A Comparison of Different Methods in Determining Load- and Time-Dependence of Vickers Hardness in Polymers

Polymer Testing 17 (1998) 495–506  1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0142-9418/98/$—see front matter PII: S0142-9418(97)00040-8

TEST METHOD

A Comparison of Different Methods in Determining Load- and Time-Dependence of Vickers Hardness in Polymers J. Suwanprateeb National Metal and Materials Technology Center, National Science and Technology Development Agency, Ministry of Science, Technology and Environment, Rama VI Road, Bangkok 10400, Thailand (Received 9 June 1997; accepted 14 August 1997)

ABSTRACT A comparison between hardnesses which were calculated by diagonal length (Hv,l) and by indentation depth (Hv,d) of polymers, polymethyl methacrylate and high density polyethylene, was carried out. It was found that the difference between the two methods was large, about ⫺60% at low load, but decreased to virtually non-significant as the load was increased. The time-dependence of both polymers was observed in both methods of calculation, but the load-dependence was observed in the indentation depth method whereas hardness calculated by diagonal length showed loadindependent behaviour. This is attributed to imperfect indentation which causes the sinking-in of materials around the flat surface of the indenter, overestimating the measurement of diagonal length and underestimating Hv,l.  1998 Elsevier Science Ltd. All rights reserved

1 INTRODUCTION Hardness is a simple, but useful test to characterise the mechanical properties of materials.1,2 It is generally defined as resistance to penetration by an indenter, though resistance to scratch is also used. The advantage of this test is that it involves only limited area for measurement, so the specimen is relatively unaffected by the test. Hardness has been well established in characteris495

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ing metallic materials and ceramics for many years, but only recently has it been widely employed for characterising polymers.3–6 The usual hardness test yields hardness numbers which are obtained from the applied load and a contact area that is determined from the diagonal length of the residual indentation. However, this measurement by direct observation is somehow difficult and subjective. To overcome the area measurement problems, a calculation of hardness from the indentation depth measurement is one of the alternatives.7 This study was thus carried out to compare two methods of hardness calculation and to study the load- and time-dependent behaviour of polymers from different methods in order to widen the knowledge in this type of test on polymers. 2 MATERIALS AND METHODS The materials employed in this investigation were polymethyl methacrylate (PMMA) and high density polyethylene (HDPE). PMMA samples were cut from a commercially available sheet of Diaglas (Diaglas company, J/V of Mitsubishi Corp., Japan) as a 650 mm ⫻ 180 mm ⫻ 5 mm thick sheet. High density polyethylene (Thaizex 7000F, Bangkok Polyethylene Co., Ltd) was supplied as a 2·5 mm-thick sheet and then cut into 650 mm ⫻ 120 mm plaques. In case of polyethylene samples, two sheets were stacked to make up the thickness of 5 mm for the test. These two materials were selected to represent rigid and soft polymers. The samples were indented at 20°C/62% RH by using a hardness tester (Instron–Wolpert Model 930/25) with a Vickers diamond pyramidal indenter having a square base and pyramidal angle of 136°. Two different methods were employed to acquire hardness values. The first method was to calculate the hardness from the diagonal lengths (d) of the indentation on the specimen. These were measured manually using an electronic ruler on the projected screen where an indentation image was displayed through Zeiss objective lenses of magnification 70 ⫻ or 140 ⫻ . Vickers hardness number was calculated using eqn (1): Hv,l ⫽ 1·854

F d2

(1)

where F is load (kg) and d is the diagonal length (mm). The second method was to calculate hardness from measuring the indentation depth electronically by a Linear Variable Differential Transducer (LVDT) in the equipment and relate it with the geometry of the indenter using the hardness equation below (see eqn (2) and Appendix 1):

Determining load- and time-dependence of polymers

Hv,d ⫽ 1·854

497

Fcos274° 4t2cos216°

(2)

where F is load (kg) and t is the depth of indentation (mm). Four different loads of 1, 2, 3 and 5 kg were used and fully applied in 1 second in the test. The dwell time in the tests were varied from 1 second to 600 seconds and five indentations were made at different parts of the specimens for each test. The values were then averaged.

3 RESULTS 3.1 Comparison between two methods Hardness calculated by indentation depth (Hv,d) was found to be higher than the values calculated by diagonal length (Hv,l). The differences in hardness between the two methods of calculation are tabulated in Tables 1 and 2 for PMMA and HDPE respectively. For both materials, it was observed that the difference was large, up to ⫺60%, at short dwell time and low load. The difference decreased slightly with increasing dwell time, but decreased significantly as the load was increased. It became virtually non-significant at the load level about 5 kg for PMMA and 2 kg for HDPE.

