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A criterion for dynamic ductile fracture initiation of tensile mode

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Abstract

Dynamic behavior of a material is essential in applications such as collision, explosion, ballistic impact, high-speed machining, and metal forming. As impact loadings, as well as accidental or malicious explosions, may impose high loading rates to engineering structures, estimating the dynamic response of a material accurately is crucial. Therefore, an analytical strain rate-dependent criterion on ductile fracture initiation is developed at the continuum scale by further developing the energy balance concept. The criterion is based on continuum modeling of energy release rates, and the critical state is reached when the rate of energy change of fractured and unfractured states becomes equal. The formulation introduces a material length scale and a material property that is a function of strain rate and temperature. The developed ductile fracture criterion is implemented into two example applications, an aluminum alloy and a titanium alloy, whose experimental data are obtained from the open literature. Fracture loci of these alloys at various strain rates and the critical energy release rates as a function of strain rate are determined. The results of the example applications agree well with the experimental results reported in the literature.

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Abbreviations

A :

Area of the fracture plane

\(A_{1}, A_{2}, A_{3}\) :

Material constants

\(c_\mathrm{{V}}\) :

Specific heat capacity at constant volume

\(\mathrm {C}_\mathrm{{I}}\) :

Specific surface energy density

du :

Plastic work increment per unit volume

dk :

Kinetic energy increment per unit volume

dw :

Mechanical work increment per unit volume (of the unfractured medium)

dW :

Mechanical work increment of the unfractured medium

d\(W^{*}\) :

Mechanical work increment of the fractured medium

d\(\varepsilon _{ij}\) :

Components of (plastic) strain increment tensor (of the unfractured medium)

d\(\varepsilon _\mathrm{{I}}, \hbox {d}\varepsilon _\mathrm{{II}}, \hbox {d}\varepsilon _\mathrm{{III}}\) :

Strain increments of the unfractured medium in principal directions

d\(\varepsilon _\mathrm{{I}}^{*}, \hbox {d}\varepsilon _\mathrm{{II}}^{*}, \hbox {d}\varepsilon _\mathrm{{III}}^{*}\) :

Strain increments of the fractured medium in principal directions

d\(\varepsilon _\mathrm{{eff}}\) :

Equivalent (plastic) strain increment

\(l_{\mathrm{{I}},0}\) :

Characteristic length (relevant to ductile fracture)

\(l_\mathrm{{I}}, l_\mathrm{{II}}, l_\mathrm{{III}}\) :

Current dimensions of the volume element

m, n :

Material constants

T :

Actual material temperature

\(T_\mathrm{{melt}}\) :

Melting temperature of the material

\(T_\mathrm{{room}}\) :

Room temperature

\(v_\mathrm{{I}}, v_\mathrm{{II}}, v_\mathrm{{III}}\) :

Components of velocity vector (in principal directions)

\(x_\mathrm{{I}}, x_\mathrm{{II}}, x_\mathrm{{IIII}}\) :

Principal directions

\(\beta \) :

Fraction of the plastic work contributing to temperature increase

\(\varepsilon _{ij}\) :

Components of true strain

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

Reference strain rate

\(\dot{\varepsilon _\mathrm{{I}}}, \dot{\varepsilon _\mathrm{{II}}}, \dot{\varepsilon _\mathrm{{III}}}\) :

True strain rates in principal directions

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

Equivalent (plastic) strain

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

Equivalent (plastic) strain at fracture

\(\lambda \) :

Nonnegative scalar factor

\(\rho \) :

Mass density of the material

\(\sigma _{ij}\) :

Components of true stress tensor

\(\sigma _\mathrm{{I}}, \sigma _\mathrm{{II}}, \sigma _\mathrm{{III}}\) :

Principal stresses of the unfractured medium

\(\sigma _\mathrm{{I}}^{*}, \sigma _\mathrm{{II}}^{*}, \sigma _\mathrm{{III}}^{*}\) :

Principal stresses of the fractured medium

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

Equivalent stress

\({\Gamma }_\mathrm{{I}}\) :

Critical effective energy release rate (of tensile mode fracture)

\({\Delta }T\) :

Increase in temperature

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Acknowledgements

The first author would like to thank Dr. Osman Darıcı for his kind help to obtain some articles.

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  1. İstanbul Teknik Üniversitesi Gemi İnşaatı ve Deniz Bilimleri Fakültesi, Maslak, İstanbul, 34469, Turkey

    Fuzuli Ağrı Akçay

  2. Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, G4 0LZ, UK

    Erkan Oterkus

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Akçay, F.A., Oterkus, E. A criterion for dynamic ductile fracture initiation of tensile mode. Continuum Mech. Thermodyn. 35, 1087–1101 (2023). https://doi.org/10.1007/s00161-021-00983-8

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  • DOI: https://doi.org/10.1007/s00161-021-00983-8

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