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THERMAL-MECHANICAL FAILURE ANALYSIS OF CRYOGENIC COMPOSITE MATERIALS USING MULTICONTINUUM THEORY

Seth NickersonProject Engineer

Firehole Technologies, Inc.Laramie, WY, USA

J. Steven MayesAssistant Professor

Mechanical EngineeringAlfred University Alfred, NY, USA

Jeffry S. WelshAerospace Engineer

Air Force Research Laboratory, VSSVKirtland AFB, NM, USA

ABSTRACTA drastic reduction in structural weight is an indispensable prerequisite to realize future high altitude area defense systems or single stage to orbit space vehicles. Boost defense programs such as the Airborne Laser (ABL) and Space-Based Laser (SBL) as well as numerous optical-based systems require the storage, transport and dispensing of large amounts of cryogenic fluids. All elements contributing to the mass of the cryogenic systems must be as light as possible, particularly the tanks which are one of the most challenging parts.Today, the majority of cryogenic tanks are made of insulated aluminum, stainless steel, or a metal liner with composite overwrap. While these tanks have high damage tolerance and chemical resistance, they do so with a relatively high mass penalty. Advanced composite materials can provide significant mass reduction due to their high specific strength and stiffness ratios, compared to metals, but are susceptible to cracking under thermal cycling. Thermally induced cracking is the result of large internal stresses generated at cryogenic temperatures due to a mismatch in coefficients of thermal expansion between the fiber and the matrix. Cracking of composite cryogenic tanks is classified as a component failure because the increased permeability of the tank results in significant loss of stored cryogens. Current state-of-the-practice analysis technologies, such as Linear Elastic Fracture Mechanics, Micromechanics, and Classical Lamination Theory have been found to be lacking in their capability to be applied in the general design of composite cryogenic tanks. Primarily in their ability to accurately and easily model thermally induced cracking in advanced composite materials. Faster and more accurate analysis techniques were needed as enabling technologies for improving composite cryogenic tank design. Thus, a research effort was initiated by the Missile Defense Agency to improve prediction and analysis methods. An alternative analysis method, called Multi-Continuum Theory (MCT), uses a classic Hill strain decomposition technique to solve for the phase averaged stress and strains in each constituent of the composite with a

minimum of computational complexity and virtually no time penalty. Constituent information is valuable because thermal damage in a composite begins at the constituent level and may in fact be limited to only one constituent. Accurate prediction of constituent failure at a single point enables the analysis of progressive damage growth throughout the composite. In this paper we describe how MCT was used to predict thermally induced composite damage, primarily matrix cracking, of carbon fiber reinforced plastic composite specimens. These composite specimens were subjected to both experimental and analytical cyclic thermal loading at cryogenic temperatures. The metric used to measure damage was the matrix microcrack density. Correlation between microcrack densities, as a function of time at temperature, number of cycles, and material architecture, were made between results of MCT analysis and experiment. Additionally, these results were benchmarked against existing analytical methods to assess any improvements in accuracy and ease of use. All numerical and experimental data will be presented and discussed.

INTRODUCTIONChallenges in cryogenic tank design begin with the cryogenic fluids stored, e.g., hydrogen, oxygen, and helium. These products create a severe environmental load characterized by extremely-low-temperatures and high chemical instability (reactive, acidic, or basic). Failure modes associated with environmental loading typically manifest themselves with cracking of the tank due to either a mismatch in thermal expansion between different tank constituents; fibers, matrix, and liner materials, or chemical attack at the fluid-tank interface. Further, the large scale of ABL and SBL components required composite cryogenic tank laminates to be relatively thick, i.e. the number of individual plies can easily exceed ten. To make matters more complex, each ply may have a different orientation to tailor the strength and stiffness of the laminate to the load it is required to sustain. Today, designers compensate for this increased complexity by assuming that the laminate is a homogenous material. They blend (combine) the constituents’ (fiber and matrix) mechanical properties to create an idealized homogeneous ply, then blend the plys’ mechanical properties into an idealized homogeneous laminate of uniform strength and stiffness, and use this to

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model the structural component. While this approach is fairly successful in developing global stiffness properties, it masks the large internal stresses that occur due to the interplay between the matrix and reinforcing fibers.

