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Research Papers

Simulation of Laser-Induced Controlled Fracturing Utilizing a Phase Field Model

[+] Author and Article Information
Alexander Schlüter

Institute of Applied Mechanics
and Computational Mechanics,
University of Kaiserslautern,
P.O. Box 3049,
Kaiserslautern D-67653, Germany
e-mail: aschluet@rhrk.uni-kl.de

Charlotte Kuhn

Computational Mechanics,
University of Kaiserslautern,
Kaiserslautern D-67653, Germany
e-mail: chakuhn@rhrk.uni-kl.de

Ralf Müller

Institute of Applied Mechanics,
University of Kaiserslautern,
Kaiserslautern D-67653, Germany
e-mail: ram@rhrk.uni-kl.de

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received December 20, 2015; final manuscript received July 31, 2016; published online January 30, 2017. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 17(2), 021001 (Jan 30, 2017) (7 pages) Paper No: JCISE-15-1422; doi: 10.1115/1.4034385 History: Received December 20, 2015; Revised July 31, 2016

This work presents an approach to simulate laser cutting of ceramic substrates utilizing a phase field model for brittle fracture. To start with, the necessary thermoelastic extension of the original phase field model is introduced. Here, the Beer–Lambert law is used in order to model the effect of the laser on the substrate. The arising system of partial differential equations—which comprises the balance of linear momentum, the energy balance, and the evolution equation that governs crack propagation—is solved by a monolithic finite-element scheme. Finally, the influences of the laser power and the initial groove size on the manufactured work piece are analyzed numerically in simulations of a laser-cutting process.

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References

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Miehe, C. , Schänzel, L. , and Ulmer, H. , 2015, “ Phase Field Modeling of Fracture in Multi-Physics Problems—Part I: Balance of Crack Surface and Failure Criteria for Brittle Crack Propagation in Thermo-Elastic Solids,” CMAME, 294, pp. 449–485.
Kuhn, C. , and Müller, R. , 2010, “ A Continuum Phase Field Model for Fracture,” Eng. Fract. Mech., 77(18), pp. 3625–3634. [CrossRef]
Kuhn, C. , and Müller, R. , 2009, “ Phase Field Simulation of Thermomechanical Fracture,” PAMM, 9(1), pp. 191–192. [CrossRef]
Amor, H. , Marigo, J.-J. , and Maurini, C. , 2009, “ Regularized Formulation of the Variational Brittle Fracture With Unilateral Contact: Numerical Experiments,” J. Mech. Phys. Solids, 57(8), pp. 1209–1229. [CrossRef]
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Kuhn, C. , Schlüter, A. , and Müller, R. , 2015, “ On Degradation Functions in Phase Field Fracture Models,” Computational Materials Science, 108(Part B), pp. 374–384.
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Kuhn, C. , 2013, “ Numerical and Analytical Investigation of a Phase Field Model for Fracture,” Ph.D. thesis, Technische Universität Kaiserslautern, Kaiserslautern, Germany.

Figures

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Fig. 1

(a) Body with internal discontinuities (sharp cracks) Γ and (b) approximation of internal discontinuities by a phase field s(x,t)

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Fig. 2

Computational model and illustration of the Beer–Lambert law. The initial crack is indicated by a dashed line.

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Fig. 3

Contour plots of the order parameter s(x,t) for all the investigated parameter sets (lcrack,I0,max): (a)t = 2.631 × 10−4 s, (b) t = 2.631 × 10−4 s, (c) t = 2.8929 × 10−4 s, (d) t = 2.829 × 10−4 s, (e) t = 2.4152 × 10−4 s, (f)t = 2.631 × 10−4 s, (g) t = 2.631 × 10−4 s, (h) t = 2.6784 × 10−4 s, (i) t = 2.501 × 10−4 s, (j) t = 1.4789 × 10−4 s, (k)t = 2.631 × 10−4 s, (l) t = 2.631 × 10−4 s, (m) t = 2.660 × 10−4 s, (n) t = 2.5220 × 10−4 s, (o) t = 1.3484 × 10−4 s, (p)t = 2.631 × 10−4 s, (q) t = 2.631 × 10−4 s, (r) t = 2.631 × 10−4 s, (s) t = 2.631 × 10−4 s, (t) t = 1.3367 × 10−4 s, (u)t = 2.631 × 10−4 s, (v) t = 2.631 × 10−4 s, (w) t = 2.631 × 10−4 s, (x) t = 2.866 × 10−4 s, and (y) t = 1.682 × 10−4 s

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Fig. 4

(a) Successive crack tip positions and (b) y-coordinate of the crack tip. In this plot, the initial crack length is kept constant at 100% lcrack and only the intensity I0,max is varied.

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Fig. 5

Elastic energy Ee (a) and fracture Energy Es (b) per unit thickness. In this plot, the initial crack length is kept constant at 100% lcrack and only the intensity I0,max is varied.

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Fig. 6

Effective crack length l¯crack as a function of the beam intensity I0,max and the initial crack length lcrack

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