Process parameter selection in laser powder bed fusion (LPBF) controls the as-printed dimensional tolerances, pore formation, surface quality and microstructure of printed metallic structures. Measuring the stochastic mechanical performance for a wide range of process parameters is cumbersome both in time and cost. In this study, we overcome these hurdles by using high-throughput tensile (HTT) testing of over 250 dogbone samples to examine process-driven performance of strut-like small features, ~1 mm2 in austenitic stainless steel (316 L). The output mechanical properties, porosity, surface roughness and dimensional accuracy were mapped across the printable range of laser powers and scan speeds using a continuous wave laser LPBF machine. Tradeoffs between ductility and strength are shown across the process space and their implications are discussed. While volumetric energy density deposited onto a substrate to create a melt-pool can be a useful metric for determining bulk properties, it was not found to directly correlate with output small feature performance.
The concept of a nonlocal elastic metasurface has been recently proposed and experimentally demonstrated in Zhu et al. (2020). When implemented in the form of a total-internal-reflection (TIR) interface, the metasurface can act as an elastic wave barrier that is impenetrable to deep subwavelength waves over an exceptionally wide frequency band. The underlying physical mechanism capable of delivering this broadband subwavelength performance relies on an intentionally nonlocal design that leverages long-range connections between the units forming the fundamental supercell. This paper explores the design and application of a nonlocal TIR metasurface to achieve broadband passive vibration isolation in a structural assembly made of multiple dissimilar elastic waveguides. The specific structural system comprises shell, plate, and beam waveguides, and can be seen as a prototypical structure emulating mechanical assemblies of practical interest for many engineering applications. The study also reports the results of an experimental investigation that confirms the significant vibration isolation capabilities afforded by the embedded nonlocal TIR metasurface. These results are particularly remarkable because they show that the performance of the nonlocal metasurface is preserved when applied to a complex structural assembly and under non-ideal incidence conditions of the incoming wave, hence significantly extending the validity of the results presented in Zhu et al. (2020). Results also confirm that, under proper conditions, the original concept of a planar metasurface can be morphed into a curved interface while still preserving full wave control capabilities.
In the pursuit of improving additively manufactured (AM) component quality and reliability, fine-tuning critical process parameters such as laser power and scan speed is a great first step toward limiting defect formation and optimizing the microstructure. However, the synergistic effects between these process parameters, layer thickness, and feedstock attributes (e.g. powder size distribution) on part characteristics such as microstructure, density, hardness, and surface roughness are not as well-studied. In this work, we investigate 316L stainless steel density cubes built via laser powder bed fusion (L-PBF), emphasizing the significant microstructural changes that occur due to altering the volumetric energy density (VED) via laser power, scan speed, and layer thickness changes, coupled with different starting powder size distributions. This study demonstrates that there is not one ideal process set and powder size distribution for each machine. Instead, there are several combinations or feedstock/process parameter ‘recipes’ to achieve similar goals. This study also establishes that for equivalent VEDs, changing powder size can significantly alter part density, GND density, and hardness. Through proper parameter and feedstock control, part attributes such as density, grain size, texture, dislocation density, hardness, and surface roughness can be customized, thereby creating multiple high-performance regions in the AM process space.
This report provides detailed documentation of the algorithms that where developed and implemented in the Plato software over the course of the Optimization-based Design for Manufacturing LDRD project.
