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Irreversibly absorbed energy and damage in GFRP laminates impacted at low velocity
Composite Structures 93 (2011) 2853–2860
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Irreversibly absorbed energy and damage in GFRP laminates impacted at low velocity G. Caprino, V. Lopresto ⇑, A. Langella, M. Durante Department of Materials and Production Engineering, University of Naples ‘‘Federico II’’, Piazzale Tecchio 80, 80125 Naples, Italy
a r t i c l e
i n f o
Article history: Available online 25 May 2011 Keywords: Glass-fibre-reinforced plastics Impact Failure modes Absorbed energy
a b s t r a c t The scope of this paper was to establish a correlation between the damage occurring in a composite as a consequence of low-velocity impact and the energy dissipated during the impact phenomenon. To this aim, instrumented impact tests were carried out on glass fabric/epoxy laminates of three different thicknesses, using different energy levels. The irreversibly absorbed energy was obtained from the force–displacement curves provided by the impact machine. To assess damage progression as a function of impact energy, ply-by-ply delamination and fibre breakages revealed by destructive tests were measured. A previous model, based on energy balance considerations, was applied to interpret the experimental results, together with an original method of data reduction, allowing for the isolation of the maximum energy portion due to indentation and vibrational effects. From the results obtained, the contribution of fibre breakage and matrix damage to the irreversibly absorbed energy is comparable at low impact energies; with increasing initial energy levels, delamination becomes predominant in determining energy dissipation. However, the critical energy-release rate required to propagate delamination, as calculated from impact data, is considerably higher than the typical values deriving from Mode II delamination tests performed under laboratory conditions. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In the last decades, many researchers have studied the response of composite materials to impact, identifying the damage mechanisms occurring in the material [1–5], as well as their effect on residual properties [3,6,7]. Despite the experimental and analytical efforts, many questions remain unanswered. The complex interaction between the failure modes, influenced by a variety of parameters such as fibre and matrix type, reinforcement architecture, and constraint conditions, can be hardly predicted by analytical and numerical tools [8–10]. The same holds for the Compression After Impact (CAI) strength [7,11], one of the most important factors affecting design allowables. Another topic quite obscure at this time is the way through which the initial energy of the projectile is introduced into the target. In a non-perforating impact, a part of this energy is stored elastically, resulting in striker rebound, and can be easily measured. On the contrary, it is hard to understand the role played by the irreversibly absorbed energy, which is partially dissipated under form of heat and vibrations, but also contributes to damage development, determining fibre breakage, delamination, intralaminar
⇑ Corresponding author. E-mail address: [email protected] (V. Lopresto). 0263-8223/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2011.05.019
splitting, permanent indentation and fractures at the fibre–matrix interface. Recognizing the relative importance of the different phenomena taking place in the absorption of irreversible energy plays a fundamental role in the development of composite materials with improved impact resistance and tolerance. Some contribution to this topic has been given, among others, by Sutherland and Guedes Soares [12]. The authors demonstrated that the evolution of absorbed energy with increasing impact energy could reveal first fibre fracture. A more ambitious objective was pursued by Delfosse and Poursartip [13], who, using energy-balance considerations, attempted to quantify the relationship between damage mechanisms and energy absorption. In what follows, the main features of the model proposed by Delfosse and Poursartip are recalled, and some limitations in its applicability, supporting the present work, are emphasized. 2. Background and scopes In a perfectly elastic impact, the initial energy U is progressively transferred to the target, where is stored elastically, during the contact; when the maximum displacement has been achieved, the rebound phase begins, at the end of which the energy has been totally given back to the striker. Different authors have shown [1,14] that composite laminates approximately behave as perfectly
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elastic materials for very low values of U. Beyond a given threshold, some of the energy is lost, as witnessed by the difference in the loading and unloading curves, giving rise to an hysteresis loop. Delfosse and Poursartip [13] tried to identify the mechanisms of energy absorption in a laminate during low-velocity impact, correlating the energy loss with the observed failure modes. The authors speculated that the absorbed energy, Ua, has two components, one of which, Udam, is employed to create the damage, and the other, Udis, is dissipated because of vibrations, heat, inelastic behaviour of the projectile or the supports, and so forth:
U a ¼ U dam þ U dis
ð1Þ
There are three types of damage possibly occurring in a laminate subjected to impact, namely permanent indentation, matrix damage (encompassing delamination and intraply splitting), and fibre breakage. Indicating with Upi, Um, Uf the associated energies, respectively, Eq. (1) becomes:
U a ¼ U pi þ U m þ U f þ U dis
ð2Þ
On the other hand, if the total area of matrix damage, Am, and the total area of broken fibres, Af, are known, it can be put:
U m ¼ G m Am
ð3Þ
U f ¼ Gf Af
ð4Þ
where Gm, Gf, are the energies required to create a unit damage area in the matrix and fibre, respectively. Taking into account Eqs. (3) and (4), Eq. (2) can be written as:
U a ¼ U pi þ Gm Am þ Gf Af þ U dis
ð5Þ
To assess their model, Delfosse and Poursartip [13] carried out impact tests at different energy levels on two CFRP laminates, one of which (based on an IM6/937 material system) characterized by a brittle matrix, and the other (T800H/3900-2) consisting of a ductile matrix. To find Am, the total delaminated area was evaluated by pulse-echo ultrasonics combined with destructive inspection. The authors recognized that this area is not rigorously coincident with Am, since intraply cracks, not accounted for in simply measuring delamination, are also created during an impact phenomenon. However, as these cracks are hard to quantify, the assumption was accepted that their development proceeds proportionally to the delaminated area, so that the latter was considered as representative of Am. To evaluate Af, the impacted panels were thermally deplied after the resin was burnt off in a furnace. The total length lf of broken bundles revealed by visual inspection, measured perpendicular to the fibre direction, was recorded; then, the area of broken fibres was calculated by multiplying lf by the ply thickness. Delfosse and Poursartip used three-point bending tests to directly estimate Gf. Measuring Gm was quite laborious, involving the selection of a range of impact energies giving rise uniquely to delamination damage, without fibre breakage. Within this range, Gm was obtained from the slope of the straight line correlating Ua and Am. Unfortunately, the range of energies allowing only delamination in the tough laminate was small (about 4.5 J), resulting in accuracy problems when Gm for the T800H/3900-2 system was determined. Having available Am, Gm, Af, Gf, Eq. (5) was used in [13] to calculate the absorbed energy deriving from matrix and fibre failure, and compared with the total absorbed energy. It was concluded that the contribution of the quantity (Upi + Udis) to Ua is negligible. It is natural to think that the energy window within which only matrix damage is encountered will become smaller and smaller as far as tougher resins are concerned, since increasing toughness delays delamination initiation. Consequently, the difficulty of measuring Gm and Gf from impact test data for the most recent resin
systems is apparent. Furthermore, evaluating Gm from the Ua–Am diagram built on the basis of impact results conceivably yields a value in excess of the actual value, since the energy portions lost for indentation and other dissipative phenomena are implicitly attributed to delamination. Indeed, Delfosse and Poursartip found Gm = 0.8 kJ/m2 and Gm = 5.0 kJ/m2 for the brittle and the tough system, respectively, whereas their GIIc counterparts obtained from quasi-static fracture toughness experiments were 0.75 kJ/m2 and 2.0 kJ/m2. The large difference between Gm and GIIC for the tough resin suggested that in this case other damage mechanisms, not caught by the measured delaminated area, could contribute significantly to energy absorption. The main scope of the present work was to assess a method of data reduction able to overcome the difficulties previously highlighted. To this aim, Eq. (5) can be written under the form:
U a Gm Am ðU pi þ U dis Þ ¼ Gf Af
ð6Þ
or, alternatively:
U a Gf Af ðU pi þ U dis Þ ¼ Gm Am
ð7Þ
If (Upi + Udis) is disregarded, Eqs. (6) and (7) become:
U a Glm Am ¼ Guf Af Ua
Glf
Af ¼
Gum
Am
ð8Þ ð9Þ
