DIMENSIONAL STABILITY OF ADVANCED MATERIALS

Ernest G. WolffPrecision Measurements & Instruments Corporation

Corvallis, OR 97333

ABSTRACT

All materials alter their shape and size in response to changes in applied and internal loads and environmental conditions, including time. Serious consequences may occur for many applications, especially in the aerospace and electronics fields. Control of dimensional instability is more complex for composite materials, components and structures because the response of each constituent is modified by all the others. Trends to more stringent designs and the advent of new materials further complicate the prediction of dimensional behavior. Developments in the design, measurement and assessment of dimensional stability are reviewed, with emphasis on further research and new applications.

KEY WORDS: Dimensional stability, testing/evaluation, optical testing

1. INTRODUCTION

1.1 Dimensional Stability Dimensional stability is a general property of a material, component or structure which enables it to maintain its shape, size, or any dimension. All components and structures have dimensional stability requirements, but often strength properties (e.g. tensile strength or impact strength) or lifetime (e.g. fatigue life) may be more important. We first review relevant materials and their dimensional response to changes in loads or stress and then their response to environmental changes, namely temperature, chemical, radiation and electromagnetic fields and time (1). A more complex situation arises when we consider that the effect of combined loads and their interactions, including causes and effects of internal damage such as microcracking.

1.2 Dimensional Control Tolerances prescribed for successful deployment must be related to the interactions of the micromechanical and thermophysical properties of the materials involved in fabrication as well as those used in construction combinations and attachments. Examples include the CTE (α) of the mold material (as in vacuum assisted resin transfer molding) and the curing and post curing of a resin part after manufacture. Residual stresses caused by the manufacturing process contribute to subsequent dimensional changes of the component. The design of a component or structure must consider potential changes in size or shape during fabrication, testing, and a lifetime of use.

1.3 Strain Magnitude We shall consider only applications where (A) dimensional stability is of critical importance, as with shape of an antenna or the spacing between components on a circuit

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board, and (B) where critical strains are on the order of the yield strength strain (0.2%) or less. (This means we can use engineering and true strain interchangeably with minimal error. For example, if the engineering strain is 0.01, the true strain is about 49.7 microstrain different, but if it is 0.001, the difference is only about 0.5 microstrain). The technology of predicting and measuring small dimensional changes is continually evolving as greater precision is required for many applications. In their 1993 SAMPE paper on dimensional stability, the authors from JPL (2) indicate that , “neither the metrology nor the technology of dimensionally stable materials has been developed to the level required for future NASA missions. Non-contact measurement of multi-axial dimensional changes down to the nanometer level are needed “. Much research is also needed to explain and predict the causes of dimensional instability… to the nanometer level”.

2. DESIGNING FOR DIMENSIONAL STABILITY

2.1 Choice of Materials Design for dimensional stability usually starts with materials which already possess stability during temperature excursions. For example, large mirrors require dimensional stability in terms of E/ρ and K/α (where K is the thermal conductivity) and consequently CFRP are primary candidates. In addition, high resolution pointing accuracy after deployment requires that their attachments, integrating structures and connections to secondary mirrors, etc., retain exceptional dimensional tolerances, both on ground based test beds and in space. Near zero CTE materials can be found in all major material categories, namely metals, plastics, ceramics. Advanced materials such as composites are more tailorable, meet several requirements simultaneously and come in a variety of shapes and sizes (See Table 1). They present new challenges in design, analysis and testing.

Table 1 Advanced Materials

New Fibers (e.g. Vectran, high E and high εf carbon, natural fibers)New lightweight materials (e.g. cyanate ester resins, glasses )Composites reinforced with short fibers, particles, whiskersMultidimensional reinforcements, e.g. C/C, 3D composites Special shapes, such as thin films, sandwich structures, New molecular structures (foams, aerogels)Smart materials (interact with electromagnetic fields) Shape Memory Polymers - reversibly recover inelastic strains Functional graded materialsNanomaterials (particles and fibers)

Carbon foam has been promoted by the Structural Materials Branch (WPAFB) to use its high stiffness, isotropy, low CTE and light weight for large space mirrors. The advantages of the pseudo-isotropic characteristics of K/α of carbon foams have also been pointed out (3). Reinforcements sponsored by AFRL/MLBC such as nanolayered hydrated aluminosilicate platelets to polymer matrices help to improve microcracking tendencies and modify the CTE mismatch between fiber and matrix. Thermal properties are important for optoelectronic devices, inasmuch as the device is assembled from a variety of materials using thermal methods of

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fabrication (welding/brazing adhesive bonding), which need to dissipate heat during use and must withstand thermal cycling.

