Availableonlineatwww.sciencedirect.com COMPOSITE STRUCTURES ELSEVIER Composite Structures 63(2004)455-467 Mechanical behaviour of glass and carbon fibre reinforced composites at varying strain rates R O. Ochola . K. Marcus G.N. Nurick. t franz Centre for Materials Engineering(CME), University of Cape Town(UCT), Prirate Bag, Rondebosch 7701, South b Department of Mechanical Engineering, University of Cape Town(UCT), Prirate Bag, Rondebosch 7701, South Africa Cardiovascular Research Unit, University of Cape Town(UCT), Prirate Bag, Rondebosch 7701, South Africa Abstract The choice of composite materials as a substitute for metallic materials in technological applications is becoming more pro- nounced especially due to the great weight savings these materials offer. In many of these practical situations, the structures are prone to high impact loads. Material and structural response vary significantly under impact loading conditions as compared to uasi-static loading. The strain rate sensitivity of both carbon fibre reinforced polymer(CFRP)and glass fibre reinforced polymer GFRP)are studied by testing a single laminate configuration, viz. cross-ply [0/90] polymer matrix composites(PMc)at strain ites of 10' and 450 s. The compressive material properties are determined by testing both laminate systems, viz. CFRP and GFRP at low to high strain rates. The laminates were fabricated from 48 layers of cross-ply carbon fibre and glass fibre epoxy Dynamic test results were compared with static compression test carried out on specimens with the same dimensions. Preliminary compressive stress-strain vs strain rates data obtained show that the dynamic material strength for GFRP increases with increasing strain rates. The strain to failure for both CfrP and gfrp is seen to decrease with increasing strain rate C 2003 Elsevier Ltd. All rights reserved. Keywords: Strain rate sensitivity: Split Hopkinson bar technique; CFRP: GFRP; Dynamic test 1. Introduction could be used to explain the variation in material strength, stress and strain with varying strain rates Polymer matrix composites(PMC) have material While metals have been studied extensively over a wide properties which are attractive for use in various engi- range of strain rates, limited information is available tiff- with regard to the effect of strain rates on fibrous com ness and strength, fatigue properties, and corrosion posites. The majority of information concerning strain resistance make these materials especially appealing to rate sensitivity of fibrous composites at rates above 100 the aerospace, civil engineering, marine and automobile s-I was obtained from tests involving projectile impact industries. Many of the applications require service as summarised by Sierakowski and Nevill [1]. However under dynamic loading conditions. In the aerospace such tests may not easily be used to determine the ma dustry primary aircraft structures such as wings and terial constitutive relations since the state of stress and impact from bird strikes or foreign objects. Automotive, easily monitored during impale orm and the stress is not turbine blades are prone to experience high velocity strain in the specimen is not uni marine and civil structures in service are also prone to At high rates of stra high velocity impact from foreign bodies. Therefore the consequently wave propagation effects become a factor, understanding of the material response under dynamic as a result the experimental technique employed must in loading becomes imperative. This is achieved through some form involve the propagation of stress waves. One experimental and theoretical analysis. The latter re- of the most extensively used experimental configurations quires the development of constitutive equations, which for high strain rate material characterisation is the Hopkinson pressure bar or Kolsky bar [2]. The concept of the Hopkinson bar involves the determination of the E-mail dres ochroboo1@ mail ct ac a (R.O. Ochola dynamic stresses, strains or displacements occurring at he end of a bar through monitoring the elastic pulses in 0263-8223/S- see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0263-8223(03)001946
Mechanical behaviour of glass and carbon fibre reinforced composites at varying strain rates R.O. Ochola a,*, K. Marcus a , G.N. Nurick b , T. Franz c a Centre for Materials Engineering (CME), University of Cape Town (UCT), Private Bag, Rondebosch 7701, South Africa b Department of Mechanical Engineering, University of Cape Town (UCT), Private Bag, Rondebosch 7701, South Africa c Cardiovascular Research Unit, University of Cape Town (UCT), Private Bag, Rondebosch 7701, South Africa Abstract The choice of composite materials as a substitute for metallic materials in technological applications is becoming more pronounced especially due to the great weight savings these materials offer. In many of these practical situations, the structures are prone to high impact loads. Material and structural response vary significantly under impact loading conditions as compared to quasi-static loading. The strain rate sensitivity of both carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) are studied by testing a single laminate configuration, viz. cross-ply [0/90] polymer matrix composites (PMC) at strain rates of 103 and 450 s1. The compressive material properties are determined by testing both laminate systems, viz. CFRP and GFRP at low to high strain rates. The laminates were fabricated from 48 layers of cross-ply carbon fibre and glass fibre