Abstract
The goal of this paper is to predict how the properties of the constituent phases and microstructure of a transformation induced plasticity steel influence its fracture resistance. The steel selected for study was a three-phase quenched and partitioned (QP) sheet steel comprised of 50% ferrite, 42% martensite and 8% retained austenite (RA) with \(\sim \) 980 MPa tensile strength. Experiments show that ductile fracture in the steel involves nucleation, growth, and coalescence of micron-scale voids. Accordingly, the failure process is modeled at the microstructure scale by idealizing the individual phases of the steel using elastic-viscoplastic constitutive relations that account for the loss of strength resulting from cavitation, as well as the effects of transformation of metastable RA to martensite. The flow behavior of the phases and the transformation kinetics of RA are calculated by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Srivastava in J Mech Phys Solids 78:46–69, 2015) while the damage parameters are determined by void cell model calculations. The microstructure-scale simulations are used to compute the fracture and instability loci for the steel, which are used to calibrate the GISSMO (Generalized Incremental Stress State Dependent Damage Model) (Andrade in Int J Fract 200:127–150, 2016). The microstructure-informed GISSMO model for QP980 is found to predict fracture strains within 18% of experimental measurements of ligament-type test specimens. Finally, a series of virtual steel microstructures are analyzed to determine the influence of the phase volume fractions on the fracture resistance of the steel. Two candidate microstructures are identified that exhibit increased engineering fracture strains (\(>57\)%) without significantly compromising (within 6%) the tensile strength when compared to the baseline QP980.
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Abbreviations
- \(A_{0}\) :
-
The initial area of the RVE face
- b :
-
Transient hardening constant
- \(c_{1}, \, c_{2}\) :
-
Phase transformation model parameters
- \(C_{ijkl}\) :
-
Elasticity component tensor
- D :
-
State variable in GISSMO model that characterizes the accumulated damage
- \(e_{11}\) :
-
Engineering strain in \(\varvec{e}_{\mathbf {1}}\) direction
- F:
-
State variable in GISSMO model that characterizes the initial material softening
- \(F_{s}\) :
-
The resultant force on an RVE face
- H :
-
Hardening rate
- \(l, \, l_{0}\) :
-
Length of the deformed and undeformed RVE along the \(\varvec{e}_{1}\) direction, respectively
- \(K_{tp}^{1}, \, K_{tp}^{2}, \, K_{tv}\) :
-
Phase transformation model parameters
- m :
-
Strain rate exponent in isotropic viscoplasticity model
- M :
-
Fading exponent in GISSMO model that governs the material strength degradation
- n :
-
Hardening exponent in isotropic viscoplasticity model
- N :
-
Damage exponent in GISSMO model
- Q :
-
Transient flow stress
- \(r_{x},{r}_{y},{r}_{z}\) :
-
The lengths of semi-axes of the deformed void in the x, y and z directions
- \(S_{ij}\) :
-
Components of deviatoric stress tensor
- \(T_{\sigma }\) :
-
Stress triaxiality
- \(T_{\sigma }^{local}\) :
-
Local stress triaxiality evaluated at single finite element in QP980 RVE
- \(T_{\sigma }^{avg}\) :
-
Strain averaged stress triaxiality
- \(V_{f}, \, V_{f}^{ini}\) :
-
Current and initial void volume fraction measured from deformed and undeformed RVE
- \(V_{f}^{n}, V_{f}^{cr}\) :
-
Normalized void volume fraction, critical normalized void volume fraction
- \(V_{void}, \, V_{cell}\) :
-
Volume of deformed void, volume of deformed cubic cell
- \(Z_{1}, \, Z_{2}\) :
-
Phase transformation model parameters
- \(\alpha (T_{\sigma }), \, \beta (T_{\sigma })\) :
-
Function that characterizes the void dilation behavior with respect to \(T_{\sigma }\), function that characterizes the void elongation behavior with respect to \(T_{\sigma }\)
- \(\epsilon _{M}\) :
-
Macroscopic plastic strain
- \(\dot{\epsilon }_{ij}\) :
-
Total strain rates
- \(\epsilon _{cri}\left( T_{\sigma } \right) \) :
-
Critical softening strain
- \(\epsilon _{f}\left( T_{\sigma } \right) \) :
-
Critical fracture strain
- \(\epsilon _{fail}\) :
-
Von-Mises strain at fracture initiation
- \(\dot{\epsilon }_{ij}^{e}\) :
-
Elastic strain rate
- \(\dot{\epsilon }_{ij}^{p}, \, \epsilon _{ij}^{p}, \, \epsilon _{0ij}^{p}\) :
-
Plastic strain rate, plastic strain, deviatoric plastic strain
- \(\dot{\epsilon }_{\mathrm {eff}}^{p}, \, \epsilon _{eff}^{p}\) :
-
Effective plastic strain rate, effective plastic strain
- \(\dot{\epsilon }_{ij}^{T}\) :
-
Martensitic transformation strain rate
- \(\lambda , \, \lambda _{cr}\) :
-
Void elongation ratio, critical void elongation ratio
- \(\sigma _{11}\) :
-
Engineering stress in \(\varvec{e}_{1}\) direction
- \(\sigma _{e}\) :
-
Von-Mises stress
- \(\dot{\sigma }_{ij}, \, \sigma _{ij}, \, \tilde{\sigma }\) :
-
Components of Cauchy stress rate and Cauchy stress and Cauchy stress for undamaged phase
- \(\sigma _{y}\) :
-
Initial yield stress
- \(\Sigma _{h}\) :
-
Macroscopic hydrostatic stress
- \(\Sigma _{m}\) :
-
Macroscopic Von-Mises stress
- \(\Sigma _{xx}, \, \Sigma _{yy}, \, \Sigma _{zz}\) :
-
Macroscopic principal stresses in the x, y and z directions
- \(\Gamma \) :
-
State variable in GISSMO model that characterizes the decay in load carrying capacity
- \(\dot{\Phi }\) :
-
Characteristic strain rate
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Li, Z., Kiran, R., Hu, J. et al. Analysis and design of a three-phase TRIP steel microstructure for enhanced fracture resistance. Int J Fract 221, 53–85 (2020). https://doi.org/10.1007/s10704-019-00405-6
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DOI: https://doi.org/10.1007/s10704-019-00405-6