2.2 Composite Design Parameters Composite materials offer the greatest flexibility in terms of design for required properties. For example, the volume fraction of particle reinforcements (e.g. in SiCp/Al, Grp/Al) can be varied to tailor the CTE to desired values (4). Design guidelines for stiffness, CTE and the coefficient of moisture expansion (CME or β) of composite panels and tubes are outlined in (1,5-7). Figure 1 shows the effect of changing the volume fraction of fibers on the CTE and CME of a (±θ)s composite. We see that we can not get αx and βx to be simultaneously zero.

Figure 1 CTEx and CMEx evolution for different values of Vf (6)

3. MECHANICAL LOADS IN SERVICE

Properties which relate to dimensional stability include the yield stress, proportional limit, strain rate sensitivity, residual stress relief, microyield stress (MYS) and general strain response, including bending, twisting and axial strains. Sample edges, ends, diameter to thickness ratios in tubes, Poisson’s ratios, and fiber/matrix interfacial properties such as shear strength also influence dimensional stability, but in more complex ways. Special geometries, such as curved panels, tubes and sandwich structures are of increasing interest. For example, possible applications of composites with multiple stable geometries are noted in a study of unsymmetrical laminate layups (8). Few, if any, materials except quartz fibers, are truly elastic. Thus any loading will result in some permanent deformation. Future predictions of dimensional instability will need to emphasize viscoelastic and viscoplastic deformation, often coupled with simultaneous stress relief such as microcracking. The MYS is a particularly good indicator of internal damage, and relates to the compliance, CTE, and other dimensional stability indicators.

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4. ENVIRONMENTAL CONSIDERATIONS

4.1 Temperature The CTE of most materials can be predicted to engineering standards with a wide variety of models (e.g. the Turner equation). The general in-plane CTE of sandwich structures can also be predicted on the basis of core geometry and basic facesheet material properties (9). However, edge and end effects are not straightforward, especially where the core thickness may be a significant compared to the in-plane dimensions. We have examined this problem both analytically and experimentally (10). Finite element predictions were used to predict the distribution of CTE as a function of position near the ends of a laminate facesheet/aluminum honeycomb core sandwich material. We have found that stresses imposed on the core by the facesheets are dissipated as the core gets thicker and this reduces the predicted extension of the facesheet. There are also periodic fluctuations in localized strain on the facesheets caused by honeycomb geometry.

4.2 Mass Absorption The coefficient of moisture expansion (CME) is a property of all organic materials, since all absorb moisture (and other low molecular weight liquids) to some extent. The saturation level, or solubility, the rate of moisture ab/desorption (diffusivity), hygrothermal aging effects and the possibility of barrier coatings and their effect on dimensional stability are often of interest. (11). Shape memory polymers are also being studied for medical applications. CME values vary over a wide range for composite materials (5 to 10,000 ppm/%M) (12). Polymers with low equilibrium moisture absorption or low moisture “pick-up” e.g., cyanate esters, or thermoplastics vs thermosetts, do not necessarily have a low CME. Natural fibers, like Kevlar, also absorb moisture. New analytical models are needed, such as percolation models to describe the moisture diffusion process (13).

4.3 Temporal Stability Measurements of temporal stability were for many years assisted by the NBS (NIST) through its development of gage blocks. These are adequate for ppm at constant temperatures near ambient. The resolution of such measurements was increased through the use of Fabry-Perot interferometry (14). Measurements on Zerodur, ULE , glasses and Invars were applied to prediction of the temporal stability of spacecraft materials, where repairs are very difficult. Some of this work has continued at JPL (2), where system drift and hence dimensional strain accuracy were on the order of 0.04 ppm. The relative effects of thermal cycling and creep on dimensional stability of CMCs and MMCs also need to be evaluated (15).

