Energy balance and macroscopic strain localization during plastic deformation of polycrystalline metals

doi:10.1016/S0921-5093(01)01061-9

Materials Science and Engineering: A

Volumes 319–321, December 2001, Pages 250-253

https://doi.org/10.1016/S0921-5093(01)01061-9 Get rights and content

Abstract

The energy balance during uniaxial test of the annealed FeSi sheet and the rolled one has been studied. The method of estimation of the energy storage rate in the stage of macroscopic strain localization has been presented. Heterogeneous temperature distribution on the surface of the loaded sample as an experimental indicator of the macroscopic localization of strain was used. The experimental evidence for the existence of recovery process during a development of the localized plastic deformation has been provided.

Introduction

Determination of energy balance during plastic deformation is of prime importance in understanding processes, which take place in deformed material.

The part of energy (e_w) expended in plastic deformation remains stored in the material. The rest of the expended energy appears as a heat (q_d) evolved in the sample.

The deformation process follows the first law of thermodynamics $e_{w} =e_{s} +q_{d}$ where e_s is the stored energy.

The storage energy phenomenon in metals was discovered by Taylor and Quinney [1]. The balance energy during the deformation process still remains the subject for a large number of experimental [2], [3], [4], [5], [6] and theoretical studies [7], [8], [9], etc.

In the presented work a method of energy balance determination without interrupting the deformation and without using a calorimeter was employed. The details of the method are described in [10], [11], [12], [13], [14].

The energy e_w is found from the load versus elongation curve. The heat q_d is determined by simulating the process of sample heating during deformation by means of controlled supply of electrical power r(t₁) in such a way that the temperature increase with time t₁ during the simulation is identical with that measured during tensile testing. When the straining and the simulation are conducted under identical conditions, then the heat, q, which would have been transferred to the surroundings if the temperature of the unloaded sample had returned to the initial temperature in both cases is the same and is equal to $q= ∫ 0 t r(t_{1}) d t_{1}$ $q_{d} =q−e_{te}$ where e_te is the energy associated with thermoelastic coupling that appears during loading and elastic unloading of the sample. During homogeneous tensile deformation, on the assumption of linear and isotropic law for the elastic behavior $e_{te} =− αT_{0} τ ρ_{0}$ where α is the coefficient of linear thermal expansion, T₀ is the initial absolute temperature, τ is the Cauchy's stress tensor and ρ₀ the density of tested metal.

From , , , , the stored energy is obtained as $e_{s} =e_{w} − ∫ 0 t r(t_{1}) d t_{1} − α ρ_{0} T_{0} τ$

The method makes possible to measure in situ the energy balance only under condition of homogeneous deformation.

The present work deals with experimental studies of energy balance during uniaxial tensile deformation, in the range where the strain becomes localized in a macroscopic scale.

The studies are based on comparison of the average temperature increment of deformed sample related to the given increment of the expended energy (for example, equal to 1 J) during a homogeneous deformation and in the range of localized one.

Isothermal surface of the sample as the indicator of homogeneous deformation in macroscopic scale has been used.

When the macroscopic strain localization occurs, the temperature in a certain area of the surface sample becomes higher than the temperature of the others, because of deformation gradient. The surface of the tested sample is no longer isothermal. The onset of the heterogeneous temperature distribution on the surface of the tested sample can be assumed as an experimental criterion of the macroscopic localization of strain.

At a given mode of loading, the onset of the macroscopic strain localization and its evolution depends on a history of deformation of the tested metal [15], [16], [17], [18]. Therefore, the onset of macroscopic strain localization can be controlled by the prestrain.

The energy balance during a uniaxial tensile test of an annealed FeSi sheet and a rolled one has been studied.

Section snippets

Foundation of estimation of energy storage rate in heterogeneous deformation range

According to the first law of thermodynamics, the given increment of the plastic deformation work (e_w) is related to the increment of the heat (Δq) emitted by the sample and the increment of the stored energy (Δe_s).

Let Δq_h, Δe_sh are increments of the heat and the stored energy in the homogeneous range of straining, which correspond to given increment of plastic deformation work (Δe_wh).

Δq_l, Δe_sl are increments of the same parameters in the heterogeneous range of strain corresponding to the

Experiments

The commercial Fe–Si alloy in form of sheet of 2.5 mm thick was chosen. The chemical composition of the steel is as follow 0.027 wt.% C, 0.67 wt.% Mn, 3.17 wt.% Si, 0.006 wt.% P, 0.026 wt.% S, 0.008 wt.% Cr, 0.019 wt.% Ni, 0.061 wt.% Cu, 0.001 wt.% Al and balance Fe.

The first part of the sheet was cold-rolled to the thickness equal to 1.5 mm and the other one was cold-rolled to the thickness equal to 1.9 mm. Then, both of them were annealed at 700 °C during 1 h.

From the first part of the sheet

Results and discussion

Fig. 1 shows the stress–strain curves and the increase of the average temperature of gauge part of the sample in tension of the samples with different initial history.

During tensile loading, the deformation of the samples annealed (T) was stable and homogeneous until the onset of necking while in cold rolled samples (2T) it was unstable and localized from the beginning of straining.

The results of the measurements of the dissipated energy in the form of heat (q_d) and the stored energy (e_s)

Conclusions

The heterogeneous distribution of temperature on the surface of deformed sample as the indicator of the strain localization in macroscopic scale was used.

The method of estimation of the energy storage rate in the stage of heterogeneous deformation has been presented.

It has been shown that during rapid development of the strain localization, some part of the energy stored, which had been stored during earlier deformation, is released in the form of heat. This shows that, in deformed material,

Acknowledgements

Gratitude is expressed to the State Committee for Scientific Research (Poland) for financial support under Grant No. 0 T00A 017 15.

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Energy balance and macroscopic strain localization during plastic deformation of polycrystalline metals

Abstract

Introduction

Section snippets

Foundation of estimation of energy storage rate in heterogeneous deformation range

Experiments

Results and discussion

Conclusions

Acknowledgements

Mech. Mater.

Acta Metall.

Acta Metall.

Mech. Mater.

J. Mech. Phys. Solids

Mater. Sci. Eng.

Mater. Sci. Eng.

Mater. Sci. Eng.

Mater. Sci. Eng.