Experimental and Numerical Investigations on Hot Deformation Behavior and Processing Maps for ASS 304 and ASS 316

Introduction

Austenitic Stainless Steels (ASS) 304 and 316 have extensively used for various applications in the field of defense and nuclear industries due to its superior properties at sea water environment [1]. Specifically, high corrosion resistance, wear resistance, high strength at elevated temperatures and better ductility make these steels are suitable for various industrial applications [2]. These steels exhibit a Dynamic Strain Aging (DSA) or Portevin–Le Chatelier (PLC) effect in certain range of strain rate and temperatures [3]. The major reason could be the mobility of solute atoms can become large enough that they can follow a dislocation during its motion and segregate to its core, while it has to wait in front of an obstacle. In such cases, serrations are observed, i. e. wavy pattern-like saw tooth in the stress–strain plot [4]. Moreover, DSA is revealed by a negative strain rate sensitivity, which results in wobbly, irregular flow [3].

Generally, material flow behaviors are very complex during hot working processes [5]. The flow behavior in hot working condition is generally governed by strain, strain rate and temperature [6]. Conversely, these microstructure changes of the material during the hot forming process in turn affect the mechanical characteristics of the material such as the flow stress; hence influence the forming processes [7]. Various deformation mechanisms such as dynamic recrystallization, metadynamic recrystallization and static recrystallization are often occurring during hot processing [8]. In case of ASS steels, the complexity of deformation behavior may be enhancing due to complex DSA phenomena. The effective knowledge of these parameters will lead to optimization of various parameters at elevated temperature conditions. The various constitutive models and processing maps are well established tool for the optimization of various process parameters [9]. Moreover, knowledge of deformation behavior will be very useful for trustworthy Finite Element (FE) analysis of various hot working processes.

The effect of deformation parameters such as temperature, strain rate and strain on flow behavior should be determined by investigating the flow stress of materials, which can be further utilized for optimization of hot working processes [10]. Developing an accurate constitutive model that considers all these deformation parameters can effectively solve this matter [11]. Recently, several efforts have been made for the development of various constitutive models to characterize deformation behavior of metals. In this work, modified Fields–Backofen (m-FB) and Khan–Huang–Liang (KHL) and are developed for ASS 304 and 316.

In 1957, Fields and Bachofen [12] proposed the generalized constitutive equation for metals. This equation is usually used to describe the stress–strain relationship and it can well express the work-hardening phenomenon by the strain-hardening exponent (n-value) and the strain-rate sensitivity exponent (m-value), which are the important parameters influencing the hot workability of metals or alloys. Cheng et al. [13] studied the mechanical behaviors of AZ31 magnesium alloy sheet over the wide range of temperatures and strain rates. Based on the experimental results, FB model is inaccurate to describe the softening behavior. Further, Quan et al. [14] modified the equation by adding the softening term in the proposed equation. The modification is very well suited for prediction of softening behaviors of 7075 aluminum alloy.

In 1992, Khan and Huang (KH) [15] proposed a constitutive visco-plastic model to simulate the behavior of coarse grained Al 1100 at wide strain-rates range. This model prediction was not consider the effect of temperature. The next modification in the model is proposed by Khan–Huang–Liang (KHL) which considers the coupled effect of strain, strain rate and temperature. In 2000, Khan and Liang [16] determined the KHL material constants for antalum, tantalum alloy and AerMet 100 steel.

Furthermore, processing map is effective method to control the processing parameters than the expensive and time-consuming trial and error methods [17]. The benefit of developing a processing map is that the safe and unsafe domains for hot working of the material can be revealed over wide range of temperatures and strain rates [18]. Processing map is based on dynamic materials model (DMM), which is an explicit representation of the response of a material in terms of power dissipation and instability maps [19]. The first processing maps was developed by Frost and Ashby in terms of strain, strain rate and temperature to recognize different regions of safe and unsafe deformation [20]. Later on Prasad et al. (1984) developed processing maps based on DMM, which consists of two superimposed maps viz. power dissipation efficiency map and the instability map at the constant strain in the frame of logarithm of strain rate and deformation temperature [18]. Till now, very few efforts have been made to develop processing maps and constitutive models for steel and its alloys [21, 22, 23].

Although there are some studies in the literature regarding the constitutive modeling development for ASS steels but there were no information regarding the processing maps development of ASS 304 and 316 steels considering the DSA and Non-DSA region and its influence on the formability of these alloys. Therefore, it is necessary to investigate deformation behavior and processing maps and its implementation in formability studies for ASS 304 and 316 alloy. In this work, the uni-axial tensile tests experiments were performed in the temperatures ranging from 150 °C–600 °C with the strain rates ranging from 0.0001–0.01s⁻¹, up to the total true strain of 0.3. The m-FB and KHL models were developed and validated with uni-axial tensile test flow stress data. Additionally, processing maps were developed safe and unsafe working domain was identified. The processing maps results will be validated with circular deep drawing experiments.

