Residual stress and thermal expansion

Residual stress and thermal expansion of graphite epoxy

laminates subjected to cryogenic temperatures

Peter Ifju *,Donald Myers,William Schulz

University of Florida,Mechanical and Aerospace Engineering,231MAE-A,Gainesville,FL 32611-6250,USA

Received 31January 2006;accepted 1February 2006

Abstract

In composite structures understanding and quantifying the existence of residual stresses is a very important issue.The presence of these residual stresses can lead to unexpected failure of structures as seen in the fuel tank of the X-33reusable launch vehicle.A study into the development of residual stresses as a function of temperature was performed to help provide insight into this situation.A recently developed optical technique,the cure reference method,and a modi?cation of traditional strain gage techniques were used in this pursuit.Di?raction gratings and strain gages were applied to IM7/977-2composite panels of di?ering stacking sequences.Strains were measured under no load while temperature was varied.Consequently stresses developed between the plies and a method to calculate them was proposed.Residual stress levels were dependent on stacking sequence and quasi-isotropic laminates perform poorly when exposed to cryogenic https://www.360docs.net/doc/e317410891.html,minates should be optimized to account for both mechanical and thermal loading.ó2006Published by Elsevier Ltd.

Keywords:Composites;C.Residual stress;https://www.360docs.net/doc/e317410891.html,minates

1.Introduction

For the next generation reusable launch vehicle to be viable,it is necessary to minimize airframe weight by both reducing fuel tank weight and using the tanks as structural members in order to increase the relative percentage of fuel weight.In order to accomplish this goal,advanced com-posite technology must be utilized.However,the operating environment of the liquid hydrogen (LH2)fuel tanks pre-sents a serious challenge for the application of laminated composite materials.In order to safely utilize laminated composites in the cryogenic environment there is a need to fully understand and measure the mechanisms that cause thermal stresses.

Thermal stresses arise because of the mismatch in coef-?cient of thermal expansion (CTE)between the ?bers and the epoxy matrix in laminates.These stresses can be quite large.In testing of the X-33LH2fuel tanks [1],failure

occurred as a result of thermal stress-induced micro-cracks,which led to hydrogen leakage.Rupture occurred during the transition back to room temperature as hydrogen trapped in the sandwich core expanded.Chemical shrink-age of the epoxy at cure can also cause signi?cant stress in laminated composites,as much 10%of thermal stresses.Taken together,these comprise the residual stress in a composite.

On the ply-scale it is possible to minimize the residual stresses by varying the ply angles.For instance,a unidirec-tional laminate has no residual stresses on the ply-scale whereas a cross-ply represents the extreme case.A unidirec-tional composite,however,is a poor choice for carrying non-axial mechanical loads.Therefore,there is a tradeo?between load carrying strength and thermal strength,the latter referring to the ability for a material to avoid micro-cracking at low temperatures.

The objective of this paper is to describe an adaptation of the cure referencing method (CRM)[2,3],and the cou-pling of moire

′interferometry [4]with conventional strain gage measurements to determine composite CTE and

0266-3538/$-see front matter ó2006Published by Elsevier Ltd.doi:10.1016/https://www.360docs.net/doc/e317410891.html,pscitech.2006.02.011

*

Corresponding author.Tel.:+13523926744;fax:+13523927303.E-mail address:ifju@u?.edu (P.Ifju).

https://www.360docs.net/doc/e317410891.html,/locate/compscitech

Composites Science and Technology 66(2006)

2449–2455

COMPOSITES SCIENCE AND TECHNOLOGY

variability.It will also present preliminary results of testing on IM7/977-2material system.

2.Experimental purpose

The increasing importance of composite materials over recent years has led to a great deal of research into methods to predict,characterize,and measure residual stress and strains in laminated composites.These methods consist of both computational and experimental techniques.Many of these experimental methods are destructive in nature and have other disadvantages.These methods[5,6]involve cutting,drilling,or sectioning to cause and measure stress relaxation.

