Modeling Silicon under Contact Loading Conditions: Aspects of Non-Associated Flow

Technologically relevant abrasive machining techniques (lapping, sawing, grinding) for silicon (Si) are based on (sub-)surface crack formation triggered by contact events. Therefore, the understanding of the inelastic deformation of Si under contact (indenter-)loading is essential to improve machining results. It has been long established that Si undergoes a series of stress driven phase transitions under compression. During subsequent pressure release part of the transformation strain is recovered. The present paper highlights the importance of the direction of inelastic flow for modeling (partially) reversible stress induced phase transitions in materials such as silicon. A phenomenological constitutive model for Si under contact loading, which captures both the cd−Si → −Si transition upon compression and the −Si → a−Si transition upon rapid decompression has been recently presented (Budnitzki and Kuna, 2012). It is shown that indentation experiments are particularly well suited to determine material parameters for this model. Further, material parameters obtained from indentation experiments with Berkovich indenter are confirmed to be valid for the numerical simulation of Knoop indentation, thus verifying a certain predictive capability of the constitutive model

A model for the interaction of dislocations with planar defects based on Allen-Cahn type microstructure evolution coupled to strain gradient elasticity

In classical elasticity theory the stress-field of a dislocation is characterized by a $1/r$-type singularity. When such a dislocation is considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces for the order parameter, resulting in non-physical (and discretization-dependent) predictions for the interaction between dislocations and phase-, twin- or grain-boundaries. We introduce a framework based on first strain gradient elasticity to regularize the dislocation core. It is shown that the use of strain energy density that is quadratic in the gradient of elastic deformation results in non-singular stresses but may result in singular driving forces, whereas a strain energy, which is quadratic in the gradient of the full deformation tensor, regularizes both stresses and driving forces for the order parameter and is therefore a suitable choice. The applicability of the framework is demonstrated using a comprehensive example

Microstructure impact on the machining of two gear steels. Part 1: Derivation of effective flow curves

A multiscale approach is presented here to investigate the effect of the ferrite-pearlite microstructure after annealing on the subsequent machining process of steel gears. The case-hardening steel 18CrNiMo7-6 and a cost efficient alternative with reduced Cr and Ni content have been studied. After detailed microstructure characterization, three different scales are defined: the nano-scale with pearlite, built of ferrite-cementite bi-lamellas, the micro-scale, which corresponds to a RVE of the ferrite/pearlite microstructure and the macro-scale. In order to derive the effective flow behaviour of pearlite, virtual uniaxial tensile and shear tests of the ferrite/cementite bi-lamella are performed at the nanoscale. The flow behaviour of the ferrite phase is described there by an extension of the Kocks-Mecking law suitable for large machining strains. Moreover, at the nanoscale, the effective flow curve of the ferrite matrix having either small MnS or NbC inclusions is determined. At the microscale, effective flow curves for both steel grades are derived from virtual tests on 3D RVE's of both steel microstructures and compared with experimental measurements

The effects of cubic stiffness on fatigue characterization resonator performance

Micromachined, kHz-frequency resonators are now routinely employed as testing structures to characterize the fatigue degradation properties of thin film materials such as polycrystalline silicon (polysilicon). In addition to stress-life (S-N) fatigue curves, important properties such as crack propagation rates may be inferred from proper resonant frequency measurements throughout a fatigue test. Consequently, any nonlinear dynamic behavior that would complicate the interpretation of resonant frequency changes should be avoided. In this paper, nonlinear frequency-response curves of a polysilicon fatigue structure are measured in a vacuum environment. Finite element models of the structure are used to identify the source of geometric nonlinearity leading to a Duffing-type cubic stiffness. Given the origin of the behavior, a parametric optimization strategy is performed to minimize the cubic stiffness. This study highlights the importance of considering the dynamic behavior when designing resonating structures, especially when they are used for mechanistic studies in various environments