epoxy. Dynamic test results were compared with static compression test carried out on specimens with the same dimensions. Preliminary compressive stress–strain vs. strain rates data obtained show that the dynamic material strength for GFRP increases with increasing strain rates. The strain to failure for both CFRP and GFRP is seen to decrease with increasing strain rate. 2003 Elsevier Ltd. All rights reserved. Keywords: Strain rate sensitivity; Split Hopkinson bar technique; CFRP; GFRP; Dynamic test 1. Introduction Polymer matrix composites (PMC) have material properties which are attractive for use in various engineering applications. Factors such as high specific stiff- ness and strength, fatigue properties, and corrosion resistance make these materials especially appealing to the aerospace, civil engineering, marine and automobile industries. Many of the applications require service under dynamic loading conditions. In the aerospace industry primary aircraft structures such as wings and turbine blades are prone to experience high velocity impact from bird strikes or foreign objects. Automotive, marine and civil structures in service are also prone to high velocity impact from foreign bodies. Therefore the understanding of the material response under dynamic loading becomes imperative. This is achieved through experimental and theoretical analysis. The latter requires the development of constitutive equations, which could be used to explain the variation in material strength, stress and strain with varying strain rates. While metals have been studied extensively over a wide range of strain rates, limited information is available with regard to the effect of strain rates on fibrous composites. The majority of information concerning strain rate sensitivity of fibrous composites at rates above 100 s1 was obtained from tests involving projectile impact as summarised by Sierakowski and Nevill [1]. However, such tests may not easily be used to determine the material constitutive relations since the state of stress and strain in the specimen is not uniform and the stress is not easily monitored during impact. At high rates of strain ( P102 s1), inertia and consequently wave propagation effects become a factor, as a result the experimental technique employed must in some form involve the propagation of stress waves. One of the most extensively used experimental configurations for high strain rate material characterisation is the Hopkinson pressure bar or Kolsky bar [2]. The concept of the Hopkinson bar involves the determination of the dynamic stresses, strains or displacements occurring at the end of a bar through monitoring the elastic pulses in * Corresponding author. Fax: +27-21-689-7571. E-mail address: ochrob001@mail.uct.ac.za (R.O. Ochola). 0263-8223/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0263-8223(03)00194-6 Composite Structures 63 (2004) 455–467 www.elsevier.com/locate/compstruct
RO. Ochola et al. Composite Structures 63(2004)455-467 Nomenclature strain rate yield stress of bars material density of Hopk E Young,s modulus of bars length of specimen time od dynamic ultimate stress kink angle D diameter of specimen number of standard deviations quasi-static ultimate stress L/D length to diameter ratio X expected stress values stress in incident bar average stress values stress in transmitter bar original specimen length reflected stress in incident bar final specimen length Umax striker velocity final velocity longitudinal wave velocit the bar some distance away. The basic principle requires depend on various composite constituent properties, that the bar remains elastic, and as a result the distur- geometric arrangement, volume fraction of reinforce- bances at the end of the bar are propagated undistorted ment as well as the size of the reinforcing fibres Siera- along the bar at the elastic wave velocity. The Hopkin- kowski and Nevill [ l] found a simple energy criterion for son bar was first developed in 1914 by Hopkinson [2] composite systems with a brittle matrix for predicting who used the induced wave propagation in a long elastic delamination Sierakowski and Nevill,s [1] work showed metal bar to measure the pressure produced during a that the high strain rate or impact failure characteristics dynamic event. Through the use of momentum traps of are often distinctly different from failure observed at low differing length, Hopkinson was able to study the evo- strain rate testing. Griffiths and Martin [6] investigated lution and the shape of stress pulses as a function of time the dynamic behaviour of unidirectional carbon fibre as they propagated along the metal bar. Davies [3] and composites at high strain rates to determine how the Kolsky [4]. working independently later, used two material behaviour is dependent on fibre volume frac Hopkinson pressure bars in series with the sample tion and fibre orientation. Results from these studies sandwiched between the bars, to measure the dynamic indicate that the dynamic stress-strain characteristics of stress-strain response of materials. Their work formed carbon-fibre composites in compression differ consid- the basis of the split Hopkinson pressure bar currently erably from those under static loading, however no high strain rate research. Johns and strain rate effects are noted for changes in strain rate Cook [5] employed a split Hopkinson pressure bar for between 320 and 550 s. It was also noted that the re- determining the material properties of metals duction in the elastic modulus at high