Estimating the Residual Fatigue Lifetimes of Impact-Damaged Composites Using

The rm oe last i c Stress Analysis GAVIN P. HORN, THOMAS J. MACKIN,, and PETER KURATH

Department of Mechanical & Industrial Engineering University of nlinois at Urbana-Champaign

1206 West Green Street Urbana, LL 61 801

A new experimental method is presented for quan-g impact damage and esti- mating the remaining fatigue lifetime of impact damaged polymer matrix composite materials. The procedure is demonstrated using composites of glass fiber reinforced polyurethane produced by injection molding and structural reaction injection mold- ing. Thennoelastic stress analysis (TSA) was used to quant@ the stress concentra- tion associated with impact-damage in test samples of each composite. Following impact and TSA imaging, the samples were fatigued to failure over a range of stress amplitudes. The TSA-derived stress concentration factors were used to determine a modified stress amplitude that collapsed the impact-fatigue data onto a master stress-life curve. This approach provides a quantitative measure of impact damage and a practical methodology for estimating the residual fatigue lifetime of impact damaged composites.

I. INTRODUCTION

ong fiber, randomly reinforced polymer matrix L composites are being investigated heavily for use in the automotive, aerospace, and commercial prod- ucts industries. These composites are inexpensive, quick to mold, and possess relatively high strength to weight ratios. Regardless of the target application, vi- brations and cyclic stresses may lead to fatigue fail- ures. As such, the Society of Automotive Engineers, through the Fatigue Design and Evaluation (SAE-FD & E) Committee, has initiated a program to investigate the fatigue behavior of structural reaction injection molded (SRIM) composites (1, 2). Research has been undertaken to quantify the fatigue performance of these composite systems and to develop methods of predicting structural lifetimes. In addition to fatigue, many composite structures will also be subjected to impact events throughout their service lifetimes, lead- ing to a key design issue: what effect does impact damage have on the residual fatigue lifetimes of com- posite materials and is it possible to quantify the damage due to the impact loading?

PorLions of this paper have been presented at: 1999 SEM Spring Conference in Cindnnati. OH June 9. 1999 TMS Annual Conference in San Diego, CA h4arc.h 2.

*Corresponding author. Email to t-mackl@uiuc.edu, Fax (217) 333-1942.

Over the past 20 years an extensive knowledge base has been generated on the impact/fatigue properties of unidirectional and random, short fiber, polymer matrix composites (PMCs) (3-8). In general, the fa- tigue lifetimes of composites have been found to de- crease with increasing impact energy ( 1 , 9-13). Though this relationship is intuitive, it is not practical for engineering design. In general, the magnitude of the impact energy is not readily available and, conse- quently, the fatigue lifetimes following impact are dBi- cult to assess. Tiwari et al. began to address this problem by developing a real-time acousto-ultrasonic method to monitor fatigue damage. However, this method has not yet been converted into a viable pre- diction technique (10). El-Zein and Reifsnider used ultrasonic C-scans to predict the static strength of im- pact damaged composites by comparing impact-dam- aged to undamaged specimens, but did not extend the approach to fatigue loading (1 1). This method of static strength determination approximates the dimensions of the damaged area and the reduction in strength is related to the size and geometry of this region. An- other interesting nondestructive method for predicting post-impact fatigue lifetimes was presented by Stanley (1). Stanley modeled the impact area as a doubly sym- metric hole and computed an associated stress con- centration factor. The drawback to this approach is that it requires a translucent specimen for visual in- spection of the impact site.

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This study dispenses with qualitative measures of impact damage in favor of a non-destructive character- ization based on infrared imaging. In essence, the pro- posed method extends the basic approach of Stanley and El-Zein and Reifsnider, but utilizes a thermal, rather than visual or ultrasonic, method to determine the stress concentration factor associated with impact damage. The advantage of this method is that it allows the nuances of the impact damaged region to be as- certained without any geometric assumptions. An infrared imaging camera was used to measure the temperature distribution across the surface of each specimen in a non-contacting, nondestructive manner. Thermoelastic stress analysis m) was then employed to relate the measured temperatures to the full field hydrostatic stress state, providing a quantitative map of the surface stress distribution and the location and magnitude of any stress concentrators. A wide range of impact damage can be imaged, including damage that is hardly discernible to the naked eye. In addition, the methodology is amenable to in-situ inspection of struc- tural components and provides an objective, quantita- tive assessment of damage.

