Ultra small scale high cycle fatigue testing by micro-cantilevers

A new method has been developed for testing high cycle and very high cycle fatigue properties of materials at the micro-scale based on micro-cantilevers. Focused ion beam was employed to cut micro-cantilevers on the surface of a selected grain in a bulk polycrystalline commercial pure Titanium. The bulk specimen was pre-examined by EBSD, so the crystal orientation of all micro-cantilevers were known. The bulk sample with prepared micro-cantilevers was then attached to a high power ultrasonic generator, which can generate mechanical vibration at the frequency 20KHz. The bulk specimen moves with the ultrasonic generator, but the micro-cantilever lags somewhat behind. The resulting deflections generate cyclic stress in the micro-cantilevers. The high vibration frequency means it can easily test into the high cycle and very high cycle regime. The design challenge is to generate enough stress to cause fatigue in these ultra-small specimens because the stress amplitude achieved in vibration is inverse to the cantilever size. Previous finite element model and experiments had shown that the classic micro-cantilever with uniform cross-section [1,2] can only generate stress a few MPa, even with the acceleration was tuned up to 107m/s2. Instead, we designed a new ‘hammer’ shape micro-cantilever as shown in Figure 1a to increase the inertia. This design now generates sufficient stress and enables fatigue testing even in Titanium, which is a challenging material due to the high strength to weight ratio (both high strength and low density require higher acceleration). SN curves in the testing range from 105 to 108 cycles have been obtained for these micro- single crystal Ti samples using a step test protocol. The stress to failure decreases systematically as the number of cycles to failure increases. However, there is strong dependence on the crystal orientation with the fatigue strength at 107 cycles for test pieces cut along the direction being approximately twice that of those cut in the direction. The fatigue strength of micro-fatigue test is significantly lower than the static strength measured on micro-cantilevers of identical size using a nanoindenter. Due to the small specimen size, it is suggested that the results reflect the behavior of fatigue nucleation rather than propagation

Crystallographic structure and mechanical behaviour of SnAgCu solder interconnects under a constant loading rate

With the continuing increase of the integration density in electronics, dimensions of interconnections for electronic components have been miniaturized to a scale that is comparable to those of their crystallographic structure. For instance, a SnAgCu solder joint in the flip chip package can contain only one or a few grains. In this case, the mechanical behaviour of the micro-joint is expected to shift from a polycrystalline-based to single-crystal one. Considering the further miniaturization, both the crystallographic structure and mechanics of each component (Ag3Sn, Cu6Sn5 and beta-Sn matrix) within a grain and the adjacent SnCu interface will play an important role in the reliability of the micro-joint due to their size comparable with that of a grain, irregular geometry, their heterogeneous distribution and considerably different properties. In addition, at such a small scale, the non-local effect on deformation of beta-Sn should be taken into account to interpret mechanical interactions between components. In this paper, a shearing test, in which it is possible to apply a constant loading to a SnAgCu joint is deigned to investigate mechanics of substructure within a SnAgCu grain and near the SnCu interface

Mesomechanical modelling of SnAgCu solder joints in flip chip

In modern microelectronic packages (considered here as a mesoscale), the size of microstructural features of an alloy is compatible with the scale of an entire element that can contain only one or a few grains. In this case, the mechanical behaviour of the element deviates from isotropic/homogenous character at the macroscopic scale of a bulk specimen, comprising a large number of randomly oriented grains. Generally, a crystal-plasticity model, which is based on dislocation sliding in certain slip systems, is applied to describe a local lattice-induced anisotropic behaviour. However, even at a room temperature, the movement of dislocations is not a single mechanism of the inelastic behaviour of eutectic SnAgCu solder due to its low melting point. Under a low-magnitude loading condition, creep also has an effect due to a movement of vacancies. At high temperatures, this creep can become a dominant mechanism for the inelastic behaviour, diminishing the role of the crystal-plasticity model. This paper accounts for the creep component of deformation and unites it with the traditional crystal-plasticity model. In addition, deformation due to thermal expansion is introduced into the constitutive equation to capture the major mechanisms of the mechanical behaviour of a SnAgCu solder micro-joint used in electronics

PVI-DSO: Leveraging Planar Regularities for Direct Sparse Visual-Inertial Odometry

The monocular Visual-Inertial Odometry (VIO) based on the direct method can leverage all the available pixels in the image to estimate the camera motion and reconstruct the environment. The denser map reconstruction provides more information about the environment, making it easier to extract structure and planar regularities. In this paper, we propose a monocular direct sparse visual-inertial odometry, which exploits the plane regularities (PVI-DSO). Our system detects coplanar information from 3D meshes generated from 3D point clouds and uses coplanar parameters to introduce coplanar constraints. In order to reduce computation and improve compactness, the plane-distance cost is directly used as the prior information of plane parameters. We conduct ablation experiments on public datasets and compare our system with other state-of-the-art algorithms. The experimental results verified leveraging the plane information can improve the accuracy of the VIO system based on the direct method

Bayesian Optimised Collection Strategies for Fatigue Testing : Constant Life Testing

