Modeling Damage Tolerance in Composite Structures: Selecting ...
MODELING DAMAGE TOLERANCE IN COMPOSITE STRUCTURES: SELECTING MATERIAL DEGRADATION PARAMETERS Ray S. Fertig III and Jerad Stack Firehole Composites 210 S 3rd Street, Suite 202 Laramie, WY 82070 Adam Biskner LoadPath 933 San Mateo Boulevard, Ste 500-326 Albuquerque, NM 87108
ABSTRACT Predicting the effects of damage in composite structures is critical to determining the safety of the structure. But even if the region of damage is well-defined, accurately simulating its effect on the performance of the structure depends on the degree to which material properties in the damaged region have been degraded. In the work reported here, we examine experimentally and computationally a variety of material property degradation schemes and biaxial composite loadings. The computational work reported utilizes multicontinuum theory to permit multiscale analysis of the composite such that fiber and matrix behavior can be separated and modeled. As such, the degradation parameters considered are specific to the fiber and matrix constituent, separately. We particularly investigate the effects of isotropic versus anisotropic material degradation, as well as the potential dependence of the degradation material parameters on the loading of the composite.
1. INTRODUCTION Despite growing acceptance of composites in a variety of applications, there continues to be difficulty in assessing the use composites in applications where low levels of damage are present either via impact loads or induced manufacturing flaws. Manufacturing flaws or damage from a low-energy impact event can include significant delamination and microcracking with little or no visible surface damage, making damage detection difficult. But this damage can still cause significant reductions in residual strength of a composite structure. The residual strength of these damaged composites needs to be evaluated in order to ensure that it exceeds damage tolerance requirements. Often these composites are already in use, so experimental testing is not possible if the part is to be returned to service. The ideal approach would be to validate damage tolerance via simulation. The difficulty with simulation is that failure of composite structures is an extremely complex event. Multiple local damage mechanisms often initiate at loads far below structural failure levels. Damage mechanisms may include void accumulation in the matrix, matrix microcracking, fiber rupture in tension, fiber kinking or crushing in compression, and delamination between
plies. Localized damage induces nonlinear behavior at several geometric scales, which can produce a nonlinear response at the structural level. Consequently, progressive failure analysis, characterized by incremental loading of a structure, is the only way to simulate a nonlinear structural response. The difficulties that are usually encountered in simulating progressive failure behavior in general purpose finite element codes stem from convergence problems and inaccurate methods for predicting multiple failure modes. In particular, failure in composite laminates can be summarized by a progression of the following events, which must be accurately captured in order to achieve an accurate failure progression simulation: • • • • •
Matrix failure initiation Matrix failure propagation Fiber failure initiation Fiber failure propagation Ultimate failure
Each failure event causes a reduction in composite stiffness, which causes stress redistribution. The sequence of events can vary depending on the loading. Additionally, this progression of discrete events occurs separately in the matrix and fiber constituents. Firehole Composites has developed the finite element add-on software Helius:MCT™ specifically to address these issues by applying distinct failure criterion to the fiber and matrix and a stiffness degradation specialized for these different composite failure states [1], [2]. The goal of the work reported here was to evaluate various constituent degradation models by modifying Helius:MCT and comparing its compressive failure results with high quality experimental data. The composite structures of interest were carbon-epoxy cruciform specimens with a specified amount of damage due to indentation. The specimens were tested to failure under various biaxial loads. Simulation results using various material property degradation schemes, both for initial damage tolerance as well as damage propagation, were qualitatively and quantitatively compared with experimental results.
2. EXPERIMENTATION 2.1 Experimental Setup The experimental work described here was performed by LoadPath, LLC. The primary objective of this effort was to create a well-defined region of fiber crushing damage to a quasi-isotropic composite laminate and evaluate its effect on the biaxial strength of the laminate. This task required two independent experimental setups, one to induce fiber crushing damage and the other to impose an in-plane, multi-axial stress state on the damaged laminate. Biaxial cruciform coupons were constructed from IM7/8552 carbon fiber/epoxy resin unidirectional tape, fabricated with a quasi-isotropic gage section, and tested to failure in the Triaxial Test Facility located on Kirtland AFB, NM. The test system, shown in Figure 1, consists of a custom electromechanical test frame that is capable of generating combinations of tensile or compressive stresses in σ1:σ2:σ3 stress space and can evaluate the uniaxial, biaxial, or triaxial response of materials. The machine computer controls six actuators (two per axis), each with a
capacity of 30 kip. A precision alignment fixture, shown on the right side of Figure 1, guides the wedge grips, assures true orthogonal loading of the specimen, and mitigates buckling in compressive load states.
Figure 1. Triaxial Test Facility and Load Frame Alignment Fixture The complement to the test facility is a well-defined biaxial cruciform specimen shown in Figure 2. Composite coupons are machined from a solid laminate that includes the center gage section and integrated reinforcing composite tabs to optimize the load path from the test frame to the specimen’s gage section. Both the general coupon shape and thickness-tapered gage section are machined using a computer numeric controlled (CNC) mill. Throughout previous work, continual improvements have been made to the geometric details of the thickness-tapered cruciform, laminate fabrication process, and coupon machining techniques. The final specimen design has since been successfully used to evaluate the biaxial strength of cross-ply, quasiisotropic, unidirectional, and woven laminate configurations.
Figure 2. Unidirectional Laminate Biaxial Cruciform
The damage test method was derived from ASTM D 6264 [3]. In this method, a quasi-static indentation (QSI) is used to obtain quantitative measurements of the damage resistance of a continuous-fiber-reinforced composite material to a concentrated indentation force. The indentation force is applied to the specimen by slowly pressing a hemispherical indenter into the surface. The procedure specifies the use of either a simply supported or rigidly backed test specimen during the damage event. The damage resistance is quantified in terms of a critical contact force versus indenter displacement. This standard was utilized because quasi-static indentations have been shown to effectively represent practical low-velocity impact events such as tool drops. The indentation test setup is shown in Figure 3. This program made two significant deviations from the ASTM standard, the test specimen geometry and indenter size. The ASTM D 6264 method and its incorporated indenter were formulated for the typical 4 inch by 6 inch plate compression after impact (CAI) coupon; however, this program is studying the effects of damage on biaxially loaded cruciform specimens. To accommodate the cruciform, which contains a gage section nominally 0.95 inch square, the hemispherical indenter’s diameter was reduced from 0.500 inch to 0.250 inch. Also shown in the figure, a rigid 0.875 inch square platen supported the impacted gage section during the damage process. The indenter was pressed into the laminate at a rate of .02 in/min until the reacting force reached -4,500 lbs. This end point was initially selected because it is twice the magnitude of an event described by Lee and Soutis [4] that caused sufficient damage in a similar laminate, and practice trials determined that it induced significant visual damage on the impacted surface, including fiber crushing, without harming the non-impacted face.