Thermoelastic Stress Analysis Thermoelastic stress analysis relates instantaneous

changes in a material's stress state to instantaneous changes in the material's temperature. The funda- mental thermoelastic relationship between tempera- ture and hydrostatic stress (14-19) is given by

where AT is the local change in specimen temperature, a is the coefficient of thermal expansion, p is the specimen density, Cp is the specific heat at constant pressure,

T is the specimen temperature, and Aukk is the change in the stress tensor invariant.

In order to obtain an experimental measure of these temperature changes, a low amplitude sinusoidal stress is applied to the specimen. The thermal re- sponse is then recorded in phase with the applied cyclic stress. The peak to peak temperature change (14-17) is given by

where o is the applied frequency and t is time. This method has been used previously to examine

stress distributions in polymer matrix composites (8, 20-26) as well as monolithic metals and ceramic matrix composites (27, 28). A DeltaTherm 1000' TSA system

'Saess Photonics, lnc. of Madison. WI.

POLYMER COMPOSITES, JUNE 2001, Vol. 22, No. 3

was used to capture full field surface temperature im- ages. This system has a minimum spatial resolution of 120 km and a temperature resolution of approximately 0.003"K.

It is important to emphasize that the TSA method requires application of an alternating stress to the damaged composite. In the present application the applied stress amplitude and frequency must be cho- sen to provide a measurable signal that does not gen- erate fatigue damage. In addition to the potential for accumulating fatigue damage during TSA imaging, it is also important to consider the possibility of hys- teretic heating. The polyurethane matrix in the injec- tion molded composite is a thermoplastic that could exhibit hysteretic heating during both TSA imaging and subsequent fatigue. The thermosetting SRIM ma- trix is less susceptible to this phenomenon. Through a series of experiments it was found that an applied stress amplitude of 2 MPa (0.5 - 2.5 MPa) at a cyclic frequency of 10 Hz provided good signal response with- out hysteretic heating. This stress level is an order of magnitude below the measured "endurance limit" of the undamaged composite samples, assuring that the impacted samples, even at locations of stress con- centration, were not damaged during the imaging proc- ess. Hysteretic heating was directly measured by cap- turing the thermal signal that is 90 degrees out of phase with the applied load (28). In practice, the out- of-phase signal is always measured before proceeding with measuring the thermoelastic signal, and the load amplitude is adjusted to eliminate the out-of-phase component. Details of the analysis employed to deter- mine the TSA loading level and frequency are avail- able in reference 29.

Materials

Two Merent material systems were used to estab- lish the utility of the proposed experimental method: a 9% by volume, long glass fiber reinforced injection molded @Zass/polyurethane) composite; and a 40?? by volume, glass fiber reinforced ( S m composite with Baydur SlR400 matrix. The injection molded compos- ite was reinforced with discontinuous fibers. The in- jection screw and barrel were designed to produce com- posites with fibers approximately 10 mm in length. In contrast, the SRIM composite was reinforced with three layers of continuous strand glass mat. It is im- portant to note that the latter material was reinforced with three layers of fiberglass mat, while the former is a single-layer, injection molded composite. Due to the multiple glass layers in the SFUM system, delamina- tion was observed as an impact damage mechanism for this composite but was not seen in the glass/ polyurethane system. These composites provide vastly different mechanical behavior and impact response: the SRIM composite is a relatively rigid thermoset with layered fiber architecture, while the glass/poly- urethane is a more compliant thermoplastic. Differ- ences cited are apparent in both the impact and the fatigue response of each composite.

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Table 1. Summary of Quasi-Static Tensile Properties.

Composite Elastic Tensile Type Modulus Strength

GlasslPolyurethane 6.65 GPa 113.9 MPa SRIM 11.45 GPa 171.4 MPa

The quasi-static tensile properties of both composite systems are summarized in Table 1. mure 1 gives the specimen dimensions for both the baseline tensile and fatigue tests. All test samples were fabricated from sheets 3.1 mm thick. Samples of the SRIM composites were cut at random orientations, all of which gave similar strength, stitkess, and fatigue properties. The glass/polyurethane tensile specimens were machined with orientations along, and transverse to, the direc- tion of injection. Again, there were no measurable ori- entation differences in the in-plane properties.

