| 1. |
- Athanasopoulos, Stefanos D., et al.
(author)
-
Mapping Grain Strains in Sand Under Load Using Neutron Diffraction Scanning
- 2018
-
In: Micro to MACRO Mathematical Modelling in Soil Mechanics. - Cham : Springer International Publishing. - 2297-0215 .- 2297-024X. - 9783319994734 - 9783319994741 ; , s. 23-33
-
Book chapter (peer-reviewed)abstract
- Towards the improvement of the understanding of force/stress distribution in granular media under load, a new experimental approach is suggested. Neutron diffraction, a non-conventional experimental technique, has been successfully used to map the evolution of intragranular strains in sand specimens loaded in a novel plane-strain apparatus. Representative preliminary results from recent experiments are presented, focusing on the correlation between the macro- and micro-scale response of the material, to highlight the potential of the experimental approach.
|
|
| 2. |
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
|
|
| 6. |
- Hektor, Johan, et al.
(author)
-
Coupled diffusion-deformation multiphase field model for elastoplastic materials applied to the growth of Cu6Sn5
- 2016
-
In: Acta Materialia. - : Elsevier BV. - 1873-2453 .- 1359-6454. ; 108, s. 98-109
-
Journal article (peer-reviewed)abstract
- A coupled diffusion-deformation, multiphase field model for elastoplastic materials is presented. The equations governing the evolution of the phase fields and the molar concentration field are derived in a thermodynamically consistent way using microforce balance laws. As an example of its capabilities, the model is used to study the growth of the intermetallic compound (IMC) Cu6Sn5 during room-temperature aging. This IMC is of great importance in, e.g., soldering of electronic components. The model accounts for grain boundary diffusion between IMC grains and plastic deformation of the microstructure. A plasticity model with hardening, based on an evolving dislocation density, is used for the Cu and Sn phases. Results from the numerical simulations suggest that the thickness of the IMC layer increases linearly with time and that the morphology of the IMC gradually changes from scallop-like to planar, consistent with previous experimental findings. The model predicts that plastic deformation occurs in both the Cu and the Sn layers. Furthermore, the mean value of the biaxial stress in the Sn layer is found to saturate at a level of −8 MPa to −10 MPa during aging. This is in good agreement with experimental data.
|
|
| 7. |
- Hektor, Johan, et al.
(author)
-
Evidence of 3D strain gradients associated with tin whisker growth
- 2018
-
In: Scripta Materialia. - : Elsevier BV. - 1359-6462. ; 144:February 2018, s. 1-4
-
Journal article (peer-reviewed)abstract
- We have used Differential Aperture X-ray Microscopy (DAXM) to measure grain orientations and deviatoric elastic strains in 3D around a tin whisker. The results show strain gradients through the depth of the tin coating, revealing a higher strain deeper in the Sn layer. These higher strains are explained by the volume change occurring during growth of the intermetallic phase Cu6Sn5 at the interface between the Cu substrate and the Sn coating and at grain boundaries between Sn grains.
|
|
| 8. |
- Hektor, Johan, et al.
(author)
-
Long term evolution of microstructure and stress around tin whiskers investigated using scanning Laue microdiffraction
- 2019
-
In: Acta Materialia. - : Elsevier BV. - 1359-6454. ; 168, s. 210-221
-
Journal article (peer-reviewed)abstract
- Scanning Laue microdiffraction was used to study the evolution of the microstructure and the stress field around two tin whiskers during ageing for up to 21 months. In the heterogeneous stress fields obtained, localised ridges of high compressive stress leading to the root of the whiskers were found. Due to the evolution of the intermetallic compound in the interface between the copper substrate and the tin coating, the stress field was also evolving with time. The temporal evolution of the stress field indicates that the regions supplying material to the whisker root is changing with time, highlighting that whisker growth is a highly dynamical process. During the experimental campaign, a new surface feature appeared in a grain boundary within the scanned area of the sample. The new feature had a twinning relationship with one of the neighbouring grains, a similar twin relation was also seen for one of the two larger whiskers. It is suggested that tin atoms diffuse out from the ridges of high compressive stress to the nearby, less compressed grain boundaries along which diffusion towards the root of the whisker occurs. The observations made from the Laue diffraction measurements also suggest that whiskers form in regions where the gradient in hydrostatic stress is large and that they grow to relax compressive stresses.
|
|
| 9. |
- Hektor, Johan, et al.
