Metallic moulds
3.8 Mechanical property determination
3.8.3 High temperature compression test procedure
Hot compression tests were carried out using the dynamic 100 kN capacity UTM. A split-type resistance heated furnace was fabricated and attached to the UTM to maintain the test specimen at a constant test temperature. Machined and heat treated H-13 die steel compression platen was fabricated and used for the test. The platens were water jacketed to prevent transfer of heat to the UTM actuators and load cell. The compression testing set-up showing the split type furnace is shown in Figure 3.4.
The cast cylindrical samples were machined to 12 mm diameter and 200 mm length.
The machined sample rods were then homogenized at 510 oC for 10 h and subsequently furnace cooled. Cylindrical compression specimen having dimensions of 10 mm diameter and 15 mm height as shown in Figure 3.5, were machined. Concentric grooves of 0.5 mm depth were machined on the top and bottom parallel surfaces of the specimens to retain the solid lubricant to minimize the friction at the sample-platen interface during the test. MoS2
paste was used as lubricant. A hole of 1 mm diameter was drilled at the mid height region of the samples for introducing the thermocouple to measure the sample temperature during the compression test.
Hot compression tests were carried out using the same UTM as mentioned in earlier section (cf. section 3.8.2). The compression platens attached to the UTM was held inside
the furnace. The specimen was placed between the platens. The sample temperature was raised at a rate of 5 oC/s to the required test temperatures. After attaining the test temperature, the sample temperature was maintained with an accuracy of ±3 oC for 15 min to ensure homogeneous temperature throughout the entire sample volume prior to the compression test. Compression tests were carried out at constant true strain rates.
Fig.3.4. The high temperature compression testing set-up
The cross head velocity of the UTM actuator was varied such that a constant true strain rate was maintained during the entire duration of the test using the relation [GEOR1988]:
) ( exp t v ε L
oε
•
•
=
(3.6)where v is the cross head velocity, ε
•
is the strain rate, Lo is the initial specimen length, and t is the time elapsed. The actuator displacement at any instant of time was controlled by the closed loop servo-hydraulic control of the UTM. MAXTM software was used for controlling the actuator movement. A computer code was used to carry out the test at constant true strain rates, (ε
•). The deformation temperatures (T) and strain rates (ε•) were in the ranges of 300 oC - 500 oC and 0.001 s-1 - 1.0 s-1, respectively. Table 3.4 shows the ε
• and T at which
experiments were performed. The compression tests were carried out up to a true strain (ε) of 0.6. The load vs. displacement plots for all the tests were recorded and true stress (σ) vs.
true strain (ε) plots were obtained.
All dimensions are in mm
Fig.3.5. The geometry of a hot compression test sample Table 3.4. Strain rates and temperatures of the compression tests
ε
• (s-1) T (oC)
0.001, 0.01, 0.1, and 1.0 300, 350, 400, 450 and 500
The following analyses were carried out on the compression test data obtained:
a) The peak flow stresses (σp) for each combination of ε• and T were obtained from the flow curves of the alloys. The constitutive analysis (cf. section 2.5.1 and section 4.5.2) was carried out for all the alloys. The activation energy of deformation (Q), Zener-Hollomon parameter (Z) and other parameters of the constitutive model were determined and the effect of Sn addition on these parameters was investigated.
b) Multiple linear regression analysis was carried out to obtain an algebraic relationship for prediction of σ as a function of ε, ε• and T (cf. section 2.5.4 and section 4.6).
c) The flow stress of all alloys was predicted by artificial neural network (ANN) modeling. The ANN modeling was carried out by the multiple layer perception (MLP) feed forward back propagation network. The input layer consisting of three neurons (ε•, ε, and T) and the flow stress, σ, in the output layer formed the data sets for training the network. The ‘Neural Network’ tool box available with the MATLAB (Release 7) software package was used for the present modeling.
Training of the neural network was done using the ANN tool kit of MATLAB software, using ‘TRAINLM’ function. ‘TRAINLM’ is a network training function that updates weights and bias values in a back propagation algorithm according to Levenberg–Marquardt optimization. Levenberg–Marquardt algorithm is a highly efficient method for solving non-linear optimization problems [ROBI2003]. Single layer hidden neurons were used in the network architecture. The number of neurons in the hidden layer, the transfer functions at the input-to-hidden layer and hidden-to- output layer were optimized by trial and error method during the network training and testing stages. The mean square error (MSE) during the training and testing was determined for each trial. The network architecture was finally frozen based on the minimum MSE value obtained during both the training and testing stages. Out of the total 120 number of data sets, 48 and 36 data sets were used for respectively training and testing. 18 data sets from the remaining were used for evaluation using the trained network architecture. Once the proper network architecture was arrived at for an alloy, the flow stress (σ) could be successfully predicted for any combination of input parameters (ε, ε&, and T), within the specified domain range.
d) The flow stress values predicted by the ANN were used to generate the processing maps for all the alloys. The detailed procedure of generating the processing maps by DMM has been discussed in section 2.5.3. The relevant calculations were performed using MATLABTM software toolkit. The strain rate sensitivity factor m was evaluated using Eq. (2.25).
Flow stress (σ) value when determined at a particular ε• , the same can be generated at the neighboring regions of the ε• values as explained in Figure 3.6. Let e be the value of ε• , corresponding to which the value of σ can be obtained by ANN.
The σ values are also determined at b (0.5 × e) and h (1.5 × e) values of ε• , considering both the directions. These three points of ε• , i.e. b, e and h are again used individually to generate two σ values at both sides of each of the three points.
For example, from e, two more ε• points are generated, d and f, which are respectively (e – 0.2e) and (e + 0.2e). Similarly, the points a, c, g and i are taken as (b – 0.2b), (b + 0.2b), (h – 0.2h) and (h + 0.2h), respectively. Therefore, nine different points of ε• are presently obtained in total from the previous three points, as shown in Figure 3.6. σ values are determined at all these points, and the slopes of ln(σ) vs. ln(ε
•
) give the incremental values of m parameter. The temperature (T) term is then included, and the same iteration is followed at the increment of 5 ºC within the temperature range studied. The power dissipation efficiency and the instability parameters are calculated by Eq. (2.33) and Eq. (2.35), respectively. The modeling gives the contour values of m, power dissipation efficiency and the instability parameters at different deforming conditions, i.e. at different values of ε• and T.
Fig.3.6. Points generated from a single ε• value for calculation of σ values and m parameter
e) Microstructural observation of the samples was carried out after the compression tests in order to identify the irreversible changes induced in the microstructure as a result of deforming them to a true stain value of 0.6.
The results obtained using these experimental and computational procedure are presented in the following chapter and discussed in detail.