5--XXXX Strength Analysis of CFRP Composite Material Consiering Multiple Fracture Moes Author, co-author (Do NOT enter this information. It will be pulle from participant tab in MyTechZone) Affiliation (Do NOT enter this information. It will be pulle from participant tab in MyTechZone) Abstract The strength characteristic of CFRP composite materials often is epenent on the internal micro-structural fracture moe. Therefore, in orer to precisely preict this strength, each fracture moe an its mutual influence must be taken into account in a simulation. In this paper, intra-ply fracture progression an loa characteristics of a cyclic loaing test were analyze, utilizing a material moel propose by Laeveze et al. The moel can evaluate ifferent fracture moes an the stiffness egraation resulting from them. The analyze results were compare with actual test results to confirm the valiity of the analysis. Another analysis was performe without consiering the mutual influence of the ifferent fracture moes, an the results were compare to iscuss the necessity of the coupling. Introuction Carbon fiber reinforce plastic (CFRP) composite material has a higher specific strength an stiffness than steel, so it is expecte to contribute to the overall weight reuction of automobile structures. Unlike metals, CFRP tens to show micro-fractures of the resin insie the structure, an often its strength is etermine by its fracture moe. Therefore, it is necessary to consier each fracture moe an its progression in orer to accurately preict its strength by simulation. In one of the methos, progression of the fracture is reprouce by applying pre-efine stiffness egraation to the location where certain criteria, which are also efine for each fracture moe, are reache. The valiity of this moel is shown by an FEM analysis of the static an ynamic loaing of automobile structure parts []. On the other han, some failure moels have been propose that apply the iea of amage to the micro-fractures insie the composite laminate for a more clear efinition of stiffness egraation [,3]. By consiering the stiffness reuction an change in stress istribution ue to that reuction, an evaluation of loa an strength characteristics becomes possible. But in orer to appropriately moel the amages, all amages an mutual influences (coupling) must be expresse in functions, which is not easily one without knowlege of the internal fracture progression. Page of 6 In this paper, a numerical analysis of composite test specimens was performe by aopting the amage moel propose by Laeveze et al. to take into account the stiffness egraation ue to the amage, an mutual coupling of ifferent amage moes. The analyze results were then compare with coupon tests to show the necessity of consiering the coupling between ifferent fracture moes, an how the coupling factor affects the reproucibility of the test results. Intra-Ply Material Moel First of all, the intra-ply fracture moel for composite laminate with uni-irectional fiber will be escribe. In this paper, the moel by Laeveze et al. is applie. Definition of Intra-ply Damage Moel Strain energy Eq. (). insie the ply is expresse by the following 3 33 3 E D 33 E E E3 E E () 3 E 33 G G 3 3 G E i an G ij are oung s moulus an shear moulus, respectively, is stress, is Poisson s ratio, an subscripts,, an 3 each represent the axis irection in the composite coorinate system, as shown in Fig.. Damage variables ij resulting from each fracture moe are introuce as in Fig., an the reuction of each moulus is efine as Eq. (). E E ( ) G E E ( ) 3 G ( ) an are the initial mouli before amage is applie. Simplifying Eq. () into a two-imensional form an combining it with Eq. () will result in two-imensional strain energy that takes into account the amage. 3 ()
