Polymer Testing 34 (2014) 10–16
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
The use of nano- and micro-instrumented indentation tests to evaluate viscoelastic behavior of poly(vinylidene fluoride) (PVDF) G.L. Oliveira a, C.A. Costa a, S.C.S. Teixeira b, M.F. Costa a, * a b
Programa de Engenharia Metalúrgica e de Materiais, Universidade Federal do Rio de Janeiro, Rio de Janeiro 68505, Brazil CENPES/PETROBRAS, Rio de Janeiro, Brazil
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 October 2013 Accepted 6 December 2013
Nano-load (n-IIT) and micro-load (m-IIT) instrumented indentation tests (IITs) were used to characterize elastic modulus and hardness in a semicrystalline polymer. The tests were conducted with loading rates ranging from 4.9 to 317 mN.min1 for n-IIT and from 300 to 10000 mN.min1 for m-IIT. A decrease in the elastic modulus was observed as the load rate increased for the n-IIT process, and the elastic modulus increased as the load rate increased for the m-IIT process. This behavior was explained by two-flow volume control under the indenter and the corresponding shear stress, which can influence the state of stress. The effect of holding time on the elastic modulus and hardness was also investigated for m-IIT. E decreased with increasing holding time up to 30 s and became constant from there on. Hardness, however, decreased for all holding times evaluated. The steady state creep was only reached after 90 s, which is significantly higher than the time for elastic modulus stabilization. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Indentation test Elastic modulus Hardness and PVDF
1. Introduction The evaluation of materials using indentation techniques dates back to the beginning of the 19th century when Brinell proposed an indentation method using hard steel balls [1]. Since then, many other techniques have been developed and applied, particularly to metals [2,3]. In the late ’80s and beginning of the ’90s, Doernear and Nix [4] and Oliver and Pharr [5] expanded indentation tests to explore material properties with more fundamental information than any of their predecessors by developing a technique known as instrumented indentation test (IIT) or depth-sensing indentation (DSI). The use of IIT in polymers was quickly recognized as a powerful technique, as demonstrated by the pioneering work of Turnbull and White [6], who used nano-IIT and * Corresponding author. E-mail addresses:
[email protected], gmail.com (M.F. Costa).
marysilvia.costa@
0142-9418/$ – see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymertesting.2013.12.006
ordinary microindentation to evaluate PVC. They noted that the viscoelastic nature of this material could affect the results both because of the lack of standardization and creep under the indenter. Since then, many researchers have directed their attention towards understanding and correctly using IIT and the Oliver and Pharr procedure. Accurate experimental determination of the actual contact area and contact point is difficult for time-dependent materials because of their viscoelastic nature affecting the results, as mechanical properties such as hardness and modulus are strain-rate and/or load-rate dependent. Among the many studies conducted in this field, the work performed by Chen et al. [7,8] is particularly significant. The authors used finite element calculations and a viscoelastic simple mechanical model to discuss the application of the Oliver and Pharr methodology to viscoelastic materials. They noted that the contact-area calculation approach for elastic and elasticplastic behavior cannot be correctly applied to time-flow materials. Furthermore, to correctly represent the elastic
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modulus, the unloading rate must also be considered. Tang et al. [9] evaluated PVDF, PMMA and epoxy via nano-IIT using different loading forces, loading rates and unloading rates and observed that, if the unloading is fast enough, viscoelastic effects can be overcome and the plasticity index becomes independent of the loading force and loading and unloading rate. Moreover, the authors also observed that the value of unloading rate for the independent plasticity index depends on the polymer chemical structure. This will occur at higher unloading rates for epoxy, which has constrained chain motion due to crosslinks, whereas for PVDF, a semicrystalline polymer where amorphous and lamellar crystalline chains act together to hold the applied force, this will occur at lower rates due to easy motion in the amorphous phase. Therefore, different polymer chemical structures will have different ideal unloading rates with minimal effect of viscoelasticity on results. Most studies conducted so far evaluate polymers in the nano-IIT load regime. Under this condition, the measured properties represent the miniscule amount of material beneath the indenter, which is subject to the constraint of the large surrounding volume, surface finishing and indenter tip profile. Additionally, the material’s response will also depend on the test conditions. Currently, several types of equipment are available for IIT in the nano- and micro-scale range (referred to here as n-IIT and m-IIT, respectively). Their concepts are similar, but the experimental controlling parameters and operation procedures are not necessarily identical. Nonetheless, the main difference between these methods is the averaged volume affected by the state of stress under the indenter at the indentation depth when evaluating materials. Thus, the scale of the material’s microstructure becomes important and should be carefully analyzed. A small indentation depth evaluates shallow layers of the surface and features that are on the same scale as the size of the indentation [6]. Furthermore, the estimated near-tip corrected area of the indenter and the contact point are of major concern, especially in polymers. Increase in the test load corresponds to larger indentation depths, and the properties measured may represent the microstructure volume averaged at a given depth, which in turn would represent the bulk properties. Furthermore, the near tip phenomenon has a smaller impact at deeper indentations. In this research, poly(vinylidene fluoride) (or PVDF) was tested in n-IIT and m-IIT load regimes using different load rates and holding times. The goal was to verify the indentation volume effect (IVE) on the elastic modulus and hardness when submitted to two different load regimes, and to understand how the holding time alters these properties.
