To process the experimental data obtained in this thesis, digital image correlation (DIC) is performed. This is a post-processing technique for measuring strains and displace-ments in experimental solid mechanics. DIC is an accurate, cheap and simple way of gathering material information. In addition, DIC makes it easy to examine the defor-mation pattern and the crack propagation.
The DIC technique compares the image of a specimen at a deformed stage (current con-figuration) to an image of the specimen at a reference stage (reference concon-figuration).
In more detail, it measures the alteration of the pixels in the images over time. The surface of the material needs to exhibit characteristic points such that the system can trace the deformation. Consequently a field of both two-dimensional (2D) and three-dimensional (3D) deformation vectors can be constructed [55]. In this thesis, 2D-DIC will be used in the material tensile tests, while 3D-DIC will be performed of the shock tube experiments.
In 2D-DIC, the deformation of the specimen is described by a set of parameters. These parameters are optimized to minimize the differences in grayscale values between the reference and current image. The optimization is performed by employing the Newton-Raphson iteration method, where the correlation functionFin Equation (3.40) may be used as the objective function [56]. This is called a subset-based DIC approach.
F=X
i∈Ω
(Ir(Xi)−Ic(xi))2 (3.40)
where,
Ir is the reference image Ic is the current image
X refers to the image coordinates in the reference configuration x refers to the image coordinates in the current configuration i represents a specific pixel
Ω is the set of pixels within the subset at the reference configuration
3D-DIC involves a typical steriovision system that employs two or more cameras to record digital images of the specimen from two or more viewpoints. This makes 3D-DIC theoretically capable of obtaining accurate, in-plane surface deformations even when the specimen is undergoing large, three-dimensional rigid body rotation and transla-tion [57]. Figure 3.15 displays a typical 3D-DIC setup whereP represents an arbitrary initial point andP0is the location after deformation.
P1
Figure 3.15:Mathematical model of a 3D-DIC system [58].
In addition to subset-based DIC, a finite element approach is possible. The FE-based DIC, formulates the correlation problem as a finite-element decomposition on a mesh of Q4 elements. The correlation applies global optimization on a mesh of elements, and the nodal displacements in the mesh are optimized. This differs from the subset-based DIC approach where individual optimization of subsets are applied, and opti-mizing involves the displacement of the center point and the displacement gradient of the subset.
The success of the correlation and the quality of the images depend on several param-eters. Some of the most important parameters involve the contrast and speckle size of the recorded grayscale pattern, in addition to the subset size and the digitization level of the grayscale values.
Materials
In this thesis, two materials are used when performing the experimental research in the shock tube. The materials are,
• Docol 600 DL steel
• Aluminium alloy EN AW-1050A-H14
While all the steel plates are produced by SSAB, the aluminium plates have two dif-ferent manufacturers. Hindalco industries and Hydro have produced the 0.8mm and 2.0mm aluminium plates, respectively. The two next sections are based on general the-ory about the two materials. There are, however, some variations between the theoret-ical material characteristics and the given values in the material card appointed by the manufacturers. The material cards with the exact material characteristics are therefore enclosed in Appendix B.
To find the material characteristics of the materials, tensile tests are performed. Subse-quently the data are processed using 2D-DIC. The tensile tests are also studied numer-ically, by applying the FE program Abaqus CAE.
4.1 Docol 600 DL Steel
Docol is a cold-rolled, high strength steel produced by SSAB in Sweden. It contains ferrite, which is soft and contributes to good formability, and martensite, which hard strengthens the material. In addition, it has good weldability due to the low content of alloying elements. There are several advantages using Docol DL; weight reduction, simplified manufacturing, increased safety, longer lifecycle, reduced total cost, among others [59].
Common areas of applications of the Docol 600 DL, are in tubes and as safety compo-nents in cars. Its chemical composition in addition to physical and mechanical prop-erties are displayed in Tables 4.1 and 4.2, respectively. Note that the steels are classified based on the lowest tensile strength, which is 600 MPa for Docol 600 DL.
Table 4.1:Chemical composition of Docol 600 DL steel [59].
Chemical Element
Composition [%] C Si Mn P S Al
General 0.100 0.400 1.500 0.010 0.002 0.040
Table 4.2:Physical and mechanical properties of Docol 600 DL steel [59] [60].
ν ρ E G Rp,02,mi n Rp,02,max Rm,mi n Rm,max
[−] [kg/m3] [MPa] [MPa] [MPa] [MPa] [MPa] [MPa]
0.30 7800 210 000 81 000 280 360 600 700
Steel has been used in structural applications since the middle of the 18t hcentury. Steel is a ductile material with high yield strength. This means that the material can undergo large plastic deformations before failure, which is an important attribute when it comes to blast loading. Steel has also great strength, uniformity and a relatively good fatigue strength. Combined with a high strength to weight ratio it makes steel an appropriate choice for structures such as high-rise buildings and long-span bridges [61].
One major disadvantage is that steel is susceptible to corrosion when exposed to air, water or humidity. This result in higher maintenance costs. Steel is also vulnerable to fire since the strength is reduced when exposed to high temperatures [62].