(author)
-
Scanning 3DXRD measurement of grain growth, stress, and formation of Cu6Sn5 around a tin whisker during heat treatment
- 2019
-
In: Materials. - : MDPI AG. - 1996-1944. ; 12:3
-
Journal article (peer-reviewed)abstract
- The 3D microstructure around a tin whisker, and its evolution during heat treatment were studied using scanning 3DXRD. The shape of each grain in the sample was reconstructed using a filtered-back-projection algorithm. The local lattice parameters and grain orientations could then be refined, using forward modelling of the diffraction data, with a spatial resolution of 250nm. It was found that the tin coating had a texture where grains were oriented such that their c-axes were predominantly parallel to the sample surface. Grains with other orientations were consumed by grain growth during the heat treatment. Most of the grain boundaries were found to have misorientations larger than 15°, and many coincidence site lattice (CSL) or other types of low-energy grain boundaries were identified. None of the grains with CSL grain boundaries were consumed by grain growth. During the heat treatment, growth of preexisting Cu6Sn5 occurred; these grains were indexed as a hexagonal η phase, which is usually documented to be stable only at temperatures exceeding 186 °C. This indicates that the η phase can exist in a metastable state for long periods. The tin coating was found to be under compressive hydrostatic stress, with a negative gradient in hydrostatic stress extending outwards from the root of the whisker. Negative stress gradients are generally believed to play an essential role in providing the driving force for diffusion of material to the whisker root.
|
|
| 10. |
- Hektor, Johan
(author)
-
Tin whiskers: experiments and modelling
- 2018
-
Doctoral thesis (other academic/artistic)abstract
- Tin whiskers are hair-like single crystals that spontaneously grow from tin-coated surfaces. Whiskers are commonly found in electronic components, where tin coatings are used in, e.g., soldering applications, and to protect components from corrosion. Whiskers are known to cause short-circuits leading to failure of electronic components. The exact mechanisms responsible for whisker formation and growth are not fully understood. It is, however, believed that whiskers grow as a way to relax stress in the tin coating and that compressive stress gradients drive the growth. The stress in the coating is mainly caused by the formation and growth of the intermetallic compound Cu6Sn5 in the interface region between the copper substrate and the tin layer.This thesis presents numerical simulations and experimental investigations related to the growth and formation of tin whiskers on tin coated copper substrates. The aim of the experimental work has been to verify the existence of a compressive stress gradient and to characterise the microstructure around tin whiskers in 2D as well as 3D. This was realised using different x-ray diffraction methods, namely scanning Laue microdiffraction, differential aperture x-ray microscopy (DAXM), and scanning 3D x-ray diffraction (3DXRD). Laue microdiffraction was used to study the evolution of the microstructure around two whiskers over a period ranging from 4 to 21 months of ageing. The hydrostatic stress field in the tin coating was estimated by assuming plane stress conditions. It was found that the stress field was highly inhomogeneous.It was possible to identify ridges of high compressive stress leading to the whisker. These ridges, which have not been observed previously, are potentially driving diffusion of tin from specific regions of the coating towards the root of the whisker.DAXM and 3DXRD were used to study the microstructure around a whisker in three dimensions. Using DAXM, through-depth variations of the deviatoric strain field were measured for the first time. Deep in the coating, where the \ce{Cu6Sn5} is present, the deviatoric strain was high. This indicates that the growth of the intermetallic phase causes plastic deformation of the tin coating. A novel scanning 3DXRD tomography technique was used to map out intragranular variations in the unit cell parameters and the grain orientations with sub-micrometre resolution. A short (4 micrometre) radial gradient in hydrostatic stress was observed around the root of the whisker.This gradient together with long-range diffusion from specific regions could provide the driving force for whisker growth.From the 3DXRD data, it was also possible to determine the location of Cu6Sn5 in the sample. A large grain of Cu6Sn5 was found right below the whisker which seems to have caused distortion of the nearby tin grains. We also studied the evolution of the microstructure during heat treatment. The heat treatment encouraged the formation of the intermetallic phase and also led to coarsening of the tin grains.The numerical simulations in this thesis are based on a multiphase field model. This model is one of few phase field models existing that includes diffusion as well as elastic and plastic deformation. The model was used to study the growth of Cu6Sn5 during room temperature ageing, specifically the effect of the curvature of the intermetallic layer on the stress and plastic deformation of the tin coating was investigated. It was found that a high curvature led to localisation of plastic deformation in the region above the highly curved grain.
|
|