Figure 3. Quasi-static Indentation Test Setup
A total of six stress ratios were tested, three tension/tension and three compression/compression. Using the nomenclature of 1-direction stress/2-direction stress, the present study examined 1/0, 1/1, and 1/5 ratios in the tension/tension failure envelope quadrant and similarly -1/0, -1/-1, and 3/-1 in the compression/compression regime. The test articles contained a 32-ply gage section, a portion of the cruciform [(90/0)3(45/-45)(45/0/-45/90)4]S layup, where the gage section contained the [(45/0/-45/90)4]S portion of the laminate. Each coupon included a Vishay CEA-06-125UT350 biaxial strain gage in the center of the gage section on the undamaged face. The QSI damage event was relatively repeatable throughout the 18 coupon set. The indenter was pressed into the laminate until a contact force of -4,500 lbs was reached within the accuracy parameters of the load frame’s control system. For each specimen, the peak load was achieved within 0.1 percent of the desired end level. The corresponding displacement of the indenter ranged from 0.043 to 0.047 inches with a mean of 0.045 inches, meaning the behavior of the material was consistent to within +/- 5 percent of the average displacement response. The diameter of subsequent indentation damage of the laminates was 0.145 to 0.175 inches with an average of 0.162 inches. 2.2 Experimental Results The observed strengths of the 18 test articles are shown in Table 1. The tension coupons demonstrated similar ultimate strengths in the 1-direction, however, the 2- direction strengths typically lagged the 1-direction since it is the slave axis in the biaxial control system. The failure stresses are roughly 10 percent lower than the expected undamaged laminate strength. The 1:5 stress ratio coupons were subjected to the desired stress ratio until initial failure occurred in the 2-direction at approximately 80 ksi, at that point the 2-direction arm reacted with only a slightly increasing amount of load while the 1-direction steadily increased until final failure was reached in both directions at nearly equivalent stresses. Results for the compression specimens were akin to the tension data set. The 1-direction failure strengths were roughly 15 percent lower than the expected undamaged laminate strength and the -3:-1 stress ratio demonstrated the same control issues as the 1:5, with the exception of the second coupon which reached ultimate failure while maintaining the prescribed stress ratio. Table 1. Biaxial Strength Summary Tension Coupons 1/0 #1 1/0 #2 1/0 #3 1/1 #1 1/1 #2 1/1 #3 1/5 #1 1/5 #2 1/5 #3
S11,ut (ksi) S22,ut (ksi) 91.0 na 92.4 na 92.1 na 90.9 88.4 88.8 90.7 92.2 88.4 84.9 91.4 91.8 86.3 91.8 83.9
Compression Coupons S11,ut (ksi) S22,ut (ksi) -1/0 #1 -82.0 na -1/0 #2 -80.2 na -1/0 #3 -82.6 na -1/-1 #1 -78.0 -75.1 -1/-1 #2 -77.4 -71.3 -1/-1 #3 -78.3 -72.3 -3/-1 #1 -72.8 -59.2 -3/-1 #2 -83.2 -28.2 -3/-1 #3 -82.6 -56.2
Both the tension and compression load ratios achieved valid composite failures in the gage section, as shown in Figure 4. The left side of the figure contains a typical 1/1 tensile failure and the picture on the right displays a -1/-1 compression failure. The legitimate failure surfaces provide confidence that the experimental test method and coupon generated accurate failure data.
Figure 4. Cruciform Failure Surface from 1/1 and -1/-1 Loading Conditions These experiments were conducted to generate a high quality set of data for comparing to damage tolerance models described in Section 3.
