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Dependency of dynamic interlaminar shear strength of composites on test technique used
Polymer Testing 42 (2015) 151e159
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
Dependency of dynamic interlaminar shear strength of composites on test technique used H.L. Gowtham, Jayaram R. Pothnis, G. Ravikumar, N.K. Naik* Aerospace Engineering Department, Indian Institute of Technology BombayPowai, Mumbai 400076, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2014 Accepted 18 January 2015 Available online 28 January 2015
Studies are presented on dependency of dynamic interlaminar shear (ILS) strength on the experimental technique used for a typical plain weave E-glass/epoxy composite. Dynamic ILS strength was determined based on two experimental techniques, namely torsional split Hopkinson bar (TSHB) apparatus using thin walled tubular specimens and compressive split Hopkinson pressure bar (SHPB) apparatus using single lap specimens. The results obtained from these techniques are compared. In general, it is observed that dynamic ILS strength for composites obtained by TSHB testing using thin walled tubular specimens is lower than the dynamic ILS strength obtained using single lap specimens in compressive SHPB. The issues involved in TSHB testing of thin walled tubular specimens made of composites are discussed and the reasons for reduced dynamic ILS strength using thin walled tubular specimens are highlighted. Finite element analysis (FEA) of thin walled tubular specimens made of composite and resin subjected to quasi-static torsional loading is presented. Using FEA results, the reasons for lower ILS strength of composite thin walled tubular specimens are substantiated. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Interlaminar shear strength High strain rate testing Thin walled tubular specimen Single lap specimen Finite element analysis
1. Introduction Laminated composites are widely used in many structural applications. Aerospace and automobile structures, windmills, defense equipment and ship hulls are typical examples. The wide usage of these materials is because of their unique architectural features, ease of handling, low fabrication cost and excellent mechanical properties. Laminated composites are orthotropic materials. These materials exhibit two types of shear properties, one along the plane of lamina, which is termed the in-plane shear and the other along the thickness of the laminate, which is termed the interlaminar shear (ILS). The ILS strength is one of the most important parameters in determining the ability of a composite material to resist delamination damage.
* Corresponding author. Tel.: þ91 22 2576 7114; fax: þ91 22 2572 2602. E-mail address: [email protected] (N.K. Naik). http://dx.doi.org/10.1016/j.polymertesting.2015.01.012 0142-9418/© 2015 Elsevier Ltd. All rights reserved.
Composites are subjected to a variety of loads during service life. These loads can be classified as quasi-static and dynamic. Material response varies significantly with quasistatic and dynamic loading conditions. Dynamic loading is also referred to as high strain rate loading. The relationship between the magnitude of the load applied and the time over which it acts plays an important role in deciding the system response. Response of laminated composites under high strain rate shear loading is an important engineering requirement. It is used in applications like composite shaft design and design of external panels of aircraft etc. In theory, mechanical properties of a material are unique. They should not change with the test technique or the specimen used. This behavior is observed in metals/ alloys as well as many the other materials. However, composites tend to display variations in dynamic interlaminar shear strength with the test technique employed. The focus of the present study is to establish the reasons for variation in dynamic ILS strength with the test
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technique used, and validate the reasons established with finite element analysis (FEA) simulation results. Studies are performed on a typical plain weave E-glass/epoxy composite. There are several methods for the determination of shear properties under dynamic loading [1]; those available for the evaluation of dynamic shear properties of composites are:
TSHB test [2e9]. Compressive SHPB test [10e14]. Tensile SHPB test [15]. Drop-weight test [16]. Hydraulic/Pneumatic machine test [17].
There are only limited studies on high strain rate ILS properties of composites. Leber and Lifshitz [3], Dai et al [4,5], Hu and Feng [6] and Naik et al [7] are among the few researchers who have studied ILS properties of composites on TSHB using thin walled tubular specimens. Researchers have also used single lap specimens for determining dynamic ILS properties of composites. Bouette et al [10], Dong and Harding [11] and Hallet et al [12,13] used compressive SHPB apparatus with single lap specimens for ILS characterization of composites. Apart from thin walled tubular specimens and single lap specimens, researchers have also used double lap specimens [18,19], V-notched specimens [20] and short beam specimens [21] to evaluate the dynamic shear properties of composites. However, TSHB testing with thin walled tubular specimens and compressive SHPB testing with single lap specimens are the most widely used techniques. In the present study, dynamic ILS strength for a typical plain weave E-glass/epoxy was evaluated on TSHB apparatus using thin walled tubular specimens, and compressive SHPB apparatus using single lap specimens. The results obtained are compared. The reasons for variation in dynamic ILS strength obtained from TSHB apparatus using thin walled tubular specimens and compressive SHPB apparatus using single lap specimens are considered. FEA of thin walled tubular specimens made of composite and resin subjected to quasi-static torsional loading is presented.
3. Specimen design and dimensions Specimens for the tests were made from plain weave Eglass/epoxy laminates. Balanced layers of thickness 0.25 mm were used for making the laminates. The laminates were made such that warp direction of all the layers was along direction 1 and fill direction of all the layers was along direction 2 (Figs. 1 and 2). Epoxy resin LY556 with hardener HY951 was used for making the laminates. The fiber volume fraction of the laminates was 0.54. 3.1. Thin wall tubular specimen A schematic arrangement of laminate configuration used for thin walled tubular specimen is presented in Fig. 1a. The axis of the specimen was along the thickness direction of the laminate. Thin walled tubular specimens with wall thickness (tS) of 3 mm and gage length (LS) of 3 mm were used. Other specimen dimensions were Di ¼ 10 mm, Do ¼ 16 mm and D ¼ 22 mm. The overall length of the specimens (L) was 9 mm and radius of edge, R, was 0.5 mm. For bonding the specimens to the incident and transmitter bars of the TSHB apparatus, Araldite adhesive was used with room temperature curing. Fig. 1b shows photograph of a fractured specimen tested on the TSHB apparatus. It can be seen that the fracture surface has a zigzag appearance. 3.2. Single lap specimen A schematic arrangement of laminate configuration and single lap specimen is shown in Fig. 2a. The dimensions of the specimen are: a ¼ 5 mm, b ¼ 27.5 mm and width (c) ¼ 20 mm, d ¼ 8.66 mm, e ¼ 12 mm. The axis of the specimen was along the warp direction (direction 1) of the laminate. Overall length, width and thickness of specimen were 51.5 mm, 20 mm and 10 mm, respectively. Loading was along direction 1 on the flat surfaces on either side of the specimen. Fracture plane area is ‘a x c’. Fig. 2b shows a photograph of a failed single lap specimen. It can be seen from the photograph that the fracture surface has a zigzag appearance. Specially designed specimen holders for specimen gripping in compressive SHPB apparatus can also be seen. Inner dimension of the fixture is 10 mm. For bonding the specimens to the fixture, Araldite adhesive was used with room temperature curing.
2. Test apparatus and calibration 4. Test methods TSHB apparatus [7,9,22] was used to evaluate dynamic ILS behavior of a typical plain weave E-glass/epoxy using thin walled tubular specimens. Compressive SHPB apparatus [10,11,23,24] was also used to evaluate dynamic ILS behavior of a typical plain weave E-glass/epoxy using single lap specimens. In both TSHB and compressive SHPB apparatus, strain gauges were mounted on the incident as well as the transmitter bar. The strain gauges were connected in half bridge configuration. Before the commencement of actual experiments, calibration was performed. Details regarding calibration of TSHB and compressive SHPB apparatus are presented in [9] and [23,24], respectively.
