Analysis of Creep Deformation Due to Grain-Boundary Diffusion/Sliding

2007 ◽  
Vol 345-346 ◽  
pp. 565-568
Author(s):  
Byung Nam Kim ◽  
Keijiro Hiraga ◽  
Koji Morita ◽  
Hidehiro Yoshida

For steady-state deformation caused by grain-boundary diffusion and viscous grain-boundary sliding, the creep rate of regular polyhedral grains is analyzed by the energy-balance method. For the microstructure, the grain-grain interaction increases the degree of symmetry of diffusional field, resulting in a decrease of the effective diffusion distance. Meanwhile, the viscous grain-boundary sliding is found to decrease the creep rate. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity.

2011 ◽  
Vol 473 ◽  
pp. 556-563 ◽  
Author(s):  
Mahmoud Farzin ◽  
Reza Jafari Nedoushan ◽  
Mohammad Mashayekhi

A constitutive model is proposed for simulations of hot forming processes. Dominant mechanisms in hot forming including inter-granular deformation, grain boundary sliding and grain boundary diffusion are considered in the constitutive model. A Taylor type polycrystalline model is used to predict inter-granular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three dimensional macro stress-strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. It is shown that for grain boundary diffusion, stress-strain rate relationship obeys the Prandtl-Reuss flow rule. The proposed model is used to simulate step strain rate tests and the results are compared with experimental data. It is concluded that the model can be used to predict flow stress for various grain sizes and strain rates. The proposed model can be directly used in simulation of hot forming processes and as an example the bulge forming process is simulated and the results are compared with experimental data.


2007 ◽  
Vol 44 (11) ◽  
pp. 1587-1602 ◽  
Author(s):  
S Vitale ◽  
J C White ◽  
A Iannace ◽  
S Mazzoli

The Apennine Pollino–Ciagola limestone unit in northern Calabria is characterized by subgreenschist, heterogeneous ductile strain localized along narrow deformation zones at several stratigraphic levels. Paleogene conglomerates and Jurassic calcareous breccias and ooidal packstones have been analyzed with the aim of characterizing the deformation of limestone as a function of the strain recorded by sedimentary markers. Reference sections parallel to principal finite strain planes were prepared at each locality for the study of specific parameters. Image analysis of polished sections by scanning electron microscopy (SEM) was used to obtain the finite strain of calcite grains by Rf/ϕ, harmonic mean and normalized Fry methods. For the range of grain sizes analyzed (1–10 µm), the ellipticity of calcite grains varies as a function of grain size according to a power-law relationship, from which the size of isometric grains is empirically predicted. The finite strain (ellipticity) determined from single calcite grains shows consistently lower values than the corresponding rock strain. For a fixed grain size, grain ellipticity initially increases with rock strain; however for larger strain, scattered ellipticity values are recorded, probably because of dynamic recrystallization. Comparison of bulk strain with grain strain suggests that intercrystalline deformation involving grain boundary sliding contributes 50%–80% of the total strain, for grain sizes in the range of 2–10 µm, increasing to 90% or more for smaller grain sizes. Microstructures (optical, SEM, transmission electron microscopy) are consistent with dominant grain boundary sliding accommodated by dislocation processes. The weakly deformed samples (Rs <4) exhibit straight and subsidiary curved mechanical twins in large grains (d >10 µm), with well-developed glide dislocation substructures in both coarse and micrite grains. In the moderately to highly deformed samples (Rs >4), large grains show curved, thick, and patchy twins, with the development of undulose extinction and subgrains. Subwalls are formed from dislocation networks and relate to subgrain rotation recrystallization in the coarsest grains. Both large and small grains exhibit complex dislocation substructures comprising dislocation networks indicative of concurrent intercrystalline and intracrystalline deformation, whereby grain boundary sliding is accommodated by dislocation processes. Integration of tectonic constraints, field observations, finite strain data, microstructures, and experimental data is consistent with natural deformation at 250 °C, 15–50 MPa, and bulk shear strain rates on the order of 10–13 s–1 to 10–12 s–1.


