Literature Review
2.6 High temperature deformation behavior of wrought alloys
shaped GP-1 phases transforms continuously to disc shaped and finally spherical shape (final θ phase) when the alloy is in over-aged condition. Transformation of θ' phase to θ phase is accompanied by an increase in the size of the precipitates leading to low coherency at the precipitates matrix interface. this results in a sudden drop in hardness and strength of the alloy. This stage of decrease in hardness with ageing time is referred as over ageing [3, 6].
During aging, the GP-1 zones transform to GP-2 zones having 10–100 nm diameter and 1–4 nm thickness. The strengthening process increases with transformation of GP-1 to θ'' phase and later to the θ' phase. During this process the coherency at the particle matrix interface changes from a coherent interphase to a semi-coherent interface and finally the interface becomes incoherent when the θ' phase transforms to the stable θ phase (CuAl2). The θ' phase has a tetragonal structure with a different lattice parameter from the matrix; no coherency strains exist, but each particle is surrounded by a ring of dislocations. The size of the θ' phase depends on time and temperature; size ranges from 10 to 600 nm diameter with a thickness of 10–
15 nm. Eventually the θ' phase is replaced by θ (CuAl2) which has the same structure and composition as the θ phase formed during solidification. The formation of θ phase results in softening of the alloy and is referred to as over-aging [3, 6].
the emphasis in creep research is for low strain rates and curtailment of total strain, even though both these studies are carried out at almost the same temperature range [27–28].
A clear understanding of the process variables and material parameters is required for successfully deforming these materials within certain range of strain rates and temperatures. The deformation behavior of these materials, which is the relationship between flow stress (σ), strain (ε), strain rate ( ̇) and process temperature (T) is dependent on the activation energy (Q) for deformation, which is a measure of the degree of difficulty for deformation. Composition and microstructure strongly influence the Q value of the materials. Considering hot deformation similar to the creep phenomenon occurring at high strain rates and stresses [58], various constitutive relationships have been developed to model the high temperature deformation behavior of materials.
Cho et al. developed a thermo–viscoplastic finite element method (FEM) model, using hot compression test data to predict the microstructural evolution in Al–5wt.%
Mg alloys during hot deformation [59]. Smith et al. proposed a unified creep–
plasticity constitutive model for the stress–strain behavior of cast Al–Cu–Si [60].
Kaibyshev et al. [61] investigated the deformation behavior of a 2219 Al alloy (Al- 6.4%Cu-0.3%Mn-0.18%Cr-0.19%Zr-0.06%Fe) in the temperature range from 250–
500 °C. The results indicate an increase in stress exponent and apparent activation energy with decrease in temperature.
Hot and warm formability studies of solutionized 2618 aluminum alloy (Al- 2.3%Cu-1.6%Mg-1.1%Fe-1.0%Ni-0.07%Ti-0.18%Si) at various strain rates and temperatures were carried out by torsion testing. The study revealed that effect of the precipitation of second phase particlesare formed during deformation [62]. The flow curves indicated temperature dependent behavior with (i) a continuous increase of flow stress up to 250 °C due to precipitation, and (ii) a peak in the flow curves above 250 °C due to precipitation and coarsening of precipitates followed by softening. The high temperature tensile deformation behavior of Al-Cu-Mg-Zr alloy, 2014, and 6082 Al alloy in a wide range of temperature and strain rate were described by a modified hyperbolic sine equation, where the peak flow stress (p) was substituted by an
effective stress, which is the difference between peak stress and a threshold stress representing the strengthening effect of the second phase precipitates in the matrix [63, 64]. Extensive investigations of the flow stress behaviors of Al-Cu-Li-Zr, Al-Mg, Al-Cu-Mg-Ag, and Al-Mg-Si-Cu alloys were carried out by several researchers [58, 65–67]. The studies reveal that the plastic deformation of these alloys at elevated temperatures (T > 0.5 Tm) is a thermally activated process. The flow stress has either an exponential or hyperbolic sine relationship with strain rate and temperature.
The Zener–Hollomon parameter, Z, is used for representing the hot deformation behavior of metallic alloys [31]. The constitutive relationships and the modeling procedures developed for predicting the flow stress behavior are discussed below in Section 2.6.1
2.6.1 Constitutive models
Based on the principles of creep deformation, models were developed to explain the high temperature deformation behavior of metallic materials. Similar to the creep deformation, high temperature deformation of metallic alloys is also a thermally activated process controlled by strain rate and temperature [68]. During the hot deformation, the strain rate is higher by several orders of magnitude as compared to creep deformation. Hence, the theories of hot deformation can be regarded as an extension of the creep deformation under high strain rate and at high stresses.
