There are multiple dynamic compression tests to investigate the constitutive response of metallic materials under extreme strain, strain rate and temperature conditions-Split-Hopkinson bar (Kolsky bar) compression, plate impact and Taylor impact tests are commonly used [1] . These tests are all uniaxial compression tests where the hydrostatic stress is compressive, and the strain imposed is typically between 10% and 30%. Each of these testing methods has some advantages and disadvantages. The Split-Hopkinson compression test allows determination of the uniaxial stress-strain response but is limited in the maximum strain and strain rates, to about 25% and 1×10 4 /s, respectively [2] . By some modifications higher strains up to 80% or more can be achieved [3] , though this is not often practiced.
Metal cutting can also be used as a test for mechanical behavior under higher strain, strain rate and temperature [4] . In orthogonal (two dimensional) metal cutting, the cutting edge of the tool is orthogonal to the plane in which the kinematics of machining can be described as shear deformation along a nominal shear plane. A shear velocity Vs added to the velocity of the incoming material Vw results in a chip velocity Vc parallel to the rake face of the tool (Figure 1 ). Material deformation actually occurs under plane strain shear over a narrow zone of material called the primary shear zone (PSZ) (Figure 1) , which surrounds the nominal shear plane (Figure 1 ). Typically only one flow stress estimate is obtained from each test, derived from the shear stress along the shear plane, which is the flow stress corresponding to the average strain, strain rate and temperature due to adiabatic heating that exist along the nominal shear plane. Typically, the strain is between 100% and 200%, the strain rate is between 10 4 /s and 10 6 /s, and the temperature is between 100 °C and 1000 °C depending on the flow stress and specific thermal capacity of the material.
There are multiple dynamic compression tests to investigate the constitutive response of metallic materials under extreme strain, strain rate and temperature conditions-Split-Hopkinson bar (Kolsky bar) compression, plate impact and Taylor impact tests are commonly used [1] . These tests are all uniaxial compression tests where the hydrostatic stress is compressive, and the strain imposed is typically between 10% and 30%. Each of these testing methods has some advantages and disadvantages. The Split-Hopkinson compression test allows determination of the uniaxial stress-strain response but is limited in the maximum strain and strain rates, to about 25% and 1×10 4 /s, respectively [2] . By some modifications higher strains up to 80% or more can be achieved [3] , though this is not often practiced.
Metal cutting can also be used as a test for mechanical behavior under higher strain, strain rate and temperature [4] . In orthogonal (two dimensional) metal cutting, the cutting edge of the tool is orthogonal to the plane in which the kinematics of machining can be described as shear deformation along a nominal shear plane. A shear velocity Vs added to the velocity of the incoming material Vw results in a chip velocity Vc parallel to the rake face of the tool (Figure 1 ). Material deformation actually occurs under plane strain shear over a narrow zone of material called the primary shear zone (PSZ) (Figure 1 ), which surrounds the nominal shear plane (Figure 1 ). Typically only one flow stress estimate is obtained from each test, derived from the shear stress along the shear plane, which is the flow stress corresponding to the average strain, strain rate and temperature due to adiabatic heating that exist along the nominal shear plane. Typically, the strain is between 100% and 200%, the strain rate is between 10 4 /s and 10 6 /s, and the temperature is between 100 °C and 1000 °C depending on the flow stress and specific thermal capacity of the material.
There are multiple dynamic compression tests to investigate the constitutive response of metallic materials under extreme strain, strain rate and temperature conditions-Split-Hopkinson bar (Kolsky bar) compression, plate impact and Taylor impact tests are commonly used [1] . These tests are all uniaxial compression tests where the hydrostatic stress is compressive, and the strain imposed is typically between 10% and 30%. Each of these testing methods has some advantages and disadvantages. The Split-Hopkinson compression test allows determination of the uniaxial stress-strain response but is limited in the maximum strain and strain rates, to about 25% and 1×10 4 /s, respectively [2] . By some modifications higher strains up to 80% or more can be achieved [3] , though this is not often practiced.
