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Kachanov, L. M.

doi:10.1023/a:1018671022008

Cited by 316 publications

(44 citation statements)

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“…The increase in creep strain rate associated with the tertiary stage is not controlled by diffusive process of dislocation movement, but rather by damage. [23][24][25] Therefore, we will not consider tertiary creep in the SSTC model.…”

Section: Solid State Transformation Creep (Sstc) Modelmentioning

confidence: 99%

Primary and secondary creep in aluminum alloys as a solid state transformation

Fernández

Bruno

González-Doncel

2016

Journal of Applied Physics

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Despite the massive literature and the efforts devoted to understand the creep behavior of aluminum alloys, a full description of this phenomenon on the basis of microstructural parameters and experimental conditions is, at present, still missing. The analysis of creep is typically carried out in terms of the so-called steady or secondary creep regime. The present work offers an alternative view of the creep behavior based on the Orowan dislocation dynamics. Our approach considers primary and secondary creep together as solid state isothermal transformations, similar to recrystallization or precipitation phenomena. In this frame, it is shown that the Johnson-Mehl-AvramiKolmogorov equation, typically used to analyze these transformations, can also be employed to explain creep deformation. The description is fully compatible with present (empirical) models of steady state creep. We used creep curves of commercially pure Al and ingot AA6061 alloy at different temperatures and stresses to validate the proposed model. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4961524] I. CREEP OF METALSCreep of metals is a key topic for different industries such as energy, transport, or chemical. The creep behavior of pure metals and alloys has been extensively investigated in the past. This behavior is usually described through the accumulated plastic deformation e (t) as a function of time t under given conditions of applied stress, r, and temperature, T. Three regions are typically distinguished, namely, a primary creep region (where € eðtÞ < 0Þ; a secondary regime, also called steady state (where € eðtÞ ¼ 0); and a tertiary region (where € eðtÞ > 0) before creep rupture occurs (double dot denotes second time derivative). Many authors, as Evans, 1 reduce the steady state regime to a single turning point from the primary to the tertiary regions in the creep curve. This is, then, called the minimum creep rate state. For simplicity, however, we will refer throughout this work to a steady state region. Most of the investigations aimed at correlating the creep behavior with microstructural parameters of the alloy under study restrict their analysis to the steady state regime, where the creep rate is independent of time, i.e., one can write _ e ¼ _ e ss ðr; TÞ (dot denotes first time derivative).

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Section: Solid State Transformation Creep (Sstc) Modelmentioning

confidence: 99%

Primary and secondary creep in aluminum alloys as a solid state transformation

Fernández

Bruno

González-Doncel

2016

Journal of Applied Physics

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“…The tilde in C indicates that it is the deviatoric or volume-preserving part of C, given by C = J −2 /3 C. The functions chosen for Ψ vol and Ψ 0 must be such that Ψ vol (J) = 0 and Ψ 0 C = 0 hold if and only if J = 1 and C = I, respectively. Expression (1) introduces an internal scalar damage variable D ∈ [0, 1] which defines a reduction factor (1 − D) similar to the one first proposed by Kachanov [1].…”

Section: Generalized Damage Model Definitionmentioning

confidence: 99%

“…Then, introducing the free energy defined in (1) and rearranging, the internal dissipation in the reference configuration, Ξ, is obtained…”

Section: Thermodynamic Basis and Damage Dissipationmentioning

confidence: 99%

“…Introducing the decoupled definition of the Helmholtz free energy in (1) and considering the definition in (6) with D = G (τ ), the material elastic-damage tangent constitutive tensor obtained is split into a volumetric and a deviatoric part…”

Section: Tangent Constitutive Tensormentioning

confidence: 99%

“…Since Kachanov [1] first introduced the concept of effective stress through the use of a reduction factor associated with the amount of damage in a material, many authors have developed formulations based on this concept of elastic degradation to model damage or degradation in 3 in which fiber and matrix have markedly different behaviors. The conclusions of the work are then stated in Section 5.…”

Section: Introductionmentioning

confidence: 99%

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A generalized finite‐strain damage model for quasi‐incompressible hyperelasticity using hybrid formulation

Comellas

Bellomo

Oller

2015

Numerical Meth Engineering

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SUMMARYA new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite strain framework is presented. A Kachanov-like reduction factor (1 − D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetricisochoric split of the Helmholtz free energy. However, in the present work it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature.

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