3. FINITE ELEMENT MODELING 3.1 Modeling Methodology For modeling the initial damage and the progression of failure in the cruciform specimen, we used Firehole Composites’ commercial off the shelf software, Helius:MCT, which is specifically developed for modeling damage tolerance and progressive failure in composite structures. Three fundamental steps are used by Helius:MCT to provide multiscale analysis of composites: (1) extraction of constituent stresses and strains from the composite strain state, (2) evaluation of failure in each constituent, and (3) appropriate degradation of the constituent and composite after failure is predicted. The purpose of this modeling effort was to evaluate the degradation methodology used in the third step of this process. Details of the general methodology used have been described elsewhere [5], [6], here we provide a brief overview to better communicate the purpose of our study. The first step in the Helius:MCT approach is to use the composite strain, in conjunction with the elastic properties of the composite and its constituents, to extract the volume averaged stresses and strains in the fiber and matrix. Multicontinuum theory (MCT) is used to perform this extraction and has been rigorously described by Garnich and Hansen [7]. This method is computationally efficient and provides access to the needed variables to describe composite failure. The next step is to use the volume averaged constituent stresses to evaluate failure in the individual constituents using constituent-specific failure criteria. For unidirectional polymerbased composites, the failure criterion used is given by a quadratic combination of transversely isotropic invariants,
±
( )−
2 2 2 A1mσ 112 ,m − ± A2 m (σ 22,m + σ 33,m ) + A3m σ 22 , m + σ 33, m + 2σ 23, m 2
(
)
[1] + A4 m σ 122 ,m + σ 132 ,m ± ± A5mσ 11,m (σ 22,m + σ 33,m ) = 1 where Ai,m is a fitted failure coefficient for the matrix constituent, the subscript m on the stresses indicates a matrix averaged stress, and the ± superscript indicates a coefficient that depends on the sign of the term being multiplied by the coefficient. For the fiber constituent, the failure criterion is given by ±
(
)
A1 f σ 112 , f + A4 f σ 122 , f + σ 132 , f = 1
[2]
where Ai,m is a fitted failure coefficient for the fiber constituent and the subscript f indicates a fiber averaged stress. If failure is detected in either constituent, the stiffness properties of the constituent(s) are degraded, and the composite stiffness is also adjusted to reflect the degraded constituent(s). For unidirectional materials, Helius:MCT currently uses isotropic degradation of the elastic moduli; the level of degradation is specified by the user. The goal of this modeling work is to examine different constituent degradation schemes for the purpose of improving the damage tolerance modeling capabilities of Helius:MCT. Specifically, we examine the effects of anisotropic degradation as well as the specific degradation parameters. 3.2 Model Setup The goal of this simulation effort was to create a finite element model with a damaged region that could be used to evaluate various material property degradation models (MPDMs) by comparison with the experimental results reported in Section 2.2. In addition to evaluating MPDMs, these simulations were designed to highlight the appropriate experimental results for calibrating the selected MPDM. Before finite element simulation of biaxial loading of the cruciform specimens was performed, a prototype version of Helius:MCT was developed. This prototype version included the ability to define damage anisotropically (different degradation parameters could be used for each material property) and allowed property degradation due to initial damage (damage tolerance) to be different from damage that occurred during loading (damage propagation). This new version permitted evaluation of a greater variety of MPDMs. A progressive damage finite element simulation of strength after damage was performed on for IM7/8552 cruciform specimens comprised of quasi-isotropic gage sections. Abaqus 6.9EF-1 was used for the modeling effort. The damaged area was taken to have the same areal dimensions as the indenter described in Section 2.1. The damaged region was assumed to have both matrix and fiber damage for the depth of the indenter penetration (top twelve plies) and have matrix failure only in the four plies below the maximum indenter depth (plies 13-16). Figure 5(left) shows a plan view of the initial damage configuration for the cruciform specimens; Figure 5(right) shows an enlarged view of the through thickness damage of the center region (blue = undamaged, green = matrix damage, red = matrix and fiber damage). The long arms of the cruciform specimen were not modeled in an effort to improve computational efficiency.
Figuure 5. (Left) Initial I Confiiguration of Damaged D Crruciform Specimen. (Rigght) Damagee Throughh Center Reg gion. (Blue = Undamageed, Green = Matrix M Damage, Red = Matrix M and Fiber F D Damage) The layuup of the crruciform sppecimens waas [(90/0)3(445/-45)(45/00/-45/90)4]S, where the gage section was w [45/0/-45/90]4S, as shown s in Figgure 6. Thuss the layup of the surfacce laminatess was [(90/0)3(445/-45)] forr each laminnate. The suurface laminnates were modeled m usiing layered solid elements. Reduced in ntegration brick b elemennts (C3D8R) were used throughout the gage secction, where lam minae were modeled usiing one elem ment per ply through t the thickness.
Figuree 6. Meshing g of Cruciforrm Laminatee Through thhe Thicknesss. (Red Indiccates the Gagge Sectioon. Blue Indiicates Surfacce Laminatess.) Loading was applied d to the cruciiform specim mens in the ratios r 1/0, 1//1, 1/5, -1/0,, -1/-1, and -3/-1, where, foor example, the load ratiio 1/5 indicaates a tensilee biaxial loaad that is fivve times highher in the y-direection than in i the y-direction. The looads in the simulation s w applied via displaceement were control. We W note thaat this is sligghtly differennt from the biaxial b tests, which werre load contrrolled via a feeddback loop to t the load head.
3.2.1 Material M Prooperty Degrradation Moodel (MPDM M) Developm ment and Evaluation E As mentiioned abovee, the goal of o this task was to deveelop a new multiscale material m prooperty degradatiion model (M MPDM) suittable for dam mage tolerannce analysis. Six differeent MPDMs were evaluatedd in this stu udy: three issotropic and three anisootropic, indiccated by thee prefix ISO O and
ANI, respectively. Each MPDM was used to predict the failure stress in the damaged cruciform specimens. The error between the predicted failure strength and the experimental strength was used to select the optimal MPDM. Table 2 shows the six MPDMs examined in this study, where the MPDM is defined by the specific stiffness degradation of the fiber and matrix constituents. Poisson ratios were held constant throughout the analyses. Table 2. MPDM Models Examined in This Study MPDM name
Matrix damage tolerance E11, E22, E33, G12, G13, G23 to 10% E11, E22, E33, G12, G13, G23 to 0.0001% E11, E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 10% E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 0.0001%
ISO-A ISO-B
ISO-C
ANI-A ANI-B
ANI-C
Matrix propagation E11, E22, E33, G12, G13, G23 to 10% E11, E22, E33, G12, G13, G23 to 0.0001% E11, E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 10% E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 0.0001%
Fiber damage tolerance E11, E22, E33, G12, G13, G23 to 1% E11, E22, E33, G12, G13, G23 to 1%
Fiber propagation E11, E22, E33, G12, G13, G23 to 1% E11, E22, E33, G12, G13, G23 to 1%
E11, E22, E33, G12, G13, G23 to 0.01% E11, G12, G13 to 1% E11, G12, G13 to 1%
E11, E22, E33, G12, G13, G23 to 1%
E11, G12, G13 to 0.01%
E11, G12, G13 to 1%
E11, G12, G13 to 1% E11, G12, G13 to 1%
3.3 Model Results
3.3.1 Evaluation of MPDMs The results of our MPDM evaluation are shown in Figure 7 and Figure 8. Figure 7 shows the failure stresses in the 1-direction predicted by each MPDM along with the experimental failure stress for each load ratio. (The 1-direction failure stress in the 1/5 tension test was invalid, and thus not used for selection of the MPDM.) Figure 8 shows the results for the 2-direction stresses. The root mean square (RMS) errors associated with each MPDM are shown in Table 3 for tensile loading, compressive loading, and for all loads. Table 3. RMS Errors Associated with Each MPDM RMS error Total Tension Compression
ISO-A 21.2% 29.7% 4.5%
ISO-B 6.6% 3.6% 8.6%
ISO-C 6.9% 4.1% 8.8%
ANI-A 22.6% 31.5% 5.2%
ANI-B 5.7% 3.6% 7.2%
ANI-C 6.1% 4.5% 7.4%
The slight difference between the isotropic and anisotropic MPDMs shown in Table 3 indicates that adopting the additional conceptual complexity of the anisotropic MPDMs or the dealing with the difficulty in properly evaluating additional degradation parameters is not justified.