With the rapid proliferation of additive manufacturing and 3D printing technologies, architected cellular solids including truss-like 3D lattice topologies offer the opportunity to program the effective material response through topological design at the mesoscale. The present report summarizes several of the key findings from a 3-year Laboratory Directed Research and Development Program. The program set out to explore novel lattice topologies that can be designed to control, redirect, or dissipate energy from one or multiple insult environments relevant to Sandia missions, including crush, shock/impact, vibration, thermal, etc. In the first 4 sections, we document four novel lattice topologies stemming from this study: coulombic lattices, multi-morphology lattices, interpenetrating lattices, and pore-modified gyroid cellular solids, each with unique properties that had not been achieved by existing cellular/lattice metamaterials. The fifth section explores how unintentional lattice imperfections stemming from the manufacturing process, primarily sur face roughness in the case of laser powder bed fusion, serve to cause stochastic response but that in some cases such as elastic response the stochastic behavior is homogenized through the adoption of lattices. In the sixth section we explore a novel neural network screening process that allows such stocastic variability to be predicted. In the last three sections, we explore considerations of computational design of lattices. Specifically, in section 7 using a novel generative optimization scheme to design novel pareto-optimal lattices for multi-objective environments. In section 8, we use computational design to optimize a metallic lattice structure to absorb impact energy for a 1000 ft/s impact. And in section 9, we develop a modified micromorphic continuum model to solve wave propagation problems in lattices efficiently.
Metallic lattice structures are being considered for shock mitigation applications due to their superior mechanical properties, energy absorption capability and lightweight characteristics inherent of the additive manufacturing process. In this study, shock compression experiments coupled to x-ray phase contrast imaging (PCI) were conducted on 316L stainless steel lattices. Meso-scale simulations incorporating the as-built lattice structure characterized by computed tomography were used to simulate PCI radiographs in CTH for direct comparison to experimental data. The methodology presented here offers robust validation for constitutive properties to further our understanding of lattice compaction at application-relevant strain rates.
The advanced materials team investigated the use of additively manufactured metallic lattice structures for mitigating impact response in a Davis gun earth penetrator impact experiment. High-fidelity finite element models were developed and validated with quasistatic experiments. These models were then used to simulate the response of such lattices when subjected to the acceleration loads expected in the Davis gun experiment. Results reveal how the impact mitigation performance of lattices can change drastically at a certain relative density. Based on these observations, an experiment deck was designed to probe the response of lattices with different relative densities during the Davis gun phase 2 shots. The expected performance of these lattices is predicted before testing based on simulation results. The results of the Davis gun phase 2 shots are expected to provide data which will be used to assess the predictive capability of the finite element simulations in such a complex impact environment.
Grain-scale microstructure evolution during additive manufacturing is a complex physical process. As with traditional solidification methods of material processing (e.g. casting and welding), microstructural properties are highly dependent on the solidification conditions involved. Additive manufacturing processes however, incorporate additional complexity such as remelting, and solid-state evolution caused by subsequent heat source passes and by holding the entire build at moderately high temperatures during a build. We present a three-dimensional model that simulates both solidification and solid-state evolution phenomena using stochastic Monte Carlo and Potts Monte Carlo methods. The model also incorporates a finite-difference based thermal conduction solver to create a fully integrated microstructural prediction tool. The three modeling methods and their coupling are described and demonstrated for a model study of laser powder-bed fusion of 300-series stainless steel. The investigation demonstrates a novel correlation between the mean number of remelting cycles experienced during a build, and the resulting columnar grain sizes.
This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.
We develop a generalized stress inversion technique (or the generalized inversion method) capable of recovering stresses in linear elastic bodies subjected to arbitrary cuts. Specifically, given a set of displacement measurements found experimentally from digital image correlation (DIC), we formulate a stress estimation inverse problem as a partial differential equation-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations. By using a combination of finite elements, DIC, and a matrix-free optimization framework, the generalized inversion method can be used on any arbitrary geometry, provided that the DIC camera can view a sufficient part of the surface. We present numerical simulations and experiments, and we demonstrate that the generalized inversion method can be applied to estimate residual stress.
While elastic metasurfaces offer a remarkable and very effective approach to the subwavelength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. In applications to electromagnetic and photonic metamaterials, some success in extending the operating dynamic range was obtained by using nonlocality. However, while electronic properties in natural materials can show significant nonlocal effects, even at the macroscales, in mechanics, nonlocality is a higher-order effect that becomes appreciable only at the microscales. This study introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements, whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase-gradient profiles that are functions of the wavenumber of the incident wave. The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semianalytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin-plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.