2. Materials and experimental procedure 2.1. Materials and processing The material selected for testing was semicrystalline aphase polymer, a common PVDF used in the pressure barrier of offshore flexible pipes.
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The PVDF was supplied in pellets, which were preheated in a vacuum oven at 150 C for 20 min to reduce the exposure time during processing. Immediately after preheating, they were transferred to a stainless steel mold (200 200 3 mm) and compression molded with six tons pressure at 220 C for 5 min. A few load/unload cycles were used to extract the entrapped air in the mold (between the pellets). After the melting process was completed, the mold was cooled at 80 C for 10 min and then at room temperature for 5 min. Subsequently, the plate was removed from the mold and left to cool at room temperature. This procedure ensured a high homogeneity of the samples. The PVDF plates were machined to prepare specimens as per ASTM D638 (Type II), as well as bars with dimensions of 45 25 3 mm. 2.2. Instrumented indentation test (IIT) The instrumented indentation tests (IIT) were performed with nano- and micro-loads. The nano-load tests were conducted with a Nanoindenter XPÔ MTS System, and the micro-load tests were conducted with a Microindentation Tester MHT-Z-AE-0000 from CSM Instruments. Both the nano- and micro-load tests were performed with a three-side pyramidal Berkovich indenter. The Nanoindenter XPÔ controls the maximum load, the time to reach the maximum load, the holding time and the time to unload the indenter. The maximum loads used in this equipment were 0.81, 1.60, 3.18, 6.56, 13.19, 26.36 and 52.37 mN; the time to reach each load value was 10 s (a different load rate for each load) and the holding time was fixed at 30 sec. Although the micro-indenter MHT-Z-AE0000 is a similar instrument, the load rate (or the strain rate) to reach the maximum load specified was controlled, and the tests were performed using a maximum load of 310 mN. The loading rate varied from 300 to 10000 mN.min1 and the holding time was 180 s. The 310 mN load represented the minimum load that resulted in a noise-free indentation curve for the PVDF. For each test condition, at least 10 good indentations needed to be obtained for the calculations. An indentation was considered good when the difference in the sides of the projected triangle was less than 5%. Furthermore, the distance between any two indentations was at least five times the diagonal length of the largest measured indentation. The elastic modulus and the hardness were calculated using the methodology proposed by Oliver and Pharr [10]. The conditions reported above facilitated the comparison of the elastic modulus with hardness under different loading rates. However, the viscoelastic nature of the material results in creep during the hold time period, which might alter the results. A parametric study of the creep phenomena has not been conducted, although different holding times have been examined [9,11,12]. A second set of experiments was conducted in only the micro-load regime to evaluate the influence of creep on indentation results, reasons for which will be explained in the discussion section. These tests were conducted with a loading and unloading rate of 600 mN.min1, a maximum load of 310 mN and holding times of 0, 5, 10, 20, 30, 60, 90, 120, 150, 180 and 210 s.