where the index ‘‘u’’ (‘‘l’’) affecting Gf (Gm) designates an upper (lower) bound value. From Eqs. (8) and (9), plotting Af (Am) against the term on the left side should result in a straight line of slope Guf Gum passing through the origin, provided the correct value is adopted for Glm Glf . Therefore, a tentative value for this quantity can be assumed, suitably changing it until the best-fit straight line fitting the experimental data actually follows the expected trend. Of course, this can be made whichever the state of damage occurring in the specimens tested. Obviously, a lower limit of the absorbed energy, Uamin, can be calculated as:
U a min ¼ Glm Am þ Glf Af
ð10Þ
so that the maximum energy associated with phenomena other than fibre and matrix damage, (Upi + Udis)max, can be easily estimated:
ðU pi þ U dis Þmax ¼ U a U a min
ð11Þ
which, taking into account Eqs. (8)–(10), yields:
ðU pi þ U dis Þmax ¼ Guf Glf Af ¼ Gum Glm Am
ð12Þ
3. Materials and test methods The laminates examined in this work were obtained from GFRP prepreg made of plain-weave E-glass fabric 295 g/m2 in areal weight and Cycom 7701 epoxy resin. Square panels 330 330 mm2 were fabricated and cured under press for 2 h at 120 °C temperature and 0.1 MPa pressure. The stacking sequence adopted was [(0, 90)n/(+45, 45)n]s, with n = 1–3, and the corresponding nominal thicknesses t were in the range 0.96–2.88 mm. From the plates, square specimens 70 70 mm2 were cut by a diamond saw. The low-velocity impact tests were carried out in a Ceast MK4 instrumented testing machine, equipped with a DAS 4000 digital acquisition system. The samples were simply supported on a steel plate with a circular opening 50 mm in diameter, and struck at their centre using a cylindrical steel striker with a hemispherical nose 19.8 mm in diameter. To prevent multiple
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impacts, the striker was caught on the rebound by a brake available in the test apparatus. A first series of tests, aiming to obtain the Force–displacement (F–d) curve up to perforation, was carried out using a mass M = 10.6 kg falling from 1 m height. From the F–d curves recorded for each panel thickness, four characteristic energy levels were selected, as better specified in the discussion of the results. In the second series of tests, devoted to non-perforating impact, the four energy levels previously chosen were reproduced by suitably combining the drop height and three masses (M = 3.6, 5.6, 7.6 kg) available in the testing machine. In all, three to six impact tests were performed for each experimental condition. After impact, the extent of the projected delaminated area was obtained exploiting the translucent appearance of the material: the damage zone was highlighted by an intense light source put on the back of the specimens, and photographed; then, the damage area was measured by an image analyzer. In order to study the ply-by-ply damage extent and type, a small hole 1 mm in diameter was drilled in correspondence of the impact point of selected specimens, which were immersed in black ink. The scope of the hole was to ease the penetration of the liquid into the interlaminar cracks. The samples were held in the liquid bath until the projected delaminated area was completely darkened by the ink; then, they were dried for a suitable time, and carefully deplied with the help of moderate heating; finally, the delaminated area in correspondence of each interlaminar surface was measured, and the in-plane length of broken fibres within each ply was evaluated by optical microscopy at low magnification, following the procedure adopted by Delfosse and Poursartip [13]. 4. Results and discussion 4.1. Impact curves and associated parameters Typical impact curves recorded during the perforation tests, obtained for the three panel thicknesses adopted, are collected in Fig. 1. Of course, for a fixed displacement, an increase in panel thickness t results in an increase in the contact force. However, irrespective of t, all the F–d curves reveal common features. At low displacement, the material behaviour is substantially linear elastic, and disturbed by oscillations the more marked, the thicker the panel is. Only in the case of the thinnest laminate, an increase in slope, due to the well-known membrane effects [15,16], is clearly observable.
Fig. 1. Typical force–displacement curves recorded during the perforation tests.
Beyond a given load level, approximately identified by the arrows in the figure, a loss in rigidity, conceivably indicating damage developing in the material, is recorded. Nevertheless, the general trend of the contact force continues to increase up to its maximum value. Around the peak load, dramatic load drops, suggesting major damage, are found, with the F–d curve flattening out. Finally, the force begins to smoothly decrease, until the perforation process is completed. The end of perforation is approximately indicated by the black circles in Fig. 1. Beyond this point, the cylindrical part of the striker slides against the sides of the hole formed in the material, contributing to further energy dissipation. From the F–d curves collected in the perforation tests, the energy in correspondence of the arrows in Fig. 1, conventionally labelled as ‘‘first failure energy’’ hereafter, and indicated by the symbol Ui, was evaluated for each panel thickness (Table 1). The open circles in Fig. 1 identify the energy levels used in the non-perforating tests, specified in Table 2. It can be noted that the first energy level was in between Ui and the energy corresponding to the peak load, whereas the others covered a sufficiently large portion of the whole F–d curve. In Fig. 2, different F–d curves, deriving from impact tests performed at different energy levels (i.e. different velocities), are superposed. The superposition is good, indicating absence of evident viscoelastic effects on the contact history. This is expected, because the velocities used in the experimental campaign were within a sufficiently narrow range, varying from 1.3 to 3.8 m/s.
Table 1 First failure energy Ui (given from the F–d curve), limit impact energy Uo (from the absorbed energy results), threshold energy for matrix damage Uom (from the damage data), and threshold energy for fibre breakage Uof (from the damage data) for the different thicknesses t tested. The values in parentheses denote standard deviation. t (mm)
Ui (J)
Uo (J)
Uom (J)
Uof (J)
0.96 1.92 2.88
1.16 (0.09) 2.16 (0.62) 4.90 (0.17)
1.07 2.54 4.23
1.19 3.63 4.17
0.58 1.93 4.86
Table 2 Energy levels U (J) adopted in the non-perforating impact tests. t (mm)
0.96 1.92 2.88
Energy level 1
2
3
4
3.1 4.1 12.0
4.7 6.8 24.0
7.8 11.7 35.8
10.4 20.3 40.5
Fig. 2. Typical force–displacement curves recorded during the tests at increasing energy levels, U. Panel thickness t = 0.96 mm.
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Due to the insensitivity of the F–d curve to velocity, the different tests will be designated referring uniquely to the energy level in what follows. In doing this, it will be implicitly assumed that also the failure modes are uniquely affected by energy. As usual, Ua was evaluated from the area enclosed within the loading–unloading F–d curves recorded during the non-perforating impact tests. The results are graphically shown in Fig. 3, where Ua is plotted versus the impact energy U. From the vertical bars affecting the symbols, denoting standard deviation, the scatter in the experimental data is quite low. The absorbed energy is linearly correlated with U, as witnessed by the best-fit straight lines fitting the experimental points, whose minimum coefficient of correlation was R2 = 0.999. Moreover, the slope of these straight lines slightly decreases when the panel thickness increases (being 1.0, 0.98, and 0.96 for t = 0.96, 1.92, and 2.88 mm, respectively), but remains very close to unity, as apparent from the comparison with the dashed line in Fig. 3, having equation U = Ua. Indicating by Uo the limit energy given by the intercept of each straight line with the x-axis, it is inferred that almost all the impact energy exceeding Uo will be lost. The Uo values, calculated from the results in Fig. 3, are shown in the third column of Table 1. Notably, Uo is very close to Ui. Taking into account the scatter affecting the data, the most significant difference is found for t = 2.88 mm, and is probably attributable to the oscillations affecting the F–d curves of the thickest panels, which render difficult the identification of the exact point where the first deviation from linearity happens. Accepting that Uo = Ui, it is concluded that, until no failures occur, all the energy is stored as elastic within the material; from the first failure in advance, the remaining energy is irreversibly absorbed. This qualitatively compares with the findings of Delfosse and Poursartip [13], who showed that the elastic portion of energy is nearly constant over a wide range of impact energies. Sutherland and Guedes Soares [12] carried out low-velocity impact tests on GFRP laminates made of different woven roving architectures, thicknesses, and resins. When the absorbed energy was plotted against U, a linear trend similar to the one found in Fig. 3 was observed for sufficiently high values of U. However, at lower impact energies a new straight line, characterized by a lower slope, was necessary to effectively fit the experimental data. By analyzing the failure modes, the authors concluded that the point of intersection of the two straight lines coincided with the onset of fibre damage, which was delayed with respect to delamination. These results suggest that the straight lines in Fig. 3 might lose their validity below the threshold energy for fibre failure. In this work, no experimental data were generated within this field. However, the analysis of the failure modes observed, illustrated in what follows,
Fig. 3. Absorbed energy, Ua versus impact energy, U.
