Numerically Efficient Gradient Crystal Plasticity with a Grain Boundary Yield Criterion and Dislocation-based Work-Hardening

This book is a contribution to the further development of gradient plasticity. Several open questions are addressed, where the efficient numerical implementation is particularly focused on. The book inspects an equivalent plastic strain gradient plasticity theory and a grain boundary yield model. Experiments can successfully be reproduced. The hardening model is based on dislocation densities evolving according to partial differential equations taking into account dislocation transport

Modeling the hall-petch effect with a gradient crystal plasticity theory including a grain boundary yield criterion

Abstract. A strain gradient crystal plasticity theory including the gradient of the equiv- alent plastic strain ∇γeq is discussed. A grain boundary yield condition is proposed in order to account for the influence of the grain boundaries. Periodic tensile test simulations show the mechanical predictions of the numerical model

A magneto‐mechanically coupled material model for magnetic sensor investigation

We consider coupled micro-magneto-mechanics with the aim to understand the processes which underpin magnetic noise in composite magnetoelectric sensors. We formulate a material model within the generalized standard material framework. This approach ensures thermodynamic consistency. Using our material model, we study the interaction of domain walls with two types of defects: geometrical defects and eigenstrains. We discuss the interaction and underlying effects in detail

Efficient numerical strategies for an implicit volume fraction transfer scheme for single crystal plasticity including twinning and secondary plasticity on the example of magnesium

In this work an efficient algorithm for a fully implicit single crystal plasticity routine including twinning and secondary plasticity is presented and implemented for the example of magnesium. The material model uses the volume fraction transfer scheme for the evolution of twinning, that is, plastic slip in newly formed twins (“secondary plasticity”) is resolved. This is considered particularly important, if the volume fractions of some twins reach the order of magnitude of the parent phase. However the resolution of secondary plasticity also implies a large number of unknowns, which is significantly reduced by a newly proposed algorithm. For magnesium a hardening model based on basal, prismatic, pyramidal a and pyramidal c+a slip modes as well as a tension and a compression twinning mode and yields a total of 18 slip systems and 12 twinning systems. As a special feature of the proposed algorithm, the total amount of 246 unknowns, due to simultaneous slip in the parent phase and the twinned phases, is reduced to only 31 unknowns. Additionally, thermodynamic consistency is ensured by including the second law with the Clausius–Duhem equation, which considers the change of free energy upon twinning as an additional driving force for twinning. Further, the setup of the time discrete nonlinear equation system using midpoint rule, as well as the analytical solution of the algorithmic tangent are given in detail. Finally, the implemented model is tested in finite element simulations and compared to single- and polycrystal compression and tension experiments

Hardness of nitric acid treated polyethylene followed by recrystallization

The hardness variation of mek crystallized polyethylene as a consequence of controlled fuming nitric exposure has been investigated using the microindentation technique. This study complements previous results obtained using other reagents (H2SO4, C1HSO3). After HNO3 exposure the microhardness of polyethylene decreases very rapidly, instead of increasing after the first hours of treatment. The hardness decrease is correlated to the volume fraction of interlamellar microvoids arising through selective acid digestion. For longer treatment times (t > 40 h) the fragility of the material increases and the sample collapses under the indenter. The hardening of the degraded material after recrystallization from the melt is followed as a function of treatment time. The results are discussed in the light of the molecular mechanisms involved. Comparison of the experimental data with hardness calculations for ideal PE lamellar structures and chain extended dicarboxylic crystals implies that the major contribution to hardening is due to electron dense gfroups attachment at the surface of a mixed lamellar structure.Peer reviewe

Computational micro-magneto-mechanics

We formulate a material model for micro-magneto-mechanics based on the generalized standard material approach. Our model includes exchange, elastic, anisotropy, demagnetizing and Zeeman energy. Furthermore we account for dissipative micro-magnetic behavior by means of a dissipation potential. For the constrained optimization problem w.r.t. magnetization we rely on the exponential map algorithm. We demonstrate our ideas with numerical examples. In particular we apply our model to a thin film composite. With this composite we represent the magneto-mechanical part of a magneto-electric composite sensor (resp. small sensor segment). Our numerical experiments focus on FeCoSiB as the magnetostrictive material. We discuss the coupling effects for the considered thin film composite in detail

On a Projection Method for the Numerical Integration of Constitutive Equations Involving Large Inelastic and Incompressible Deformations

Finite deformation plasticity often involves the multiplicative split of the deformation gradient into an elastic and plastic part. Motivated by observations in physics, the plastic part is assumed to be volume preserving, i.e., the plastic part of the deformation gradient is unimodular. In order to not accumulate errors, in the best case, one fulfills this constraint exactly to obtain accurate results (see, e.g., [3]). While other approaches where pursued as well, many authors therefore adopted the use of the exponential map, which is a geometric integrator preserving the plastic incompressibility. However, it's computation is not straightforward and performing the eigenvalue decomposition and it's linearization for the exponential function is numerically elaborate. Therefore, in this work, a new approach which also exactly preserves the incompressibility constraint is developed. It makes use of a projection of all symmetric tensors onto the manifold of unimodular tensors. The proposed method is compared to models utilizing the exponential map in numerical experiments

Gradient-extended brittle damage modeling

An elastic-brittle anisotropic model is presented based on the work by Fassin et al. (2019a). After discussing the local model equations and the incorporation of crack-closure, the gradient extension using the micromorphic approach according to Forest (2009) is briefly summarized. In order to run unit cell simulations on the microlevel, relevant material parameters have to be identified. Therefore, the energy dissipation provides a differential equation with a linear and quadratic term for the damage variable. Finally, the isotropic damage model is used to show numerical examples with variation of fracture toughness and volume fraction of pores

Micro-mechanical testing of transition metal (oxy)nitride coatings

Transition metal (oxy)nitride coatings are used in polymer forming operations for a combination of outstanding wear resistance and chemical compatibility with the polymer materials. Varying the chemical composition and deposition parameters for the coatings will optimise mechanical properties by a combination of chemistry and microstructural optimisation. By developing a representative model for these materials, these materials can be rapidly and efficiently prototyped and improved. However, as both chemistry and microstructure play a role in the material properties, both of these variables must be taken account of in this model. This work demonstrates the first steps in linking quantum-mechanics, micro-mechanics, and meso-scale finite element models together in order to fully understand the behaviour of these coatings. Please click Additional Files below to see the full abstract