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2.3. Analysis methodology
3. Results and discussion
The physical data acquired during the IIT tests included load, indentation depth and time. After the test, the indentation impression can be measured. The data analysis followed the methodology proposed by Oliver and Pharr [10], which determines the elastic modulus and hardness. Two different tips were used, one each for the nano- and the micro-load tests. The indenter-area function used was in-line with the indenter/equipment vendor recommendations. Tests were performed on standard calibration blocks, and the results were within standard deviation. The indenter area function [10] was expected to significantly affect the nano-load tests because the very close tip of the indenter plays a major role in this load regime. The hardness values for both the nano- and micro-tests were calculated using Eq. (1):
3.1. Evaluation of loading rate effect on PVDF
H ¼
Pmax A
(1)
where Pmax is the maximum load and A is the projected contact area at that load. The elastic modulus (E) was derived from the slope of the initial unloading curve for all conditions, using the relationship between the contact area (A), unloading stiffness (S) and the effective elastic modulus (Eeff), represented by Eq. (2) and Eq. (3) [10]. pffiffiffi 2 S ¼ b pffiffiffi Eeff A
(2)
1 1 n2 1 n2i ¼ Eeff E Ei
(3)
p
The effective elastic modulus (Eeff) considers that both the specimen (E and n) and the indenter (Ei and ni) will be subjected to elastic displacement, whereas Eq. (2) is valid beyond the pure elastic regime, such as in the elasticplastic region [10]. In essence, the combination of Eqs. (2) and (3) can measure the instantaneous elastic component of a given material at the moment it is unloaded. The materials exhibit creep behavior during the holding period, and measuring the extent of this behavior becomes very important from the standpoint of methodology as well as the resulting properties. Thus, the strain rate (_ε), used to evaluate creep behavior, was calculated via Eq. (4) [4,13]:
ε_ ¼ c
1 dh h dt
The traditional evaluation of materials using indentation tests was based on hardness machines that use fixed loads during a specific time. Hardness is calculated as load divided by the impression dimensions [6,11,14]. The development of a continuous depth sensing recording device resulted in a broader and deeper understanding of the material properties through an instrumented indentation test (IIT). IITs have mostly been used with nano-scale loads using the analysis method developed by Oliver and Pharr [5,10]. Although it was initially applied to materials that are considered well behaved, problems related to yielding, non-elastic effects and the correct contact area strongly influenced the measured values of the hardness and elastic modulus. The application of the same methodology to viscoelastic solids requires additional care in the analysis because the holding time, maximum load, loading rate (or strain rate) and temperature alter the time-flow characteristics of this type of material [6,14,15]. The nature of viscoelastic behavior can be observed in Fig. 1, which shows the load-displacement curve for m-IIT of PVDF. Stiffness decreased, and initial maximum indentation depth was 1 mm deeper when the load rate was reduced from 2000 to 300 mN.min1. The load-displacement curves for both n-IIT (not shown) and m-IIT had the same shape for all load rates used in this work. No “bulge” or “nose” was observed during unloading. A “nose” in the unloading curve was reported by Chen et al. [7,8] as the typical response of a linear viscoelastic solid when unloading is not sufficiently fast, leading to error of up to 45% in indentation depth and corresponding contact area, both of which form the basis of calculating modulus and hardness. The PVDF tested here is a viscoelastic polymer and does not behave linearly [16]. It is also possible that the unloading times used were fast
(4)
where c is a material constant usually equal to 1, h is the instantaneous indenter displacement and dh/dt is the displacement rate. 2.4. Tensile test Tensile tests were conducted by a universal test machine (Instron, model 5582) at 23 C, and strain was measured by a video extensometer. The tests were conducted under a crosshead speed of 50 mm/min, which was approximately 2.7 104 N.min1 at the beginning of the test.
Fig. 1. Load-displacement curves of PVDF tested with 300 and 2000 mN.m1, up to 310 mN, that were held for 180 seconds and then unloaded with the same loading rate.
