Tool Sharpness as a Factor in Machining Tests to Determine Toughness
B. R. K. Blackman*, T. R. Hoult*, Y. Patel*,J. G. Williams*+.
* Mechanical Engineering Department, Imperial College London
+ University of Sydney
Abstract
An orthogonal cutting test has recently been proposed for determiningGc in polymers. This is of particular value when applied to tough and/or ductile polymers, when the conditions of LEFM are often violated.However, concerns exist about the effects of tool sharpness and the contribution of ploughing to Gc. Here, tools with varying sharpness have been employed and the results critically analysed. It is shown that cutting with sharp tools does give Gc, and that when cutting with blunter tools the ploughing contribution can be rationalised by comparing the tool tip radius with the height of the fracture process zone.
Keywords
Cutting, polymers, fracture toughness, ploughing, tool sharpness.
Nomenclature
Greek alphabet
tool rake angle
radius of curvature (sharpness) of the tool tip
cheight of the fracture process zone
shear plane angle
oshear plane angle obtained from the intercepts (Figure 11)
angle around the tool tip in contact with workpiece (or half angle in wire cutting)
coefficient of friction between tool and workpiece
Yyield stress of the workpiece material
English alphabet
bwidth of cut
Fcdriving force on the tool in the cutting direction
Fttransverse force on the tool generated by Fc.
Gcfracture toughness
hdepth of cut
hedepth of elastic recovery (following ploughing)
hpploughed depth
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1. Introduction
The inclusion of a fracture toughness term in the analysis of cutting and machining has a long history. The machining of metals literature has generally not included the fracture term on the grounds that it would be small compared to that for plastic work [e.g. 1]. It was also excluded because cracks were not observed in ductile machining experiments. Atkins [2, 3] has revisited the issue and pointed out that the fracture term is not necessarily small and rederived the analysis including fracture. He shows that the toughness/strength ratio of a material is a controlling factor in cutting behaviour. Lake et. al [4] had previously studied the cutting of rubber and successfully treated it as a fracture problem.
This approach has been pursued by the present authors [5, 6] for the machining of polymers and it has been proposed as a method for measuring the Fracture Toughness, Gc, for polymers. It is of particular interest for polymers of high toughness and low yield stress which are difficult to test conventionally because of crack blunting. The method has proved successful [6] and the toughness values obtained are in good agreement with those for conventional tests when the latter are possible. The method consists of machining layers of varying thickness from a plate and measuring the cutting and transverse forces. These are then analysed and, by extrapolation, the plastic workto shear the chip is separated from the fracture component. Suchmethods require care since the fracture term is usually significantly less than that dissipated by the plastic shearing and/or bending of the chip [7]. The tool is assumed to be “sharp” in the analysis in that no local plastic work is done around the tool tip. In the experiments the tools used are sharpened to give radii in the range 5 – 10m.
In a recent paper, Childs [8] challenges the notion that a fracture term needs to be included in the analysis.Using a numerical code, a finite radiustool tip is included but there is no fracture term perse. The programme computes the plastic dissipation around the tip of the tool, which here we will term the “ploughing” contribution. Since new surfaces are created the programme requires some form of separation process to run and this is achieved by remeshingin the tool tip region. Some extrapolations from FEM simulation are explored and it is concluded that what is measured is the “ploughing” termandthat the energy changes associated with remeshingare small. By implication the use of the method to determined fracture toughness is in doubt. This paper addresses the issue by performing cutting tests with blunt tools, i.e. with tip radii of up to 400m, to measure the ploughing term. The analysis presented for the removal of a surface layer with a blunt tool includes both fracture toughness and the ploughing term such that it will be clearly evident if it is indeed ploughing, rather than fracture, that is measured.
2. Preliminary Observations
Before considering the experiments it is useful to explore some of the existing data in the literature to see if they would suggest that the ploughing term, rather than fracture, was dominant. A recent paper [7] looked at a range of surface layer removal processes starting from elastic cutting with tools of high rake angles () as shown in Figure. 1. The tip of the tool is shown as blunt and takes no direct part in the fracture process as it does not come into contact with the crack tip. A fracture process zone is shown with a tip opening of c. In this case there isno contact between theworkpiece and the tip of thetool and there is no plasticity such that it is a classical elastic fracture problem. If there is no frictionalong the tool-chip interface then [7]
/ Equation 1This analysis may be extended to include plastic bending of the chip (again in the absence of contact between the tool and crack tip) and a fracture process results.