TABLE 1 The difference in hardness between the calculation from diagonal length (Hv,l) and from indentation depth (Hv,d) of PMMA

Dwell time (Seconds) 1 5 10 20 60 180 360 600 *%Difference ⫽

Load ⫽ 1 kg ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺

59 55 54 50 46 45 50 51

Hv,l ⫺ Hv,d ⫻ 100 Hv,d

Difference between Hv,l and Hv,d (%)* Load ⫽ 2 kg Load ⫽ 3 kg Load ⫽ 5 kg ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺

27 26 28 25 23 26 27 27

⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺

19 25 24 24 23 22 21 19

⫺5 ⫺4 ⫺4 ⫺5 ⫺5 ⫺9 ⫺ 11 ⫺ 13

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TABLE 2 The difference in hardness between the calculation from diagonal length (Hv,l) and from indentation depth (Hv,d) of HDPE

Dwell time (Seconds) 1 5 10 20 60 180 360 600 *%Difference ⫽

Load ⫽ 1 kg ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺

60 53 52 50 48 47 38 41

Difference between Hv,l and Hv,d (%)* Load ⫽ 2 kg Load ⫽ 3 kg Load ⫽ 5 kg ⫺ 15 ⫺9 ⫺ 10 ⫺4 4 ⫺3 ⫺ 11 ⫺4

⫺2 ⫺4 ⫺7 ⫺5 ⫺3 ⫺8 ⫺ 11 ⫺9

⫺ 12 ⫺9 ⫺6 ⫺4 ⫺8 ⫺8 ⫺9 ⫺8

Hv,l ⫺ Hv,d ⫻ 100 Hv,d

3.2 Load- and time-dependence in diagonal length measurement Figure 1 shows the logarithmic curves of Hv,l of PMMA and HDPE versus dwell time at various loads. The hardness of both materials appeared to decrease as the dwell time or the time under load was increased. This relationship was linear with PMMA having higher Vickers hardness than HDPE. For each material, all the curves at different loads were superimposed on one another. Figure 2 illustrates the effect of load upon Hv,l of PMMA at different dwell times. It was observed that the curves were parallel to the x-axis, load, and the curves shifted down vertically with increasing dwell time. Therefore, no change in hardness with applied load can be observed for PMMA. This loadindependence was found to be the case for HDPE as well, Fig. 3. 3.3 Load- and time-dependence in indentation depth measurement Figure 4 depicts the logarithmic plots of Hv,d of PMMA and HDPE versus dwell time, similar to Fig. 1. However, hardness in Fig. 4 was calculated from the depth of indentation. Both materials showed a decrease in hardness with increasing dwell time. The relationship was observed to be linear with PMMA having higher hardness than HDPE. At different loads, the curves of both materials were not superimposed on one another. For PMMA, the curves shifted down vertically with increasing applied load. In case of HDPE, the

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Fig. 1. Effect of dwell time on the hardness calculated by diagonal length of PMMA and HDPE at various loads.

curves at different loads were superimposed on one another except the curve at a load of 1 kg which had higher hardness than the others. The effect of load on the hardness of PMMA is illustrated in Fig. 5. It was found that hardness decreased as the load was increased. All the curves displaced down vertically with increasing dwell time. The decrease was large initially and then leveled off at higher load with the slope of curves at short dwell time steeper than ones at longer dwell time. HDPE also showed similar behaviour as shown in Fig. 6.

4 DISCUSSION 4.1 Comparison of hardness by different methods Generally, the values of hardness calculated by different methods should be similar. However, it was found in this study that the difference in hardness

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Fig. 2. Effect of load on the hardness calculated by diagonal length of PMMA at various dwell times.

numbers, between the values calculated by diagonal length and by indentation depth, existed. This was caused by an imperfect indentation. Ideally, a perfect indentation made with a perfect Vickers indenter would be a square as shown in Fig. 7(a). However, the indentations of PMMA and HDPE were not perfectly square, causing a sinking-in of the material around the flat faces of the pyramid, Fig. 7(b). This type of imperfect indentation was also reported to be found in some types of metal, such as annealed metals.2 This obviously causes overestimation of the measurement of the diagonal length, which implies that the hardness calculated by diagonal length is lower than the value calculated by indentation depth. In the case of HDPE, the indentation is more perfect, only a small amount of sinking-in was observed, Fig. 7(c). Therefore, the difference disappeared at lower loads than with PMMA. In addition, it can be seen that the difference is reduced from the initial value of ⫺60% at 1 kg to less than ⫺10% at a load of 5 kg for PMMA and 2 kg for HDPE, respectively. This is due to the difference in the degree of perfection of indentation when both materials were measured. From the obser-

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Fig. 3. Effect of load on the hardness calculated by diagonal length of HDPE at various dwell times.

vation, PMMA exhibited sinking-in type of indentation, whereas HDPE exhibited more square indentation therefore the difference in HDPE disappeared at lower load. When the load is increased, the better indentation geometry is achieved for both materials, particularly for PMMA, thus reducing the difference because the effect of sinking of materials around the indenter becomes negligible. 4.2 Time and load-dependence Polymers are viscoelastic materials, therefore, their behaviour is time-dependent. Their properties are not single values, but vary with time under observation. In this study, both methods of calculation demonstrated similar timedependent hardness of both materials. The hardness decreased as the time elapsed. This is analogous to creep behaviour when the materials deform under constant load. Additionally, the hardness value produced by the application of the load can be related to the rigidity of the materials.