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enough to avoid the “nose” as linear and non-linear viscoelastic solid do behave completely differently during unloading. The IIT data showed a pattern similar to the Oliver and Pharr analysis [10] using their methodology. 3.2. Elastic and yielding response of PVDF measured by n-IIT and m-IIT Fig. 2 shows the data obtained with n-IIT equipment, where a fixed time was established to reach the desired load. The elastic modulus decreased from 1826 to 1609 MPa (11% reduction), and the maximum indentation depth increased from 594 to 5454 nm as the applied load increased from 0.81 to 52.87 mN, corresponding to loading rates from 4.9 to 317 mN.min1, respectively (a 65-fold increase in applied rate). This general behavior has been observed in polymers tested with nano-scale loads and has been explained by the indentation size effects (ISEs), which may combine any imperfection of the indenter, miscalibration, contact point determination, quality of the surface finish or any surface modification to induce hardening [11,14,17]. The authors do agree that the n-IIT data cannot be explained by ISE, as illustrated below. Additionally, a closer look in Fig. 2 reveals a sharp reduction in elastic modulus as load rate increases up to 100 mN.min1 and a subsequent asymptotic value. As is evident from Fig. 3, completely different behavior was observed for m-IIT tests with a fixed load set at 310 mN and varied load rate, when the load magnitude increased. An increase in the elastic modulus from 1412 to 1820 (22% increasing) and a decrease in the maximum indentation depth from 13441 to 12100 nm were observed as the load rate increased from 300 to 10000 mN.min1 (a 33-fold increase). This is the expected viscoelastic behavior, in contrast to that shown in Fig. 2. It is notable that the elastic modulus increases very steeply up to 1000 mN.min1 and then slows to 5000 mN.min1, where it practically stabilizes. The tests performed in n-IIT and m-IIT load scale showed contrasting behavior. The former showed no time effect whereas the latter did, even although a plateau was reached for load rates above 5000 mN.min1. It is thus
Fig. 2. Effect of loading rate on elastic modulus, and maximum depth for PVDF by n-IIT.
Fig. 3. Effect of loading rate on elastic modulus and maximum depth measurements for PVDF by m-IIT.
hypothesized that the phenomenon controlling the process is the combination of distinct flow volumes associated with the stress field under the indenter, and the overall behavior can be represented as shown in Fig. 4. Fig. 4 can be explained as follows: for very small load and load rates going up to 100 mN.min1, the plastically deformed volume is very small and is constrained by the surrounding elastic field, both similar in magnitude. The deformation is accommodated by elastic expansion of the surrounding material following Johnson’s model for onset of plastic yield of inelastic solids [18]. In a viscoelastic material, the beginning of the plastic deformation is the result of chain movements located in the amorphous region (higher free volume) and is constrained by the crystalline phase, which acts as the elastic part of the system. The amorphous phase is in fact quite sensitive to localized shear stresses and, as Eyring theory suggests [19], an increase in the applied stress causes a localized temperature build up and results in reduction of the viscosity in this small flow volume. The measured reduction of the elastic modulus for PVDF at these load levels should be expected because it has a Tg ¼ 40 C and approximately 60% of amorphous phase,
Fig. 4. Proposed elastic modulus behavior as a function of loading rate for as processed PVDF.
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which may in fact be even higher and much less constrained because of its near surface location. It can thus be inferred that the mechanical response of thermoplastic materials is very sensitive to the local phases present when the stress/strain field is of the same order of magnitude as the Eyring flow volume. In such cases, the local phase behavior is greatly reflected both by the high modulus measured for the lowest load, which can represent the crystalline phase, and by the abrupt drop in modulus caused by reduced viscosity. The viscosity reduction can also be attested by the indentation depth, which increases as the load rate increases, making creep flow easier due to viscosity reduction. The contribution of the compressive hydrostatic pressure under the indenter in this load (load rate) scale is nil, yielding a shear activated rate process acting on a small volume reducing its viscosity. A smaller load corresponds to a smaller resulting shear and a lower viscosity drop. Tang et al. [9] have also reported similar behavior with PMMA, PVDF and epoxy. They reported an increase in plasticity with load rate for nano-scale IIT experiments. The authors proposed that as the yield is a thermally activated process, flow volume controls the deformation process and plasticity was increased because of local heating generated during deformation, as stated by Eyring. Nevertheless, in n-IIT, as load and load rate increases from 150 to 1000 mN.min1, the flow volume increases and controls the yielding process, where a cooperative motion of the phases present is required. Heating is still generated by local shear stress, but its effect on viscosity is significantly reduced because the amorphous phase