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Determination of Parameters for Johnson-Cook Dynamic Constitutive and Damage Models for E250 Structural Steel and Experimental Validations

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Abstract

Structural steel (E250 grade) is used in several engineering applications involving loadings from quasi-static to high strain rates (blast discs, explosion vents, etc.), which introduce large deformation, strain and strain rate hardening, thermal softening, and damage to the material. The material’s dynamic constitutive behaviour can be aptly modelled by a visco-plasticity-based Johnson–Cook (J–C) strength model and damage initiation and complete failure by the J–C’s damage model. In the latter, damage initiation is modelled through continuum damage mechanics and propagation by the fracture mechanics. This paper focuses on the determination of 10 different J–C’s dynamic constitutive and damage model parameters for E250 structural steel by conducting several experiments involving tensile tests at different strain rates (0.0003–1.0 s-1), stress triaxialities (0.33–0.95), temperatures (30–800 °C), and SHPB experiments (at 3000 and 8000 s-1). It explains the processes and step-by-step procedures for extracting the model parameters from the experimental results. A different approach is followed in arriving at fracture strain for extracting damage model parameters to suit fracture mechanic-based damage evolution available in the existing FEA codes. The constitutive and damage model parameters thus determined are validated through numerical simulations and comparison with three independent experiments viz. i) experiment of a plain tensile specimen, ii) tensile experiment of a notched specimen, and iii) hydrostatic burst experiment of a flat burst disc. The responses and failure patterns from numerical simulations agreed very well in all three experiments, thereby validating the determined model parameters. The determined model parameters can be utilised directly in the commercially available nonlinear explicit FEA codes.

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Data Availability

All the data required to reproduce these findings are provided in the manuscript as graphs instead of raw data. This is also used as part of an ongoing study by the authors.

Abbreviations

A :

J–C parameter representing yield stress (MPa)

A s :

Cross-sectional area of SHPB specimen (mm2)

A t :

Cross-sectional area of the incident and transmitter bars (mm2)

A 0 :

Initial cross-sectional area of the tensile specimen (mm2)

A f :

Cross-sectional area of the tensile specimen after the experiment (mm2)

B :

Strain hardening coefficient (MPa)

C :

Strain rate coefficient

c 0 :

Fundamental longitudinal velocity of the elastic stress wave (m/s)

D i :

Damage initiation variable

D :

Damage propagation variable

D 1 , D 2 , D 3 :

Stress triaxiality dependent fracture strain parameters

D 4 :

Strain rate dependent fracture strain parameter

D 5 :

Temperature dependent fracture strain parameter

E :

Young’s modulus (MPa)

G f :

Fracture energy (N/mm)

L s :

The thickness of the specimen in the SHPB experiment (mm)

m :

Thermal softening exponent

n :

Strain hardening exponent

P :

Equivalent force in the incident and transmitted bar (N)

P 1, P 2 :

Forces on the left and right end of the specimen in SHPB experiment (N)

\(\dot{P}\) :

Incident pressure loading rate in burst experiment (MPa/s)

P b :

Burst pressure (MPa)

T :

Temperature in material (°C)

\({T}^{*}\) :

Homologous temperature (°C)

\({T}_{0}\) :

Reference temperature (°C)

\({T}_{\mathrm{m}}\) :

Melting temperature of the material (°C)

t :

Time interval for the stress wave propagation through an element (s)

t d :

Natural time period (s)

u 1, u 2 :

Displacements at the left and right end of the specimen in the SHPB experiment

\({u}^{\mathrm{pl}}\) :

Plastic displacement

\({u}_{\mathrm{f}}^{\mathrm{pl}}\) :

Plastic displacement at failure

w l :

Crack tip opening displacement (mm)

x, y :

Horizontal and vertical coordinate axes, respectively

σ :

True stress/von-Mises tensile flow stress (MPa)

\({\sigma }_{\mathrm{m}}\) :

Average of the three normal stresses, i.e. mean stress (MPa)

\(\tilde{\sigma }\) :

Von-Mises equivalent stress (MPa)

σ * :

Dimensionless pressure, i.e. stress ratio or stress triaxiality

\({\sigma }_{0}\) :

Stress at the onset of damage (MPa)

\({\sigma }_{\mathrm{t}}\) :

Tensile strength of the material (MPa)

\({\sigma }_{\mathrm{y}}\) :

Dynamic yield stress (MPa)

\({\sigma }_{\mathrm{D}}\) :

Stress at damaged state (MPa)

\(\varepsilon\) :

True strain/plastic strain

\({\varepsilon }_{0}\) :

Equivalent plastic strain at the onset of damage

\(\dot{\varepsilon }\) :

Strain rate (s−1)

\({\dot{\varepsilon }}_{0}\) :

Reference strain rate (s−1)

\({\dot{\varepsilon }}^{*}\) :

Dimensionless normalised plastic strain rate

\({\dot{\varepsilon }}_{\mathrm{s}}\) :

Strain rate in SHPB specimen (s−1)

\({\varepsilon }_{\mathrm{f}}\) :

Fracture strain

\({\varepsilon }_{\mathrm{i}}\) :

Incident strain pulse

\({\varepsilon }_{\mathrm{r}}\) :

Reflected strain pulse

\({\varepsilon }_{\mathrm{s}}\) :

Strain in SHPB specimen

\({\varepsilon }_{\mathrm{t}}\) :

Transmitted strain pulse

\(\Delta \varepsilon\) :

Incremental plastic strain

\({\omega }_{\mathrm{n}}\) :

Fundamental natural frequency (Hz)

ρ :

Density of the material (kg/m3)

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Acknowledgments

The authors thank the support provided by Mr. Swati Kiran, Research Scholar at IIT Hyderabad and engineers at our Laboratory in conducting various experiments.

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Authors and Affiliations

  1. Systems Integration (Mechanical), Research Centre Imarat, Hyderabad, 500069, India

    K. Gopinath & V. Narayanamurthy

  2. Mechanical Engineering, BITS Pilani-Hyderabad, Hyderabad, 500078, India

    K. Gopinath & Y. V. D. Rao

  3. Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Sanga reddy, 502285, India

    S. N. Khaderi

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  1. K. Gopinath
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Correspondence to V. Narayanamurthy.

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Gopinath, K., Narayanamurthy, V., Khaderi, S.N. et al. Determination of Parameters for Johnson-Cook Dynamic Constitutive and Damage Models for E250 Structural Steel and Experimental Validations. J. of Materi Eng and Perform (2023). https://doi.org/10.1007/s11665-023-08733-4

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