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void diameter |
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initial void diameter |
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Burgers vector |
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void volume fraction |
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the rate of increase in the total fraction of voids |
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actual void volume fraction |
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initial void volume fraction (for unstrained material) |
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critical void volume fraction at the onset of coalescence initiation |
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the rate of increase in the fraction of voids resulting from their rapid joining under shear stresses |
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void volume fraction at failure |
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the rate of increasing the fraction of existing voids |
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the rate of increase in nucleated voids’ volume fraction |
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anisotropy coefficient |
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multiplier in power hardening law |
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coefficient depending on the particle shape |
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coefficient depending on the shape (aspect ratio) of the particle and its orientation in relation to the loading direction |
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maximum value of principal stress in the particle |
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maximum value of the stress normal to the phases contact surface |
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exponent in power hardening law |
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stress concentration factor, correction factor in GTN model |
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Tvergaard coefficients |
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polar coordinate measured from the “head” of dislocation pile-up |
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characteristic length |
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standard deviation |
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coefficient expressing the ratio of the void elongation to the specimen elongation rate (on a macroscopic scale) in Brown and Embury model,
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Young’s modulus of the matrix |
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matrix plastic equivalent modulus of elasticity |
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Lode parameter |
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particle radius |
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void radius growth rate |
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initial particle radius |
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actual particle radius |
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remote normal stress |
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total volume of material |
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|
volume of voids and second phase particles |
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void aspect ratio |
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coefficient in Brown–Embury model, coefficient depending on matrix hardening exponent in Thomason model |
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radial coordinate of particle surface in Thomason model |
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surface energy |
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generalized radial coordinate in Thomason model |
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strain |
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strain rate |
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critical strain of particle–matrix separation |
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increase in effective plastic strain |
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void nucleation strain |
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plastic strain |
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longitudinal strain of the cylinder in McClintock model |
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stress state triaxiality ratio |
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Lode angle |
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stress concentration factor at the interface of phases |
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coefficient of normal stress concentration inside the particle |
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coefficient in Beremin nucleation model, depending on particle shape |
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shear modulus |
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coefficient depending on the elastic parameters of particle, matrix, and the geometric characteristics of particle |
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stress |
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yield stress |
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principal stresses |
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maximum value of global tensile principal stress |
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rate of the maximum global principal stress increase |
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critical stress, dependent on the nucleation mechanism, matrix, particle, and the interface strength |
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|
critical stress at the phase interface |
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mean value of void nucleation stress |
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theoretical strength of the particle material |
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von Mises equivalent stress |
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rate of von Mises equivalent stress increase |
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Hill’s equivalent stress |
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maximum local normal stress at the “head” of dislocation pile-up |
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mean stress (hydrostatic pressure) |
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critical normal stress in Thomason model |
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yield stress at pure shear |
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ratio of void length to the distance between neighboring voids |
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|
equivalent plastic strain |
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damage function of the particle–matrix interface |
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equivalent Poisson coefficient |