Metal cutting can also be used as a test for mechanical behavior under higher strain, strain rate and temperature [4] . In orthogonal (two dimensional) metal cutting, the cutting edge of the tool is orthogonal to the plane in which the kinematics of machining can be described as shear deformation along a nominal shear plane. A shear velocity Vs added to the velocity of the incoming material Vw results in a chip velocity Vc parallel to the rake face of the tool (Figure 1 ). Material deformation actually occurs under plane strain shear over a narrow zone of material called the primary shear zone (PSZ) (Figure 1 ), which surrounds the nominal shear plane (Figure 1 ). Typically only one flow stress estimate is obtained from each test, derived from the shear stress along the shear plane, which is the flow stress corresponding to the average strain, strain rate and temperature due to adiabatic heating that exist along the nominal shear plane. Typically, the strain is between 100% and 200%, the strain rate is between 10 4 /s and 10 6 /s, and the temperature is between 100 °C and 1000 °C depending on the flow stress and specific thermal capacity of the material.
There are multiple dynamic compression tests to investigate the constitutive response of metallic materials under extreme strain, strain rate and temperature conditions-Split-Hopkinson bar (Kolsky bar) compression, plate impact and Taylor impact tests are commonly used [1] . These tests are all uniaxial compression tests where the hydrostatic stress is compressive, and the strain imposed is typically between 10% and 30%. Each of these testing methods has some advantages and disadvantages. The Split-Hopkinson compression test allows determination of the uniaxial stress-strain response but is limited in the maximum strain and strain rates, to about 25% and 1×10 4 /s, respectively [2] . By some modifications higher strains up to 80% or more can be achieved [3] , though this is not often practiced.
Metal cutting can also be used as a test for mechanical behavior under higher strain, strain rate and temperature [4] . In orthogonal (two dimensional) metal cutting, the cutting edge of the tool is orthogonal to the plane in which the kinematics of machining can be described as shear deformation along a nominal shear plane. A shear velocity Vs added to the velocity of the incoming material Vw results in a chip velocity Vc parallel to the rake face of the tool ( Figure 1 ). Material deformation actually occurs under plane strain shear over a narrow zone of material called the primary shear zone (PSZ) (Figure 1 ), which surrounds the nominal shear plane ( Figure 1 ). Typically only one flow stress estimate is obtained from each test, derived from the shear stress along the shear plane, which is the flow stress corresponding to the average strain, strain rate and temperature due to adiabatic heating that exist along the nominal shear plane. Typically, the strain is between 100% and 200%, the strain rate is between 10 4 /s and 10 6 /s, and the temperature is between 100 °C and 1000 °C depending on the flow stress and specific thermal capacity of the material.
48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to COVID- 19) This paper presents an extension of metal cutting as a test for material behavior at lower strains. This is achieved by using high rake angle tools along with chip pulling to reduce the strain along the nominal shear plane to 50%. Under these conditions it is shown that the flow stress of Al6061-T6 obtained from machining tests coincides with that obtained from Kolsky bar tests modified to apply higher strains.
In orthogonal metal cutting, the cutting tool induces localized shear deformation over a narrow zone of the work material extending from the sharp edge of the tool to the free surface of the specimen, that is named the primary shear zone (PSZ) (Figure 1 ).Plane strain shear deformation occurs under a compressive hydrostatic stress that is of the order of the shear strength of the material. A chip is separated from the specimen through this shear deformation. The nominal shear plane angle φ can be calculated from the measured thickness of the chip.
Knowing φ and α, the chip velocity and total shear strain in the chip can be calculated from the hodograph shown [5] . Using models such as Merchant's model [6] , the shear force and shear stress along the shear plane can be determined from the cutting and thrust force measured by a dynamometer. Oxley's analysis [7] can be used to estimate the width of the shear zone, from which the strain rate along the nominal shear plane can be estimated. The strain rate can also be more precisely established from digital image correlation of high speed images.