indicates that this is probably not the case for the material system examined in this work. 4.2. Damage In Fig. 4, a typical picture of the damage visually observed after impact is shown. The figure refers to the back face of the panel, where visible damage attained its maximum dimensions. A diamond-shaped delaminated area, with the axes coinciding with the warp–weft directions of the surface fabric layer (horizontal and vertical directions in the figure) is clearly visible. Besides, fibre fracture occurs along two lines of length slightly lower than the major axes of delamination. Observing Fig. 4, other cross fibre failures, occurring in the internal layers oriented at 45°, are also perceived, together with a darker area fully contained in the projected delamination, suggesting multiple delaminations developing along the thickness. The length of the major axes of the projected delamination increased with increasing impact energy and, for a given energy, was larger for thinner laminates; its maximum value, found for t = 2.88 mm, was about 40 mm, so that no interference of the damage with the supports was found in all the tests performed. In Fig. 5, two typical damage features revealed by the ply-by-ply analysis are shown. Depending on the layer position, large delaminated areas, eventually accompanied by fibre breakages, were discovered at specific interfaces (Fig. 5a). In other cases (Fig. 5b), the area of matrix damage was much narrower, extending only few millimetres around the zone of broken fibres, and consisting of finely dispersed intralaminar cracks. The total delaminated area Am was determined as the sum of all the dark areas evidenced by the black ink (see Fig. 5a) after deplying, which were measured by an image analyzer. To account in some way of the intralaminar cracks, also the extent of the black areas as those visible in Fig. 5b was included in the estimation of Am. The lines along which the fibre breakage proceeded in a single layer where very well highlighted by the black ink (see Fig. 5). To evaluate Af, the length of these lines in each ply was measured, and the total length lf was obtained by summation; then, the equivalent reinforcement thickness tf = 0.116 mm of the single ply was estimated from its areal weight (295 g/m2), assuming a fibre density cf = 2.55 g/cm3; finally, Af was calculated as tf times lf. Generally, the damage development in a composite laminate subjected to a concentrated force is driven by intralaminar tensile
Fig. 4. Typical damage zone after impact. Panel thickness t = 1.92 mm. Impact energy U = 11.7 J. Back face.
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Fig. 5. Damage revealed by ply-by-ply analysis in the: (a) fourth layer and (b) last layer of a 2.88 thick laminate. Impact energy U = 40.5 J.
and shear cracks occurring in the layers farther from and nearer to the contact point [17]. From these cracks, delaminations are generated at interfaces between plies with different orientations, mainly propagating in the direction of the fibres in the lower ply, and extending the more, the larger is their distance from the contact point. At sufficient high impact energies, fibre breakage follows. Delamination and broken fibres were found together in all the analyses performed in the present work. Nevertheless, some of the previous features were clearly recognized in the thinnest laminates tested. In fact (Fig. 6), no delamination was discovered at the interface between layers having ±45 orientation (indicated as 45/ 45 in the figure), even when the energy level was 10.4 J, very close to perforation (see Fig. 1). Furthermore, the extent of delamination was larger near to the back face (on the right in Fig. 6) than to the contact point. The length of broken fibres (Fig. 7) increased steadily with increasing U, as well as with approaching the back face of the panel. The length of the vertical bars in Figs. 6 and 7, representing standard deviation, is in general low, and only occasionally moderate, supporting the conclusions drawn. For t > 0.96 mm, the maximum delamination extent at low energies took place at the midplane, developing at the interface between layers with the same ±45 orientation, in agreement with the findings in [18,19]. This is shown in Fig. 8, where only the experimental points associated to the maximum and minimum impact energies have been collected, to avoid crowding of data. Minor delaminations were found within the ±45 block, and at the 0/45 interfaces. When the impact energy was increased, the delaminations located at interfaces between plies with different orientations grew at a faster rate than the others. Consequently, the largest
Fig. 7. Typical trend of the ply-by-ply broken fibre length, lf, in the 0.96 mm thick laminate with increasing impact energy, U.
Fig. 8. Typical trend of the ply-by-ply delaminated area, Am, in the 2.88 mm thick laminate with increasing impact energy, U.
Fig. 6. Typical trend of the ply-by-ply delaminated area, Am, in the 0.96 mm thick laminate with increasing impact energy, U.
delamination extent was found at the 45/0 interface when the maximum U value was adopted. A remarkable feature, emerging from Fig. 9, concerns the development of fibre breakage in the laminates with t > 0.96 mm. For the lowest impact energy level, major fibre damage was discovered in the front and back laminae, gradually decreasing towards the internal layers, and typically becoming nil in a block of layers located near the front face of the specimen (see arrows in Fig. 9). This suggests two independent fracture processes, one induced by the local compression stresses at the striker-panel contact point, and the other caused by the tensile stresses deriving from laminate
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Fig. 9. Typical trend of the ply-by-ply broken fibre length, lf, in the 2.88 mm thick laminate with increasing impact energy, U.
bending. Some support to this interpretation is given by the microscopic observation of two reinforcement bundles, shown in Fig. 10. The first bundle (Fig. 10a) was located in the top layer of the laminate, directly in contact with the loading nose, whereas the other (Fig. 10b) pertained to the bottom layer, stressed in tension during panel bending. The tensile stresses arising during impact result in a single fracture surface (see arrow in Fig. 10b), crossing the entire fibre bundle. On the contrary, multiple fibre crushing, randomly spaced along the fibre length (some of which are indicated by arrows in Fig. 10a) and conceivably induced by local compression stresses, is present near the striker-material contact point. Of course, the latter figure generates numerous fracture surfaces, which are not taken into account when Af is evaluated through the method adopted in this work. With increasing energy, the ply-by-ply length of broken fibres in Fig. 9 tends to exhibit a more and more uniform distribution along the laminate thickness, except in the ±45 layer nearest to the back face, in which lf attains its maximum value. In Fig. 11, the variation of total delaminated area (black symbols) and total area of broken fibres (open symbols) with increasing impact energy is plotted for all the thicknesses studied. In general, the scatter in the data, represented by the vertical bars (denoting standard deviation), tends to increase with increasing
Fig. 11. Total delaminated area, Am, and total area of broken fibres, Af, versus impact energy, U.
both t and the energy level. However, the relationship between U and the damage parameters is sensibly linear, as indicated by the best-fit straight lines fitting the experimental points, whose minimum coefficient of correlation was R2 = 0.97. A linear increase of the damage parameters with U was also observed by previous researchers [13,20]. The intercept of each of the straight lines in Fig. 11 with the xaxis can be interpreted as the threshold energy necessary to initiate the damage mode considered. The values of these threshold energies are collected in the last two columns in Table 1, designated by the symbols Uof, Uom, where the indexes ‘‘m’’, ‘‘f’’ distinguish matrix and fibres, respectively. From Table 1, the impact energy determining first failure depends to some extent on the method used to evaluate it. However, in the light of the scopes of the present work, it is important to note that the experimental window of impact energies within which only fibre breakage, or only matrix damage, is likely to occur is very narrow, rendering impracticable the procedure followed by Delfosse and Poursartip [13] to calculate the unit energies Gm, Gf. The closeness of Uof to Uom probably explains why the bi-linear trend correlating U and Ua, observed by Sutherland and Guedes Soares [12], was absent in the data in Fig. 3.