Experimental details

The material used in this study is ASS 304 and 316 alloy of 1 mm thickness sheet. The chemical composition of the material is given in Table 1. Uniaxial isothermal tensile tests were performed to analyze the deformation behavior of ASS 304 and 316. The dimensions of the specimen are as per ASTM E8/E8M-11 sub-size standard specimen as shown in Figure 1. The samples are machined out of the raw material sheet by wire-cutting electro-discharge machining process for high accuracy and finish. The machine has a maximum load capacity of 100 kN and it is equipped with a controlled system to impose an exponential increase of the actuator speed to obtain constant true strain rates. A three zone split furnace with resistance heating is used to heat the tensile test specimens. The schematic of the setup is shown in Figure 2. The tests were conducted at an interval of 150 °C starting from 150 °C–600 °C and at strain rates of (0.0001, 0.001, and 0.01s⁻¹). A computer control system is used to record the load versus displacement data, which were converted into true stress versus true plastic strain curves.

Figure 1:

The dimension of the uniaxial tensile test specimen.

Figure 2:

Schematic diagram of UTM of 100 kN capacity with resistance heating three zone furnace.

Phenomenological-based constitutive models

Flow stress data obtained from the uniaxial tensile tests were used for the KHL and m-FB constitutive model development.

Comparison between constitutive modeling and experimental flow stresses

Based on the tensile tests flow stress, DSA (serrations in the flow stress curve) phenomena has been observed for specific strain rates and temperature range. Table 4 shows a summary of the results of these observations regarding the presence of serrations in true stress vs. strain curves for ASS 304 and 316 respectively. From Table 4, it shows that DSA phenomena is observed form 450 °C and 600 °C for all the strain rates. Furthermore, negative strain rate sensitivity (m) index is considered one of the parameters that can characterize DSA phenomena. The m values have been calculated and mentioned in Table 5. It can be seen that m has a negative value in the temperature range of 450 °C to 600 °C. Therefore, negative m along with the appearance of serrations in the true stress–strain curves confirms the presence of DSA phenomena.

Table 4:

Presence of serrations in flow stress curves (DSA) for ASS 304 and 316.

Strain Rate (/sec)	Temperature (°C)
	150	300	450	600
0.01	N	N	Y	Y
0.001	N	N	Y	Y
0.0001	N	N	Y	Y

1. Note: “Y” represents presence; while “N” represents absence).

Table 5:

Strain rate sensitivity (m) value for ASS 304 and 315 alloys.

Temperature (°C)	150	300	450	600
Strain rate sensitivity (m) for ASS 304	0.0141	0.0151	−0.009	−0.0193
Strain rate sensitivity (m) for ASS 316	0.0139	0.0153	−0.008	−0.0195

Graphical comparison between the experimental and the predicted values of flow stress for m-FB and KHL models for ASS 304 and ASS 316 is shown in Figures 3–6. Correlation coefficient (R) is a commonly used statistical tool which provides information on the strength of linear relationship between the experimental and predicted values. Although the value of R might be high, it is not necessary that the performance of the model is high, as the model might have a tendency to be biased toward higher values or lower values of the data [24]. Hence, average absolute error (Δ), which is computed through a term by term comparison of the relative error, is an unbiased statistics for measuring the predictability of the model. Thus, the prediction capability of constitutive models has been assessed by correlation coefficient (R), average absolute error (Δ) and its standard deviation (S). Also, the suitability of these models is compared based on the number of material constants to be evaluated and the procedure of their evaluation. Tables 6 and 7 show comparison of based on statistical measures for m-FB and KHL model respectively. Figures 7 and 8 show the R graphs for m-FB and KHL model for ASS 304 and 316, respectively.

Figure 3:

Comparison of experimental and predicted flow stress for m-FB model for ASS 304 for strain rates of (a) 0.0001 s⁻¹ (b) 0.001 s⁻¹ (c) 0.01 s⁻¹.

Figure 4:

Comparison of experimental and predicted flow stress for m-FB model for ASS 316 for strain rates of (a) 0.0001 s⁻¹ (b) 0.001 s⁻¹ (c) 0.01 s⁻¹.

Figure 5:

Comparison of experimental and predicted flow stress for KHL model for ASS 304 for strain rates of (a) 0.0001 s⁻¹ (b) 0.001 s⁻¹ (c) 0.01 s⁻¹.

Figure 6:

Comparison of experimental and predicted flow stress for KHL model for ASS 316 for strain rates of (a) 0.0001 s⁻¹ (b) 0.001 s⁻¹ (c) 0.01 s⁻¹.

