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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.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A finite micro-rotation material point method for micropolar solid and fluid dynamics with three-dimensional evolving contacts and free surfaces

This paper introduces an explicit material point method designed specifically for simulating the micropolar continuum dynamics in the finite deformation and finite microrotation regime. The material point method enables us to simulate large deformation problems while circumventing the potential mesh distortion without remeshing. To eliminate rotational motion damping and loss of angular momentum during the projection, we introduce the mapping for microinertia and angular momentum between particles and grids through the affine particle-in-cell approach. The microrotation and the curvature at each particle are updated through zero-order forward integration of the microgyration and its spatial gradient. We show that the microinertia and the angular momentum are conserved during the projections between particles and grids in our formulation. We verify the formulation and implementation by comparing with the analytical dispersion relation of micropolar waves under the small strain and small microrotation, as well as the analytical soliton solution for solids undergoing large deformation and large microrotation. Additionally we also demonstrate the capacity of the proposed computational framework to handle a wide spectrum of simulations that exhibit size effects in the geometrical nonlinear regime through three representative numerical examples, i.e., a cantilever beam torsion problem, a fragment-impact penetration problem, and a micropolar fluid discharging problem.

42 ENGINEERING↗
DOE OSTI2021

Tool-workpiece stick-slip conditions and their effects on torque and heat generation rate in the friction stir welding

Friction stir welding (FSW) has found increased applications in automotive and aerospace industries due to its advantages of solid-state bonding, no fusion and melting, and versatility in various working conditions and material combinations. However, the relationship among processing parameters, material properties, and bonding extent and fidelity remains largely empirical, primarily because of the lack of the mechanistic understanding of the tool-workpiece frictional behavior that affects our subsequent understanding of microstructural evolution and interface bonding formation. While the tool-workpiece stick-slip condition is believed to dictate the resulting torque and heat generation rate during the welding process, it remains rare and elusive to conduct a quantitative experimental measurement of such interfacial field. On the other hand, numerical simulations based on Computational Fluid Dynamics (CFD) rely on ad hoc assumptions of interfacial pressure and shear-stress conditions, but predictions can only be validated via the medium- and far-range temperature field which is known to be insensitive to the interfacial frictional behavior. This work first presents a comparison among two CFD-based simulation methodologies and the Coupled Eulerian Lagrangian (CEL) model in finite element method, the last of which uses the Coulomb friction so that the stick-slip is naturally developed. Based on the Hill-Bower similarity relationship in the contact analysis, an analytical model is developed here to prove why a constant stick-slip fraction will be developed in the steady state, to correlate the stick-slip fraction to processing parameters such as the tool spin rate, and further to derive dimensionless functions for torque and heat-generation-rate predictions. Pros and cons of various numerical approaches in predicting stick-slip are discussed, and our analytical model has been found to agree well with our numerical simulation and literature experimental results. These analyses provide the critical strain-rate and temperature fields that are needed for the bonding analysis in our future work.

36 MATERIALS SCIENCE↗
DOE OSTI2021

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

Abstract The PRISMS-Fatigue open-source framework for simulation-based analysis of microstructural influences on fatigue resistance for polycrystalline metals and alloys is presented here. The framework uses the crystal plasticity finite element method as its microstructure analysis tool and provides a highly efficient, scalable, flexible, and easy-to-use ICME community platform. The PRISMS-Fatigue framework is linked to different open-source software to instantiate microstructures, compute the material response, and assess fatigue indicator parameters. The performance of PRISMS-Fatigue is benchmarked against a similar framework implemented using ABAQUS. Results indicate that the multilevel parallelism scheme of PRISMS-Fatigue is more efficient and scalable than ABAQUS for large-scale fatigue simulations. The performance and flexibility of this framework is demonstrated with various examples that assess the driving force for fatigue crack formation of microstructures with different crystallographic textures, grain morphologies, and grain numbers, and under different multiaxial strain states, strain magnitudes, and boundary conditions.