Consequently, we restricted our selection off MPDMs too isotropic models. m We observe o that ISOA (matrixx degradatio on to 10%) produced p the best resultts for comprressive loadiing, while IS SO-B (matrix degradation d to t 0.0001%)) produced thhe best resullts for tensille loading. However, H beccause our curreent code is not equippeed to handlee different MPDMs M forr tensile verrsus compreessive failure we w chose the MPDM bassed on total RMS error. However, we w note thatt future efforts to incorporaate load-dep pendent degrradation parrameters aree likely to im mprove resuults. Thus, ISO-B IS was selected as the preferred MPDM. M Finally, Figure 7 and Figuure 8 show that tensionn and compresssion OHT tests on a quasi-isotroopic samplee should bee sufficient to calibratee the degradatiion parametter of the matrix. m The degradation d for the fibeer did not apppreciably affect a results— —provided th hat a fiber-faailed elemennt doesn’t support s signiificant load,, it will givve the same resuults regardleess of degraddation param meter.
Figuree 7. Compariison of MPD DM Predictioons with Expperimental Strengths S in the t 1-direction
Figuree 8. Compariison of MPD DM Predictioons with Expperimental Strengths S in the t 2-direction
3.3.2 Comparison C n of Simulati tion Results with Experriment Using thhe ISO-B MP PDM, the progression p o failure inn the simulaations was examined annd the of results were w comparred with exxperiment. Figure F 9 andd Figure 100 show failuure patterns of a representtative ply for each of thee loading coonfigurationss. Photos of the experim mental failurees for the 1/1 and a -1/-1 load cases are shown s in Figgure 4 for coomparison. Our O simulatiion results match m well withh these failu ure modes. In the case of tension, failure occuurred first inn the arm of o the cruciform m. In the casse of comprression, failuure occurredd along a diaagonal line through t the gage section. However, H th he region of the cruciform m where thee surface lam minate thicknness decreasses to zero (shoown by the gray g region in Figure 5 (left)) was modeled m as perfectly boonded to the gage section. In I the experiiments, this section parttially delaminated from the t gage secction. Thus, some of the prredicted failu ure in the arms a as oppoosed to the gage sectionn may have been due to t the inability to accurately y capture thiis effect.
Figure 9. 9 Tension After A Damagge Simulationn Results--O Only Gage Seection Is Shoown. (Top Left) L Load Ratio R 1/0. (Toop Right) Looad Ratio 1/11. (Bottom) Load L Ratio 1/5.
Figure 10. Compreession After Damage D Sim mulation Ressults--Only the t Gage Secction Is Show wn. (Toop Left) Load d Ratio -1/0. (Top Rightt) Load Ratioo -1/-1. (Boottom) Load Ratio -3/-1.
4. CON NCLUSIO ONS The prim mary goal of o this studyy was to evvaluate matterial properrty degradattion modelss and corresponnding test methodologie m es for determ mining damaage tolerancce inputs. Ussing results from the expeerimental prrogram in conjunctionn with finitte element modeling revealed seeveral importannt results for future damaage tolerancee modeling efforts. e •
Anisotropic damage A d effeects did nott substantiallly change the t qualitative nature of o the faailure cascad de or the quuantitative ultimate u strenngth values of the cruciiform specim mens. T Thus, isotrop pic stiffness degradationn is sufficieent for proggressive faillure modelinng of damage toleraance.
•
Appropriate degradation parameterss for the MPDM A M weree dependent on whetheer the faailure was a tensile or compressivve failure. A matrix deegradation parameter p of 0.1
provided the best compressive strength predictions, while a matrix degradation parameter of 10-6 provided the best tensile strength predictions. •
Because isotropic degradation parameters were sufficient to capture the effect of damage tolerance, a battery of experiments is not required to calibrate our damage tolerance software. Our simulation results were relatively insensitive to the fiber degradation parameter—presumably because the most important consideration for fiber failure is the complete load transfer to the neighboring materials. Thus, only the matrix degradation parameter needs to be calibrated. This can be done using tension and compression OHT results for a quasi-isotropic laminate.
5. ACKNOWLEDGEMENTS This research was supported by the Air Force Office of Scientific Research (AFOSR) under contract number FA8650-10-M-3014 under the direction of Dr. Stephen Clay.
6. REFERENCES [1] E. Nelson and J. Welsh, “Failure analysis of large composite space structures using multicontinuum technology,” Edinburgh, UK, 2009. [2] E. Nelson, A. Hansen, and J. Mayes, “Failure analysis of composite laminates subjected to hydrostatic stresses: A multicontinuum approach,” Accepted as part of the Second Worldwide Failure Exercise, 2009. [3] ASTM D 6264 Standard Test Method for Measuring Damage Resistance of Fiber-Reinforced Polymer-Matrix Composites to Concentrated Quasi-Static Indentation Force. . [4] J. Lee and C. Soutis, “Experimental Investigation on the Behaviour of CFRP Laminated Composites under Impact and Compression After Impact (CAI),” in EKC2008 Proceedings of the EU-Korea Conference on Science and Technology, vol. 124, pp. 275-286, 2008. [5] A. Hansen, D. Kenik, and E. Nelson, “Multicontinuum failure analysis of composites,” Edinburgh, UK, 2009. [6] R. Fertig, “An accurate and efficient method for constituent-based progressive failure modeling of a woven composite,” in Supplemental Proceedings: Volume 2: Materials Characterization, Computation, Modeling and Energy, vol. 2, pp. 223-230, 2010. [7] M. Garnich and A. Hansen, “A Multicontinuum Theory for Thermal-Elastic Finite Element Analysis of Composite Materials,” Journal of Composite Materials, vol. 31, no. 1, pp. 71-86, Jan. 1997.