is constrained by both the incipient hydrostatic stress at the core (underneath the intender) and the crystalline phase. Additionally, the stress field is composed of an almost plain strain at the core and plane stress at the small elasticplastic region. This combination results in the practical stabilization of the elastic modulus from 150 to 314 mN.min1 (Fig. 2), with a strong reduction of the indenter depth rate. This behavior is expected to occur up to approximately 1000 mN.min1. In this load (load rate) scale, as the load increases, the flow volume enlarges, as does the compressive hydrostatic stress underneath the indenter and the hindrance of the elastic-plastic region, diminishing the shear activated rate process by constraining the low viscosity chain movement. Further increase in load or load rate will result in an upward inflection of the curve, and the material’s response should be the same as that observed for m-IIT (Fig. 4), where a new stress field is developed under the indenter. The m-IIT result (Fig. 3) shows the existence of three regimes: one up to 1000 mN.min1, where modulus increases very steeply; a second one from a 1000 to 5000 mN.min1, where the slope decreases gradually; and a third one above 5000 mN.min1, where it becomes stable. The indenter depth shows an inverse correspondent behavior, deeper for low load rates and shallower as it increases, becoming practically stable above 5000 mN.min1. It is worth mentioning that the load applied in m-IIT is sixfold higher than the maximum load used in n-IIT, and the corresponding indentation depth is approximately 2.3 times greater. In this situation, a completely different stress
field must exist under the indenter, and this stress field must take into account the viscoelastic behavior measured. An elastic-viscoelastic-plastic indentation field is proposed, as shown schematically in Fig. 5, where the size and response of each region is determined by the load and load rate applied, as long as the load is high enough to produce this stress field (above 53 mN herein). This concept is an extension of elastic-plastic indentation proposed by Johnson [18]. For these load levels (or depths), the plastic flow volume increases considerably and embraces the plastic and viscoelastic regions, as schematically shown in Fig. 5. The phase distribution very close to the tip is diminished in importance, leading to the bulk behavior of the material taking over the process. Yielding is now dependent on large cooperative chain movements in the plastic and viscoelastic regions, the constraint imposed by the stress fields and the relaxation time in the viscoelastic region. For the mIIT load and load rates up to 1000 mN.min1, a rapid increase in modulus and decrease in indentation depth is observed, which can be accounted for by the reduction of the relaxation time as load rate increased, and the viscoelastic-plastic boundary moves toward the core, reducing the size of the plastic radius. This agrees well with the known increase in the elastic modulus and yield strength as stress rate is increased [20,21], and deformation is still affected by the shear component (deviatory stress). As the load rate increases to 5000 mN.min1, the viscoelastic region becomes constrained by the elastic and plastic boundaries to a limit of 5000 mN.min1, where chain movements end and yielding is equalized across the whole stress field so that the elastic modulus and depth are stable. In fact, the elastic modulus may be representative of the elastic behavior of the material without any viscous (shear) component, as a similar value was measured at the smallest load for n-IIT. The stabilization of the stress field was also demonstrated when the holding time effect on elastic modulus was observed to be constant, as shown below (item 3.3). Polymers show higher elastic modulus and yielding stress in compression than in tension [19], and compression should be used to better compare with values obtained by IIT because they are conducted under similar conditions,
Fig. 5. Schematic stress field region separation under the indenter tip.
G.L. Oliveira et al. / Polymer Testing 34 (2014) 10–16
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although the IIT state of stress has more constraint than uniaxial compression, where shear can largely contribute to plastic deformation. Fig. 5 also shows the result of the elastic modulus measured from a tensile test, where the load rate was 2,77E7 mN.min1 (similar to 50 mm/min), a condition where yielding is controlled by shear. The average value (1515 MPa) was in the same range as is proposed for the shear stress to be very influential in indentation tests. Thus, IITs conducted under conditions where shear is suppressed does not represent a common day-to-day application, and the higher modulus measured must be used very carefully. 