Figure 7:

Correlation coefficient (R) for m-FB constitutive model (a) ASS 304 (b) ASS 316.

Figure 8:

Correlation coefficient (R) for KHL constitutive model (a) ASS 304 (b) ASS 316.

Table 6:

Statistical parameters for m-FB model.

	Correlation coefficient (R)	Avg. absolute error (Δ) (%)	Standard deviation (S) (%)
ASS 304	0.9218	9.7522	6.7961
ASS 316	0.9470	8.4313	6.1945

Table 7:

Statistical parameters for KHL model.

	Correlation coefficient (R)	Avg. absolute error (Δ) (%)	Standard deviation (S) (%)
ASS 304	0.9704	5.1312	5.0419
ASS 316	0.9604	5.2781	5.1554

Considering the correlation coefficient, KHL model shows high degree of goodness of fit as the R value is above 0.96 for both the materials. Moreover, average absolute error (Δ) and its standard deviation (S) are approximately equal to 5 %. However, m-FB model prediction is poor in terms of correlation coefficient, average absolute error and its standard deviation. Additionally, number of material constants required to determine is more in case of m-FB model. Thus, KHL model is more suitable for accurate prediction of flow stress.

Processing maps

The processing maps are effective method for characterizing the formability, optimizing the hot working process. Generally, to construct a processing map the DMM approach is used, which represents the response of material. The dissipation power, P of a material is the multiplication of stress times the strain rates. The processing maps comprise a superimposition of power dissipation and instability maps. According to DMM model, the total energy absorbed by an object undergoing the process of hot deformation dissipates mainly through the following two aspects: consumption in plastic deformation and structural transformation. So the total energy absorbed by the object can be determined as

where P represents the total power absorbed by the object, G is the power consumed in plastic deformation, J refers to the power consumed in structural transformation. The relationship between the flow stress and strain rate sensitivity parameter m can be expressed as follows:

So the ratio between G and J can be determined by the strain rate sensitivity m as

ƞ is the parameter that is used to describe the efficiency of power dissipation, i. e. the proportion of the energy consumed in structural transformation. It can be described as

where ƞ is determined by εε˙ and T. When strain is a constant, ƞ can be determined by strain rate and temperature. In the processing efficiency maps, larger value indicates that the proportion of the energy consumed in structural transformation is larger and the proportion of the dynamic recrystallization is also larger, which indicates the better processing property [25]. However, the value of processing efficiency may be also high when the processing condition is in instability domain, the forms of instability include break, fold and so on [26]. At this time, simply relying on processing efficiency maps cannot really reflect the processing property, so processing instability maps is necessary. Prasad criterion can be expressed as follows:

where, m= d lnσd lnε˙, cubic spline function is adopted to fit the curves between lnσ and lnε˙. So the relationship between strain rate sensitivity m under a certain temperature and strain can be described as m=A+Blnε˙+ Clnε˙2

Thus the Prasad criterion can be expressed as

The processing maps of ASS 304 and 316 for the different true strain values are shown in Figures 9 and 10 respectively. Processing map is the combination of superimposed maps, viz. power dissipation efficiency and the instability phenomenon. Flow instability phenomenon will happen if the value of this criterion is less than zero. This means localization will occur when the entropy change of the system is less than strain rate in the process of plastic deformation. The power dissipation efficiency is shown by the isoefficiency lines and shaded area represents instability. It has been observed from Figures 9 and 10 that the strain value has a greater significance on the processing maps. In case of both the materials, there are two instability domains, which indicate the material is not workable in that particular region. The instability region is mainly located between 500 °C and 650 °C in case of ASS 304 and ASS 316. The decrease in the workability of the material is due to presence of predominant DSA phenomena in that particular temperature range.

Figure 9:

Processing maps of ASS 304 under different strain levels (a) 0.4 (b) 0.8 (c) 0.12 (d) 0.16 (e) 0.20.

Figure 10:

Processing maps of ASS 316 under different strain levels (a) 0.4 (b) 0.8 (c) 0.12 (d) 0.16 (e) 0.20.

Validation of processing maps

Tensile properties

The strain hardening exponent (n), yield stress (σ_y) and ductility (% elongation) are the crucial material properties, which indicate the workability of the material [27]. n value is determined by the dependence of the flow (yield) stress on the level of strain. In materials with a high n value, the flow stress increases rapidly with strain. This tends to distribute further strain to regions of lower strain and flow stress. A high n value leads to a large difference between yield strength and ultimate tensile strength, which is an indication of good formability. Moreover, higher ductility and lower yield stress values indicate superior formability. Figures 11 and 12 show the variation of material properties with respect to temperatures for different strain rates of ASS 304 and ASS 316 respectively. It has been observed from Figures 11 and 12, n value increases in the range of 150 °C to 300 °C and then it start to decreases in the range of 450 °C to 600 °C. Moreover, as expected, yield stress decreases and ductility increases with respect to temperature. Based on these observations, it can be concluded that the formability may not be increase in the DSA region (450 °C to 600 °C). This can be consider as one kind of preliminary validation of processing maps results.