strains rates ap- The experience of the use of split Hopkinson pressure pears to be due to the specimen geometry and is bar for the investigation of metals led to the adaptation therefore not an intrinsic property of the composite of this technique for the characterization of laminated The dynamic compressive behaviour of unidirectional polymer composites at strain rates ranging from 10 to and transversely isotropic glass-epoxy composite are P s. However, only in the recent past has significant determined by Kumar et al. [7, using the Kolsky pressure efforts been made to examine the high strain rate be- bar technique for six fibre orientations, viz. 0, 10, 300 haviour using the split Hopkinson bar, of more brittle 45, 60 and 90 at a strain rate, E, of 265(+50)s materials such as composites and ceramics, to measure Studies were carried out on cylindrical specimens of high strain rate response of materials under varying varying lengths 12-35 mm, and diameters 16-17 mm, loading conditions( tension, compression, shear and respectively. Quasi-static stress-strain curves at strain torsion [1, 7-9D rates of 2x- are compared to corresponding dy The focus of this paper is on the compression re- namic curves. The results indicate that for all orienta- ponse of fibrous composites. Early research on high tions of glass epoxy there is a change in the failure modes, strain rate response of laminate composites dates back as well as an increase in strength at higher strain rates almost three decades. Sierakowski and Nevill [l]in 1971 Specimens of 00 orientation fracture along the fibres by investigated the compressive strength and failure of steel tensile splitting, due to the compressive loads causing reinforced epoxy composites. The investigation involved transverse tensile strains because of Poisson's effect mechanical testing at strain rates ranging from 10- to Therefore, as the transverse tensile strain exceeds the 104 s-l. For the composites tested, strain rates effects transverse ultimate strain, failure occurs by tensile spli
the bar some distance away. The basic principle requires that the bar remains elastic, and as a result the disturbances at the end of the bar are propagated undistorted along the bar at the elastic wave velocity. The Hopkinson bar was first developed in 1914 by Hopkinson [2] who used the induced wave propagation in a long elastic metal bar to measure the pressure produced during a dynamic event. Through the use of momentum traps of differing length, Hopkinson was able to study the evolution and the shape of stress pulses as a function of time as they propagated along the metal bar. Davies [3] and Kolsky [4], working independently later, used two Hopkinson pressure bars in series with the sample sandwiched between the bars, to measure the dynamic stress–strain response of materials. Their work formed the basis of the split Hopkinson pressure bar currently employed in high strain rate research. Johnson and Cook [5] employed a split Hopkinson pressure bar for determining the material properties of metals. The experience of the use of split Hopkinson pressure bar for the investigation of metals led to the adaptation of this technique for the characterization of laminated polymer composites at strain rates ranging from 10 to 104 s1. However, only in the recent past has significant efforts been made to examine the high strain rate behaviour using the split Hopkinson bar, of more brittle materials such as composites and ceramics, to measure high strain rate response of materials under varying loading conditions (tension, compression, shear and torsion [1,7–9]). The focus of this paper is on the compression response of fibrous composites. Early research on high strain rate response of laminate composites dates back almost three decades. Sierakowski and Nevill [1] in 1971 investigated the compressive strength and failure of steel reinforced epoxy composites. The investigation involved mechanical testing at strain rates ranging from 105 to 104 s1. For the composites tested, strain rates effects depend on various composite constituent properties, geometric arrangement, volume fraction of reinforcement as well as the size of the reinforcing fibres. Sierakowski and Nevill [1] found a simple energy criterion for composite systems with a brittle matrix for predicting delamination. Sierakowski and Nevills [1] work showed that the high strain rate or impact failure characteristics are often distinctly different from failure observed at low strain rate testing. Griffiths and Martin [6] investigated the dynamic behaviour of unidirectional carbon fibre composites at high strain rates to determine how the material behaviour is dependent on fibre volume fraction and fibre orientation. Results from these studies indicate that the dynamic stress–strain characteristics of carbon–fibre composites in compression differ considerably from those under static loading, however no strain rate effects are noted for changes in strain rate between 320 and 550 s1. It was also noted that the reduction in the elastic modulus at high strains rates appears to be due to the specimen geometry and is therefore not an intrinsic property of the composite. The dynamic compressive behaviour of unidirectional and transversely isotropic glass–epoxy composite are determined by Kumar et al. [7], using the Kolsky pressure bar technique for six fibre orientations, viz. 0, 10, 30, 45, 60 and 90 at a strain rate, e_, of 265(±50) s1. Studies were carried out on cylindrical specimens of varying