3.3. Holding time effect on elastic modulus and hardness The evaluation of any material by the n-IIT or m-IIT technique must consider the “nose effect” on the loaddisplacement curve, which results in misleading information for the properties measured. This phenomenon has been well documented [6,22,23]. To avoid such a problem, the maximum load must be held long enough to minimize the creep phenomenon [6,11,24,25,26]. In polymers, the viscoelastic behavior must also be considered during the experimental procedure. However, the ideal hold time is not well established because the time-dependent properties are a function of the polymer and the test parameters used. In fact, several studies that adopt different holding times can be found in the literature, most of which were arbitrarily chosen. Koch and Seidler [27] and González et al. [28] tested a holding time of 30 s, Conté et al. [23] reported holding times of 100 s for PMMA; and Turnbull et al. [6] employed a holding time of 200 s for weathered unplasticized poly(vinyl chloride) (UPVC) and showed that the specific holding time may differ for each polymer. To evaluate the holding time condition, the load and unload rates were set to 600 mN.min1 because this condition resulted in comparable values for n-IIT, m-IIT and tension tests. Furthermore, this rate avoided overshoot at the maximum desired load. Fig. 6 shows the change in depth with the holding time at a constant maximum load of approximately 310 mN. The depth is seen to increase continuously with increase in the hold time of up to 150 sec, a common creep behavior, following which there is practically no change in depth. Nevertheless, a minimum hold period that does not influence the mechanical properties should be evaluated and defined. The creep rate calculated by Eq. 4 is presented in Fig. 7, which shows the primary and secondary creep. The figure indicates that the steady state was initiated at 90 s, with a strain rate of approximately 2 102 s1. The evaluation of the holding time on the m-IIT hardness (MH) and elastic modulus (EIT) calculated for each holding time depicted in Fig. 6 is presented in Fig. 8. A decrease of approximately 16% and 10%, were observed for MH and EIT, respectively, for holding times of up to 30 s. After 30 s, the elastic modulus stabilized and the influence of the creep effects on this property could be neglected. If the elastic modulus measurement is a reaction of the material to the indenter, the state of the stress under the indenter stabilizes at this period in time and the viscoelastic nature of the
Fig. 6. Curves of the change in depth as function of the holding time. Maximum load of 310 mN and loading rate of 600 mN.min1.
Fig. 7. Indentation penetration and the corresponding strain rate curves at the holding time up to 180 s for PVDF.
material ceases its effect, even though the indenter still penetrates the material, as shown in Fig. 6. Conversely, MH did not stabilize during the entire time period used here; it continually declined as the maximum depth increased, but the rate of decline decreased, as expected. Similar behavior
Fig. 8. Elastic modulus and micro-hardness as a function of hold time at the maximum load for PVDF.
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was also observed by Conté et al. [23] for poly(methyl methacrylate) (PMMA), an amorphous polymer. They suggested that 100 s would be sufficient to minimize the viscoelastic effect on this property. Here, two decay regimes were measured: the first reaches 30 s and shows a reduction of approximately 16%. In the second regime, the MH reduction is much lower, approximately 10%, for a hold time of 210 s. Although the influence of the holding time on MH is less significant in the second regime, the establishment of a defined time requires further evaluation. The present results for PVDF demonstrate that E can be considered to be a material property for a specific load rate if it reaches a constant value before reaching steady state creep. The hardness never reached a constant value, even during steady state creep. Experimentally, the use of two different holding times is very time consuming. Choosing between holding times of 30 and 40 s guaranteed a constant modulus and represented a good approach for MH for the present material. 4. Conclusions The instrumented indentation tests showed that characterization in the nano- and micro-load regimes did not lead to the same results. The former showed a decrease in the elastic modulus as the load rate increased, stabilized and then followed the same behavior as the m-IIT tests. It was suggested that this behavior is a consequence of the combination of distinct flow volumes associated with the stress field under the indenter. For nano scale loads, the small volume deformed is dominated by the shear stresses and local heating build up during deformation, thus leading to a viscosity decrease and subsequent drop in elastic modulus. When the volume under the indenter becomes large enough, an elastic-viscoelastic-plastic indentation field acts and a material’s response will depend on indentation parameters such as load and load or strain rate. The effect of the holding time on the elastic modulus and hardness showed that the former becomes constant and can be considered as a material property after 30 s, whereas the hardness continually decreases at decreasing rates. Steady state creep was noted to begin after 90 s, which is significantly after EIT reaches a constant value. In this situation, the elastic field beneath the indenter stabilizes very quickly for PVDF after 30 s. Acknowledgments This project was supported by CNPq and ANP-PRH 35. The authors would like to thank Prof. Carlos Maurício Lepienski (Nanomechanical Properties Laboratory of UFPR) for conducting nano-load scale tests. References [1] J.A. Brinell, in: II. Cong. Int. Méthodes d’Essai, Paris. For the first English account see A. Wahlberg (1901), J. Iron & Steel Inst.59, 243. Apud in D. Tabor, The Hardness of Metals, Oxford University Press, 1951.
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