Plastic shearing in the chip generally occurs when smaller rake angles (are employed and, in the simplest solution, we have the situation shown in Figure 2a. This shows an infinitely sharp tool ( = 0) touching the crack tip. It would be remarkable if this configuration does not involve fracture whilst that discussed above does. Figure 2b depicts a fracture process zone and the tip opening, c,where c and the contact is within the process zone. There is no ploughing in Figure 2b but when ca ploughing contribution outside the zone is possible as shown in Figure 2c. The larger tool radius requires the fracture or separation to occur at some point around the radius at an angle such that the cut depth h is reduced by hp, the ploughing depth, i.e.
hp = (1-cos) / Equation 2The material in the layer hpisboth plastically and visco-elastically deformedand recovers tohe as the tool passes over and the surface plastic flow leads to lateral deformation and the formation of burrs. The forces per unit width due to ploughing, and may be computed from equilibrium in the two orthogonal directions; we assume that the radial stress is equal to the yield stress, Y,and for a friction coefficient of we have (see Figure 3)
/ Equation 3The angle is determined by the fracture or separation point, i.e. the “stagnation” point in [8]. There may be some contribution from the recovering material on the clearance surface but it is not included here since in the short test time the recovery is likely to be small.
It is of interest to note that this deformation mode also occurs in wire cutting testson soft solids [9] as is shown in Figure 4, where the analysis is used successfully. In this case so that by adding each half we have,
and, from symmetry / Equation 4
Wires of varying diameters are used in the test to cut a soft material and the cutting force per unit widthis measured. This is then plotted against the radius of the wire,and the resulting linear relationship gives an intercept on the Fc/b axis of Gc. This is an example of a case wherecand, of course, no chip is produced and Ft = 0 because of symmetry. Unfortunately it will not work for polymers or metals, because sufficiently strong wires are not available.
If the notion is correct that the cutting test measures an apparent Gc value dominated by ploughing, and as the tests are performed with sharp tools with the same tip radius, it would lead naturally to the conclusion that the apparent Gcmeasured would be proportional to the yield stress of the cut material. Table 1 shows values of the yield stress on the shear plane, Y,and Gc from cutting tests taken from three references in the literature including some metals. The Y values are generally higher than the quasi-static tensile values by a factor of about 2.5 because of work hardening in the shear zone and because of constraint [5]. The first two rowsin Table 1 show that the proportionality does not exist since the Gc values are the same but theYvalues vary by a factor of 7. The remaining polymer values further demonstrate the lack of correlation and this can be quantified by assuming thati.e. that the constrained yield stress is an approximation to the cohesive stress.If Gc is proportional to y. and also proportional to y.c, then if is constant, c should be constant. However, cvaries by a factor of 45. In most cases, c, althoughin some low toughness materialscapproaches the lower limit of . The metals data have markedly different values of Y and Gc but the c values vary significantly and are greater than the tool radii, so that ploughing would be expected.
3. Machining Tests
3.1 Sharp Tools
The normal “sharp”tool is made by lapping the two tool faces whichproduces a tip radius in the region of 5-10m. Optical microscopy reveals a rather uneven surface (see Figure 5) so this is not a smooth radius. Similar problems in defining sharpness in razor blades have been reported [4]. The blunt tools used here were made using a CNC grinding machine and thus did have smooth surfaces around the nose. Tool radii of 33, 41, 100, 200, 300 and 400 m were producedto an accuracy of ±2%. The radii were measured using lead indentation and surface profilometry. Figure 6 shows a micrograph of the 200 m tool.
1
Testing was performed with a rake angle =10° and with a width of cut b=6mm on two polymers; polypropylene (PP)and high impact polystyrene (HIPS). Steady-state values of and were measured as a function of cut thickness, h,for the two polymers using a sharp tool. Figure 7a and b shows the results for PP and HIPS respectively. After each cut the chip thickness hc was measured and the shear plane angle was determined from [6].
/ Equation 5Gc was determined by what is referred to in [6] as Method 2*, i.e.
/ Equation 6This analysis method requires that the values ofbe plotted against. The result is linear and the regression givesYas the slope and Gcas the intercept. The results for the two polymers are shown in Figure 8 and both materials show good linearity (R2 = 0.998). The values of Yand Gcmeasured were:
PP Y = 79.0 ± 0.6MPaGc = 3.14 ± 0.07 kJm-2
HIPS Y = 121 ± 1.0MPaGc = 0.57 ± 0.11 kJm-2
The yield stress values, deduced from the slope, have a standard error1% while theGcvalues, deduced from the intercept,have standard errors of about 2% for PP and 20%for HIPS. A large number of small thickness cuts, i.e. h< 50 m, are required to define the rather low Gc value for HIPS. As mentioned previously the Y values are elevated above the tensile values due to work hardening and constraint.
1
*This method is prefered since it does not involve any assumptions such as Merchant’s meothd to find . It does however, involve an extra measurement, hc, with attendant errors. It also avoids any detailed consideration of the friction effects.
Single edge notched bend (SENB) tests were performed according to the LEFM standard for determining Gc in polymers [12]. The specimens were 6mm thick and it was found that all tests failed the linearity criterion with Fmax/F5%calculated to be greater than 1.4. This was expected because both materials have lowquasi static tensile yield stresses, i.e. about 12-20 MPa. It is for this very reason that cutting tests have been developed as a way to measure Gc when LEFM is violated. In PP the initial sharp crack tip blunts in the test. However, an estimate of Gc can be made from theF5%point (i.e. the load for a 5% reduction in compliance) and this gave a value of 4.0 ± 0.1 kJ m-2. For HIPS the rubber toughening of the polymer leads to crazing around the particles and the absence of shear yielding. Hence, the initial sharp crack in the HIPS did not blunt. However, after crack initiation, the energy dissipation associated with crazing leads to a large increase in toughness(i.e. a strongly rising resistance ‘R’ curve is observed). For HIPS the value at F5%was about 0.4kJ/m2.