4.4 Radiation Space radiation effects (1) and also various types of electromagnetic radiation lead to interactions between strength of fields and sample deformation. The Faraday effect relates the rotation of polarization of light to the magnitude of a magnetic field and the distance the light travels in the (transparent) material. It is used to measure the strength of the applied magnetic field but is also sensitive to changes in the material’s dimensions due to mechanical or other loads. (The Kerr effect is an electric field induced linear birefringence, the Pockels effect is a birefringence change proportional to the electric field). External forces will alter the shape of embedded fiber optics which in turn alters their birefringence. Magnetostrictive materials expand in the presence of applied magnetic fields.

4.5 Smart Materials Smart materials utilize dimensional changes induced by electromagnetic fields. Electrorheological fluid materials respond to electric fields by alterations in viscosity,

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plasticity and elasticity, providing a means to alter the damping characteristic and other dimensional instabilities of components and structures (16). The interaction of elastic, electric and magnetic effects are of importance to the crack growth and stability of smart materials such as piezoelectric materials (PZTs) and magnetic alloys (17). For example, PZT ceramic fibers actively dampen vibrations and then use the energy to create an electrical force to control the shape (e.g. of a composite sport article, such as a ski or tennis racket)(18). In other words, dimensional instability or mechanical deflections are converted to a source or electrical power. In infrastructure applications, the vibration causes an electrical signal which , via a microprocessor, sends back a signal which can either stiffen or relax the PZT actuators, producing a self-adjusting or smart structure. PZT actuators help to minimize deflections that may be caused by damage or manufacturing imperfections (19). The use of such PZT based smart materials to dampen space structure vibrations is also discussed in (20). They point out that this approach replaces, in part, the need for high stiffness, suggesting a shift from passive to active control of dimensional stability.

4.6 Structural Health Monitoring Structural health monitoring is intimately correlated with dimensional stability. New smart materials techniques are being developed to monitor reductions of stiffness through damage, such as delamination in CFRP laminates. Fiber Bragg grating sensors and PZT Lamb wave actuators can be used to determine the delamination length (21). Metastable austenitic ferrous alloy inserts embedded in a laminate transform through strain to more stable martensite with changes in magnetic susceptibility giving a strain memory effect and hence using dimensional instability to warn of loss of structural integrity. (22).

4.7 Microcracking Stress or thermally induced microcracking has come under scrutiny in recent years because of its effects on stiffness and CTE changes in composites. New polymers such as cyanate esters exhibit increased resistance to microcracking. Other factors, such as laminate thickness, fiber type, thermal cycling temperature range (23), and the orientation of nanofiber reinforcements or whiskers (e.g., SiCw/Al) are also important (24).

4.8 Combined Effects Future research in dimensional stability is needed to assess the coupling effects of combinations of stress, temperature, moisture, damage, radiation, and time (25). In other words, the basic Duhamel-Newman relation, which sums up the (linear) strains (ε) due to various influences, is only a good starting point to describe dimensional instability:

Σε = SΔσ + αΔT + βΔM + ηΔt + ψΔQ +…… [1]

where η and ψ are the coefficients of temporal and radiation induced expansion. A matrix approach as in Table 2 is needed for more precise predictions of combined effects. For example, the stress effect (σ) on thermal expansion (α) is related to the thermoelastic coefficient (γ) via the elastic modulus (E) as

(δα / δσ ) T = - γ / E [2]

Examples of relevant phenomena that require coupling constants include thermal spiking, reverse thermal effects, the mechanosorptive effect and changes in dimensions due to microcracking after thermal or stress cycling. The subjects of physical and chemical aging, residual stress relief,

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creep, viscoplastic flow all impact dimensional instability with time and are major topics on their own. The work of Sih and co-workers on thermohygroelasticity (26) summarizes methods to measure the coupling between heat and mass flow in a composite material (T300 graphite /5208 resin). Figure 2 illustrates one of the few attempts (via a curve fitting technique) to determine coupling constants ν and λ (the mutual contributions of mass transport and heat flow).

Table 2 An Extended Hygrothermoelasticity Matrix

Figure 2 Normalized moisture content as a function of time for λν = 0.25 and different u = f(diffusivites, etc) values at 21oC for a T300/5208 composite (26).

