Modelling the effect of feed rate on residual stresses induced due to milling using experimental and numerical methods

The surface integrity of any manufactured product produced in machining process has proved to have a significant impact on the performance of the product. Many parameters influence the integrity of the surface, few of which are microstructure of the material, surface roughness, residual stresses etc. Out of which the present work focuses on the residual stress of the machining, which majorly effects the fatigue strength of the product. Understanding the significance of residual stresses in machining, and influencing it using three basic parameters: feed, cutting speed and depth of cut to increase the products performance and life by optimizing these measures to best possible combination. It is done using both experimental and numerical methods and authors have compared the numerical and experimental values. For experimental purposes AISI 1045 steel was used and the residual stresses measurement was done using Xray diffraction method.


Introduction
To manufacture any product, machining is a very important and crucial process. It determines the quality and the life of the product. There are several methods for machining any product. The quality of the product is basically recognized by two factors, one is safety and the other is reliability. The quality varies upon the machining operation preferred and executed. This machining process influences the surface integrity of the product or component. Surface integrity can be understood in three main fields: surface roughness, transformations of micro-structures and residual stresses. One way to judge the surface quality is surface roughness. However, residual stresses are not that evident like roughness, though play a decisive role in the performance of the component. It is a key factor, which influences the fatigue life, corrosion resistance, dimensional accuracy, etc. These residual stresses are majorly evaluated for turning and grinding operations all over the world. These stresses are found directly related to the cutting parameters like cutting speed, feed, and depth of cut. Moreover, there is no much attention given to understand the formation of residual stresses in milling with important machining phenomena like the dynamic cutting forces and cutting temperature. In the present work investigation is done on the influence of cutting parameters (specifically feed) on the formation of residual stresses while milling a slot on mild steel using both experimental and numerical methods.

Literature review
Due to the several factors residual stresses are induced within the part or component. Often stresses are developed and retained due to non-uniform cooling of the other and the inner surface of the component. Residual stresses in metals are also caused due to the non-uniform plastic deformation throughout the cross-section of the part to be deformed.
In this context, the focus is on modelling of residual stresses and parameters which influence the stresses using mathematical methods and testifying it with experimenting techniques. There has been many research's going on understanding the induced residual stresses in machining. The research work in residual stresses previously dealt with the experimental tests investigating the behavior of residual stresses.
Although major work was in predicting residual stresses in orthogonal cutting operation by using mathematical models and validating it with experiments. The residual stress formation mechanism changes with many parameters like cutting condition, tool, work piece material, process parameters like the cutting speed, lubrication, tool rake angle, tool and work piece combination, feed rate, amount of material being removed [1]. Apart from these, few cutting conditions like temperature and cutting forces also affect the residual stress distribution. The results through this research have proved that residual stresses increase with increase in cutting parameters, uncut chip thickness and radius of cutting tool edge. But, out of these parameters, the chip thickness before being cut seems to influence the residual stresses the most. The research has extended in the mathematical modelling (FEM) of residual stresses and comparing it with the experimental results. There were many scholars who like Guo and Liu who have proved the influence of cutting parameters in the distribution of residual stresses in orthogonal cutting of steels [2]. In Wiesner's approach, he showed experimentally that high tensile stresses up to 700 MPa were induced in the AISI 304 steel. He has experimentally validated it using X-Ray diffraction method and proposed a FE model and presented the effect of temperature and mechanical loads on the residual stresses [3]. Further research by Guo and Liu proved that the residual stresses will turn compressive with sequential cuts on the material. They showed that, with decreasing the thickness of the chip before cutting, the residual stresses are more compressive type and it is concluded that it is appropriate to have a favorable finishing cut conditions for better residual stress distribution.
The present work focusses on developing a numerical model which will enable researchers to determin the residual stresses in machining (milling) and compare the same with experimental values. Numerical simulations help the researchers to understand the structural, flow behavior in a system [4][5][6]. The developed model is 3d oblique cutting unlike many researches which are orthogonal.

Experimentation
The work pieces of dimension 80 × 50 × 6 mm were prepared from AISI 1045 steel plate. This was done to accommodate the work-piece in the XRD machine. The tool used for milling process is a end mill of diameter 6 mm with 4 flutes. The tool is made of tungsten carbide material for its rigid characteristics while cutting. The machining was done using a vertical milling machine. The Residual stresses measurement was done using a non-destructive method X-Ray Diffraction method. [7]. In this analysis the experimental data were analyzed using Taguchi's orthogonal array, which is more about focusing on the effects of variation than on the mean value variations. I assume the residual stress needs to be minimized. To minimize residuals stress, an optimal operational parameter (speed, feed DOC) setup has to be determined using "signal-to-noise ratios" (SN). Also, factors that are significant to the process are determined using ANOVA procedure [8] . In this data set three levels and three parameters were used which corresponds to L9 orthogonal array, which requires a low number of experiments in determining significant factors an effect to the residual stress. The following table shows the values of process parameters for each level. The Measured residual stresses values for the L9 design are given in Table 2.

