# Prevention of solidification cracking during pulsed laser beam welding

Prevention of solidification cracking during pulsed laser beam welding We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coefficients depend on the temperature, this leads to a quasi‐linear parabolic partial differential equation. It is our goal to prevent solidification cracking. We address this problem by means of optimal control. It is the intensity profile of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidification interface need to be properly penalized in order to deal with and avoid cracking phenomena. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

# Prevention of solidification cracking during pulsed laser beam welding

2 pages

/lp/wiley/prevention-of-solidification-cracking-during-pulsed-laser-beam-welding-uJ9rXaVS2W
Publisher
Wiley Subscription Services, Inc., A Wiley Company
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710172
Publisher site
See Article on Publisher Site

### Abstract

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coefficients depend on the temperature, this leads to a quasi‐linear parabolic partial differential equation. It is our goal to prevent solidification cracking. We address this problem by means of optimal control. It is the intensity profile of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidification interface need to be properly penalized in order to deal with and avoid cracking phenomena. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

### Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

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