11. EXPERIMENTAL PROCEDURE

Specimens for impact testing were machined into plaques measuring 102 X 152 mm from sheets of each composite. These dimensions were chosen so the samples would fit into the pneumatic clamp of an in- strumented Dynatup/Instron Model 8250 falling weight impact machine, with an extra 50 mm of

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length for gripping during TSA and fatigue testing. The samples were loaded into the impact tower and struck using a 12.7 mm diameter hemispherical tip attached to a 13.35 kN load cell. The falling crosshead mass was fixed at 5.3 kg, while the drop heights var- ied over a range of 8, 16, 23, 33, 50, and 76 cm, cor- responding to crosshead kinetic energies of approxi- mately 4, 8, 12, 17, 26, and 39 Joules. For the partial penetration impact tests in which the tup did not pass through the specimen, data taken during impact re- veals that the samples absorbed at least 95Vo of the theoretical crosshead kinetic energy. After initial im- pact, pneumatic brakes restrained the crosshead to prevent repeated impact with the specimen.

The chosen range of impact energies created dam- age in the glass/polyurethane samples that appeared as cracks radiating outward from the locus of impact. Damage ranged from cracks hardly visible to the naked eye to cracks that propagated near to the speci- men boundaries. At the 76 cm drop height, cracks propagated to the boundaries of the 76 mm diameter clamp and were deflected. With these specimens, the absorbed energy determined by ASTM D-3029 was not valid, and the crack extent was so large that they were not used for TSA imaging or fatigue testing.

The SRIM composite samples were only tested at crosshead kinetic energies of 17 and 39 Joules to allow a direct comparison with the experiments previ- ously reported by Stanley (1). Damage in these com- posites appears as diffuse cracking accompanied by delamination between the reinforcing glass mat layers. At the 76 cm drop height, the impacting tup passed through the composite thickness. The material only absorbed approximately 30 J of energy as measured via the Dynatup software as defined in ASTM D-3029. Subsequent references to impact energy will be to ab- sorbed quantities.

Following impact, the specimens were spray-painted flat black to ensure d o r m emissivity for thermoelas- tic imaging. Samples were then transferred to a servo- hydraulic load frame where cyclic tension-tension stress was applied and full-field temperature images of the impact-damaged composites were captured. A modified stress concentration factor, mSCF, was then determined by taking a ratio of the highest infrared signal in the damaged region to the average IR signal measured in the far field as shown in Q. 2. In order to find a valid far field region in the TSA image, a line scan is drawn across the sample, perpendicular to the loading direction, to find a region of relatively con- stant TSA signal intensity. The area that is used to determine the far-field signal must be sufficiently far from the impact site and the sample grips to obtain a valid far-field signal. Line scans provide visual and quantitative indications of the signal variability, sim- phfymg the location of areas of constant signal. The far field signal is defined as the average measured thermal signal in this area. Line scanning and area averaging interrogation functions are built into the DeltaTherm 1000 imaging software. The mSCF that is

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(a) (b) Flg. 2. Representative impact-damaged glass/polyurethane sample: [a) Optical image, the ratio of local maKimurn to the average far-Jield stress.

lSA scan showing definition of mSCF as

being determined is not based on a single stress com- ponent as traditionally defined, rather it is a ratio of a stress tensor invariant, ukk,

(3)

This ratio eliminates any influences of specimen-to- specimen variations in ambient temperature and the thermoelastic constant.

Following impact and TSA imaging, the glass/poly- urethane samples were fatigued to failure, while the mSCFs measured for the SRIM composites were related to Stanley’s impact/fatigue results through a statisti- cal analysis. A detailed explanation of the statistical approach is presented in the Resnlta and Dimcummion section. Fatigue tests on all un-notched and impact- damaged composites were conducted at a frequency of 2 Hz and a load ratio of R = 0.1 over a range of stress amplitudes. Lower frequencies were used for fatigue testing than during TSA image acquisition. The stress amplitudes employed during TSA imaging were cho- sen such that they not develop fatigue damage. How- ever, when running tests to q u a n w fatigue damage, higher stresses must be applied. As thermal failure was to be avoided, the loading frequency was set to 2 Hz to reduce the possibility of hysteresis. Fatigue fail- ure was defined as specimen separation.

A stress-life relation was plotted using a modified stress and compared with the fatigue tests on un- notched samples. The modified stress for the impact/ fatigued samples was defined as follows:

(4)

where mSCF is as defined by Eq 3 and uapp is the gross section applied stress. For the purpose of com- parison, baseline fatigue tests were conducted on smooth-sided samples of both composites. Test sam- ples of each composite were fatigued to failure at stress amplitudes of 27 through 54 MPa. Results of these experiments appear as the baseline data in the fatigue life plots presented in the following sections. The goal of this project is to quant@ the impact-in- duced damage by assigning each sample a mSCF. Employing Eq 4, the modified stress can be plotted on stress-life (S-N) axes and compared with the baseline fatigue data.

