Inclusion content

This section presents the work done in determining the inclusion content of S770QL steel.

Determining the inclusion content is an important step in the material characterization because it serves as a proxy measurement of an initial void volume ratio. Procedures are here briefly summarized and main results reported.

Fig. 3.3 presents a schematic of the geometry and orientation of metallographic specimens cut out from tube to plate specimens used in Chapter 4.

Fig. 3.4 shows a convention followed for naming of the specimens used for determining the inclusion content. The following region designations were used: BM - Base Material (BM);

W - Weld (W) material; WT - near Weld Toe (WT) of a loaded tube specimen. For WT cases, unfortunately representative samples near the weld toe were hard to get, leading to sampling away from the weld toe. This means that the statistics that are presented are closer to the BM than to the actual weld toe. All specimens were cut and placed in a resin mold and then polished to within 1μm of abrasive (diamond) particles. No etching was used. Two types of analyses were conducted - see Fig. 3.5.

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3.2. Inclusion content

L

T

LS face S

T

S area to grind to get LT face

Figure 3.3 – Orientation of micrographs w.r.t. to tube sample

BM_LT _1

region

face

specimen number

Figure 3.4 – Specimen designation for metallographic analyses

The first is designated by Automatic Image Processing (AIP) and consists of a script that for each micrograph of a given specimen executes the following procedure: 1 - opens the file; 2 - removes the scale; 3 - converts the image to black and white; 4 - given a certain threshold of greyscale (depends on the lighting conditions and the camera sensor of the optical microscope) recognizes a certain pixel as being an inclusion and marks it as pure black and all other pixels as white; 5 - counts the number of black pixels in the image and divides it by the total number of pixels of that image to obtain an estimate of the void volume fraction f₀^AIP. The total area surveyed with this method follows [ASTM, 2013a] i.e.

a minimum of 160mm².

The second method consists of building a digital drawing file(e.g. dxf ) in a Computer-Aided Design (CAD) software with demarcations of inclusions taken manually over the micrographs.

Two types of basic elements were used in the demarcations: circles and ellipses (for more elongated inclusions). Using a script that is able to parse through the dxf file, one is able to obtain key geometric information like the position and areas for circles (from the inclusion’s diameter Dinc) as well as Aspect Ratio (AR) and orientation for ellipses (θell). Due to the high number of inclusions in a certain micrograph only about 1 to 5% of the AIP area is

Chapter 3. Material characterization and behavior

L

T

automatic image processing (AIP)

CAD demarcation of inclusions

Dinc

θell

Lnn

Figure 3.5 – Steps in metallographic analyses of inclusions

covered.

A statistical analysis was carried out on the variables obtained with the CAD method and probability distribution functions were fit to the observed data. Parameters for these functions (namely Generalized Extreme Value (GEV) and Beta distributions) were obtained using maxi-mum likelihood estimation integrated in the scientific library package SCIPY [Oliphant, 2007]

for the scripting language Python within the IPython environment [Pérez and Granger, 2007].

Probability-Probability (PP) plots and parameters can be found in Appendix B as well as more detailed data. Nearest neighbor calculations were also conducted with SCIPY using a spatial KDTree search, which organizes a set of spatial points according to the closest euclidean distance (L_nn). Searches were conducted using both circles and ellipses drawn over micrographs. For the definition of the inclusion ligament size ratio, i.e. the inclusion diameter divided by its corresponding nearest neighbor distance (χinc), only circles were used.

40

3.2. Inclusion content

Table 3.3 summarizes the data obtained for both methods by specimen. Fig. 3.6 gives an example of the frequency of observed D_inc and compares it to a GEV probability density function fit with maximum likelihood estimation to specimen BM_1_1.

Some key observations can made with the data from the CAD analyses. The inclusion content does not vary significantly between weld and base material. The mean size of circular inclusions is on the order of 5μm in diameter. The inclusion volume ratio for AIP revolves around 3e− 3 but can vary significant w.r.t measurements done by CAD, chiefly because it involves a smaller sample size. Elongated inclusions measured on LT faces do not have a preferential orientation i.e. θell is just as likely to be found as 0 or 90 Deg. On LS (through thickness) faces a slight tendency was found for ellipses to be oriented in the longitudinal direction.

It is important at this stage to point out how this knowledge can be leveraged in micro mechanical models. In Chapter 2 it was seen that these models rely on internal variables such as the porosity, void aspect ratio, void orientation and intervoid spacing. One can now quantify these variables.

For the porosity, the inclusion content can serve as proxy measurements because voids will tend to nucleate and grow around them. Since not all inclusions will nucleate voids, it seems reasonable to assume as an initial void volume ratio (f₀) a value on the order of magnitude of inclusion volume ratio, for example 1e− 3.

For the shape and orientation of the voids, since no preferential direction for ellipses was clearly observed, the hypothesis will be made that the material behavior will be best described by initially spherical voids.

In void coalescence models, such as the TBL presented in Chapter 2, a key quantity for defining the limit load on the inter-void ligament is the ratio between the void and the RVE’s radii. The statistics performed this section w.r.t. the void’s size and nearest neighbor distance can arguably provide some insight into the order of ratios that can be considered in coalescence criteria. According to Table 3.3 for base material that value should arguably be around 0.2.

Chapter 3. Material characterization and behavior

Table3.2–ChemicalCompositionofS770QL CMnSiNiCrMoVCuPSC^{IIW eq}CAWS eq 101.6×10mm0.16%1.44%0.39%0.54%0.10%0.37%0.07%0.17%0.012%0.002%0.55%0.61% 219.1×22.2mm0.15%1.37%0.25%0.12%0.40%0.45%0.00%0.16%0.012%0.001%0.57%0.61% Table3.3–Summaryofinclusionstatistics SpecimenDinc(μm)Lnn(μm)ARχincfCAD 0fAIP 0 BM_LT_15.5063.000.650.150.00230.0038 BM_LS_13.0738.430.420.160.00160.0026 BM_LT_26.5736.000.520.280.00800.0047 BM_LS_27.0137.450.570.290.01080.0033 BM_LS_34.4753.890.610.120.00270.0026 W_LT_14.6631.500.540.310.00380.0037 WT_LT_13.3031.520.430.170.00260.0013 WT_LT_25.7631.500.590.290.00830.0036 WT_LS_17.4041.910.570.280.00960.0042 (overlineindicatestheaveragemeasurement) 05101520 VoidDiameters-μm Frequency

/probabilit ydensit

y

GEVFitting Data Figure3.6–CirculardiametersandGEVdistributionfitting forBM_LT_1

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