A critical review of experimental results and constitutive descriptions for metals and alloys in hot working

Abstract

In industrial forming processes, the metals and alloys are subject to complex strain, strain-rate, and temperature histories. Understanding the flow behaviors of metals and alloys in hot working has a great importance for designers of metal forming processes. In order to study the workability and establish the optimum hot formation processing parameters for some metals and alloys, a number of research groups have made efforts to carry out the thermo-mechanical experiments (compressive, tensile and torsion tests) over wide forming temperatures and strain-rates, and some constitutive equations were developed to describe the hot deformation behaviors. This paper presents a critical review on some experimental results and constitutive descriptions for metals and alloys in hot working, which were reported in international publications in recent years. In this review paper, the constitutive models are divided into three categories, including the phenomenological, physical-based and artificial neural network models, to introduce their developments, prediction capabilities, and application scopes, respectively. Additionally, some limitations and objective suggestions for the further development of constitutive descriptions for metals and alloys in hot working are proposed.

Introduction

Material flow behavior during hot forming process is often complex. The hardening and softening mechanisms are both significantly influenced by many factors such as strain, strain-rate, and forming temperature. On the one hand, a given combination of thermo-mechanical parameters yields a particular metallurgical phenomenon (microstructure evolution); on the other hand, microstructure changes of the metal during the hot forming process in turn affect the mechanical characteristics of the metal such as the flow stress, and hence influence the forming processes. Understanding the flow behaviors of metals and alloys at hot deformation condition has a great importance for designers of metal forming processes (hot rolling, forging and extrusion) because of its effective role on metal flow pattern as well as the kinetics of metallurgical transformation (for example, static, dynamic, and metadynamic recrystallization behaviors) [1], [2], [3], [4], [5]. The constitutive relations are often used to describe the plastic flow properties of the metals and alloys in a form that can be used in computer code to model the forging response of mechanical part members under the prevailing loading conditions. Meanwhile, numerical simulations can be truly reliable only when a proper constitutive model is built. Therefore, based on the experimentally measured data, a number of research groups have made efforts to develop constitutive equations to describe the hot deformation behaviors of metals and alloys.

Some thermo-mechanical experiments over wide forming temperature and strain-rate indicate that: (1) In the initial stage of the forming process, the stress abruptly increases to a peak due to the dominance of work hardening; (2) When the strain-rate increases while the temperature is fixed, or the temperature decreases while the strain-rate is kept constant, the overall level of the flow curve enhances correspondingly due to the growing work hardening; (3) The flow stress shows steady-state region due to the equilibrium of work softening and work hardening. Fig. 1a shows the typical true stress–strain curves obtained from the hot compression of 42CrMo steel [6]. It is obvious that the effects of the temperature and strain-rate on the flow stress are significant for all the tested conditions. The true stress–true strain curves exhibit a peak stress at a small strain, after which the flow stresses decrease monotonically until high strains, showing a dynamic flow softening. The stress level decreases with increasing deformation temperature and decreasing strain-rate. This is because lower strain-rates and higher temperatures provide longer time for energy accumulation and higher mobilities at boundaries for the nucleation and growth of dynamically recrystallized grains and dislocation annihilation and thus reduce the flow stress level. Meanwhile, due to the combined effect of work hardening and thermally activated softening mechanisms, the flow stress obtained from experiments consist of four different stage, i.e., Stage I (Work hardening stage), Stage II (Transition stage), Stage III (Softening stage) and Stage IV (Steady stage), as shown in Fig. 1b. In stage I (Work hardening stage), the work hardening (WH) rate is higher than the softening rate induced by dynamic recovery (DRV), and thus the stress rises steeply at micro-strain deformation then increases at a decreased rate, followed by stage II (Transition stage). In transition stage, the competition between the work hardening and the softening phenomenon induced by dynamic recovery, as well as the dynamic recrystallization (DRX), takes place. In addition, the flow stress still increases, but the increase rate continuously decreases. In stage III (Softening stage), the stress drops steeply, which is related with dynamic recovery, dynamic recrystallization, etc. Finally, stage IV (Steady stage): the stress becomes steady when a new balance between softening and hardening appears [6].

Generally, an ideal plasticity model for metals and alloys should be able to accurately describe the material properties such as strain-rate dependence, forming temperature dependence, strain and strain-rate history dependence, work hardening or strain-hardening behavior (both isotropic and anisotropic hardening). However, a complete description of all of these phenomena in a single constitutive model is an extremely difficult task. Therefore, some assumptions were given before some plastic flow stress models are proposed [7]. In recent years, a number of constitutive models have been proposed or modified to describe the strain-rate, stain and temperature-dependent flow behavior of metals and alloys. These models all show that increasing the strain-rate and decreasing the temperature can both enhance the resistance of plastic deformation and cause a rise of the flow stress. For the original constitutive models, there are always some limitations when the authors firstly proposed for their studied materials. So, some other investigators continue to modify the original constitutive models to accurately predict the flow behaviors for the different metals or alloys by considering the special effects of the forming processing parameters. Then, some extended or modified constitutive models were developed.

The followings mainly present a critical review on constitutive descriptions for metals and alloys in hot working, which were reported in international publications in recent years. The constitutive models are mainly divided into the following three categories [8], [9]:

• Phenomenological constitutive model. It provides a definition of the flow stress based on empirical observations, and consists of some mathematical functions. However, the phenomenological constitutive model is lack of physical background that just fits experimental observations. Additionally, the notable feature is that they reduce number of material constants and can be easily calibrated. However, due to their empirical characteristics, they are usually used in limited application fields (covering limited ranges of strain-rate and temperature) and they exhibit the reduced flexibility (detailed formulation for determined materials).

• Physical-based constitutive model. It accounts for physical aspects of the material behaviors. Most of them are involved in the theory of thermodynamics, thermally activated dislocation movement, and kinetics of slips. Compared to the phenomenological descriptions, they allow for an accurate definition of material behavior under wide ranges of loading conditions by some physical assumptions and a larger number of material constants.

• Artificial neural network (ANN). The above methods are to carry out the regression analysis with the experimental results on the basis of the phenomenological or physical-based constitutive models to obtain the material constants. However, the response of the deformation behaviors of the materials under elevated temperatures and strain-rates is highly nonlinear, and many factors affecting the flow stress are also nonlinear, which make the accuracy of the flow stress predicted by the regression methods low and the applicable range limited. While the attraction of artificial neural networks (ANN) is that they are best suited to solve the problems that are the most difficult to solve by traditional computational methods. Neural networks can provide a fundamentally different approach to materials modeling and material processing control techniques than statistical or numerical methods. One of the main advantages of this approach is that it is not necessary to postulate a mathematical model at first or identify its parameters using a artificial neural network.