4.1. TSHB testing TSHB apparatus was used to evaluate the ILS properties of WF E-glass/epoxy thin walled tubular specimens [7]. Tests were carried out over a shear strain rate range of 192e457 per second with at least five specimens under identical test conditions. Signals from strain gauges mounted on the incident and transmitter bars of TSHB were obtained on an oscilloscope and are presented in Fig. 3. With the help of incident (I), transmitted (T) and reflected (R) strain gauge signals, torque histories of incident and transmitter bars were obtained. Starting with the signals
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Fig. 1. (a) Schematic arrangement of laminate and thin walled tubular specimen, TSHB testing, (b) Photograph of failed thin walled tubular specimen tested on THPB apparatuses.
and using one dimensional wave propagation theory [7,9], shear stress - shear strain plots were generated. A typical plot is shown in Fig. 4. Point ‘B’ indicates peak shear stress within the specimen, i.e., shear strength of the specimen. Point ‘P’ indicates end of rise time during TSHB testing (Fig. 3). It may be noted that intensity of transmitted pulse is less than the intensity of the sum of incident and reflected pulses (Fig. 3). This is because of stress wave attenuation within the specimen during TSHB testing. As a conservative estimate, transmitted signal data is considered for obtaining resultant shear stress e shear strain response. 4.2. Compressive SHPB testing Compressive SHPB apparatus was used to evaluate ILS properties of WF E-glass/epoxy single lap specimens [10]. Studies were carried out in an axial strain rate range of 300e1500 per sec. Experiments were performed on at least five specimens under identical test conditions. Signals from strain gauges mounted on the incident and transmitter bars of compressive SHPB apparatus were obtained on an oscilloscope and are presented in Fig. 5. Loading was along direction 1 on the flat surfaces of the specimen on either side. With the help of incident (I), transmitted (T) and reflected (R) strain gauge signals, force histories of incident
and transmitter bars were obtained. Starting with the signals and using one dimensional wave propagation theory, a stress-strain diagram (Fig. 6) was generated [23]. The cross sectional area of the specimen considered for determining the forces is “a x c” (Fig. 2a). 5. Results and discussion: experimental studies 5.1. TSHB testing A typical failed specimen during TSHB testing is shown in Fig. 1b. It was observed that the failure is along the mid span of the gage length. It is evident that the failure is by interlaminar fracture and confined to a very small region on a plane parallel to the reinforcement layers. This indicates that the specimen has not buckled and failure was under pure shear. The zigzag edge at the plane of failure of the specimen is due to the undulated nature of the woven fabric at the interface between the adjacent layers. On application of dynamic shear load on the TSHB apparatus, a finite time is taken for shear strain to attain a constant value, which is termed rise time [7]. End of rise time is represented by point P in Fig. 3. For the case considered, the rise time is 50 microseconds. Shear strain rate is nearly constant after point P is reached.
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Fig. 2. (a) Schematic arrangement of laminate and single lap specimen, compressive SHPB testing, (b) Photograph of failed single lap specimen with holders.
Fig. 4 presents the variation of shear stress with shear strain. The peak ILS stress is indicated by point B. The peak ILS stress is 25.1 MPa and the corresponding ultimate shear strain is 1.05%. The peak ILS stress indicates dynamic ILS strength of the material. Interlaminar shear strengths at different strain rates are presented for plain weave E-glass/epoxy in Table 1 and
Fig. 7. The data presented in Table 1 are averages of five test results. Studies were carried out in the strain rate range of 192e457 per sec. It can be observed that interlaminar shear strength is enhanced at high strain rate loading compared with that at quasi-static loading. Further, it can be observed that interlaminar shear strength increases with increasing strain rate within the range of strain rates considered (Table 1 and Fig. 7). For the typical plain weave E-glass/epoxy composite studied, the interlaminar shear strength enhancement at strain rate of 205 per sec is 32% compared to that at quasi-static loading. 5.2. Compressive SHPB testing As explained earlier, experimental studies were carried out on single lap specimens of WF E-glass/epoxy under high strain rate compressive loading for obtaining stress-
Fig. 3. High strain rate TSHB testing, strain gauge signals on oscilloscope, thin walled tubular specimen, Ѓ ¼ 205 per sec, WF E-glass/epoxy.
Fig. 4. Shear stress - shear strain plot, high strain rate TSHB testing, thin walled tubular specimen, Ѓ ¼ 205 per sec, WF E-glass/epoxy.
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Fig. 7. Shear strain rate versus interlaminar shear strength plot, TSHB testing, thin walled tubular specimen, WF E-glass/epoxy.
Fig. 5. High strain rate compressive SHPB testing, strain gauge signals on oscilloscope, single lap specimen, έ ¼ 455 per sec, WF E-glass/epoxy.
out in the axial strain rate range of 300e1500 per sec. It can be observed that ILS strength increases as the axial strain rate increases. Also, it can be inferred that the ILS strength is enhanced at high strain rate loading compared with that at quasi-static loading. It was also observed that, for single lap specimens, the failure occurred in the gage length region in a plane parallel to the axis of load application. 6. Comparison of experimental results
Fig. 6. Stress - strain plot, high strain rate compressive SHPB testing, single lap specimen, έ ¼ 455 per sec, WF E-glass/epoxy.
strain plots (Fig. 6). The peak ILS stress is 92 MPa and the corresponding ultimate axial strain is 6.1%. ILS stress was obtained by dividing the transmitted force by shear area given by “b x c” (Fig. 2a). Interlaminar shear strength at different high strain rates is presented for plain weave Eglass/epoxy in Table 2 and Fig. 8. The data presented in Table 2 are averages of five test results. Studies were carried
Table 1 Interlaminar shear strength of WF E-glass/epoxy under high strain rate loading using thin walled tubular specimens on TSHB apparatus. Shear strain rate, (per sec)
Shear strength, (MPa)
QS 192 205 325 352 457
19.0 25.0 25.1 25.1 27.3 30.7
Tables 1 and 2 present ILS strength of a typical plain weave E-glass/epoxy obtained by both the techniques. By comparing the results, it is evident that dynamic ILS strength of the typical plain weave E-glass/epoxy evaluated using single lap specimens is significantly higher than that obtained from thin walled tubular specimens. The range of ILS strength obtained using thin walled tubular specimens on TSHB is 25.0e30.7 MPa (Table 1), whereas the range of ILS strength obtained using single lap specimens on compressive SHPB is 87.0e98.0 MPa (Table 2). Figs. 7 and 8, also show that interlaminar shear strength obtained using single lap specimens on SHPB is significantly higher than that obtained using thin walled tubular specimens on TSHB, even at the same strain rate range, i.e., up to strain rate of 500 per sec. One of the fundamental assumptions in high strain rate shear characterization of materials using thin walled tubular specimens is uniform shear stress distribution in the specimen within the shear plane. This implies that the
Table 2 Interlaminar shear strength of WF E-glass/epoxy under high strain rate loading using single lap specimens on compressive SHPB apparatus. Axial strain rate, (per sec)
Shear strength, (MPa)
300 455 540 684 920 1020 1500
87 92 94 85 78 96 98
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Fig. 8. Axial strain rate versus interlaminar shear strength plot, compressive SHPB testing, single lap specimen, WF E-glass/epoxy.