Fig. 10. Microscopic view of two reinforcement bundles, located in: (a) the top layer and (b) the bottom layer of a 2.88 mm thick panel. Impact energy U = 12.0 J.
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4.3. Mechanisms of energy absorption In order to determine the upper and lower bound values for Gm, Gf using Eqs. (8) and (9), the experimental results were arranged according to the diagrams in Figs. 12 and 13, where different symbols denote the different panel thicknesses. Using the method of data reduction previously illustrated, the best-fit straight lines shown in the figures were drawn through all the data points. Indeed, despite some scatter mainly affecting the data in Fig. 12, the straight lines fit reasonably well the experimental trends, supporting the applicability of the energy criterion proposed in [13]. The Guf ; Glf ; Glm ; Gum values obtained from Figs. 12 and 13 are collected in Table 3. In agreement with the findings of Delfosse and Poursartip [13], the unit energy associated with fibre breakage is far higher than its matrix counterpart. Nevertheless, the latter is notably (about five times) higher than usually measured in a Mode II delamination test for a tough resin [21]. It is difficult to say whether this is due to friction, or other phenomena correlated with propagation rate under dynamic loads. Indeed, a further factor possibly affecting accuracy in evaluating the unit energies is the method adopted to measure Af, which, as noted previously, is not able to represent the multiple, finely dispersed fracture surfaces created by fibre crushing underneath the point of contact between striker and target (Fig. 10a). The importance of this factor is expected to be
Table 3 Upper and lower bound values of the unit energies for matrix damage and fibre breakage. Guf ðkJ=m2 Þ
Glf ðkJ=m2 Þ
Gum ðkJ=m2 Þ
Glm f ðkJ=m2 Þ
131.0
126.3
10.1
10.4
Fig. 12. Diagram for the calculation of the upper (lower) bound value of unit energy for fibre breakage (matrix damage).
the more relevant, the higher is the maximum contact force experienced during impact, which is responsible for the local contact effects. From Table 3, the difference between the upper and lower bound values of Gf, Gm is negligible. Of course, this indicates that the portion of energy dissipated in indentation and vibrations is low. For instance, using Eq. (12) and the values in Table 3, it is immediately found (Upi + Udis)max = 5.3 kJ/m2Af. The maximum Af value measured in this work (Fig. 11) was about 100 mm2, occurring when U = 40.5 J. Consequently, the maximum energy absorbed for indentation and vibrations was 0.53 J, approximately 1.3% of the impact energy. In fact, the maximum value of (Upi + Udis)max/U recovered in this work was 1.7%. Substituting in Eq. (8) (or, equivalently, Eq. (9)) the values in Table 3, Ua was calculated and compared with the measured values. The comparison is graphically shown in Fig. 14, where the theoretical values are indicated by Uacalc. Evidently, all the experimental points fall with good accuracy along the continuous straight line drawn in the figure, having slope 45°. From the unit energies Guf ; Glm in Table 3, it was possible to evaluate the energy portions absorbed by matrix and fibre for all the specimens subjected to the ply-by-ply analysis. The results are plotted in Fig. 15, where the continuous lines are best-fit secondorder polynomials, drawn to highlight the trend of the Um and Uf data points. From Fig. 15, Um grows at an increasing rate with increasing Ua, whereas the opposite occurs for Uf. As a consequence, up to Ua 10 J, both the mechanisms of matrix damage and fibre breakage contribute in a comparable way to energy absorption, while delamination becomes the more effective mechanism of energy absorption beyond this limit. When Ua 36 J, about 23 J (64%) are used for matrix damage, and 13 J (36%) for fibre breakage. Interestingly, this situation is opposite to the CFRP laminates examined in [13], where 70–74% of the absorbed energy was due to fibre damage, and the remaining energy to delamination. The meaning of the dashed lines in Fig. 15 is similar to that of the continuous lines, except for the fact that they were fitted through the data obtained using Glf ; Gum in Table 3. The data points
Fig. 13. Diagram for the calculation of the upper (lower) bound value of unit energy for matrix damage (fibre breakage).
Fig. 14. Calculated absorbed energy, Uacalc versus experimental absorbed energy, Ua.
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conditions; among other factors, the method adopted to measure the area of broken fibres might contribute to this result; at low impact energies, the energy dissipation due to matrix damage and fibre breakage is comparable; with increasing impact energy, matrix damage becomes predominant, accounting for more than 60% of the absorbed energy.
References
Fig. 15. Absorbed energy portions attributable to matrix (Um) and fibre (Uf) damage versus total absorbed energy, Ua.
are not shown for clarity. From Eq. (12), the importance of the energy absorbing mechanisms other than matrix damage and fibre breakage (represented by the vertical distance of each dashed line from the corresponding continuous line) is negligible.
5. Conclusions The damage induced in glass fabric/epoxy laminates of three different thicknesses by low-velocity impact tests carried out using various impact energy levels was studied, in order to find a correlation between absorbed energy and failure mechanisms. To interpret the experimental results, a model previously proposed by Delfosse and Poursartip [13], based on energy balance considerations, was used, together with an original method of data reduction, allowing for the estimation of the maximum energy expended in vibrations and indentation. From the results obtained, the main conclusions are as follows: vibrational effects and indentation play a negligible role in dissipating energy, since less than 2% of the impact energy is dissipated through these mechanisms; the energy required for the creation of a unit area of fibre breakage is an order of magnitude higher than its counterpart associated with matrix damage; the unit energy for matrix damage, as calculated from impact tests, is considerably larger than expected from the values obtained by delamination tests conducted under quasi-static
[1] Schoeppner G, Abrate S. Delamination threshold loads for low velocity impact on composite laminates. Composites Part A 2000;31:903–15. [2] Li CF, Hu N, Cheng JG, Fukunaga H, Sekine H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part II. Verification and numerical investigation. Composites Part A 2002;33:1063–72. [3] Davies GAO, Olsson R. Impact on composite structures. Aeronaut J 2004;108:541–63. [4] Baucom JN, Zikry MA. Low-velocity impact damage progression in woven Eglass composite systems. Composites Part A 2005;36:658–64. [5] David-West OS, Nash DH, Banks WM. An experimental study of damage accumulation in balanced CFRP laminates due to repeated impact. Compos Struct 2008;83:247–58. [6] Feraboli P, Kedward KT. Enhanced evaluation of the low-velocity impact response of composite plates. AIAA J 2004;42:2143–52. [7] Williams GJ, Bond IP, Trask RS. Compression after impact assessment of selfhealing CFRP. Composites Part A 2009;40:1399–406. [8] Donadon MV, Iannucci L, Falzon BG, Hodgkinson JM, Almeida SFM. A progressive failure model for composite laminates subjected to low velocity impact damage. Comput Struct 2008;86:1232–52. [9] Tita V, de Carvalho J, Vandepitte D. Failure analysis of low velocity impact on thin composite laminates: experimental and numerical approaches. Compos Struct 2008;83:413–28. [10] Lopes CS, Camanho PP, Gürdal Z, Maimí P, González EV. Low-velocity impact damage on dispersed stacking sequence laminates. Part II: Numerical simulations. Compos Sci Technol 2009;69:937–47. [11] Uda N, Ono K, Kunoo K. Compression fatigue failure of CFRP laminates with impact damage. Compos Sci Technol 2009;69:2308–14. [12] Sutherland LS, Guedes Soares C. Impact of low fibre-volume, glass/polyester rectangular plates. Compos Struct 2005;68:13–22. [13] Delfosse D, Poursartip A. Energy-based approach to impact damage in CFRP laminates. Composites Part A 1997;28A:647–55. [14] Lagace PA, Wolf E. Impact damage resistance of several laminated material systems. AIAA J 1995;33:1106–13. [15] Caprino G, Langella A, Lopresto V. Elastic behaviour of circular composite plates transversely loaded at the centre. Composites Part A 2002;33:1191–7. [16] Fan J, Cantwell WJ, Guan ZW. The low-velocity impact response of fiber-metal laminates. J Reinf Plast Compos 2011;30:26–35. [17] Abrate S. Impact on composite structures. Cambridge: Cambridge University Press; 1998. [18] Kaczmerek H. Ultrasonic detection of damage in CFRPs. J Compos Mater 1995;29:59–95. [19] Hosur MV, Murthy CRL, Ramamurthy TS, Shet A. Estimation of impact-induced damage in CFRP laminates through ultrasonic imaging. NDT&E Int 1998;31:359–74. [20] Cantwell WJ. Geometrical effects in the low velocity impact response of GFRP. Compos Sci Technol 2007;67:1900–8. [21] Kageyama K, Kimpara I, Ohsawa I, Hojo M, Kabashima S. Mode I and mode II delamination growth of interlayer toughened carbon/epoxy (T800H/3900-2) composite system. In: Martin RH, editor. Composite materials: fatigue and fracture, vol. 5. Philadelphia: ASTM STP 1110; 1994.
