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An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity
Lbmn/mire sfrucrurl~s35 (1996) 375-3X6 Putdished hy Elsevier Science Ltd Printed in Great Britain 0263~8223/%/%15.ot~ Pll:SO263-8223(96)00046-3
ELSEVIER
An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity Department
ofAeronautics
and
B. Wham II* & A. N. Palazotto Astronautics, Air Force Institute qf Technology OH 45433- 7765, USA
Wtight-Patterson Air Force Base,
The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [O”,,], [90°Lb], [ f45°]4,, [0’/90’],,,, and [O”/f45°/90”],,V. In the experimentation, [90”] ,br [O”/900]4s, and [O’/ f 45”/90“],,, laminates, as well as three of the [O”],,, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [ *45”],, specimens failed to support the load due to an internal crack that originated from the hole’s edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally. Published by Elsevier Science Ltd.
with a centrally located cutout. This research was conducted to include the nonlinear stressstrain behavior of the matrix material in the evaluation of Gr/PEEK. The purpose of this research was to determine (using both experimental and analytical methods) the basic material properties of Gr/PEEK, the initiation and progression of compressive failure, the stress-strain response of the material, and the ultimate failure load of Gr/PEEK with a centrally located 1.27 cm (05”) circular cutout. The Gr/PEEK specimens were end loaded experimentally using a Boeing Open Hole Compression apparatus, BSS-7260.* The composite was loaded at room temperature. The ply layups used for the investigation were [O”],,, [90”] 16, [ f 45°]4S, [0”/90”],,, and [O”/+ 45”/90”],,. Once the experimental portion of the research was completed, the results were compared to a nonlinear ply-by-ply finite element technique developed by Dr R. S. Sandhu of Wright Laboratories, Wright-Patterson Air Force Base, Ohio.?
INTRODUCTION Composite materials are finding an increasing number of applications. Not only have composites found extensive use in the aerospace industry due to their excellent fracture toughness and high strength-to-weight ratios, but they are also finding an increasing usage in the construction industry. Graphite polyetheretherketone (Gr/PEEK), a thermoplastic composite material, has an advantage over traditional thermoset composite materials because of its high impact toughness and damage tolerance; rapid, automated, economical fabrication processes; environmental resistance; and ease of repair. ’ A large body of research conducted on Gr/ PEEK exists and includes the investigation of Gr/PEEK under both tension and compression
*Present address: System Facilities; F-22, 2130 5th Street, Wright-Patterson, Air Force Base, OH 45433-7003, USA. 375
376
B. Wham II, A. N. Palazotto
EXPERIMENTAL STUDIES
Once the fabrication procedure was complete, all the panels were subjected to a C-Scan evaluation to ensure that there were no major defects such as entrained air, resin starved areas, and fiber bunching. The C-scan was conducted by the Non-Destructive Branch of the Materials Laboratory (WL, WPAFB). A total of seven panels were manufactured. The first two were used in determining the material properties of this batch of Gr/PEEK. The specimens were cut into two sets. The first set consisted of three layups (O’, 90”, 44.5”) of
Material system The material system, Gr/PEEK, used in this study consisted of Hercules AS4 graphite fibers in a polyaromatic resin. The specimens were constructed by Beta Industries of Dayton, OH using continuous pre-preg tape, 30.5 cm (12”) width. All the panels were laid up by hand and fabricated according to the tape manufacturer’s, ICI Fibrite Ltd, specifications.
20” TAB TAPER
!!
[
!I
IL-
a. SpecimenOT
-
50.8mm -
I
127mm
-
50.8 mm
-
I
I
20” TAB TAPER
I 2‘i.4mm b. Specimen 9OT,& (i45)T TB R
I
6.4 mm 57.2 mm Sqaure End Tabs
Teflon Insects
6.4 mm
,
127mm
<
I
6.4 mm 57.2 mm 6.4 mm
I
’
-l19mmI-
c. Compression Specimens
Fig. 1.
Geometry
of materials
property
specimens.
377
An investigationof graphite PEEK composite
the loading edge of the specimen so that a gross stress state of the specimen could be calculated given a load using the formula
tensile specimens and two layups (O“, 90”) of compression specimens. The dimensions of these specimens are shown in Fig. 1. The specimens were fitted with tabs constructed of G-10 glass epoxy. These tabs provided for a uniform transfer of load from the testing machine to the specimens as well as a contact area for the hydraulic mounting grips of the Instron machine. The tabs also prevented damage inflicted on the specimen by the grips. The other five panels were used for compressive testing within the Boeing Open Hole Compression apparatus. The specimens were constructed to specifications written by the Boeing Corporation in BSS-7260* and shown in Fig. 2. The holes in the Boeing specimens were produced by drilling a small initial hole in the center of the specimen, then expanding the hole by gradually increasing the bit size until the desired diameter was obtained. The incremental increase of the bit size had to be very slight so that the drilling process did not introduce any failures or delamination around the hole. The dimensions of the specimens were verified using mechanical measuring devices to check parallelism and to ensure that no eccentric loading conditions were introduced. The measurements of each specimen’s width and thickness were taken to ensure that any specimen with a highly variable width or thickness was eliminated. The thicknesses and widths were then averaged to obtain an average area of
I
load G=
(1)
width x thickness
Basic material property data Back-to-back strain gage rosettes were affixed to the center of all material property specimens and the specimens were tested to yield the basic property data. Table 1 shows a comparison of the materials property data obtained with the averages determined by the ICI Fibrite Corporation in their published data sheets on Gr/PEEK.4 The five data sets obtained from each of the ply layups tested were averaged to produce the basic properties required for the nonlinear finite element (NFE) program used in this study. The properties were determined from the experimental stress-strain data presented in Table 1. The NFE program will be discussed later in the paper. The Rolfes-Sendeckyj device, used for testing of the material property specimens, was recommended for compression materials property testing in an investigation by Daniels and Sandhu” of compression fixtures. Their findings demonstrated that the device produced the most uniform state of stress of all of the
304.8 mm
0 t-
I
12.7mm 12.7 mm.08
mm Diameter Hole
c 12.7 mm Fig. 2.
Geometry
of Boeing specimens.