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Fig. 4. Effect of dwell time on the hardness calculated by indentation depth of PMMA and HDPE at various loads.

In case of load-dependence, the use of a Vickers indenter which has a square base and pyramidal angle is intended to avoid the load-dependence of the hardness number because the indentation mark is assumed to be geometrically similar. However, both load-dependence, either increasing or decreasing with load, and load-independence were reported many times.3,8–10 In this study, the load-independence was found to be the case in the diagonal length method, see Figs 3 and 4. However, when the calculation of hardness was carried out by the alternating indentative depth method, it was observed that the hardness was load-dependent. Hv,d decreased with increasing load. This contradiction is due to the imperfect indentation which was discussed previously in Section 4.1. The measured diagonal length was not the actual value, but was overestimated by the distorted indentation. Therefore, it is likely that the study of load- and time-dependence of hardness of polymers should be studied by the indentation depth method if the indentation image is distorted. Considering the indentation depth method, Hv,d was load-dependent. This is because the indentation depth itself is nonlinearly related to the applied load in a decreasing manner. Double the load did not double the depth. Therefore, the hardness would decrease as the load is increased as implied by eqn

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Fig. 5. Effect of load on the hardness calculated by indentation depth of PMMA at various dwell times.

(2). The degree of load-dependence will also be governed by the testing dwell time. It could be seen that the degree of dependence was large at short dwell times, steep slope, and decreased as the dwell time was increased, shallow slope. Therefore, the combination of load and dwell time greatly influence the hardness of polymers. Testing at long dwell times and high load will produce a hardness which is more uniform and comparable than the value at short dwell times and low load.

5 CONCLUSIONS Hardness values of polymers rely upon perfection of indentation. Imperfect indentation will cause uncertainty in measuring the diagonal length and cause a difference in hardness calculated by different methods and also a difference in the load- and time-dependence of hardness. It is likely that the time- and

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Fig. 6. Effect of load on the hardness calculated by indentation depth of HDPE at various dwell times.

Fig. 7. Illustrations of various indentation marks on samples: (a) perfect indentation, (b) PMMA, (c) HDPE.

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load-dependence of hardness should be studied by the indentation depth method, if the indentation is distorted.

ACKNOWLEDGEMENT Bangkok Polyethylene Co., Ltd is thanked for the supply of high density polyethylene sheets.

REFERENCES 1. Askeland, D. R., The Science and Engineering of Materials, 2nd edn. Chapman and Hall, 1984. 2. Fee, A. R., Segabache, R. and Tobolski, E. L., ASM Handbook, Vol. 8: Mechanical Testing. ASM International, USA, 1995, p. 90. 3. Handerson, P. J. and Wallace, A. J., Polymer, 1989, 30, 2209–2214. 4. Katare, R., Bajpai, R. and Datt, S. C., Polymer Testing, 1994, 13, 107–112. 5. Mishra, V., Bajpai, R. and Datt, S. C., Polymer Testing, 1994, 13, 435–440. 6. Balta Calleja, F. J., Ohm, O. and Bayer, R. K., Polymer, 1994, 35, 4775–4779. 7. Benabdallah, H. and Chalifoux, J. -P., Polymer Testing, 1994, 13, 377–394. 8. Li, H., Ghosh, A., Han, Y. H. and Bradt, R. C., J. Mater. Res., 1993, 8, 1028– 1032. 9. Atkinson, M., J. Mater. Res., 1995, 10, 2908–2915. 10. Vander Voort, G. F., Factors that Affect the Precision of Mechanical Tests. ASTM STP 1025, ed. R. Papirno and H. C. Weiss, USA, 1989, p. 3.

APPENDIX From the geometry of the indenter (see figure below), the diagonal length (d) can be calculated from the measured depth of indentation (t) by the equations below: Since d ⫽ lcos 16° 2

(A.1)

Rearranging yields, l⫽

d 2cos 16°

(A.2)

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And t ⫽ lcos 74°

(A.3)

Rearranging yields, l⫽

t cos 74°

(A.4)

Therefore, eqn A.(2) is equal to eqn A.(4) d t ⫽ 2cos 16° cos 74° d⫽

2tcos 16° cos 74°

(A.5)

Vickers hardness number (Hv) was normally calculated using equation; Hv ⫽ 1·854

F d2

(A.6)

Substituting eqn A.(5) in eqn A.(6) yields, Hv,d ⫽ 1·854

Fcos2 74° 4t2cos2 16°

(A.7)