ABSTRACT Predicting the effects of damage in composite structures is critical to determining the safety of the structure. But even if the region of damage is well-defined, accurately simulating its effect on the performance of the structure depends on the degree to which material properties in the damaged region have been degraded. In the work reported here, we examine experimentally and computationally a variety of material property degradation schemes and biaxial composite loadings. The computational work reported utilizes multicontinuum theory to permit multiscale analysis of the composite such that fiber and matrix behavior can be separated and modeled. As such, the degradation parameters considered are specific to the fiber and matrix constituent, separately. We particularly investigate the effects of isotropic versus anisotropic material degradation, as well as the potential dependence of the degradation material parameters on the loading of the composite.
1. INTRODUCTION Despite growing acceptance of composites in a variety of applications, there continues to be difficulty in assessing the use composites in applications where low levels of damage are present either via impact loads or induced manufacturing flaws. Manufacturing flaws or damage from a low-energy impact event can include significant delamination and microcracking with little or no visible surface damage, making damage detection difficult. But this damage can still cause significant reductions in residual strength of a composite structure. The residual strength of these damaged composites needs to be evaluated in order to ensure that it exceeds damage tolerance requirements. Often these composites are already in use, so experimental testing is not possible if the part is to be returned to service. The ideal approach would be to validate damage tolerance via simulation. The difficulty with simulation is that failure of composite structures is an extremely complex event. Multiple local damage mechanisms often initiate at loads far below structural failure levels. Damage mechanisms may include void accumulation in the matrix, matrix microcracking, fiber rupture in tension, fiber kinking or crushing in compression, and delamination between
plies. Localized damage induces nonlinear behavior at several geometric scales, which can produce a nonlinear response at the structural level. Consequently, progressive failure analysis, characterized by incremental loading of a structure, is the only way to simulate a nonlinear structural response. The difficulties that are usually encountered in simulating progressive failure behavior in general purpose finite element codes stem from convergence problems and inaccurate methods for predicting multiple failure modes. In particular, failure in composite laminates can be summarized by a progression of the following events, which must be accurately captured in order to achieve an accurate failure progression simulation: • • • • •
Matrix failure initiation Matrix failure propagation Fiber failure initiation Fiber failure propagation Ultimate failure
Each failure event causes a reduction in composite stiffness, which causes stress redistribution. The sequence of events can vary depending on the loading. Additionally, this progression of discrete events occurs separately in the matrix and fiber constituents. Firehole Composites has developed the finite element add-on software Helius:MCT™ specifically to address these issues by applying distinct failure criterion to the fiber and matrix and a stiffness degradation specialized for these different composite failure states [1], [2]. The goal of the work reported here was to evaluate various constituent degradation models by modifying Helius:MCT and comparing its compressive failure results with high quality experimental data. The composite structures of interest were carbon-epoxy cruciform specimens with a specified amount of damage due to indentation. The specimens were tested to failure under various biaxial loads. Simulation results using various material property degradation schemes, both for initial damage tolerance as well as damage propagation, were qualitatively and quantitatively compared with experimental results.
2. EXPERIMENTATION 2.1 Experimental Setup The experimental work described here was performed by LoadPath, LLC. The primary objective of this effort was to create a well-defined region of fiber crushing damage to a quasi-isotropic composite laminate and evaluate its effect on the biaxial strength of the laminate. This task required two independent experimental setups, one to induce fiber crushing damage and the other to impose an in-plane, multi-axial stress state on the damaged laminate. Biaxial cruciform coupons were constructed from IM7/8552 carbon fiber/epoxy resin unidirectional tape, fabricated with a quasi-isotropic gage section, and tested to failure in the Triaxial Test Facility located on Kirtland AFB, NM. The test system, shown in Figure 1, consists of a custom electromechanical test frame that is capable of generating combinations of tensile or compressive stresses in σ1:σ2:σ3 stress space and can evaluate the uniaxial, biaxial, or triaxial response of materials. The machine computer controls six actuators (two per axis), each with a
capacity of 30 kip. A precision alignment fixture, shown on the right side of Figure 1, guides the wedge grips, assures true orthogonal loading of the specimen, and mitigates buckling in compressive load states.
Figure 1. Triaxial Test Facility and Load Frame Alignment Fixture The complement to the test facility is a well-defined biaxial cruciform specimen shown in Figure 2. Composite coupons are machined from a solid laminate that includes the center gage section and integrated reinforcing composite tabs to optimize the load path from the test frame to the specimen’s gage section. Both the general coupon shape and thickness-tapered gage section are machined using a computer numeric controlled (CNC) mill. Throughout previous work, continual improvements have been made to the geometric details of the thickness-tapered cruciform, laminate fabrication process, and coupon machining techniques. The final specimen design has since been successfully used to evaluate the biaxial strength of cross-ply, quasiisotropic, unidirectional, and woven laminate configurations.
Figure 2. Unidirectional Laminate Biaxial Cruciform
The damage test method was derived from ASTM D 6264 [3]. In this method, a quasi-static indentation (QSI) is used to obtain quantitative measurements of the damage resistance of a continuous-fiber-reinforced composite material to a concentrated indentation force. The indentation force is applied to the specimen by slowly pressing a hemispherical indenter into the surface. The procedure specifies the use of either a simply supported or rigidly backed test specimen during the damage event. The damage resistance is quantified in terms of a critical contact force versus indenter displacement. This standard was utilized because quasi-static indentations have been shown to effectively represent practical low-velocity impact events such as tool drops. The indentation test setup is shown in Figure 3. This program made two significant deviations from the ASTM standard, the test specimen geometry and indenter size. The ASTM D 6264 method and its incorporated indenter were formulated for the typical 4 inch by 6 inch plate compression after impact (CAI) coupon; however, this program is studying the effects of damage on biaxially loaded cruciform specimens. To accommodate the cruciform, which contains a gage section nominally 0.95 inch square, the hemispherical indenter’s diameter was reduced from 0.500 inch to 0.250 inch. Also shown in the figure, a rigid 0.875 inch square platen supported the impacted gage section during the damage process. The indenter was pressed into the laminate at a rate of .02 in/min until the reacting force reached -4,500 lbs. This end point was initially selected because it is twice the magnitude of an event described by Lee and Soutis [4] that caused sufficient damage in a similar laminate, and practice trials determined that it induced significant visual damage on the impacted surface, including fiber crushing, without harming the non-impacted face.