38mmd.13mm I
378
B. Wham II, A. N. Palazotto Table 1. Comparison of material properties
Property
ICI Fibrite Ltd values
Experimental values
G‘,
137895 MPa (20000000 psi) 128932 MPa (18700000 psi) 10204 MPa ( 1480 000 psi) 5654 MPa (820 000 psi) 0.30
135 268 MPa (19619000 psi) 126 346 MPa 18 325 000 psi) 9993.3 MPa (1449 400 psi) 5208 MPa (754 970 psi) 0.34
E:; E:; G,, \‘IZ
compression test devices by using strips of Teflon under the tabs. However, research by Scobbo and Nakajima discovered that specimens with a longer gage length demonstrated a lower strength and modulus than those with a shorter gage length. The gage length of the Boeing specimen is the entire length of the specimen, 30.5 cm (12”) while the gage length of the Rolfes-Sendeckyj is determined to be 0.83 cm (0.325”). Since the compressive properties for the materials properties data were determined using the Rolfes-Sendeckyj device, the analytical results may be expected to demonstrate a stiffer behavior due to the higher moduli and strengths that were determined.” Failure analysis data Of the specimens produced from each of the [PI ,(,, [9p] rh, [ 2 45°]4s, [0”/90”1,,, and [oo! I- 45”/90”],, composite panels, six of each of the Boeing specimens were instrumented with back-to-back WA-03-30UR-120 stacked strain gage rosettes near the hole and back-to-back CEA 13-125UR-350 in the far field. The location of each of the gages is shown in Fig. 3. The gages were positioned to be in line with elements of the finite element mesh. The position of the gage with respect to the finite element mesh near the hole is shown in Fig. 4. By placing the gage this way, the experimental strain state at the point can be determined and correlated to the analytical strains obtained from the output information of the NFE program. The instrumented open hole specimens were placed in a Boeing Open Hole Compression fixture that had been modified, as shown in Fig. 5, to perform these types of experiments. The specimens were loaded until failure, and the strain and load data were recorded. The aver-
Percentage difference 1.94 2.05 2,11 8.61 11.76
age ultimate strengths of each of the five types of layups are shown in Table 2. The data were used for producing the specific stress-strain relationships of the laminate to compare against analytical data obtained from a NFE program. The data collected were averaged using a cubic spline program developed by Dr Sandhu to assist in his NFE.2 One concern of this investigation is whether the stresses and strains are being accurately predicted by the finite element model. To verify the accuracy of the mesh, the stress concentrations were calculated around the hole, and the values were compared to values predicted by Peterson.’ This was done by treating the composite as an isotropic material with E, 1=E,,=135 137 MPa (19600000 psi), G,Z=96527 MPa (14000000 psi), and v=O*30. The stress concentration obtained was 3.275 which compares favorably to the 3.46 value obtained by Peterson. Fisher and Daniels also performed this analysis and discovered that the value of stress concentration converges monotonically towards the value of 3.27. The analysis was run again using the modulus of steel, which Peterson used in his analysis, and a value of 3.40 was found. This result also agrees favorably with the Peterson value of 3.46. Thus, the finer mesh produced a better representation of the stresses and strains obtained than the coarser meshes used in earlier investigations.“, “’
ANALYTICAL STUDIES Analytical studies were conducted using a NFE program developed by Dr R. S. Sandhu of Wright Laboratory. The program was developed to model the material nonlinearity exhibited by Gr/PEEK composites. The basic concepts of
379
An investigation of graphite PEEK composite I
WA-O3-30UR-120
\
0 I *
I
E19mm
CEA 13-125UR-350
/ I
Fig. 3.
Placement
the increment
Direction
of hole gage with respect to finite element mesh.
this program have been presented in earlier works,8-‘2 so only a brief description of the program’s essentials are covered. The essentials consist of the data set representing the material properties data, incremental constitutive relations, and a predetermined failure criteria. Material
properties
data
The computer program incorporates the data obtained from the material properties testing and represents them as a series of curves using piecewise cubic spline interpolation functions. The use of piecewise cubic spline interpolation functions in representing stress-strain curves provides smoothness of the curves and differentiation of the functions yields the tangent moduli. Constitutive
I
relations
Gr/PEEK exhibits nonlinear properties in almost every loading condition. The use of an incremental form of the constitutive law models the response of the composite well, but two key assumptions must be made: (1) Increments of strain depend on the strain state and the increments of stress.
of strain is proportional of stress.
to
Because of these assumptions, Hooke’s law must be rewritten in an incremental constitutive law form for an anisotropic material as d&i=S, do
Location
53 mm
of gages on the Boeing specimen.
(2) The increment
Fig. 4.
19mm
(i,j= 1,2,6)
(2)
In this equation dr,, dE2, and d&, are the normal strain increments in the fiber direction, normal strain increment in the transvese direction, and shear strain increment, respectively and do,, dcr2, and do, are the normal stress increments in the fiber direction, normal stress increment in the transverse direction, and shear stress increment, respectively. S, represent the plane stress constitutive expressions. Finite element procedure The finite element method is incorporated an incremental procedure obtaining [Ki] {Aui}={ARi)
with (3)
where [&I, {AU;}, and {ARi} are the system’s stiffness matrix, the incremental displacements and incremental loads of the model in the ith increment, respectively. In this NFE method, the system’s stiffness matrix, [Ki], is not constant from increment to increment since the material constants will change due to the material nonlinear nature. In order to calculate the material properties in a given increment, an iterative predictor-corrector procedure is used for each iteration until the strain increment is less than 0.1% of the calculated value. It should be pointed out that [Ki] is the stiffness affected by the material ply response. Each ply within the bilinear element is considered in plane stress, and then stacked with node constraints to form the global elements’ stiffness. For example, in a 16-ply orientation there
380
B. Wham II, A. N. Palazotto
-
MODIFICATION FOR i45 MODIFICATION
0 0
76 mm
I.
--I-====+Fig. 5.
Modification
Table 2. Average ultimate stress of layups Specimen layup
Average ultimate stress
Standard deviation
V’,,l (CRACK)
323.2 MPa (46 873 psi) 365.2 MPa ‘l;;“:7&)
2.3 MPa (335 psi) 17.8 MPa 2575 psi) 7.4MPa Yg7;f;i)
Lo”,,1 (SPLlT) [90°1hl
j;4;;0
[o”/ +_45”/90”],,
232.4 MPa (33 711 psi)
(883 psi) ’ 12.3 MPa (1786 psi)
would be 16 bilinear plane stress elements interconnected at the elements’ nodes. The 16 elements then contribute to the model’s stiffness matrix. Through the thickness bending is assumed to be nonexistent. References 8-12 discuss the element formulation in more detail.
.
Stability Plate
to Boeing specimens.
In addition, a complete convergence study was carried out by systematically reducing the element size and making comparisons of stress functions distributed in areas surrounding the opening. ’ The final model shown throughout the paper is the one judged to produce a converged solution. Failure criterion To determine the failure of an element under load, a failure criterion is established using the strain energies as independent parameters under simple load conditions. The finite element procedure simulates plane stress loading conditions. Thus, failure occurs when C(w,/W,)=l
(i=1,2,6)
(4)
where wi is the current energy level in the fiber direction, matrix direction, and shear and Wj is the total energy under the stress-strain curve in the fiber direction, matrix direction, and shear.
