9.7 Effect of L/W ratio of voids and shear strains

The L/W ratio of voids was correlated with various shear stresses calculated from Mohr's circle like γ12, γ13, γ<sup>23</sup> and γ12/ε<sup>m</sup> at all annealing temperature conditions which has been shown in Figures 14–16. For sheets annealed at 350°C, negative sloped curves were obtained due to high L/W ratio, whereas the sheet annealed at

Figure 16. L/W ratio of void vs. shear strains at various annealing temperatures for Al1350 alloy.

200°C showed positive sloped curves because of their low L/W ratio. These findings were in good agreement with those of Narayanasamy et al. [1, 26].

magnetic hysteresis) and of aluminium cans (since deep drawing requires extreme

Texture significantly affects the formability which is usually evaluated in terms of forming limit diagrams [1]. Although much research has been carried out, their correlations have not yet been completely clarified. Aluminium alloys exhibit typical pure metal texture (Cu-type) on rolling comprising of Cu {1 1 2}<111>, brass {1 1 0}<112> and S {1 2 3}<634> orientations, and Cube {1 0 0}<001 > and Goss {1 1 0}<001> components were common during annealing [7, 10]. In this aspect an attempt has been made to correlate the tensile properties, formability properties and void coalescence parameters, with texture of sheet metal at different annealing temperatures. The effect of the cube texture on the initiation of localized necking has been studied using numerical methods by Wu et al. [12]. They have inferred that, when a sheet undergoes biaxial tension, ideal cube texture significantly delays the initiation of localized necking [11]. Aluminium alloys exhibit typical pure metal texture (Cu {1 1 2} <111>-type) on rolling comprising of Cu {1 1 2}<111>{1 1 2}<111>, brass {1 1 0}<112> and S {1 2 3}<634> orientations, and Cube {1 0 0}<001> and Goss {1 1 0}<001> components are common during annealing [10] as seen in Figure 1. An Al 8011 aluminium alloy sheet cold-rolled by 95% had a typical fibre texture, which runs from the copper orientation {1 1 2}<1 1 1> over the S-orientation {1 2 3}<634> to the brass orientation {1 1 0}<112> in the Euler space. The results were discussed, based on the interaction between precipitation and recrystallization [13, 14]. The cube component recovered quite easily during deformation after large strains as well as during the first step of the

annealing treatment, as per the findings of Gerber et al. [15].

beta fibre, the following discussions were made (Figure 17).

11.1 Volume fraction

11.2 Al alloy

49

annealing temperature of 300°C.

Matthies et al. [16] have consolidated all methods of the analysis of texture by pole figure and orientation distribution function (ODF) in Euler space. Knorr et al. [17] and Kocks et al. [18] studied the material property such as strength and deformation behaviour, through texture and failure analysis. Bennett et al. [6] examined the cube (1 0 0)<001> grains before and after stretching and found that there was a translocation. In this aspect this work investigates the mode of evolution of texture components, in commercially available aluminium alloy sheets of three different thicknesses at three different annealing temperatures using numerical modelling practice. The works related to the crystal plastic models are given below. From the results of Al 8011, Al 1145 and Al 1350 alloy, pole figures ODF and alpha-

A plot of the texture component with the annealing temperature for Al 8011 alloy showed a linear relationship for the cube and Goss component. Similarly from Figures 17 and 18, cube and RD cube were increasing linearly for Al 1145 alloy. The components S and Cu were in decreasing nature, and a deviation occurred at an

The evolution of Goss intensity was very negligible in Al 1145 alloy as compared to alloy 8011. The dominant texture component in the annealed microstructure,

and relatively uniform plasticity) [8].

Aluminium and Its Interlinking Properties DOI: http://dx.doi.org/10.5772/intechopen.86553

11. Texture properties

### 10. Crystallographic texture

A crystal is characterized by the periodic arrangement of its elements (atoms, ions) in space. In the field of material science and engineering, the distribution of the crystallographic orientations of a polycrystalline sample is called as texture. If these orientations were fully random in a sample, it had no texture. If the crystallographic orientations have some preferred orientation but were not random, then the sample has different textures, namely, weak, moderate and strong. The crystal having the preferred orientation and its degree was dependent on the percentage [6]. Texture can have a great influence on the material properties and is seen in almost all engineered materials. If all crystallites had the same orientation, the anisotropy of the polycrystal exactly equals that of the single crystal [7]. In an isotropic texture, all orientations occur with the same probability; the behaviour of the polycrystalline material was isotropic even though every single element (crystallite) showed an anisotropic behaviour (Engler et al., 2001).

#### 10.1 Crystallographic texture analysis

Texture can be determined by various methods, namely, quantitative analysis and qualitative analysis. In quantitative techniques, the most widely used is X-ray diffraction using texture goniometry. Often texture has been represented using a pole figure, in a stereographic projection, a specified crystallographic axis (or pole) from each of which a representative number of crystallites which was plotted, along with the directions relevant to the material's processing history. These defined directions are called as a sample reference frames.

#### 10.2 Common textures

The commonly found textures in processed materials are cube (0 0 1)<100>, brass (1 1 0)<112>, copper (1 1 2)<1 1 –1> and S(1 2 3)<6 3 –4> [9]. These were given in miller indices for simplification purposes.

#### 10.3 Orientation distribution function

The ODF is defined as the volume fraction of grains with a certain orientation. The orientation is normally identified using three Euler angles. The orientation distribution function cannot be measured directly by any technique. But it can be state by a sum of functions or expand it in a series of harmonic function [9]. Others, known as discrete methods, divide the ODF space in cells and focus on determining the value of the ODF in each cell.

#### 10.4 Origin

The making of metal sheet often involves compression in one direction and, in efficient rolling operations, tension in another, which can orient crystallites in both axes, by a process known as the grain flow. New crystallites that arise with annealing usually have a different texture [7]. The control of texture was extremely important during the making of a silicon steel sheet for transformer cores (to reduce magnetic hysteresis) and of aluminium cans (since deep drawing requires extreme and relatively uniform plasticity) [8].
