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Effective Simulation and Optimization of a Laser Peening Process A dissertation submitted in partial fulfillment of the requirements for the degree of the Doctor of Philosophy By GULSHAN SINGH B.S., Jai Narain Vyas University, Jodhpur, India, 2001 M.Tech., Indian Institute of Technology, Kanpur, India, 2003 2009 Wright State University Wright State University SCHOOL OF GRADUATE STUDIES August 10, 2009 I HEREBY RECOMMEND THAT THE DISSERTATION PREPARED UN- DER MY SUPERVISION BY GULSHAN SINGH ENTITLED Effective Simulation and Optimization of a Laser Peening Process BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy . Ramana V. Grandhi, Ph.D. Dissertation Director Ramana V. Grandhi, Ph.D. Director, Engineering Ph.D. Program Joseph F. Thomas, Jr., Ph.D. Dean, School of Graduate Studies Committee on Final Examination Ramana V. Grandhi, Ph.D. Nathan Klingbeil, Ph.D. Ravi Penmetsa, Ph.D. Allan H. Clauer, Ph.D. Robert Brockman, Ph.D. ii Abstract Singh, Gulshan, Ph.D. in Engineering Program, Wright State University, 2009. Effective Simulation and Optimization of a Laser Peening Process. Laser peening (LP) is a surface enhancement technique that has been applied to improve fatigue and corrosion properties of metals. The ability to use a high energy laser pulse to generate shock waves, inducing a compressive residual stress field in metallic materials, has applications in multiple fields such as turbomachinery, airframe structures, and medical appliances. In the past, researchers have investigated the effects of LP parameters experimentally and performed a limited number of simulations on simple geometries. However, monitoring the dynamic, intricate relationships of peened materials experimentally is time consuming, expensive, and challenging. With increasing applications of LP on complex geometries, these limited experimental and simulation capabilities are not sufficient for an effective LP process design. Due to high speed, dynamic process parameters, it is difficult to achieve a consistent residual stress field in each treatment and constrain iii detrimental effects. With increased computer speed as well as increased sophistication in non-linear finite element analysis software, it is now possible to develop simulations that can consider several LP parameters. In this research, a finite element simulation capability of the LP process is developed. These simulations are validated with the available experimental results. Based on the validated model, simplifications to complex models are developed. These models include quarter symmetric 3D model, a cylindrical coupon, a parametric plate, and a bending coupon model. The developed models can perform simulations incorporating the LP process parameters, such as pressure pulse properties, spot properties, number of shots, locations, sequences, overlapping configurations, and complex geometries. These models are employed in parametric investigations and residual stress profile optimization at single and multiple locations. In parametric investigations, quarter symmetric 3D model is used to investigate temporal variations of pressure pulse, pressure magnitude, and shot shape and size. The LP optimization problem is divided into two parts: single and multiple locations peening optimization. The single-location peening optimization problems have mixed design variables and multiple optimal solutions. In the optimization literature, many researchers have solved problems involving mixed variables or multiple optima, but it is difficult to find multiple solutions for mixed-variable problems. A mixed-variable Niche Particle Swarm Optimization (MNPSO) is proposed iv that incorporates a mixed-variable handling technique and a niching technique to solve the problem. Designing an optimal residual stress profile for multiple-location peening is a challenging task due to the computational cost and the nonlinear behavior of LP. A Progressive Multifidelity Optimization Strategy (PMOS) is proposed to solve the problem. The three-stage PMOS, combines low- and high- fidelity simulations and respective surrogate models and a mixed-variable handling strategy. This strategy employs comparatively low computational-intensity models in the first two stages to locate the design space that may contain the optimal solution. The third stage employs high fidelity simulation and surrogate models to determine the optimal solution. The overall objective of this research is to employ finite element simulations and effective optimization techniques to achieve optimal residual stress fields. v Contents References............................... ix 1 Surface Enhancement Techniques 1 1.1 Surface Enhancement Processes . 3 1.1.1 Shot Peening . 5 1.1.2 Low Plasticity Burnishing . 6 1.1.3 Waterjet Peening . 7 1.2 Laser Peening . 8 1.2.1 Laser Generation . 9 1.2.2 Component Preparation . 10 1.2.3 Residual Stresses . 14 1.2.4 LP Advantages and Disadvantages . 20 1.3 Dissertation Organization . 21 1.4 Chapter Summary . 