Finite element analysis of laser transformation hardening

The problem of determining stresses, phase compositions and temperature distributions during the transformation hardening of steel with a CO-laser beam is investigated. To model the different phases in each material point a parallel fraction model is used, in which each fraction represents one phase. The description of phase transformations is obtained by an incremental formulation of the Avrami-equation for isothermal transformation. A model is developed to describe the superheating of ferrite and pearlite. The model is demonstrated by a detailed computation of stresses, deformations and phase compositions in the case of a stationary laser flash

Robust optimization based on analytical evaluation of uncertainty propagation

Optimization under uncertainty requires proper handling of those input parameters that contain scatter. Scatter in input parameters propagates through the process and causes scatter in the output. Stochastic methods (e.g. Monte Carlo) are very popular for assessing uncertainty propagation using black-box function metamodels. However, they are expensive. Therefore, in this article a direct method of calculating uncertainty propagation has been employed based on the analytical integration of a metamodel of a process. Analytical handling of noise variables not only improves the accuracy of the results but also provides the gradients of the output with respect to input variables. This is advantageous in the case of gradient-based optimization. Additionally, it is shown that the analytical approach can be applied during sequential improvement of the metamodel to obtain a more accurate representative model of the black-box function and to enhance the search for the robust optimum

Dynamic substructuring and reanalysis methods in a surrogate based design optimization environment

Abstract In light weight structure design, vibration control is necessary to meet strict stability requirements and to improve the fatigue life of structural components. Due to ever-increasing demands on products, it is generally more convenient to include vibration prerequisites in a design process instead of using vibration control devices on fixed designs. One of the main difficulties associated to design optimization of complex and/or large structures is the numerous computationally demanding Finite Element (FE) calculations. The objective of this research is to present a novel strategy for efficient and accurate optimization of vibration characteristics of structures. In the proposed strategy, a sub-structuring method is utilized. The FE model of the complete structure is partitioned, educed and then reassembled. This increases the computational efficiency of dynamic analyses. Moreover, this method is coupled with a novel reanalysis technique to speed up the repeated structural analyses. These methods are finally embedded in a surrogate-based design optimization procedure. An academic test problem is used for the validation of this novel approach. Keywords Dynamic substructuring · Reanalysis methods · Surrogate-based optimizatio

Comparison of ALE finite element method and adaptive smoothed finite element method for the numerical simulation of friction stir welding

In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane\ud strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of\ud the disc is clamped. Two numerical methods are used to solve this problem and an analytical solution is derived. The analytical\ud model is complementary to validate the two numerical methods, i.e. the arbitrary Lagrangian-Eulerian (ALE) method and the\ud adaptive smoothed finite elements method (ASFEM)

Constitutive modelling of Sandvik 1RK91

A physically based constitutive equation is being developed for the maraging\ud stainless steel Sandvik 1RK91. The steel is used to make precision parts. These parts are formed through multistage forming operations and heat treatments from cold rolled and annealed sheets. The specific alloy is designed to be thermodynamically unstable, so that deformation even at room temperatures can bring about a change in the phase of face centred cubic austenite to either hexagonal closed packed martensite and/or, body centred cubic martensite. This solid state phase change is a function of the strain path, strain, strain rate and temperature. Thus, the fraction of the new phase formed depends on the state of stress at a given location in the part being formed. Therefore a set of experiments is being conducted in order to quantify the stress-strain behavior of this steel under various stress states, strain, strain rate as well as temperature. A magnetic sensor records the fraction of ferromagnetic martensite formed from paramagnetic austenite. A thermocouple as well as an infra red thermometer is used to log the change in temperature of the steel during a mechanical test. The force-displacement data are converted to stress-strain data after correcting for the changes in strain rate and temperature. These data are then cast into a general form of constitutive equation and the transformation equations are derived from Olson-Cohen type functions

Free surface modeling of contacting solid metal flows employing the ALE formulation

In this paper, a numerical problem with contacting solid metal flows is presented and solved with an arbitrary Lagrangian-Eulerian (ALE) finite element method. The problem consists of two domains which mechanically interact with each other. For this simulation a new free surface boundary condition is implemented for remeshing of the boundary elements. It uses explicitly that the integral of the convective velocity along a boundary element remains zero. Steady state solutions are obtained only if the integral of the convective velocities along each free surface boundary element remains zero. The new remeshing option for the free surface is tested on a cladding problem employing friction stir welding (FSW). The problem describes two elasto-viscoplastic aluminum material flows which mechanically interact