interlaminar shear stress is uniform along the radial direction and along the circumferential direction as well as along the gage length. The focus of the further study is to look into these aspects for composite specimens as well as resin specimens. Leung [25] carried out an elastic-plastic stress analysis of aluminum thin-walled tubular specimens under torsional loading. He reported that flanges of the specimen remain elastic and there is uniform shear stress distribution along the gage length of the specimen. Leber and Lifshitz [3] carried out dynamic simulation of thin-walled tubular specimens using MSC/NASTRAN finite element code. They reported pure shear stress distribution in the fracture surface. They could also achieve relatively constant stress along the gage length of the specimen. Gilat and Cheng [26,27] performed time independent elasticeplastic finite element analysis of the quasi-static tests on 1100-O aluminum alloy thin walled tubular specimens using ABAQUS code. Loading was applied by fixing one end and rotating the other. They reported stress concentration near the curved boundary of the gage length and shear plane. They further reported variation in shear stress in radial and tangential directions in the fracture plane. In the interlaminar region, within the specimen gage length of thin walled tubular specimen, the induced shear stress may not be constant for composites. This is because
of the inherent nature of the fabric used and the material properties along different directions. Interlaminar shear stresses S13, S23 and Sq may not be the same. Here, suffixes 13, 23 and q refer to 13 plane, 23 plane and any other plane with an orientation of q. Fig. 9 presents a sectional view of a thin walled tubular specimen of laminated composite at a plane that is located at the middle of the gage length. The interlaminar stresses at points A, B, C and so on may not be the same at the fracture plane for composites because of different mechanical properties along the circumferential direction. On the other hand, the stresses at different locations on the fracture plane would be the same for isotropic materials. For composites, the induced interlaminar stresses would be different at different locations on the fracture plane leading to stress concentrations. The stress concentration on the fracture plane would lead to early interlaminar failure. The objective of the further study is to evaluate interlaminar shear stress variation for composite thin walled tubular specimens under torsional loading. The studies were carried out using ANSYS V.14.0 finite element analysis software under quasi-static torsional loading. The stress distribution is obtained along the radial direction, the circumferential direction as well as the gage length. The studies were carried out under quasi-static loading since the objective of the investigation is to assess possible stress concentration locations on the fracture plane within the thin walled tubular specimens under torsional loading. The variation in induced interlaminar shear stress in the fracture plane depicted in Fig. 9 arises because of variation in the stiffness co-efficients (Sij) of the materials in the circumferential direction. For isotropic materials, the Sij are the same throughout the circumference. For composites, Sij do not remain the same along the circumferential direction. The variation of Sij depends on the angular position of the points considered on the fracture plane. Variation of Sij can be found by multiplying the Sij matrix in the xy plane of the laminated composite with the 3D transformation matrix [28]. As Sij varies in the circumferential direction for composites, the induced interlaminar stress would not be uniform in the plane of fracture. This would lead to stress concentrations, resulting in early failure of the composite thin walled tubular specimens. 7. Finite element analysis
Fig. 9. Cross-section of composite thin-walled tubular specimen at the fracture plane.
To visualize the stress distribution in a typical thin walled tubular composite specimen under quasi-static torsional loading, FEA was carried out using ANSYS V.14.0 finite element analysis software. Modeling of the specimen was performed considering a wall thickness (tS) of 0.25 mm, gage length (LS) of 3 mm, flange thickness (tf) of 3 mm and overall length (L) of 9 mm. Meshing was done using eight noded solid brick elements with six degrees of freedom. The complete thin walled tubular specimen has 10281 elements and 12294 nodes in the meshed model. This was worked out based on convergence study. A unit moment (1 Nm) was applied about the axis of the specimen on one of the external faces of the specimen flange. Contact elements Conta-175 Tange170 was used to distribute the moment about the axis to
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the nodes on the external face of the specimen flange. Thus, uniform distribution of torque load was ensured. The other external face of the flange was constrained in all degrees of freedom. For comparison purpose, stress analysis was conducted on two meshed models. In the first model, isotropic (resin) material was considered. Such a model is referred to as isotropic model (Fig. 10a). In the second model, laminated composite (WF E-glass/epoxy) material was considered. Such a model is referred to as composite model (Fig. 10b). For the composite model, stiffness matrix for E-glass/epoxy composite at different locations was calculated from basic nine elastic properties [29] of the material. The stress distribution was obtained along the radial direction, the circumferential direction as well as the gage length.
7.1. Stress variation along radial direction Fig. 11a and b present the ILS stress variation along the radial direction for a resin specimen and composite specimen, respectively. For the resin specimen, ILS stress variation is presented from inner radius (ri) to outer radius (ro) in the gage length region. It may be noted that the radial stress is higher at the outer radius by 4.5% (Fig. 11a). This is valid for all the angular locations.
Fig. 11. Interlaminar shear stress variation along radial direction: (a) resin specimen, (b) WF E-glass/epoxy composite specimen.
For the composite specimen, ILS stress variation is presented from inner radius (ri) to outer radius (ro) in the gage length region. ILS stress variation depends upon the angular orientation. At 0 and 90 degree orientations, the ILS stress is marginally higher at inner radius compared to that at outer radius. On the other hand, at 45 degree orientation, ILS stress is higher at outer radius compared to that at inner radius. The maximum variation is at 45 degree orientation, up to 21.1% (Fig. 11b). 7.2. Stress variation along circumferential direction Fig. 12a and b present ILS stress variation along the circumferential direction for resin and composite specimens, respectively. There is no variation of ILS stress along the circumferential direction for the resin specimen at a given radius. For the composite specimen, there is variation of ILS stress with angular location at any given radius. This variation is minimal at inner radius, whereas it is predominant at outer radius. Further, ILS stress tends to increase from 0 to 45 degree and reduce from 45 to 90 degree orientation. The ILS stress variation between 0 to 45 degree locations at outer radius of the specimen at mid gage length is 25.8%. 7.3. Stress variation along gage length Fig. 10. Thin walled tubular specimen for TSHB testing: (a) FEA discretization for resin specimen, (b) FEA discretization of gage length of WF E-glass/ epoxy composite specimen.
Fig 13 presents ILS stress variation along the gage length for a WF E-glass/epoxy composite specimen. Stress is considerably lower in the flange region of the specimen.
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flange e gage length interface. This is due to abrupt change in specimen geometry. 7.4. Conclusions based on FEA From the FEA of isotropic and composite models, the following conclusions can be made. The ILS stress is marginally higher at outer radius compared to that at inner radius for isotropic materials in the gage length region of the specimen. The ILS stress for the composite specimen depends on the angular position of the reference point. The maximum stress was found at the outer radius at 45 degree location. There is no variation of ILS stress in the circumferential direction for isotropic materials for a given radius. For the composite specimen, there is large variation of shear stress in the circumferential direction. The maximum ILS stress is induced at outer radius at 45 degree angular orientation. ILS stress along the gage length depends on the geometry of the specimen. The maximum ILS stress for the specimen with fillet radius is induced at the mid gage length region whereas, for the specimen without fillet radius, the maximum ILS stress is induced at the interface of flange and gage length. Fig. 12. Interlaminar shear stress variation along circumferential direction: (a) resin specimen, (b) WF E-glass/epoxy composite specimen.