381
An investigation of graphite PEEK composite
In a composite, if the matrix should fail the structure can still carry part of the load using the fibers. A load can be carried parallel to the fibers but will not be supported in the transverse or shear directions. If the fiber fails, the lamina will not be able to carry any significant loads and the load will be transferred to adjacent laminas and their elements. If the value of the ratio of eqn (5) is greater than or equal to O-1, then fiber failure occurs. If the element has met the criterion for failure but the value of the ratio is less than O-1 then the matrix has failed instead of the fiber. (The criterion can be modified depending on the relationship between fiber and matrix materials.) This value is determined using fracture testing experience with several different types of composites and has been found to yield accurate results” rr
COMPARISON OF ANALYTICAL EXPERIMENTAL DATA
oi
(i= 1,2,6)
0” Laminates Six tests were conducted to determine the ultimate strength of 0” unidirectional specimens. Three of the specimens displayed a crack at the hole similar to the failure modes shown on the top specimens in Fig. 6(a). The other three specimens exhibited a longitudinal split at the
(5)
d I:~ I
(4
(4
Fig. 6.
Typical
failures
AND
Figure 6 shows the types of failures experienced experimentally by each type of laminate with holes used in this investigation.
1
=check C ki i=( 1.2.3) [i’,
where k,, k,, k, is the total area under the stress-strain curve in the 1, 2, 6 direction, dcj is the strain increment of the 1, 2, 6 direction, and (T;is the stress increment in the 1, 2, 6 direction. Using these concepts, the analytical responses for the [[O”],, [90”],,, [ ?45°]4.s, [O”/90”],,V,and [Oo!+ 45”/90”],,, laminates were investigated.
of compression
specimens.
382
B. Wham II, A. N. Palazotto
edge of the hole traveling in a direction parallel to the compressive load as shown in the bottom specimen in Fig. 6(a). The splitting occurred at a higher ultimate load than the transverse cracking. The failure in both the splitting and cracking failure modes was instantaneous, with the load dropping off by 453.6 kg (1000 lb) on average and then leveling off for approximately 2 s until the test was stopped. The tests were stopped to preserve the end of the specimen so that it could be examined with a scanning electron microscope. The vertical splits failed at a stress level between 351 MPa (50.9 ksi) and 385 MPa (558 ksi). The specimens that failed due to a horizontal crack failed between 321 MPa (46.5 ksi) and 324.7 MPa (47.1 ksi). This type of failure has been observed before in Gr/PEEK specimens under tension in research conducted by Martin.8 In research started by Martin in 1988 and concluded by Sandhu in 1992, it was discovered that the splitting could be the result of shear stress around the hole.‘* To check this theory, gages were placed on two specimens at various orientations to the hole to determine if there was any eccentricity in the strain at the hole. The specimens were loaded to failure in tension. The splitting occurred and the changes in strain were recorded. Those gages normal to the loading direction displayed a marked increase in strain when the splitting occurred. Those gages parallel to the loading direction recorded much different strain values as the specimen approached failure. As the splitting occurred, the gage above the split showed an increase in strain, while the gage at the bottom of the split showed a rapid decrease in strain to the point that it was almost unloaded before the test was stopped. An opinion was suggested that when the shear stresses exceed those of the matrix, the split forms at the hole edge and
Fig. 7.
One-quarter
finite element
mesh.
quickly propagates up the length of the specimen towards the loaded ends. The result of this type of failure was that the Boeing specimen, instead of being loaded as one approximately 38.1 mm (1.5”) wide specimen with a 12.7 mm (0.5”) diameter hole was instead loaded as two separate approximately 12.7 mm (0.5”) wide plates. This ‘two-plate’ theory could have been tested, if the loading had been allowed to proceed after the splitting occurred. However, with the obstructions of gages and restraint plate within the Boeing fixture, it was extremely difficult to determine the failure mode until the specimen was removed from the apparatus. The removal procedure usually resulted in the debonding of the strain gage, thus obtaining more strain information was impossible. Since the specimen was not broken into two separate pieces during the procedure it could not be surveyed by the electron microscope, without destroying the failure areas. The failed specimens were investigated using an ultrasonic analysis. The examination failed to detect even traces of the initiation of a horizontal crack in the specimen. The crack formation was not always symmetric in nature and as a result could not be predicted. The finite element comparison provided some insight into what may have been the cause of the splitting phenomenon. The specimen was modeled using a one-quarter mesh as shown in Fig. 7. The mesh was designed to be extremely fine (24 elements around the edge, each with an area of 0.00157 cm2 (0*000244 in”)) around the area of the hole so as to detect failures that might signal the initiation of failure. The finite element modeling produced a failure that was similar in nature to the vertical splitting-type failure, but at a much lower load. On the first increment where damage initiated within the finite element model, there were six elements which failed at the edge of the hole. On the next increment at 296.6 MPa (43-O ksi) the entire model failed as shown in Fig. 8. The catastrophic type of failure is indicative of the type of failure that was experienced in the experimental specimens that failed due to a vertical split. While the specimen interfered with the observation of the specimen, those specimens that failed because of a horizontal crack experienced an extended period of audible cracking, while the specimens that experienced a vertical split suffered an instantaneous failure. This indicates the horizontal failure was a
383
An investigation of graphite PEEK composite 0 DEGREE FAILURE MESH
ace 0 INCREMENT#14
4
0 applied = 282.2 h4Pa
LOADING
(o applied = 40930 psi)
DIRECTION
INCREMENT #I5 oapplied = 296.6 &%‘a
Fig. 8.
Progression
of failure for 0” model.
progressive phenomenon instead of an instantaneous one experienced by the vertically cracked specimens and finite element model. 90” Laminates All six of the 90” specimens displayed the same type of failure surface. The specimens however did exhibit some deviation in the ultimate strength. The average ultimate strength of the experimental specimens was 129 MPa (18.7 ksi) with a standard deviation of 7.4 MPa (1.1 ksi). As seen in the material properties tests (Table l), in compression testing 90” specimens have a much lower compressive strength than the 0 specimens. Since the PEEK matrix material is not an extremely brittle material and exhibits extensive material nonlinearity, the stress-strain response of the specimens is nonlinear. There
Fig. 9.
40 xl 3oooo moo 2oooo LongitudinalStraln ‘-1,CllNl,WM (mm/mm)
Analytical-experimental
comparison
of 90”.