lengths 12–35 mm, and diameters 16–17 mm, respectively. Quasi-static stress–strain curves at strain rates of 2 · 104 s1 are compared to corresponding dynamic curves. The results indicate that for all orientations of glass epoxy there is a change in the failure modes, as well as an increase in strength at higher strain rates. Specimens of 0 orientation fracture along the fibres by tensile splitting, due to the compressive loads causing transverse tensile strains because of Poissons effect. Therefore, as the transverse tensile strain exceeds the transverse ultimate strain, failure occurs by tensile splitNomenclature e_ strain rate q material density of Hopkinson bars L length of specimen rd dynamic ultimate stress D diameter of specimen rs quasi-static ultimate stress L=D length to diameter ratio ri stress in incident bar rt stress in transmitter bar rr reflected stress in incident bar v velocity of transmitted pulse vmax striker velocity C0 longitudinal wave velocity ry yield stress of bars E Youngs modulus of bars t time b kink angle s number of standard deviations SD standard deviation Xexpected expected stress values X average stress values l0 original specimen length l final specimen length v1 initial velocity v2 final velocity 456 R.O. Ochola et al. / Composite Structures 63 (2004) 455–467
RO. Ochola et al. Composite Structures 63 (2004)455-467 ting. Specimens of 10, 30 and 45 orientation fracture distinct points will shift. The ultimate stress increases along the fibre predominantly by interlaminar shear, al- and the point at which complete separation takes place though cracks caused by a degree of tensile splitting are also seen on the surface of some of the specimens. Kumar delay) in the mode of failure at increasing strain rates et al. [7] deduced that the dynamic stress-strain curves Conclusion from this work also state that the test are linear up to fracture for angles of0 and 100, and non- specimens should maintain the same length to diameter linear for orientations greater than 100 ratio, L/D=l, and that the ultimate compressive stress Most of the research work in the area of dynamic is not influenced by the strain rate for values of &< 100 compressive testing of PMC has, however, been under- s-I but varies linearly with the strain rate for values of taken in the last decade. Work in 1991 by El-Habak [8] 100 <E< 1000 s-. Inherently the strain rate sensitivity investigated the behaviour of woven glass fibre rein- was found to be dependent on the matrix type and the forced composites subjected fibre volume fraction loading. The compression split Hopkinson bar was usec Tay et al. [12] studied specimens of cross-woven gl to produce failure at strain rates ranging from 10 to 10 fibre reinforced epoxy and pure epoxy resin was sub- s-l Results illustrated a slight increase in the compres- jected to dynamic compressive loading. Quasi-static sive strength for all composite variables such as fibre (E 10-3s-)and low strain rate(E 10 s-)tests were orientation and fibre volume fraction. The research conducted on a hydraulic tester, while a split Hopkinson concentrated on the comparison of selected matrix sys- pressure bar was used for tests at dynamic strain rates tems viz. vinyl ester, polyester and epoxy. The highest (E 10s"). Tay et al. [12] therefore proposed a simple strength is obtained from the composite based on vinyl empirical equation based on experimental results that ester matrix. Harding [9] investigated the effect of strain showed the behaviour of glass fibre reinforced polymer rate and specimen geometry of woven glass reinforced (GFRP) and pure epoxy to be strain rate sensitive. The epoxy laminate on two different specimen designs: (1)a non-linear stress-strain behaviour is inherently a matrix- olid cylinder, as commonly used with the compression dominated property, therefore the same form of equa- version of the Hopkinson bar and (2)a thin strip, wa- tion developed is applicable to both pure epoxy and isted in the thickness direction, as generally recom- GFRP. Unidirectional glass fibre reinforced polymer mended for composite laminate compression testing. composites are investigated by Takeda and Wan [13] Mean stress-strain curves for both specimen geometries using the improved SHPB apparatus that eliminates indicated a significant increase in the initial modulus, multiple loading of the compressive specimen, which is strength and the strain at failure with increasing strain prevalent in the conventional SHPB. Scanning electron rate. Generally under compression loading the shear microscopic analysis of the tested specimens revealed resistance of the epoxy resin matrix is likely to con- that the compressive failure of the unidirectional GFRP tribute considerably to both the elastic properties of t is caused by micro-buckling of the fibres under both laminate and to the resistance to shear band formation. impact and static loading conditions. The compressive The mechanical propert of epoxy resin are known strength is related to the non-linear in-plane shear be strongly rate dependent [10], therefore the effect of modulus of unidirectional composites, and the theoret strain rate on the initial Young,s modulus and the ulti- ical prediction shows good agreement with the experi- mate compressive strength is detected mental results. These results show an increase in El-Habak [11] studied the effects of various composite compressive strength with increasing strain rates [13] properties such as fibre volume fraction and specimen The compressive behaviour