CTF and its deployment (Method II)

Following a similar methodology to the CTFP model, a new yield loci description based on the simple FC-Taylor model was proposed; it is compared with different macroscopic yield functions in chapter 7. The new methodology focuses on calibrating the initial yield loci of the BBC2005 for two aluminium alloys (Al-Mg-Si alloys). Simplicity and efficiency are the main intrinsic features of the proposed model.

The CTF model is a texture-based model which is based on the full-constraint Taylor’s model referred to as TF. Therefore, as a starting point, the TF models for the two considered aluminium alloys were derived using the MTM-FHM software. The main inputs for the TF model were the texture in terms of the c-coefficients and the slip system (i.e. making the assumption that slipping occurs on {111} crystallographic planes in <110> directions for the considered aluminium grades). The full-constraint models for the two aluminium alloys were derived and compared with the BBC2005. It is clear that the full-constraint (TF) model when applied on both materials does overestimate the stretching regimes (i.e. first quadrants of the yield loci). However, the TF model is a good predictor of the other strain states.

The CTF model might be used to skip the biaxial test and uniaxial test in the transverse direction, which can be used to identify the biaxial yield stress YSb and the uniaxial yield

stress in the transverse direction YS90 that are used as inputs for advanced yield functions

such as BBC2005. A careful comparison between the TF model and measured yield locus (BBC2005) for two aluminium grades indicates that the TF are more elongated in the stretching regions.

First, the resulting yield loci derived using the CTF model was validated by comparing its prediction with the performance of the BBC2005 macroscopic yield function. The BBC2005 yield function, which was experientially fitted with data obtained from mechanical tests, was used to measure the yield loci of the considered aluminium alloys.

It was observed for the considered aluminium alloys that the proposed CTF model could predict well both the equibiaxial yield stress YSb and uniaxial yield stress in the transverse

direction YS90. In terms of accuracy, the CTF model predicted an equibiaxial yield stress

(CTF Biaxial) corresponding exactly with the measured experimentally balanced points (Experimental Biaxial) for both of the considered aluminium alloys. The CTF model overestimated the biaxial points for both materials by 1% at the most, which was negligible. Moreover, the CTF model gave an accurate prediction and overestimated the uniaxial yield stress in the transverse direction YS90 for the AC600 alloy by less than 2%,

with a value of approximately 2 MPa. However, the prediction for the yield stress in the transverse direction YS90 for the AA6111-T4 material was less accurate. The model over-

predicted the YS90 by about 6%, with a value of approximately 7 MPa.

It was demonstrated that the proposed texture-based model, referred to as the CTF model, could predict the yield stresses for the two different stress states, namely the Yb and Y90,

accurately, but its accuracy could not be guaranteed in other strain states. Therefore, the CTF model will be deployed to fit the advanced yield criterion denoted as BBC2005.

A method, denoted as Method II, was suggested. The method combines strengths of the polycrystalline plasticity approach and the phenomenological approach. Method II

combines the data obtained from the CTF model, experimental work, and Backofen [197] description for the balanced biaxial strain ratio.

In this suggested method, the same experimental data presented to derive fully the BBC2005 yield function with mechanical testing that is referred to as Method I were used, except for the following quantities:

● Uniaxial yield stress perpendicular to the rolling direction (YS90) were predicted from

the newly proposed model known as CTF.

● Biaxial yield stress Yb was extracted from the CTF model.

● The R-value in the transverse direction R90 was estimated using the Backofen

equation [197], which is (Rb=R0/R90) (i.e. the R90 was a function of the R0 obtained

experimentally from uniaxial tensile tests performed in the rolling direction and Rb

obtained experimentally from the compression test).

To summarise (see Table 10.1), the eight mechanical inputs required to define fully the BBC2005 were determined either experimentally (Method I) or using the combined procedure, denoted as Method II.

Table 10.1. Method I vs. Method II. 0 YS [MPa] 45 YS [MPa] 90 YS [MPa] b YS [MP] 0 R [-] 45 R [-] 90 R [-] b R [-]

Method I Tensile Tensile Tensile Bulge Tensile Tensile Tensile Compression Method II Tensile Tensile CTF CTF Tensile Tensile Backofen Compression

It was observed that the new suggested method (Method II: BBC2005 fitted with CTF), for both of the considered aluminium alloys, performed better than the other yielding descriptions.

It was seen that the R90 value using the Backofen equation deviated by -3% and +6% for

AC600 and AA6111-T4. However, the effect of such discrepancy on the shape of the yield loci and the calculated normal plastic anisotropyR of the two materials was negligible.

The BBC20005 when fitted with the CTF model improved the yield function performance more specifically at the plane strain states in the rolling and transverse directions. Consequently, the uncertainties of yielding behaviour in the plane strain states were minimised when the new suggested model (Method II) was used. The new procedure gave almost identical yield locus as the one identified fully with experimental work.

To conclude, the practical use of texture-based yield loci can be summarised as

● Currently stamping simulation cannot accept texture-based yield loci.

● For a 6xxx material, the following steps will enable its use in stamping simulation:

• Carry out texture measurement using X-ray machine.

• Obtain texture-based yield locus derived by the full-constraint Taylor model (TF).

• Scale the TF model following the scheme described in chapter 4 in section 4.11.

• Extract the biaxial yield stress YSb and uniaxial yield stress in the transverse

direction YS90.

• Carry out two tensile tests in the (0º,45º).

• Estimate the R-value in the transverse direction R90 using the Backofen equation

[197], which is a function of the R0 obtained experimentally from uniaxial tensile

tests performed in the rolling direction and Rb obtained experimentally from the

compression test.

• Input to simulation.

● Therefore, to enable current simulation to accept texture-based yield locus, a hybrid solution (Method II) is suggested.

The key intrinsic features of this hybrid method that are looked for at the proposing phase are

● Good accuracy

● Simplicity

● Efficiency