Current approaches, both experimental and analytical, have been shown to be insufficient for the purpose of general component design in cryogenic composite applications. Flaggs and Kural1 were among the first significant studies to show the importance and inadequacy of classic composite failure analyses when predicting matrix cracking, especially as a result of thermal loading.

Many techniques were tried in the following years, including more strength based failure prediction methods such as those using adjacent ply edge effective areas and Weibull statistical methods2, all of which were shown to be insufficient.

Shear-lag stress analyses have found their way into common practice among those who have tried to predict matrix microcracking. In fact, much of the current literature to date involves some form of shear-lag stress analysis coupled with an energy release rate failure criterion3,4,5,6,7,8.

No method currently available has shown the ability to predict matrix microcracking in the general case as reliably as needed for component design.

MULTICONTINUUM THEORYStructural damage of a composite material begins at the level of its constituents and may, in fact, be limited to only one constituent in some situations. Conventional analysis using blending methodology loses the capability to examine constituent level behavior where damage initiates, making it impossible to accurately predict pre-, ongoing, and post-damage conditions of the laminate. Conversely, the ability to accurately predict constituent damage throughout a laminate allows for a high resolution failure analysis of any composite structure from the initiation of damage to ultimate rupture, promoting more efficient remedies to improve the design.

This research contained herein centers on an enabling technology that provides a unique alternative to modeling the deformation response of composite structures. The approach, referred to as Multicontinuum Theory (MCT) 9, incorporates the basic constituents of the composite (fiber, matrix, etc.) into structural analysis as separate but linked continua, in contrast to the more conventional

representation of the composite as a single equivalent homogeneous continuum, so that the responses of these most basic components are determined at every point in the structure. MCT does this in an extremely efficient manner that results in a high resolution window on the behavior of a composite structure at its most basic level, i.e., the individual constituents. More specifically, MCT incorporates a classic micromechanics based strain-decomposition into a numerical algorithm that extracts, virtually without a time penalty, the stress and strain fields for a composites’ constituents as user defined function of commercially available finite element analyses (FEA) software. Constituent stress-based failure criterion can then be used to construct a nonlinear progressive failure algorithm for investigating the material failure strengths of composite laminates.

The capability of MCT is illustrated in Figure 1. Consider a continuous fiber, transversely isotropic, unidirectional composite material with linear elastic fibers and matrix. The composite has a fiber volume fraction of 60% and a matrix volume fraction of 40%. Composite and constituent elastic constants are listed in Table 1 and strengths are listed in Table 29.

Table 1 Elastic constants for a AS4/3501 composite

Composite AS4 fiber 3501epoxyE11(GPa) 126. 208. 4.50E22(GPa) 11.2 25.0 4.50G12(Gpa) 6.33 95.0 1.68G23(GPa) 3.95 9.20 1.68ν12 0.27 0.24 0.34ν23 0.43 0.36 0.34α11 (µε/°C) -0.011 -0.0117 35.0α22 (µε /°C) 26.3 15.0 35.0

Table 2 Strengths for a AS4/3501 composite.

Composite AS4 fiber 3501epoxy

11S+ (MPa) 1950. 3202. 42.3

11S− (MPa) -1480. -2431. -176.

22S+ (MPa) 48. 42.3

22S− (MPa) -200. -176.

12S (MPa) 79. 120. 49.5

23S (MPa) 33. 33. 25.0

A thermal load (uniform temperature decrease) is applied to the block of material which is free to deform. Since the composite is unconstrained, there is no net stress at the structural level as the first line of analysis results listed in Table 3 shows. This result is representative of the current

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state of FEA technology in use today. That is, all stress and strain information is homogenized, or blended together.