Several researchers have used machining as a test for mechanical properties to obtain the flow stress under machining conditions [8, 9, 10, 11, 12, 13] . However, there is no standardized approach that has been validated to provide flow stress measurements that match those obtained from other tests. Most of the studies focus on a narrow range of cutting conditions of interest to them. In some cases, cutting experiments are conducted under conditions that produce shear banded chips, while models of continuous chip formation are used to estimate the material flow stress. Additionally, analytical models used to derive material model coefficients employ many other simplifications, assuming the shear zone width to be a certain ratio of its length, assuming the indentation component of cutting force to be negligible, etc. In reality, there is a ploughing effect of the tool on the workpiece during cutting since there is always a finite radius of the tool edge. This ploughing effect introduces an indentation force ( Figure 2 ) at the cutting edge radius that is included in the measured cutting and thrust forces. It is necessary to remove the indentation force in order to calculate shear stress and flow stress along the shear plane.
An advantage of orthogonal cutting compared to dynamic compression tests is that the strain rate and strain can be controlled independently by changing the cutting speed and the tool geometry, respectively. The strain rate is directly proportional to the cutting speed, neglecting second order changes caused by changes in shear zone thickness. Changing the rake angle ( Figure 1 ) changes the strain. The higher the rake angle, the lower the strain in the chip, and vice versa. Under most cutting conditions the strain in the chip is typically greater than 100% and so the metal cutting can only be used to test the flow stress under very high strains.
Chip pulling is a technique that can be used to reduce the strain induced in the specimen [14, 15] . A tensile force is applied to the chip during the cutting process, as if to pull it away from the shear plane. It was claimed in Nakayama's work that chip pulling can reduce the tool-chip friction, chip thickness, and both components of tool forces by up to 70% [14] . Shamoto et al. [15] observed similar effects of chip pulling, that the chip thickness and the cutting force can be reduced by about half. This is attributed to the tensile force pulling the chip away from the rake face of the tool, thereby reducing the chip-tool contact length and friction force at the chip-tool interface. The objective of Shamoto's work was to use chip pulling to reduce the thrust force so that accurate finished dimensions could be obtained without the need for finish machining at low depths of cut or the use of spring passes.
As the pulling force increases, the shear angle increases, the shear strain decreases and the chip becomes thinner. In addition, the hydrostatic stress becomes less compressive and the process tends towards pure shear.
The main objective of this work is to use chip pulling to reduce the strain in the chip, and to use the measured machining forces to infer the flow stress of the work material at low strain values so that flow stress values obtained by machining can be compared to those obtained from Kolsky bar testing under similar strain rates and equal values of strain. This has been accomplished using Al6061-T6 as the work material. Nomenclature Figure 3 shows a picture of the experimental setup that includes four main components: cutting system, pulling system, force acquisition system, and imaging system. The planing-type cutting system is comprised of two linear slides in parallel (for increased stiffness) that support a feed slide that holds the workpiece and provides the cutting motion of the workpiece past a stationary cutting tool. The ball screw of the slide is driven by a feed motor through a 3:1 reduction gearbox in order to achieve smooth cutting at lower cutting speeds of the order of 0.1 m/s, which result in strain rates comparable to the strain rate of about 2000/s that is obtained in the Kolsky bar tests. The feed slide provides the feed motion before each planing cut, which sets the feed (also called the depth of cut) for orthogonal cutting. The cutting tool is held on a dynamometer (Kistler 9272) which measures the cutting and thrust force components.
The imaging system comprises of a high speed camera (along with flash lamps) that records high speed images of the PSZ at high spatial resolution [16] . Eight frame sequences are captured at a frame rate of 125 kHz and the spatial resolution of each pixel is about 0.2 µm. Digital image correlation (DIC) of the images is used to measure the strain rate distribution over the PSZ during cutting [17, 18] .