There is a sharp increase in stress in the gage length region. This increase is attributed to the change in the geometry of the thin walled tubular specimen. Thin walled tubular specimens with fillet radius has uniform stress along the gage length, and maximum ILS stress is encountered at mid gage length. Thin walled tubular specimens without fillet radius have a sharp increase in ILS stress in the gage length region, and maximum ILS stress is encountered at the
8. Overall conclusions The range of ILS strength obtained using thin walled tubular specimens on TSHB for composites is 25.0e30.7 MPa, whereas the range of ILS strength obtained using single lap specimens on compressive SHPB for composites is 87.0e98.0 MPa. It can be observed that ILS strength obtained for composites using thin walled tubular specimens on TSHB is lower. This is because of stress concentrations in the fracture planes for composite specimens during TSHB testing.
Fig. 13. Interlaminar shear stress variation along the gage length, WF E-glass/epoxy composite specimen.
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The ILS strength obtained either by TSHB testing of thin walled tubular specimens or by SHPB testing of single lap specimens can be used appropriately based on the loading conditions of the composite structures. For the analysis and design of composites shafts, ILS strength obtained by TSHB testing of thin walled tubular specimens can be used. On the other hand, for composite structures where the loading is primarily in-plane, ILS strength obtained by SHPB testing of single lap specimens can be used. References [1] R.L. Sierakowski, S.K. Chaturvedi, Dynamic Loading and Characterization of Fiber-reinforced Composites, John Wiley and Sons Inc, New York, 1997, pp. 15e99. [2] N.A. Fleck, W.J. Stronge, J.H. Liu, High strain-rate shear response of polycarbonate and polymethyl methacrylate, P Roy Soc. London A 429 (1990) 459e479. [3] H. Leber, J.M. Lifshitz, Interlaminar shear behavior of plain-weave GRP at static and high rates of strain, Compos Sci. Technol. 56 (1996) 391e405. [4] L.H. Dai, Y.L. Bai, S.W.R. Lee, Experimental investigation of the shear strength of a unidirectional carbon/aluminum composite under dynamic torsional loading, Compos Sci. Technol. 58 (1998) 1667e1673. [5] L.H. Dai, Y.L. Bai, S.W.R. Lee, Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading, Key Eng. Mater. 141e143 (1998) 651e670. [6] Y. Hu, R. Feng, On the use of a Kolsky torsion bar to study the transient large-strain response of polymer melts at high shear rates, J. Appl. Mech. 71 (2004) 441e449. [7] N.K. Naik, A. Asmelash, V.R. Kavala, Ch Veerraju, Interlaminar shear properties of polymer matrix composites: strain rate effect, Mech. Mater. 39 (2007) 1043e1052. [8] A. Gilat, R.K. Goldberg, G.D. Roberts, Strain rate sensitivity of epoxy resin in tensile and shear loading, J. Aerosp Eng. 20 (2007) 75e89. [9] N.K. Naik, G. Ravikumar, N.M. Thoram, V.R. Kavala, Ch Veerraju, Shear properties of epoxy under high strain rate loading, Polym. Eng. Sci. 50 (2010) 780e788. [10] B. Bouette, C. Cazenuve, C. Oytana, Effect of strain rate on interlaminar shear properties of carbon/epoxy composites, Compos Sci. Technol. 45 (1992) 313e321. [11] L. Dong, J. Harding, A single-lap shear specimen for determining the effect of strain rate on the interlaminar shear strength of carbon fibre-reinforced laminates, Composites 25 (1994) 129e138. [12] S.R. Hallett, C. Ruiz, Material characterization tests and modelling of carbon fibre T300/1914 at impact rates of strain, J. Phys. IV France 7 (1997) 465e470.
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[13] S.R. Hallett, C. Ruiz, J. Harding, The effect of strain rate on the interlaminar shear strength of a carbon/epoxy cross-ply laminate: comparison between experiment and numerical prediction, Compos Sci. Technol. 59 (1999) 749e758. [14] S.M. Werner, C.K.H. Dharan, The dynamic response of graphite fiberepoxy laminates at high shear strain rates, J. Compos Mater. 20 (1986) 365e374. [15] J.M. Lifshitz, H. Leber, Response of fiber-reinforced polymers to high strain-rate loading in interlaminar tension and combined tension/ shear, Compos Sci. Technol. 58 (1998) 987e996. [16] K.H. Sayers, B. Harris, Interlaminar shear strength of a carbon fibre reinforced composite material under impact conditions, J. Compos Mater. 7 (1973) 129e133. [17] P.M. Jelf, N.A. Fleck, The failure of composite tubes due to combined compression and torsion, J. Mater. Sci. 29 (1994) 3080e3084. [18] J. Harding, Y.L. Li, Determination of interlaminar shear strength for glass/epoxy and carbon/epoxy laminates at impact rates of strain, Compos Sci. Technol. 45 (1992) 161e171. [19] J. Harding, L. Dong, Effect of strain rate on the interlaminar shear strength of carbon-fibre reinforced laminates, Compos Sci. Technol. 51 (1994) 347e358. [20] J.W. Gillespie Jr., B.A. Gama, C.E. Cichanowski, J.R. Xiao, Interlaminar shear strength of plain weave S2-glass/SC79 composites subjected to out-of-plane high strain rate compressive loadings, Compos Sci. Technol. 65 (2005) 1891e1898. [21] J.A.P. Mouritza, J. Gallagher, A.A. Goodwinb, Flexural strength and interlaminar shear strength of stitched GRP laminates following repeated impacts, Compos Sci. Technol. 57 (1997) 509e522. [22] T.A. Gelu, S.S. Joshi, N.K. Naik, Shear properties of acrylic under high strain rate loading, J. Appl. Polym. Sci. 121 (2011) 1631e1639. [23] J.R. Pothnis, G. Ravikumar, M. Joshi, K. Akella, S. Kumar, N.K. Naik, High strain rate compressive behavior of epoxy LY 556: radial constraint effect, Mater. Sci. Eng. A 538 (2012) 210e218. [24] G. Ravikumar, J.R. Pothins, M. Joshi, K. Akella, S. Kumar, N.K. Naik, Analytical and experimental studies on mechanical behavior of composites under high strain rate compressive loading, Mater. Des. 44 (2013) 246e255. [25] E.K. Leung, An elastic-plastic stress analysis of the specimen used in torsional Kolsky bar, J. Appl. Mech. 47 (1980) 278e282. [26] A. Gilat, C.S. Cheng, Torsional split Hopkinson bar tests at strain rates above 104 s-1, Exp. Mech. 40 (2000) 55e59. [27] A. Gilat, C.S. Cheng, Modeling torsional split Hopkinson bar tests at strain rates above 10,000 s-1, Int. J. Plast. 18 (2002) 787e799. [28] Tsu-Wei Chou, Microstructural Design of Fiber Composites. Dynamic Loading and Characterization of Fiber-reinforced Composites. Thermo Elastic Behavior of Laminated Composites, Cambridge university press, Cambridge, 1992, pp. 29e77. [29] N.K. Naik, Y. Chandra Sekher, M. Sailendra, Polymer matrix woven fabric composites subjected to low velocity impact: part I e damage initiation studies, J. Reinf Plast. Compos 19 (2000) 912e954.