Product designs from a wide range of industries such as aerospace, automotive, biomedical, and others can benefit from new metamaterials for mechanical energy dissipation. In this study, we explore a novel new class of metamaterials with unit cells that absorb energy via sliding Coulombic friction. Remarkably, even materials such as metals and ceramics, which typically have no intrinsic reversible energy dissipation, can be architected to provide dissipation akin to elastomers. The concept is demonstrated at different scales (centimeter to micrometer), with different materials (metal and polymer), and in different operating environments (high and low temperatures), all showing substantial dissipative improvements over conventional non-contacting lattice unit cells. Further, as with other ‘programmable’ metamaterials, the degree of Coulombic absorption can be tailored for a given application. An analytic expression is derived to allow rapid first-order optimization. This new class of Coulombic friction energy absorbers can apply broadly to many industrial sectors such as transportation (e.g. monolithic shock absorbers), biomedical (e.g. prosthetics), athletic equipment (e.g. skis, bicycles, etc.), defense (e.g. vibration tolerant structures), and energy (e.g. survivable electrical grid components).
Additively manufactured metamaterials such as lattices offer unique physical properties such as high specific strengths and stiffnesses. However, additively manufactured parts, including lattices, exhibit a higher variability in their mechanical properties than wrought materials, placing more stringent demands on inspection, part quality verification, and product qualification. Previous research on anomaly detection has primarily focused on using in-situ monitoring of the additive manufacturing process or post-process (ex-situ) x-ray computed tomography. In this work, we show that convolutional neural networks (CNN), a machine learning algorithm, can directly predict the energy required to compressively deform gyroid and octet truss metamaterials using only optical images. Using the tiled nature of engineered lattices, the relatively small data set (43 to 48 lattices) can be augmented by systematically subdividing the original image into many smaller sub-images. During testing of the CNN, the prediction from these sub-images can be combined using an ensemble-like technique to predict the deformation work of the entire lattice. This approach provides a fast and inexpensive screening tool for predicting properties of 3D printed lattices. Importantly, this artificial intelligence strategy goes beyond ‘inspection’, since it accurately estimates product performance metrics, not just the existence of defects.
Due to the direct relationship between thermal history and mechanical behavior, in situ thermal monitoring is key in gauging quality of parts produced with additive manufacturing (AM). Accurate monitoring of temperatures in an AM process requires knowledge of environment and object parameters including object emissivity. The emissivity is dependent on several variables, including: wavelength, material composition, temperature, and surface topography. Researchers have been concerned with the thermal emissivity dependence on temperature since large ranges are seen in metal powder bed processes, but there is also an extensive range of surfaces produced by AM. This work focused on discovering what roughness characteristics control thermal emissivity through investigation of prototypic 316 stainless steel AM samples produced with a range of build conditions on a laser powder bed fusion machine. Through experimental measurements of emissivity using hemispherical directional reflectance (HDR), guided by simulations using a finite-difference time-domain (FDTD) Maxwell solver, it was found that combinations of existing roughness parameters describing both height and slope of the surface correlate well with emissivity changes. These parameters work well due to their apt description of surface features encouraging internal reflection, which is the phenomenon that increases emissivity when a surface falls under the geometric optical region conditions.
Recent work in metal additive manufacturing (AM) suggests that mechanical properties may vary with feature size; however, these studies do not provide a statistically robust description of this phenomenon, nor do they provide a clear causal mechanism. Because of the huge design freedom afforded by 3D printing, AM parts typically contain a range of feature sizes, with particular interest in smaller features, so the size effect must be well understood in order to make informed design decisions. This work investigates the effect of feature size on the stochastic mechanical performance of laser powder bed fusion tensile specimens. A high-throughput tensile testing method was used to characterize the effect of specimen size on strength, elastic modulus and elongation in a statistically meaningful way. The effective yield strength, ultimate tensile strength and modulus decreased strongly with decreasing specimen size: all three properties were reduced by nearly a factor of two as feature dimensions were scaled down from 6.25 mm to 0.4 mm. Hardness and microstructural observations indicate that this size dependence was not due to an intrinsic change in material properties, but instead the effects of surface roughness on the geometry of the specimens. Finite element analysis using explicit representations of surface topography shows the critical role surface features play in creating stress concentrations that trigger deformation and subsequent fracture. The experimental and finite element results provide the tools needed to make corrections in the design process to more accurately predict the performance of AM components.