The rake angle in this cutting setup is 45° (Figure 1) , which is higher than what is commonly used in machining experiments. The reason for using a high rake angle is to reduce the strain induced in the chip. A special microtome knife is used as the cutting tool in the experiments. The edge radius of the cutting tool was measured to be 1 micrometer. This was measured using two different micro metrology instruments-an Alicona InfiniteFocus 4 profilometer and a Keyence VK-X1000 scanning laser microscope, both of which were in agreement. The small but finite edge radius leads to a ploughing effect that also contributes to the measured cutting forces ( Figure 2 ). Determination of flow stress along the PSZ requires the estimation and removal of the ploughing [19] or indentation component [20] from the measured cutting and thrust forces. The chip pulling system comprises a hanging weight, held up by a fine string and a system of pulleys that exerts a constant force on the chip through a clamp. The weight can be changed to change the applied force. All chip pulling experiments reported here have been carried out with a 1.032 kg weight. The actual pulling force applied to the chip is measured by inserting a small load cell in the path of the string and is found to be 9.2 N (i.e. pulley system efficiency ≈ 90.4%). The angle at which the force is applied can be determined by measuring the angle between the string and the rake face, and is found to be 15.9°w
ith respect to the rake face. Each chip pulling experiment consists of two steps, pre-cutting without chip pulling and cutting with chip pulling. In the pre-cutting step, only the first 15 mm of the workpiece is cut at a low speed, to generate a partial chip. The weight is then hung onto the partially formed chip via a clamp. After this, the cutting experiment is continued with the pulling force applied and experimental data such as forces and high speed images are gathered.
The workpiece is made from a 1" thick plate of aluminum alloy 6061-T6. The length and the thickness of the workpiece are 44mm and 1.93mm, respectively. The length and thickness also represent length of cut and the width of cut. The surface of the sample is prepared with 1200 grit sand paper for obtaining images with a large number of surface features that can be correlated by DIC. Experiments with and without chip pulling are performed under similar conditions except for the pulling force that is applied during chip pulling experiments. Since the cutting motion is stopped and restarted during the chip pulling experiments, the cutting speed is lower in the chip pulling experiments. However, the acceleration of the workpiece is low (80mm/s 2 ) and does not have a significant effect on the chip pulling force. Another factor that can be ignored is temperature. Given the low cutting speed, low forces, and the high thermal conductivity of aluminum, it is found using Boothroyd's thermal model that the thermal number is very low (R tan(φ) = 0.02), for which the fraction of heat staying in the chip, and the temperature rise at the primary shear zone is zero, i.e., all the heat generated during machining is conducted into the workpiece. Figure 4 and Figure 5 show schematic sketches of the forces in experiments with and without chip pulling, for an ideal tool that is perfectly sharp. The equations used for obtaining the flow stress are listed below.
The shear angle can be obtained as
where is depth of cut and is chip thickness. The equivalent strain is given by
where is the rake angle.
The shear plane area is obtained as
where is the width of cut, and the shear force F s ′ is obtained by resolving the cutting force F c ′ and thrust force F t ′ along the shear plane as
The flow stress is obtained as,
The above equations are valid for an ideal cutting tool that is perfectly sharp (edge radius is zero), in which case there would be no indentation force due to the ploughing effect. Since the tool has a finite cutting edge radius, the cutting force and thrust force measured by the dynamometer are processed to remove the indentation force before they are substituted in the above equations to obtain the flow stress.
The tool edge indentation force can be obtained as
where is the tool edge radius. Removal of the indentation force requires simultaneous iterative computation of both the flow stress and the indentation force since they are dependent on one another [21] .
