DISLOCATION DEPENDENT DEFORMATION IN MICROSCALE LASER SHOCK PEENING

As the laser spot size in micro-scale laser shock peening is in the order of magnitude of several microns, the anisotropic response of grains will have a dominant influence on its mechanical behavior of the target material. Furthermore, conventional plasticity theory employed in previous studies needs to be reexamined due to the length scale effect. In the present work, the length scale effects in microscale laser shock peening have been investigated. The crystal lattice rotation underneath the shocked surface was determined via Electron Backscatter Diffraction (EBSD). From these measurements, the geometrically necessary dislocations (GND) density that the material contains has been estimated. The yield strength increment was then calculated from the GND distribution by using Taylor model and integrated into each material point of the FEM simulation. Finite element simulations, based on single crystal plasticity, were performed of the process for both with and without considering the GND hardening and the comparison has been conducted. INTRODUCTION Micro-scale laser shock peening (μLSP), which aims to improve fatigue performance by imparting a compressive residual stress into the target material surface layer using laser induced shock waves, has been the focus of several recent investigations [1, 2]. This process is desirable for metallic components of micro-devices which encounter cyclic loading, such as micro-switches, micro-blades of a micro turbine, etc. Previous work has shown [1, 2] through both numerical analysis and experiments that through μLSP, one can manipulate the compressive residual stress distribution in a region close to the shocked surface with micron spatial resolution. Recent experiments in both bending and indentation have shown that the apparent material hardening increases as the size of specimen decreases to micron level [3, 4] where classical plasticity theory has been unable to account for the observed phenomena. It is well known now [5, 6, 7] that this hardening is due to length scale effects. Therefore, when the laser beam spot size is reduced to several microns, i.e. the same order of grain size, the size scale will have significant influence on mechanical behavior and the conventional plasticity theory must be reexamined as well. However, the numerical models developed before [1, 2] to predict the material response to the μLSP process are simplified and approximated without considering length scale effects and all based on the conventional plasticity theory. In order to better understand μLSP process and more accurately simulate the process, it is necessary to understand the length scale effect on the process and integrate this into the simulation model. In micro-scale deformation, strain gradient effects may be large enough such that the yield strength of a material depends not only on the strain, but also on the strain gradient. The motivation behind the use of strain gradients is based on the framework of geometrically necessary dislocations (GNDs), which were first introduced by Nye [8] and furthered by Ashby [9], who have given a physical basis for strain gradient dependent material behavior. Strain gradient theories have been physically motivated by developments in dislocation mechanics. More details about geometrically necessary 1 Copyright © 2008 by ASME dislocations in single crystals and polycrystalline materials can be found in Arsenlis and Parks [6]. In particular, several strain gradient models have been developed to numerically capture length scale effects where the underlying physics is sometimes related to the geometrically necessary dislocation [5, 10]. There have been a number of investigations on geometrically necessary dislocation density under constant loading or punch configurations for anisotropic materials [11, 12]. For example, Kysar et al. [12] estimated the distribution of geometrically necessary dislocation density on a cross section of a wedge indented aluminum single crystal via EBSD measurement. As lattice curvature induced by μLSP is relatively small compared with those of a constant load or a punch, length scale effects are not obvious in μLSP and can not simply be copied from their works. The objective of the present work is to find the spatial distribution of the geometrically necessary dislocation density after μLSP process from both numerical and experimental results for single crystal aluminum under plane strain condition. Gaussian pressure loading, corresponding to the pressure caused by laser shock peening, was assumed in the numerical simulation and the resulting plastic deformation was analyzed to find the distribution of the geometrically necessary dislocation density. The remainder of the chapter is organized as follows. Section 2 gives details about experimental conditions and postpeening material characterization, which includes lattice rotation quantification by EBSD. Principles of the evaluation of geometrically necessary dislocations density are described in Section 3. In Section 4, finite element simulation employed to study the length scale effect in the target material after μLSP is presented. Section 5 gives the results and discussion. Following are concluding marks. Fig. 1 Experimental set-up EXPERIMENTAL CONDITIONS AND POST-PEENING MATERIAL CHARACTERIZATION A frequency tripled Q-switched Nd:YAG laser ( nm 355 = λ ) in TEM00 mode was used for the μLSP experiments with a 50ns pulse duration and a 12μm beam diameter, as shown in Fig. 1. A thin layer of high vacuum grease (about 10 microns thick) was spread evenly on the sample surface, and a 16μm thick polycrystalline aluminum foil, chosen for its relatively low threshold of vaporization, was tightly pressed onto the grease. The sample was placed in a shallow container filled with distilled water approximately 3 mm above the sample’s top surface. A line of μLSP shocks were created on the sample surface with a 25 μm spacing along the [110] direction as shown in Fig. 1. A pulse energy of 228μJ was used which corresponded to a laser intensity of 4.03GW/cm 2 . After shock processing, the coating layer and the vacuum grease were manually removed. A single crystal aluminum with the orientation ( ) 4 1 1 is chosen because when shocks applied along [ ] 110 direction approximate plane strain condition is achieved [13] and under the Gaussian pressure loading only one slip system is activated. Furthermore, aluminum is a popular material used in micro metallic devices so it is of interest to study its mechanical behavior under μLSP. In preparation for laser shock peening, the sample surface was polished mechanically by using grit 600 sand paper and then repeated by using grit 1200 sand paper. After sandpaper polish, the specimen was polished using diamond paste with lapping oil as a lubricant, first 6 μm paste and then 1μm with minimum pressure was used until no directionally preferential scratches were visible under optical microscope with 100x magnification. In order to remove any residual stress induced during the mechanical polish process, the sample was electro-polished before shocking. Fig. 2 Deformed geometry of shocked line by using SPM with scan area=80×80μm and data scale=1μm The shocked region was measured using scanning probe microscopy (SPM, Digital Instruments Nanoscope Inc.) as shown in Fig. 2 for a scanning area of 80μm×80μm. After the shock peening, EBSD data was collected using a system supplied by HKL Technology and attached to a JEOL JSM 5600LV scanning electron microscope (SEM). All data were acquired in the automatic mode, using external beam scanning and employing a 3μm step size as the preliminary investigation revealed negligible levels of orientation difference at finer scales of inquiry. The scan area chosen was 150μm(width)×100μm(depth) on the cross section as the effected area by μLSP is usually smaller than this area. The EBSD results from each individual scan comprise data containing the position coordinates and the three Euler angles which describe the orientation of the particular interaction volume relative to the orientation of the specimen in the SEM allowing in-plane and out-of-plane lattice rotations to be calculated relative to the known undeformed crystallographic orientation, which serves as a reference state. 2 Copyright © 2008 by ASME EVALUATION OF GEOMETRICALLY NECESSARY DISLOCATION DENSITY AND ITS HARDENING EFFECT Based on the work by Kysar et al. [12], the evaluation principles of the geometrically necessary dislocation density are briefly summarized here as follows. First, the lattice curvature, global coordinate x, y, z and local coordinate systems x’, y’ and z’ are defined as shown in Fig. 3. By naming the lattice rotation about the x, y and z coordinates as ω1, ω2 and ω3, respectively, the crystal lattice curvature tensor, κij can be described as [8]: