Theory of the Thermal Breakaway of a Pinned Dislocation Line with Application to Damping Phenomena

Teutonico, L. J.; Granato, A. V.; Lücke, K.

doi:10.1063/1.1713074

Cited by 157 publications

(21 citation statements)

References 8 publications

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“…Instead, Kocks favors a trough model in which the eect of the solutes is postulated to be equivalent to a continuous locking of the dislocations along their entire lengths, during every waiting time. The trough model was invented to describe the unlocking of dislocations from segregated solute atmospheres (in particular, in Fe-C) [10], and has been used in a description of internal friction [11,12]. Investigating the properties of this model, Kocks [2] concludes that the model appears to satisfy all the requirements of a viable theory.…”

Section: Rate Equation For Plastic Deformationmentioning

confidence: 99%

A model for experimentally-observed high-strain-rate dynamic strain aging in titanium

Cheng

Nemat‐Nasser

2000

Acta Materialia

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AbstractÐRecent high-strain-rate experimental results have shown an anomalous response by commercially pure titanium at relatively high temperatures: for a ®xed high strain rate and a suitable strain, the¯ow stress which is a monotonically decreasing function of the temperature, suddenly begins to increase with increasing temperature, and then begins to decrease, displaying a dynamic strain-aging behavior. This phenomenon may be caused by the interaction between moving dislocations and mobile point defects in the dislocation core area. Based on this supposition, a model is developed which, both qualitatively and quantitatively, describes the experimentally observed results. This model assumes that the anomalous response is, in fact, dynamic strain aging caused by the drag of the core atmosphere, the evolution of the dislocation structure, and the associated interaction processes. The model combines the concepts of athermal long-range and thermally activated, short-range barriers, with the model of a``trough'' for the thermally activated breakaway of dislocations from the core atmosphere. The evolution of the core atmosphere concentration is included in the model, based on the strong interaction force between dislocations and point defects in the core area. The ®nal product is a uni®ed model which seems to accurately predict the response of commercially pure titanium, over a broad range of strain rates and temperatures. 7

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Section: Rate Equation For Plastic Deformationmentioning

confidence: 99%

A model for experimentally-observed high-strain-rate dynamic strain aging in titanium

Cheng

Nemat‐Nasser

2000

Acta Materialia

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“…Although the temperature, 3 He concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid 4 He connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.The change in the shear modulus µ and the dissipation Q −1 of solid 4 He at low temperature [1-9] have been understood thoroughly by the Granato-Lucke (GL) model [10][11][12]. According to this model, in a dislocation network, dislocations glides under applied stress, which leads to an additional strain field.…”

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confidence: 99%

“…The change in the shear modulus µ and the dissipation Q −1 of solid 4 He at low temperature [1][2][3][4][5][6][7][8][9] have been understood thoroughly by the Granato-Lucke (GL) model [10][11][12]. According to this model, in a dislocation network, dislocations glides under applied stress, which leads to an additional strain field.…”

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confidence: 99%

Simultaneous investigation of shear modulus and torsional resonance of solidHe4

Shin¹,

Choi²,

Shirahama

et al. 2016

Phys. Rev. B

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We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid 4 He by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. Although the temperature, 3 He concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid 4 He connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.The change in the shear modulus µ and the dissipation Q −1 of solid 4 He at low temperature [1-9] have been understood thoroughly by the Granato-Lucke (GL) model [10][11][12]. According to this model, in a dislocation network, dislocations glides under applied stress, which leads to an additional strain field. This strain decreases the µ of a solid from its intrinsic value. However, the slip motion can be effectively damped by binding of dislocation segments with impurities at low temperatures. The pinning of dislocations is regulated by the finite binding energy, E b , between dislocations and impurities in a solid, such that the pinning can be promoted only at sufficiently low temperatures. These weakly bound impurities on the dislocations are detached as a result of increasing temperature and/or external stress, which can be described by the Debye relaxation process and characterized by a relaxation time τ and an activation energy E b [4,8,9]. Solid 4 He is a golden testbed for the GL model because the only impurities in solid 4 He are an extremely low concentration of 3 He atoms. The properties of dislocation in solid 4 He, such as the average network length, dislocation density, and length distribution have been extensively studied by .Another interesting observation of solid 4 He is that the resonant period of a torsional oscillator (TO) containing solid 4 He decreases below 0.2 K [13][14][15][16][17][18][19][20][21][22][23][24][25]. This was initially interpreted as a result of the reduction of the rotational inertia of solid 4 He, and considered as the appearance of a putative supersolid phase. Nevertheless, both the µ and TO response exhibited fundamentally identical dependences on the temperature, driving amplitude, frequency, and amount of 3 He impurities [1,25,26]. To investigate the underlying relationships between them, Kim et al.[25] measured the shear modulus change (∆µ) and the resonant period drop (∆prd) simultaneously by inserting a pair of flat piezoelectric transducers (PZT) into the center of a TO. Even though a similar temperature dependence was observed, the drive amplitude responses were different. When a large AC voltage was applied to a driving transducer, the ∆µ of solid 4 He at the center channel was fully suppressed, but the shift in the resonance period of the TO was ...