Figure 1 Unidirectional composite under thermal load

Additional MCT results, listed in the second and third line of Table 3, show that due to a mismatch in constituent’s thermal properties, the fiber reinforcement experiences a compressive stress in the axial and transverse directions while the matrix experiences an opposing tensile stresses. Analogous results can be shown for a mechanical load. This type of information is typically unavailable to analysts today because it is not produced by conventional FEA.

Table 3 MCT stress results for a unidirectional laminate under a thermal load.

Composite AS4 fiber 3501epoxyσ11 (MPa) 0.0. -33.2. 49.8σ22 (MPa) 0.0 -8.86 13.3σ33 (MPa) 0.0 -8.86 13.3τ12, (MPa) 0.0 0.0 0.0τ13, (MPa) 0.0 0.0 0.0τ23 (MPa) 0.0 0.0 0.0

Further, consider a failure analysis of this component. A simple maximum stress approach, σij/

±Sij, would not even be considered by an analyst because of the zero valued macro-stress in the composite. However, a maximum stress assessment based on constituent micro-stresses (Table 3) and the constituent strengths (Table 2), indicate composite damage at the micro level due to matrix tensile failure in the 11 direction. To completely assess the effect of micro-level damage on the structure’s global operational performance requires a more detailed analysis. Analysis of this type, progressive micro-damage effects on macro-structural performance, is the subject of this project.

In summary, other than MCT, no other existing technology is capable of efficiently bringing

constituent information to bear on a structural analysis. Constituent information brings tremendous value to the analysts interested in predicting composites’ failure. For instance, advanced failure theories for composites may be implemented in a more straight-forward and general manner at the constituent level. Accurate predictions of constituent level failure enables the development of progressive failure analyses of the entire structure. Permitting one constituent to fail while keeping the others intact in an FEA simulation can allow a shift in the structures’ load path to undamaged areas. This approach has been ignored in the past because constituent information is unavailable in standard FE analysis. MCT is a revolutionary advance in this regard.

Structural design, verification, and potential post-mortem failure analysis of advanced composite cryogenic storage tanks require an analytical method that accurately predicts structural response to applied loads and temperatures. MCT presents such a method. Increased confidence through structural analysis methods will allow mass efficient composite cryogenic tanks concepts to be designed with minimum risk.

TEST PROCEDURESA carbon fiber/epoxy composite (AS4/3501-6) pre-preg was used in this study because it has been shown to crack readily at modest temperature differentials. Cross-ply laminates were fabricated with [(0/90)4]s, [(02/902)2]s, and [(04/904)]s laminate stacking sequences to test for in situply thickness effects.

Figure 2 AS4/3501-6 Cure Cycle

Figure 2 shows the standard cure cycle for the AS4/3501-6 composite. The cure cycle is important because it determines the “stress-free” temperature of the laminate and the subsequent residual stresses within the laminate due to local variations in cooling rates and mismatches in thermal expansion coefficients of the fiber and matrix. All ramp rates are kept relatively slow (~3oC/min). Vacuum bag pressure was kept at greater than 22 inches of mercury the entire cycle. The laminates were then post-cured at 350oF for 8 hours. All cures were performed in a PID temperature controlled hot press.

∆T= -250°C

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Router cut samples of approximately 0.75”x 1.25” in size were cut from the laminates. The specimens’ edges were then ground several tenths of an inch on each side to avoid cutting induced defects such as delaminations. Finally, the approximately 0.5”x 1.0” samples edges are polished to a 1 micron finish.

Next the specimens were placed in a dewar flask which, in turn, was filled with liquid nitrogen. The specimens were allowed to reach a steady state temperature (in liquid nitrogen they were visibly observed and left in the nitrogen between 15-20 minutes per cycle). The pieces were then removed from the nitrogen and immediately put in a desiccator until they warmed to room temperature.

With the pieces warmed to room temperature they were put under an optical microscope and inspected at 200x and 500x high resolution magnification for matrix cracking. This process is repeated for as many samples and thermal cycles as needed.