Chemistry↗
DOE OSTI2023

Initial Fracture Propagation Modeling of Graphite Components with Grizzly

Graphite has historically been extensively used in power reactor cores and will be used in multiple types of advanced reactors currently under development. These graphite structural components can experience significant stresses due to nonuniform volumetric strains induced by irradiation and thermal expansion, which can lead to fracture. Robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors are important for evaluating component integrity, developing design standards, and interpreting experimental results to characterize graphite performance. The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program has been developing degradation models for other structural components in nuclear reactors within the Grizzly and BlackBear codes. This report documents an effort to develop initial capabilities for modeling graphite fracture within these codes, building on prior efforts to model fracture in other materials. Major elements of this effort include developing a new system for modeling fracture nucleation and growth in two dimensions using the extended finite element method and incorporating a damage and plasticity model. These capabilities are applied here to model a representative graphite component and a splitting disc experiment used to obtain tensile strength.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Assessment of reverse gun taylor cylinder experimental configuration

Experimental efforts for Taylor-anvil impact tests have often been limited to near room temperature. The ‘Reverse Gun’ method proposed by Gust in 1982 allows for the Taylor impact specimen to be uniformly heated without temperature losses before impact. Through the use of finite element analysis, we explore two topics in this work. First, we examine whether the reverse gun experimental configuration is comparable to the traditional Taylor-anvil setup. Second, we assess the accuracy of several commonly employed flow strength models in terms of their ability to predict the reverse gun experimental results which involve dynamic loading conditions and complex thermo-mechanical coupling. The reverse gun simulations are performed for tantalum targets at initial temperatures in the range 295 K to 1295 K and velocities from 135 m/s to 242 m/s. We show that with suitable care in the modeling of the preheated reverse gun experiments one can make valuable assessments of flow strength models. Given the conditions explored, these observations probe the thermal softening, strain hardening, and strain rate sensitivity of the material.

42 ENGINEERING↗
DOE OSTI2020

Sample problems for Section III, Division 5 design by inelastic analysis of Grade 91 components

This report works through two sample design analyses of representative Grade 91 components using the ASME Boiler & Pressure Vessel Code Section III, Division 5, Appendix HBB-T rules for the strain and deformation and creep-fatigue design criteria using a design by inelastic analysis approach. The component geometries and loadings were selected to span a wide variety of potential applications. The sample components are an endplate geometry, which is fairly representative of typical pressure vessel construction, and a core block, representing a critical component in a heat pipe microreactor, which has a complicated geometry and complex thermal stress history. These sample problems serve several functions. First, they are complete worked examples of how to apply the current design by inelastic analysis rules. Second, they serve as test cases to evaluate the current rules and provide feedback on how they could be optimized to deal with complicated component geometries or to be better automated in modern finite element analysis software. Finally, the analysis here uses an inelastic constitutive model for Grade 91 developed by Argonne National Laboratory and proposed for inclusion in the ASME Boiler & Pressure Vessel Code Section III, Division 5 rules as a reference constitutive model. Using this constitutive model in the sample problem analyses tests the model in the context of the ASME Code rules. The final conclusions of this report are that the material model and the current Code rules are satisfactory, but that the Code rules could be optimized to simplify automation and reduce over conservatism. Future work should address the specific optimization topics discussed in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Development of Graphite Thermal and Mechanical Modeling Capabilities in Grizzly

Nuclear-grade graphites are used extensively in the core designs of multiple types of advanced nuclear reactors. In the reactor environment, graphite is exposed over long durations to extreme conditions, including high temperatures, radiation and potentially molten salt and oxygen. Exposure to these conditions can cause several degradation mechanisms in graphite, including nonuniform volumetric strains induced by irradiation and thermal expansion, which lead to stresses that can compromise the performance of graphite components. Evaluating component integrity, predicting component performance over the reactor lifetime, and developing design standards all require robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors. This report documents progress in an ongoing effort to develop modeling and simulation tools in the Grizzly code for predicting the performance of graphite exposed to reactor conditions. Recent developments include a set of thermal and mechanical models that now include the IG-110, NBG-18, and H-451 graphite grades. Improvements have also been made to a nonlinear damaged plasticity model applicable to predicting damage under tension and compression to quasibrittle materials, including graphite. In addition, enhancements have been made to the extended finite element method implementation targeted at simulating graphite fracture. These include new capabilities for crack nucleation in the interior of a solid body, improved treatment of crack nucleation on free surfaces, and more robust modeling approaches for crack growth approaching free surfaces or other cracks.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Designing Cladded Components for High Temperature Nuclear Service: Part I—Analysis Methods