Figure 3. Quasi-static Indentation Test Setup
A total of six stress ratios were tested, three tension/tension and three compression/compression. Using the nomenclature of 1-direction stress/2-direction stress, the present study examined 1/0, 1/1, and 1/5 ratios in the tension/tension failure envelope quadrant and similarly -1/0, -1/-1, and 3/-1 in the compression/compression regime. The test articles contained a 32-ply gage section, a portion of the cruciform [(90/0)3(45/-45)(45/0/-45/90)4]S layup, where the gage section contained the [(45/0/-45/90)4]S portion of the laminate. Each coupon included a Vishay CEA-06-125UT350 biaxial strain gage in the center of the gage section on the undamaged face. The QSI damage event was relatively repeatable throughout the 18 coupon set. The indenter was pressed into the laminate until a contact force of -4,500 lbs was reached within the accuracy parameters of the load frame’s control system. For each specimen, the peak load was achieved within 0.1 percent of the desired end level. The corresponding displacement of the indenter ranged from 0.043 to 0.047 inches with a mean of 0.045 inches, meaning the behavior of the material was consistent to within +/- 5 percent of the average displacement response. The diameter of subsequent indentation damage of the laminates was 0.145 to 0.175 inches with an average of 0.162 inches. 2.2 Experimental Results The observed strengths of the 18 test articles are shown in Table 1. The tension coupons demonstrated similar ultimate strengths in the 1-direction, however, the 2- direction strengths typically lagged the 1-direction since it is the slave axis in the biaxial control system. The failure stresses are roughly 10 percent lower than the expected undamaged laminate strength. The 1:5 stress ratio coupons were subjected to the desired stress ratio until initial failure occurred in the 2-direction at approximately 80 ksi, at that point the 2-direction arm reacted with only a slightly increasing amount of load while the 1-direction steadily increased until final failure was reached in both directions at nearly equivalent stresses. Results for the compression specimens were akin to the tension data set. The 1-direction failure strengths were roughly 15 percent lower than the expected undamaged laminate strength and the -3:-1 stress ratio demonstrated the same control issues as the 1:5, with the exception of the second coupon which reached ultimate failure while maintaining the prescribed stress ratio. Table 1. Biaxial Strength Summary Tension Coupons 1/0 #1 1/0 #2 1/0 #3 1/1 #1 1/1 #2 1/1 #3 1/5 #1 1/5 #2 1/5 #3
S11,ut (ksi) S22,ut (ksi) 91.0 na 92.4 na 92.1 na 90.9 88.4 88.8 90.7 92.2 88.4 84.9 91.4 91.8 86.3 91.8 83.9
Compression Coupons S11,ut (ksi) S22,ut (ksi) -1/0 #1 -82.0 na -1/0 #2 -80.2 na -1/0 #3 -82.6 na -1/-1 #1 -78.0 -75.1 -1/-1 #2 -77.4 -71.3 -1/-1 #3 -78.3 -72.3 -3/-1 #1 -72.8 -59.2 -3/-1 #2 -83.2 -28.2 -3/-1 #3 -82.6 -56.2
Both the tension and compression load ratios achieved valid composite failures in the gage section, as shown in Figure 4. The left side of the figure contains a typical 1/1 tensile failure and the picture on the right displays a -1/-1 compression failure. The legitimate failure surfaces provide confidence that the experimental test method and coupon generated accurate failure data.
Figure 4. Cruciform Failure Surface from 1/1 and -1/-1 Loading Conditions These experiments were conducted to generate a high quality set of data for comparing to damage tolerance models described in Section 3.
3. FINITE ELEMENT MODELING 3.1 Modeling Methodology For modeling the initial damage and the progression of failure in the cruciform specimen, we used Firehole Composites’ commercial off the shelf software, Helius:MCT, which is specifically developed for modeling damage tolerance and progressive failure in composite structures. Three fundamental steps are used by Helius:MCT to provide multiscale analysis of composites: (1) extraction of constituent stresses and strains from the composite strain state, (2) evaluation of failure in each constituent, and (3) appropriate degradation of the constituent and composite after failure is predicted. The purpose of this modeling effort was to evaluate the degradation methodology used in the third step of this process. Details of the general methodology used have been described elsewhere [5], [6], here we provide a brief overview to better communicate the purpose of our study. The first step in the Helius:MCT approach is to use the composite strain, in conjunction with the elastic properties of the composite and its constituents, to extract the volume averaged stresses and strains in the fiber and matrix. Multicontinuum theory (MCT) is used to perform this extraction and has been rigorously described by Garnich and Hansen [7]. This method is computationally efficient and provides access to the needed variables to describe composite failure. The next step is to use the volume averaged constituent stresses to evaluate failure in the individual constituents using constituent-specific failure criteria. For unidirectional polymerbased composites, the failure criterion used is given by a quadratic combination of transversely isotropic invariants,
±
( )−
2 2 2 A1mσ 112 ,m − ± A2 m (σ 22,m + σ 33,m ) + A3m σ 22 , m + σ 33, m + 2σ 23, m 2
(
)
[1] + A4 m σ 122 ,m + σ 132 ,m ± ± A5mσ 11,m (σ 22,m + σ 33,m ) = 1 where Ai,m is a fitted failure coefficient for the matrix constituent, the subscript m on the stresses indicates a matrix averaged stress, and the ± superscript indicates a coefficient that depends on the sign of the term being multiplied by the coefficient. For the fiber constituent, the failure criterion is given by ±
(
)
A1 f σ 112 , f + A4 f σ 122 , f + σ 132 , f = 1
[2]