was close correspondence between the analytical model and experimentation in the early stages of the loading process. The graph of stress versus strain in Fig. 9 shows that there is some deviation of the analytical model from the experimental specimens as the load increases. The analytical model experienced the failure of a large number of elements at 151 MPa (21.9 ksi), this is evidenced in a slight shift of the data line around 151 MPa in Fig. 9. This corresponds within 10% of the ultimate experimental stress. The analytical curve does not closely model the nonlinear behavior of the composite that is present in the experimental curves throughout the loading process. This may be a result of comparing a mathematical model to a structurally imperfect specimen or the stiffer material properties derived from the material property specimens as discussed earlier in this paper. This may explain why the model may have exhibited a stiffer response than the experimental specimens. 0”/90” Laminates In the experimental results, the crossply failed similarly to the 90”, from a horizontal crack occurring at the edge of the hole normal to the load and progressing to the outer edge of the specimen. The stress-strain response of the V/90” specimen is compared to the experimental in Fig. 10. There is a anomaly occurring at 215.8 MPa (31.3 ksi) where the longitudinal stress at the hole decreases while the strain
B. Wham II, A. N. Palazotto
384
increases. This also models the same effect that is present in the experimental specimen immediately prior to the final failure of the composite. The total energy of the system was checked three increments prior to and four increments after the discontinuity and the system remained conservative throughout that time. However, the energy of the element being plotted was discovered to have decreased when this discontinuity occurred. The appearance of this anomaly within Fig. 10 may be an indication of when failure occurred in the analytical model. The progression of failure of the analytical model was studied and seemed to be slower in comparison to the experimental results. There were no major cascades of failed elements until 383 MPa (55.6 ksi) where 14 elements failed. This is much higher than the experimental ultimate stress of 223 MPa (32.4 ksi). Overall, comparing the analytical response to the experimental response shows that there is good agreement between the two. + 45” Laminates The +45” model produced the best comparison of the experimental to the analytical. The model exhibited the nonlinear behavior of the k45” specimens, both of which are shown in Fig. 11. The analytical stress-strain curve was stiffer than the experimental portion. Part of the reason the analytical response was stiffer is that it does not model the scissoring of the plies that was present in the experimental results. There was also an area present where the far field 300
experienced a sudden change in the slope of the far-field curve without similar corresponding change in stress. This occurred at 140 MPa (20 ksi) and well within the average maximum experimental load of 142 MPa (20 ksi). While it is uncertain, because of the obstructing nature of the Boeing fixture, when the failure of the +45” specimens occurred experimentally, it was assumed that failure of the specimens occurred at or about 139 MPa (20 ksi). There are two notable features present within the graph. The first is the sharp decrease in strain which occurred at 134.5 MPa (19.5 ksi). The element being tracked shed more than half of its longitudinal strain and approximately half of its total energy. There is no change in the loading, which continues to increase, but many of the elements near the tracked element seem to also shed strain to the other elements in the region. The far-field gage is also stiffer than the analytical, but may be the effect of scissoring of the fibers within the experimental specimens. The scissoring in the experimental curves seems to start at the point at which the experimental curve deviates from the analytical curve and starts to progress towards a state where strain increases without an increase in stress. Both the far-field gage measurements demonstrate an increase in slope towards the end of the loading. This may the effect of the fixture closing before the test was stopped. This feature was present in each of the far-field response curves. A plot of the progression of failure was made for both the +45” and -45” layups and the most interesting item present was the fact that
-l
150
-
Anatyllcal
(hiPa)
9
0
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Analytical-experimental
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Fig. 11.
Analytical-experimental
comparison
of + 45”.
An investigation of graphite PEEK composite 300
200 3
E
z 5 loo
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Fig. 12.
4&o
6&o
8600
1t
lo
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Analytical-experimental _t 45”/90”.
comparison
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385
paper. In the graphs of the +45” in Fig. 11, it is evident that the strain at the hole was on the same order of magnitude as the far field data. This seems to create the same effect within the quasi-isotropic meshes. of failure in the study The progression showed that the 0” laminates failed first before any of the laminates start to be affected by the load. The 90” ply does not suffer any failures throughout the loading process. There is a rather large cascade of failed elements at a load of 250 MPa (36.2 ksi). If the cascading is the event that signifies the failure of the composite then there is a favorable comparison with the experimental ultimate stress of 232 MPa (33.6 ksi).
O”/
CONCLUSION the failure was not symmetric. A crack formed at the hole edge at an angle of 42” to the edge of the hole normal to the loading direction. The crack propagated through the model very quickly and reached the outer edge at 167 MPa (24.2 ksi). The angle of the failure coincided well with experimental specimens where the angle of the failure appears to be at an angle of approximately 30” away from the hole edge. oO/f 45”/90” Laminates
The modeled response of the laminate seems to incorporate some of the features displayed by the other specimen models. The graph of the stress-strain response, Fig. 12, shows a very well-behaved laminate. The graphs of the experimental data demonstrate a very linear behavior until the end of the load when the curves start to go nonlinear. The analytical graph shows the same kind of linear behavior, however the nonlinearity towards the end of the loading is not as obvious. Like the other models, the loading of the finite element model continues well past the ultimate experimental stress of the 0”/90’ and k4.5” specimens. The difference between this model and the rest of the models is that the change in the slope of the strain, defined as the anomaly, did not occur. The analytical longitudinal hole is stiffer than the experimental data, as seen in Fig. 12. This may be the result of the incorporation of +45” plies into the lamnate or the stiffer material properties data as discussed earlier in this
Based on the analysis of the experimental and of the [ -+45”],,, analytical investigations [O”/90”],,V,and [o”/ _+45°/900],,Yspecimens loaded in compression, the analytical technique predicted the initiation and progression of the failure with reasonable accuracy. However, the analytical method did not accurately model the nonlinearity exhibited by the [90”],, specimens, but this may be due to the use of the Rolfes-Sendeckyj device to determine materials property data for the 90” materials property specimens test under compression. If a different method for determining materials properties for specimens under compression were used, the analytical may be able to better approximate the experimental. The analytical method appeared to model the splitting phenomenon in the [0”],, specimens with reasonable accuracy. However, further investigation of this layup should be accomplished to determine the exact cause of failure to check the validity of comparing the analytical and experimental results.
REFERENCES Wham, B., II, An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity. MS thesis, AFIT!GA/EN/93M. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, March, 1993. SAMCA SMR 3-88, Open hole compression properties of oriented fiber-resin composites, Association brochure, Suppliers of Advanced Composite Materials Association, Cleveland, 1988.
B. Wham II, A. N. Palazotto 3. Sandhu, R. S., Nonlinear behavior of unidirectional and angle ply laminates. J. Aircraft, 1976, 13, 104-l 11. 4. ICI Composites Inc., Thermoplastic Composite Materials Handbook. Fibrite Composite Materials, Tempe, AZ, 1992. 5. Daniels, J. A. and Sandhu, R. S., Evaulation of compression specimens and fixtures for testing unidirectional composite laminates. In Composite Materials: Testing and Design, ASTM STP 1206, ed. E. T. Camponeschi. American Society for Testing and Materials, Philadelphia, 1993, Vol. 11, pp. 103-23. 6. Scobbo, J. J. and Nakajima, N., Effect of gage length on compressive properties of unidirectional fiber composites. J. Thermoplastic Composite Mater., 1990, 3, 190-201. 7. Peterson, R. E., Stress Concentration Factors. John Wiley, New York, 1974, p. 150. 8. Martin, J., A study of failure characteristics in thermoplastic composite materials. MS thesis, AFIT/ GA/AA/88M-2. School of Engineering, Air Force
9.
10.
1 I.
12.