Use of corrosion-resistant cladding can greatly extend the design life of structural components in many advanced reactor systems. However, there are currently no ASME design rules for cladded components to guard against creep-fatigue failure and ratcheting strain accumulation in elevated temperature nuclear service. This paper, presented in two parts, addresses this gap by proposing a design strategy for cladded components that do not require long-term testing of clad materials. The proposed approach relies on approximate design analysis methods for two types of clad materials—a soft clad that creeps much faster than and has lower yield stress than the class A base material and a hard clad that creeps much slower than and has higher yield stress than the class A base material. Part I discusses the approximate analysis strategies for the clad materials—treat a soft clad as perfectly compliant and a hard clad as linear elastic—and Part II develops a complete set of design rules for each of the two types of cladded components. In conclusion, finite element analyses of representative high temperature reactor components show that the proposed design analysis methods can bound the design quantities in soft cladded components and approximate the design quantities in hard cladded components.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Predicting System Response at Unmeasured Locations

Traditional techniques to derive dynamic specification for components have a great deal of uncertainty. One of the major sources of uncertainty is that the number of response measurements in the operational system environment is insufficient to determine the component motion. This inadequacy is due to logistical limitations for data recording in field testing and space limitations for accelerometers, strain gages and associated wiring. Available measurements are often some distance from the component and therefore do not represent component motion. Typical straight-line envelopes of these unrepresentative measurements guarantee an increase in the uncertainty. In this paper multiple methods are attempted to expand a sparse set of field test measurements on a system to responses of interest that cannot be measured in the field due to the limitations. Proof of concept is demonstrated on the Modal Analysis Test Vehicle (MATV). The responses of interest, known as “truth responses”, are measured in a system vibration environment along with an optimized sparse set of 30 field responses. Methods to expand the field responses to the truth responses are demonstrated by comparing the acceleration spectral density of the expanded response to the measured response. Two methods utilize a validated finite element model of the MATV. One is developed from purely experiment based frequency response functions of a laboratory pre-test. Finally, these approaches are designed to drastically reduce the uncertainty of the component in-service motion as a basis for developing specifications that are guaranteed to be conservative with a known (instead of unknown) conservatism.

42 ENGINEERING↗
DOE OSTI2021

Radiation effects on stress evolution and dimensional stability of large fusion energy structures

Here we assess the effects of neutron irradiation on the deformation and stress evolution of large-scale fusion energy structures. This is accomplished through non-linear finite element structural analysis of the coupled thermal and mechanical fields at the Beginning-Of-Life (BOL), at 45 dpa, and at 90 dpa. Radiation effects include volumetric swelling and the influence of radiation on the mechanical properties. The system studied here is a large section of a full inboard module of an integrated structure comprising the First Wall and Blanket (FW/B) of a Dual Cooled Lithium-Lead (DCLL) energy conversion unit in the Fusion Nuclear Science Facility (FNSF). The structural material is the ferritic/martensitic steel F82H. We analyze several radiation effects phenomena that can lead to significant impact on the mechanical design and lifetime of the structure. These include volumetric swelling effects on the assembly and disassembly of modules and the impact of spatial gradients in neutron damage and helium generation on deformation, stress evolution, and plastic strain accumulation. We show that the stress state is strongly influenced by the accumulation of swelling strains, radiation hardening and softening, and by spatial gradients in displacement damage and helium gas generation. Several key regions in the FW/B structure are identified where severe plastic strains accumulate and may be potential sites for failure, especially during cyclic reactor operations. We finally show that minimum gaps between Inboard (IB) blanket sectors must be present during assembly so as to avoid excessive stress and strain in FW/B modules critical regions and raising chances of failure. A range of structural displacements are shown, from as low as 4 mm at BOL for free side walls to as high as 46 mm at 90 dpa for fully constrained side walls.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