111. RESULTS AND DISCUSSION

GlaadPolyruathPne Composite Reaulta

Typical optical and TSA images of impact-damaged glass/polyurethane composite samples are shown in Q. 3. Impact damage in the glass/polyurethane com- posites most often appeared as three cracks radiating from the locus of impact. The results of impact and TSA testing are summarized in Table 2. The coefficient of variation (C,) of the measured stress concentration factors was approximately twenty times larger than that of the absorbed impact energies measured by the Dynatup software. This variability in stress concentra- tion is due to the random orientation of the cracks rel- ative to the applied loading axis. The absolute size of these cracks was proportional to the impact energy while the orientation was random. Clearly, the orienta- tion of these cracks with respect to the applied loading axis will affect both the stress concentration factor and the resulting fatigue life. That is to say that, for a

Table 2. mSCF Data for Impact-Damaged GlasslPolyurethane Composites.

Damage Level Just Visible Cracks on Back Side Crack Through ~~ ~~ ~

Impact Energy (J) mSCF Impact Energy (J) mSCF Impact Energy (J) mSCF Median 8.22 1 .a0 11.8 2.27 17.1 2.97 Std. Dev. 0.05 0.10 0.03 0.12 0.12 0.59 Yo c, 0.61% 5.5% 0.25% 5.2% 0.70% 19.9%

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(4 (b)

Flg. 3. Qpical optical (upper) and TSA images (lower) of glass/polyurethane composites following impact at: (a) 17 and (b) 26 J.

given impact level, a wide range of damage results. Hence, even if a value of impact energy were known, TSA offers a refinement in assessing the damage. Figures 4 a and b contrast the impact/fatigue ap-

that these plots include fatigue lives from samples tested at three impact energies. Each level of crosshead kinetic energy generated a distinct type of damage in these specimens:

plied stress-life data with that obtained using the modified stress amplitude presented in Eq 4. Though there is no significant statistical trend in the raw data

1) 8 J of kinetic energy produced dimpling damage just visible to the naked eye:

(Fig. 4a) use of the modified stress increases the cor- relation of the data (Fig. 4b). It is important to note

2) 12 J of kinetic energy caused cracks visible only on the back side of the plate:

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Flg. 4. Stress-life data for impact-damaged glass/polyurethane composite specimens. (a) N o correlation can be seen when the applied stress is plotted against cycles to failure, but (b) the impact/fatigue data collapse onto a single curve when plotted using the proposed rnodi@d stress.

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3) 17 J of kinetic energy generated cracks that propa- gated entirely through the thickness of the plate.

Some of the 17 J specimens and all of the 26 J sam- ples had cracks that propagated nearly to the speci- men boundaries, making it impossible to obtain a reli- able far field stress. Samples impacted with energies of 4 J did not display damage when inspected with TSA. These samples were not subjected to fatigue loading and are therefore not included in the data shown in Fig. 4. mure 5 compares the residual fatigue life of im-

pact-damaged specimens with baseline fatigue data for the glass/polyurethane composites. The impact/ fatigue data are nearly coincident with the baseline data and exhibit nearly the same scatter as indicated by the Pearson product moment correlation coefficient (r). Furthermore, both the impact-damaged and un- notched baseline data converge to a stress range of 27 MPa at lo6 cycles. These data are found to diverge in the high stress amplitude regime. Thus, at short life- times, or large stress amplitudes, the proposed TSA method over-predicts the stress concentration factor that is acting during cyclic fatigue in the glass/poly- urethane composites.

TWO reasons are postulated for the divergence be- tween baseline and impact/fatigue in the short life regime. First, great care was taken to avoid cyclic hys- teresis and to assure elastic response during TSA imaging. During fatigue testing in the short life regime, however, the stresses in the damaged region are large enough to promote hysteresis and matrix heating in the thermoplastic matrix (30). After impact, a smaller highly stressed volume will result fi-om the stress con- centration near the damaged region. A smaller region with high stress and temperature allows greater ability to dissipate the local heating, reducing the fatigue damage. This argument can be used to explain the impact-damaged specimen curve being above the

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baseline at shorter lives. Second, the high stress levels associated with the short life regime may exceed the proportional limit of the material, generating an effec- tive stress concentration that is less than that mea- sured using TSA. Fortunately, the error associated with the proposed elastic approach over-predicts the stress amplitude and provides a conservative, and therefore safe, estimate of residual life. This discrep- ancy in ‘effective’ stress concentration factors has also been found in the metals community, where the fa- tigue of notched samples is described using a fatigue stress concentration rather than an elastic stress con- centration factor (3 1). Again, this hypothesis supports the trends observed in Fig. 5.