Institute of Technology, Wright Patterson AFB, OH, March, 1988. Fisher, J. M., A study of failure characteristics in a thermoplastic composite material at high temperature. MS thesis, AFIT/GAE/AA88D-15. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, December 1988. Daniels, J. A., A study of failure characteristics in thermoplastic laminates due to an eccentric circular discontinuity. MS thesis, AFIT/GAE/ENY/89D-06. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, December, 1989. Sandhu, R. S. and Sendeckyj, G. P.. On delamination of (+ 0,,,/90,&, laminates subjected to tensile loading. Air Force Wright Aeronautical Laboratories Technical Report, AFWDL-TR-87-3058, July, 1987. Martin, L., Sandhu, R. S. and Palozotto, A. N., Experimental and analytical comparisons of failure in thermoplastic composite laminates. J. Exp. Mech.. 1994, 53-65.
ELSEVIER
An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity Department
ofAeronautics
and
B. Wham II* & A. N. Palazotto Astronautics, Air Force Institute qf Technology OH 45433- 7765, USA
Wtight-Patterson Air Force Base,
The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [O”,,], [90°Lb], [ f45°]4,, [0’/90’],,,, and [O”/f45°/90”],,V. In the experimentation, [90”] ,br [O”/900]4s, and [O’/ f 45”/90“],,, laminates, as well as three of the [O”],,, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [ *45”],, specimens failed to support the load due to an internal crack that originated from the hole’s edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally. Published by Elsevier Science Ltd.
with a centrally located cutout. This research was conducted to include the nonlinear stressstrain behavior of the matrix material in the evaluation of Gr/PEEK. The purpose of this research was to determine (using both experimental and analytical methods) the basic material properties of Gr/PEEK, the initiation and progression of compressive failure, the stress-strain response of the material, and the ultimate failure load of Gr/PEEK with a centrally located 1.27 cm (05”) circular cutout. The Gr/PEEK specimens were end loaded experimentally using a Boeing Open Hole Compression apparatus, BSS-7260.* The composite was loaded at room temperature. The ply layups used for the investigation were [O”],,, [90”] 16, [ f 45°]4S, [0”/90”],,, and [O”/+ 45”/90”],,. Once the experimental portion of the research was completed, the results were compared to a nonlinear ply-by-ply finite element technique developed by Dr R. S. Sandhu of Wright Laboratories, Wright-Patterson Air Force Base, Ohio.?
INTRODUCTION Composite materials are finding an increasing number of applications. Not only have composites found extensive use in the aerospace industry due to their excellent fracture toughness and high strength-to-weight ratios, but they are also finding an increasing usage in the construction industry. Graphite polyetheretherketone (Gr/PEEK), a thermoplastic composite material, has an advantage over traditional thermoset composite materials because of its high impact toughness and damage tolerance; rapid, automated, economical fabrication processes; environmental resistance; and ease of repair. ’ A large body of research conducted on Gr/ PEEK exists and includes the investigation of Gr/PEEK under both tension and compression
*Present address: System Facilities; F-22, 2130 5th Street, Wright-Patterson, Air Force Base, OH 45433-7003, USA. 375
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B. Wham II, A. N. Palazotto
EXPERIMENTAL STUDIES
Once the fabrication procedure was complete, all the panels were subjected to a C-Scan evaluation to ensure that there were no major defects such as entrained air, resin starved areas, and fiber bunching. The C-scan was conducted by the Non-Destructive Branch of the Materials Laboratory (WL, WPAFB). A total of seven panels were manufactured. The first two were used in determining the material properties of this batch of Gr/PEEK. The specimens were cut into two sets. The first set consisted of three layups (O’, 90”, 44.5”) of
Material system The material system, Gr/PEEK, used in this study consisted of Hercules AS4 graphite fibers in a polyaromatic resin. The specimens were constructed by Beta Industries of Dayton, OH using continuous pre-preg tape, 30.5 cm (12”) width. All the panels were laid up by hand and fabricated according to the tape manufacturer’s, ICI Fibrite Ltd, specifications.
20” TAB TAPER
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a. SpecimenOT
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127mm
-
50.8 mm
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6.4 mm 57.2 mm Sqaure End Tabs
Teflon Insects
6.4 mm
,
127mm
<
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6.4 mm 57.2 mm 6.4 mm
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c. Compression Specimens
Fig. 1.
Geometry
of materials
property
specimens.
377
An investigationof graphite PEEK composite
the loading edge of the specimen so that a gross stress state of the specimen could be calculated given a load using the formula
tensile specimens and two layups (O“, 90”) of compression specimens. The dimensions of these specimens are shown in Fig. 1. The specimens were fitted with tabs constructed of G-10 glass epoxy. These tabs provided for a uniform transfer of load from the testing machine to the specimens as well as a contact area for the hydraulic mounting grips of the Instron machine. The tabs also prevented damage inflicted on the specimen by the grips. The other five panels were used for compressive testing within the Boeing Open Hole Compression apparatus. The specimens were constructed to specifications written by the Boeing Corporation in BSS-7260* and shown in Fig. 2. The holes in the Boeing specimens were produced by drilling a small initial hole in the center of the specimen, then expanding the hole by gradually increasing the bit size until the desired diameter was obtained. The incremental increase of the bit size had to be very slight so that the drilling process did not introduce any failures or delamination around the hole. The dimensions of the specimens were verified using mechanical measuring devices to check parallelism and to ensure that no eccentric loading conditions were introduced. The measurements of each specimen’s width and thickness were taken to ensure that any specimen with a highly variable width or thickness was eliminated. The thicknesses and widths were then averaged to obtain an average area of
I
load G=
(1)
width x thickness
Basic material property data Back-to-back strain gage rosettes were affixed to the center of all material property specimens and the specimens were tested to yield the basic property data. Table 1 shows a comparison of the materials property data obtained with the averages determined by the ICI Fibrite Corporation in their published data sheets on Gr/PEEK.4 The five data sets obtained from each of the ply layups tested were averaged to produce the basic properties required for the nonlinear finite element (NFE) program used in this study. The properties were determined from the experimental stress-strain data presented in Table 1. The NFE program will be discussed later in the paper. The Rolfes-Sendeckyj device, used for testing of the material property specimens, was recommended for compression materials property testing in an investigation by Daniels and Sandhu” of compression fixtures. Their findings demonstrated that the device produced the most uniform state of stress of all of the
304.8 mm
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12.7mm 12.7 mm.08
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c 12.7 mm Fig. 2.
Geometry
of Boeing specimens.