of unidirectional carbon/ size at high strain rates on glass fibre in a polyester and epoxy composites was investigated at varying strain epoxy resin, respectively. Results illustrated in the form rates by Hsiao and Daniel [14]. The transverse com- stress-strain and stress vs. strain rate curves show pressive strength increases at dynamic strain rates, to three distinct regions. The first being the maximum approximately twice the quasi-static value [14. The ul values of the strain rate achieved while the glass epoxy timate strain shows no strain rate effect, which implies a pecimen is being deformed elastically. The corre- strain dominated failure criterion for analysis under ponding value on the stress curve may be expressed as dynamic loadings. Longitudinal and cross-ply com- the elastic limit. The next region represents plastic de- pressive properties were obtained for varying strain formation. The final point represents the ultimate stress rates. The results show increases in strength and ultimate and the corresponding value of strain rate. This point on strain but only a moderate increase in initial elastic the stress-strain curve represents the maximum resis- modulus. Studies have also been carried out on ofl-axis tance of the specimen to fracture. An inflection point thermoplastic composite laminate specimens, which were exists beyond the final point on the stress-strain curve, tested at a wide range of strain rates. It was found that the after which the stress decreases more rapidly. This point composite behaviour is elastic up to failure in the fibre may be taken as the start of complete separation be- direction. Significant non-linear and strain rate depen tween the fibres and matrix. At higher strain rates these dent behaviour is exhibited by off-axis and angle-ply
ting. Specimens of 10, 30 and 45 orientation fracture along the fibre predominantly by interlaminar shear, although cracks caused by a degree of tensile splitting are also seen on the surface of some of the specimens. Kumar et al. [7] deduced that the dynamic stress–strain curves are linear up to fracture for angles of 0 and 10, and nonlinear for orientations greater than 10. Most of the research work in the area of dynamic compressive testing of PMC has, however, been undertaken in the last decade. Work in 1991 by El-Habak [8] investigated the behaviour of woven glass fibre reinforced composites subjected to compressive impact loading. The compression split Hopkinson bar was used to produce failure at strain rates ranging from 10 to 103 s1. Results illustrated a slight increase in the compressive strength for all composite variables such as fibre orientation and fibre volume fraction. The research concentrated on the comparison of selected matrix systems viz. vinyl ester, polyester and epoxy. The highest strength is obtained from the composite based on vinyl ester matrix. Harding [9] investigated the effect of strain rate and specimen geometry of woven glass reinforced epoxy laminate on two different specimen designs: (1) a solid cylinder, as commonly used with the compression version of the Hopkinson bar and (2) a thin strip, waisted in the thickness direction, as generally recommended for composite laminate compression testing. Mean stress–strain curves for both specimen geometries indicated a significant increase in the initial modulus, strength and the strain at failure with increasing strain rate. Generally under compression loading the shear resistance of the epoxy resin matrix is likely to contribute considerably to both the elastic properties of the laminate and to the resistance to shear band formation. The mechanical properties of epoxy resin are known to be strongly rate dependent [10], therefore the effect of strain rate on the initial Youngs modulus and the ultimate compressive strength is detected. El-Habak [11] studied the effects of various composite properties such as fibre volume fraction and specimen size at high strain rates on glass fibre in a polyester and epoxy resin, respectively. Results illustrated in the form of stress–strain and stress vs. strain rate curves show three distinct regions. The first being the maximum values of the strain rate achieved while the glass epoxy specimen is being deformed elastically. The corresponding value on the stress curve may be expressed as the elastic limit. The next region represents plastic deformation. The final point represents the ultimate stress and the corresponding value of strain rate. This point on the stress–strain curve represents the maximum resistance of the specimen to fracture. An inflection point exists beyond the final point on the stress–strain curve, after which the stress decreases more rapidly. This point may be taken as the start of complete separation between the fibres and matrix. At higher strain rates these distinct points will shift. The ultimate stress increases and the point at which complete separation takes place are delayed. El-Habak [8] therefore shows a change (or delay) in the mode of failure at increasing strain rates. Conclusion from this work also state that the test specimens should maintain the same length to diameter ratio, L=D ¼ 1, and that the ultimate compressive stress is not influenced by the strain rate for values of e_ < 100 s1 but varies linearly with the strain rate for values of 100 < e_ < 1000 s1. Inherently the strain rate sensitivity was found to be dependent on the matrix type and the fibre volume fraction. Tay et al. [12] studied specimens of cross-woven glass fibre