SAVY-4000 Finite-Element Drop Test Analysis

PFE Auxiliary Systems conducted drop testing on SAVY-4000 containers to evaluate structural response under 12-foot drop conditions. In support of that effort, a finite-element modeling capability was developed to simulate drop response across multiple container sizes and impact orientations. The purpose of this work was to provide a consistent analysis framework that could support interpretation of testing, compare response trends across multiple configurations, and generate quantities of interest for later comparison with experimental data. More broadly, the analysis and testing were intended to assess whether the containers continued to perform their primary function after a 12-foot drop, namely maintaining structural integrity and containment of the contents. The modeling approach combined an implicit preload analysis with an explicit drop simulation so that each drop event began from a mechanically realistic assembled condition, including compression of the silicone O-ring. Separate models were developed for 2-quart, 5-quart, 12-quart, and 10-gallon containers. The results were evaluated in terms of strain-gauge response, collar-lid gap behavior, and accumulated plastic strain. In addition, parametric studies were performed on the 2-quart container to assess sensitivity to O-ring stiffness, friction, canister thickness, geometry tolerance, and mesh density. The simulations showed that predicted drop responses depended strongly on both container size and drop orientation. Gap metrics identified cases in which the predicted collar-lid opening exceeded the nominal O-ring cross-section threshold, while plastic strain metrics identified localized regions of elevated permanent deformation. Parametric studies showed that the predicted response was especially sensitive to the assumed O-ring stiffness and contact friction, while the geometry tolerance study produced smaller changes in the cases examined. The main value of this work was that it established a repeatable modeling and simulation workflow to support drop-test implementation, evaluate effects of future configuration changes, and understand modeling assumptions that most influenced predicted response. At the current stage, the results were viewed as preliminary model predictions rather than validated predictions. The next step would be to compare drop-test data to the model so that predictive values of the workflow could be refined and used with greater confidence to assess whether the containers maintained structural integrity and containment of the contents after a 12-foot drop.

42 ENGINEERING↗
DOE OSTI2023

A combined experimental and crystal plasticity study of grain size effects in magnesium alloys

This work presents a method to incorporate the micro Hall-Petch equation into the crystal plasticity finite element (CPFE) framework accounting for the microstructural features to understand the coupling between grain size, texture, and loading direction in magnesium alloys. The effect of grain size and texture is accounted for by modifying the slip resistances of individual basal and prismatic systems based on the micro Hall-Petch equation. The modification based on the micro Hall-Petch equation endows every slip system at each microstructural point with a slip system-level grain size and maximum compatibility factor, which are in turn used to modify the slip resistance. While the slip-system level grain size is a measure of the grain size, the maximum compatibility factor encodes the effect of the grain boundary on the slip system resistance modification and is computed based on the Luster-Morris factor. The model is calibrated using experimental stress-strain curves of Mg-4Al samples with three different grain sizes from which the Hall-Petch coefficients are extracted and compared with Hall-Petch coefficients predicted using original parameters from previous work. The predictability of the model is then evaluated for a Mg-4Al sample with different texture and three grain sizes subjected to loading in different directions. The calibrated parameters are then used for some parametric studies to investigate the variation of Hall-Petch slope for different degrees of simulated spread in basal texture, variation of Hall-Petch slope with loading direction relative to basal poles for a microstructure with strong basal texture, and variation of yield strength with change in grain morphology. The proposed approach to incorporate the micro Hall-Petch equation into the CPFE framework provides a foundation to quantitatively model more complicated scenarios of coupling between grain size, texture and loading direction in the plasticity of Mg alloys.

Crystal plasticity↗
DOE OSTI2022

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗
DOE OSTI2024

Characterization of electromigration-induced short-range stress development in Al(0.25 at. % Cu) conductor line

Scanning x-ray microbeam topography and fluorescence experiments were conducted in situ to study the electromigration behavior of a 0.5 μm thick, 10 μm wide, and 200 μm long Al(0.25 at. % Cu) conductor line with 1.5 μm-thick SiO2 passivation on a single crystal Si substrate. The strain sensitivity of x-ray topography measurement allowed detailed examination of the electromigration-induced stress distribution and evolution in the conductor line in response to the depletion of Cu solute early in the electromigration process. Upon electromigration at 0.4 MA/cm2 and 303 °C, a short-range stress gradient was quickly induced by Al migration in the Cu-depleted cathode region to counteract further Al flow. The stress gradient was fully developed during the 5.3 h incubation time, extending over the critical Blech length of about 66 μm from the cathode end. Plastic deformation then occurred at the downstream end of the Cu-depleted region. The preferential electromigration of Cu did not cause detectable stress change outside the Cu-depleted region, except for the significant stress development from the Al2Cu precipitation at the anode end which appeared to initiate the fracture in the passivation. Preliminary finite difference modeling was undertaken to simulate the experimental observations, from which important parameters dictating electromigration in Al(Cu) line were extracted: an apparent effective valence of −5.6 and −1.9 for Cu and Al in Al(Cu), respectively, and a critical Cu concentration of 0.16 at. % above which Al grain boundary diffusion is effectively blocked.

