Crystal plasticity phase transformation model for metastable austenitic stainless steel Satyapriya Gupta, Anxin Ma, Alexander Hartmaier

Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum

Metastable austenitic stainless steel Austenitic stainless steels are known as potential steels for automotive application because of their excellent mechanical properties. Transformation Induced Plasticity (TRIP) has a large contribution in providing high strength with high ductility to these steels. Metastable austenite (a softer phase) transforms into martensite (hard phase) during the deformation of the steel. This enhances the strain hardening behaviour and postpones the necking phenomenon. We have proposed a precise micromechanical model to describe the mechanical behaviour of this steel which can also be extended for TRIP steels in future.

Modeling challenges and salient features of model To predict the evolution of phase transformation and it’s influence on deformation behaviour of steel.

Effects of grain boundaries on deformation and phase transformation (considering non-local effects (see Fig.1(b)) provided by GNDs)

Total transformation is separated into strain induced nucleation and stress assisted growth of martensite.

Orientation dependent nucleation and growth has been achieved (see Fig.1(a))

Hardening provided by GNDs at the Grain Boundary

Orientation dependent evolution of transformed martensite

Fig 1(a) Fig 1(b)

Phase transformation and crystal plasticity The contribution of phase transformation to the total deformation in addition to slip based plastic deformation is formulated as [1]

∑=

=TN

1III

tr NηL

Plastic deformation

∑=

=SN

1ααα

p MγL

ααα nmM ⊗= III dbN ⊗=

stressI

strainII ηηη +=

III IUR −=

Phase transformation

)τ(signτ

γγm

c0 αα

αα τ=

pe FtrFFF =

Rate of strain induced nucleation is a function of probability ( ) with which intersection of fault bands can act as martensitic nuclei (Olson and Cohen approach [2])

strainI

N

1βIβnuc

strainI ζP)η(1Cη

T

∑−==

Rate of stress assisted growth depends on driving force available for transformation and amount of nuclei provided by strain induced transformation.

)F,,G,(f eIstressI σ∆η=ζ∑ ζη−η+η=η

=ββ

TN

1

stressI

strainI

0Igro

stressI )1)((C Where

Transformed martensite lamella hinders the dislocation motion and provides hardening which is added in flow rule (1st Augmentation of flow rule )

totalhrdMart C µη=τα)sign(ττττγγ α

m

αMart

αc

α

0α

+= Where

Addition of non-locality and validation of non-local model

IP

Non local effects are captured by taking GNDs (geometrically necessary dislocations) into consideration

Addition of two non-local terms in flow rule

Slip resistance (Isotropic hardening by GNDs )

Back stress (Kinematic hardening by GNDs )

2nd Augmentation of flow rule

)αGNDk

α(

m

αMart

αGNDi

αc

αGNDk

α

0α ττsign

τ̂τ̂τ̂ττγγ +

++

+=

evolves with the first gradient of plastic strain

evolves with plastic strain

evolves with the second gradient of plastic strain

β=β

αβ ρχµ=τ ∑9

11

αGNDi bC

mnα

klij, PmnijklαGNDk M)F(τ A=

Super GND pileups

Indentation size effect captured via non-local crystal plasticity model

Fig 2(a) Regular increase in hardness with decreasing indenter radius (R)

Bending size effect captured via non-local crystal plasticity model

Fig 2(b) Regular increase in normalized bending moment with decreasing thickness of sheet.

Super GND ijp )F( ∇×−=Λ ij

αGNDiτ̂

αcτ̂

αGNDkτ

[3]

Effect of non-locality on phase transformation (grain boundary effect)

Mises stress [MPa]

Transformed Volume fraction

Von Mises stress state after 20 % tensile deformation Higher stresses at the grain boundary due to non-local effects provided by GNDs.

Local TRIP Non-Local TRIP

Transformed volume fraction of martensite after 20 % tensile deformation Non-locality has affected the transformation kinetics. Not only misorientation but grain boundary elevation also plays an important role.

Fig 5(a) Enhanced strain hardening and transformation with addition of non-locality

References [1] Ma A., Hartmaier A., International Journal of plasticity (under Review) [2] Olson G., Cohen M., J. Less-Common Metals 1972 [3] Ma A., Hartmaier A., 2013, Philosophical Magazine. [4] Engels P.S., Begau C., Gupta S., Schmaling B., Ma A., Hartmaier A., Multiscale Modeling of Nanoindentation: Springer book chapter 2014

Fig 5(b) Increase in stress assisted growth with addition of non-locality

Tensile test of polycrystal with non-local TRIP model

Fig. 3(a) Mises stress state after 40 % tensile deformation

Fig. 3(b) Total transformed volume fraction after 40 % tensile deformation

Stress state depends on the volume fraction of transformed martensite.

Transformation behaviour highly depends on the orientation of the crystal.

Enhanced strain hardening behaviour after the formation of certain amount of martensite. Strain induced nuclei start to form nearly at 18 % strain and growth of these nuclei takes place via stress assisted transformation.

Fig 4(a) Evolution of total transformed vol fraction of martensite with tensile deformation

Fig 4(b) Evolution of stress assisted and strain induced martensitic transformation with deformation

Application of TRIP model to metastable austenitic stainless steel

[4]

stressIζ