Kounadis A.N., Gdoutos E.E. (Eds.) Recent Advances in Mechanics

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Structural Integrity and Residual Strength of Composites Exposed to Fire 219

that the ends are restrained; therefore, beyond a certain level of deformation, the

structure starts to “pull” from the ends rather than “push” against the ends.

Based on the axial support force obtained, the deformation of the column can

be determined from Equation (28). It is found that the deformation increases with

the exposure time from t = 60 s until t = 300 s. Actually, the increasing of the de-

formation before t = 120 s is smaller than that of the deformation after t = 120 s.

The reason for that is coming from the decreasing of the bending rigidity EI

which is strongly associated with the thickness of the column.

Fig. 6. The axial constraint stress

vs. exposure time t. A 2

order polynomial curve

was obtained to fit the variation trend.

With increasing the heat exposure time, the thickness of the column decreases

due to the resin material decomposition, which results in the decreasing of the

bending rigidity EI

, therefore the column bends more with even lower thermal

bending moment. The mid-point deflection w

normalized by the original thick-

ness of the column is shown in Figure 7. The variation of the mid-point deflection

is not smooth, however the linear curve can be obtained to fit it approximately. It

can be seen that the mid-point deflection of the column increases in general

with the exposure time. Since the direction of the mid-point deflection is always

positive, this means that the column bends toward the heat source under the

220 G.A. Kardomateas

constrained boundary conditions. In the experimental study reported in the subse-

quent section, a positive deflection can be observed in the tests for the column ex-

posed to the heat flux Q = 25 kW/m

under the constant compressive axial load P,

corresponding to a stress of 10.5 MPa (based on the original section).

Fig. 7. The normalized mid-point transverse deflection vs. exposure time for the con-

strained column under the heat flux due to fire, Q = 25 kW/m

Figure 8 presents a plot of the axial support force P vs the mid-point deflection

for different exposure times. In each case, the mid-point deflection w

was cal-

culated from the linear analysis for the pinned column under the external heat flux

and the end of the column is free to move, so the constraint condition shown in

Equation (26) is not applicable. The solution of the problem is in Equation (28)

and the variation between the axial force P and the mid-point deflection w

can be

obtained from Equation (29). The Figure shows that, at the beginning of the heat

exposure, the axial force P increases initially with only a small bending deflection;

But as P approaches the classical buckling load, P

Euler

, the transverse deflection

then increases rapidly. The column behaves much like an “imperfect” column.

Eventually, in all cases, the axial support force approaches P

Euler

as the mid-span

deflection becomes large. The temperature change through the thickness has effec-

tively an analogous role for an axially restrained column, as that of an imperfec-

tion on a mechanically loaded column.

Structural Integrity and Residual Strength of Composites Exposed to Fire 221

Fig. 8. Axial force vs mid-point deflection for a pinned beam with external fire heat flux Q

= 25 kW/m

at different exposure times; the axial force and the mid-point deflection are

normalized by the Euler buckling load, P

euler

, and the length of the column L, repetitively.

The ends of the columns are free to move axially (unconstrained case).

4 Experiments

The goal of the present experimental investigation was to characterize the com-

pressive mechanical response, failure mode and time-to-failure for a fiberglass-

reinforced polymeric composite simultaneously exposed to high heat flux and

compressive axial loading. The experiments utilized a specially modified cone

calorimeter that permitted direct mechanical loading of samples during simultane-

ous exposure to heat fluxes of 25 kW/m

, 25 kW/m

and 75 kW/m

. In order to

analyze the response of the test samples and compare the experimental data with

theoretical results, the axial displacement and mid-point transverse deflection were

measured. Many of the test data presented herein are from Liu et al [14].

A fiberglass-reinforced vinyl-ester (Derakane 510A) composite laminate was

used in the experiments. The laminate panels were manufactured with twenty plies

(Seemann Composites Inc., Gulfport, MS) in the form of flat 24-inch × 24-inch

panels. The 12.5 mm thick panels had a [(0/90/45/-45/)

] ply lay-up. Test coupons

were machined dry from the panels using carbide tooling. Two different specimen

222 G.A. Kardomateas

lengths, 150 mm and 100 mm, were utilized in the experiments. In both cases, the

nominal thickness was 12.5 mm and the width was 25.4 mm. The broad (25.4 mm

wide) faces of the specimens, one of which was exposed to the heat source, were

left in the as processed condition.

The ends of the composite specimens fit into flat-bottom cavities that were ma-

chined by EDM into Inconel 718 alloy grips. Each grip had a fixed cavity depth of

25 mm. For the shorter 100 mm long specimens, inserts were placed in the grip cavi-

ties to fix the heated length of the specimens to 74 mm. For the 150 mm long speci-

mens, the distance between grip faces was 100 mm (this corresponds to the heated

length of the specimen); for the 100 mm long specimens the distance between grip

faces was 74 mm.

