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

Tamás Csanádi, ELTE University, Department of Materials Physics

6th PhD Seminar, Vienna 30. Jun.-1. Jul., 2011

• 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

Introduction

Connection between models

Outline

• Investigation of polycrystalline fcc metal group

at constant temperature RT (293 K) in wide range of deformation

• macroscopic

description: phenomenological approach

• microscopic

description: dislocation based model

• Analysis of aluminum at different temperatures

(293 K-738 K) in large-scale deformation region

• macroscopic model
• microscopic model

Well describes the stress-strain curves The same relationship is true at different temperature

• Procedure:
• uniaxial tensile test (small

deformation ~0.2) at constant 10-3 s-1 strain rate

• ECAP route Bc

(high deformation ~1-10)

• 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

Experiment: fcc metals at room T

Chinh N.Q., Csanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

• 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: macroscopic 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

Modelling: microscopic description

Gubicza J., Chinh N.Q., Lábár J.L., Hegedűs Z., Xu C., Langdon T.G.–Scripta Mater 58 (2008) 775.

• Kubin and Estrin established a

model based on the evolution of mobile (

m)

and forest (

f)

dislocations

• Microscopic parameters: C1, C2, C3, C4
• C1 – Multiplication of mobile dislocations
• C2 – Mutual trapping of mobile dislocations
• C3 – Interaction of mobile and forest dislocations
• C4 – Dynamic recovery of forest dislocations
• Requirements of numerical solution:
• Initial Ci parameters were derived from experimental data
• Initial values of

m= f = 0/2 were chosen in the region of 1011-1013

m-2 depending on metal

Kubin L.P., Estrin Y.–Acta Mater 38 (1990) 697.

Modelling: microscopic description

• Fitted parameters:
• Numerical result fitting well the

experimental data

Results: fcc metals at room temperature

C3

f 1/2 is negligible

C2 and C4 are practically the same

Chinh N.Q., Csanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

• 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., Csanádi T., Gubicza J., Langdon T.G. – Acta Mater 58 (2010) 5015.

Results: fcc metals at room temperature

• Considering the fitting results, the Kubin-Estrin can be simplify

as the following:

• C3

f 1/2=0

• C2=C4
• Simplified K-E model can be written in the following form:
• It has an analytical solution:

Results: simplified Kubin-Estrin model

• Precise

fitting the experimental data

• Predicts

the saturation value of stress much better, than the previous models from the initial deformation region

• Plastic stress deriving from the simplified K-E model using

Taylor equation:

Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

Results: simplified Kubin-Estrin model

• Plastic stress deriving from the macroscopic model:
• Plastic stress deriving from the simplified K-E model :
• Considering their equality at

high strains,

1:

Results: relationship between parameters

Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

• The equality of the plastic stresses can be simplified, as

0 is 2-3

• rders of magnitude smaller, than 2C1/C4
• We can obtain at = c :
• The solution of this equation is

C4 c=0.93-1.02 for the different metals

• It is reasonable to accept that

c:

Results: relationship between parameters

Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

• 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

• Making the derivatives of the plastic stresses deriving from

macroscopic and simplified K-E models at = c, using C4 c=1 we

• btain:
• The parameter n is only

slightly depends on C1 and C4

Results: relationship between parameters

Csanádi T., Chinh N.Q., Gubicza J., Langdon T.G. – Acta Mater 59 (2011) 2385.

• 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.

Experiment: Al at different temperature

• The

exponential power-law function is fitting well the stress- strain curves

• in wide range of strain
• through

the analyzed temperature region

Modelling: macroscopic description

Chinh N.Q., Illy J., Horita Z., Langdon T.G. – Mater Sci Eng A 410 (2005) 234.

• 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

Modelling: microscopic description

• Temperature dependence of microscopic parameters:
• C1 decreases exponentially with T
• C4 increases linearly with T

Results: Al at different temperature

Transition at ~0.5 Tm The multiplication and the annihilation processes change

• The same relationship can be found between the parameters of the

macroscopic and the microscopic models than previously

Results: relationship between parameters

• 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

• f

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

Summary and conclusion

Thank you for your attention!

The end