reinforced epoxy and pure epoxy resin was subjected to dynamic compressive loading. Quasi-static (e_ 103 s1) and low strain rate (e_ 10 s1) tests were conducted on a hydraulic tester, while a split Hopkinson pressure bar was used for tests at dynamic strain rates (e_ 103 s1). Tay et al. [12] therefore proposed a simple empirical equation based on experimental results that showed the behaviour of glass fibre reinforced polymer (GFRP) and pure epoxy to be strain rate sensitive. The non-linear stress–strain behaviour is inherently a matrixdominated property, therefore the same form of equation developed is applicable to both pure epoxy and GFRP. Unidirectional glass fibre reinforced polymer composites are investigated by Takeda and Wan [13] using the improved SHPB apparatus that eliminates multiple loading of the compressive specimen, which is prevalent in the conventional SHPB. Scanning electron microscopic analysis of the tested specimens revealed that the compressive failure of the unidirectional GFRP is caused by micro-buckling of the fibres under both impact and static loading conditions. The compressive strength is related to the non-linear in-plane shear modulus of unidirectional composites, and the theoretical prediction shows good agreement with the experimental results. These results show an increase in compressive strength with increasing strain rates [13]. The compressive behaviour of unidirectional carbon/ epoxy composites was investigated at varying strain rates by Hsiao and Daniel [14]. The transverse compressive strength increases at dynamic strain rates, to approximately twice the quasi-static value [14]. The ultimate strain shows no strain rate effect, which implies a strain dominated failure criterion for analysis under dynamic loadings. Longitudinal and cross-ply compressive properties were obtained for varying strain rates. The results show increases in strength and ultimate strain but only a moderate increase in initial elastic modulus. Studies have also been carried out on off-axis thermoplastic composite laminate specimens, which were tested at a wide range of strain rates. It was found that the composite behaviour is elastic up to failure in the fibre direction. Significant non-linear and strain rate dependent behaviour is exhibited by off-axis and angle-ply R.O. Ochola et al. / Composite Structures 63 (2004) 455–467 457
R.O. Ochola et al. Composite Structures 63(2004)455-467 laminates. Comparison of the dynamic stress-strain curves with the quasi-static stress-strain curve shows the &s au f fects of strain rate, as noted by Weeks and Sun [15] There is no standardized test specimen geometry for Differentiating the strain in Eq.(2)with respect to the tests on composites with the SHPB. An attempt by time, t, gives the velocity investigate the effects of varying the length to diameter t au Woldesenbet and Vinson [16 was therefore made to at spect to the material properties at varying strain rates of where f" denotes the differentiation of f with respect to between 4x102 and 1.3x 103 s-1 The results show no x. The velocity in terms of the strain, a, and wave ve- statistically significant effect of either L/D or geometry locity, Co, is given by for carbon/epoxy laminates tested at varying strain rates. Both specimen shapes tested result in similar high (4) strain rate properties, therefore comparison can be made between varying test specimen shapes Gary and Zhao [17] employed the use of low im- pedance material such as nylon, for the incident and transmitter bars of the split Hopkinson bar, to test the substituting a=Ee and E= Cop, Eq. (5)can be re- strain rate behaviour of glass epoxy composite plates written as The failure strength of the glass epoxy plate tested by Gary and Zhao [17] is reported to be strain rate sensi U=-COE pCo tive. Fibre orientation effects on high strain rate prop. erties were considered recently for a carbon epoxy system. Vinson and Woldensenbet's [18] results show that the ultimate stress increases with increasing strain rate. Attempts to characterize the high strain rate be- where p is the density of the bar. haviour of fibl off-axis laminates and Due to convention in wave theory the negative sign in he split Hopkinson bar were carried out by Ninan et al Eq.(7) indicates the direction of the tensile [19]. Increases in the stress values of the off-axis glass therefore in this case the tensile pulse moves poxy composites are noted when the strain rate of the positive x direction (Fig. I). The compressive compressive loads is increased from static to dynamic taken as positive can be deduced from for the varying fibre orientations. Hosur et al. [20]in- o=pC vestigated the response of carbon/epoxy laminated composites under high strain rate compression loading The stress at the incident bar/specimen interface The results from this study indicate that the dynamic lown as A in Fig. 1, is given by strength and youngs modulus exhibit considerable in creases as compared to the static value (a-Or)ABar The objective of this paper is to investigate the com- pressive behaviour on cylindrical specimens of cross-ply and the stress at the specimen/transmitter bar interface, GFRP and carbon fibre reinforced polymer( CFRP) at labelled B in Fig. 1, is given by quasi-static and dynamic strain rates using a hydraulic compression rig and the split Hopkinson bar. A const utive relation is developed from the experimental data a B lo 2. Hopkinson bar theory a wave propagating in an elastic bar in the positive x direction is considered. The general solution of the lementary wave equation theory [23] becomes ncident bar Transmitter bar u=f(x-Cot) where u is the displacement, t the time and x the di placement of the particle. The one-dimensional strain is determined by differentiating the displacement equation Fig. 1 Schematic diagram of a compressive split Hopkinson pressure (1) with respect to x to give
