# Metal forming and materials processing

Beside casting and machining, forming is one of the main processes for manufacturing of components from metallic materials. Forming processes include sheet metal forming as well as bulk metal forging. Metal forming generally involves significant plastic deformations, elevated temperatures, high deformation velocities and an increased risk for initiation of cracks in the material. These macroscopic process conditions are intimately connected to the microstructure evolution inside the material.

In Hallberg et al. (2007) and Hallberg et al. (2010), deep-drawing of stainless steel is used as application examples for constitutive models where martensitic phase transformation is considered, see the illustration below. As the martensite phase is much harder than the parent austenitic phase, the material properties may change dramatically in the presence of this kind of diffusionless - and thus rapid - phase transformation.

The influence of deformation rate and material pre-processing in metal forging is studied in Hallberg et al. 2009. Different behavior of a 100Cr6 steel, due to previous tempering or annealing, was studied in high strain rate axisymmetric compression, experimentally as well as through numerical simulations.

The illustration below is taken from Hallberg et al. 2009. Note the development of a "shear cross" (white lines) in the tempered - and much harder - material. This localized deformation is absent in the annealed specimen.

Another example of metal forming is rolling, for example discussed in Hallberg (2013). A conventional rolling process can be made asymmetric by different methods in order to increase the deformation imposed onto the sheet.

The asymmetry of the process can be induced by having different radii $r$ of the rolls, by different roller velocities, i.e. $\omega_{1}\ne\omega_{2}$ or by different friction/lubrication conditions at each side of the sheet. The asymmetry increases the shear deformation of the rolled sheet and hence the total amount of effective plastic deformation. This is utilized in severe plastic deformation (SPD) processes for production of very fine-grained metals.

# Martensitic phase transformation and fracture

As the relatively ductile austenite phase is transformed in to harder and more brittle martensite in the vicinity stress-concentrations, the material conditions change and also the conditions for crack formation and propagation. Fatigue fracture can be considerably influenced by this kind of diffusionless phase transformation due to the higher fracture strength of martensite, compared to that of austenite. In Hallberg et al. (2012) the influence of martensite formation on fracture behavior and crack tip conditions is investigated, as illustrated below.

# Continuum scale modeling of phase transformation

Taking a continuum-mechanical perspective, the isothermal model in Hallberg et al. (2007) introduces the volume fraction of martensite as an internal variable. Along with a transformation condition, dependent on the state of deformation and on temperature, this allows the evolution of the martensitic phase to be traced. The presence of a transformation condition allows establishment of a transformation potential surface, much like the yield condition and yield surface found in plasticity theory. The transformation surface is illustrated in deviatoric stress space and in the meridian plane below.

Depending on which one is active, the yield and transformation conditions determine the response of the material. The relative influence of austenite and martensite on mechanical material properties is considered through a homogenization procedure, based on the phase fractions.

The above isothermal model is further elaborated in Hallberg et. al (2010b), where full thermo-mechanical coupling is considered. These models are suitable for large-scale simulations of metal forming processes involving materials exposed to martensitic phase transformation. The application to sheet metal forming is illustrated below by images from simulations of a deep-drawing process.