This paper presents a statistical framework enabling optimal sampling and robust analysis of fatigue data. We create protocols using Bayesian maximum entropy sampling, which build on the staircase and step methods, removing the requirement of prior knowledge of the fatigue strength distribution for data collection. Results show improved sampling efficiency and parameter estimation over the conventional approaches. Statistical methods for distinguishing between distribution types highlight the role of the protocol in model distinction. Experimental validation of the above work is performed, showing the applicability of the methods in laboratory testing.Comment: 25 pages, 12 figures + 1 SI figur

Grain features of SnAgCu solder and their effect on mechanical behaviour of micro-joints

SnAgCu alloy, which promises compatible properties with Sn-Pb solder, has been identified as one of the most potential Lead-free solders for electronic interconnections. However, due to the miniaturization of solder joints, a micro-joint of this material contains only few grains. In this case, the mechanical behaviour of solder alloys shifts from the polycrystal-based to single-crystal based. Since P-Sn, the matrix of SnAgCu solder, has a contracted body-centred tetragonal structure, its grains are expected to have anisotropic properties, which are important, the reliability of a micro-joint. The present paper studies the inelastic anisotropic behaviour of this material. In order to analyse the effect of grain features, solder joints at different size are formed under the different cooling rate. An in-situ shear test is then performed to correlate the mechanical behavior of a joint to its microstructural features. The results show that the decrease in the joint's dimension results in the diminishment of the number of grains, and that the inelastic behaviour of SnAgCu grains is orientation-dependen

Formation of Sn dendrites and SnAg eutectics in a SnAgCu solder

The formation behaviour of grains and their components, including Sn dendrites, Cu6Sn5 and Ag3Sn intermetallic compounds (IMCs), in a SnAgCu alloy is investigated in an experiment, capable to obtain the solid reactants directly from the liquid solder during the liquid-to-solid phase transformation. The results show that Cu6Sn5 IMCs are formed first in a grain; then large Sn dendrites; fibre-like Ag3Sn IMCs are formed ahead of the β-Sn matrix in the coupling process generating eutectics

Formation of Ag3Sn plates in SnAgCu solder bumps

Special experiments are designed to obtain the solid reactants directly from a liquid solder during phase transformation. Series of such tests performed throughout reflow, which enables to investigate the entire formation process of intermetallic Ag3Sn plates out of liquid SnAgCu solder bumps. The results show that Ag3Sn plates are formed first in the middle of the cooling stage. In the plane, they have two preferable growth directions. By varying thermal conditions during reflow, the formation mechanism of these plates is discussed

From micro-cantilever testing to deformation patterning in HCP polycrystals

For several years now we have been using micro-scale cantilever bend tests to probe the considerable anisotropy of elastic and plastic deformation behaviour in the hexagonal packed metals Ti and Zr [1-3]. The wider aim of the work has been understanding and modeling the heterogeneous patterns of stress, strain and dislocation density that develop during deformation of HCP polycrystals. Crystal plasticity finite element analysis (CP-FEA) of representative volumes are used to simulate these deformation fields and enable modelling of representative volume elements to aid understanding of in-service component performance. Critical resolved shear stress (CRSS) values for the important slip systems are required inputs for the constitutive laws and populating these has been the aim of our micro-cantilever studies. We follow a well-established route of using a focused ion beam (FIB) to machine micro-cantilevers of triangular cross-section into the sample surface [1]. EBSD is used to identify grains in which cantilevers with suitable orientation can be cut so that the targeted slip systems can be activated individually. The samples are then passed to a nano-indenter with a nano-positioning stage and loaded, with the load point accurately located at the free end of the cantilever using an AFM-like scan with low contact force. Load-displacement data generated from the experiment are compared to CP-FEA simulations of the cantilever bending and the CRSS for each cantilever is varied until a good fit is achieved [1]. The CRSS data show a significant size effect, where smaller cantilevers are apparently stronger. This is very obvious at cantilever widths below ~5 µm but also persists to larger sizes. The size effect is found to be well represented by where is the effective CRSS measured for a cantilever of width , is the CRSS for bulk samples and is a constant representing the strength of the size effect [2]. During bending strains are largest near the built-in end at the top (tensile) and bottom (compressive) regions (twice as large at the bottom due to the orientation of the triangular section). Dislocations tend to be generated in these regions and propagate progressively in towards the neutral axis of the beam where they pile-up. The back-stress from these pile-ups acts against further dislocations being generated and moving to join the pile-up. This effect is seen in discrete dislocation plasticity simulations that inherently capture the size effect [3], but are not present in the length scale independent CP-FEA simulations, where the size effect is manifested instead as an apparent increase in CRSS for smaller cantilever width. This pile-up effect has been confirmed with post-mortem TEM observations of the dislocation pile-ups in Ti alloys [4,5]. Examples of cantilever studies in Ti and Zr alloys will be shown. We will also demonstrate that this approach generates CRSS values which allow the bulk flow stresses of macroscopic polycrystal aggregates to be determined, so enabling micromechanical studies to inform component level performance of industrial alloys [6]

Mechanical Behaviour of Grains in SnAgCu Solder Joints

A collection of slides from the authors conference presentation is given