PHS Simulation

Press Hardened Steels

Forming simulation of cold forming processes has matured to the point where most commercial simulation software packages easily predict global formability concerns such as necking failures. The strain distribution and final mechanical properties in the formed part come from details such as the hardening curve, yield surface, and constitutive laws, along with assumptions of tribology through the coefficient of friction.

In contrast, simulation of hot forming is substantially more complex due to the interactions of mechanical properties with temperature and microstructure.  These are all interrelated, and are summarized in Figure 1. In most processes, tools are drilled with cooling channels for heat extraction. In some simulation software the heat transfer to the coolant medium may also be calculated. ^B-14

Figure 1: Physics involved and their interrelations (re-created after B-14).

In 2000’s metal forming simulation software was lacking the capacity to couple the multi-physics shown in Figure 1. General purpose Finite Element Analysis (FEA) software was able to run coupled thermo-mechanical processes. However, one study in 2007 found that hot forming of a blank of 420 x 170 mm, 1.75 mm thickness took 10 hours to complete.^T-53  Figure 2 shows a study from 2008, where a forming simulation software was used to run : (a) isothermal simulation, no thermal calculations, considering uniform temperature distribution, and (b) non-isothermal simulation. When temperature effects were not considered, thinning was estimated to be 14%. The non-isothermal simulation however showed a maximum thinning of almost 40%.^H-69

Figure 2: Some of the earliest hot stamping simulation results: (a) isothermal simulation, (b) non-isothermal simulation (re-created after H-69).

In terms of the material characterization, mechanical properties as determined in a tensile test are temperature dependent. Further influencing the stress-strain response is the strain rate at which the deformation occurs (Figure 3). For hot stamping purposes, it is also important to note that these tensile tests are done after austenitizing followed by soaking then slowly cooling to test temperature. In other words, the test at 700°C is not just heating to 700°C, but heating to over 900°C, soaking there, slowly cooling to 700°C and then testing at 700°C.^B-14

Figure 3: Flow stress curves at various temperatures and strain rate levels (re-created after B-14).

Material properties such as the Elastic Modulus and Poisson’s ratio also change with temperature, along with heat conductivity and specific heat. These parameters are summarized in Table I using data from Citation S-93.

  
 
Several research groups tried to implement forming limit curves, tested at different temperatures.^S-92 However, the effects of strain rate and cooling rate are mostly missing in these curves. The necking initiation can also be predicted by strain rate changes in neighboring elements. Figure 4 shows both approaches.^B-84

Figure 4: Necking prediction in hot stamping simulations: (a) temperature dependent forming limit curve^S-92, (b) onset of necking by strain rate in high strain element (re-created after B-84).

Temperature distribution on the part has critical importance on the thinning distribution and necking initiation. The blank loses temperature to the tool via a thermal contact conductance (TCC, typically shown by h_c). New generation software can use a TCC to be a function of gap and pressure, as shown in Figure 5.^B-14

Figure 5: Thermal contact conductance (TCC) as a function of both gap an pressure (re-created after B-14).

The spacing, diameter, and distance from the surface of these channels all influence the heat transfer capabilities of the tool design. The tool material as well as the flow and heat transfer characteristics of the cooling fluid also plays a significant role. The factors affecting heat extraction from the blank to the cooling fluid are summarized in Figure 6.  Many hot stamped parts achieve tailored properties across the part, through either using tailor welded/rolled/patch blanks or undergo differential heating or cooling to produce soft zones. Accurate simulation predictions require capturing the forming and cooling differences of these approaches. Further improvements occur when simulations incorporate how temperature influences the changes which occur to tool deformation and tooling thermal expansion.

Figure 6: Different modes of heat transfer for extracting the heat from blank to the cooling fluid (re-created after B-14).

Key to heat extraction is good contact between the sheet steel and the tool surfaces. However, this is challenging to achieve with vertical or near-vertical walls. These areas may be severely deformed and thinned. Thus, these areas are at risk of not achieving the desired microstructure and strength if the lack of tool contact prevents sufficient heat extraction. Locally, this also changes the residual stress distribution.

Incorporating all details related to the forming and cooling of press hardened steels requires the use of coupled thermo-mechanical-metallurgical finite element models which capture the deformation and phase transformations which occur throughout the the different stages of the process, as shown in Figure 7.

Figure 7: Stages of a hot stamping simulation and the physics involved in each stage (re-created after B-14)).

Improved accuracy occurs with additional refinement in the models, such as incorporating the effects of deformation occurring while the steel is still fully austenitic. Austenite grain boundaries are major nucleation sites for diffusional transformation to ferritic phases, and deformation increases dislocation density and reduces the grain size, promoting the conditions for at least some ferrite formation instead of martensite.

A 2014 study considered both conditions, where a grain refinement model included the effects of prior austenite deformation in the hot stamping simulation of a hat-shaped part.^B-57 Without considering austenitic deformation, sidewall hardness remains above 450 HV and therefore can be assumed to be fully martensitic (Figure 8a). Incorporating the influence of part deformation occurring while the steel is in the austenite region, the model shows a substantial strength reduction in the highly-deformed wall region (Figure 8b). The model projects hardness levels close to 200 HV on the surface layers where the deformation is more severe than the core layer of the part. In contrast, core layer hardness is projected to be slightly over 300 HV, as indicated in Figure 8c which shows the cross-sectional profile in the thickness direction. These hardness levels suggest that martensitic transformation has not fully occurred in this location along the sidewall, either at the surface or at the core.

Nonetheless, this phenomenon can be avoided by using proper die and process design capable of providing sufficiently rapid cooling rates.

Figure 8: Incorporating prior austenite grain size in simulation lowers predicted hardness in highly deformed areas. (re-created after B-57)

Thanks are given to Eren Billur, Ph.D., Billur MetalForm, who contributed this article.