EXPERIMENTAL RESULTSA study to determine the importance of polishing resolution on the optical detection of microcracks was performed. Certain studies (ie, Uebelhart10) used a 600 grit (~14 micron) edge polish to look for microcracking. From initial observations it was hypothesized that 600 grit polish may in fact create misleading observable crack densities. It is shown below that a 1 micron finish is needed to accurately count all matrix microcracks.

A plate was fabricated, (AS4/3501-6 carbon fiber/epoxy material with a [04/904]s stacking sequence), and was router cut and polished. The specimens were initially polished to approximately a 14µm finish (600 grit) and examined under the microscope at 200x magnification (see Figure 3).

Figure 3: 600 Grit (~14 micron) polish with matrix crack (200x)

Crack counts were taken at the 600 grit polish after which the specimen was polished to a 1µm finish (see Figure 4).

Figure 4: 1 micron polish with matrix crack (200x)

A crack count at this level revealed more cracks, typically a finer crack than what was seen with the 600 grit finish. These samples were then thermally cycled. A summary of results can be seen in Figure 5.

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0.0

2.

4.

6.0

8.0

10

12

14

16.

18.

20.

600 Grit 1 micron1 2 3 4 5

Thermal Cycles

Crack Density (cracks/inch)

Figure 5: Crack density in middle 90º plies as a function of thermal cycles

Interestingly, data provided by Uebelhart10, shows initial crack densities and final crack densities for similar thermal cycles (with the exception of elevated temperature between cycles) of AS4/3501-6 near identical with our results. His crack densities were recorded with a 600 grit finish. Note the difference between our 600 grit finish and our 1 micron finish crack densities. It is our speculation that due to the increased optical resolution, we were able to see all of the cracks present and at 600 grit, many cracks were initially masked. This may help explain the discrepancy between our damage occurring over the first cycle and Uebelhart’s (and others) occurring over approximately five or six cycles.

Several more cross-ply lay-ups of AS4/3501-6 provided crack densities for plies of varying thickness using identically oriented adjacent plies with counts of 1,2,4 and 8 layers ,[((0°)M/(90°)P)N]S, while keeping the total number of plies in the laminate constant. The results of our test matrix of 1 to 8 plies is shown in Figure 6 which indicate a strong dependence of crack density on ply thickness.

0

2

4

6

8

10

12

14

16

18

20

CrackDensity (cracks/inch)

0 1 2 3 4 5 6

Cycle #

1 Ply2 Ply4 Ply

8 Ply

Figure 6: Crack density as a function of the number of thermal cycles for different ply thickness for AS4/3501.

Several observations should be noted when looking at Figure 6. First, the literature reports crack densities as an average value of fully developed cracks, i.e., cracks extending through the entire ply thickness. There are, incertain cases, a significant amount of partial cracks present, i.e., cracks that did not extend the full thickness of the ply. Whether or not an investigator can see the partial cracks depends in large part on the level of polish used on the specimen. It is our experience that many partial and narrow width (fine) cracks are visible only when a 1 micron polish is used. Many of the reports in the literature did not polish to this level. Thus to compare with the literature, our crack densities include only fully developed cracks. We did however, record data for partial crack density if the need for this information arises. Second, thin plies with cracks had several distinct characteristics that the cracked thick plies did not have. Thin plies had many partial cracks when compared to the thick ply. Further, the cracks in thin plies were much finer cracks than those in thick plies. In other words, the crack opening displacement looked much smaller for the thin plies than the thick plies. It has been shown in the literature11 that thin ply edge cracks or partial cracks can be completely immobile up to the strain at which the laminate fails, thus never fully propagating across the thickness of the sample. The observations in our thin ply samples showing very fine cracks may imply that the cracks do not extend the full width of the specimens. Dye penetrant x-radiography and ultrasonic imaging as well as other techniques may be used to fully characterize this type of cracks. Perhaps the best description of the different cracking phenomenon between thin and thick plies was referenced by Pagano11 and states the fact that thick ply transverse matrix cracking is initiation controlled while thin ply cracking is propagation controlled. He also states that thin ply cracks often times may not become fully developed before catastrophic laminate failure.

