Underpinning and benchmarking multi-scale models with micro- and nanoscale experiments

Predictive models of materials behavior depend on: accurate databases of constitutive material properties, identification of underlying deformation mechanisms, and the availability of experimentally measured benchmarks with which to compare. Micro- and nano-scale experiments can be used to facilitate collection of salient mechanical properties of individual phases at appropriate temperatures, chemistries and microstructural states. Coupling with TEM observations allows one to identify underlying deformation mechanisms and to imbibe models with the requisite fundamental physics and materials science. Simulations must be benchmarked with experiments, conducted at scale with relevant material volumes and identifiable microstructures. This presentation will outline efforts to characterize the constitutive behavior of materials, to identify deformation mechanisms, and to benchmark crystal plasticity simulations at appropriate length scales. Micro-scale experiments designed and conducted to complement crystal plasticity modeling of two different microstructural variants of Ni-base superalloys, polycrystalline Rene 88 and directionally solidified GTE 444, will be presented. If size-scale effect can be avoided, constitutive (single-crystalline) data may be obtained with micro-tensile tests at various orientations and temperatures. Moreover, preparing and testing specimens with reduced volumes and a finite number of grains allows for direct comparison with crystal plasticity simulations of stress-strain behavior as well as strain localization. With regard to the latter, digital image correlation (DIC) of spatially resolved surface displacements produces strain maps that provide a much more rigorous benchmark for crystal plasticity predictions than stress-strain curves. Using directionally solidified specimens allows for 2.5D microstructures (grains that extend through the thickness of the specimen) and greatly simplifies such comparisons. Moving beyond uniaxial tension, micro-bending resonance fatigue experiments provide an opportunity to measure the number of cycles, location, and microstructural features associated with slip, intragranular crack formation, and eventual transgranular crack growth. These experimental measures can in turn be used to inform and benchmark multi-scale fatigue simulations. Similarly, strain-controlled fracture experiments involving 2.5D unidirectional polymer matrix composites (PMC) have been developed and are being used to identify the microstructural features and fracture paths that govern delamination and fracture. The availability of orientation mapping techniques (EBSD, PACOM, TKD) now allows for nano-scale characterization of underlying deformation mechanisms and their relation to crystallographic microstructures and surrounding neighborhoods. Studies investigating the role of grain growth, twinning and dislocation plasticity will be presented. Special attention will be placed on attempts to measure intragranular strains that can be related to the accumulation of geometrically necessary dislocations (GNDs) and compared with crystal plasticity simulations. Support for these projects has been provided through the AFOSR and AFRL funded Center of Excellence on Integrated Materials Modeling and the DOE office of Basic Energy Sciences

Endogenous Growth in the Presence of Informal Credit Markets: A Comparative Analysis Between Credit Rationing and Self-Revelation Regimes

This paper examines whether the presence of informal credit markets reduces the cost of credit rationing in terms of growth. In a dynamic general equilibrium framework, we assume that firms are heterogenous with different degrees of risk and households invest in human capital development. With the help of Indian household level data we show that the informal market reduces the cost of rationing by increasing the growth rate by 0.7 percent. This higher growth rate, in the presence of an informal sector, is due to the ability of the informal market to separate the high risk from the low risk firms thanks to better information. But even after such improvement we do not get the optimum outcome. The findings, based on our second question, suggest that the revelation of firms' type, based on incentive compatible pricing, can lead to almost 2 percent higher growth rate as compared to the credit rationing regime with informal sector.credit rationing, informal credit markets, self revelation mechanism