laminates. Comparison of the dynamic stress–strain curves with the quasi-static stress–strain curve shows the effects of strain rate, as noted by Weeks and Sun [15]. There is no standardized test specimen geometry for tests on composites with the SHPB. An attempt by Woldesenbet and Vinson [16] was therefore made to investigate the effects of varying the length to diameter (L=D) ratio and/or geometry of the specimen with respect to the material properties at varying strain rates of between 4 · 102 and 1.3 · 103 s1. The results show no statistically significant effect of either L=D or geometry for carbon/epoxy laminates tested at varying strain rates. Both specimen shapes tested result in similar high strain rate properties, therefore comparison can be made between varying test specimen shapes. Gary and Zhao [17] employed the use of low impedance material such as nylon, for the incident and transmitter bars of the split Hopkinson bar, to test the strain rate behaviour of glass epoxy composite plates. The failure strength of the glass epoxy plate tested by Gary and Zhao [17] is reported to be strain rate sensitive. Fibre orientation effects on high strain rate properties were considered recently for a carbon epoxy system. Vinson and Woldensenbets [18] results show that the ultimate stress increases with increasing strain rate. Attempts to characterize the high strain rate behaviour of fibre composites using off-axis laminates and the split Hopkinson bar were carried out by Ninan et al. [19]. Increases in the stress values of the off-axis glass epoxy composites are noted when the strain rate of the compressive loads is increased from static to dynamic for the varying fibre orientations. Hosur et al. [20] investigated the response of carbon/epoxy laminated composites under high strain rate compression loading. The results from this study indicate that the dynamic strength and Youngs modulus exhibit considerable increases as compared to the static values. The objective of this paper is to investigate the compressive behaviour on cylindrical specimens of cross-ply GFRP and carbon fibre reinforced polymer (CFRP) at quasi-static and dynamic strain rates using a hydraulic compression rig and the split Hopkinson bar. A constitutive relation is developed from the experimental data. 2. Hopkinson bar theory A wave propagating in an elastic bar in the positive x direction is considered. The general solution of the elementary wave equation theory [23] becomes u ¼ f ðx C0tÞ ð1Þ where u is the displacement, t the time and x the displacement of the particle. The one-dimensional strain is determined by differentiating the displacement equation (1) with respect to x to give e ¼ ou ox ¼ f 0 ð2Þ Differentiating the strain in Eq. (2) with respect to the time, t, gives the velocity v ¼ ou ot ¼ C0f 0 ð3Þ where f 0 denotes the differentiation of f with respect to x. The velocity in terms of the strain, e, and wave velocity, C0, is given by ou ot ¼ C0 ou ox ð4Þ or v ¼ C0e ð5Þ substituting r ¼ Ee and E ¼ C2 0q, Eq. (5) can be rewritten as v ¼ C0 r E ¼ r qC0 ð6Þ giving r ¼ qC0v ð7Þ where q is the density of the bar. Due to convention in wave theory the negative sign in Eq. (7) indicates the direction of the tensile pulse, therefore in this case the tensile pulse moves in the positive x direction (Fig. 1). The compressive stresses taken as positive can be deduced from r ¼ qC0v ð8Þ The stress at the incident bar/specimen interface, shown as A in Fig. 1, is given by rs1 ¼ ðri rrÞABar AsðtÞ ð9Þ and the stress at the specimen/transmitter bar interface, labelled B in Fig. 1, is given by Fig. 1. Schematic diagram of a compressive split Hopkinson pressure bar. 458 R.O. Ochola et al. / Composite Structures 63 (2004) 455–467
R.O. Ochola et al. Composite Structures 63(2004)455-467 Ct 032=A(0) (10) mens used in both the SHPB and the hydraulic machine are shown in Fig. 2. The displacement in the two bars results in true strain of 3.2. Quasi-static compressive tests the specimen A hydraulic testing machine was used to determine In the compressive strengths of carbon and glass fibre specimens at quasi-static strain rates. The specimens By differentiating Eq.(11)with respect to time, t, the were tested between two flat metal cylinders one at- strain rate in the specimen is given as tached to the grips and the second at the load cell. The U1-U2 assembly was placed so that the specimens were cen- o(1) (12) trally located between the metal stages, and compressed at a rate of 0.5 mm/min, equivalent to a strain rate of 2x10-'s. The quasi-static results were recorded in the form of load displacement curves with maximum loads 3. Experimental set-up and procedure of 30 kN for displacements of 0.4-0.7 mm. This data converted into stress-strain curves to determine the 3.1. Materials and specimens strain and ultimate compressive strengths. The quasi static experimental set-up was designed so as to enable a In this study 48-ply layered cross-ply laminates were direct comparison of the compressive material strengtH manufactured for the purpose of investigating strain parameters from the quasi-static tests with those of the rate effects. The gfRP