23 2 Literature Survey 24 2.1 Initial Developments . 25 2.2 Growth Challenges . 26 2.3 Motivation . 34 2.4 Chapter Summary . 36 3 Finite Element Simulation 37 3.1 Simulation Parameters . 38 3.1.1 Laser Spot Shape & Size . 39 3.1.2 Pressure Pulse Magnitude and Shape . 40 3.1.3 Geometric Modeling and Meshing . 41 3.1.4 Material Modeling . 44 vi 3.2 Simulation Procedure . 47 3.2.1 Explicit and Implicit Algorithms . 49 3.2.2 Ohio Supercomputing Center for Simulations . 54 3.3 Two-Dimensional Simulation . 54 3.4 Three-Dimensional Simulation . 55 3.4.1 Mesh Convergence . 55 3.4.2 Preliminary results . 60 3.4.3 Experimental Validation . 63 3.4.4 Residual Stress Profile . 67 3.5 Two Shots Sequence Model . 67 3.6 Seven Shots Sequence at Multiple Locations Model . 69 3.7 Parametric Plate Model . 70 3.8 Rectangular Coupon Model . 71 3.9 Chapter Summary . 73 4 LP Optimization: Introduction and Parametric Investigations 74 4.1 Mathematical Formulation of Mixed-variable Optimization . 75 4.2 Optimization Methods . 77 4.2.1 Gradient-Based Methods . 77 4.2.2 Non-gradient Based Optimization . 78 4.2.3 Advantages and Disadvantages . 80 4.3 Automated Data Transfer Procedure . 81 4.3.1 One-time Setup . 84 4.3.2 Procedure Steps . 84 4.3.3 Advantages of the Procedure . 85 4.4 Surrogate Models . 86 4.5 Parametric Investigations . 87 4.5.1 Temporal Variation of Pressure . 88 4.5.2 Pressure Pulse Magnitude . 90 4.5.3 Spot Size . 91 4.5.4 Spot Shape . 91 4.5.5 Thickness of Component . 94 4.5.6 Multiple LP Treatments at the Same Location . 99 4.5.7 Two Shots Sequence at Multiple Locations . 102 4.5.8 Seven Shot Sequence at Multiple Locations . 106 4.6 Chapter Summary . 108 vii 5 LP Optimization: One Location 110 5.1 Mixed-variable Niche Particle Swarm Optimization . 111 5.2 LP Multimodal Problem . 115 5.2.1 LP Design Space for Multimodal Optimization . 116 5.2.2 Multimodal Problem Formulation . 118 5.3 Proposed Method: Mixed-variable Niching PSO . 120 5.3.1 Initial Particle Generation . 120 5.3.2 Niche Updating . 121 5.3.3 Integer Variable Technique . 126 5.3.4 Parallel Processing . 128 5.4 Multimodal Test Problems . 129 5.4.1 A Periodic Function with Peaks of Equal Size and In- terval ..........................129 5.4.2 A Periodic Function With Peaks of Unequal Size and Interval . 130 5.4.3 Multimodal Bump Function . 131 5.5 Multimodal LP Optimization and Results . 135 5.5.1 Design of Experiments-based Surrogate Model . 135 5.5.2 Results and Discussion . 137 5.6 Chapter Summary Remarks . 140 6 LP Optimization: Multiple Locations 142 6.1 Progressive Multifidelity Optimization Strategy (PMOS) . 143 6.1.1 Sub-parametric Surrogate Model . 147 6.1.2 PMOS: Advantages and Disadvantages . 149 6.2 Multiple Locations Peening Optimization . 150 6.2.1 Multiple Simulation Models . 151 6.3 Problem Formulation, PMOS Implementation, Validation, and Results . 152 6.3.1 Optimization Formulation: MVO . 152 6.3.2 Optimization Strategies Implementation . 154 6.3.3 Step 1: Optimization using a 2D Model . 154 6.3.4 Step 2: Optimization using a symmetric 3D model . 156 6.3.5 Methodology Validation . 157 6.3.6 Step 3: Optimization using a Parametric Plate Model . 159 6.4 Discussion . 165 viii 7 Summary and Future Directions 168 7.1 Contributions . 168 7.1.1 FE Simulation . 168 7.1.2 Optimization . 169 7.2 Research Summary . 172 7.3 Future Direction . 172 References 173 ix List of Figures 1.1 Schematic of shot peening process . 6 1.2 Schematic of the low plasticity burnishing process . 7 1.3 Schematic of Laser Peening process . 13 1.4 Shock wave in a material . 15 1.5 Schematic of residual stress generation . 18 2.1 Laser pulse and resulting pressure pulse on a target (Peyre et. al. 1996) . 30 3.1 Temporal loading profile of pressure pulse (Nam, 2002) . 42 3.2 Schematic of 2-D axi-symmetric FE model . 43 3.3 Schematic FEA model of a quarter section . 45 3.4 Schematic of discretized spot for spatial pressure variation . 45 3.5 Flow-chart of simulation process . 48 3.6 Mesh convergence results . 57 3.7 History of internal energy, artificial strain energy, kinetic en- ergy, plastic dissipation and external work . 60 3.8 Resultant residual stress distribution plot for 3 GPa peak pres- sure pulse . 62 3.9 Averaging Schematic . 65 3.10 Comparison of experimental results with simulation at 1 mm from spot center line . 66 3.11 Schematic of sequential LP at multiple locations on a FEA model 68 3.12 Cylindrical model for sequence investigation . 70 3.13 FEA model of a plate with five shots . 71 3.14 FE model of the four point bend specimen . 72 4.1 Flow-chart of the simulation-based optimization process . 82 x 4.2 Temporal loading profile of pressure pulse . 89 4.3 Three spot shapes investigated . 92 4.4 Residual stress field for three spot shapes . 93 4.5 Residual stress field comparison for depth from 3 mm to 10 mm 95 4.6 Residual stress field comparison for depth from 3 mm to 10 mm 97 4.7 Average residual stress field for multiple treatments of LP at the same location .

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