Constitutive equations for creep rupture

Leckie, F. A.; Hayhurst, D. R.

doi:10.1016/0001-6160(77)90135-3

Cited by 332 publications

(119 citation statements)

References 6 publications

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“…Using equations from crack propagation (Das and Scholz, 1981) and damage mechanics (Leckie and Hayhurst, 1977;Bufe and Varnes, 1993) a formula for the cumulative elastic energy release ε(t) is derived:…”

Section: Test Of the Acceleration Of The Precursory Electromagnetic Ementioning

confidence: 99%

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

Kapiris

Eftaxias

Νομικός

et al. 2003

Nonlin. Processes Geophys.

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Abstract. In analogy to the study of critical phase transitions in statistical physics, it has been argued recently that the fracture of heterogeneous materials could be viewed as a critical phenomenon, either at laboratory or at geophysical scales. If the picture of the development of the fracture is correct one may guess that the precursors may reveal the critical approach of the main-shock. When a heterogeneous material is stretched, its evolution towards breaking is characterized by the appearance of microcracks before the final break-up. Microcracks produce both acoustic and electromagnetic (EM) emission in the frequency range from VLF to VHF. The microcracks and the associated acoustic and EM activities constitute the so-called precursors of general fracture. These precursors are detectable not only at laboratory but also at geophysical scales. VLF and VHF acoustic and EM emissions have been reported resulting from volcanic and seismic activities in various geologically distinct regions of the world. In the present work we attempt to establish the hypothesis that the evolution of the Earth's crust towards the critical point takes place not only in a mechanical but also in an electromagnetic sense. In other words, we focus on the possible electromagnetic criticality, which is reached while the catastrophic rupture in the Earth's crust approaches. Our main tool is the monitoring of micro-fractures that occur before the final breakup, by recording their radioelectromagnetic emissions. We show that the spectral power law analysis of the electromagnetic precursors reveals distinguishing signatures of underlying critical dynamics, such as: (i) the emergence of memory effects; (ii) the decrease with time of the anti-persistence behaviour; (iii) the presence of persistence properties in the tail of the sequence of the precursors; and (iv) the acceleration of the precursory electromagnetic energy release. Moreover, the statistical analysis of the amplitudes of the electromagnetic fluctuations reveals the breaking of the symmetry as the theory predicts. Finally, we try to answer the question: how universal the observed Correspondence to: K. A. Eftaxias (ceftax@phys.uoa.gr) electromagnetic critical behaviour of the failing system is?

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Section: Test Of the Acceleration Of The Precursory Electromagnetic Ementioning

confidence: 99%

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

Kapiris

Eftaxias

Νομικός

et al. 2003

Nonlin. Processes Geophys.

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“…In the theories, it is assumed that once the values of specified damage variables reach certain levels, the material cannot sustain the applied load any more and failure takes place. This has been used to study the failure of materials under high temperature creep (Hayhurst, 1972;Leckie and Hayhurst, 1977) and creep-cyclic plasticity (Chaboche, 1987;Lin et al, 1999). This concept has also been extended into metal forming to study the formability of materials, especially for cold forming (Gelin, 1998).…”

Section: Introductionmentioning

confidence: 99%

“…Based on the concept of Kachanov (1958), many constitutive equations have been developed to describe the phenomenological aspects of the creep damage process (Leckie and Hayhurst, 1977). In addition to rupture times, secondary and tertiary creep behavior of metallic materials can be well predicted using the phenomenological equations in which the material is treated as a continuum.…”

Section: Introductionmentioning

confidence: 99%

A Review on Damage Mechanisms, Models and Calibration Methods under Various Deformation Conditions

Lin

Liu

Dean

2005

International Journal of Damage Mechanics

144

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The development of microdamage under the deformation conditions of high temperature creep, cold metal forming, superplastic forming, and hot metal forming has been reviewed and discussed, and typical constitutive equations developed to model the individual damage mechanisms are summarized. Based on the microstructural analysis of the key damage features for metallic materials under a wide range of deformation conditions, a set of schematic diagrams is designed to illustrate the major types of damage mechanisms. This helps researchers and engineers to understand the major cause of failure of materials under different deformation conditions and to select simple and appropriate mechanism-based damage equations to predict the damage evolution. Further discussions are carried out on the dominant damage mechanisms in hot metal forming conditions and it is concluded that the dominant damage mechanism can be 'grain boundary (creeptype) damage' or 'plasticity-induced (ductile) damage' depending on the material microstructure and deformation rate. In the case of grain boundary damage in hot forming, the shape of microdefects is different from those in high temperature creep and superplastic forming although all of those result in intergranular failure of materials. Furthermore, damage calibration techniques for different conditions of plastic deformation are summarized and discussed.KEY WORDS: damage mechanisms, damage calibrations, creep and viscoplasticity, cold and hot metal forming.

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“…Kachanov (1958) was perhaps the first one to introduce the continuous damage variable as a measure of nucleation, growth, and coalescence of defects, such as microvoids and microcracks, for modeling creep failure. After Kachanov, other researchers [6,[102][103][104][105] have also used the concept of the damage variable to model creep damage. In creep damage, however, treating material as a continuum medium, and also describing damage via a single damage variable, may overshadow the influence of microstructural features (e.g., grain size, grain orientation, and slip systems) on the damage evolution [105].…”

Section: Creep Damagementioning

confidence: 99%

An Entropy-Based Damage Characterization

Amiri

Modarres

2014

Entropy

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This paper presents a scientific basis for the description of the causes of damage within an irreversible thermodynamic framework and the effects of damage as observable variables that signify degradation of structural integrity. The approach relies on the fundamentals of irreversible thermodynamics and specifically the notion of entropy generation as a measure of degradation and damage. We first review the state-of-the-art advances in entropic treatment of damage followed by a discussion on generalization of the entropic concept to damage characterization that may offers a better definition of damage metric commonly used for structural integrity assessment. In general, this approach provides the opportunity to described reliability and risk of structures in terms of fundamental science concepts. Over the years, many studies have focused on materials damage assessment by determining physics-based cause and affect relationships, the goal of this paper is to put this work in perspective and encourage future work of materials damage based on the entropy concept.

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Constitutive equations for creep rupture

Cited by 332 publications

References 6 publications

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

A Review on Damage Mechanisms, Models and Calibration Methods under Various Deformation Conditions

An Entropy-Based Damage Characterization

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