In order to minimize heat loss from the specimen to the grips, the

surfaces of the specimens located within the grips were insulated with a thin ceramic

layer (Zircar Inc., Alumina Cement) approximately 0.4 mm thick. IN-718 shims be-

tween the sides of the specimen and grip cavity were used to firmly fix specimen

within the grips and minimize any transverse specimen movement in the grips. The

grips approximated clamped end-conditions for axial loading.

A cone-calorimeter equipped with a 5000 W electric cone-heater was used as

the heat source for the simulated fire tests (Fire Testing Technology Limited, West

Sussex, U.K.). In a cone-calorimeter, the heat flux is applied to only one surface

of a test specimen. The exit diameter of the cone heater was 158 mm. For this exit

diameter and cone design, uniform heat fluxes as high as 100 kW/m

were possi-

ble over a 100 mm x 100 mm surface area. In the present investigation, the region

of uniform heating limited the maximum length of test specimens to 100 mm. Al-

though larger specimen widths were possible, a 25.4 mm specimen width was

chosen to reduce the size of the test fixtures and actuator used to apply axial com-

pressive loads. To minimize heating of the specimen sides, a thin (0.3 – 0.4 mm

thick) alumina ceramic layer was applied to both sides of the specimens (along the

12.5 mm faces). In an initial study, performed to determine the effect of surface

insulation on failure time, several experiments were conducted with 150 mm long

specimens with and without surface coatings on the unheated specimen face.

These trial experiments showed that coating the backside of the specimens did not

significantly affect failure time or failure mode. Therefore, all remaining experi-

ments discussed in this paper were performed with the specimens coated only on

their sides and along the surfaces located within the loading grips.

For all tests, the distance between the exit of the cone heater and the specimen

surface was maintained at 25 mm. The applied heat flux was varied from 25

kW/m

to 75 kW/m

to simulate the surface heating expected for fires ranging

from small to large intensity. Prior to testing, a heat flux meter was used to meas-

ure the heat flux at the surface of the specimens.

To investigate the effect of simultaneous mechanical loading on the compres-

sive behavior of the composite laminate, a load frame with pneumatic actuator

was designed to fit directly beneath the cone heater . A load cell mounted at one

end of the load frame was used to monitor specimen load level. To minimize

transverse and axial deflections that can occur with low stiffness load cells, a load

100 mm was the maximum length over which uniform heating could be obtained in the

cone-calorimeter.

Structural Integrity and Residual Strength of Composites Exposed to Fire 223

cell with very high axial and lateral stiffness was utilized (110 kN capacity, Inter-

face Inc., Model # 120AF-25K). The grip at one end of the specimen was rigidly

attached to a load cell. The grip at the opposite end of the specimen was attached

to an aluminum H-block that was mounted to a linear bearing system; this ar-

rangement permits axial motion only. An LVDT was used to measure the axial

displacement of the specimen.

The time-to failure data for all specimens are summarized in Table 2. Failure

times were readily determined since all specimens exhibited catastrophic collapse.

Analysis of the video recordings from the experiments showed that, for all speci-

mens, the final failure event was exceedingly rapid (the transition from an intact,

load bearing specimen, to catastrophic collapse was less than 50 ms). For a heat

flux of 25 kW/m

, failure times ranged from approximately 2549 s at 3.5 MPa to

251 s at 10.5 MPa. At 50 kW/m

, failure times were considerably shorter, 404 s

at 3.5 MPa and 131 s at 10.5 MPa. For the highest heat flux used, 75 kW/m

, fail-

ure times were much shorter, 191 s at 3.5 MPa and 123 s at 7.0 MPa.

As shown in Figure 9, the relationship between time-to-failure and axial applied

load is nonlinear, and the slope of the curve decreases with increasing compressive

load. The non-linear variation is most likely caused by char formation and degrada-

tion of the material properties. The rate of char formation decreases with increasing

exposure time since the char layer influences the transport rate of oxygen to the

combustion front and, because of its lower thermal conductivity, reduces heat con-

duction to the un-charred material. Notice that two specimen lengths were used:

150 mm (100 mm heated length) and 125 mm (74 mm heated length).

Table 2. Time-to-failure (t

) of fiberglass-reinforced vinyl-ester composites under simulta-

neous surface heating and axial compressive loading. At 50 kW/m

, heated specimen

lengths of 100 mm and 74 mm were studied.

Heat flux

(kW/m

Axial Compressive Stress, MPa

)

3.5 5.25

7.0

10.5

25 t

= 2549 s t

= 660 s t

= 366 s t

= 251 s

50 100

404 242 178 131

50 385 207 133 117

75 191 171 123

---

224 G.A. Kardomateas

Fig. 9. Relationship between the time-to-failure and compressive axial force for specimens

subjected to single-sided heat flux levels of 25 kW/m

, 50 kW/m

and 75 kW/m

Fig. 10. Effect of heat flux on the post-fire compressive response (experiments).

Structural Integrity and Residual Strength of Composites Exposed to Fire 225

Post Fire Compression Tests

Compressive tests were conducted following exposure to fire of specific intensity

and for a specific exposure time.

Figure 10 shows the effect of heat flux on the compressive response for an ex-

posure time of 325 s. The peak load is reduced as the heat flux increases.