38mmd.13mm I
378
B. Wham II, A. N. Palazotto Table 1. Comparison of material properties
Property
ICI Fibrite Ltd values
Experimental values
G‘,
137895 MPa (20000000 psi) 128932 MPa (18700000 psi) 10204 MPa ( 1480 000 psi) 5654 MPa (820 000 psi) 0.30
135 268 MPa (19619000 psi) 126 346 MPa 18 325 000 psi) 9993.3 MPa (1449 400 psi) 5208 MPa (754 970 psi) 0.34
E:; E:; G,, \‘IZ
compression test devices by using strips of Teflon under the tabs. However, research by Scobbo and Nakajima discovered that specimens with a longer gage length demonstrated a lower strength and modulus than those with a shorter gage length. The gage length of the Boeing specimen is the entire length of the specimen, 30.5 cm (12”) while the gage length of the Rolfes-Sendeckyj is determined to be 0.83 cm (0.325”). Since the compressive properties for the materials properties data were determined using the Rolfes-Sendeckyj device, the analytical results may be expected to demonstrate a stiffer behavior due to the higher moduli and strengths that were determined.” Failure analysis data Of the specimens produced from each of the [PI ,(,, [9p] rh, [ 2 45°]4s, [0”/90”1,,, and [oo! I- 45”/90”],, composite panels, six of each of the Boeing specimens were instrumented with back-to-back WA-03-30UR-120 stacked strain gage rosettes near the hole and back-to-back CEA 13-125UR-350 in the far field. The location of each of the gages is shown in Fig. 3. The gages were positioned to be in line with elements of the finite element mesh. The position of the gage with respect to the finite element mesh near the hole is shown in Fig. 4. By placing the gage this way, the experimental strain state at the point can be determined and correlated to the analytical strains obtained from the output information of the NFE program. The instrumented open hole specimens were placed in a Boeing Open Hole Compression fixture that had been modified, as shown in Fig. 5, to perform these types of experiments. The specimens were loaded until failure, and the strain and load data were recorded. The aver-
Percentage difference 1.94 2.05 2,11 8.61 11.76
age ultimate strengths of each of the five types of layups are shown in Table 2. The data were used for producing the specific stress-strain relationships of the laminate to compare against analytical data obtained from a NFE program. The data collected were averaged using a cubic spline program developed by Dr Sandhu to assist in his NFE.2 One concern of this investigation is whether the stresses and strains are being accurately predicted by the finite element model. To verify the accuracy of the mesh, the stress concentrations were calculated around the hole, and the values were compared to values predicted by Peterson.’ This was done by treating the composite as an isotropic material with E, 1=E,,=135 137 MPa (19600000 psi), G,Z=96527 MPa (14000000 psi), and v=O*30. The stress concentration obtained was 3.275 which compares favorably to the 3.46 value obtained by Peterson. Fisher and Daniels also performed this analysis and discovered that the value of stress concentration converges monotonically towards the value of 3.27. The analysis was run again using the modulus of steel, which Peterson used in his analysis, and a value of 3.40 was found. This result also agrees favorably with the Peterson value of 3.46. Thus, the finer mesh produced a better representation of the stresses and strains obtained than the coarser meshes used in earlier investigations.“, “’
ANALYTICAL STUDIES Analytical studies were conducted using a NFE program developed by Dr R. S. Sandhu of Wright Laboratory. The program was developed to model the material nonlinearity exhibited by Gr/PEEK composites. The basic concepts of
379
An investigation of graphite PEEK composite I
WA-O3-30UR-120
\
0 I *
I
E19mm
CEA 13-125UR-350
/ I
Fig. 3.
Placement
the increment
Direction
of hole gage with respect to finite element mesh.
this program have been presented in earlier works,8-‘2 so only a brief description of the program’s essentials are covered. The essentials consist of the data set representing the material properties data, incremental constitutive relations, and a predetermined failure criteria. Material
properties
data
The computer program incorporates the data obtained from the material properties testing and represents them as a series of curves using piecewise cubic spline interpolation functions. The use of piecewise cubic spline interpolation functions in representing stress-strain curves provides smoothness of the curves and differentiation of the functions yields the tangent moduli. Constitutive
I
relations
Gr/PEEK exhibits nonlinear properties in almost every loading condition. The use of an incremental form of the constitutive law models the response of the composite well, but two key assumptions must be made: (1) Increments of strain depend on the strain state and the increments of stress.
of strain is proportional of stress.
to
Because of these assumptions, Hooke’s law must be rewritten in an incremental constitutive law form for an anisotropic material as d&i=S, do
Location
53 mm
of gages on the Boeing specimen.
(2) The increment
Fig. 4.
19mm
(i,j= 1,2,6)
(2)
In this equation dr,, dE2, and d&, are the normal strain increments in the fiber direction, normal strain increment in the transvese direction, and shear strain increment, respectively and do,, dcr2, and do, are the normal stress increments in the fiber direction, normal stress increment in the transverse direction, and shear stress increment, respectively. S, represent the plane stress constitutive expressions. Finite element procedure The finite element method is incorporated an incremental procedure obtaining [Ki] {Aui}={ARi)
with (3)
where [&I, {AU;}, and {ARi} are the system’s stiffness matrix, the incremental displacements and incremental loads of the model in the ith increment, respectively. In this NFE method, the system’s stiffness matrix, [Ki], is not constant from increment to increment since the material constants will change due to the material nonlinear nature. In order to calculate the material properties in a given increment, an iterative predictor-corrector procedure is used for each iteration until the strain increment is less than 0.1% of the calculated value. It should be pointed out that [Ki] is the stiffness affected by the material ply response. Each ply within the bilinear element is considered in plane stress, and then stacked with node constraints to form the global elements’ stiffness. For example, in a 16-ply orientation there
380
B. Wham II, A. N. Palazotto
-
MODIFICATION FOR i45 MODIFICATION
0 0
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I.
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Modification
Table 2. Average ultimate stress of layups Specimen layup
Average ultimate stress
Standard deviation
V’,,l (CRACK)
323.2 MPa (46 873 psi) 365.2 MPa ‘l;;“:7&)
2.3 MPa (335 psi) 17.8 MPa 2575 psi) 7.4MPa Yg7;f;i)
Lo”,,1 (SPLlT) [90°1hl
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[o”/ +_45”/90”],,
232.4 MPa (33 711 psi)
(883 psi) ’ 12.3 MPa (1786 psi)
would be 16 bilinear plane stress elements interconnected at the elements’ nodes. The 16 elements then contribute to the model’s stiffness matrix. Through the thickness bending is assumed to be nonexistent. References 8-12 discuss the element formulation in more detail.
.
Stability Plate
to Boeing specimens.
In addition, a complete convergence study was carried out by systematically reducing the element size and making comparisons of stress functions distributed in areas surrounding the opening. ’ The final model shown throughout the paper is the one judged to produce a converged solution. Failure criterion To determine the failure of an element under load, a failure criterion is established using the strain energies as independent parameters under simple load conditions. The finite element procedure simulates plane stress loading conditions. Thus, failure occurs when C(w,/W,)=l
(i=1,2,6)
(4)
where wi is the current energy level in the fiber direction, matrix direction, and shear and Wj is the total energy under the stress-strain curve in the fiber direction, matrix direction, and shear.
381
An investigation of graphite PEEK composite
In a composite, if the matrix should fail the structure can still carry part of the load using the fibers. A load can be carried parallel to the fibers but will not be supported in the transverse or shear directions. If the fiber fails, the lamina will not be able to carry any significant loads and the load will be transferred to adjacent laminas and their elements. If the value of the ratio of eqn (5) is greater than or equal to O-1, then fiber failure occurs. If the element has met the criterion for failure but the value of the ratio is less than O-1 then the matrix has failed instead of the fiber. (The criterion can be modified depending on the relationship between fiber and matrix materials.) This value is determined using fracture testing experience with several different types of composites and has been found to yield accurate results” rr
COMPARISON OF ANALYTICAL EXPERIMENTAL DATA
oi
(i= 1,2,6)
0” Laminates Six tests were conducted to determine the ultimate strength of 0” unidirectional specimens. Three of the specimens displayed a crack at the hole similar to the failure modes shown on the top specimens in Fig. 6(a). The other three specimens exhibited a longitudinal split at the
(5)
d I:~ I
(4
(4
Fig. 6.
