The results of the ABAQUS/Standard simulations are discussed first, beginning with the results for the viscoplastic fully dense material. The results of the slow upsetting are illustrated in Figure 1.3.16–2 to Figure 1.3.16–4. The results for the fast upsetting coupled temperature-displacement analysis are illustrated in Figure 1.3.16–5 to Figure 1.3.16–7; those for the adiabatic static stress analysis are shown in Figure 1.3.16–8 and Figure 1.3.16–9. Figure 1.3.16–2 and Figure 1.3.16–5 show the configuration that is predicted at 60% upsetting. The configuration for the adiabatic analysis is not shown since it is almost identical to the fast upsetting coupled case. Both the slow and the fast upsetting cases show the folding of the top outside surface of the billet onto the die, as well as the severe straining of the middle of the specimen. The second figure in each series (Figure 1.3.16–3 for the slow case, Figure 1.3.16–6 for the fast case, and Figure 1.3.16–8 for the adiabatic case) shows the equivalent plastic strain in the billet. Peak strains of around 180% occur in the center of the specimen. The third figure in each series (Figure 1.3.16–4 for the slow case, Figure 1.3.16–7 for the fast case, and Figure 1.3.16–9 for the adiabatic case) shows the temperature distributions, which are noticeably different between the slow and fast upsetting cases. In the slow case there is time for the heat to diffuse (the 60% upsetting takes place in 100 sec, on a specimen where a typical length is 10 mm), so the temperature distribution at 100 sec is quite uniform, varying only between 180°C and 185°C through the billet. In contrast, the fast upsetting occurs too quickly for the heat to diffuse. In this case the middle of the top surface of the specimen remains at 0°C at the end of the event, while the center of the specimen heats up to almost 600°C. There is no significant difference in temperatures between the fast coupled case and the adiabatic case. In the outer top section of the billet there are differences that are a result of the severe distortion of the elements in that region and the lack of dissipation of generated heat. The temperature in the rest of the billet compares well. This example illustrates the advantage of an adiabatic analysis, since a good representation of the results is obtained in about 60% of the computer time required for the fully coupled analysis.

The results of the slow and fast upsetting of the billet modeled with the porous metal plasticity model are shown in Figure 1.3.16–10 to Figure 1.3.16–15. The deformed configuration is identical to that of Figure 1.3.16–2 and Figure 1.3.16–5. The extent of growth/closure of the voids in the specimen at the end of the analysis is shown in Figure 1.3.16–10 and Figure 1.3.16–13. The porous material is almost fully compacted near the center of the billet because of the compressive nature of the stress field in that region; on the other hand, the corner element is folded up and stretched out near the outer top portion of the billet, increasing the void volume fraction to almost 0.1 (or 10%) and indicating that tearing of the material is likely. The equivalent plastic strain is shown in Figure 1.3.16–11 (slow upsetting) and Figure 1.3.16–14 (fast upsetting) for the porous material; Figure 1.3.16–12 and Figure 1.3.16–15 show the temperature distribution for the slow and the fast upsetting of the porous metal. The porous metal needs less external work to achieve the same deformation compared to a fully dense metal. Consequently, there is less plastic work being dissipated as heat; hence, the temperature increase is not as much as that of fully dense metal. This effect is more pronounced in the fast upsetting problem, where the specimen heats up to only 510°C, compared to about 600°C for fully dense metal.

Figure 1.3.16–16 to Figure 1.3.16–18 show predictions of total upsetting force versus displacement of the die. In Figure 1.3.16–16 the slow upsetting viscoplastic and porous plasticity results are compared with several elastic-plastic and rigid-plastic results that were collected by Lippmann (1979) and slow viscoplastic results obtained by Taylor (1981). There is general agreement between all the rate-independent results, and these correspond to the slow viscoplastic results of the present example and of those found by Taylor (1981). In Figure 1.3.16–17 rate dependence of the yield stress is investigated. The fast viscoplastic and porous plasticity results show significantly higher force values throughout the event than the slow results. This effect can be estimated easily. A nominal strain rate of 6 sec is maintained throughout the event. With the viscoplastic model that is used, this effect increases the yield stress by 68%. This factor is very close to the load amplification factor that appears in Figure 1.3.16–17. Figure 1.3.16–18 shows that the force versus displacement prediction of the fast viscoplastic adiabatic analysis agrees well with the fully coupled results.

Two cases using an element-based rigid surface to model the die are also considered in ABAQUS/Standard. To define the element-based rigid surface, the elements are assigned to rigid bodies using the *RIGID BODY, ISOTHERMAL=YES option. The results agree very well with the case when the analytical rigid surface is used.

The automatic load incrementation results suggest that overall nominal strain increments of about 2% per increment were obtained, which is slightly better than what was anticipated in the initial time increment suggestion. These values are typical for problems of this class and are useful guidelines for estimating the computational effort required for such cases.

The results obtained with ABAQUS/Explicit compare well with those obtained with ABAQUS/Standard, as illustrated in Figure 1.3.16–19, which compares the results obtained with ABAQUS/Explicit (without adaptive meshing) for the total upsetting force versus the displacement of the die against the same results obtained with ABAQUS/Standard. The agreement between the two solutions is excellent. Similar agreement is obtained with the results obtained from the ABAQUS/Explicit simulation using adaptive meshing. The mesh distortion is significantly reduced in this case, as illustrated in Figure 1.3.16–20.