Strain Rate and Temperature Effects on the Nonlinear Behavior of Woven Composites

Transcription

1 ICCM 17 UK 29 Strain Rate and Teperature Effects on the Nonlinear Behavior of Woven Coposites Liqun Xing, Ken Reifsnider Departent of Mechanical Engineering University of South Carolina, Colubia, SC Abstract A polyer-based woven coposite was selected and has been characterized using off-axis coposite speciens at different strain rates and teperature. A strain rate teperature equivalence principle is introduced to describe the nonlinear behavior of selected coposites. Experiental data shows the validation of the proposed ethod. An application of coparing the large-strain constitutive theory for describing the nonlinear behavior of woven coposites under dynaic loading and the strain rate teperature equivalence ethodology for experient ipleentation was presented. 1 Introduction Many structure applications of coposite aterials incorporate woven fiber architectures. These aterials have very different response to uniaxial loading in different directions relative to the principle fiber directions that can be odeled by the large-strain constitutive theory [1-4]. They also have a strong dependency on strain rate and teperature. The evolution of stiffness and strength of the coposite aterials subject to different tie period and teperature during creep or fatigue process has been investigated and showed a tie-teperature equivalent [5]. However, ost of the studies focus on the effect of evaluated teperature and its relation with the roo teperature in a long-ter deforation. The ai of this study was to investigate the relation of coposite aterials behavior between low teperature quasi- static conditions with the roo teperature high strain rate conditions. In this study, a plain-weave vinyl ester coposite aterial was selected and a nuber of different strain rate and teperature tensile tests of off-axis coupon speciens were conducted. Coparison of coposite nonlinear behavior under different strain rate and teperature indicated that there was a strain rate teperature relationship between the. Two strain rate teperature equivalence odels based on Willias-Landel-Ferry relationship, Monkan-Grant concept and Arrhenius equation were developed to represent the effects of different strain rate and teperature. The stress-strain analysis that involved in coparing the large-strain constitutive theory and the strain rate teperature equivalent ethodology for different strain rates was presented. 2 Experiental Tensile tests were perfored at various strain rates fro low (.1/s) to oderate (.1/s) on an Instron TM servo-hydraulic testing achine with a axiu loading capacity of 2, lb.; tests were controlled with a digital control loop using Instron TM Fast-Track 88 software. Data collection was done by Instron Fast-Track 88 progra and a clip gage fabricated by the authors. The roo teperature is 26 C and other test teperature was set up in the range of -15 C ~7 C by the cooling and heating chaber syste. The aterial tested was E-glass/vinyl ester coposite, a ten-ply lainated plate configuration as [º, 9º, º, 9º, º, 9º, º, 9º, º, 9º] s. The thickness of the plate was.18 in. Rectangular speciens with gauge length 3in and width.75in were cut fro the plate in directions of θ=º, 15º, 3º, 45º, 6º, 9º with respect to the outer ply reinforceent direction. There was 1.5 in grip length on both ends of the specien that yielded the specien size of in with a gauge length of 3 in, as shown in Fig.1.

2 ICCM 17 UK 29 Fig.1. Geoetry and diensions of specien 2.1 Mechanical behavior at different strain rate and teperature Fig. 2 & 3 show results for one specien angle at different strain rates. It shows that strain rate dependence is evident in such aterials, even for strain rates that differ by only a few orders of agnitude. Fig. 4 & 5 show results for one strain rate of speciens under different teperature. It shows high nonlinear stress-strain relationships that strongly relate to different teperature /s.1/s.2/s % 1% 2% 3% 4% 5% 6% Fig.2 Tensile behavior pulled at different strain rate at 15º to the principal aterial direction /s % 4% 8% 12% 16% 2%.2/s.1/s Fig.3 Tensile behavior pulled at different strain rate at 45º to the principal aterial direction T=C T=5C T=7C Stress (Psi) T=25C T=5C T=7C 1 1 % 1% 2% 3% 4% 5% 6% Fig.4 Stress-Strain of 15º Specien in Different Teperature at.1/s Strain Rate 5 % 2% 4% 6% 8% 1% 12% 14% 16% Strain (in) Fig.5 Stress-Strain of 6º Specien in Different Teperature at.1/s Strain Rate 3 Model for Strain Rate and Teperature Effects Fro the test data, it can be seen that different teperature has the siilar effects on the nonlinear behavior of woven coposite at a fixed strain rate. It gives us the idea that teperature and strain rate ay have an equivalent effect on the coposite aterials behavior.