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5. NEW TEST METHODS

5.1 Thermal Expansion A recent review of optical interferometry methods for thermal expansion measurements was given in (27). The principal ASTM standard is E289 which has recently been extended to cover Michelson interferometry, generally the best approach to high precision linear deformations with arbitrary size and shape components and structures. The advantages of this technique include high accuracy or length resolution (to < 1nm), use over a wide temperature range (0 - >1300K), a suitability for simultaneous opto-acoustic emission for crack detection and analysis. Difficulties with this technique include compensation for optical component stability, reflecting surfaces, avoidance of back reflections to the laser and sensitivity to optical path variations at gas pressures > 100 mTORR. Figure 3 illustrates a method of making two simultaneous CTE measurements on flat panels without incurring distortions due to edge or end effects. Mirrors on steel razors held upright by quartz rods give a well defined Lo (28).

5.2 Thermal Expansion Uniformity Measurements of CTE to ppb/C are required to monitor the uniformity of large astronomical mirror blanks made from zero expansion glass ULE TM. Negligible differential coefficients of thermal expansion are needed at every fusion joint for optimum performance (29). A non-destructive technique based on determining the ultrasonic velocity was found to correlate with CTE – basically a 0.2 ppb/C was equivalent to measuring the ultrasonic velocity to one part in 10-6 cm/μsec. Results included the observation that the total data population for a large mirror blank lay between +3 and –3 ppb/oC for a 5o to 35oC mean CTE. (Note: since” billion” means 1012 in Europe and 109 in the USA, it is preferable to refer to “nanostrain” instead of ppb).

Figure 3 Two composite panels set up for longitudinal CTE measurement using Michelson laser interferometry. Laser beams enter through a vacuum window from the sides.

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Another important application for CTE uniformity measurements is with glass seals (30). One hard-to-answer question is – at what temperature does the glass transform from visco-plastic to elastic deformation on cooling? Residual stress release due to viscoelastic behavior ceases below the “setting” point, which depends on many variables, including composition, cooling rate, elastic modulus of the other sealing material, etc. Optical retardation coupled with photoelasticity and comparison to ultrasonic methods were able to show equivalence in CTE between glasses at a 1 ppb/oC resolution level.

5.3 3D Deformations Figure 4 illustrates a method for hoop CTE of very large tubes – a carbon fiber tow or quartz filament is wrapped around a Teflon coated hoop section. The ends are connected to a quartz frame and LVDTs outside the heated/cooled zone. The wrapped filament is compared to an identical filament passing tangentially over the test sample. The increasing need to characterize the overall shape change, e.g., 3D warpage, leads to full field imaging methods, such as Moiré, holograpraphic interferometry, speckle and shearography. Each method has pros and cons. To date there has been limited use of these methods for thermal or moisture expansion measurements. Speckle size and laser beam characteristics affect sensitivity. High diffuse reflectivity and surface roughness are also important factors which may limit the dimensional change sensitivity. The relatively high level of speckle noise and sensitivity to vibration and air turbulence with electronic speckle pattern correlation (ESPI) creates difficulties for damage detection in composite laminates (31). Complex fringe analysis is required. Shearography measures strains on an arbitrarily curved surfaces but in-plane displacements are difficult to measure independently. Work is continuing in this area – for example, optical interferometers using both fast Fourier transform and phase-shifting methods, microscopic optics, CCD cameras and PZT nanoscanning give 3D deformations of microcomponents, surface contours for MEMS devices and nano-technology in general. (32).

Figure 4 Method to determine hoop CTE of large tubes. The tube is supported by an axial quartz rod in a heater/cooler box and central tapes. Tows or filaments are wrapped around the tube and

connected to LVDTs

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5.4 Measurement of CME The CME is usually derived from different combinations of weight and length measurements at different humidities. However, the best approach is simultaneous real time weight and length measurement, since the polymer stress state will be different between ab- and desorption (33). Figure 5 illustrates an instrument for CME determination designed to handle small samples of thin polymer foils.. By this method the CME can be determined in a period of minutes or hours but the diffusivity still requires knowledge of the saturation moisture content, which can often take days, depending on the specimen thickness. This can be determined independently by weight measurements.