The mechanical properties of additively manufactured metals tend to show high variability, due largely to the stochastic nature of defect formation during the printing process. This study seeks to understand how automated high throughput testing can be utilized to understand the variable nature of additively manufactured metals at different print conditions, and to allow for statistically meaningful analysis. This is demonstrated by analyzing how different processing parameters, including laser power, scan velocity, and scan pattern, influence the tensile behavior of additively manufactured stainless steel 316L utilizing a newly developed automated test methodology. Microstructural characterization through computed tomography and electron backscatter diffraction is used to understand some of the observed trends in mechanical behavior. Specifically, grain size and morphology are shown to depend on processing parameters and influence the observed mechanical behavior. In the current study, laser-powder bed fusion, also known as selective laser melting or direct metal laser sintering, is shown to produce 316L over a wide processing range without substantial detrimental effect on the tensile properties. Ultimate tensile strengths above 600 MPa, which are greater than that for typical wrought annealed 316L with similar grain sizes, and elongations to failure greater than 40% were observed. It is demonstrated that this process has little sensitivity to minor intentional or unintentional variations in laser velocity and power.
Porosity in additively manufactured metals can reduce material strength and is generally undesirable. Although studies have shown relationships between process parameters and porosity, monitoring strategies for defect detection and pore formation are still needed. In this paper, instantaneous anomalous conditions are detected in-situ via pyrometry during laser powder bed fusion additive manufacturing and correlated with voids observed using post-build micro-computed tomography. Large two-color pyrometry data sets were used to estimate instantaneous temperatures, melt pool orientations and aspect ratios. Machine learning algorithms were then applied to processed pyrometry data to detect outlier images and conditions. It is shown that melt pool outliers are good predictors of voids observed post-build. With this approach, real time process monitoring can be incorporated into systems to detect defect and void formation. Alternatively, using the methodology presented here, pyrometry data can be post processed for porosity assessment.
Residual stress is a common result of manufacturing processes, but it is one that is often overlooked in design and qualification activities. There are many reasons for this oversight, such as lack of observable indicators and difficulty in measurement. Traditional relaxation-based measurement methods use some type of material removal to cause surface displacements, which can then be used to solve for the residual stresses relieved by the removal. While widely used, these methods may offer only individual stress components or may be limited by part or cut geometry requirements. Diffraction-based methods, such as X-ray or neutron, offer non-destructive results but require access to a radiation source. With the goal of producing a more flexible solution, this LDRD developed a generalized residual stress inversion technique that can recover residual stresses released by all traction components on a cut surface, with much greater freedom in part geometry and cut location. The developed method has been successfully demonstrated on both synthetic and experimental data. The project also investigated dislocation density quantification using nonlinear ultrasound, residual stress measurement using Electronic Speckle Pattern Interferometry Hole Drilling, and validation of residual stress predictions in Additive Manufacturing process models.