Once a specimen has been so tested it is no longer viable for use or further evaluation.For this reason many non-destructive techniques have been developed and imple-mented.These include sensor embedding,X-ray di?raction and CRM.

The goal is to accurately measure the residual stresses and thermal expansion coe?cients as functions of temper-ature in a non-destructive manner via CRM and conven-tional strain gage technology.Several samples of each of three IM7/977-2prepreg laminates were:

1.Uni:13layer unidirectional lay-up[013].

2.RLV:Quasi-isotropic lay-up?45=903=à45= O3

S .

3.OAP:Optimized angle ply[(±25)]3S.

The RLV lay-up is taken from the design of the LH2 tank used in the NASA X-33project.The lay-up of the OAP sample stems from a reliability optimization per-formed by Qu[7],of a LH2fuel tank constructed from an IM600/133graphite-epoxy system.The stacking sequence for the tank was[±h1/±h2]S.Optimal designs had ply angles h1and h2near25°,and nearly equal;the stacking sequence was thus simpli?ed to[±h]S.Monte Carlo simulation gave a probability of failure of approxi-mately1in15,000for the[±25]S design.It should be noted that this optimized ply sequence is for a di?erent material system.The OAP was used as a starting point to accrue sta-tistical data on typical lay-ups.

3.Experimental techniques

3.1.Cure reference method and moire′interferometry

The residual and thermal stresses are determined by using the cure reference method developed by the authors to measure the residual strain in unidirectional or multidi-rectional composite laminates.CRM uses the full-?eld laser-based optical method of moire′interferometry to doc-ument strains on the surface of laminates that initiate dur-ing the high temperature curing process.The method involves replicating a high frequency di?raction grating on the specimen while in the autoclave.The grating acts as a reference to the stress free condition just prior to resin solidi?cation.Subsequent strains result from two mecha-nisms,the chemical shrinkage of the polymer matrix and the thermal mismatch between the resin and matrix.Strains and stresses due to the chemical shrinkage are a one-time event which develop during the curing process,while the thermal mismatch contribution is dependent on service temperature of the component.

In order to be able to measure the residual strains on the composite laminate,a di?raction grating is applied during the cure cycle of the laminate.Since the grating is cured with the composite,it carries the same thermal strain and chemical shrinkage information as the composite cools.

The process in which a di?raction grating is produced for application to a composite laminate involves several steps.The?nal stage is production of the autoclave tool that consists of an aluminized grating on a500·500·1/200 piece of Astrositallò.Astrositallòis an ultra low expansion (ULE)glass with a coe?cient of thermal expansion(CTE) of0.3·10à7mm/mm/°C.The low expansion of the tool is necessary so that the tool does not transfer any strain to the panel during the transfer process in the autoclave.

Most high performance composite laminates are pro-duced with the use of an autoclave(Fig.1a).The autoclave is a pressure oven that has vacuum line connections within the pressurized chamber.Once the stacking sequence for the speci?c laminate is chosen,one can begin to process the laminate in the following steps:

https://www.360docs.net/doc/e317410891.html,y-up:produce the properly‘‘stacked’’prepreg lami-

nate according to the speci?ed stacking sequence.

2.Vacuum bagging:Fig.1b shows a schematic of the vac-

uum bag assembly.The ULE tool with the grating side up is placed at the base of the assembly.The surface is then covered with a nonporous release?lm.A hole of approximately1.500diameter is cut into the release?lm.

The hole allows for the grating to be exposed to the composite surface during the cure cycle.The thickness of the?lm is important.It is critical that it is as minimal as possible so that it will not indent the surface of the composite during the cure process as the resin begins to polymerize.The prepreg laminate is then placed on top of the release?lm,centered over the ULE tool.