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Irreversibly absorbed energy and damage in GFRP laminates impacted at low velocity G. Caprino, V. Lopresto ⇑, A. Langella, M. Durante Department of Materials and Production Engineering, University of Naples ‘‘Federico II’’, Piazzale Tecchio 80, 80125 Naples, Italy
a r t i c l e
i n f o
Article history: Available online 25 May 2011 Keywords: Glass-fibre-reinforced plastics Impact Failure modes Absorbed energy
a b s t r a c t The scope of this paper was to establish a correlation between the damage occurring in a composite as a consequence of low-velocity impact and the energy dissipated during the impact phenomenon. To this aim, instrumented impact tests were carried out on glass fabric/epoxy laminates of three different thicknesses, using different energy levels. The irreversibly absorbed energy was obtained from the force–displacement curves provided by the impact machine. To assess damage progression as a function of impact energy, ply-by-ply delamination and fibre breakages revealed by destructive tests were measured. A previous model, based on energy balance considerations, was applied to interpret the experimental results, together with an original method of data reduction, allowing for the isolation of the maximum energy portion due to indentation and vibrational effects. From the results obtained, the contribution of fibre breakage and matrix damage to the irreversibly absorbed energy is comparable at low impact energies; with increasing initial energy levels, delamination becomes predominant in determining energy dissipation. However, the critical energy-release rate required to propagate delamination, as calculated from impact data, is considerably higher than the typical values deriving from Mode II delamination tests performed under laboratory conditions. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In the last decades, many researchers have studied the response of composite materials to impact, identifying the damage mechanisms occurring in the material [1–5], as well as their effect on residual properties [3,6,7]. Despite the experimental and analytical efforts, many questions remain unanswered. The complex interaction between the failure modes, influenced by a variety of parameters such as fibre and matrix type, reinforcement architecture, and constraint conditions, can be hardly predicted by analytical and numerical tools [8–10]. The same holds for the Compression After Impact (CAI) strength [7,11], one of the most important factors affecting design allowables. Another topic quite obscure at this time is the way through which the initial energy of the projectile is introduced into the target. In a non-perforating impact, a part of this energy is stored elastically, resulting in striker rebound, and can be easily measured. On the contrary, it is hard to understand the role played by the irreversibly absorbed energy, which is partially dissipated under form of heat and vibrations, but also contributes to damage development, determining fibre breakage, delamination, intralaminar
⇑ Corresponding author. E-mail address: [email protected] (V. Lopresto). 0263-8223/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2011.05.019
splitting, permanent indentation and fractures at the fibre–matrix interface. Recognizing the relative importance of the different phenomena taking place in the absorption of irreversible energy plays a fundamental role in the development of composite materials with improved impact resistance and tolerance. Some contribution to this topic has been given, among others, by Sutherland and Guedes Soares [12]. The authors demonstrated that the evolution of absorbed energy with increasing impact energy could reveal first fibre fracture. A more ambitious objective was pursued by Delfosse and Poursartip [13], who, using energy-balance considerations, attempted to quantify the relationship between damage mechanisms and energy absorption. In what follows, the main features of the model proposed by Delfosse and Poursartip are recalled, and some limitations in its applicability, supporting the present work, are emphasized. 2. Background and scopes In a perfectly elastic impact, the initial energy U is progressively transferred to the target, where is stored elastically, during the contact; when the maximum displacement has been achieved, the rebound phase begins, at the end of which the energy has been totally given back to the striker. Different authors have shown [1,14] that composite laminates approximately behave as perfectly
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elastic materials for very low values of U. Beyond a given threshold, some of the energy is lost, as witnessed by the difference in the loading and unloading curves, giving rise to an hysteresis loop. Delfosse and Poursartip [13] tried to identify the mechanisms of energy absorption in a laminate during low-velocity impact, correlating the energy loss with the observed failure modes. The authors speculated that the absorbed energy, Ua, has two components, one of which, Udam, is employed to create the damage, and the other, Udis, is dissipated because of vibrations, heat, inelastic behaviour of the projectile or the supports, and so forth:
U a ¼ U dam þ U dis
ð1Þ
There are three types of damage possibly occurring in a laminate subjected to impact, namely permanent indentation, matrix damage (encompassing delamination and intraply splitting), and fibre breakage. Indicating with Upi, Um, Uf the associated energies, respectively, Eq. (1) becomes:
U a ¼ U pi þ U m þ U f þ U dis
ð2Þ
On the other hand, if the total area of matrix damage, Am, and the total area of broken fibres, Af, are known, it can be put:
U m ¼ G m Am
ð3Þ
U f ¼ Gf Af
ð4Þ
where Gm, Gf, are the energies required to create a unit damage area in the matrix and fibre, respectively. Taking into account Eqs. (3) and (4), Eq. (2) can be written as:
U a ¼ U pi þ Gm Am þ Gf Af þ U dis
ð5Þ
To assess their model, Delfosse and Poursartip [13] carried out impact tests at different energy levels on two CFRP laminates, one of which (based on an IM6/937 material system) characterized by a brittle matrix, and the other (T800H/3900-2) consisting of a ductile matrix. To find Am, the total delaminated area was evaluated by pulse-echo ultrasonics combined with destructive inspection. The authors recognized that this area is not rigorously coincident with Am, since intraply cracks, not accounted for in simply measuring delamination, are also created during an impact phenomenon. However, as these cracks are hard to quantify, the assumption was accepted that their development proceeds proportionally to the delaminated area, so that the latter was considered as representative of Am. To evaluate Af, the impacted panels were thermally deplied after the resin was burnt off in a furnace. The total length lf of broken bundles revealed by visual inspection, measured perpendicular to the fibre direction, was recorded; then, the area of broken fibres was calculated by multiplying lf by the ply thickness. Delfosse and Poursartip used three-point bending tests to directly estimate Gf. Measuring Gm was quite laborious, involving the selection of a range of impact energies giving rise uniquely to delamination damage, without fibre breakage. Within this range, Gm was obtained from the slope of the straight line correlating Ua and Am. Unfortunately, the range of energies allowing only delamination in the tough laminate was small (about 4.5 J), resulting in accuracy problems when Gm for the T800H/3900-2 system was determined. Having available Am, Gm, Af, Gf, Eq. (5) was used in [13] to calculate the absorbed energy deriving from matrix and fibre failure, and compared with the total absorbed energy. It was concluded that the contribution of the quantity (Upi + Udis) to Ua is negligible. It is natural to think that the energy window within which only matrix damage is encountered will become smaller and smaller as far as tougher resins are concerned, since increasing toughness delays delamination initiation. Consequently, the difficulty of measuring Gm and Gf from impact test data for the most recent resin