E D E ( ) E ( ) E E G( ) (3) an represent tensile an compressive stress, respectively. Here, thermoynamic force ij is introuce as efine by Eq. (4). The coupling of two amage variables is efine as follows using the coefficient b 3. (7) b3 Figure shows the relationship between an. is the energy where amage is initiate, s is the critical energy value where amage reaches. ij E D ij (4) Therefore, E D E D E D E G ( ( E ( As can be seen from Eq. (5), amage variables ij can be efine as functions of thermoynamic forces ij. These thermoynamic forces can be seen as energies impacting the ifferent amages. When these energies increase, each relate amage variable ij will also increase. ) ) ) (5) Figure.Comparison of Shear an Transverse Damage Characteristics Definition of Resin Plasticity an Fiber Nonlinearity The effect of permanent eformation ue to the plastic strain of resin is accounte for in the moel using following equation. ~ R Kp (8) is equivalent shear stress, R is yiel stress, p is permanent strain, an K an are both material parameters. p is efine as an accumulation of plastic shear strain, using the following equation. ~ (9) p p p ( ) On the other han, the non-linearity of the fiber moulus is also taken into account using the following equation. Figure. Schematic Drawing of Composite Coorinate System an Damage Moes Definition of Damage Coupling Parameter The amage by shear an the amage in the transverse irection with respect to the fiber are both ue to the fracture of the resin. Therefore, some kin of mutual influence must be consiere. An equivalent thermoynamic force is efine as a combination of both energies in the shear an in transverse irections, applying the coefficient b. b (6) E E () + an - are coefficients for tension an compression, respectively. Damage Parameter Ientification Process In this section, the ientification process for the CAE parameters regaring the efinition of each amage variable will be iscusse. Each parameter is ientifie through a series of coupon tests with ifferent ply configurations. For the ientification of these parameters, FEM analysis is not necessary. Page of 6
Ientification of Fiber Damage Property The amage characteristic for the fiber tension irection is obtaine from a tension test of either [] ns or [/9] ns coupon. Since fibers show brittle fractures, the amage evolution woul look like that shown in Fig. 3. Fiber fracture stress max is first erive from the ultimate stress of the tension test, then the critical thermoynamic force t is calculate from the following equation. t () E max Figure 5. Shear Damage Characteristic The critical thermoynamic force c in the compression irection can be obtaine in a manner similar to that of the tensile test. Figure 3. Damage Characteristic of Fiber Ientification of Shear Damage Property The amage characteristic in the shear irection can be erive from a cyclic tension test of [+45/-45] ns coupon specimen. In a cyclic tension test, the specimen is repeately loae an unloae with increasing loa after every cycle. Then, as shown in Fig. 4, shear mouli are etermine in each loa cycle to obtain the amage from the Eq. (). Next, is calculate from Eq. (5) for every loa cycle. Finally, calculate an are plotte on the graph to obtain the shear amage characteristic as shown in Fig. 5. Ientification of Transverse Damage Property an Coupling Parameters The amage characteristic in the fiber s transverse irection, an the coupling coefficients with the shear amage, b an b 3, are erive from a [+67.5/-67.5] ns cyclic test together with the previously mentione [+45/-45] ns cyclic test results. From the stress-strain measure in the [+67.5/-67.5] ns test, shear stressstrain - an transverse stress-strain - relations are first calculate. Then using both stress-strain relations,,,, an for each loa cycle is erive in a way similar to that explaine in the previous section. To obtain coupling parameter b, its value is fixe so that plotte as a function of equivalent thermoynamic force, match with plot in Fig. 5, which was obtaine from a [+45/-45] ns test. The two functions are plotte together with the ientifie value of b in Fig. 6. Figure 6. Ientification of b A similar proceure is use to efine b 3. Consiering the relation shown in Eq. (7), the value of b 3 is set so that ( ) erive from the [+45/-45] ns test an ( ) from the [+67.5/-67.5] ns test overlap each other. Figure 4. Stress-Strain Curve of [+45/-45] ns Cyclic Test Page 3 of 6
