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. 2021 Aug 2;14(15):4321. doi: 10.3390/ma14154321
a void diameter
a0 initial void diameter
b Burgers vector
f void volume fraction
f˙ the rate of increase in the total fraction of voids
f* actual void volume fraction
f0 initial void volume fraction (for unstrained material)
fc critical void volume fraction at the onset of coalescence initiation
f˙coalescence the rate of increase in the fraction of voids resulting from their rapid joining under shear stresses
fF void volume fraction at failure
f˙growth the rate of increasing the fraction of existing voids
f˙nucl the rate of increase in nucleated voids’ volume fraction
h anisotropy coefficient
k multiplier in power hardening law
km coefficient depending on the particle shape
ks coefficient depending on the shape (aspect ratio) of the particle and its orientation in relation to the loading direction
maxσ1pδβ maximum value of principal stress in the particle
maxσηηδ=β maximum value of the stress normal to the phases contact surface
n exponent in power hardening law
q stress concentration factor, correction factor in GTN model
q1, q3 Tvergaard coefficients
r polar coordinate measured from the “head” of dislocation pile-up
r1 characteristic length
sN standard deviation
C coefficient expressing the ratio of the void elongation to the specimen elongation rate (on a macroscopic scale) in Brown and Embury model, C1,2
E Young’s modulus of the matrix
Ep matrix plastic equivalent modulus of elasticity
L Lode parameter
R particle radius
R˙ void radius growth rate
R0 initial particle radius
Ractual actual particle radius
S remote normal stress
Vmaterial total volume of material
Vvoids volume of voids and second phase particles
W void aspect ratio
α coefficient in Brown–Embury model, coefficient depending on matrix hardening exponent in Thomason model
β radial coordinate of particle surface in Thomason model
γ surface energy
δ generalized radial coordinate in Thomason model
ε strain
ε˙ strain rate
εcrit critical strain of particle–matrix separation
ε˙e increase in effective plastic strain
εN void nucleation strain
εp plastic strain
εz longitudinal strain of the cylinder in McClintock model
η stress state triaxiality ratio
θ Lode angle
κI stress concentration factor at the interface of phases
κp coefficient of normal stress concentration inside the particle
λ coefficient in Beremin nucleation model, depending on particle shape
μ shear modulus
μ* coefficient depending on the elastic parameters of particle, matrix, and the geometric characteristics of particle
σ stress
σ0 yield stress
σ1, σ2, σ3 principal stresses
σ1max maximum value of global tensile principal stress
σ˙1max rate of the maximum global principal stress increase
σcrit critical stress, dependent on the nucleation mechanism, matrix, particle, and the interface strength
σcritinterface critical stress at the phase interface
σcritmean mean value of void nucleation stress
σcritparticle theoretical strength of the particle material
σe von Mises equivalent stress
σ˙e rate of von Mises equivalent stress increase
σh Hill’s equivalent stress
σlocr maximum local normal stress at the “head” of dislocation pile-up
σm mean stress (hydrostatic pressure)
σn critical normal stress in Thomason model
τ0 yield stress at pure shear
χ ratio of void length to the distance between neighboring voids
eq equivalent plastic strain
Ø damage function of the particle–matrix interface
νp equivalent Poisson coefficient