Figure 11:

Variation of material properties of ASS 304 with respect to temperatures for different strain rates (a) Strain hardening exponent (b) Yield stress (c) % Elongation.

Figure 12:

Variation of material properties of ASS 316 with respect to temperatures for different strain rates (a) Strain hardening exponent (b) Yield stress (c) % Elongation.

Fractography study

The fracture surface of the fully deformed tensile test samples is comprehensively examined using a scanning electron microscope (SEM). The samples for observation are sectioned parallel to the fracture surface. The fracture surfaces are observed at higher magnifications to determine the macroscopic fracture mode and to concurrently characterize the intrinsic features on the tensile fracture surface during uniaxial tensile deformation.

Representative fractographs of the tensile fracture surface of ASS 304 and ASS 316 at various temperatures are shown in Figures 13 and 14. Overall morphology of the tensile fracture surface appeared to be rough and uneven as shown over the range of temperature. Observation of fracture surface at higher magnification revealed a healthy population of dimples of varying size and shapes as shown in Figures 13(a, b) and 14(a, b). The cavities arise from inclusions or coarser precipitates are enlarged during further yielding so that the material between them is necked and sheared. In the non-DSA region (up to 300 °C), fracture occurred through significant plastic deformation resulting in large dimples, which confirms the nature of fracture to be ductile. Whereas in DSA region (above 450 °C), fractured surface has small dimples and cleavages, which indicates that fracture is less ductile. The possible reason for the cleavages is strain-induced martensite due to DSA phenomena. This could be an evidence of decrease in the formability of ASS 304 and ASS 316 in the DSA region.

Figure 13:

SEM micrographs of fractured tensile specimens for ASS 304 at various temperatures (a) 150 °C (b) 300 °C (C) 450 °C (d) 600 °C.

Figure 14:

SEM micrographs of fractured tensile specimens for ASS 316 at various temperatures (a) 150 °C (b) 300 °C (C) 450 °C (d) 600 °C.

Figure 15:

LDR variation with respect to temperatures.

Experimental deep drawing study

Deep drawing is one of the widely used sheet metal working processes and also serves as a basic test for the formability evaluation [28]. In the present study, circular deep drawing process has been used to evaluate the formability of ASS-304 and ASS-316 at various temperatures. Formability is difficult to be defined and quantified accurately. In case of deep drawing, one of the widely used parameters to quantify the formability is Limiting Draw Ratio (LDR). LDR is defined in a simple way as ratio of the diameter of the initial blank to the punch diameter. Circular blanks have been cut from 60 mm diameter onwards. The various diameter blanks have been tested from 150 °C to 600 °C at an interval of 2 mm. Figure 15 shows variation of LDR with respect to temperature. It can be observed that maximum LDR obtained at 300 °C. However, LDR decreases after 300 °C due to presence of DSA phenomena.

Conclusions

The hot deformation behavior of ASS 304 and ASS 316 has been analyzed by means of phenomenological-based constitutive models and processing maps. The processing maps results are validated with deep drawing experiments. The important conclusions are listed below:

1. The phenomenological-based constitutive models namely m-FB and KHL have been developed and verified with experimental flow stress data. Based on the statistical measures, the predictions of KHL model have least deviation than m-FB model. Thus, KHL models preferred for the flow stress prediction of ASS 304 and ASS 316.

2. Based on the theory of DMM, the processing maps of ASS 304 and ASS 316 have been established for the strain from 0.4 to 0.20. The strain has a great influence on the processing maps. There are two instability domains in both the materials, which indicate poor formability in that particular domain. The optimum hot working parameters for both the materials are identified using the established processing maps.

3. The processing maps results are validated using material properties, fractography studies and deep drawing experimentation. Based on the material properties studies, it has been observed that formability may decreases in the temperature range of 450 °C to 600 °C due to presence of DSA phenomena. Moreover, fractography study revealed small dimples and cleavages type of fracture in that region, which indicates poor formability.

4. The optimized processing maps parameters have been used for circular deep drawing experiments. The experimental results are verified with processing map parameters. The LDR has been chosen as a quantifiable formability parameters. The maximum LDR has been obtained at 300 °C. However, LDR has been decreased significantly in case of DSA region (450 °C to 600 °C), which indicates poor formability in DSA region. The accurate validation of results shows suitability of processing maps for optimizing the process parameters in sheet metal forming processes.