ANALYSIS AND CORRELATIONA computer program was developed to predict the 2 dimensional, plane stress, deformation response of composite materials. The program was based on classical lamination theory (CLT)12 along with Multicontinuum Theory (MCT). The software is built as a Visual Basic for Applications (VBA) program that uses Microsoft Excel as the graphical user interface (GUI). The code, named MCLT (Multicontinuum Lamination Theory), allows for stress and strain solutions to be found at the ply scale and the constituent (fiber and matrix) scale. Using these macro- and micro-level stresses and strains, alternate failure criteria can be applied for a constituent level or first ply failure analysis. Four failure criteria were selected for comparison using the MCLT: Maximum Stress13, 2D Tsai-Wu14, 2D Modified-Hashin9, and SIFT15.

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The first three criteria are stress based and the last is strain based (Strain Invariant Failure Theory). Tsai-Wu and Mod-Hashin are both quadratic, stress-interactive criteria while Maximum Stress and SIFT are not interactive. Maximum Stress can be applied at either the composite (macro-) or the constituent (micro-) scale. Tsai-Wu is applied only at the macro-scale while Mod-Hashin and SIFT are applied only at the micro-scale. A fifth failure criterion used software written by Maddocks and McManus16 to compare a shear lag stress analysis coupled with a critical value for energy release rate (using Linear Elastic Fracture Mechanics).

Previous work4 by Maddocks and McManus in developing the Crack-O-Matic software allowed for the use of material properties consistent with those used in the MCLT analyses. The additional information needed to run Crack-O-Matic was material fracture toughness, GIc and a curve fit parameter for the shear lag stress analysis, γ. A GIc

value of 141 J*m2 was used while varying between common γ values of 0.5 to 2.0. Maddocks and McManus have shown reasonably good correlation between experimental and predicted results of AS4/3501-6 using a γ value of 1.0.

The analysis assumed a thermal load applied to a symmetric, cross-ply laminate of AS4/3501-6 with unconstrained (free) boundary conditions. In all cases the absolute stress-free temperature of the laminate was unknown. Only the change in temperature, ∆T, relative to a 0oC reference point necessary to cause failure, defined as matrix cracking, was calculated.

A summary of the results from an alternative failure criteria comparison are shown in Table 4 & Table 5below.

Table 4: Failure Criteria Prediction Comparison (Except Crack-O-Matic predictions)

MaterialScale

MaxStress

Tsai-Wu

ModHashin SIFT

Composite -199̊ C -199̊ C N/A N/A

Constituent -150̊ C N/A -156̊ C -175̊ C

It should be noted that Crack-O-Matic analyses predicted cracks to occur exclusively in the 90o plies at the reported temperatures where as the MCLT based failure criteria predict equal states of failure in both inner and outer plies.

Table 5: Shear Lag and Energy Release Rate Failure Initiation Temperatures as a Function of Shear Lag Curve

Fit Coefficient as Predicted by Crack-O-Matic12

Shear Lag Parameter

(γγγγ)Crack Initiation

Temperature (oC)

∆∆∆∆T (oC)

0.5 11 -1651 -57 -233

1.5 -109 -2852 -154 -330

Ply level failure predictions using both Maximum Stress and Tsai-Wu failure criteria produced identical results but were 49̊C lower than the Maximum Stress failure criteria applied at the matrix level as shown in Table 4. There is a difference of 44̊C between the ply level criteria and the MCT failure criterion1 (quadratic stress interactive) which is applied at the matrix level. Finally, SIFT applied to the matrix level showed a 24˚C difference compared to the ply level criteria.

Experimentally, damage was found present at room temperature, a ∆T of approximately -156oC. The only failure criteria that allow for failure at this temperature were the Maximum Stress and the 2D Modified-Hashin. Both of these criteria used matrix stress fields that were MCT derived.