DOE (Design of Experiments) is useful technique in scientific research
Observing the results in 3 it was found that for the confidence interval p-value is only significant for feed rate ( p < 0.05). In another words, feed rate is the most influencing process parameter on the residual stress generation. The other two process parameters (speed and DOC) are not statistically significant. Having found that, feed has more influence on the stresses induced due to machining, further study was narrowed down to effect of feed on residual stresses. To identify significant process parameters on the residual stress, the general linear model of ANOVA [1] with 0.95 confidence interval is applied. The results are shown in Table .   Table 3. ANOVA results

Finite element model
There has been more research on computational models of simulating the residual stresses using different approaches. Few authors have revealed experimentally, that high tensile stress observed externally, and then a peak of compression below in a turning operation of AISI316L stainless steel. Analytical models [9][10][11][12][13] have been proposed which made the calculation of residual stresses much easier. Also, there are other works on numerical Lagrangian formulation for removal of material [3,10,14,15]. There are different models used based on the effecting parameters like the plain strain finite element model by Shih and Mishra developed a model based on finite element method to predict residual stresses induced because of a moving heat source. The present work involves the modelling of residual stress numerically for a milling operation and comparing the test results of the experiment with numerical values. The machining induced residual stresses play contradicting roles at different situations of time. Investigating the residual stress behavior by modelling using finite element modelling will help the researchers to have a better understanding on the formation of stresses and the stresses that are left behind after the machining load is removed.
Mathematical modelling helps us to provide a link between the input parameters (independent variables) and the output variables (dependent variables). The experimental way of determining the stresses that are left behind in the parts after machining as explained in the previous section is an expensive method and effort is needed to make sure that the results obtained are accurate [16][17][18][19][20][21]. A lot depends on the specimen preparation and measurement; hence a mathematical model will help us to predict the residual stresses for a particular machining condition. This will help in the reduction of time spent in the conduction of experiments and it will be cost effective.
In the present work it is observed that, for the purpose of simulating the residual stresses that are induced during the machining process, the combined use of Johnson-Cook material model and Johnson-Cook damage model is very effective.

Material model
Material modelling is one of the key steps in the simulation of the metal cutting processes. Like any other finite element analysis, the basic material properties required for the analysis is fed. In addition to that the material properties required to simulated large deformation process is also fed to the software. In the machining process the chip is separated from the parent material. In other words, the material removal happens in the form of chips. To capture the shearing of the material and formation of the chips Johnson-Cook material model along with Johnson-Cook damage model is used in tandem so that the metal cutting process can be simulated [22].

Damage model
For the material removal to happen damage initiation and damage evolution are parameters of importance. Johnson-Cook damage criterion along with Johnson-Cook material model is used in the present research work.

Model
The Finite element was done using commercially available Abaqus software. The tool and the work piece are assembled as shown in Figure 1. An explicit dynamic analysis was done and the residual stresses were predicted using the model. The model was assigned with the properties of AISI 1045 steel for work piece and a rigid tool was considered for the analysis. Stresses that were induced during the machining was determined. Figure 2 shows the distribution of residual stresses for one of the cutting conditions. Cutting force variation is depicted in Figure 3. The residual stresses that were obtained from the model is tabulated in Table 3.
The following table shows the residual stress values for at conditions.  Speed and depth of cut was kept constant and the feed rate was varied in the FE analysis whose results are tabulated in Table 5. From the measured values, it is understood that the compressive stress is more due to milling performed with less feed rate. The variation between the experimental work and the FE analysis is shown in Figure 4.

Conclusion
Taguchi method was used to design the experimental design and to determine the effects of process parameters on the residual stress in material after machining. Speed, Feed and Depth of cut are the parameters, that is thae machining parameters considered in this study. Based on data analysis with 95% confidence interval, the following conclusions were drawn: • Thus, based on the data results, the most influencing parameter on the residual stress is feed rate. It has the largest main effect of 4.51 on the residual stress, then DOC of 3.11 and finally the speed of 1.17. • Relationship between residual stress and process parameter was mathematically described and most influencing relationship is determined. Feed rate is statistically significant, and can be only considered in predicting residual stress. The data for this study were normally distributed and assumptions for the linear relationship, equality of variance without outliers were adequate.
In the current research work a 3D model was developed to predict the residual stresses that are induced due to machining. Experimentally the residual stresses were determined for different cutting conditions. For the same cutting conditions, the FE model was used to compare with the experimental values. It was observed that the FE model was able to predict the residual stresses with a very good accuracy. It was observed the feed rate had significant effect on the machining induced residual stresses, the feed rate reduces the compressive residual stresses.