laminates were fabricated from split Hopkinson bar. The focus is on keeping constant unidirectional (UD)standard E glass in an Ampreg 20 specimen geometry for both sets of tests viz. the quasi epoxy matrix. The CFRP was fabricated using UT static and dynamic strain rates C300/500 carbon tows in an epoxy matrix. Laminates in the form of plates of thickness 10.8 mm were cured at 60 3.3. High strain rate compressive tests for 2 h. The plates were machined into specimens with diameter (D)8.0 mm and length 8.0 mm. The For the high strain rate test a split Hopkinson bar set lengths (L)are reduced to 4.0 mm from subsequent up was employed. A schematic of the set-up is shown in polishing of the specimen. Extreme care was exercised Fig 3. The set-up comprises a gas gun/test chamber(D), when shaping the specimens to the desired geometry to striker bar (2), incident bar (4), transmitter bar (6). ensure dimensional accuracy and to prevent delamina- strain gauges(3i, 1), on incident bar and transmitter bar tions in the composite specimens due to machining. The and momentum trap or stopper(7). In the SHPB tech dimensions, geometry and nique a small st elastic bars (4 and 6) of similar cross-sectional area and Youngs modulus. The test chamber pressure of the Hopkinson bar varied from 400 to 600 kPa, results in strain rates of between 200 and 900 s-. An elastic stress pulse is imparted into the incident bar (4) by impacting it with a striker bar(2). The impact of the striker bar generates a longitudinal compressive incident stress L pulse, i, equal to twice the length of the striker bar, that travels down the incident bar and is recorded by the pecten Geometry Direction strain gauge(3i) at the incident bar. The pulse then reaches the incident bar/specimen interface where part Fig. 2. Geometry and loading direction for specimens. of the pulse is reflected in the form of a tensile stress I Gas gun 2 Striker bar 3 Strain gauges 4 Incident bar 5 Specimen 6 Transmitter bar Fig. 3. Schematic diagram of a compressive split Hopkinson pressure bar[23]
rs2 ¼ rtABar AsðtÞ ð10Þ The displacement in the two bars results in true strain of the specimen etrue ¼ ln l l0 ð11Þ By differentiating Eq. (11) with respect to time, t, the strain rate in the specimen is given as e_ ¼ v1 v2 l0ðtÞ ð12Þ 3. Experimental set-up and procedure 3.1. Materials and specimens In this study 48-ply layered cross-ply laminates were manufactured for the purpose of investigating strain rate effects. The GFRP laminates were fabricated from unidirectional (UD) standard E glass in an Ampreg 20 epoxy matrix. The CFRP was fabricated using UTC300/500 carbon tows in an epoxy matrix. Laminates in the form of plates of thickness 10.8 mm were cured at 60 C for 2 h. The plates were machined into specimens with diameter (D) 8.0 mm and length 8.0 mm. The lengths (L) are reduced to 4.0 mm from subsequent polishing of the specimen. Extreme care was exercised when shaping the specimens to the desired geometry to ensure dimensional accuracy and to prevent delaminations in the composite specimens due to machining. The dimensions, geometry and loading directions of the specimens used in both the SHPB and the hydraulic machine are shown in Fig. 2. 3.2. Quasi-static compressive tests A hydraulic testing machine was used to determine the compressive strengths of carbon and glass fibre specimens at quasi-static strain rates. The specimens were tested between two flat metal cylinders one attached to the grips and the second at the load cell. The assembly was placed so that the specimens were centrally located between the metal stages, and compressed at a rate of 0.5 mm/min, equivalent to a strain rate of 2 · 103 s1. The quasi-static results were recorded in the form of load displacement curves with maximum loads of 30 kN for displacements of 0.4–0.7 mm. This data is converted into stress–strain curves to determine the strain and ultimate compressive strengths. The quasistatic experimental set-up was designed so as to enable a direct comparison of the compressive material strength parameters from the quasi-static tests with those of the split Hopkinson bar. The focus is on keeping constant specimen geometry for both sets of tests viz. the quasistatic and dynamic strain rates. 3.3. High strain rate compressive tests For the high strain rate test a split Hopkinson bar setup was employed. A schematic of the set-up is shown in Fig. 3. The set-up comprises a gas gun/test chamber (1), striker bar (2), incident bar (4), transmitter bar (6), strain gauges (3i; t), on incident bar and transmitter bar and momentum trap or stopper (7). In the SHPB technique a small specimen (5) is sandwiched between two elastic bars (4 and 6) of similar cross-sectional area and Youngs modulus. The test chamber pressure of the Hopkinson bar varied from 400 to 600 kPa, results in strain rates of between 200 and 900 s1. An elastic stress pulse is imparted into the incident bar (4) by impacting it with a striker bar (2). The impact of the striker bar generates a longitudinal compressive incident stress pulse, ri, equal to twice the length of the striker bar, that travels down the incident bar and is recorded by the strain gauge (3i) at the incident bar. The pulse then reaches the incident bar/specimen interface where part of the pulse is reflected in the form of a tensile stress Fig. 3. Schematic diagram of a compressive split Hopkinson pressure bar [23]. Fig. 2. Geometry and loading direction for specimens. R.O. Ochola et al. / Composite Structures 63 (2004) 455–467 459