Description of plastic deformation in fcc metals over a wide range - PowerPoint PPT Presentation

Description of plastic deformation in fcc metals over a wide range of strain and temperature 6th PhD Seminar, Vienna 30. Jun.-1. Jul., 2011 Tamás Csanádi, ELTE University, Department of Material s Physics

Introduction • Recently nanocrystalline materials are extensively investigated because of their special properties • Severe plastic deformation is frequently used to create bulk ultrafine-grained metals: • equal-channel angular pressing (ECAP) • high-pressure torsion (HPT) • Important to characterize the deformation behavior over the wide range of strain, and temperature • Numerous models are established to describe the features of plastic deformation: • macroscopically • microscopically

Outline • Investigation of polycrystalline fcc metal group at constant temperature RT (293 K) in wide range of deformation • macroscopic Well describes description: phenomenological the stress-strain approach curves • microscopic description: dislocation based model Connection between models • Analysis of aluminum at different temperatures (293 K-738 K) in large-scale deformation region • macroscopic model The same • microscopic model relationship is true at different temperature

Experiment: fcc metals at room T • Materials: • high purity polycrystalline Al (4N), Au (4N), Cu (OFHC) and Ni (4N) were investigated • samples were annealed for 1 h at 673 K, 773 K, 873 K and 973 K temperatures respectively • Procedure: • uniaxial tensile test (small deformation ~0.2) at constant 10 -3 s -1 strain rate • ECAP route B c (high deformation ~1-10) Chinh N.Q., C sanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

Modelling: macroscopic description • The below exponential power-law function was used to describe the stress-strain curves, which: • gives a suitable fitting in wide range of strain • describes well the analyzed fcc metal group • contains few parameters • Macroscopic parameters: 0 , 1 , c , n • Includes the well-known Hollomon and Voce type functions, which: • Hollomon model - good for only small deformation • Voce model - give just the global tendency Chinh N.Q., Horváth Gy. , Horita Z., Langdon T.G. – Acta Mater 52 (2004) 3555.

Modelling: macroscopic description • Hollomon function is derived from small deformation region: • Voce function is derived from wide deformation region:

Modelling: microscopic description • Experiments show that the plastic stress essentially determined by the interactions between dislocations in wide range of deformation • The relationship between the plastic stress and the dislocation density can be described by Taylor equation: • The can be considered constant for all investigated metals, =0.7 • For the evolution of numerous model are established, we use mobile ( m ) and forest f ) dislocations, thus m f Gubicza J., Chinh N.Q., Lábár J.L., Hegedűs Z., Xu C., Langdon T.G.– Scripta Mater 58 (2008) 775.

Modelling: microscopic description • Kubin and Estrin established a model based on the evolution of mobile ( m ) and forest ( f ) dislocations • Microscopic parameters: C 1 , C 2 , C 3 , C 4 • C 1 – Multiplication of mobile dislocations • C 2 – Mutual trapping of mobile dislocations • C 3 – Interaction of mobile and forest dislocations • C 4 – Dynamic recovery of forest dislocations • Requirements of numerical solution: • Initial C i parameters were derived from experimental data • Initial values of 0 /2 were chosen in the region of 10 11 -10 13 m = f = m -2 depending on metal Kubin L.P., Estrin Y. – Acta Mater 38 (1990) 697.

Results: fcc metals at room temperature • Fitted parameters: • Numerical result fitting well the experimental data 1/2 is negligible C 3 f C 2 and C 4 are practically the same Chinh N.Q., C sanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

Results: fcc metals at room temperature • Saturation values of m and f are similar • Trapping of mobile dislocations, and the annihilation of forest dislocations are controlled by thermally activated non-conservative motion of dislocations Chinh N.Q., C sanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

Results: simplified Kubin-Estrin model • Considering the fitting results, the Kubin-Estrin can be simplify as the following: • C 3 1/2 =0 f • C 2 =C 4 • Simplified K-E model can be written in the following form: • It has an analytical solution:

Results: simplified Kubin-Estrin model • Plastic stress deriving from the simplified K-E model using Taylor equation: • Precise fitting the experimental data • Predicts the saturation value of stress much better, than the previous models from the initial deformation region Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

Results: relationship between parameters • Plastic stress deriving from the simplified K-E model : • Plastic stress deriving from the macroscopic model: • Considering their equality at high strains, 1 : Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

Results: relationship between parameters • The equality of the plastic stresses can be simplified, as 0 is 2-3 orders of magnitude smaller, than 2C 1 /C 4 • We can obtain at = c : • The solution of this equation is C 4 c =0.93-1.02 for the different metals • It is reasonable to accept that c : Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

Results: relationship between parameters • Making the derivatives of the plastic stresses deriving from macroscopic and simplified K-E models at = c , using C 4 c =1 we obtain: • The parameter n is only slightly depends on C 1 and C 4 • It is not affected by the multiplication and the annihilation of dislocations • Calculated n is in good agreement with those obtained from the fitting of the experimental data Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

Experiment: Al at different temperature • Material: • high purity (99,99%) polycrystalline Al was investigated • at 293 K, 353 K, 393 K, 433 K, 473 K, 623K, 673 K and 738 K temperatures • samples were annealed at 673 K, average grain size ~190 m • Procedure: • uniaxial tension at small deformation ( ~0.1-0.2) at constant 10 -2 s -1 strain rate • ECAP at high deformation T<473 K ( ~8, 10) • after ECAP average grain size ~1.2 m Chinh N.Q., Szommer P., Csanádi T ., Langdon T.G. – Mater Sci Eng A 434 (2006) 326.

Modelling: macroscopic description • The exponential power-law function is fitting well the stress- strain curves • in wide range of strain • through the analyzed temperature region Chinh N.Q., Illy J., Horita Z., Langdon T.G. – Mater Sci Eng A 410 (2005) 234.

Modelling: microscopic description • The Kubin-Estrin model can be simplified again • The simplified Kubin-Estrin model describes well the stress- strain data • in large-scale deformation region • every investigated temperature

Results: Al at different temperature • Temperature dependence of microscopic parameters: • C 1 decreases exponentially with T Transition at ~0.5 T m • C 4 increases linearly with T The multiplication and the annihilation processes change

Results: relationship between parameters • The same relationship can be found between the parameters of the macroscopic and the microscopic models than previously

Summary and conclusion • Plastic behavior were investigated in wide range of strain: • at room temperature for fcc metals (Al, Au, Cu, Ni) • at different temperature in case of Al • In both cases the plastic deformation were analyzed: • macroscopically – exponential power-law function • microscopically – Kubin-Estrin model • From K-E model, over a wide range of strain at room temperature: • The interaction between forest and mobile dislocations is negligible comparing to the interaction between mobile dislocations • Both the trapping of m and the annihilation of f are controlled by thermally activated non-conservative motion of dislocations • Simplifying the K-E model, giving an analytical formula for and a relationship between parameters of the macroscopic and microscopic descriptions • At different temperature: • The regions belonging to the high and low temperature deformations can be distinguished by the changes of the microscopic parameters characterizing the multiplication of dislocation and the annihilation process • The same quantitative correlations were found between the parameters

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