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Test method
Dependency of dynamic interlaminar shear strength of composites on test technique used H.L. Gowtham, Jayaram R. Pothnis, G. Ravikumar, N.K. Naik* Aerospace Engineering Department, Indian Institute of Technology BombayPowai, Mumbai 400076, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 December 2014 Accepted 18 January 2015 Available online 28 January 2015
Studies are presented on dependency of dynamic interlaminar shear (ILS) strength on the experimental technique used for a typical plain weave E-glass/epoxy composite. Dynamic ILS strength was determined based on two experimental techniques, namely torsional split Hopkinson bar (TSHB) apparatus using thin walled tubular specimens and compressive split Hopkinson pressure bar (SHPB) apparatus using single lap specimens. The results obtained from these techniques are compared. In general, it is observed that dynamic ILS strength for composites obtained by TSHB testing using thin walled tubular specimens is lower than the dynamic ILS strength obtained using single lap specimens in compressive SHPB. The issues involved in TSHB testing of thin walled tubular specimens made of composites are discussed and the reasons for reduced dynamic ILS strength using thin walled tubular specimens are highlighted. Finite element analysis (FEA) of thin walled tubular specimens made of composite and resin subjected to quasi-static torsional loading is presented. Using FEA results, the reasons for lower ILS strength of composite thin walled tubular specimens are substantiated. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Interlaminar shear strength High strain rate testing Thin walled tubular specimen Single lap specimen Finite element analysis
1. Introduction Laminated composites are widely used in many structural applications. Aerospace and automobile structures, windmills, defense equipment and ship hulls are typical examples. The wide usage of these materials is because of their unique architectural features, ease of handling, low fabrication cost and excellent mechanical properties. Laminated composites are orthotropic materials. These materials exhibit two types of shear properties, one along the plane of lamina, which is termed the in-plane shear and the other along the thickness of the laminate, which is termed the interlaminar shear (ILS). The ILS strength is one of the most important parameters in determining the ability of a composite material to resist delamination damage.
* Corresponding author. Tel.: þ91 22 2576 7114; fax: þ91 22 2572 2602. E-mail address: [email protected] (N.K. Naik). http://dx.doi.org/10.1016/j.polymertesting.2015.01.012 0142-9418/© 2015 Elsevier Ltd. All rights reserved.
Composites are subjected to a variety of loads during service life. These loads can be classified as quasi-static and dynamic. Material response varies significantly with quasistatic and dynamic loading conditions. Dynamic loading is also referred to as high strain rate loading. The relationship between the magnitude of the load applied and the time over which it acts plays an important role in deciding the system response. Response of laminated composites under high strain rate shear loading is an important engineering requirement. It is used in applications like composite shaft design and design of external panels of aircraft etc. In theory, mechanical properties of a material are unique. They should not change with the test technique or the specimen used. This behavior is observed in metals/ alloys as well as many the other materials. However, composites tend to display variations in dynamic interlaminar shear strength with the test technique employed. The focus of the present study is to establish the reasons for variation in dynamic ILS strength with the test
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technique used, and validate the reasons established with finite element analysis (FEA) simulation results. Studies are performed on a typical plain weave E-glass/epoxy composite. There are several methods for the determination of shear properties under dynamic loading [1]; those available for the evaluation of dynamic shear properties of composites are:
TSHB test [2e9]. Compressive SHPB test [10e14]. Tensile SHPB test [15]. Drop-weight test [16]. Hydraulic/Pneumatic machine test [17].
There are only limited studies on high strain rate ILS properties of composites. Leber and Lifshitz [3], Dai et al [4,5], Hu and Feng [6] and Naik et al [7] are among the few researchers who have studied ILS properties of composites on TSHB using thin walled tubular specimens. Researchers have also used single lap specimens for determining dynamic ILS properties of composites. Bouette et al [10], Dong and Harding [11] and Hallet et al [12,13] used compressive SHPB apparatus with single lap specimens for ILS characterization of composites. Apart from thin walled tubular specimens and single lap specimens, researchers have also used double lap specimens [18,19], V-notched specimens [20] and short beam specimens [21] to evaluate the dynamic shear properties of composites. However, TSHB testing with thin walled tubular specimens and compressive SHPB testing with single lap specimens are the most widely used techniques. In the present study, dynamic ILS strength for a typical plain weave E-glass/epoxy was evaluated on TSHB apparatus using thin walled tubular specimens, and compressive SHPB apparatus using single lap specimens. The results obtained are compared. The reasons for variation in dynamic ILS strength obtained from TSHB apparatus using thin walled tubular specimens and compressive SHPB apparatus using single lap specimens are considered. FEA of thin walled tubular specimens made of composite and resin subjected to quasi-static torsional loading is presented.
3. Specimen design and dimensions Specimens for the tests were made from plain weave Eglass/epoxy laminates. Balanced layers of thickness 0.25 mm were used for making the laminates. The laminates were made such that warp direction of all the layers was along direction 1 and fill direction of all the layers was along direction 2 (Figs. 1 and 2). Epoxy resin LY556 with hardener HY951 was used for making the laminates. The fiber volume fraction of the laminates was 0.54. 3.1. Thin wall tubular specimen A schematic arrangement of laminate configuration used for thin walled tubular specimen is presented in Fig. 1a. The axis of the specimen was along the thickness direction of the laminate. Thin walled tubular specimens with wall thickness (tS) of 3 mm and gage length (LS) of 3 mm were used. Other specimen dimensions were Di ¼ 10 mm, Do ¼ 16 mm and D ¼ 22 mm. The overall length of the specimens (L) was 9 mm and radius of edge, R, was 0.5 mm. For bonding the specimens to the incident and transmitter bars of the TSHB apparatus, Araldite adhesive was used with room temperature curing. Fig. 1b shows photograph of a fractured specimen tested on the TSHB apparatus. It can be seen that the fracture surface has a zigzag appearance. 3.2. Single lap specimen A schematic arrangement of laminate configuration and single lap specimen is shown in Fig. 2a. The dimensions of the specimen are: a ¼ 5 mm, b ¼ 27.5 mm and width (c) ¼ 20 mm, d ¼ 8.66 mm, e ¼ 12 mm. The axis of the specimen was along the warp direction (direction 1) of the laminate. Overall length, width and thickness of specimen were 51.5 mm, 20 mm and 10 mm, respectively. Loading was along direction 1 on the flat surfaces on either side of the specimen. Fracture plane area is ‘a x c’. Fig. 2b shows a photograph of a failed single lap specimen. It can be seen from the photograph that the fracture surface has a zigzag appearance. Specially designed specimen holders for specimen gripping in compressive SHPB apparatus can also be seen. Inner dimension of the fixture is 10 mm. For bonding the specimens to the fixture, Araldite adhesive was used with room temperature curing.
2. Test apparatus and calibration 4. Test methods TSHB apparatus [7,9,22] was used to evaluate dynamic ILS behavior of a typical plain weave E-glass/epoxy using thin walled tubular specimens. Compressive SHPB apparatus [10,11,23,24] was also used to evaluate dynamic ILS behavior of a typical plain weave E-glass/epoxy using single lap specimens. In both TSHB and compressive SHPB apparatus, strain gauges were mounted on the incident as well as the transmitter bar. The strain gauges were connected in half bridge configuration. Before the commencement of actual experiments, calibration was performed. Details regarding calibration of TSHB and compressive SHPB apparatus are presented in [9] and [23,24], respectively.