Physics↗
DOE OSTI2021

Initial demonstration of automated fuel performance modeling with 1977 EBR-II metallic fuel pins using BISON code with FIPD and IMIS databases

Using the BISON fuel performance code, simulations were conducted using an automated process to read initial and operating conditions from the Fuels Irradiation and Physics Database (FIPD) and Integral Fast Reactor materials information system (IMIS) database, which contains metallic fuel data from the Experimental Breeder Reactor-II (EBR-II). This work demonstrates use of an integrated framework to access the vast majority of EBR-II experimental fuel pin data to support rapid development of fuel performance models for next-generation metallic fuel systems. With this capability, validation for fuel qualification can be performed rapidly. Between IMIS and FIPD, there is enough information to conduct 1977 unique EBR-II metallic fuel pin histories from 24 different experiments, at varying levels of detail between the two databases. Each of these histories includes a high-resolution power history, flux history, coolant channel flow rates, and coolant channel temperatures. Fission gas release (FGR), cumulative damage fraction (CDF), fuel axial swelling, cladding profilometry, and burnup were all simulated in BISON. The results were compared to post-irradiation examination (PIE) results for the initial demonstration of automated BISON modeling. BISON simulations conducted with IMIS and FIPD were in rough agreement with PIE measurements and calculations. Cladding profilometry, FGR, and fuel axial swelling were found to be in rough agreement with PIE measurements, depending on the physics used within the BISON input files. Here, the mechanical contact solver chosen was found to significantly impact axial fuel swelling and cladding strain predictions. CDF values were assessed to see whether pin failure may have been predicted (CDF ≥ 1). This work suggests that continued development of an automated tool for BISON should focus on inclusion of the Fast Flux Test Facility (FFTF) experimental data for a larger database for metallic fuel, improved physical models to better capture fuel performance, such as fuel-cladding interactions, and a more detailed comparison with available PIE data to further the BISON model development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Ligand-Controlled Energetics and Charge Transfer in Pure and Doped Nanocrystals

The research in this award period initially focused on the spectroscopy and dynamics of spherical CdSe nanocrystals and CdSe nanoplatelets. In the later part of the grant period we turned our attention to InP-based nanocrystals. It has long been believed that the transient absorption signal from approximately spherical CdSe nanocrystals is dominated by conduction band state filling. However, this long-held belief has recently been challenged, based on femtosecond absorption measurements. However, the recent studies challenging the conventional wisdom do not account of finite rates of spin-lattice relaxation. Our work showed that this is a crucial error and that the recent results are misinterpreted, that is, the previous prevailing wisdom is correct. Another study focused on CdSe nanocrystal photochemistry used transient absorption (TA) spectroscopy to determine the spatial extents of CdSe nanoplatelet (NPL) excitons. Our work shows that the spatial extents of the excitons in the NPLs are far less than the physical dimension of the NPL. Using a model developed to understand the transient absorption spectroscopy, we obtain an average excitonic area of 21.2 ± 2.5 nm 2 , independent of the nanoplatelet size. Our work on InP/ZnSe and InP/ZnS core/shell nanocrystals shows that when there is a small lattice mismatch (InP-ZnSe, 3.5%) a coherent core-shell interface is obtained. In contrast, the InP-ZnS lattice mismatch is much larger, 8.3%. In this case, the experimental results showed best agreement with calculations in which lattice strain is ignored, indicating that the interfaces in InP/ZnS nanocrystals are largely incoherent.

14 SOLAR ENERGY↗
DOE OSTI2022

Revisiting Multi-Material Composite Structures with Homogenized Composite Properties

Composite structures inherently develop residual stresses during their curing process. Driven predominately by mismatched thermal strains between differing materials or ply orientations, but also affected by curing process phenomena like polymer shrinkage, these residual stresses can lead to failure within composite structures. There are several methods varying in complexity that can be used to model the development of residual stresses, all of which are capable of capturing sufficient detail to understand the residual stress state at the ply level. However, explicitly modeling all plies of a layup in a composite structure can be prohibitively expensive based on the number of plies, structure size, and required element size. The computational cost can be reduced through the homogenization of the composite layup without losing much fidelity of the overall response of the structure. The homogenization process reduces the many plies of a laminate to a single lamina that reduces complexity and increases the mesh size where a single element can span multiple plies. This report focuses on verification and validation efforts for a homogenization process using a suite of finite element simulations rather than an analytic solution derived from classical laminate theory. Initial verification using representative element volumes indicated there was minimal error in the homogenization process; however, this compounded to a small, but acceptable error in strip and split ring experimental composite structures. The error does under predict the residual stress state in the strip and split ring and should be accounted for when simulating composite structures with homogenized properties.

36 MATERIALS SCIENCE↗