites that possess lamellar-like and hierarchical “brick-and-mortar” (BAM) microstructures. First, the approach is used to simulate tensile loading of W-Ni/Fe specimens cut out from hot-rolled W-Ni/Fe plates which possess lamellar-like microstructures. The finite element model of the gage section of the specimen consists of a W-Ni/Fe dual-phase microstructural domain in which the constitutive behaviors of W and Ni/Fe phases are described by an elastic-plastic damage model. The predicted material stress-strain response and crack pattern development as a function of loading are then compared to the corresponding experimental results to determine the constitutive model parameters for W and Ni/Fe. Subsequently, the model parameters are used to analyze W-Ni/Fe BAM microstructures that are artificially created to investigate the effects of microstructural features and morphologies on the composite stress-strain response, damage, and fracture patterns. The modeling shows that regular BAM microstructures that experience bridging mechanism combined with crack penetration across W-phase regions exhibit significantly higher strengths than the rather random lamellar-like microstructures. More significantly, however adjusting the brick’s length-to-height ratio, the BAM microstructure can be designed to allow a more distributed damage zone which leads to increased strength, ductility and fracture energy.