5.5 Miscellaneous Developments Continued improvements in techniques for measuring dimensional stability properties are expected. For example, thermal conductivity, thermal diffusivity, effusivity and specific heat can now be measured simultaneously by several different methods. Modulated thermal analysis can acquire properties both dependent upon the temperature rate of change (e.g. CTE) and properties associated with both time and temperature (stress relaxation, softening and heat shrinking. Techniques such as modulated differential scanning calorimetry are progressing for thin film thermophysical properties (34).

Figure 5 Schematic Layout of Environmental Chamber (controlled humidity and temperature) for Simultaneous Determination of Weight and Dimensional Change. B = microbalance,

L=LVDT, S = sample, Q = quartz frames, C = clamps .

6. EXPERIMENTAL VERIFICATION

Design and manufacturing limitations impose error bars which are frequently on the same order of magnitude as the required dimensional tolerances. Consequently, experimental verification is needed to assure the design is based on realistic material property inputs and that fabrication maintains the assumptions of the behavior algorithms. For example, have the ply angles assumed in the analysis been maintained during laminate layup?. Is the material fully cured.? Do the

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expected conditions change the material properties, e.g. is there microcracking after thermal cycling? PMIC is involved in the verification test phase for many components and structures, both for the prototype and flight articles. Figure 6 illustrates a typical telescope component set up in a thermal-vac chamber for dimensional analysis, in many cases down to cryogenic temperatures.

6. 1 The Mars Reconnaissance Camera (as described by Nancy Pottish (5)). Vanguard designed the CTE of the bench assembly to be –0.14 ppm/C . To ensure that the camera structure met CTE requirements both flat coupons and the 20 cm diameter by 23 cm long camera cylinder structure were tested at PMIC using Michelson interferometry, where the CTE can be determined to 10 ppb/C in real time over a wide range temperatures and sample sizes. This enabled the fine tuning of the location of the optical elements and detector in the bench for optimal performance. Other space components where dimensional stability is critical include the Telkom 2.0 Meter reflector, the CRISM Mineral Detection Instrument and the WFC3 Optical Bench (5).

6.2 The Deployable Comparative Active Telescope Testbed (DCATT) In support of the Next Generation Space Telescope (NGST) program (35) it was found that a limitation to the use of composites for a ground-based optical assembly was the CME. During development of a zero thermal expansion nano-actuator system using composites and Invar for the positioning of the meter-sized mirror segments of NASA’s next generation space telescope, it was predicted that a 5% relative humidity change in the lab would cause the composite tube to expand by about 100 nanometers in four hours, bring the optics out of alignment. PMIC was selected to determine the moisture diffusivity of coated and uncoated tubes. The (beneficial) use of a Parylene–C coating was shown to retard the moisture induced expansion sufficiently to remove their interference with the fine tuning of the CTE .

Figure 6 Telescope Assembly for thermal/vac/dimensional testing at PMIC(Courtesy of Vision Composites)

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7. CONCLUSIONS

General laminate design approaches, such as evolutionary optimization and Monte Carlo analyses, can optimize the layup for mechanical, thermal and hygral loads and can also account for manufacturing inaccuracies (6). Further manufacturing challenges (for deployable optical telescope testbeds) were described in (36). MMCs are slight less sensitive to manufacturing errors than PMCs, and of course are not sensitive to moisture variations. Otherwise, in terms of laminate properties, PMCs and MMCs are equivalent. Extension of this work to determine sensitivity to delaminations reflects the current trends to predict composite dimensional stability behavior for combined loads, including the effect of damage.

Interest continues in the dimensional stability of a wide range of materials, but we are seeing increasing need to predict and test the deformation of smart composites and nanofiber or nanoparticle reinforced composites. Long term measurements relate to structural health monitoring. For example, thermal stability is often related to time effects such as post curing (37). Other topics of increasing interest include cryogenic properties, the effects of fittings and attachments, and combined effects such as internal damage (microcracking) effects on CTE, CME. New damage detection and metrology techniques will help to formulate better crack growth models and other explanations for dimensional instabilities.

8. ACKNOWLEDGEMENTS

The author wishes to acknowledge the dimensional stability group at PMIC, especially Darrell Oakes, Hong Chen, Eric Henthorne, James Sharp, David Stumpff and Scott Radke for precise measurements of dimensional changes on many components and structures.

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