4.1. TSHB testing TSHB apparatus was used to evaluate the ILS properties of WF E-glass/epoxy thin walled tubular specimens [7]. Tests were carried out over a shear strain rate range of 192e457 per second with at least five specimens under identical test conditions. Signals from strain gauges mounted on the incident and transmitter bars of TSHB were obtained on an oscilloscope and are presented in Fig. 3. With the help of incident (I), transmitted (T) and reflected (R) strain gauge signals, torque histories of incident and transmitter bars were obtained. Starting with the signals
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Fig. 1. (a) Schematic arrangement of laminate and thin walled tubular specimen, TSHB testing, (b) Photograph of failed thin walled tubular specimen tested on THPB apparatuses.
and using one dimensional wave propagation theory [7,9], shear stress - shear strain plots were generated. A typical plot is shown in Fig. 4. Point ‘B’ indicates peak shear stress within the specimen, i.e., shear strength of the specimen. Point ‘P’ indicates end of rise time during TSHB testing (Fig. 3). It may be noted that intensity of transmitted pulse is less than the intensity of the sum of incident and reflected pulses (Fig. 3). This is because of stress wave attenuation within the specimen during TSHB testing. As a conservative estimate, transmitted signal data is considered for obtaining resultant shear stress e shear strain response. 4.2. Compressive SHPB testing Compressive SHPB apparatus was used to evaluate ILS properties of WF E-glass/epoxy single lap specimens [10]. Studies were carried out in an axial strain rate range of 300e1500 per sec. Experiments were performed on at least five specimens under identical test conditions. Signals from strain gauges mounted on the incident and transmitter bars of compressive SHPB apparatus were obtained on an oscilloscope and are presented in Fig. 5. Loading was along direction 1 on the flat surfaces of the specimen on either side. With the help of incident (I), transmitted (T) and reflected (R) strain gauge signals, force histories of incident
and transmitter bars were obtained. Starting with the signals and using one dimensional wave propagation theory, a stress-strain diagram (Fig. 6) was generated [23]. The cross sectional area of the specimen considered for determining the forces is “a x c” (Fig. 2a). 5. Results and discussion: experimental studies 5.1. TSHB testing A typical failed specimen during TSHB testing is shown in Fig. 1b. It was observed that the failure is along the mid span of the gage length. It is evident that the failure is by interlaminar fracture and confined to a very small region on a plane parallel to the reinforcement layers. This indicates that the specimen has not buckled and failure was under pure shear. The zigzag edge at the plane of failure of the specimen is due to the undulated nature of the woven fabric at the interface between the adjacent layers. On application of dynamic shear load on the TSHB apparatus, a finite time is taken for shear strain to attain a constant value, which is termed rise time [7]. End of rise time is represented by point P in Fig. 3. For the case considered, the rise time is 50 microseconds. Shear strain rate is nearly constant after point P is reached.
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Fig. 2. (a) Schematic arrangement of laminate and single lap specimen, compressive SHPB testing, (b) Photograph of failed single lap specimen with holders.
Fig. 4 presents the variation of shear stress with shear strain. The peak ILS stress is indicated by point B. The peak ILS stress is 25.1 MPa and the corresponding ultimate shear strain is 1.05%. The peak ILS stress indicates dynamic ILS strength of the material. Interlaminar shear strengths at different strain rates are presented for plain weave E-glass/epoxy in Table 1 and
Fig. 7. The data presented in Table 1 are averages of five test results. Studies were carried out in the strain rate range of 192e457 per sec. It can be observed that interlaminar shear strength is enhanced at high strain rate loading compared with that at quasi-static loading. Further, it can be observed that interlaminar shear strength increases with increasing strain rate within the range of strain rates considered (Table 1 and Fig. 7). For the typical plain weave E-glass/epoxy composite studied, the interlaminar shear strength enhancement at strain rate of 205 per sec is 32% compared to that at quasi-static loading. 5.2. Compressive SHPB testing As explained earlier, experimental studies were carried out on single lap specimens of WF E-glass/epoxy under high strain rate compressive loading for obtaining stress-
Fig. 3. High strain rate TSHB testing, strain gauge signals on oscilloscope, thin walled tubular specimen, Ѓ ¼ 205 per sec, WF E-glass/epoxy.
Fig. 4. Shear stress - shear strain plot, high strain rate TSHB testing, thin walled tubular specimen, Ѓ ¼ 205 per sec, WF E-glass/epoxy.
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Fig. 7. Shear strain rate versus interlaminar shear strength plot, TSHB testing, thin walled tubular specimen, WF E-glass/epoxy.
Fig. 5. High strain rate compressive SHPB testing, strain gauge signals on oscilloscope, single lap specimen, έ ¼ 455 per sec, WF E-glass/epoxy.
out in the axial strain rate range of 300e1500 per sec. It can be observed that ILS strength increases as the axial strain rate increases. Also, it can be inferred that the ILS strength is enhanced at high strain rate loading compared with that at quasi-static loading. It was also observed that, for single lap specimens, the failure occurred in the gage length region in a plane parallel to the axis of load application. 6. Comparison of experimental results
Fig. 6. Stress - strain plot, high strain rate compressive SHPB testing, single lap specimen, έ ¼ 455 per sec, WF E-glass/epoxy.
strain plots (Fig. 6). The peak ILS stress is 92 MPa and the corresponding ultimate axial strain is 6.1%. ILS stress was obtained by dividing the transmitted force by shear area given by “b x c” (Fig. 2a). Interlaminar shear strength at different high strain rates is presented for plain weave Eglass/epoxy in Table 2 and Fig. 8. The data presented in Table 2 are averages of five test results. Studies were carried
Table 1 Interlaminar shear strength of WF E-glass/epoxy under high strain rate loading using thin walled tubular specimens on TSHB apparatus. Shear strain rate, (per sec)
Shear strength, (MPa)
QS 192 205 325 352 457
19.0 25.0 25.1 25.1 27.3 30.7
Tables 1 and 2 present ILS strength of a typical plain weave E-glass/epoxy obtained by both the techniques. By comparing the results, it is evident that dynamic ILS strength of the typical plain weave E-glass/epoxy evaluated using single lap specimens is significantly higher than that obtained from thin walled tubular specimens. The range of ILS strength obtained using thin walled tubular specimens on TSHB is 25.0e30.7 MPa (Table 1), whereas the range of ILS strength obtained using single lap specimens on compressive SHPB is 87.0e98.0 MPa (Table 2). Figs. 7 and 8, also show that interlaminar shear strength obtained using single lap specimens on SHPB is significantly higher than that obtained using thin walled tubular specimens on TSHB, even at the same strain rate range, i.e., up to strain rate of 500 per sec. One of the fundamental assumptions in high strain rate shear characterization of materials using thin walled tubular specimens is uniform shear stress distribution in the specimen within the shear plane. This implies that the
Table 2 Interlaminar shear strength of WF E-glass/epoxy under high strain rate loading using single lap specimens on compressive SHPB apparatus. Axial strain rate, (per sec)
Shear strength, (MPa)
300 455 540 684 920 1020 1500
87 92 94 85 78 96 98
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Fig. 8. Axial strain rate versus interlaminar shear strength plot, compressive SHPB testing, single lap specimen, WF E-glass/epoxy.
