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IRG 2: Multiscale Mechanics of Complex Microstructures


Rational for the Technical Thrust:
Developing materials to withstand stress, often combined with an extreme environment, is central to many current technologies such as aircraft structures, gas turbines, and lightweight engines for automotive applications.  Emerging materials of particular current interest include advanced aluminum, titanium, and magnesium alloys; particulate reinforced composites such as Al-SiC or Ti-TiC, and new multiphase Mo- and Nb- silicide-based systems intended for high temperature applications.  These materials derive their properties from a complex microstructure, in which a matrix phase is combined with a distribution of second-phase particles to achieve a desirable mechanical response.  Their properties can, in principle, be adjusted by tuning the microstructure appropriately.

The ability to control microstructures at nanometer length scales is a particularly exciting development, offering the opportunities to create novel materials with Gigapascal-level strengths, as demonstrated in Cu, Fe, and Ni and its alloys.  Properties such as modulus, flow stress, ductility, fracture toughness, and fatigue resistance can be optimized by engineering the material’s grain size and texture; the size, shape and distribution of the second phase; as well as the chemistry, structure and strength of grain boundaries and interfaces between matrix and second phase.  Understanding the relationship between these microstructural variables and the performance of the material is critical to this effort.

Mechanics has played a critical role in elucidating the relationship between microstructure and properties.  In particular, computer simulations that predict the response of a material to stress are an integral part of modern materials design. Considerable progress has been made in developing computational methods to address material behavior both at continuum length scales and at the atomic scale.  For example, continuum finite element simulations can accurately predict properties such as elastic modulus, yield stress, creep rates and strain hardening rates for two-phase microstructures in terms of microstructural variables such as the crystallographic texture, particle volume fraction, and the elastic and plastic properties of the matrix and particles.  Atomistic and ab-initio simulations can now compute a range of material parameters such as defect energies and traction-separation relations for ideal interfaces, and can also be used to model directly the atomic scale processes in a small volume of material for short periods of time.

Despite such notable successes, enormous challenges remain.  In particular, efforts to simulate failure mechanisms, such as crack nucleation, fracture, or fatigue, and other localized phenomena not amenable to homogenization, remain rudimentary.  Furthermore, capturing the influence of grain size or particle size on constitutive response and failure resistance is fundamentally outside the scope of standard continuum, and is usually introduced through ad-hoc “Hall-Petch”-type scaling, and are too large for direct atomistic simulation.  A major impediment to progress is that failure resistance of a material is determined by a complex interaction of physical processes, involving material features with sizes between 1 nm and 100 microns or greater.  Simulations must therefore model, and experiments capture, in detail both the small-scale features and processes that trigger damage, as well as the larger-scale surrounding regions that generate high local stresses.  In particular, crack nucleation, monotonic and cyclic crack growth, and flow strength dependence on microstructural scale, are all determined to a large extent by mesoscale phenomena (length scales ~100 nm to ~1000 nm) involving the collective behavior of large numbers of dislocations and the inherently discrete nature of plastic flow.  Furthermore, methodologies to relate atomic, meso- and continuum-scale phenomena are needed.

Broad Goals of IRG2:
In this IRG, we extend and apply novel computational and experimental techniques to elucidate the mechanisms of deformation and failure in complex multiphase and anoscale microstructures.  A particular focus will be on fracture and fatigue, motivated partly by the obvious technological importance of these phenomena, and in part because these are quintessential multiscale mechanics problems.  Specifically, we address three distinct issues at the continuum, meso-, and nano- scales, respectively, as illustrated schematically in the Figure below.  First, at the continuum scale, we use our capability for generating model random microstructures together with cohesive zone models of fracture to study the role of particle distribution and matrix/particle properties in controlling crack nucleation and propagation in complex microstructures.  These simulations will be supported by in-situ scanning electron microscope studies of fracture and deformation in both model and practical microstructures.  Second, at the mesoscale, we use discrete dislocation simulations and front tracking finite element methods to model phenomena that cannot be addressed by continuum simulations, including the size-dependent and small-scale mechanisms of deformation, fracture, and fatigue in two-phase and anoscale microstructures.  The structure and properties of grain boundaries and particle/matrix interfaces are important in both types of microstructures, and so we will focus our effort on modeling the role of interfaces in mediating deformation and damage.  Our simulations at these length scales will be guided and verified by experimental observations (using in-situ and ex-situ atomic force and electron microscopy, and displacement mapping techniques) of deformation, damage nucleation and evolution in both model and practical microstructures.  Third, at the anoscale, we use the coupled atomistic/discrete-dislocation method to simulate atomic scale processes that control defect nucleation and propagation at interfaces.  The three sets of issues are closely connected: the atomic-scale studies provide insight and constitutive parameters for the meso-scale simulations while the meso-scale simulations elucidate the behavior that must be approximated by constitutive laws used in the continuum level computations.  The cohesive zone framework is the primary mechanism by which smaller-scale fracture information will be passed to higher scale methods.  Conversely, the longer length-scale simulations provide boundary conditions for the computations at shorter length-scales and identify how the microstructure generates local stresses and hot spots. 

Figure 1: A schematic illustrating connections between computations and experiments at the atomic scale, the mesoscale and continuum length scales in the proposed work.  Coupled atomistic/discrete-dislocation simulations and high resolution microscopy elucidate atomic scale deformation and failure mechanisms, and provide constitutive parameters, such as cohesive zones for fracture, used in mesoscale simulations.  Discrete dislocation and front-tracking computations and in-situ transmission electron microscopy are used to study the influence of interactions between defects at the mesoscale, and provide constitutive relations, such as cohesive zones for fracture, used in continuum simulations.  Continuum finite element models and in-situ scanning electron microscopy show the influence of microstructural features at micron and larger length-scales on the local conditions driving deformation and failure.