SRIM Composite R e ~ ~ l t s

The proposed experimental method was applied to the SRIM impact-fatigue data gathered previously by Stanley (1). He reported that 20 to 30 samples were tested at crosshead kinetic energy levels of 17 and 39 Joules resulting in absorbed energies of 17 and 30 Joules. Stanley fatigued these specimens to failure at a load ratio of R = 0.1 and frequency of 2 Hz, using gross section stress ranges of 29, 34, and 42 MPa. As these tests were performed prior to the current pro- ject, it was not possible to determine mSCFs directly on Stanley’s samples. Instead, a statistical approach was employed to relate Stanley’s fatigue results to mSCFs measured using TSA in this investigation.

The SAE-FD & E committee provided SRIM samples for testing, which were produced by Miles Inc., and are identical to that which the committee provided Stanley. For both investigations, all samples were pro- duced using Baydur STR 400 Resin, Owens-Corning Fiberglas M-8610 mat, and using the same mold. In the present study specimens were impacted at both of the cross head kinetic energies reported by Stanley, resulting in damage that was similar to that described

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Table 3. Summary of Median Modified Stress Concentration Factor and Fatigue Lifetimes for the SRIM Composite.

lmact Energy Cycles to Failure mSCF

42 MPa 34 MPa 29 MPa

17J 48,257 697,620 - 2.59 30 J 6,323 44,447 152,560 3.58

by Stanley (in terms of visual appearance and dimen- sions of the damaged region). Stress concentration factors were determined using the TSA procedure described previously using from eight to ten samples impacted at each energy level.

The present mSCFs were related to Stanley’s fatigue tests as follows: First, fatigue data collected by Stanley was plotted on probability axes (Flg. 6). The median

probability of failure determined by the Gauss- ian distribution of each data set was used to charac- terize the residual life at that applied stress level. This value is found from the x-intercept of a linear fit to the data plotted on probability axes. Next, median mSCF values were established using a characteristic Gauss- ian distribution for each impact energy. Table 3 sum- marizes the results of both Stanley’s fatigue data and the mSCF results from TSA experiments. Finally, these data were plotted as a modified stress (the product of the stress applied by Stanley and the median mSCF determined using TSA imaging) versus the median residual life determined by Stanley.

W i c a l optical and TSA images of impact damage in the SRIM composites are shown in Flg. 7. At 17 Joules of impact energy the SRIM panels exhibited diffuse matrix damage throughout the specimen thickness. At 30 Joules, the striker punched through the panels. Close inspection of the back side of the full penetration panels showed a blossom of delaminated material

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extending well beyond the observable damage on the impact side of the panel, Fig. 8. Although the visual damage appeared more extensive on the backside, TSA measurements were made on the impact side, and revealed a higher mSCF for the impact side. In essence, the delaminated zone results in a net section loss near the impact site that is reflected by the higher TSA signal on the impact side. Better correla- tion was found between the baseline and the impact data using the backside TSA measurements. Unfortu- nately, this requires access to the backside of the panel, which is a serious constraint when extending the method to actual service conditions. The mSCF data reported here is that from the impact side of the samples.

Inspection of the failed baseline specimens revealed that many of these samples had failed in the shoulder region. In fact, nearly all of the SRIM baseline samples failed in the shoulder while only a small number of the glass/polyurethane composite baseline samples failed in this region. TSA imaging was used to measure the stress concentration in the shoulder to account for the stresses in the shoulder region. TSA images were collected on ten dog-bone specimens of each compos- ite. Typical sample images are shown in Fig. 9. The average mSCF in the shoulder region of the SRIM samples was approximately 1.45, while the average mSCF found in the glass/polyurethane composite

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(b) Flg. 6. Ga~~sian distribution off- liyetimes for impact-damaged SRlM composites loaded at an amplitude of 33.5 MPa, R=0.1 after absorbed impact energies of (4) 17 and (b) 30 J. ( R w data is from Stanley.)