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“…We used the thermally assisted breakaway model to describe better both the temperature and drive dependences of the shear modulus change in solid helium at low temperature [21,22]. Assuming that the interaction between an impurity atom and a dislocation is given as a simplified Cottrell force [23], the potential energy of the system consists of three terms: a dislocation tensile line energy and an impurity-dislocation binding energy that likely lead to a pinned state, and the strain energy, which favors an unpinned state [21].…”

mentioning

confidence: 99%

“…Assuming that the interaction between an impurity atom and a dislocation is given as a simplified Cottrell force [23], the potential energy of the system consists of three terms: a dislocation tensile line energy and an impurity-dislocation binding energy that likely lead to a pinned state, and the strain energy, which favors an unpinned state [21]. The total potential energy of the system has a double-well shape with two minima as a function of the distance between the impurity and the dislocation line: a pinned state at a short distance and an unpinned state at a longer distance.…”

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confidence: 99%

Stress- and temperature-dependent hysteresis of the shear modulus of solid helium

Kang

Kim

et al. 2013

Phys. Rev. B

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The shear modulus of solid 4 He below 200 mK exhibits an unusual increase, the characteristics of which show remarkable similarities to those of the period reduction in torsional oscillator experiments. We systematically studied the drive strain and temperature dependence of the shear modulus at low temperatures. The hysteretic behavior depends strongly on the drive and cooling history, which can be associated with the thermally assisted Granato-Lucke dislocation theory. The phase diagram of the shear modulus is constructed on the basis of the emerging hysteretic behavior.An anomalous increase in the shear modulus at low temperatures was recently observed in solid helium [1]. The anomaly exhibits temperature, frequency, and 3 He concentration dependences resembling those of the nonclassical rotational inertia (NCRI) in torsional oscillator (TO) experiments [2,3]. These remarkable similarities have attracted theoretical and experimental attention [4,5]. For instance, a dislocation vibration model for the NCRI is proposed. The temperature dependence of the period of a torsional oscillator containing solid helium is derived from the variation in the average pinning length of dislocations in solid helium [6]. Other efforts to provide a non-supersolid explanation for the TO response were also motivated by the similarities between the two phenomena [4,5,7,8]. The Cornell group recently reported that the TO motion was controlled by the same microscopic excitation that is agitated by temperature and stress independently, which they suggested can be understood within the framework of a dissipation model in which the elastic properties change at low temperatures [9]. Nevertheless, the resonant period reduction found in some earlier TO measurements, including Ref.[9], can be ascribed to the change in the elastic properties of solid helium filling a torsion rod [10]. Thus, the similar response of TO to the drive and temperature agitation can be understood in terms of the dislocation pinning mechanism.The shear modulus increase can be interpreted as the pinning of dislocations by 3 He impurities according to the Granato-Lucke (GL) dislocation theory [11]. The original GL theory considers only the unpinning of dislocations by applied stress without a thermal-fluctuationinduced unbinding mechanism: a large stress reduces the number of pinning points by detaching 3 He impurities from dislocations, thus suppressing the shear modulus. Nevertheless, the effects of stress and temperature on the shear modulus are similar, so its temperature dependence can be explained by the variation in the dislocation loop length with progressive lengthening of freely vibrating dislocation segments due to thermal evaporation of 3 He impurities [1,6,12]. Moreover, the softening of the shear modulus is not a phase transition but a crossover of the thermally activated relaxation process from a stiff (pinned) state to a relaxed (unpinned) state.The discrepancy in the effects of the drive stress and temperature appears when the hysteretic behaviors dur...

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Theory of the Thermal Breakaway of a Pinned Dislocation Line with Application to Damping Phenomena

Cited by 157 publications

References 8 publications

A model for experimentally-observed high-strain-rate dynamic strain aging in titanium

A model for experimentally-observed high-strain-rate dynamic strain aging in titanium

Simultaneous investigation of shear modulus and torsional resonance of solidHe4

Stress- and temperature-dependent hysteresis of the shear modulus of solid helium

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