interlaminar shear stress is uniform along the radial direction and along the circumferential direction as well as along the gage length. The focus of the further study is to look into these aspects for composite specimens as well as resin specimens. Leung [25] carried out an elastic-plastic stress analysis of aluminum thin-walled tubular specimens under torsional loading. He reported that flanges of the specimen remain elastic and there is uniform shear stress distribution along the gage length of the specimen. Leber and Lifshitz [3] carried out dynamic simulation of thin-walled tubular specimens using MSC/NASTRAN finite element code. They reported pure shear stress distribution in the fracture surface. They could also achieve relatively constant stress along the gage length of the specimen. Gilat and Cheng [26,27] performed time independent elasticeplastic finite element analysis of the quasi-static tests on 1100-O aluminum alloy thin walled tubular specimens using ABAQUS code. Loading was applied by fixing one end and rotating the other. They reported stress concentration near the curved boundary of the gage length and shear plane. They further reported variation in shear stress in radial and tangential directions in the fracture plane. In the interlaminar region, within the specimen gage length of thin walled tubular specimen, the induced shear stress may not be constant for composites. This is because
of the inherent nature of the fabric used and the material properties along different directions. Interlaminar shear stresses S13, S23 and Sq may not be the same. Here, suffixes 13, 23 and q refer to 13 plane, 23 plane and any other plane with an orientation of q. Fig. 9 presents a sectional view of a thin walled tubular specimen of laminated composite at a plane that is located at the middle of the gage length. The interlaminar stresses at points A, B, C and so on may not be the same at the fracture plane for composites because of different mechanical properties along the circumferential direction. On the other hand, the stresses at different locations on the fracture plane would be the same for isotropic materials. For composites, the induced interlaminar stresses would be different at different locations on the fracture plane leading to stress concentrations. The stress concentration on the fracture plane would lead to early interlaminar failure. The objective of the further study is to evaluate interlaminar shear stress variation for composite thin walled tubular specimens under torsional loading. The studies were carried out using ANSYS V.14.0 finite element analysis software under quasi-static torsional loading. The stress distribution is obtained along the radial direction, the circumferential direction as well as the gage length. The studies were carried out under quasi-static loading since the objective of the investigation is to assess possible stress concentration locations on the fracture plane within the thin walled tubular specimens under torsional loading. The variation in induced interlaminar shear stress in the fracture plane depicted in Fig. 9 arises because of variation in the stiffness co-efficients (Sij) of the materials in the circumferential direction. For isotropic materials, the Sij are the same throughout the circumference. For composites, Sij do not remain the same along the circumferential direction. The variation of Sij depends on the angular position of the points considered on the fracture plane. Variation of Sij can be found by multiplying the Sij matrix in the xy plane of the laminated composite with the 3D transformation matrix [28]. As Sij varies in the circumferential direction for composites, the induced interlaminar stress would not be uniform in the plane of fracture. This would lead to stress concentrations, resulting in early failure of the composite thin walled tubular specimens. 7. Finite element analysis
Fig. 9. Cross-section of composite thin-walled tubular specimen at the fracture plane.
To visualize the stress distribution in a typical thin walled tubular composite specimen under quasi-static torsional loading, FEA was carried out using ANSYS V.14.0 finite element analysis software. Modeling of the specimen was performed considering a wall thickness (tS) of 0.25 mm, gage length (LS) of 3 mm, flange thickness (tf) of 3 mm and overall length (L) of 9 mm. Meshing was done using eight noded solid brick elements with six degrees of freedom. The complete thin walled tubular specimen has 10281 elements and 12294 nodes in the meshed model. This was worked out based on convergence study. A unit moment (1 Nm) was applied about the axis of the specimen on one of the external faces of the specimen flange. Contact elements Conta-175 Tange170 was used to distribute the moment about the axis to
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the nodes on the external face of the specimen flange. Thus, uniform distribution of torque load was ensured. The other external face of the flange was constrained in all degrees of freedom. For comparison purpose, stress analysis was conducted on two meshed models. In the first model, isotropic (resin) material was considered. Such a model is referred to as isotropic model (Fig. 10a). In the second model, laminated composite (WF E-glass/epoxy) material was considered. Such a model is referred to as composite model (Fig. 10b). For the composite model, stiffness matrix for E-glass/epoxy composite at different locations was calculated from basic nine elastic properties [29] of the material. The stress distribution was obtained along the radial direction, the circumferential direction as well as the gage length.
7.1. Stress variation along radial direction Fig. 11a and b present the ILS stress variation along the radial direction for a resin specimen and composite specimen, respectively. For the resin specimen, ILS stress variation is presented from inner radius (ri) to outer radius (ro) in the gage length region. It may be noted that the radial stress is higher at the outer radius by 4.5% (Fig. 11a). This is valid for all the angular locations.
Fig. 11. Interlaminar shear stress variation along radial direction: (a) resin specimen, (b) WF E-glass/epoxy composite specimen.
For the composite specimen, ILS stress variation is presented from inner radius (ri) to outer radius (ro) in the gage length region. ILS stress variation depends upon the angular orientation. At 0 and 90 degree orientations, the ILS stress is marginally higher at inner radius compared to that at outer radius. On the other hand, at 45 degree orientation, ILS stress is higher at outer radius compared to that at inner radius. The maximum variation is at 45 degree orientation, up to 21.1% (Fig. 11b). 7.2. Stress variation along circumferential direction Fig. 12a and b present ILS stress variation along the circumferential direction for resin and composite specimens, respectively. There is no variation of ILS stress along the circumferential direction for the resin specimen at a given radius. For the composite specimen, there is variation of ILS stress with angular location at any given radius. This variation is minimal at inner radius, whereas it is predominant at outer radius. Further, ILS stress tends to increase from 0 to 45 degree and reduce from 45 to 90 degree orientation. The ILS stress variation between 0 to 45 degree locations at outer radius of the specimen at mid gage length is 25.8%. 7.3. Stress variation along gage length Fig. 10. Thin walled tubular specimen for TSHB testing: (a) FEA discretization for resin specimen, (b) FEA discretization of gage length of WF E-glass/ epoxy composite specimen.
Fig 13 presents ILS stress variation along the gage length for a WF E-glass/epoxy composite specimen. Stress is considerably lower in the flange region of the specimen.
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flange e gage length interface. This is due to abrupt change in specimen geometry. 7.4. Conclusions based on FEA From the FEA of isotropic and composite models, the following conclusions can be made. The ILS stress is marginally higher at outer radius compared to that at inner radius for isotropic materials in the gage length region of the specimen. The ILS stress for the composite specimen depends on the angular position of the reference point. The maximum stress was found at the outer radius at 45 degree location. There is no variation of ILS stress in the circumferential direction for isotropic materials for a given radius. For the composite specimen, there is large variation of shear stress in the circumferential direction. The maximum ILS stress is induced at outer radius at 45 degree angular orientation. ILS stress along the gage length depends on the geometry of the specimen. The maximum ILS stress for the specimen with fillet radius is induced at the mid gage length region whereas, for the specimen without fillet radius, the maximum ILS stress is induced at the interface of flange and gage length. Fig. 12. Interlaminar shear stress variation along circumferential direction: (a) resin specimen, (b) WF E-glass/epoxy composite specimen.