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(a) (b) Flg. 8. ll~pical optical and ?sA images oJ [J the impact side, and b) the back side of an SRlM sample which absorbed 30 J of impactenergy.

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- 2 180

Fig. 9. reduced section

m e s of SRIM dogbone specimens: (4 sample with a stress concentraiion in the shoulder; and fb j unvom stress in the

A 17 J IWaCt a 30 J Impact

samples was negligible. To account for the stress con- centration in the baseline SRIM specimens, a modified stress, where mSCF = 1.45, was used to plot the base- line data. As this effect was not observed in the glass/ polyurethane composite, the baseline curve was not modified.

Again, for the SRIM material system, there was no correlation between applied stress and residual fatigue life when the applied stress was based on gross section nominal stress (Rg. 1w. However, using the modified stress amplitude presented in Eq 4, the impact-dam- aged data collapses onto a s q l e master curve in the stress-life plane (Rg. lob). It is important to note that each point in the baseline and impact damaged sets now represents the mean value of approximately ten tests and that the impact/fatigue data takes the same shape as the baseline fatigue data. The baseline and impact-damaged stress-life curves in the SRIM system appear parallel throughout the applied stress range.

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Using the proposed modified stress now consistently over-predicts the stress acting in the impact-damaged SRIM composites regardless of impact energy or ap- plied nominal stress. This result is in contrast to that in the glass/polyurethane composite where the over- prediction occurred only at higher stresses.

Several explanations for these observations have been postulated. First, nonlinear effects noted in the glass/polyurethane system were not expected to be present in the SRIM due to its thermoset matrix and higher glass content. As such, divergence solely at high stresses did not occur. Second, delamination damage leads to a high measured stress near the im- pact site that may not be representative of the full section. Flaws or cracks evident in the surface lami- nae are isolated from the other layers and do not propagate through the panel thickness as they would in a continuous material. Finally, delamination is a damage state that is generally not characterized by

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Fig. 10. Stress-life data for impact-dmnaged SRIM composite specimens. (4 No correlation can be seen when the applied stress is plotted crgainst cycles to f&e, but (b) the impmt/'-ue data collapse onto a single m e when plotted using the proposed modijkd stress.

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the baseline fatigue testing. As noted earlier, the mSCF values determined for impact-damaged SFUM speci- mens over-predicts the stress in the damaged region, resulting in a conservative estimate of residual fatigue life.

On the Application of S-N Fatigue to Composite Materiala

The fatigue process in composites is a complicated micromechanistic phenomenon that, nonetheless, in- volves nucleation of a self-similar crack and sub- sequent fatigue crack growth. Nucleation dominated phenomena are well described using an S-N approach, while large crack growth is often described using a Paris-type description. The present study applied an S-N method to impact damaged composites, begging the question: does impact circumvent the nucleation process and disqualifv the S-N approach?

This question was addressed in two separate inves- tigations:

1) By measuring the change in stiffness in the impact damaged samples during fatigue loading,

2) By capturing thermal images during fatigue test- ing to monitor damage accumulation and possible crack growth.

Figure 1 1 shows a typical plot of the normalized stiffness against normalized cycles to failure for three sample types: SRIM panels that absorbed 17 and 30 J of impact energy, and a glass/polyurethane composite impacted at 8 J. As impact damage is rather diffuse, it was not reasonable to use an extensometer to meas- ure strain. Instead, the crosshead displacement was used to determine the stiffness of these samples. All stiffness values normalized by that measured during the first loading cycle, while the cycles to failure were normalized by the fatigue life at specimen separation.

These data show that the stiffness does not change by more than 10% until the final 10Yo to 20% of life. This relatively steady stiffness value is an indication that at least 80% of the lifetime is spent nucleating a self- similar fatigue crack, while less than 20% of the life involves large crack growth.

Figure 12 shows a progression of thermal images from an impact-damaged glass/polyurethane sample during a fatigue test. The initial position of the crack is located 22.5 mm from the right edge (Q. 32a). Im- ages from the first half of the test appear nearly iden- tical, and by the time 70% of life has expired, the crack front has moved only 4 mm (Q. 124. As visible through thickness cracking from impact alone was more prevalent in the glass/polyuethane system, it is fair to assume that the SRIM composite, with smaller initial cracks, will show similar trends.

These two tests indicate that even after severe im- pact damage, the measured fatigue lifetimes are domi- nated by crack nucleation, which is reasonably evalu- ated using an S-N approach. This phenomenon is attributed to the complex micromechanics associated with forming a self-similar crack in a composite mate- rial. The mechanisms will involve combinations of ma- trix craclang, interface debonding and sliding, and the formation of fiber bridging zones.