where Ai,m is a fitted failure coefficient for the fiber constituent and the subscript f indicates a fiber averaged stress. If failure is detected in either constituent, the stiffness properties of the constituent(s) are degraded, and the composite stiffness is also adjusted to reflect the degraded constituent(s). For unidirectional materials, Helius:MCT currently uses isotropic degradation of the elastic moduli; the level of degradation is specified by the user. The goal of this modeling work is to examine different constituent degradation schemes for the purpose of improving the damage tolerance modeling capabilities of Helius:MCT. Specifically, we examine the effects of anisotropic degradation as well as the specific degradation parameters. 3.2 Model Setup The goal of this simulation effort was to create a finite element model with a damaged region that could be used to evaluate various material property degradation models (MPDMs) by comparison with the experimental results reported in Section 2.2. In addition to evaluating MPDMs, these simulations were designed to highlight the appropriate experimental results for calibrating the selected MPDM. Before finite element simulation of biaxial loading of the cruciform specimens was performed, a prototype version of Helius:MCT was developed. This prototype version included the ability to define damage anisotropically (different degradation parameters could be used for each material property) and allowed property degradation due to initial damage (damage tolerance) to be different from damage that occurred during loading (damage propagation). This new version permitted evaluation of a greater variety of MPDMs. A progressive damage finite element simulation of strength after damage was performed on for IM7/8552 cruciform specimens comprised of quasi-isotropic gage sections. Abaqus 6.9EF-1 was used for the modeling effort. The damaged area was taken to have the same areal dimensions as the indenter described in Section 2.1. The damaged region was assumed to have both matrix and fiber damage for the depth of the indenter penetration (top twelve plies) and have matrix failure only in the four plies below the maximum indenter depth (plies 13-16). Figure 5(left) shows a plan view of the initial damage configuration for the cruciform specimens; Figure 5(right) shows an enlarged view of the through thickness damage of the center region (blue = undamaged, green = matrix damage, red = matrix and fiber damage). The long arms of the cruciform specimen were not modeled in an effort to improve computational efficiency.
Figuure 5. (Left) Initial I Confiiguration of Damaged D Crruciform Specimen. (Rigght) Damagee Throughh Center Reg gion. (Blue = Undamageed, Green = Matrix M Damage, Red = Matrix M and Fiber F D Damage) The layuup of the crruciform sppecimens waas [(90/0)3(445/-45)(45/00/-45/90)4]S, where the gage section was w [45/0/-45/90]4S, as shown s in Figgure 6. Thuss the layup of the surfacce laminatess was [(90/0)3(445/-45)] forr each laminnate. The suurface laminnates were modeled m usiing layered solid elements. Reduced in ntegration brick b elemennts (C3D8R) were used throughout the gage secction, where lam minae were modeled usiing one elem ment per ply through t the thickness.
Figuree 6. Meshing g of Cruciforrm Laminatee Through thhe Thicknesss. (Red Indiccates the Gagge Sectioon. Blue Indiicates Surfacce Laminatess.) Loading was applied d to the cruciiform specim mens in the ratios r 1/0, 1//1, 1/5, -1/0,, -1/-1, and -3/-1, where, foor example, the load ratiio 1/5 indicaates a tensilee biaxial loaad that is fivve times highher in the y-direection than in i the y-direction. The looads in the simulation s w applied via displaceement were control. We W note thaat this is sligghtly differennt from the biaxial b tests, which werre load contrrolled via a feeddback loop to t the load head.
3.2.1 Material M Prooperty Degrradation Moodel (MPDM M) Developm ment and Evaluation E As mentiioned abovee, the goal of o this task was to deveelop a new multiscale material m prooperty degradatiion model (M MPDM) suittable for dam mage tolerannce analysis. Six differeent MPDMs were evaluatedd in this stu udy: three issotropic and three anisootropic, indiccated by thee prefix ISO O and
ANI, respectively. Each MPDM was used to predict the failure stress in the damaged cruciform specimens. The error between the predicted failure strength and the experimental strength was used to select the optimal MPDM. Table 2 shows the six MPDMs examined in this study, where the MPDM is defined by the specific stiffness degradation of the fiber and matrix constituents. Poisson ratios were held constant throughout the analyses. Table 2. MPDM Models Examined in This Study MPDM name
Matrix damage tolerance E11, E22, E33, G12, G13, G23 to 10% E11, E22, E33, G12, G13, G23 to 0.0001% E11, E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 10% E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 0.0001%
ISO-A ISO-B
ISO-C
ANI-A ANI-B
ANI-C
Matrix propagation E11, E22, E33, G12, G13, G23 to 10% E11, E22, E33, G12, G13, G23 to 0.0001% E11, E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 10% E22, E33, G12, G13, G23 to 0.0001% E22, E33, G12, G13, G23 to 0.0001%
Fiber damage tolerance E11, E22, E33, G12, G13, G23 to 1% E11, E22, E33, G12, G13, G23 to 1%
Fiber propagation E11, E22, E33, G12, G13, G23 to 1% E11, E22, E33, G12, G13, G23 to 1%
E11, E22, E33, G12, G13, G23 to 0.01% E11, G12, G13 to 1% E11, G12, G13 to 1%
E11, E22, E33, G12, G13, G23 to 1%
E11, G12, G13 to 0.01%
E11, G12, G13 to 1%
E11, G12, G13 to 1% E11, G12, G13 to 1%
3.3 Model Results
3.3.1 Evaluation of MPDMs The results of our MPDM evaluation are shown in Figure 7 and Figure 8. Figure 7 shows the failure stresses in the 1-direction predicted by each MPDM along with the experimental failure stress for each load ratio. (The 1-direction failure stress in the 1/5 tension test was invalid, and thus not used for selection of the MPDM.) Figure 8 shows the results for the 2-direction stresses. The root mean square (RMS) errors associated with each MPDM are shown in Table 3 for tensile loading, compressive loading, and for all loads. Table 3. RMS Errors Associated with Each MPDM RMS error Total Tension Compression
ISO-A 21.2% 29.7% 4.5%
ISO-B 6.6% 3.6% 8.6%
ISO-C 6.9% 4.1% 8.8%
ANI-A 22.6% 31.5% 5.2%
ANI-B 5.7% 3.6% 7.2%
ANI-C 6.1% 4.5% 7.4%
The slight difference between the isotropic and anisotropic MPDMs shown in Table 3 indicates that adopting the additional conceptual complexity of the anisotropic MPDMs or the dealing with the difficulty in properly evaluating additional degradation parameters is not justified.