3 ICCM 17 UK Constituent Behavior Model and Fro the test data we can get the epirical odel of the strain rate and teperature effects as follows: Where E, εσ,, T b E = B log ε + C 1 1 σ b = B2 log ε+ C 2 E = E ( ) ( ) T + D T T σ = σ ( T b b ) + k ( T T ) (2) Represent the elastic odulus, strain rate, strength and teperature. (1) Strength(Ksi) Log(strain rate1/sec) 15 degree 45 degree 9 degree Fig.6 Variation of the coposite strength Vs strain rate Strength (Psi) degree 6 degree Teperature (K) Fig.7 Variation of the coposite strength Vs teperature 3.2 Monkan-Grant odel For the relationship between tie to failure and strain rate, there is a siple and widely used equation, usually known as Monkan-Grant equation as: tb ε = C 1 (3) relationship. Where t b is the failure tie and is a constant, C 1 is a aterial constant. Fig. 9 shows this Log( tie to failure) 15 degree 45 degree 9 degree Log(strain rate 1/s) Fig.8 Variation of the coposite tie to failure Vs strain rate T=26C at.1/s_1 T=5C at.1/s T=26C at.1/s_2 % 2% 4% 6% 8% 1% 12% 14% 16% 18% Fig.9 3 specien test data at different strain rate and teperature 4 Model for Strain Rate and Teperature Equivalence Fro the above sections, it can be seen that echanical properties of woven coposite aterials are a function of strain rate and teperature. The equivalence between strain rate effects and the teperature effect on the sae state of aterials can be proposed for such aterials. This can be done through

4 ICCM 17 UK 29 equation of (1) to (3). The objective would be to specify the equivalent teperature, T, for a strain rate, or inversely, to specify the equivalent strain rate for a specified teperature T. 4.1 LWF Approach Fro equation (1) we can get E = b1 logε + c1 σb = b2 logε+ c2 Bi Bi ( bi =, ci = log C2 + Ci, i = 1,2... n) (4) By cobining equation (3) and (4) we can get: logεt = log ε + kt ( T) D2 ( k = b ) 2 T (5) 4.2 Attherrius Equation Approach Attherrius Equation ΔH ε = Aexp( 2.33GT ) (6) Then we have logε = log + k ( ) ΔH ( k = ) a T 1 1 ε T a T T 2.33G (7) 1 ( ) T ε ε T = ka log T + 1 T (8) Where, T and T represent different teperature in absolute teperature unit. 5. Validation of strain rate and teperature equivalent By coparing the data shown in Fig. 2 to 7 we can get Fig. 9 as below. It can be found that test data of strain rate at.1/s in T=26(C is alost identical to strain rate at.1/s in T=5(C. Based on this observation and equation (7) we can get the value of EMBED Equation.DSMT4 is.124. If we want to get the equivalent test in teperature T=26(C and strain rate at.1/s, we can set the test strain rate at.1/s and use the sae EMBED Equation.DSMT4 value in equation (8) to get the teperature, which turns out to be T=5(C. The validation test result is shown in Fig.1

5 ICCM 17 UK % 2% 4% 6% 8% 1% 12% 14% 16% 18% T=5C at.1/s T=26C at.1/s_1 T=26C at.1/_ test date odel prediction % 2% 4% 6% 8% 1% 12% 14% 16% 18% 2% Fig.1 Validation of 3 specien test data at different strain rate and teperature Fig.11 Coparison of s test data of T= -12 C at strain rate.1/ with odel prediction of T=26 C 6. Application of the strain rate and teperature equivalent The rate dependent nonlinear behavior of woven coposite can be odeled by constitutive equation as the prior work [1-3]. Using that odel we can predict the nonlinear behavior of the coposite at a high strain rate condition. But it is usually difficult to get accurate coposite aterials behavior in high strain rate through experient in order to validate the odel prediction. By using the strain rate and teperature equivalent concept we can to overcoe this difficulty. Fig. 11 shows the coparison of constitutive odel prediction at strain rate 1/s of roo teperature and the odel calculated equivalent experient condition data at strain rate.1/s of T= -12(C. It shows a good agreeent. 7. Conclusion Tensile tests were conducted on off-axis woven glass reinforced vinyl ester coposite lainate speciens with different strain rates and teperature. Effects of strain rate and teperature to the nonlinear aterial behavior were analyzed. It shows that quasi-static test at low teperature has a siilar nonlinear response behavior as the high strain rate at roo teperature. The proposed ethod based on LWF and Attherrius equations can be used for describing the strain rate and teperature equivalence. Validation of the odel was conducted through the test data and showed a good agreeent with the odel prediction. A useful application of the proposed equivalent odel was also discussed. Continuing efforts focus on odeling the structural response of coposites and lainates subjected to general dynaic loading and environental conditions. Acknowledgeents

6 ICCM 17 UK 29 The authors gratefully acknowledge the support of this research by the Office of Naval Research under contract nuber N References [1] Tauzs, V., Dzelzitis, K. and Reifsnider, K.L., Applied Coposite Materials, Vol.11 No.5, , 24 [2] Tauzs, V., Dzelzitis, K. and Reifsnider, K.L., Applied Coposite Materials, Vol.11 No.5, , 24 [3] Ogihara, S. and Reifsnider, K.L., Applied Coposite Materials, Vol.9, , 22 [4] Sun C.T. and Chen, J.L., Coposite Materials, 23, , 1989 [5] Reifsnider, K.L and Case, S., Daage tolerance and durability of aterial systes, John Wily & Sons, New York, 22.