Proposed Method for Lifetime Prediction of Components

A new method is presented to q u a n ~ impact dam- age by determining a modified stress concentration factor (mSCF) with TSA. The mSCF is then used to de- termine a modified stress amplitude during subse- quent fatigue testing. To a reasonable approximation, the fatigue lifetimes determined using the modified stress amplitude were found to collapse onto the baseline fatigue data. As a result, an estimate of the residual fatigue lifetime can be determined as follows:

POLYMER COMPOSITES, JUNE 2001, Vol. 22, No. 3 429

G a v i n P. Horn, Thornas J. Mackin, and Peter Kurath

Fig. 12. Progression of thermal images that track crack growth in an impact-damaged glass/polyurethane sample during fa@=.

1) Use TSA to scan the impact damaged component

2) Multiply the operative fatigue stress by the mea- sured mSCF to determine a modified fatigue stress amplitude.

3) Estimate the fatigue lifetime by locating the modi- fied stress amplitude on a baseline S-N curve for the material.

The proposed thermoelastic method provides an ef- fective means for quantifjmg the effect of impact dam- age on the fatigue lifetimes of composite materials. Experiments on both the SRWI and glass/polyurethane composites revealed that this procedure provides con- servative estimates of the residual lifetimes following impact. The method is non-contacting and simple to use, but does require application of a low amplitude oscillating stress. However, the oscillating stress need not be sinusoidal, nor does it need to be of constant frequency or amplitude. Work is currently under way to show that TSA scans can be made while the com- ponent is in service by using the in-service vibrations to provide the stress input.

and determine an mSCF.

Iv. SUMMARY

factor associated with impact damage. A modified fa- tigue stress amplitude is calculated by multiplying the applied gross section stress amplitude by the mea- sured stress concentration factor. This modified stress amplitude is then used to estimate the residual fa- tigue lifetime of the impact-damaged composite utiliz- ing an undamaged specimen stress-life curve. Compa- rable results for two vastly different composites (from the perspective of both chemistry and resulting im- pact damage) were achieved.

The thermoplastic glass/polyurethane composite showed impact damage that was dominated by through- thickness bulk matrix cracking at high impact ener- gies. At lower impact energies, minimal backside cracking was accompanied by dimpling on the impact side. Damage in the thermoset SRIM composite was more localized than that seen in the glass/polyure- thane system and consisted of a diffuse damage zone around the impact site for low impact energies. Higher impact energies punched completely through the com- posite, generating a diffise damage zone around the impact site accompanied by ply delamination that was only visible on the back side of the sample. For both material systems, these vast ranges of impact damage were quantified with a single stress life relation when plotted using the modified stress.

A new experimental non-destructive method has been presented that quantifies the effect of impact damage on the residual fatigue lifetimes in polymer matrix composites. The method involves using thermo- elastic stress analysis to assign a stress concentration

In order to predict residual life of each composite and to locate the impact-damaged samples in the stress- life plane, the impact-damaged stress-life relation was compared to that of smooth baseline specimens. The baseline and fatigue after impact data were observed

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Estimating the Residual Fatigue Lifetimes

to converge at long lifetimes in the glass/polyurethane system, while at short lifetimes, the impact/fatigue data were found to lie above the baseline data. The di- vergence at short lifetimes is attributed to hysteretic heating and a relatively small proportional limit in the glass/polyurethane system. For the SFUM system, the two life curves are parallel over the entire range of lifetimes. Here, the nonlinear effects noted in the glass/ polyurethane system are not expected to play a role. Instead, delamination introduces a damage mecha- nism that is not present in the baseline fatigue data. However, for both material systems, design estimates utilizing the baseline curve would be, at worst, con- servative and safe. This result suggests that one can use the proposed modified stress to determine a resid- ual lifetime from a baseline stress-life curve in the event that impact-fatigue curves are not available.

REFERENCES 1. E. Stanley, Effect of Prior Impact Damage On Subsequent Fatigue Behavior of an SRIM Polymer Matriw Composite, MSME Thesis, University of Toledo (1995).

2. A. R. Kallmeyer and R. I. Stephens, SAE Tech. Pap., No. 990408, SAE International Congress and Exposition, Detroit, MI (1993).