Typical
failures
AND
Figure 6 shows the types of failures experienced experimentally by each type of laminate with holes used in this investigation.
1
=check C ki i=( 1.2.3) [i’,
where k,, k,, k, is the total area under the stress-strain curve in the 1, 2, 6 direction, dcj is the strain increment of the 1, 2, 6 direction, and (T;is the stress increment in the 1, 2, 6 direction. Using these concepts, the analytical responses for the [[O”],, [90”],,, [ ?45°]4.s, [O”/90”],,V,and [Oo!+ 45”/90”],,, laminates were investigated.
of compression
specimens.
382
B. Wham II, A. N. Palazotto
edge of the hole traveling in a direction parallel to the compressive load as shown in the bottom specimen in Fig. 6(a). The splitting occurred at a higher ultimate load than the transverse cracking. The failure in both the splitting and cracking failure modes was instantaneous, with the load dropping off by 453.6 kg (1000 lb) on average and then leveling off for approximately 2 s until the test was stopped. The tests were stopped to preserve the end of the specimen so that it could be examined with a scanning electron microscope. The vertical splits failed at a stress level between 351 MPa (50.9 ksi) and 385 MPa (558 ksi). The specimens that failed due to a horizontal crack failed between 321 MPa (46.5 ksi) and 324.7 MPa (47.1 ksi). This type of failure has been observed before in Gr/PEEK specimens under tension in research conducted by Martin.8 In research started by Martin in 1988 and concluded by Sandhu in 1992, it was discovered that the splitting could be the result of shear stress around the hole.‘* To check this theory, gages were placed on two specimens at various orientations to the hole to determine if there was any eccentricity in the strain at the hole. The specimens were loaded to failure in tension. The splitting occurred and the changes in strain were recorded. Those gages normal to the loading direction displayed a marked increase in strain when the splitting occurred. Those gages parallel to the loading direction recorded much different strain values as the specimen approached failure. As the splitting occurred, the gage above the split showed an increase in strain, while the gage at the bottom of the split showed a rapid decrease in strain to the point that it was almost unloaded before the test was stopped. An opinion was suggested that when the shear stresses exceed those of the matrix, the split forms at the hole edge and
Fig. 7.
One-quarter
finite element
mesh.
quickly propagates up the length of the specimen towards the loaded ends. The result of this type of failure was that the Boeing specimen, instead of being loaded as one approximately 38.1 mm (1.5”) wide specimen with a 12.7 mm (0.5”) diameter hole was instead loaded as two separate approximately 12.7 mm (0.5”) wide plates. This ‘two-plate’ theory could have been tested, if the loading had been allowed to proceed after the splitting occurred. However, with the obstructions of gages and restraint plate within the Boeing fixture, it was extremely difficult to determine the failure mode until the specimen was removed from the apparatus. The removal procedure usually resulted in the debonding of the strain gage, thus obtaining more strain information was impossible. Since the specimen was not broken into two separate pieces during the procedure it could not be surveyed by the electron microscope, without destroying the failure areas. The failed specimens were investigated using an ultrasonic analysis. The examination failed to detect even traces of the initiation of a horizontal crack in the specimen. The crack formation was not always symmetric in nature and as a result could not be predicted. The finite element comparison provided some insight into what may have been the cause of the splitting phenomenon. The specimen was modeled using a one-quarter mesh as shown in Fig. 7. The mesh was designed to be extremely fine (24 elements around the edge, each with an area of 0.00157 cm2 (0*000244 in”)) around the area of the hole so as to detect failures that might signal the initiation of failure. The finite element modeling produced a failure that was similar in nature to the vertical splitting-type failure, but at a much lower load. On the first increment where damage initiated within the finite element model, there were six elements which failed at the edge of the hole. On the next increment at 296.6 MPa (43-O ksi) the entire model failed as shown in Fig. 8. The catastrophic type of failure is indicative of the type of failure that was experienced in the experimental specimens that failed due to a vertical split. While the specimen interfered with the observation of the specimen, those specimens that failed because of a horizontal crack experienced an extended period of audible cracking, while the specimens that experienced a vertical split suffered an instantaneous failure. This indicates the horizontal failure was a
383
An investigation of graphite PEEK composite 0 DEGREE FAILURE MESH
ace 0 INCREMENT#14
4
0 applied = 282.2 h4Pa
LOADING
(o applied = 40930 psi)
DIRECTION
INCREMENT #I5 oapplied = 296.6 &%‘a
Fig. 8.
Progression
of failure for 0” model.
progressive phenomenon instead of an instantaneous one experienced by the vertically cracked specimens and finite element model. 90” Laminates All six of the 90” specimens displayed the same type of failure surface. The specimens however did exhibit some deviation in the ultimate strength. The average ultimate strength of the experimental specimens was 129 MPa (18.7 ksi) with a standard deviation of 7.4 MPa (1.1 ksi). As seen in the material properties tests (Table l), in compression testing 90” specimens have a much lower compressive strength than the 0 specimens. Since the PEEK matrix material is not an extremely brittle material and exhibits extensive material nonlinearity, the stress-strain response of the specimens is nonlinear. There
Fig. 9.
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Analytical-experimental
comparison
of 90”.