Some of the primary barriers to widespread adoption of metal additive manufacturing (AM) are persistent defect formation in built components, high material costs, and lack of consistency in powder feedstock. To generate more reliable, complex-shaped metal parts, it is crucial to understand how feedstock properties change with reuse and how that affects build mechanical performance. Powder particles interacting with the energy source, yet not consolidated into an AM part can undergo a range of dynamic thermal interactions, resulting in variable particle behavior if reused. In this work, we present a systematic study of 316L powder properties from the virgin state through thirty powder reuses in the laser powder bed fusion process. Thirteen powder characteristics and the resulting AM build mechanical properties were investigated for both powder states. Results show greater variability in part ductility for the virgin state. The feedstock exhibited minor changes to size distribution, bulk composition, and hardness with reuse, but significant changes to particle morphology, microstructure, magnetic properties, surface composition, and oxide thickness. Additionally, sieved powder, along with resulting fume/condensate and recoil ejecta (spatter) properties were characterized. Formation mechanisms are proposed. It was discovered that spatter leads to formation of single crystal ferrite through large degrees of supercooling and massive solidification. Ferrite content and consequently magnetic susceptibility of the powder also increases with reuse, suggesting potential for magnetic separation as a refining technique for altered feedstock.
Additive manufacturing (AM) is known for its large variance in mechanical properties. This is not only true for properties like strength, but also surface roughness. Build settings, which affect surface roughness, are often chosen to optimize strength or ductility. As part requirements change, build settings change, thereby changing resultant surface roughness. When describing surfaces, arithmetic roughness (Ra) is the most common parameter. However, it may not provide an adequate representation of surface topography for AM parts. Traditional surface roughness parameters for defining surface topography were well-established before the advent of AM, and a need has arisen to investigate applicability of these parameters to the unusual surfaces created through various AM technologies. This study demonstrates that Ra is not a suitable parameter in correlating surface topography to AM build parameters. Other existing parameters and combination of parameters will be investigated for their suitability in describing the AM process.
This SAND report fulfills the final report requirement for the Born Qualified Grand Challenge LDRD. Born Qualified was funded from FY16-FY18 with a total budget of ~$13M over the 3 years of funding. Overall 70+ staff, Post Docs, and students supported this project over its lifetime. The driver for Born Qualified was using Additive Manufacturing (AM) to change the qualification paradigm for low volume, high value, high consequence, complex parts that are common in high-risk industries such as ND, defense, energy, aerospace, and medical. AM offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this effort.
This report summarizes the data analysis activities that were performed under the Born Qualified Grand Challenge Project from 2016 - 2018. It is meant to document the characterization of additively manufactured parts and processe s for this project as well as demonstrate and identify further analyses and data science that could be done relating material processes to microstructure to properties to performance.
The powder-bed laser additive manufacturing (AM) process is widely used in the fabrication of three-dimensional metallic parts with intricate structures, where kinetically controlled diffusion and microstructure ripening can be hindered by fast melting and rapid solidification. Therefore, the microstructure and physical properties of parts made by this process will be significantly different from their counterparts produced by conventional methods. This work investigates the microstructure evolution for an AM fabricated AlSi10Mg part from its nonequilibrium state toward equilibrium state. Special attention is placed on silicon dissolution, precipitate formation, collapsing of a divorced eutectic cellular structure, and microstructure ripening in the thermal annealing process. These events alter the size, morphology, length scale, and distribution of the beta silicon phase in the primary aluminum, and changes associated with elastic properties and microhardness are reported. The relationship between residual stress and silicon dissolution due to changes in lattice spacing is also investigated and discussed.
The design, fabrication, and performance of InGaAs and InGaP/GaAs microcells are presented. These cells are integrated with a Si wafer providing a path for insertion in hybrid concentrated photovoltaic modules. Comparisons are made between bonded cells and cells fabricated on their native wafer. The bonded cells showed no evidence of degradation in spite of the integration process that involved significant processing including the removal of the III-V substrate.
Additive manufacturing enables the rapid, cost effective production of customized structural components. To fully capitalize on the agility of additive manufacturing, it is necessary to develop complementary high-throughput materials evaluation techniques. In this study, over 1000 nominally identical tensile tests are used to explore the effect of process variability on the mechanical property distributions of a precipitation hardened stainless steel produced by a laser powder bed fusion process, also known as direct metal laser sintering or selective laser melting. With this large dataset, rare defects are revealed that affect only ≈2% of the population, stemming from a single build lot of material. The rare defects cause a substantial loss in ductility and are associated with an interconnected network of porosity. The adoption of streamlined test methods will be paramount to diagnosing and mitigating such dangerous anomalies in future structural components.