systems is apparent. Furthermore, evaluating Gm from the Ua–Am diagram built on the basis of impact results conceivably yields a value in excess of the actual value, since the energy portions lost for indentation and other dissipative phenomena are implicitly attributed to delamination. Indeed, Delfosse and Poursartip found Gm = 0.8 kJ/m2 and Gm = 5.0 kJ/m2 for the brittle and the tough system, respectively, whereas their GIIc counterparts obtained from quasi-static fracture toughness experiments were 0.75 kJ/m2 and 2.0 kJ/m2. The large difference between Gm and GIIC for the tough resin suggested that in this case other damage mechanisms, not caught by the measured delaminated area, could contribute significantly to energy absorption. The main scope of the present work was to assess a method of data reduction able to overcome the difficulties previously highlighted. To this aim, Eq. (5) can be written under the form:
U a Gm Am ðU pi þ U dis Þ ¼ Gf Af
ð6Þ
or, alternatively:
U a Gf Af ðU pi þ U dis Þ ¼ Gm Am
ð7Þ
If (Upi + Udis) is disregarded, Eqs. (6) and (7) become:
U a Glm Am ¼ Guf Af Ua
Glf
Af ¼
Gum
Am
ð8Þ ð9Þ
where the index ‘‘u’’ (‘‘l’’) affecting Gf (Gm) designates an upper (lower) bound value. From Eqs. (8) and (9), plotting Af (Am) against the term on the left side should result in a straight line of slope Guf Gum passing through the origin, provided the correct value is adopted for Glm Glf . Therefore, a tentative value for this quantity can be assumed, suitably changing it until the best-fit straight line fitting the experimental data actually follows the expected trend. Of course, this can be made whichever the state of damage occurring in the specimens tested. Obviously, a lower limit of the absorbed energy, Uamin, can be calculated as:
U a min ¼ Glm Am þ Glf Af
ð10Þ
so that the maximum energy associated with phenomena other than fibre and matrix damage, (Upi + Udis)max, can be easily estimated:
ðU pi þ U dis Þmax ¼ U a U a min
ð11Þ
which, taking into account Eqs. (8)–(10), yields:
ðU pi þ U dis Þmax ¼ Guf Glf Af ¼ Gum Glm Am
ð12Þ
3. Materials and test methods The laminates examined in this work were obtained from GFRP prepreg made of plain-weave E-glass fabric 295 g/m2 in areal weight and Cycom 7701 epoxy resin. Square panels 330 330 mm2 were fabricated and cured under press for 2 h at 120 °C temperature and 0.1 MPa pressure. The stacking sequence adopted was [(0, 90)n/(+45, 45)n]s, with n = 1–3, and the corresponding nominal thicknesses t were in the range 0.96–2.88 mm. From the plates, square specimens 70 70 mm2 were cut by a diamond saw. The low-velocity impact tests were carried out in a Ceast MK4 instrumented testing machine, equipped with a DAS 4000 digital acquisition system. The samples were simply supported on a steel plate with a circular opening 50 mm in diameter, and struck at their centre using a cylindrical steel striker with a hemispherical nose 19.8 mm in diameter. To prevent multiple
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impacts, the striker was caught on the rebound by a brake available in the test apparatus. A first series of tests, aiming to obtain the Force–displacement (F–d) curve up to perforation, was carried out using a mass M = 10.6 kg falling from 1 m height. From the F–d curves recorded for each panel thickness, four characteristic energy levels were selected, as better specified in the discussion of the results. In the second series of tests, devoted to non-perforating impact, the four energy levels previously chosen were reproduced by suitably combining the drop height and three masses (M = 3.6, 5.6, 7.6 kg) available in the testing machine. In all, three to six impact tests were performed for each experimental condition. After impact, the extent of the projected delaminated area was obtained exploiting the translucent appearance of the material: the damage zone was highlighted by an intense light source put on the back of the specimens, and photographed; then, the damage area was measured by an image analyzer. In order to study the ply-by-ply damage extent and type, a small hole 1 mm in diameter was drilled in correspondence of the impact point of selected specimens, which were immersed in black ink. The scope of the hole was to ease the penetration of the liquid into the interlaminar cracks. The samples were held in the liquid bath until the projected delaminated area was completely darkened by the ink; then, they were dried for a suitable time, and carefully deplied with the help of moderate heating; finally, the delaminated area in correspondence of each interlaminar surface was measured, and the in-plane length of broken fibres within each ply was evaluated by optical microscopy at low magnification, following the procedure adopted by Delfosse and Poursartip [13]. 4. Results and discussion 4.1. Impact curves and associated parameters Typical impact curves recorded during the perforation tests, obtained for the three panel thicknesses adopted, are collected in Fig. 1. Of course, for a fixed displacement, an increase in panel thickness t results in an increase in the contact force. However, irrespective of t, all the F–d curves reveal common features. At low displacement, the material behaviour is substantially linear elastic, and disturbed by oscillations the more marked, the thicker the panel is. Only in the case of the thinnest laminate, an increase in slope, due to the well-known membrane effects [15,16], is clearly observable.
Fig. 1. Typical force–displacement curves recorded during the perforation tests.
Beyond a given load level, approximately identified by the arrows in the figure, a loss in rigidity, conceivably indicating damage developing in the material, is recorded. Nevertheless, the general trend of the contact force continues to increase up to its maximum value. Around the peak load, dramatic load drops, suggesting major damage, are found, with the F–d curve flattening out. Finally, the force begins to smoothly decrease, until the perforation process is completed. The end of perforation is approximately indicated by the black circles in Fig. 1. Beyond this point, the cylindrical part of the striker slides against the sides of the hole formed in the material, contributing to further energy dissipation. From the F–d curves collected in the perforation tests, the energy in correspondence of the arrows in Fig. 1, conventionally labelled as ‘‘first failure energy’’ hereafter, and indicated by the symbol Ui, was evaluated for each panel thickness (Table 1). The open circles in Fig. 1 identify the energy levels used in the non-perforating tests, specified in Table 2. It can be noted that the first energy level was in between Ui and the energy corresponding to the peak load, whereas the others covered a sufficiently large portion of the whole F–d curve. In Fig. 2, different F–d curves, deriving from impact tests performed at different energy levels (i.e. different velocities), are superposed. The superposition is good, indicating absence of evident viscoelastic effects on the contact history. This is expected, because the velocities used in the experimental campaign were within a sufficiently narrow range, varying from 1.3 to 3.8 m/s.
Table 1 First failure energy Ui (given from the F–d curve), limit impact energy Uo (from the absorbed energy results), threshold energy for matrix damage Uom (from the damage data), and threshold energy for fibre breakage Uof (from the damage data) for the different thicknesses t tested. The values in parentheses denote standard deviation. t (mm)
Ui (J)
Uo (J)
Uom (J)
Uof (J)
0.96 1.92 2.88
1.16 (0.09) 2.16 (0.62) 4.90 (0.17)
1.07 2.54 4.23
1.19 3.63 4.17
0.58 1.93 4.86
Table 2 Energy levels U (J) adopted in the non-perforating impact tests. t (mm)
0.96 1.92 2.88
Energy level 1
2
3
4
3.1 4.1 12.0
4.7 6.8 24.0
7.8 11.7 35.8
10.4 20.3 40.5
Fig. 2. Typical force–displacement curves recorded during the tests at increasing energy levels, U. Panel thickness t = 0.96 mm.
