State Variable Theories Based on Hart’s Formulation

Korhonen, M. A.; Hannula, Simo‐Pekka; Li, Che Yu

doi:10.1007/978-94-009-3439-9_2

Cited by 24 publications

(15 citation statements)

References 57 publications

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“…How σ* is chosen depends on the equation used to fit the data. To determine σ*, the data in Figure 18 were fit to Hart's high‐temperature equation: where * is the strain rate at which the stress falls to σ*/ e , and λ, a shape factor (constant) describing the curve, equals 0.15 [ Hart , 1976; Korhonen et al , 1987]. The fit provides σ* = 15.3 MPa for the master curve.…”

Section: Discussionmentioning

confidence: 99%

Similarity and scaling in creep and load relaxation of single‐crystal halite (NaCl)

Stone¹

2004

J. Geophys. Res.

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[1] This work explores the physical basis for Hart's mechanical equation of state in hightemperature plasticity. The experiments seek to identify a possible microstructural basis for the ''hardness'' parameters associated with load relaxation curves. The experiments also seek to examine the microstructural basis for scaling in load relaxation data and to explore the relationship between creep and load relaxation. Constant stress creep and load relaxation tests were conducted on [100] oriented single crystals of halite at 700°C and stresses between 0.6 and 3 MPa. Load relaxation tests were performed at 400°C up to a stress level of 13 MPa. After testing, specimens were sectioned, and dislocation densities and subgrain size distributions were measured. Results at 700°C reveal that distributions of subgrain size in crystals crept at different stress levels are similar to each other; that is, they have the same shape but different average subgrain sizes depending on stress level. Hardness curves obtained from load relaxation experiments at different levels of work hardening were found to correspond to different average subgrain size. Load relaxation data from 700°C and 400°C belong to a single-parameter family of curves, with hardness curves translating onto each other with a scaling slope m = 0.33 ± 0.05. Subgrain size distributions generated in creep are statistically identical to those from load relaxation. The hardness parameter, s*, specified as the (apparent) high-strain rate limit of stress in the load relaxation data, is approximately 50Gb/D I , where G is the shear modulus, b is the Burgers vector, and D I is the mean intercept subgrain diameter. During creep under constant stress the subgrain size evolves until a steady value is approached. The experimental data lend credence to Hart's interpretation that load relaxation data represent (nearly) constant ''structure'' with subgrain size playing the role of the structural variable.

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Section: Discussionmentioning

confidence: 99%

Similarity and scaling in creep and load relaxation of single‐crystal halite (NaCl)

Stone¹

2004

J. Geophys. Res.

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“…Consequently, the implications of the results, both for assessing the potential for applying Hart's description to Carrara marble at T > 400øC and for addressing the experimental problem of verifying the existence of steady state during deformation by intracrystalline slip processes, are discussed. A comprehensive account of Hart's description [Hart, 1970[Hart, , 1976Korhonen et al, 1987], the physical significance of the mechanical state variable incorporated within it, and its application to Carrara marble, has been given elsewhere [Covey-Crump, 1992, 1994 and is not repeated here.…”

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confidence: 99%

Evolution of mechanical state in Carrara marble during deformation at 400° to 700°C

Covey-Crump¹

1998

J. Geophys. Res.

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Abstract. The evolution of the mechanical state of Carrata marble during deformation up to strains of 0.2 at 400 ø to 700øC and strain rates of 10 -4 to 10 -6 s -1 has been investigated by applying Hart's [1976] state variable description of inelastic deformation to the results of isothermal, constant displacement rate experiments performed at these conditions. At T • 600øC the magnitude of the mechanical state increases over the full range of strains investigated even when the deformation occurs at almost constant stress and strain rate, although the rate of increase at given strain decreases with increasing temperature and decreasing strain rate. The deformation microstructures suggest that under these conditions mechanical twinning controls the deformation behavior, with twin boundary migration becoming significant at T • 450øC. As a dynamic recovery process, twin boundary migration is as efficient as strain-induced grain boundary migration. At T > 600øC the magnitude of the mechanical states attained is difficult to evaluate reliably using the method employed, but the continuing evolution of the deformation microstructures suggests that a steady state is not attained by strains of 0.2. At these conditions, mechanical twinning is replaced by other intracrystalline slip processes and by grain boundary bulge nucleated dynamic recrystallization. Hart's description of inelastic deformation, as previously evaluated for Carrara marble at T < 400øC, may be extrapolated to 600øC provided the mechanical state evolution equation is modified to accommodate twin boundary migration and the influence of annealing-type recovery processes. Extrapolation to higher temperatures may require modifications to the equation of state in that description. Although at the conditions investigated steady state appears to be a poor approximation, steady state flow laws of exponential and power law type do provide a good empirical description of the data. However, the observation that steady state is not attained indicates that any microphysical interpretation of the magnitude of the material parameters in such steady state flow law fits should be treated with caution.

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“…The conformance of our data to the lambda law and the scaling of this behavior with stress indicate that the constant‐hardness behavior of polycrystalline ice depends upon the applied stress. Furthermore, deviation from the lambda law at low stress is consistent with a material deforming via grain boundary sliding [ Korhonen et al ., ; cf. Crossman and Ashby , ].…”

Section: Discussionmentioning

confidence: 99%

“…Hart [] postulated that for a material deforming plastically via dislocation creep, deformation‐induced microstructure (that is, microstructure that is sensitive to the deviatoric stress and established by a minimum amount of finite strain) can be quantified by a single state variable that he termed the “hardness.” Experimentally, hardness is determined by measuring strain rate versus stress (the creep compliance) at nominally constant strain [ Korhonen et al ., ]. Stone et al .…”

Section: Introductionmentioning

confidence: 99%

The constant‐hardness creep compliance of polycrystalline ice

Caswell

Cooper

Goldsby

2015

Geophysical Research Letters

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We have performed creep and stress‐reduction experiments on polycrystalline ice (grain sizes, d ≈ 30 and ≈ 245 µm) in the grain boundary sliding and dislocation creep regimes (stresses σ = 0.5–5 MPa, temperature T = 233 K) to determine the constant‐hardness creep compliance under these conditions. Our results are consistent with a microstructural state‐variable description of dislocation‐effected deformation whose rate is accelerated by grain boundary sliding. The fine‐grained specimens reveal no subgrain boundaries, indicating that the stress‐sensitive microstructural feature upon which the state‐variable behavior is founded may be the dislocation structure of the grain boundaries. Deviations of our constant‐hardness data from the behavior predicted by the state‐variable formulation allow estimation of the viscosity of the grain boundaries, which is ~4.8 × 106 Pa s at this temperature.

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State Variable Theories Based on Hart’s Formulation

Cited by 24 publications

References 57 publications

Similarity and scaling in creep and load relaxation of single‐crystal halite (NaCl)

Similarity and scaling in creep and load relaxation of single‐crystal halite (NaCl)

Evolution of mechanical state in Carrara marble during deformation at 400° to 700°C

The constant‐hardness creep compliance of polycrystalline ice

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