Figure 11 shows the effect of exposure time for a heat flux of 50 kW/m

. We

can see how the peak load is decreased with an increase in exposure time.

Fig. 11. Effect of exposure time on the post-fire compressive response (experiments).

Acknowledgments

The financial support of the Office of Naval Research, Grant N00014-03-1-0189,

and the interest and encouragement of the Grant Monitor, Dr. Luise Couchman, is

gratefully acknowledged.

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Melbourne, Victoria, Australia (2006)

Theory and Application of Sampling Moiré

Method

Yoshiharu Morimoto

and Motoharu Fujigaki

Moire Institute Inc.,

2-1-4-804, Hagurazaki, Izumisano, Osaka 598-0046, Japan

morimoto@moire.or.jp

Departement of Opto-Mechatronics, Faculty of Systems Engineering,

Wakayama University,

930 Sakaedani, Wakayama 640-8510, Japan

fujigaki@sys.wakayama-u.ac.jp

Abstract. Sampling moiré method is a newly developed moiré method using an

image processor for a grating pattern to measure shape or displacement or strain

distributions. A grating pattern on an object is recorded by a digital camera.

Though the digitized image shows the grating, a moiré fringe pattern appears by

thinning-out the pixels, i.e., sampling the image with a larger pitch than the pixel

pitch. If the sampling pitch is changed, the moiré pattern is changed very much.

If the phase of the sampling is changed, the phase of the moiré pattern is

changed. The phase analysis of moiré pattern provides accurate result of dis-

placement of the grating. If the number of the phase-shifted moiré patterns i.e.

the number of pixels for a pitch of grating is larger, the resolution of phase analy-

sis becomes more accurate but the spatial resolution becomes worse. Since the

sampling moiré method is useful to analyze the phases of a moiré fringe and a

grating from one image of a grating pattern, it is possible to analyze dynamic de-

formation accurately.

In this paper, the theory of the sampling moiré method is introduced and some

applications of the sampling moiré method to displacement measurement of a

beam, and shape and strain measurement of a rubber structure are shown.

1 Introduction

It is important for integrity and safety of structures to measure shape, deformation

and strain distributions of the structures. Optical methods such as grating projec-

tion method, moire method, moire interferometry, speckle interferomrty digital

image correlation method are used for the measurement [1-4].

Since these optical

methods use the characterictics of light, it is basically possible to measure them

228 Y. Morimoto and M. Fujigaki

accurately with non-contact and high resolution using phase analysis. Especially

moire method has long history as visualized measurement method to obtain the

distributions of height, displacement and strain [5-38].

In order to analyze fringe patterns, it is possible to perform quantitative analysis

using image processing with a computer. Furthermore, by the phase analysis of

grating or fringe patterns, the analysis becomes accurate and high speed[12-21].

Moiré method has been investigated by many researchers such as Theocaris [5],

Durelli [6], Suzuki [7], and Post [8]. A moiré fringe pattern appears as the inter-

ference between a specimen grating and a reference grating. However, a moiré

fringe pattern also appears when the specimen grating lines are sampled by the

scanning lines of a TV camera or by the pixels of an image processor [22-33].

This method is called ‘scanning moiré method’.

The authors also developed scanning moiré method which does not use a refer-

ence grating on the specimen [23,24,28,31-33]. A specimen grating pattern on an

object was recorded by a TV camera or a digital camera. Though the digitized

image shows only the grating, a moiré fringe pattern appears by thinning-out the

pixels, i.e., sampling the image with a larger pitch than the pixel pitch. If the sam-

pling pitch is changed, the moiré pattern is changed very much. If the phase of the

sampling is changed, the phase of the moiré pattern is changed. The phase analysis

of a moiré pattern provides accurate result of displacement of the grating. The

phase analysis of the sampling moiré method using interpolation is proposed by

Arai et. al. [25,27,29] If the number of the phase-shifted moiré patterns is larger,

the resolution of phase analysis becomes more accurate, but the spatial resolution

becomes worse. This method can analyze phase values from one image of a grat-

ing pattern. The analyzed phase is very accurate because several phase-shifted

moiré fringe patterns are obtained by changing the sampling phase. This method is

called ‘sampling moiré method’.

Phase-shifting method is the most popular method in the phase analysis meth-

ods. However, this method cannot be usually applied to dynamic phenomenon

measurement because it requires movement of the master grating for phase-

shifting and capturing the specimen grating more than three or four images. Fur-

thermore, if the grating is drawn on the specimen surface, the phase shifting of the

grating cannot be performed. However, the sampling moiré method uses only one

image and then it can be applied to dynamic phenomena.

In this paper, the theory of sampling moire method and the applications for de-

flection distribution measurement of a beam and shape and strain distribution

measurement of a rotating object at high speed are introduced[32-38].

2 Theory of Moiré Method

The relationship between the moiré fringe pattern and the deformation of a grating

has been described by many researchers already [5-11]. Here, the basic essence is

introduced in order to explain sampling moiré method.