Numerical Simulation of Stresses due to Solid State Transformations : The Simulation of Laser Hardening

The properties of many engineeringmaterialsmay be favourablymodified by application of a suitable heat treatment. Examples are precipitation hardening, tempering and annealing. One of the most important treatments is the transformation hardening of steel. Steel is an alloy of iron and carbon. At room temperature the sollubility of carbon in steel is negligible. The carbon seggregates as cementite (Fe3C). By heating the steel above austenization temperature a crystal structure is obtained in which the carbon does solve. When cooled fast the carbon cannot seggregate. The resulting structure, martensite is very hard and also has good corrosion resistance. Traditionally harding is done by first heating the whole workpiece in an oven and then quenching it in air, oil or water. Other methods such as laser hardening and induction hardening are charaterized by a very localized heat input. The quenching is achieved by thermal conduction to the cold bulk material. A critical factor in these processes is the time required for the carbon to dissolve and homogenize in the austenite. This thesis consists of two parts. In the first part algorithms and methods are developed for simulating phase transformations and the stresses which are generated by inhomogeneous temperature and phase distributions. In particular the integration of the constitutive equations at large time increments is explored. The interactions between temperatures, stresses and phase transformations are cast into constitutive models which are suitable for implementation into a finite element model. The second part is concerned with simulation of steady state laser hardening. Two different methods are elaborated, the Arbtrary Lagrangian Eulerian (ALE) method and a direct steady state method. In the ALE method a transient calculation is prolonged until a steady state is reached. An improvement of the convection algorithm enables to obtain accurate results within acceptable calculation times. In the steady state method the steadiness of the process is directly incorporated into the integration of the constitutive equations. It is a simplified version of a method recently published in the literature. It works well for calculation of temperatures and phase distributions. When applied to the computation of distortions and stresses, the convergence of the method is not yet satisfactory. ix