SUMMARYSuccessful experimental procedures were established for the thermally inducing matrix microcracking in AS4/3501-6 carbon fiber/epoxy cross-ply laminates. It was shown that for optical inspection of specimen edges at 200 magnification, a 1 micron surface polish is needed for accurate identification and compilation of crack densities. Experimental correlations were shown between crack densities, ply thickness, matrix cracking resistance, and damage modes. Analytical failure initiation predictions were performed at both the constituent (micro-) and composite (macro-) scale using five alternative failure criteria. For the data set generated, stress-based, constituent scale failure predictions had the best correlation with experimental results. The authors believe this to add to the growing evidence that composite failure initiates at the constituent scale thus dictating that failure analysis should also operate at that scale to fully capture the evolution of constituent failure to composite damage.

ACKNOWLEDGEMENTSAcknowledgements to Alfred University, Firehole Technologies, the Air Force Research Laboratories Space Vehicles Directorate and the Missile Defense Agency are given for the support of this work.

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REFERENCES1. D.L. Flaggs and M.H. Kural, "Experimental Determination of the In Situ Transverse Lamina Strength in Graphite/Epoxy Laminates," Journal of Composite Materials, 16 103-15 (1982).2. K.E. Jackson, "Prediction of First Ply Failure in Scaled Cross-Ply Composite Laminates," pp. 11-21 in, Vol. 55, Proceedings of the ASME Aerospace Division. ASME, 1997.3. S.S. Kessler, T. Matuszeski, and H. McManus, "The Effect of Cryocycling on the Mechanical Properties of IM7/977-2." Technology Laboratory for Advanced Composites\Department of Aeronautics and Astronautics\Massachusetts Institute of Technology, 2001 (Completed).4. J.R. Maddocks and D.H. McManus, "Prediction of Microcracking in Composite Laminates Under Thermomechanical Loading," Tenth International Conference on Composite Materials (ICCM-10), August 1994.5. C.H. Park and H.L. McManus, "Thermally Induced Damage in Composite Laminates: Predictive Methodology and Experimental Investigation,"Composites Science and Technology, 56 [10] 1209-19 (1996).6. J. Fan and J. Zhang, "In-Situ Damage Evolution and Micro/Macro Transition for Laminated Composites," Composites Science and Technology,47 [2] 107-18 (1993).7. J. Fan, “Proceedings of the 1996 Symposium on Applications of Continuum Damage Mechanics to Fatigue and Fracture,May 21 1996”, Vol. 1315, p. 46-64. ASTM, Conshohocken, PA, USA, Orlando, FL, USA, 1997.

8. J. Zhang, J. Fan, and K.P. Herrmann, "Delaminations Induced by Constrained Transverse Cracking in Symmetric Composite Laminates," International Journal of Solids and Structures, 36 [6 Feb] 813-46 (1999).9. J.S. Mayes, "Micromechanics Based Failure Analysis of Composite Structural Laminates," Naval Surface Warfare Center, Carderock Division, Survivability, Structures, and Materials Directorate Technical Report, Report Number NSWCCD-65-TR-1999, September 1999.10. S.A. Uebelhart, "Gas Permeability of Graphite-Epoxy Composites," Massachusetts Institute of Technology, Report Number 16.622, December 8, 1997.11. N.J. Pagano, G.A. Schoeppner, R. Kim, and F.L. Abrams, "Steady-State Cracking and Edge Effects in Thermo-Mechanical Transverse Cracking of Cross-Ply Laminates," Composites Science and Technology, 58 1811-25 (1998).12. M.W. Hyer, Stress Analysis of Fiber-Reinforced Composite Materials, Chapter 6, pp 212-252, McGraw-Hill, New York, NY, 199813. Ibid, pp 355-38514. S.W. Tsai and E.M. Wu, "A General Theory of Strength for Anisotropic Materials," Journal of Composite Materials, 5 58 (1971).15. J.H. Gosse and S. Christensen, "Strain invariant failure criteria for polymers in composite materials," 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit Technical Papers, Apr 16-19 2001, 1 45- 55 (2001).16. J.R. Maddocks and D.H. McManus, Crackomatic II [Fortran Computer Program]. Cambridge, MA, 1996.