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Numerical simulation of void growth in front of a blunting crack-tip in plastically compressible solids

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Abstract

Effect of plastic compressibility on void growth ahead of a moving crack-tip is investigated numerically for a mode I crack subjected to plane strain deformation with small-scale yielding. Exploration is made for quasi-static finite deformations of isotropic hardening elastic–viscoplastic solids. For comparison purpose, both plastically incompressible and plastically compressible solids are considered to study the crack-tip deformation, void growth and interaction between the crack-tip and a nearby void by examining the near tip distributions of plastic strain, hydrostatic stress, effective stress and stress triaxiality. The plastic compressibility is found to have strong effect on the crack-tip deformation and stress–strain fields in the ligament and void region. The shape of void growth in front of the crack-tip is significantly influenced by the plastic compressibility. The present results show that in the case of plastically compressible solids, the rate of void growth in the direction perpendicular to the crack plane is more than the corresponding in the direction parallel to the crack and this observation is in sharp contrast to the void growth behavior observed in plastically incompressible solids. The predictions of the crack-tip and void interaction in the presence of plastic compressibility may be very helpful in understanding the crack growth and void coalescence in some relatively newer materials having very high energy absorption capacity, highly desired electrical and thermal as well as radiation-resistant properties, properties of bioimplants, etc.

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Abbreviations

\(a_{1}\) and \(a_{2}\) :

Current vertical radius and horizontal diameter of the void, respectively

\(b\) :

Current crack opening

\(b_{0}\) :

Initial notch radius

CTOD:

Crack-tip opening displacement

HRR:

Hutchinson, Rice, Rosengren

\(d_{0}\) :

Center of the void from the notch center

d :

Rate of deformation tensor

\({\mathbf{d}}^{{\text{e}}}\) :

Elastic part of rate of deformation tensor

\({\mathbf{d}}^{{\text{p}}}\) :

Plastic part of rate of deformation tensor

E :

Young’s modulus

F :

Deformation gradient

\(g\) :

Hardness function

I :

Identity tensor

J :

Jacobian

\(J_{{{\text{app}}}}\) :

Applied J-integral

\(K_{{\text{I}}}\) :

Mode I stress intensity factor

\({\mathbf{L}}\) :

Elastic moduli tensor

m :

Strain rate sensitivity exponent

N :

Power law hardening exponent

\({\mathbf{p}}\) :

Deviatoric part of Kirchhoff stress tensor

\(R_{0}\) :

Outer radius of the semicircular geometry

\(\dot{u}_{1}\) and \(\dot{u}_{2}\) :

Rate of displacement in x and y directions, respectively

\(\alpha\) :

Plastic compressibility parameter

\({\varvec{\sigma}}\) :

Cauchy stress tensor

\({\varvec{\tau}}\) :

Kirchhoff stress

v :

Poisson’s ratio

\({\hat{\varvec{\uptau }}}\) :

Jaumann rate of Kirchhoff stress

\(\varepsilon_{{\text{p}}}\) :

Plastic strain

\(\dot{\varepsilon }_{{\text{p}}}\) :

Plastic strain rate

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

Reference strain rate

\(\varepsilon_{0}\) :

Yield strain

\(\sigma_{{\text{e}}}\) :

Effective stress

\(\sigma_{{\text{h}}}\) :

Hydrostatic stress

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology (BHU) Varanasi, Varanasi, 221005, India

    Prakhar Bandil, Debashis Khan, Pakshal Shah, Shivansh Kaul & Rahul Goswami

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  1. Prakhar Bandil
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  2. Debashis Khan
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  3. Pakshal Shah
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  4. Shivansh Kaul
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  5. Rahul Goswami
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Correspondence to Debashis Khan.

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Technical Editor: João Marciano Laredo dos Reis.

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Bandil, P., Khan, D., Shah, P. et al. Numerical simulation of void growth in front of a blunting crack-tip in plastically compressible solids. J Braz. Soc. Mech. Sci. Eng. 43, 152 (2021). https://doi.org/10.1007/s40430-021-02855-3

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