was close correspondence between the analytical model and experimentation in the early stages of the loading process. The graph of stress versus strain in Fig. 9 shows that there is some deviation of the analytical model from the experimental specimens as the load increases. The analytical model experienced the failure of a large number of elements at 151 MPa (21.9 ksi), this is evidenced in a slight shift of the data line around 151 MPa in Fig. 9. This corresponds within 10% of the ultimate experimental stress. The analytical curve does not closely model the nonlinear behavior of the composite that is present in the experimental curves throughout the loading process. This may be a result of comparing a mathematical model to a structurally imperfect specimen or the stiffer material properties derived from the material property specimens as discussed earlier in this paper. This may explain why the model may have exhibited a stiffer response than the experimental specimens. 0”/90” Laminates In the experimental results, the crossply failed similarly to the 90”, from a horizontal crack occurring at the edge of the hole normal to the load and progressing to the outer edge of the specimen. The stress-strain response of the V/90” specimen is compared to the experimental in Fig. 10. There is a anomaly occurring at 215.8 MPa (31.3 ksi) where the longitudinal stress at the hole decreases while the strain
B. Wham II, A. N. Palazotto
384
increases. This also models the same effect that is present in the experimental specimen immediately prior to the final failure of the composite. The total energy of the system was checked three increments prior to and four increments after the discontinuity and the system remained conservative throughout that time. However, the energy of the element being plotted was discovered to have decreased when this discontinuity occurred. The appearance of this anomaly within Fig. 10 may be an indication of when failure occurred in the analytical model. The progression of failure of the analytical model was studied and seemed to be slower in comparison to the experimental results. There were no major cascades of failed elements until 383 MPa (55.6 ksi) where 14 elements failed. This is much higher than the experimental ultimate stress of 223 MPa (32.4 ksi). Overall, comparing the analytical response to the experimental response shows that there is good agreement between the two. + 45” Laminates The +45” model produced the best comparison of the experimental to the analytical. The model exhibited the nonlinear behavior of the k45” specimens, both of which are shown in Fig. 11. The analytical stress-strain curve was stiffer than the experimental portion. Part of the reason the analytical response was stiffer is that it does not model the scissoring of the plies that was present in the experimental results. There was also an area present where the far field 300
experienced a sudden change in the slope of the far-field curve without similar corresponding change in stress. This occurred at 140 MPa (20 ksi) and well within the average maximum experimental load of 142 MPa (20 ksi). While it is uncertain, because of the obstructing nature of the Boeing fixture, when the failure of the +45” specimens occurred experimentally, it was assumed that failure of the specimens occurred at or about 139 MPa (20 ksi). There are two notable features present within the graph. The first is the sharp decrease in strain which occurred at 134.5 MPa (19.5 ksi). The element being tracked shed more than half of its longitudinal strain and approximately half of its total energy. There is no change in the loading, which continues to increase, but many of the elements near the tracked element seem to also shed strain to the other elements in the region. The far-field gage is also stiffer than the analytical, but may be the effect of scissoring of the fibers within the experimental specimens. The scissoring in the experimental curves seems to start at the point at which the experimental curve deviates from the analytical curve and starts to progress towards a state where strain increases without an increase in stress. Both the far-field gage measurements demonstrate an increase in slope towards the end of the loading. This may the effect of the fixture closing before the test was stopped. This feature was present in each of the far-field response curves. A plot of the progression of failure was made for both the +45” and -45” layups and the most interesting item present was the fact that
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-
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385
paper. In the graphs of the +45” in Fig. 11, it is evident that the strain at the hole was on the same order of magnitude as the far field data. This seems to create the same effect within the quasi-isotropic meshes. of failure in the study The progression showed that the 0” laminates failed first before any of the laminates start to be affected by the load. The 90” ply does not suffer any failures throughout the loading process. There is a rather large cascade of failed elements at a load of 250 MPa (36.2 ksi). If the cascading is the event that signifies the failure of the composite then there is a favorable comparison with the experimental ultimate stress of 232 MPa (33.6 ksi).
O”/
CONCLUSION the failure was not symmetric. A crack formed at the hole edge at an angle of 42” to the edge of the hole normal to the loading direction. The crack propagated through the model very quickly and reached the outer edge at 167 MPa (24.2 ksi). The angle of the failure coincided well with experimental specimens where the angle of the failure appears to be at an angle of approximately 30” away from the hole edge. oO/f 45”/90” Laminates
The modeled response of the laminate seems to incorporate some of the features displayed by the other specimen models. The graph of the stress-strain response, Fig. 12, shows a very well-behaved laminate. The graphs of the experimental data demonstrate a very linear behavior until the end of the load when the curves start to go nonlinear. The analytical graph shows the same kind of linear behavior, however the nonlinearity towards the end of the loading is not as obvious. Like the other models, the loading of the finite element model continues well past the ultimate experimental stress of the 0”/90’ and k4.5” specimens. The difference between this model and the rest of the models is that the change in the slope of the strain, defined as the anomaly, did not occur. The analytical longitudinal hole is stiffer than the experimental data, as seen in Fig. 12. This may be the result of the incorporation of +45” plies into the lamnate or the stiffer material properties data as discussed earlier in this
Based on the analysis of the experimental and of the [ -+45”],,, analytical investigations [O”/90”],,V,and [o”/ _+45°/900],,Yspecimens loaded in compression, the analytical technique predicted the initiation and progression of the failure with reasonable accuracy. However, the analytical method did not accurately model the nonlinearity exhibited by the [90”],, specimens, but this may be due to the use of the Rolfes-Sendeckyj device to determine materials property data for the 90” materials property specimens test under compression. If a different method for determining materials properties for specimens under compression were used, the analytical may be able to better approximate the experimental. The analytical method appeared to model the splitting phenomenon in the [0”],, specimens with reasonable accuracy. However, further investigation of this layup should be accomplished to determine the exact cause of failure to check the validity of comparing the analytical and experimental results.
REFERENCES Wham, B., II, An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity. MS thesis, AFIT!GA/EN/93M. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, March, 1993. SAMCA SMR 3-88, Open hole compression properties of oriented fiber-resin composites, Association brochure, Suppliers of Advanced Composite Materials Association, Cleveland, 1988.
B. Wham II, A. N. Palazotto 3. Sandhu, R. S., Nonlinear behavior of unidirectional and angle ply laminates. J. Aircraft, 1976, 13, 104-l 11. 4. ICI Composites Inc., Thermoplastic Composite Materials Handbook. Fibrite Composite Materials, Tempe, AZ, 1992. 5. Daniels, J. A. and Sandhu, R. S., Evaulation of compression specimens and fixtures for testing unidirectional composite laminates. In Composite Materials: Testing and Design, ASTM STP 1206, ed. E. T. Camponeschi. American Society for Testing and Materials, Philadelphia, 1993, Vol. 11, pp. 103-23. 6. Scobbo, J. J. and Nakajima, N., Effect of gage length on compressive properties of unidirectional fiber composites. J. Thermoplastic Composite Mater., 1990, 3, 190-201. 7. Peterson, R. E., Stress Concentration Factors. John Wiley, New York, 1974, p. 150. 8. Martin, J., A study of failure characteristics in thermoplastic composite materials. MS thesis, AFIT/ GA/AA/88M-2. School of Engineering, Air Force
9.
10.
1 I.
12.
Institute of Technology, Wright Patterson AFB, OH, March, 1988. Fisher, J. M., A study of failure characteristics in a thermoplastic composite material at high temperature. MS thesis, AFIT/GAE/AA88D-15. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, December 1988. Daniels, J. A., A study of failure characteristics in thermoplastic laminates due to an eccentric circular discontinuity. MS thesis, AFIT/GAE/ENY/89D-06. School of Engineering, Air Force Institute of Technology, Wright Patterson AFB, OH, December, 1989. Sandhu, R. S. and Sendeckyj, G. P.. On delamination of (+ 0,,,/90,&, laminates subjected to tensile loading. Air Force Wright Aeronautical Laboratories Technical Report, AFWDL-TR-87-3058, July, 1987. Martin, L., Sandhu, R. S. and Palozotto, A. N., Experimental and analytical comparisons of failure in thermoplastic composite laminates. J. Exp. Mech.. 1994, 53-65.