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Due to the insensitivity of the F–d curve to velocity, the different tests will be designated referring uniquely to the energy level in what follows. In doing this, it will be implicitly assumed that also the failure modes are uniquely affected by energy. As usual, Ua was evaluated from the area enclosed within the loading–unloading F–d curves recorded during the non-perforating impact tests. The results are graphically shown in Fig. 3, where Ua is plotted versus the impact energy U. From the vertical bars affecting the symbols, denoting standard deviation, the scatter in the experimental data is quite low. The absorbed energy is linearly correlated with U, as witnessed by the best-fit straight lines fitting the experimental points, whose minimum coefficient of correlation was R2 = 0.999. Moreover, the slope of these straight lines slightly decreases when the panel thickness increases (being 1.0, 0.98, and 0.96 for t = 0.96, 1.92, and 2.88 mm, respectively), but remains very close to unity, as apparent from the comparison with the dashed line in Fig. 3, having equation U = Ua. Indicating by Uo the limit energy given by the intercept of each straight line with the x-axis, it is inferred that almost all the impact energy exceeding Uo will be lost. The Uo values, calculated from the results in Fig. 3, are shown in the third column of Table 1. Notably, Uo is very close to Ui. Taking into account the scatter affecting the data, the most significant difference is found for t = 2.88 mm, and is probably attributable to the oscillations affecting the F–d curves of the thickest panels, which render difficult the identification of the exact point where the first deviation from linearity happens. Accepting that Uo = Ui, it is concluded that, until no failures occur, all the energy is stored as elastic within the material; from the first failure in advance, the remaining energy is irreversibly absorbed. This qualitatively compares with the findings of Delfosse and Poursartip [13], who showed that the elastic portion of energy is nearly constant over a wide range of impact energies. Sutherland and Guedes Soares [12] carried out low-velocity impact tests on GFRP laminates made of different woven roving architectures, thicknesses, and resins. When the absorbed energy was plotted against U, a linear trend similar to the one found in Fig. 3 was observed for sufficiently high values of U. However, at lower impact energies a new straight line, characterized by a lower slope, was necessary to effectively fit the experimental data. By analyzing the failure modes, the authors concluded that the point of intersection of the two straight lines coincided with the onset of fibre damage, which was delayed with respect to delamination. These results suggest that the straight lines in Fig. 3 might lose their validity below the threshold energy for fibre failure. In this work, no experimental data were generated within this field. However, the analysis of the failure modes observed, illustrated in what follows,
Fig. 3. Absorbed energy, Ua versus impact energy, U.
indicates that this is probably not the case for the material system examined in this work. 4.2. Damage In Fig. 4, a typical picture of the damage visually observed after impact is shown. The figure refers to the back face of the panel, where visible damage attained its maximum dimensions. A diamond-shaped delaminated area, with the axes coinciding with the warp–weft directions of the surface fabric layer (horizontal and vertical directions in the figure) is clearly visible. Besides, fibre fracture occurs along two lines of length slightly lower than the major axes of delamination. Observing Fig. 4, other cross fibre failures, occurring in the internal layers oriented at 45°, are also perceived, together with a darker area fully contained in the projected delamination, suggesting multiple delaminations developing along the thickness. The length of the major axes of the projected delamination increased with increasing impact energy and, for a given energy, was larger for thinner laminates; its maximum value, found for t = 2.88 mm, was about 40 mm, so that no interference of the damage with the supports was found in all the tests performed. In Fig. 5, two typical damage features revealed by the ply-by-ply analysis are shown. Depending on the layer position, large delaminated areas, eventually accompanied by fibre breakages, were discovered at specific interfaces (Fig. 5a). In other cases (Fig. 5b), the area of matrix damage was much narrower, extending only few millimetres around the zone of broken fibres, and consisting of finely dispersed intralaminar cracks. The total delaminated area Am was determined as the sum of all the dark areas evidenced by the black ink (see Fig. 5a) after deplying, which were measured by an image analyzer. To account in some way of the intralaminar cracks, also the extent of the black areas as those visible in Fig. 5b was included in the estimation of Am. The lines along which the fibre breakage proceeded in a single layer where very well highlighted by the black ink (see Fig. 5). To evaluate Af, the length of these lines in each ply was measured, and the total length lf was obtained by summation; then, the equivalent reinforcement thickness tf = 0.116 mm of the single ply was estimated from its areal weight (295 g/m2), assuming a fibre density cf = 2.55 g/cm3; finally, Af was calculated as tf times lf. Generally, the damage development in a composite laminate subjected to a concentrated force is driven by intralaminar tensile
Fig. 4. Typical damage zone after impact. Panel thickness t = 1.92 mm. Impact energy U = 11.7 J. Back face.
G. Caprino et al. / Composite Structures 93 (2011) 2853–2860
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Fig. 5. Damage revealed by ply-by-ply analysis in the: (a) fourth layer and (b) last layer of a 2.88 thick laminate. Impact energy U = 40.5 J.
and shear cracks occurring in the layers farther from and nearer to the contact point [17]. From these cracks, delaminations are generated at interfaces between plies with different orientations, mainly propagating in the direction of the fibres in the lower ply, and extending the more, the larger is their distance from the contact point. At sufficient high impact energies, fibre breakage follows. Delamination and broken fibres were found together in all the analyses performed in the present work. Nevertheless, some of the previous features were clearly recognized in the thinnest laminates tested. In fact (Fig. 6), no delamination was discovered at the interface between layers having ±45 orientation (indicated as 45/ 45 in the figure), even when the energy level was 10.4 J, very close to perforation (see Fig. 1). Furthermore, the extent of delamination was larger near to the back face (on the right in Fig. 6) than to the contact point. The length of broken fibres (Fig. 7) increased steadily with increasing U, as well as with approaching the back face of the panel. The length of the vertical bars in Figs. 6 and 7, representing standard deviation, is in general low, and only occasionally moderate, supporting the conclusions drawn. For t > 0.96 mm, the maximum delamination extent at low energies took place at the midplane, developing at the interface between layers with the same ±45 orientation, in agreement with the findings in [18,19]. This is shown in Fig. 8, where only the experimental points associated to the maximum and minimum impact energies have been collected, to avoid crowding of data. Minor delaminations were found within the ±45 block, and at the 0/45 interfaces. When the impact energy was increased, the delaminations located at interfaces between plies with different orientations grew at a faster rate than the others. Consequently, the largest
Fig. 7. Typical trend of the ply-by-ply broken fibre length, lf, in the 0.96 mm thick laminate with increasing impact energy, U.
Fig. 8. Typical trend of the ply-by-ply delaminated area, Am, in the 2.88 mm thick laminate with increasing impact energy, U.
