Measurement of Grain Size, Study notes of Law

Download Measurement of Grain Size and more Study notes Law in PDF only on Docsity!

Measurement of Grain Size

George F. Vander Voort

Consultant – Struers Inc.

Westlake, Ohio USA

Grain Requirements

 Shapes must be space filling

 Surfaces must exhibit minimum surface area and minimum surface tension (Plateau, 1873)

Tetrakaidecahedron

Lord Kelvin (1887) showed that the optimum grain shape meeting these requirements was a polyhedron called a tetrakaidecahedra with 14 faces

 24 Corners

 36 Edges

But, the tetrakaidecahedron does not exhibit 120 dihedral angles between grain boundaries where 3 adjacent grains meet at an edge – unless the faces exhibit curvature.

C.H. Desch (1919)

First to study actual grain shapes by LME of β - brass in liquid Hg. For isolated grains, he found:

Avg. No. Faces/Grain = 14.5 (11 to 20)

Avg. No. Edges/Face = 5.14 (3 to 8) 5-sided grains were most frequent

W.M Williams and C.S. Smith

Used stereomicroradiography to study grains and found:

Avg. No. Edges/Face = 5. Avg. No. Faces/Grain = 12.

Euler’s Law

For a single polygon, B = 1 and C – E + F = 2

The two- dimensional form of Euler’s Law for an array of polygons is

C – E + F = 1

5/16 Sieve 4 Sieve

8 Sieve

14 Sieve

Separation of grains by sieving after liquid metal embrittlement of  Brass in Hg

Actual Grain Shapes

3.3 mm (^) 3.3 mm

3.3 mm

3.3 mm

Grain Size Measurement

Types of Grain Sizes

- Non -twinned(ferrite, BCC metals, Al) - Twinned FCC Metals (austenite) - Prior -Austenite (Parent Phase in Q&T Steels)

Grain Size Measurements

- Number of Grains/inch^2 at 100X: G - Number of Grains/mm^2 at 1X: NA - Average Grain Area, μm^2 : A **- Average Grain Diameter, μm: d

• Mean Lineal Intercept Length, μm:** l

Definition of ASTM Grain Size

n = 2 G-

n = number of grains/in^2 at 100X G = ASTM Grain Size Number

ASTM Grain Size Equation

Introduced when E 91 – ASTM Method for Estimating the Average Grain Size of Non-Ferrous Metals, Other Than Copper, and Their Alloys – was introduced in 1951. The equation was developed by Timken Co.

Current ASTM Standards for Grain Size

ASTM E 112: For equiaxed, single- phase grain structures

ASTM E 930: For grain structures with an occasional very large grain

ASTM E 1181: For characterizing duplex grain structures

ASTM E 1382: For image analysis measurements of grain size, any type

Metric Equivalents

Other countries established grain size scales using the metric system, based on the number of grains per sq. mm at 1X, NA:

Sweden (SIS 11 11 01); Italy (UNI 3245); Russia (GOST 5639); France (NF A04-102); and ISO (ISO 643) according to: M = 8 (2Gm)

where m = No. Grains/mm^2 at 1X