Nanocrystalline Materials

In collaboration with Dr. Tamer El Sayed


Nanocrystalline (nc) materials are known to posses several distinct features when compared to coarse grained polycrystals. These include high strength and fatigue resistance, low ductility, pronounced rate dependence, tension-compression asymmetry and susceptibility to plastic instability. We develop a variational multi-scale constitutive models in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization where a log-normal grain size distribution is assumed. It is shown that the proposed model is able to capture the enhanced rate sensitivity and the inverse Hall-Petch effect, i.e., loss of strength with grain size refinement.


Related publications:

E. Gürses, T. El Sayed, A Constitutive Model of Nanocrystalline Metals Based on Competing Grain Boundary and Grain Interior Deformation Mechanisms, Submitted to Materials Letters, 2011.

E. Gürses, T. El Sayed, Constitutive Modeling of Strain Rate Effects in Nanocrystalline and Ultrafine Grained Polycrystals, International Journal of Solids and Structures, vol. 48, pp. 1610-1616, 2011.

E. Gürses, T. El Sayed, A Variational Multiscale Constitutive Model for Nanocrystalline Materials, Journal of the Mechanics and Physics of Solids, vol. 59, pp. 732-749, 2011.

E. Gürses, T. El Sayed, On Tension-Compression Asymmetry in Ultrafine-Grained and Nanocrystalline Metals, Computational Materials Science, vol. 50, pp. 639-644, 2010.

Explosives

In collaboration with Dr. Julian Rimoli and Dr. Michael Ortiz

Microscopic defects such as voids are thought to be a prime source of hot spots in crystalline energetic materials. For instance, the formation of jets during the collapse of voids may result in temperatures and pressures that greatly exceed values in the bulk, thereby promoting molecular decomposition. The impact sensitivity of defect-free energetic single crystals is comparatively less well-understood, but dislocation-mediated plastic deformation suggests itself as an explanation for the observed orientation dependencies. It is well-known that dislocation-mediated plastic deformation is almost universally inhomogenous at the sub-grain level and exhibits microstructural patterns that include localization of deformation and temperature to slip lines. We investigate the role of such slip lines as possible hot-spots for initiation in void-free energetic polycrystals.

We develop a multiscale model for the shock ignition in defect-free polycrystalline high energetic materials. The model consists of three levels: (i) a polycrystalline structure at macroscale, (ii) a single crystal plasticity at mesoscale and (iii) subgrain microstructures at microscale. The development of sub-grain level microstructures is taken into account by an energetically optimal explicit construction of sequential lamination. The explicit construction exhibits microstructural patterns that include localization of deformation and temperature to slip lines. We investigated the role of such slip lines as possible hot spots for initiation in a defect-free energetic polycrystalline PETN. Strong localization of temperature in the hot spots causes molecular decomposition which was modeled by an Arrhenius type depletion law. The sub-grain microstructure construction is integrated into a finite element framework and the proposed model is used to simulate the response of PETN in a plate-impact configuration. The pop-plot data generated from numerical simulations yields a linear relation in a log-log plot as observed in experiments.

Related publications:

J. Rimoli, E. Gürses, M. Ortiz Shock-Induced Subgrain Microstructures as Possible Homogenous sources of Hot Spots and Initiation Sites in Energetic Polycrystals, Physical Review B, vol. 81, p. 014112, 2010.

Fracture Mechanics

In collaboration with Dr. Christian Miehe

We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element based computational framework for propagation of cracks in three-dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality in the sense of Coleman's method. Consequently, the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. In a consistent way with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The crucial step for the success of this procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness, providing a robust algorithmic setting in the postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations.

Related publications:

E. Gürses, C. Miehe, A Computational Framework of Three Dimensional Configurational Force Driven Brittle Crack Propagation, Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 1413-1428, 2009.

C. Miehe, E. Gürses, M. Birkle, A Computational Framework of Configurational-Force-Driven Brittle Fracture Based on Incremental Energy Minimization, International Journal of Fracture, vol. 145, pp. 245-259, 2007.

C. Miehe, E. Gürses, A Robust Algorithm for Configurational-Force-Driven Brittle Crack Propagation with R-Adaptive Mesh Alignment, International Journal for Numerical Methods in Engineering, vol. 72, pp. 127-155, 2007.

E. Gürses, Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation, PhD Thesis, University of Stuttgart, 2007. (pdf) .

Semicrystalline Polymers

In collaboration with Dr. Serdar Göktepe

Nonconvex Problems and Microstructures

In collaboration with Dr. Christian Miehe

Microstructures that are observed in nature often show complex patterns with length scales much smaller than characteristic macroscopic dimensions of the problem considered. It is possible mathematically to describe these microstructures bynon-convex variational problems. Furthermore, it has been shown that non-existence of minimizers in these variational problems are closely related to fine scale oscillatory infimizing sequences which are interpreted as microstructures. In particular, there is a strong parallelism between the microstructures that develop in martensitic phase transformations and fine scale oscillatory infimizing sequences of energy functionals describing phase transforming elastic crystals.

The existence of solutions for the boundary value problems of nonlinear elasticity demands the sequential weak lower semicontinuity of the energy functional which is ensured provided that the energy storage function possesses particular weak convexity and growth conditions. For vector valued variational problems the crucial weak convexity notion is the quasiconvexity. Non-convex variational problems which often suffer from the lack of solutions in the classical sense can be treated by the relaxation theory which is the replacement of the non-quasiconvex storage function by its quasiconvex envelope. However, quasiconvexity is a global integral condition which is hard to verify in practice. More manageable condition is the slightly weaker rank-one convexity notion that is considered to be a close approximation of quasiconvexity. We investigate two model problems, namely single crystal plasticity and the damage mechanics, where non-convex potentials arise and develop numerical relaxation schemes based on rank-one convexification. The performance of the relaxation methods is shown by the well-behaved objective global response of the finite element solutions.

Related publications:

E. Gürses, C. Miehe, On Evolving Deformation Microstructures in Non-Convex Partially Damaged Solids, Journal of the Mechanics and Physics of Solids, vol. 59, pp. 1268-1290, 2011.

C. Miehe, M. Lambrecht, E. Gürses, Analysis of Material Instabilities in Inelastic Solids by Incremental Energy Minimization and Relaxation Methods: Evolving Deformation Microstructures in Finite Plasticity, Journal of the Mechanics and Physics of Solids, vol. 52, pp. 2725-2769, 2004.

E. Gürses, A. Mainik, C. Miehe, A. Mielke, Analytical and Numerical Methods for Finite Strain Elastoplasticity, In R. Helmig, A. Mielke, B. Wohlmuth, editors, Multifield Problems in Fluid and Solid Mechanics. Series Lecture Notes in Applied and Computational Mechanics, 28:443-481. Springer, 2006.

E. Gürses, Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation, PhD Thesis, University of Stuttgart, 2007. (pdf) .