Figure 7 Ientification of b 3 FEM Moel Figure 8 shows the coupon moel use for FEM analysis. The moel consists of soli elements with an overall length of mm an a with of 5mm. The thickness of each ply is.7mm, an the single soli is.86mm, which correspons to 8 plies. There are three-ply configurations, [+45/-45] s, [+67.5/-67.5] s, an [+67.5/+.5] s, with egree on the loaing irection. Shell elements are attache to the surface to measure the strains on loaing irection an transverse irection. One en of the moel is constraine an the other en is given a cyclic tension loa. The amage is assume to only act two imensionally. The coupling parameters are b =.5 an b 3=.6. The implicit solver SAMCEF was use for the analysis. Figure 9. Shear Stress-Strain Comparison of [+45/-45] s Lay-up Figure 8. FEM Coupon Moel Simulation Results Using the previously ientifie parameters an FEM moel, a cyclic tension loaing test was simulate. To iscuss the importance of the coupling parameters, analyses were performe both taking them into account an not taking them into account. Results Consiering the Coupling Parameter Figures 9 an show the simulate an experimental results of the [+45/-45] s an [+67.5/-67.5] s configurations, respectively. For the [+45/-45] s configuration, stress-strain on the shear irection is shown, while for [+67.5/-67.5] s, stressstrain on both the shear an transverse irections are shown. Although an FEM analysis was not use for parameter ientification, the simulate results accurately reprouce the stiffness egraation ue to amage progression, an permanent eformation after unloaing. Figure. Stress-Strain Comparison of [+67.5/-67.5] s Lay-up Figure shows a similar result for the [+67.5/-.5] s configuration, which was not use for parameter ientification. Since fibers o not intersect perpenicularly, longituinal strain L an transverse strain T are use for the comparison. The simulate results correlate with the experimental ones with this ply configuration also. It can be sai that this amage moel Page 4 of 6
can be applie for amage evaluation for composites with any ply configuration. coupling parameter is essential to ensure the accuracy of the intra-ply fracture analysis of composites. Figure. Stress-Strain Comparison of [+67.5/+.5] s Lay-up Results without the Coupling Parameter In this section, the simulate result which i not take into account the amage coupling parameter b 3 is presente. When b 3 is ignore, the amage in the fiber s transverse irection will not be taken into account. Figure shows the result for the [+45/-45] s configuration. In this lay-up, the absence of b 3 has only a small influence because the stress in the transverse irection is small. The only ifference is the fracture before the final loa cycle. Because the amage in the transverse irection is not consiere, the stress increases, resulting in a slight early increase in shear amage, an early failure. Figure 3. Shear Stress-Strain Comparison of [+67.5/-67.5] s Lay-up with b 3= Summary/Conclusions Figure. Shear Stress-Strain Comparison of [+45/-45] s Lay-up with b 3= Figure 3 shows a similar result for the [+67.5/-67.5] s lay-up. It can clearly be seen that there is a ifference in the transverse stress an strain. This is because the amage in the transverse irection was not consiere. Therefore, no stiffness reuction occurre an the stress rose higher than in the experiment. This will result in an over-estimation of composite stress. It can be conclue that consieration of the. The fracture moel propose by Laeveze et al. aopts the iea of amage variables an stiffness egraation ue to amage for the analysis of uni-irectional continuous fiber laminate composites.. A process for eriving FEM parameters from coupon tests was presente, an it was emonstrate that vali parameters can be ientifie without FEM analysis. 3. It was confirme that with the ientifie parameters, the amage progression in cyclic loaing tests can be reprouce. 4. The importance of amage coupling between the shear an transverse irections was iscusse. References. Abe, D., Urushiyama,., Examination on Dynamic Bening Characteristics of a CFRP Beam Using a Progressive Fracture Moel, Transactions of the Society Page 5 of 6
of Automotive Engineers of Japan, 9457, 4(5):39-44, 9.. Laeveze, P., Le Dantec, E., Damage moeling of the elementary ply for laminate composites, Composites Science an Technology 43:57-67, 99. 3. Matzenmiller, A., Lubliner, J., Taylor, R.L., A constitutive moel for anisotropic amage in fiber-composite, Mechanics of Materials : 5-5, 995. Contact Information Taashi Naito Hona R&D Co., Lt. Automobile R&D Center 493 Shimotakanezawa, Haga-machi, Haga-gun, Tochigi 3-3393, Japan. taashi_naito@n.t.r.hona.co.jp Page 6 of 6