The non-porous release?lm placed between the tool and the laminate prevents the epoxy from curing to the tool.A layer of porous release?lm is placed on the upper surface of the laminate,which provides two functions.It allows for excess resin to be drawn o?the laminate and into the bleeder cloth,as well as allowing for separation from the bleeder cloth.The bleeder cloth is a porous material that absorbs excess resin drawn out of the laminate via vacuum.Absorbing this excess resin allows an appropriate?ber volume fraction to be achieved.The breather cloth,which can be the same material as the bleeder cloth,is used to distribute the vacuum throughout the entire bag.Another layer of non-porous release?lm is placed between the bleeder and the breather cloths so that excess resin is not trans-

2450P.Ifju et al./Composites Science and Technology66(2006)2449–2455

ferred into the breather material.This could result in

resin being drawn into the vacuum line or clogging the breather cloth which would prevent an even vacuum dis-tribution on the laminate during cure.Finally,the ULE and laminate assembly are placed into a vacuum bag.The bag is sealed with a sealant tape and placed in the autoclave for curing.

3.Cure preparation:the vacuum bag is placed inside the oven and connected to the vacuum line.Vacuum is applied and a leak check is performed.It is imperative that the vacuum integrity is maintained,throughout the necessary portions of the curing process.

4.Cure:execute the appropriate cure cycle for the epoxy matrix material.At the heart of the cure referencing method is the tech-nique of moire

′interferometry.Moire ′interferometry is an optical technique that can be used to determine in-plane

displacements.Moire

′is characterized by high displacement and strain sensitivity,high spatial resolution,and a high signal-to-noise ratio [4].It is a non-contacting,full-?eld method capable of measuring both normal and shear

strain.A schematic of the moire

′interferometry setup can be seen in Fig.2.Moire

′interferometry is based on the prin-cipal of the destructive and constructive interference of light.The result of the interference is a very characteristic pattern of light and dark fringes as seen in Fig.3.These fringe patterns can be used to directly determine the in-plane displacements and residual strains,which lead to residual stresses in each ply.The method of analysis will be discussed later.3.2.Strain gage technique

After the specimens have gone through the cure cycle

and the CRM and moire

′measurements have been taken,traditional strain gages were applied.The gages were applied at room temperature and any measurement of strains must be referenced from this point.This is not pos-sible without the initial information provided by CRM.Four Vishay Measurements Group WK-13-250BG-350gages are applied to each specimen with MBond 610.These gages and the adhesive were selected for their performance ability in the selected temperature range.Gages from the same batch were also applied to Astrositall and Ti6-4Al-4V which were used as reference materials to compensate for temperature e?ects described later in the analysis.The strains were recorded from the gages by use of National Instruments data acquisition https://www.360docs.net/doc/e317410891.html,rmation acquired was combined with the CRM results to develop strain,stress,and CTE curves across the entire temperature range for each specimen.Temperatures ranged from the cure temperature 182°C down to the cryogenic realm of à190°C.

4.Data analysis

The experimental technique described previously leads

to the acquisition of moire

′fringe patterns describing

the Fig.1.(a)Autoclave and (b)vacuum bag

schematic.

Fig.2.Schematic of 4-beam moire

′interferometry.P.Ifju et al./Composites Science and Technology 66(2006)2449–24552451

in plane displacements on the surface of each laminate.The

relationship between fringe order,N ,and displacement is as follows:U ?N x f e1TV ?

N y

f

e2T

where f is the frequency of the virtual reference grating;(f =2400lines/mm)U and V are the displacements in the x and y directions and the subscripts on N refer to the fringe orders in the U and V displacement ?elds.The abso-lute strain using the following strain displacement equa-tions (for small strain)can also be directly determined

from the moire ′fringes e x ?o U o x ?1f o N x o x ?1f D N x

D x

e3T

e y ?