There is a sharp increase in stress in the gage length region. This increase is attributed to the change in the geometry of the thin walled tubular specimen. Thin walled tubular specimens with fillet radius has uniform stress along the gage length, and maximum ILS stress is encountered at mid gage length. Thin walled tubular specimens without fillet radius have a sharp increase in ILS stress in the gage length region, and maximum ILS stress is encountered at the
8. Overall conclusions The range of ILS strength obtained using thin walled tubular specimens on TSHB for composites is 25.0e30.7 MPa, whereas the range of ILS strength obtained using single lap specimens on compressive SHPB for composites is 87.0e98.0 MPa. It can be observed that ILS strength obtained for composites using thin walled tubular specimens on TSHB is lower. This is because of stress concentrations in the fracture planes for composite specimens during TSHB testing.
Fig. 13. Interlaminar shear stress variation along the gage length, WF E-glass/epoxy composite specimen.
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The ILS strength obtained either by TSHB testing of thin walled tubular specimens or by SHPB testing of single lap specimens can be used appropriately based on the loading conditions of the composite structures. For the analysis and design of composites shafts, ILS strength obtained by TSHB testing of thin walled tubular specimens can be used. On the other hand, for composite structures where the loading is primarily in-plane, ILS strength obtained by SHPB testing of single lap specimens can be used. References [1] R.L. Sierakowski, S.K. Chaturvedi, Dynamic Loading and Characterization of Fiber-reinforced Composites, John Wiley and Sons Inc, New York, 1997, pp. 15e99. [2] N.A. Fleck, W.J. Stronge, J.H. Liu, High strain-rate shear response of polycarbonate and polymethyl methacrylate, P Roy Soc. London A 429 (1990) 459e479. [3] H. Leber, J.M. Lifshitz, Interlaminar shear behavior of plain-weave GRP at static and high rates of strain, Compos Sci. Technol. 56 (1996) 391e405. [4] L.H. Dai, Y.L. Bai, S.W.R. Lee, Experimental investigation of the shear strength of a unidirectional carbon/aluminum composite under dynamic torsional loading, Compos Sci. Technol. 58 (1998) 1667e1673. [5] L.H. Dai, Y.L. Bai, S.W.R. Lee, Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading, Key Eng. Mater. 141e143 (1998) 651e670. [6] Y. Hu, R. Feng, On the use of a Kolsky torsion bar to study the transient large-strain response of polymer melts at high shear rates, J. Appl. Mech. 71 (2004) 441e449. [7] N.K. Naik, A. Asmelash, V.R. Kavala, Ch Veerraju, Interlaminar shear properties of polymer matrix composites: strain rate effect, Mech. Mater. 39 (2007) 1043e1052. [8] A. Gilat, R.K. Goldberg, G.D. Roberts, Strain rate sensitivity of epoxy resin in tensile and shear loading, J. Aerosp Eng. 20 (2007) 75e89. [9] N.K. Naik, G. Ravikumar, N.M. Thoram, V.R. Kavala, Ch Veerraju, Shear properties of epoxy under high strain rate loading, Polym. Eng. Sci. 50 (2010) 780e788. [10] B. Bouette, C. Cazenuve, C. Oytana, Effect of strain rate on interlaminar shear properties of carbon/epoxy composites, Compos Sci. Technol. 45 (1992) 313e321. [11] L. Dong, J. Harding, A single-lap shear specimen for determining the effect of strain rate on the interlaminar shear strength of carbon fibre-reinforced laminates, Composites 25 (1994) 129e138. [12] S.R. Hallett, C. Ruiz, Material characterization tests and modelling of carbon fibre T300/1914 at impact rates of strain, J. Phys. IV France 7 (1997) 465e470.
159
[13] S.R. Hallett, C. Ruiz, J. Harding, The effect of strain rate on the interlaminar shear strength of a carbon/epoxy cross-ply laminate: comparison between experiment and numerical prediction, Compos Sci. Technol. 59 (1999) 749e758. [14] S.M. Werner, C.K.H. Dharan, The dynamic response of graphite fiberepoxy laminates at high shear strain rates, J. Compos Mater. 20 (1986) 365e374. [15] J.M. Lifshitz, H. Leber, Response of fiber-reinforced polymers to high strain-rate loading in interlaminar tension and combined tension/ shear, Compos Sci. Technol. 58 (1998) 987e996. [16] K.H. Sayers, B. Harris, Interlaminar shear strength of a carbon fibre reinforced composite material under impact conditions, J. Compos Mater. 7 (1973) 129e133. [17] P.M. Jelf, N.A. Fleck, The failure of composite tubes due to combined compression and torsion, J. Mater. Sci. 29 (1994) 3080e3084. [18] J. Harding, Y.L. Li, Determination of interlaminar shear strength for glass/epoxy and carbon/epoxy laminates at impact rates of strain, Compos Sci. Technol. 45 (1992) 161e171. [19] J. Harding, L. Dong, Effect of strain rate on the interlaminar shear strength of carbon-fibre reinforced laminates, Compos Sci. Technol. 51 (1994) 347e358. [20] J.W. Gillespie Jr., B.A. Gama, C.E. Cichanowski, J.R. Xiao, Interlaminar shear strength of plain weave S2-glass/SC79 composites subjected to out-of-plane high strain rate compressive loadings, Compos Sci. Technol. 65 (2005) 1891e1898. [21] J.A.P. Mouritza, J. Gallagher, A.A. Goodwinb, Flexural strength and interlaminar shear strength of stitched GRP laminates following repeated impacts, Compos Sci. Technol. 57 (1997) 509e522. [22] T.A. Gelu, S.S. Joshi, N.K. Naik, Shear properties of acrylic under high strain rate loading, J. Appl. Polym. Sci. 121 (2011) 1631e1639. [23] J.R. Pothnis, G. Ravikumar, M. Joshi, K. Akella, S. Kumar, N.K. Naik, High strain rate compressive behavior of epoxy LY 556: radial constraint effect, Mater. Sci. Eng. A 538 (2012) 210e218. [24] G. Ravikumar, J.R. Pothins, M. Joshi, K. Akella, S. Kumar, N.K. Naik, Analytical and experimental studies on mechanical behavior of composites under high strain rate compressive loading, Mater. Des. 44 (2013) 246e255. [25] E.K. Leung, An elastic-plastic stress analysis of the specimen used in torsional Kolsky bar, J. Appl. Mech. 47 (1980) 278e282. [26] A. Gilat, C.S. Cheng, Torsional split Hopkinson bar tests at strain rates above 104 s-1, Exp. Mech. 40 (2000) 55e59. [27] A. Gilat, C.S. Cheng, Modeling torsional split Hopkinson bar tests at strain rates above 10,000 s-1, Int. J. Plast. 18 (2002) 787e799. [28] Tsu-Wei Chou, Microstructural Design of Fiber Composites. Dynamic Loading and Characterization of Fiber-reinforced Composites. Thermo Elastic Behavior of Laminated Composites, Cambridge university press, Cambridge, 1992, pp. 29e77. [29] N.K. Naik, Y. Chandra Sekher, M. Sailendra, Polymer matrix woven fabric composites subjected to low velocity impact: part I e damage initiation studies, J. Reinf Plast. Compos 19 (2000) 912e954.