Kim Lau Nielsen

Collapse and coalescence of spherical voids subject to intense shearing: studied in full 3D

Micro-mechanical 2D cell model studies have revealed ductile failure during intense shearing to be governed by the interaction of neighbouring voids, which collapse to micro-cracks and continuously rotate and elongate until coalescence occurs. For a three-dimensional void structure, this implies significant straining of the matrix material located on the axis of rotation. In particular, the void surface material is severely deformed during shearing and void surface contact is established early in the deformation process. This 3D effect intensifies with decreasing stress triaxiality and complicates the numerical analysis, which is also reflected in published literature. Rather than moving towards very low triaxiality shearing, work has focused on extracting wide-ranging results for moderate stress triaxiality (T ~ 1), in order to achieve sufficient understanding of the influence of initial porosity, void shape, void orientation etc. The objective of this work is to expand the range of stress triaxiality usually faced in 3D cell model studies, such that intense shearing is covered, and to bring forward details on the porosity and void shape evolution. The overall material response is presented for a range of initial material configurations and loading conditions. In addition, a direct comparison to corresponding 2D cell model predictions for circular cylindrical voids under plane strain shearing is presented. A quantitatively good agreement of the two model configurations (2D vs. 3D) is obtained and similar trends are predicted. However, the additional layer of matrix material, connecting voids in the transverse direction, is concluded to significantly influence the void shape evolution and to give rise to higher overall ductility. This 3D effect is demonstrated for various periodic distributions of voids.

Effect of Contact Conditions on Void Coalescence at Low Stress Triaxiality Shearing

Recent numerical cell-model studies have revealed the ductile failure mechanism in shear to be governed by the interaction between neighboring voids, which collapse to micro-cracks and continuously rotate and elongate until coalescence occurs. Modeling this failure mechanism is by no means trivial as contact comes into play during the void collapse. In the early studies of this shear failure mechanism, Tvergaard (2009, “Behaviour of Voids in a Shear Field,” Int. J. Fract., 158 , pp. 41-49) suggested a pseudo-contact algorithm, using an internal pressure inside the void to resemble frictionless contact and to avoid unphysical material overlap of the void surface. This simplification is clearly an approximation, which is improved in the present study. The objective of this paper is threefold: (i) to analyze the effect of fully accounting for contact as voids collapse to micro-cracks during intense shear deformation, (ii) to quantify the accuracy of the pseudo-contact approach used in previous studies, and (iii) to analyze the effect of including friction at the void surface with the main focus on its effect on the critical strain at coalescence. When accounting for full contact at the void surface, the deformed voids develop into shapes that closely resemble micro-cracks. It is found that the predictions using the frictionless pseudo-contact approach are in rather good agreement with corresponding simulations that fully account for frictionless contact. In particular, good agreement is found at close to zero stress triaxiality. Furthermore, it is shown that accounting for friction at the void surface strongly postpones the onset of coalescence, hence, increasing the overall material ductility. The changes in overall material behavior are here presented for a wide range of initial material and loading conditions, such as various stress triaxialities, void sizes, and friction coefficients.

Rolling at Small Scales

The rolling process is widely used in the metal forming industry and has been so for many years. However, the process has attracted renewed interest as it recently has been adapted to very small scales where conventional plasticity theory cannot accurately predict the material response. It is well-established that gradient effects play a role at the micron scale, and the objective of this study is to demonstrate how strain gradient hardening affects the rolling process. Specifically, the paper addresses how the applied roll torque, roll forces, and the contact conditions are modified by strain gradient plasticity. Metals are known to be stronger when large strain gradients appear over a few microns; hence, the forces involved in the rolling process are expected to increase relatively at these smaller scales. In the present numerical analysis, a steady-state modeling technique that enables convergence without dealing with the transient response period is employed. This allows for a comprehensive parameter study. Coulomb friction, including a stick–slip condition, is used as a first approximation. It is found that length scale effects increase both the forces applied to the roll, the roll torque, and thus the power input to the process. The contact traction is also affected, particularly for sheet thicknesses on the order of 10 μm and below. The influences of the length parameter and the friction coefficient are emphasized, and the results are presented for multiple sheet reductions and roll sizes.

On the Experimental Investigation of a Wave Power Converter

Since 1978 utilization of ocean wave power has been investigated at the Department of Ocean Engineering, the Technical University of Denmark. A wave power converter has been developed after the KN principle from an idea to a small prototype with installed turbine and generator of lkW. During 1985 the prototype will be on a sea trial in the Danish sound Oresund to demonstrate, how well both principle and design are able to deal with the forces of nature. If the construction stands the trial, future development can follow. The principal will be illustrated by the experimental research, presented in this paper. Presentation will involve experiments with: a) one buoy, dampened by two single working piston pumps, b) a manifolded system of four of these in an attenuator configuration, and c) test results from a five times larger model of the attenuator (the prototype due for sea trail).