o V o x ?1f o N y o y ?1f D N y

D y

e4TThese equations were used to determine the strains on the faces of unidirectional and multidirectional laminates.These strains are a result of the thermal contraction,which is a function of the temperature di?erence between the cure temperature and operating temperature;chemical shrink-age of the matrix,which is not temperature dependent,occurring only during cure;and the thermal expansion of the autoclave tool,which will be neglected in analysis.After determining the strain that exists on the surface via CRM the next step is to acquire and analyze the e?ect of varying temperature from cure to cryogenic conditions.This is done by the strain gage method describe above.The total output of the gage must be adjusted for the tempera-ture e?ects on gage factor,transverse sensitivity,and the extension or contraction of the gage itself.The strain out-put,e T(G/S)is the combination of the thermally induced expansion of the gage,e G ,and specimen,e S e T eG =S T?

b G

F G

D T tee S àe G Te5T

where b G is the thermal coe?cient of resistance of the gage grid material,F G is the strain gage factor,and D T is the temperature change.

A dummy compensation method is used to obtain the strain experienced by the specimen itself.When a reference material is subjected to the same conditions the strain out-put,e T(G/R),is the combination of the thermally induced expansion of the gage,e G ,and reference,e R e T eG =R T?

b G

F G

D T tee R àe G Te6T

If the true expansion of the reference material is know at any temperature then (6)subtracted from (5)yields the strain of the specimen e S e S ?e T eG =S Tàe T eG =R T

e7T

This operation is performed for each gage on the speci-men.Adding the values of strain determined by (7)at any temperature to the values determined by (3)and (4)pro-duces the total surface strain seen by the laminate in either the x or y direction at that temperature.

By determining the state that each ply would reach if the bonds between them were liberated the stresses that held them together can be de?ned.This liberated strain will be referred to as the residual strain,{e res }k .Using the assump-tions of laminate theory,where plane sections remain plane,for symmetric lay-ups,the strain on the surface matches that at any point in the interior,as long as the location is a few ply thicknesses away from the free edge.The residual strain in each ply becomes:f e res g k ?f e uni g à?T k áf e lam g

e8T

where [T ]k is the transformation matrix associated with the ply orientation,{e uni }is the strain on the unidirectional laminate,and {e lam }is the strain on the face of the laminate.

After the residual or liberated strain is de?ned,the stres-ses,r res ,that develop in the various laminates can be determined

r res1r res2s res128><>:9>=>;k ?Q 11Q 120Q 21Q 22000Q 6626437

5k e res1e res2e res128><>:

9>

=>;k e9T

where [Q ij ]is the sti?ness matrix for an individual ply.

The strain data can also be transformed into a linear coe?cient of thermal expansion,CTE,from cure to

the

Fig.3.Typical moire

′interferometry fringe patterns.The circular scribe mark provides a scale.2452P.Ifju et al./Composites Science and Technology 66(2006)2449–2455

testing temperature.The data was taken in 15°intervals allowing the CTE of the laminates to be calculated as a function of temperature.The change in strain over the tem-perature interval (e T2àe T1),was divided by that interval (T 2àT 1),from cure to cryogenic

CTE x ?

ee T2x àe T1x T

eT 2àT 1Te10TCTE y ?ee T2y àe T1y T

eT 2àT 1Te11T

5.Results and discussion

The analysis method described previously was used to characterize the expansion of the chosen laminates.Fig.4

displays typical moire

′patterns for each laminate that resulted from bringing the specimen down from cure to room temperature,a D T of à158°C.

Fig.4a,the U displacement of the unidirectional lami-nate,demonstrates very low fringe density,which indicates

that the laminate is near the null pattern of zero displace-ment or zero fringes.From this result it was veri?ed that the CTE is very near zero in the ?ber direction.Since there is negligible displacement in the ?ber direction,the residual strain will be treated as a function of the matrix direction strain only.

