【正文】 rocessing history of the part, and represented as a certain most probable orientation for any grain in the material. This is of great important when considering the processing of many real metallic materials, and their use in a wide range of applications.MicrotextureThis is used to refer to the determination and study of the orientation of single grains in a material, paying attention to the spatial location of the grains studied within the sample. It is thus a bination of the study of texture and microstructure. This type of study is particularly useful in probing grain boundary structure, phase relationships (including before and after transformation), and sub grain dislocation structures, amongst others.Origin of TextureAny process that affects a material in an anisotropic way can give rise to texture. This can include solidification (where the direction of greatest heat extraction will be the direction of solidification, leading to texture in materials where crystals grow more easily along certain directions, see Figure 1), deformation (as materials may deform more easily in certain directions).Figure 1 – A solidification microstructure, showing anisotropic grain shapes. Note that, although this material does show texture, this cannot be concluded from the image. All we can say for certain is that the grains have an anisotropic shape, we can say nothing about their crystallographic orientation.Why is Texture Important?The importance of the texture of a material es from the fact that in many crystalline materials, the properties can depend on the direction relative to the crystallographic axis in which they are measured. For example, the elastic modulus of most single crystal metal samples would in fact vary depending on the direction it was tested in. The same is true of such properties as the Poisson’s ratio, magnetic permeability, electrical conductivity and thermal expansion coefficient, to name a few. These materials are anisotropic (the reason that most materials we encounter do not present such anisotropy is that the random orientation of the grains tends to blend out such variations).However, in a material with a preferred orientation, with a texture, the properties will not blend together equally, and we many find that a macroscopic sample can show a variation in properties.Example – Texture in Aluminium Deep DrawingWhen rolled, metals can develop a texture, which can influence their behaviour in subsequent processing. In the case of aluminium, rolling can produce a texture that means it deforms more easily along two perpendicular directions in the plane of the sheet than at 45176。Quantification of Microstructure and Texture True Size and Size Distributions of Second PhasesQuantification of Microstructure and Texture7. True Size and Size Distributions of Second PhasesMetallographic images are a 2D representation of a 3D structure, and as such the measurements of size that we make using the image may not be the same as the sizes of the features in reality. Conventionally, this is not a concern for the grain size, where values reported are those measured in 2D, and generally, the mean intercept length is a good way of characterising the dimensions of features that will be sampled by many processes (. by dislocations moving during plastic deformation) in the material. There remain, however, some situations where the precise true size is of interest. The first part of this lecture is concerned with the relationship between the 2D sections of features observed in metallographic images and the true size of such features. The second part considers what information can be extracted from the measurements concerning the distribution of sizes. Note that, while the linear intercept method can give enough information to allow the determination of the true size of features, individual measurements of features (such as by the method of equivalent circles) is necessary in order to obtain size distributions.Determination of True SizesAlthough grain sizes are by convention reported as the sizes measured in the plane of the section, there may be occasions when we need to know the true size of grains or, more monly, second phase particles in a microstructure. It is clear on considering a spherical particle, Figure 1, that random sections are unlikely to reveal a section with diameter equal to the real diameter of the sphere. Rather, the mean diameter of spherical inclusions as determined by the linear intercept method will be somewhat less than the true value.Figure 1 – Possible sections through a spherical particles and the apparent particle diameter measured as a result.The relationship between the true size of a particle and the mean linear intercept length is given by S I Tomkeieff, Nature, 155 (1945) 24: (1)where V and S are the volume and surface area of the particle respectively. How this is applied can be demonstrated by considering the sphere in Figure 1. This has V = 4/3 p r3 and S = 4 p r2. Substituting into Eqn. (1) gives: (2)where r and d are the radius and diameter of the sphere. Thus for spherical inclusions, the average value of the diameter measured on the section will be 2/3 that of the true diameter.Similar calculations can be performed for other shapes of particle. Example results are given in Table 1.ShapeVolume, VSurface Area, SMean Intercept LengthSphereRadius, rDiskRadius, rThickness, tr tCylinderRadius, rHeight, hr ~ hRodRadius, rLength, ll rHemisphereRadius, rProlate Spheroid*Radius 1, aRadius 2, ca c. for a=2cOblate Spheroid*Radius 1, aRadius 2, ca cTable 1 – The relationship between the size of features of different shapes measured on 2D sections and the true size in 3D (*Spheroids are formed by the rotation of an ellipse, and have 2 defined rad