During the cutting experiments several sets of eight successive high speed images were obtained by the imaging system. The time interval between image sets is 404 ms, and the frame rate for each image set is 80 kHz (i.e. the interframe time is 125µs). The spatial displacement field was obtained by DIC of the four adjacent pairs of images within each set (both images of a pair are taken by the same camera and can be correlated with the least noise). The spatial velocity field is obtained by dividing the displacements by the inter-frame time. The gradient of the velocity field gives the strain rate field. Table 1 shows values of the experimentally measured and derived variables, for both cutting with and without chip pulling. The indentation force I is estimated to be about 2.5N in all cases. F c ′ and F t ′ are obtained from the measured forces by subtracting the components of the indentation force in the cutting and thrust force directions. The computed values for equivalent strain, shear angle and flow stress along the shear Figure 4 Resolving the forces along the shear plane to obtain the shear force in experiments without chip pulling. Figure 5 The effect of the pulling force on the shear force in chip pulling experiments.
plane are shown in Table 2 . By comparing the results from experiments with and without chip pulling significant changes can be noted. With chip pulling, the shear angle nearly doubles to about 50°, from a value around 25° in the absence of chip pulling. Correspondingly, the equivalent strain is reduced from an average of 0.94 without chip pulling to 0.54 with chip pulling. The decrease in equivalent strain causes a corresponding decrease in the flow stress along the PSZ. Table 2 Flow stress and equivalent strain derived from measurements. Figure 6 and Figure 7 are sample DIC results for the two conditions, without chip pulling and with chip pulling, respectively. The tool is oriented the same way as in Figures 4  and 5 , as also annotated for clarity. Fringes of the incremental shear strain field derived from the displacement field are shown. By dividing the values by the time interval between images, the strain rate field can be obtained. It can be seen from the two pictures that when the chip is pulled, the shear angle is higher and the strain increment over the 12.5 µs interval between images is smaller. This implies a lower strain rate in chip pulling experiments. The peak strain rate, averaged along the length of the PSZ, is ≈2300/s for tests without chip pulling and is ≈800/s for the chip pulling tests. However, it should be noted that the thickness of the shear zone obtained by DIC is very broad in comparison to the length of the shear zone. This indicates that the strain rate is likely underestimated due to smoothing of the displacement field to reduce noise in strain rate. Smoothing was necessitated by the low resolution of the images in comparison to the small depth of cut used (30 µm). However, several researchers who have studied the strain rate sensitivity of Al 6061-T6 have found that the flow stress is sensitive to strain rate for strain rate values greater than 500/s. Yadav et al. [22] , found that at a strain of 0.1 the flow stress increases by ≈ 100 MPa when the strain rate increases from 380/s to 3600/s. Lee and Huang [23] show that true stress at 0°C corresponding to a true strain of 0.5 increases by 35 MPa from a strain rate of 1000/s to 3000/s. These suggest that the difference in strain rate between machining and Kolsky bar tests may account for the small difference in flow stress observed. While the strain rate in the Kolsky bar tests is about 6000/s, the strain rate observed from DIC is of the order of 860/s. This difference in strain rate might account for the slightly lower flow stress estimated from the chip pulling machining tests. Figure 6 A DIC picture of experiment without chip pulling. The spectrum on the left side represents the magnitude of maximum shear strain, the range of which is from 0 to 0.016. Figure 7 A DIC picture of chip pulling experiment. The spectrum on the left side represents the magnitude of maximum shear strain, the range of which is from 0 to 0.009.
High rake angle cutting tests help reduce the strain in the chip to about 95%, but it is still larger than the maximum strain of 80% obtained in Kolsky bar tests. Using the chip pulling technique, the equivalent strain along the nominal shear plane in orthogonal machining tests has been reduced from 95% to less than 55%. The flow stress correspondingly decreases from 420 MPa to 380 MPa. Flow stress measurements obtained from chip pulling cutting tests agree well with those from Kolsky bar tests.
This document is an official contribution of the National Institute of Standards and Technology (NIST) and is not subject to copyright in the USA. The National Institute of Standards and Technology does not recommend or endorse commercial equipment or materials, nor does it imply that the equipment or materials shown are necessarily the best available for the purpose.
This report was prepared as an account of work sponsored by an agency, National Nuclear Safety Administration (NNSA), of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.