Fig. 6. Typical trend of the ply-by-ply delaminated area, Am, in the 0.96 mm thick laminate with increasing impact energy, U.
delamination extent was found at the 45/0 interface when the maximum U value was adopted. A remarkable feature, emerging from Fig. 9, concerns the development of fibre breakage in the laminates with t > 0.96 mm. For the lowest impact energy level, major fibre damage was discovered in the front and back laminae, gradually decreasing towards the internal layers, and typically becoming nil in a block of layers located near the front face of the specimen (see arrows in Fig. 9). This suggests two independent fracture processes, one induced by the local compression stresses at the striker-panel contact point, and the other caused by the tensile stresses deriving from laminate
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Fig. 9. Typical trend of the ply-by-ply broken fibre length, lf, in the 2.88 mm thick laminate with increasing impact energy, U.
bending. Some support to this interpretation is given by the microscopic observation of two reinforcement bundles, shown in Fig. 10. The first bundle (Fig. 10a) was located in the top layer of the laminate, directly in contact with the loading nose, whereas the other (Fig. 10b) pertained to the bottom layer, stressed in tension during panel bending. The tensile stresses arising during impact result in a single fracture surface (see arrow in Fig. 10b), crossing the entire fibre bundle. On the contrary, multiple fibre crushing, randomly spaced along the fibre length (some of which are indicated by arrows in Fig. 10a) and conceivably induced by local compression stresses, is present near the striker-material contact point. Of course, the latter figure generates numerous fracture surfaces, which are not taken into account when Af is evaluated through the method adopted in this work. With increasing energy, the ply-by-ply length of broken fibres in Fig. 9 tends to exhibit a more and more uniform distribution along the laminate thickness, except in the ±45 layer nearest to the back face, in which lf attains its maximum value. In Fig. 11, the variation of total delaminated area (black symbols) and total area of broken fibres (open symbols) with increasing impact energy is plotted for all the thicknesses studied. In general, the scatter in the data, represented by the vertical bars (denoting standard deviation), tends to increase with increasing
Fig. 11. Total delaminated area, Am, and total area of broken fibres, Af, versus impact energy, U.
both t and the energy level. However, the relationship between U and the damage parameters is sensibly linear, as indicated by the best-fit straight lines fitting the experimental points, whose minimum coefficient of correlation was R2 = 0.97. A linear increase of the damage parameters with U was also observed by previous researchers [13,20]. The intercept of each of the straight lines in Fig. 11 with the xaxis can be interpreted as the threshold energy necessary to initiate the damage mode considered. The values of these threshold energies are collected in the last two columns in Table 1, designated by the symbols Uof, Uom, where the indexes ‘‘m’’, ‘‘f’’ distinguish matrix and fibres, respectively. From Table 1, the impact energy determining first failure depends to some extent on the method used to evaluate it. However, in the light of the scopes of the present work, it is important to note that the experimental window of impact energies within which only fibre breakage, or only matrix damage, is likely to occur is very narrow, rendering impracticable the procedure followed by Delfosse and Poursartip [13] to calculate the unit energies Gm, Gf. The closeness of Uof to Uom probably explains why the bi-linear trend correlating U and Ua, observed by Sutherland and Guedes Soares [12], was absent in the data in Fig. 3.
Fig. 10. Microscopic view of two reinforcement bundles, located in: (a) the top layer and (b) the bottom layer of a 2.88 mm thick panel. Impact energy U = 12.0 J.
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4.3. Mechanisms of energy absorption In order to determine the upper and lower bound values for Gm, Gf using Eqs. (8) and (9), the experimental results were arranged according to the diagrams in Figs. 12 and 13, where different symbols denote the different panel thicknesses. Using the method of data reduction previously illustrated, the best-fit straight lines shown in the figures were drawn through all the data points. Indeed, despite some scatter mainly affecting the data in Fig. 12, the straight lines fit reasonably well the experimental trends, supporting the applicability of the energy criterion proposed in [13]. The Guf ; Glf ; Glm ; Gum values obtained from Figs. 12 and 13 are collected in Table 3. In agreement with the findings of Delfosse and Poursartip [13], the unit energy associated with fibre breakage is far higher than its matrix counterpart. Nevertheless, the latter is notably (about five times) higher than usually measured in a Mode II delamination test for a tough resin [21]. It is difficult to say whether this is due to friction, or other phenomena correlated with propagation rate under dynamic loads. Indeed, a further factor possibly affecting accuracy in evaluating the unit energies is the method adopted to measure Af, which, as noted previously, is not able to represent the multiple, finely dispersed fracture surfaces created by fibre crushing underneath the point of contact between striker and target (Fig. 10a). The importance of this factor is expected to be
Table 3 Upper and lower bound values of the unit energies for matrix damage and fibre breakage. Guf ðkJ=m2 Þ
Glf ðkJ=m2 Þ
Gum ðkJ=m2 Þ
Glm f ðkJ=m2 Þ
131.0
126.3
10.1
10.4
Fig. 12. Diagram for the calculation of the upper (lower) bound value of unit energy for fibre breakage (matrix damage).
the more relevant, the higher is the maximum contact force experienced during impact, which is responsible for the local contact effects. From Table 3, the difference between the upper and lower bound values of Gf, Gm is negligible. Of course, this indicates that the portion of energy dissipated in indentation and vibrations is low. For instance, using Eq. (12) and the values in Table 3, it is immediately found (Upi + Udis)max = 5.3 kJ/m2Af. The maximum Af value measured in this work (Fig. 11) was about 100 mm2, occurring when U = 40.5 J. Consequently, the maximum energy absorbed for indentation and vibrations was 0.53 J, approximately 1.3% of the impact energy. In fact, the maximum value of (Upi + Udis)max/U recovered in this work was 1.7%. Substituting in Eq. (8) (or, equivalently, Eq. (9)) the values in Table 3, Ua was calculated and compared with the measured values. The comparison is graphically shown in Fig. 14, where the theoretical values are indicated by Uacalc. Evidently, all the experimental points fall with good accuracy along the continuous straight line drawn in the figure, having slope 45°. From the unit energies Guf ; Glm in Table 3, it was possible to evaluate the energy portions absorbed by matrix and fibre for all the specimens subjected to the ply-by-ply analysis. The results are plotted in Fig. 15, where the continuous lines are best-fit secondorder polynomials, drawn to highlight the trend of the Um and Uf data points. From Fig. 15, Um grows at an increasing rate with increasing Ua, whereas the opposite occurs for Uf. As a consequence, up to Ua 10 J, both the mechanisms of matrix damage and fibre breakage contribute in a comparable way to energy absorption, while delamination becomes the more effective mechanism of energy absorption beyond this limit. When Ua 36 J, about 23 J (64%) are used for matrix damage, and 13 J (36%) for fibre breakage. Interestingly, this situation is opposite to the CFRP laminates examined in [13], where 70–74% of the absorbed energy was due to fibre damage, and the remaining energy to delamination. The meaning of the dashed lines in Fig. 15 is similar to that of the continuous lines, except for the fact that they were fitted through the data obtained using Glf ; Gum in Table 3. The data points
Fig. 13. Diagram for the calculation of the upper (lower) bound value of unit energy for matrix damage (fibre breakage).
Fig. 14. Calculated absorbed energy, Uacalc versus experimental absorbed energy, Ua.
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conditions; among other factors, the method adopted to measure the area of broken fibres might contribute to this result; at low impact energies, the energy dissipation due to matrix damage and fibre breakage is comparable; with increasing impact energy, matrix damage becomes predominant, accounting for more than 60% of the absorbed energy.
References
Fig. 15. Absorbed energy portions attributable to matrix (Um) and fibre (Uf) damage versus total absorbed energy, Ua.
are not shown for clarity. From Eq. (12), the importance of the energy absorbing mechanisms other than matrix damage and fibre breakage (represented by the vertical distance of each dashed line from the corresponding continuous line) is negligible.
5. Conclusions The damage induced in glass fabric/epoxy laminates of three different thicknesses by low-velocity impact tests carried out using various impact energy levels was studied, in order to find a correlation between absorbed energy and failure mechanisms. To interpret the experimental results, a model previously proposed by Delfosse and Poursartip [13], based on energy balance considerations, was used, together with an original method of data reduction, allowing for the estimation of the maximum energy expended in vibrations and indentation. From the results obtained, the main conclusions are as follows: vibrational effects and indentation play a negligible role in dissipating energy, since less than 2% of the impact energy is dissipated through these mechanisms; the energy required for the creation of a unit area of fibre breakage is an order of magnitude higher than its counterpart associated with matrix damage; the unit energy for matrix damage, as calculated from impact tests, is considerably larger than expected from the values obtained by delamination tests conducted under quasi-static
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