3. J. E. Masters and K. L. Reifsnider, AS?M STP 775. K L. Reifsnider, Ed., ASTM (1982). pp. 40-62.

4. K. L. Reifsnider and Z . Gao. lnt. J . Fat . 13, 2, (1991), pp. 149-156.

5. A. Razvan, R. A. Simonds, K. L. Reifsnider, and W. W. Stinchcomb, J. Rein$ Plast. Compos., 11, March (1992), pp. 310-323.

2, (1983) pp. 114-134.

pos. Muter., 21. December (1987). pp. 1084-1105.

Stinchcomb, ASTM STP 1059, (1990), pp. 349-370.

6. S. S. W a g and E. S.-M. Chim, J. Cornpas. Mater.. 17,

7. S. S. Wang, H. Suemasu, and E. S.-M. Chim, J. Com-

8. C. E. Bakis, R. A. Simonds, L. W. Wick, and W. W.

9. G. E. Husman, J. M. Whitney, and J. C. Haplin. ASTM

10. A. Tiwari, E. G. Henneke 11, and K. L. Reifsnider, J.

11. M. S. El-Zein and K. L. Reifsnider, J. Compos. TechnoL

S7P 568, (1975). pp. 92-1 13.

Compos. TechnoL Res., 17, 3 (1995). pp. 221-227.

Res., 12, 3 (1990). pp. 147-154.

12. W. J. Cantwell, P. T. Curtis, and J. Morton, lnt J . Fat.,

13. R L. Ramkumar, ASTMSTP813, (1983). pp. 116-135. 14. N. F. Enke. Thennographic Stress Analysis of Isotropic

Materials”, Ph.D. Thesis, Department of Engineering Mechanics, University of Wisconsin-Madison, (1989).

15. N. Harwood and W. M. Cummings, ZRermoetastic Stress Analysis, Adam Hilger, IOP publishing (1991).

16. A. K. Wong, J. G. Sparrow, and S. A. Dunn, J . Phys . Chem Solid, 4 9 . 4 (1988). pp. 395-400.

17. A. K. Wong, R. Jones, and J. G. Sparrow, J . Phys. Chem Solid, 48,8 (1987). pp. 749-753.

18. B. Budiansky and R. J. OConnell. J . Geophys. Res., 88, B12 (1983). pp 10, 343-348.

19. B. Budiansky, J. Compos. Mater., 4 (1970). pp. 286- 295.

20. C. E. Bakis, H. R. Yih, W. W. Stinchcomb, and K. L. Reifsnider, ASTMSTP 1012, (1989). pp. 68-63.

21. R. A. Simonds, C. E. Bakis, and W. W. Stinchcomb, ASlMSTP 1012, (1989), pp. 5-18.

22. W. W. Stinchcomb and C. E. Bakis, Fat Compos. Muter., Edited by K. L. Reifsnider, Elsevier Science Publishers B. V., (1990) pp. 105-180.

23. K. L. Reifsnider and C. E. Bakis, Char. Adu. Mater., Edited by W. Altergott and E. Henneke, Plenum Press, New York, (1991) pp. 65-76.

24. K. L. Reifsnider. W. W. Sljnchcomb. C. E. Bakis. and H. R. Yih, Damage Mechanisms in Composites-AD, 12. Edited by A. S. D. Wang and G. K. Haritos, ASM, (1987), pp. 65-72.

25. C. E. Bakis and K. L. Reifsnder, Re- of Progress in gwntitatiue Nondestructive Evaluation, 7B. Edited by D. 0. Thompson and D. E. Chimend, Plenum Publish- ing Corp., (1988), pp. 1109-1 116.

26. K. Liao, L. H. Tenek, and K. L. Reifsnider, J. Compos. TechnoL Res., 14, 3 (1992). pp. 176-181.

27. T. J. Mackin, T. E. Purcell, Y. H. Ming, and A. G. Evans, J . A m Ceram. Soc.. 78, 7 (1995). pp. 1719-1728.

28. T. J. Mackin and M. C. Roberts, J . Am Ceram. Soc., 88.

29. G. Horn, Quanii&ing Damage in Polymer MatriW Compos- ites Using Thermoelastic Stress Analysis, MSME Thesis, University of Illinois (2000).

30. A. R. Kallmeyer, Personal Communication, SAEFD & E committee.

31. N. E. Dowling. Mechanical Behavior of Materials. Pren- tice-Hall, Inc. (1993).

8, 2 (1984), pp. 113-1 18.

2 (ZOOO), pp. 337-343.

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