Consequently, we restricted our selection off MPDMs too isotropic models. m We observe o that ISOA (matrixx degradatio on to 10%) produced p the best resultts for comprressive loadiing, while IS SO-B (matrix degradation d to t 0.0001%)) produced thhe best resullts for tensille loading. However, H beccause our curreent code is not equippeed to handlee different MPDMs M forr tensile verrsus compreessive failure we w chose the MPDM bassed on total RMS error. However, we w note thatt future efforts to incorporaate load-dep pendent degrradation parrameters aree likely to im mprove resuults. Thus, ISO-B IS was selected as the preferred MPDM. M Finally, Figure 7 and Figuure 8 show that tensionn and compresssion OHT tests on a quasi-isotroopic samplee should bee sufficient to calibratee the degradatiion parametter of the matrix. m The degradation d for the fibeer did not apppreciably affect a results— —provided th hat a fiber-faailed elemennt doesn’t support s signiificant load,, it will givve the same resuults regardleess of degraddation param meter.
Figuree 7. Compariison of MPD DM Predictioons with Expperimental Strengths S in the t 1-direction
Figuree 8. Compariison of MPD DM Predictioons with Expperimental Strengths S in the t 2-direction
3.3.2 Comparison C n of Simulati tion Results with Experriment Using thhe ISO-B MP PDM, the progression p o failure inn the simulaations was examined annd the of results were w comparred with exxperiment. Figure F 9 andd Figure 100 show failuure patterns of a representtative ply for each of thee loading coonfigurationss. Photos of the experim mental failurees for the 1/1 and a -1/-1 load cases are shown s in Figgure 4 for coomparison. Our O simulatiion results match m well withh these failu ure modes. In the case of tension, failure occuurred first inn the arm of o the cruciform m. In the casse of comprression, failuure occurredd along a diaagonal line through t the gage section. However, H th he region of the cruciform m where thee surface lam minate thicknness decreasses to zero (shoown by the gray g region in Figure 5 (left)) was modeled m as perfectly boonded to the gage section. In I the experiiments, this section parttially delaminated from the t gage secction. Thus, some of the prredicted failu ure in the arms a as oppoosed to the gage sectionn may have been due to t the inability to accurately y capture thiis effect.
Figure 9. 9 Tension After A Damagge Simulationn Results--O Only Gage Seection Is Shoown. (Top Left) L Load Ratio R 1/0. (Toop Right) Looad Ratio 1/11. (Bottom) Load L Ratio 1/5.
Figure 10. Compreession After Damage D Sim mulation Ressults--Only the t Gage Secction Is Show wn. (Toop Left) Load d Ratio -1/0. (Top Rightt) Load Ratioo -1/-1. (Boottom) Load Ratio -3/-1.
4. CON NCLUSIO ONS The prim mary goal of o this studyy was to evvaluate matterial properrty degradattion modelss and corresponnding test methodologie m es for determ mining damaage tolerancce inputs. Ussing results from the expeerimental prrogram in conjunctionn with finitte element modeling revealed seeveral importannt results for future damaage tolerancee modeling efforts. e •
Anisotropic damage A d effeects did nott substantiallly change the t qualitative nature of o the faailure cascad de or the quuantitative ultimate u strenngth values of the cruciiform specim mens. T Thus, isotrop pic stiffness degradationn is sufficieent for proggressive faillure modelinng of damage toleraance.
•
Appropriate degradation parameterss for the MPDM A M weree dependent on whetheer the faailure was a tensile or compressivve failure. A matrix deegradation parameter p of 0.1
provided the best compressive strength predictions, while a matrix degradation parameter of 10-6 provided the best tensile strength predictions. •
Because isotropic degradation parameters were sufficient to capture the effect of damage tolerance, a battery of experiments is not required to calibrate our damage tolerance software. Our simulation results were relatively insensitive to the fiber degradation parameter—presumably because the most important consideration for fiber failure is the complete load transfer to the neighboring materials. Thus, only the matrix degradation parameter needs to be calibrated. This can be done using tension and compression OHT results for a quasi-isotropic laminate.
5. ACKNOWLEDGEMENTS This research was supported by the Air Force Office of Scientific Research (AFOSR) under contract number FA8650-10-M-3014 under the direction of Dr. Stephen Clay.
6. REFERENCES [1] E. Nelson and J. Welsh, “Failure analysis of large composite space structures using multicontinuum technology,” Edinburgh, UK, 2009. [2] E. Nelson, A. Hansen, and J. Mayes, “Failure analysis of composite laminates subjected to hydrostatic stresses: A multicontinuum approach,” Accepted as part of the Second Worldwide Failure Exercise, 2009. [3] ASTM D 6264 Standard Test Method for Measuring Damage Resistance of Fiber-Reinforced Polymer-Matrix Composites to Concentrated Quasi-Static Indentation Force. . [4] J. Lee and C. Soutis, “Experimental Investigation on the Behaviour of CFRP Laminated Composites under Impact and Compression After Impact (CAI),” in EKC2008 Proceedings of the EU-Korea Conference on Science and Technology, vol. 124, pp. 275-286, 2008. [5] A. Hansen, D. Kenik, and E. Nelson, “Multicontinuum failure analysis of composites,” Edinburgh, UK, 2009. [6] R. Fertig, “An accurate and efficient method for constituent-based progressive failure modeling of a woven composite,” in Supplemental Proceedings: Volume 2: Materials Characterization, Computation, Modeling and Energy, vol. 2, pp. 223-230, 2010. [7] M. Garnich and A. Hansen, “A Multicontinuum Theory for Thermal-Elastic Finite Element Analysis of Composite Materials,” Journal of Composite Materials, vol. 31, no. 1, pp. 71-86, Jan. 1997.