Two points in the data are noteworthy. The values of h(the cut thickness) were measured by traversingthe specimen surface before and after cutting and taking the difference. The transverse force, Ft, is much less than the cutting force Fc as is usually the case for sharp tool cutting [6]. It should also be noted that the Gc and Y combinations measured here are not in accordance with the notion that the toughness measurement arises from ploughing. In that case, high Gc values would result from materials with high Y values. This is clearly not observed.
3.2 Blunt Tools
Cutting tests using the range of blunt tools were performed onthe two polymers. It was possible to produce chips for all of the radii except for the 400m tool. This tool failed to produce chips, with ploughing occurring instead. Figure 9a shows the values recorded for PP of versus hfor tests which produced chips. It was noted that only values of h>0.10mm could be achieved with the 300m tool. However, all the blunt tools gave lines which are parallel to the “sharp” test data. The values ofversus hare shown in Figure 9b for all tests which produced chips.These data are again parallel to the sharp tool data but are muchhigher and increase with tool radius. Similar data were also obtained for HIPS and these results are shown in Figures 10a and b.
3.3 Discussion of results
The values of the intercepts from theand versus h values (i.e. extrapolated to h = 0) are plotted against the tool tip radius in Figures11a and 11b for PP and HIPS respectively. There is a linear dependency for the 33 to 300m values. However, for the sharp tool the values fall below the linear fits for the lines, i.e. the force containing Gc.
It is proposed here that the cutting and ploughing processesare additive. Thus the cutting contribution at h = 0 is given by Equation6 and is,
The ploughing terms are given by Equation 3, so that the totals are:
The various parameters may be estimated from the experimental data. From the versush data inFigures 7 it can be seen that there aremostly negative slopes. This arises from the tool-chip interaction which gives [5]
where is the rake angle, (=10oin this case), i.e. tan = 0.18. Thus must be less than tan to give the negative slope and here we will assume it is approximately zero. The slope and intercepts of Figures 7, 8 and 11 are given in Table 2. From the slopes of the plots of intercept versus tool radius, Figures 11a and 11b, we may determine the values of which were calculated to be 61o for PP and 52o for HIPS. In addition we may determine Yand this was found to be 114MPa for PP and 182MPa for HIPSusing equation 3. These values may be compared with those derived from the shear plane analysis in the sharp tool data (Figure 8) which gave 79 MPa and 121 MPa respectively, i.e. a factor of about 1.4 higher. These latter values are much higher than the tensile yield stresses and arise from the very high strains in the shear plane and accompanying work hardening. The blunt tools, on the other hand, indent the surface giving a very high local constraint. The concept that the process works at a constant yield stress appears to fit the observations but if the indentation gave permanent deformation the observed original chip thickness h would include the hp term, i.e. (1-cos ) i.e. 0.5 in this case. This would arise because of the measurement method of h and would not be the true value. The chips are measured after the test to find hc and when this is done there is no difference between sharp tools and blunt suggesting that hpin these materials is almost fullyrecovered elastically. This can be clearly seen in Figure 12a which shows the forces acting on a sharp and the 200 m tool at a cut depth of 0.13 mm. Figure 12b shows the subsequent measured forces acting on the tool on a second pass with no additional cut depth applied. It is seen that there is very little interaction between the tool and workpiece after a cut with the sharp tool. However, a second ‘non-cutting’ pass with the blunt tool shows significant forces are measured. It should be noted that there is no material removal during the second pass suggesting that there is elastic deformation and recovery associated with the ploughing term in blunt tool cuts. The values of and for the non-cutting pass can be predicted from the slopes of the and intercept lines given in Table 2, which were derived from Figure 11b. For Figure 12b, the 200m tool would imply a ploughing force, =70.9 MPa ×0.2 ×10-3 m. For a tool width of 6mm, this would suggest a force, Fc = 85 N would be generated, as shown by the lower dashed line in Figure 12b. This is very close to the maximum value of Fc attained in the second pass. For the transverse force due to ploughing, =143.4 MPa ×0.2 ×10-3 m, which, for the same tool width, would imply a transverse force, Ft = 172 N. This is shown as the upper dashed line in Figure 12b and is again very close to the maximum value of Ft attained in the second pass. The observation that both the Fc and Ft values increase with time during the second pass is indicative of visco-elastic effects being present; on the second pass, the far end of the ploughed surface has had longer to recover and thus higher forces are induced. The value of h was also cross-checked by comparing with changes in the tool setting. The two values were close but not identical because of compliance effects.