Additive manufacturing offers unprecedented opportunities to design complex structures optimized for performance envelopes inaccessible under conventional manufacturing constraints. Additive processes also promote realization of engineered materials with microstructures and properties that are impossible via traditional synthesis techniques. Enthused by these capabilities, optimization design tools have experienced a recent revival. The current capabilities of additive processes and optimization tools are summarized briefly, while an emerging opportunity is discussed to achieve a holistic design paradigm whereby computational tools are integrated with stochastic process and material awareness to enable the concurrent optimization of design topologies, material constructs and fabrication processes.
An adage within the Additive Manufacturing (AM) community is that “complexity is free”. Complicated geometric features that normally drive manufacturing cost and limit design options are not typically problematic in AM. While geometric complexity is usually viewed from the perspective of part design, this advantage of AM also opens up new options in rapid, efficient material property evaluation and qualification. In the current work, an array of 100 miniature tensile bars are produced and tested for a comparable cost and in comparable time to a few conventional tensile bars. With this technique, it is possible to evaluate the stochastic nature of mechanical behavior. The current study focuses on stochastic yield strength, ultimate strength, and ductility as measured by strain at failure (elongation). However, this method can be used to capture the statistical nature of many mechanical properties including the full stress-strain constitutive response, elastic modulus, work hardening, and fracture toughness. Moreover, the technique could extend to strain-rate and temperature dependent behavior. As a proof of concept, the technique is demonstrated on a precipitation hardened stainless steel alloy, commonly known as 17-4PH, produced by two commercial AM vendors using a laser powder bed fusion process, also commonly known as selective laser melting. Using two different commercial powder bed platforms, the vendors produced material that exhibited slightly lower strength and markedly lower ductility compared to wrought sheet. Moreover, the properties were much less repeatable in the AM materials as analyzed in the context of a Weibull distribution, and the properties did not consistently meet minimum allowable requirements for the alloy as established by AMS. The diminished, stochastic properties were examined in the context of major contributing factors such as surface roughness and internal lack-of-fusion porosity. This high-throughput capability is expected to be useful for follow-on extensive parametric studies of factors that affect the statistical reliability of AM components.
No industry-wide standards yet exist for minimum properties in additively manufactured (AM) metals. While AM alloys such as 17-4 precipitation hardened stainless steel have been shown to have average properties that can be comparable to wrought or cast product, they suffer from inconsistent performance. Variability in the feedstock powder, feature sizes, thermal history, and laser performance can lead to unpredictable surface finish, chemistry, phase content, and defects. To address this issue, rapid, efficient, high-throughput mechanical testing and data analysis was developed, providing profound statistical insight into the stochastic variability in properties. With this new approach, 1000’s of comprehensive tensile tests can be performed for the cost of 10’s of conventional tests. This new high-throughput approach provides a material qualification pathway that is commensurate with the quick turn-around benefit of AM.
Microsystems Enabled Photovoltaics (MEPV) is a relatively new field that uses microsystems tools and manufacturing techniques familiar to the semiconductor industry to produce microscale photovoltaic cells. The miniaturization of these PV cells creates new possibilities in system designs that can be used to reduce costs, enhance functionality, improve reliability, or some combination of all three. In this article, we introduce analytical tools and techniques to estimate the costs associated with a hybrid concentrating photovoltaic system that uses multi-junction microscale photovoltaic cells and miniaturized concentrating optics for harnessing direct sunlight, and an active c-Si substrate for collecting diffuse sunlight. The overall model comprises components representing costs and profit margin associated with the PV cells, concentrating optics, balance of systems, installation, and operation. This article concludes with an analysis of the component costs with particular emphasis on the microscale PV cell costs and the associated tradeoffs between cost and performance for the hybrid CPV design.