The absolute strains were then compared with results from Classical Laminate Theory (CLT).CLT is an analyt-ical tool that allows you to analyze laminates with arbitrary ply sequences,which can lead to coupling e?ects.These coupling e?ects can cause combinations of extensional,?exural and torsional deformation.A program implement-ing CLT was written in MATLAB to calculate the strains in the given laminates.Inputs such as:

?Combined material properties for the ?ber and matrix (E 1,E 2,G 12,m 12,a 1,a 2).

?Stacking sequence and ply thickness.?D T from cure.

?Loading

conditions.

Fig.4.Moire

′interferometry patterns for each laminate.P.Ifju et al./Composites Science and Technology 66(2006)2449–24552453

Only the strain due to the temperature change of the laminate was considered in the program since the thermally induced strains are our main interest.

Table1shows a comparison of the average values of absolute strain from the CRM method compared with the value generated from CLT with material properties obtained by a micro-mechanical model developed by Dr. Bhavani Sankar and Sukjoo Choi of the University of Florida to evaluate residual stress in laminates.A deviation is to be expected between these two values for three main reasons.The?rst is that CLT makes the assumption that each ply is in a state of plane stress;interlaminar stresses are neglected.Second is that CLT does not account for chemical shrinkage.The third reason for the deviation is that the material properties for the matrix/?ber system are based on a micro-mechanics model rather than actual measured quantities.

Matrix properties are signi?cantly weaker than those of the?ber.For this reason the?rst damage seen in a lami-nate will often appear as micro-cracks in the matrix.The stresses have been transformed into the components that will act in the transverse direction of each ply.The stresses in this direction would likely control the micro-crack initi-ation and have been displayed on the ply level as a function of temperature in Fig.5.

It should be noted that high absolute strain on the sur-face does not correlate directly to high residual strain.In the unidirectional laminate a high strain value is deter-mined from the moire′techniques;however,this is a free expansion strain.There is in fact no residual strain present in the unidirectional laminate.Recall that the residual strain as de?ned in this paper is the di?erence between the constrained ply strain and the free expansion strain.

Fig.6displays the coe?cient of thermal expansion in the laminate0°and90°directions for each lay-up from cure to cryogenic temperature.The average coe?cient of thermal expansion is given by the moire′and strain gage results and Eqs.(10)and(11).The value of CTE for the unidirectional laminate will be used in conjunction with other material properties from the previously discussed micro-mechanical model.

It can be seen that residual stresses of the OAP opti-

mized design are signi?cantly less than those of the RLV design.This result was expected as the OAP design was optimized to give the greatest reliability and performance values of load carrying capability versus susceptibility to thermally induced residual stresses.

6.Future work

In addition,the CTE can and will be decoupled from the chemical shrinkage that is a one time event during the cur-ing process.Also,material properties are to be determined by mechanical testing to verify the micro-mechanical model.This material data will be used also to compare physical results with CLT again to yield more accurate results.E?orts will also be made to provide a large data set that can be used by the optimization group to develop reliability studies.

Table1

Comparison of CRM with CLT(micro-strain)

CRM average CLT%Di?erence Unidirectional e x000

[013]T e yà6878à789214.7%

RLV e xà570.84à875.553.4%

?45=903=à45= O3 S e yà207à31350.9%

OAP e x842.1105725.5%

[25/à25]3S e xà5040à6115

21.3%

2454P.Ifju et al./Composites Science and Technology66(2006)2449–2455

7.Conclusions

Methods to characterize residual stresses,strains and the coe?cient of thermal expansion have been proposed and examined.From this examination the following conclusions have been reached.General agreement was found between composite laminate theory and the results from the CRM method,providing proof of con-cept.The optimized laminate lay-up sequence is in fact much less sensitive to thermal e?ects than the stacking sequence originally proposed and implemented in the hydrogen storage tank of the X-33project.These meth-ods should and will be extended into the cryogenic realm to provide vital data on laminate properties under those conditions.

Acknowledgements

Portions of the work presented in this paper have been supported by the University of Florida Experimental Stress Analysis Lab and the NASA Langley Research Center.

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