The initial development of the constitutive relationships was based on the assumption that the flow stress (σ) is a function of only the instantaneous values of strain (ε), strain rate ( ̇) and temperature (T) [48, 68], i.e.
, , ,
0.f
T (2.6)This is analogous to the expression for a thermodynamic system in equilibrium, which can be expressed by the state variables viz., pressure (P), volume (V) and temperature (T), i.e.
, ,
0.f P V T (2.7)
It was soon realized that plastic deformation is an irreversible process, so that strain and strain rate are not state functions like pressure (P), volume (V) and temperature
(T). Instead, the flow stress depends on the dislocation structure which in turn is related to the metallurgical factors strain (ε), strain rate ( ̇) and temperature (T) [68].
A sine hyperbolic relationship which is particularly useful for correlating stress, temperature and strain rate under hot working conditions was first proposed by Sellars and Tegart [68–69] Subsequently, a set of constitutive relations was developed [70] to analyze constant true strain rate, strain rate change, stress relaxation and creep test data. A computer representation of the constitutive relations was developed [71] for analyzing high temperature deformation.
Strain rate ( ̇) depends on temperature (T) and activation energy (Q) for deformation by an Arrhenius type equation that can be expressed as [60, 61]:
( ) exp Q
,
A f RT
(2.8)where Q is the activation energy for deformation (J/mole), A is a constant, R is universal gas constant and f() is the stress function which can be expressed by any of the following relationships [72–78]:
( ) n1,
f
(2.9)( ) exp( ),
f
(2.10)( ) [sinh( )] .n
f
(2.11)Combining Eq. (2.8) with Eq. (2.9), (2.10) and (2.11), the following constitutive equations can be obtained:
1
1 n exp Q
,
RT
A
(2.12)
2exp( ) exp Q
,
RT
A
(2.13)
3[sinh( )] expn Q
.
RT
A
(2.14)
In the above equations, though flow stress, σ is generally taken as the peak flow stress (σp) [74], the steady state flow stress (σs) has also been used in a few instances.
Flow curve at hot working conditions generally exhibits a peak flow stress (σp), especially when the deformation is carried out at high temperatures and low strain
rates. After achieving the peak flow stress, the flow curve may start decreasing at a constant rate (flow softening) when dynamic recrystallization sets in. If the rate of strain hardening is equal to the rate of dynamic recrystallization the flow curve remains at a steady state value (σs). The term α is the stress multiplier used in the mathematical fitting procedure. The terms of n1, β, n, A1, A2 and, A3 are material constants. The power law equation (Eq. 2.12) breaks down at high stress values whereas the exponential equation (Eq. 2.13) breaks down at low stress values [27, 58, 67, 72, 73]. Over a wide range of stresses, the hyperbolic sine law (Eq. 2.14) is found to be most suitable form for describing high temperature deformation behavior of materials.
It has been observed in many instances that peak flow stress (σp) and steady state flow stress (σs) have a linear relationship. It has also been found that the Zener–
Hollomon parameter is a useful tool in describing the high temperature deformation behavior of metallic materials [75].
2.6.2 Zener-Hollomon parameter (Z) and activation energy (Q)
The flow stress of the material σ during hot deformation can be expressed as [68, 69, 79]:
, ,T .
(2.15)Generalized form of peak flow stress (σp) is possible using the Zener–Hollomon parameter Z. The Z, which correlates strain rate ( ̇), deformation temperature (T), and activation energy (Q), can be expressed as [20]:
exp
Q. Z
RT
(2.16)The physical meaning of Z is the so called temperature-modified strain rate.
Combining Eq. (2.14) and Eq. (2.16), the expression for Z can be expressed as
exp sinh .
3
Q RT
Z
A
n
(2.17)The activation energy, Q, indicates the energy for plastic deformation and is determined from the following relationship [77–81]:
ln sinh
ln ln sinh 1
T
Q R
T
(2.18) = R n S.
In the above relationship, n is the mean slope of ln( ̇) versus ln[sinh(ασ)] plots obtained at different T and S the mean slope of the ln[sinh(ασ)] versus (1000/T) plots at various strain rate ( ̇).
Survey of the literature indicates that so far the focus has been to determine Z, Q, α, n, etc. of commercially available Al alloys. These parameters are known to be influenced by even small variations in the composition and microstructure of the alloys. Investigations on the effect of microalloying on the high temperature deformation behavior of the wrought aluminum alloys are still sparse.