Author(s):  
L. C. Lee ◽  
S. J. S. Morris ◽  
J. Wilkening

Using analytical and numerical methods, we analyse the Raj–Ashby bicrystal model of diffusionally accommodated grain-boundary sliding for finite interface slopes. Two perfectly elastic layers of finite thickness are separated by a given fixed spatially periodic interface. Dissipation occurs by time-periodic shearing of the viscous interfacial region, and by time-periodic grain-boundary diffusion. Although two time scales govern these processes, of particular interest is the characteristic time t D for grain-boundary diffusion to occur over distances of order of the grain size. For seismic frequencies ωt D ≫1, we find that the spectrum of mechanical loss Q −1 is controlled by the local stress field near corners. For a simple piecewise linear interface having identical corners, this localization leads to a simple asymptotic form for the loss spectrum: for ωt D ≫1, Q −1 ∼const. ω − α . The positive exponent α is determined by the structure of the stress field near the corners, but depends both on the angle subtended by the corner and on the orientation of the interface; the value of α for a sawtooth interface having 120 ° angles differs from that for a truncated sawtooth interface whose corners subtend the same 120 ° angle. When corners on an interface are not all identical, the behaviour is even more complex. Our analysis suggests that the loss spectrum of a finely grained solid results from volume averaging of the dissipation occurring in the neighbourhood of a randomly oriented three-dimensional network of grain boundaries and edges.


2011 ◽  
Vol 682 ◽  
pp. 153-158
Author(s):  
Ying Guang Liu ◽  
Jian Qiu Zhou

A theoretical model based on self-consistent approximation is proposed to explore the effect of grain size distribution on the local mechanical response of nanocrystalline (nc) materials. The representative volume element (RVE) is composed of grains randomly distributed with a grain size distribution following a log-normal statistical function. The grain interior and grain boundary are taken as an integral object to sustain deformation mechanisms of grain-boundary sliding, grain-boundary diffusion and grain-interior plasticity. Local plastic strains and internal stresses, developing within the RVE, have been recorded and discussed.


2011 ◽  
Vol 473 ◽  
pp. 610-617 ◽  
Author(s):  
Mahmoud Farzin ◽  
Reza Jafari Nedoushan ◽  
Mohammad Mashayekhi

Constitutive models based on dominant mechanisms in hot forming are proposed. These models consider inter-granular deformation, grain boundary sliding, grain boundary diffusion and grain growth. New stress-strain rate relationships are proposed to predict deformation due to grain boundary sliding and grain boundary diffusion. Beside a Taylor type polycrystalline constitutive model, a visco-plastic relation in conjunction with a yield function is used to predict inter-granular deformation with much less computational costs. The proposed models are calibrated with tensile test data of AA5083 at . The calibrated models closely fit simple tension experimental data for various strain rates and strains. Then as an example the models are used to simulate a tray forming experiment. Dome heights and tray thicknesses at various positions during forming time can well predict experimental observations.


1999 ◽  
Vol 601 ◽  
Author(s):  
F. Gutierrez-Mora ◽  
A. Dominguez-Rodriguez ◽  
M. Jimenez-Melendo ◽  
R. Chaim ◽  
G. B. Ravi ◽  
...  

AbstractSteady-state creep and joining of alumina/zirconia composites containing alumina volume fractions of 20, 60, and 85% have been investigated between 1250 and 1350°C. Superplasticity of these compounds is controlled by grain-boundary sliding and the creep rate is a function of alumina volume fraction, not grain size. Using the principles of superplasticity, pieces of the composite have been joined by applying the stress required to achieve 5 to 10% strain to form a strong interface at temperatures as low as 1200°C


1990 ◽  
Vol 196 ◽  
Author(s):  
R. W. Siegel

ABSTRACTThe ultrafine grain sizes and high diffusivities in nanophase materials assembled from atomic clusters suggest that these materials may have a strong tendency toward superplastic mechanical behavior. Both small grain size and enhanced diffusivity can be expected to lead to increased diffusional creep rates as well as to a significantly greater propensity for grain boundary sliding. Recent mechanical properties measurements at room temperature on nanophase Cu, Pd, and TiO2, however, give no indications of superplasticity. Nonetheless, significant ductility has been clearly demonstrated in these studies of both nanophase ceramics and metals. The synthesis of cluster-assembled nanophase materials is described and the salient features of what is known of their structure and mechanical properties is reviewed. Finally, the answer to the question posed in the title is addressed.


2021 ◽  
Vol 15 (9) ◽  
pp. 4589-4605
Author(s):  
Mark D. Behn ◽  
David L. Goldsby ◽  
Greg Hirth

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.


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