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Effect of radial stress relaxation on fibre stress in filament winding of thick composites
Composites
Manujircturing
6 (199.5)
61-11
c 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0956-7143/95/$10.00
Effect of radial stress relaxation on fibre stress in filament winding of thick composites
Evan
A. Kempner”
University
of California
and
H. Thomas
at Los Angeles,
Hahn Los Angeles,
CA 90024-
7597,
USA
During filament winding of thick cylinders, fibre wrinkling often occurs which severely decreases compressive strength. To eliminate fibre wrinkling, appropriate processing conditions must be found. Fibre migration and stress relaxation due to resin flow are generally considered the most important factors affecting fibre buckling. Therefore, the effect of stress relaxation on fibre wrinkling during the filament winding process was investigated. To study the stress development during filament winding of thick cylinders, experiments were carried out using graphite/epoxy prepreg tows as well as dry graphite fibre. Cylinders of approximately 12 mm thickness were hoop wound on a 50.8 mm diameter aluminium mandrel. Winding tensions ranged from 13 to 34 N and winding speed was constant. A foil-type pressure sensor was applied on the mandrel to monitor the interface pressure throughout winding and storage of the cylinder. Significant stress relaxation was found to occur during winding with prepreg tow. Mandrel pressure increased over the winding of the first eight layers or so. However, between the winding of one layer and the next. mandrel pressure dropped quickly. Also, it began to decrease after reaching a maximum value. A stress relaxation analysis was carried out to determine the stress in the cylinders during winding. Several parameters were not known a priori and had to be inferred from the data. Stress distributions following winding were calculated for each case. The radial stress in prepreg wound cylinders was found to relax nearly to zero in the inner part of the tubes. Compressive circumferential stresses occurred throughout each of the cylinders. However, they reached greater magnitudes in the dry wound cylinders due to very low radial moduli. No fibre wrinkling was evident in any of the wound cylinders. (Keywords:
filament
winding;
thick
cylinders;
stress
relaxation
INTRODUCTION
analysis)
of fibre tows on the mandrel and to improve consolidation, a tensile force called the winding tension is applied to the fibre tows. The winding tension exerts radial pressure on the previously wound layers and compacts the cylinder. Compaction occurs because fibres are not tightly packed. The radial fibre motion associated with the compaction reduces the tension in the fibres and continued compaction could cause compressive stresses to develop. However, the very radial pressure that causes compaction also supports the fibres and helps prevent buckling. Thus, compressive axial fibre stress and compressive radial stress are the two competing mechanisms for fibre buckling. As the fibre tows are compacted, the resin is squeezed out. The rate of flow due to compaction will depend on the viscosity of the resin. In dry winding, resins of higher viscosity are used, and hence relatively little resin flow occurs during winding itself. However, during curing, the temperature rise causes a drop in the resin viscosity, and the resin can flow easily accompanied by fibre motion
Filament winding is the predominant manufacturing process for composite cylinders. While winding of thin cylinders is fairly straightforward, fabrication of thick cylinders often results in wavy fibre tows which are detrimental to the compressive strength. To effectively use thick, filament-wound cylinders in compressioncritical applications, proper processing conditions must be found to eliminate the occurrence of fibre wrinkling. Fibre wrinkling results from the development of compressive axial fibre stresses combined with high radial compliance in the filament winding process. This could occur during the winding and/or curing stage. During winding, continuous bands of resin-impregnated fibres are wrapped on to a rotating mandrel. The fibres could be impregnated on-line by pulling them through a liquid resin bath; this is called wet winding. Alternatively, during dry winding, fibres pre-impregnated with B-staged resin (prepregs) are used. For accurate placement
until
* To whom correspondence should be addressed
The stress development during winding has been studied by a number of investigators’-5. A comprehensive
COMPOSITES
cure sets in.
MANUFACTURING
Volume 6 Number 2 1995
67
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
discussion on the stress development at various stages of the filament winding process is given by Tamapol’skii and Beil”. One of the difficulties with the stress analysis is that the effective stress-strain behaviour in the radial direction is non-linear. Tamapol’skii and Beil” presented results based on linear, piecewise linear and non-linear elastic analyses, Cai et ~1.~used a piecewise linear elastic analysis while Springer and co-workers233 as well as Spencer’ used a linear elastic analysis based on an effective radial modulus. Since these investigators (except Tamapol’skii and Beil”) were interested in modelling the whole filament winding process, no experimental correlation was provided for the stressesdue to winding only. As the initial phase of the current research, the stress development was investigated6 during winding of dry glass fibres on a circular mandrel of 58 mm diameter. The wound composite cylinders were about 25 mm thick and contained more than 100 layers. A linear elastic analysis was used and an effective radial modulus was found by fitting the prediction to the experimentally measured pressure at the mandrel surface. The ratio of the hoop modulus to the inferred radial modulus was of the order of 104, indicating a much higher anisotropy than discussed by Tarnapol’skii and Beil”. From the theory-experiment correlation it was concluded that the axial fibre stress was compressive, although small in magnitude, throughout most of the cylinder thicknes8. The compressive nature of the fibre stress was also pointed out elsewhere’. While the small elastic compressive stresses resulting from winding are unlikely to cause fibre buckling, any fibre motion through the viscous resin may change the state of stress further to favour fibre buckling. The change of stress resulting from fibre motion has been studied by the same investigators mentioned earlier2-5. In all cases, Darcy’s law was used in one form or another to represent the resin flow. During winding with prepreg tows, however, the effect of resin flow is typically neglected due to the relatively high viscosity resins used. In ref. 4, the stress development due to winding and curing was assumed to be one of two limiting cases. In one case, resin flow completes during the winding operation. This would occur when using very low viscosity resins as in wet winding. In this situation the stresses due to fibre motion are very important during winding. However, for dry winding, resin flow was assumed to be negligible because winding. time will be much greater than the flow time. In this case, the material was considered as an elastic material during winding. An alternative approach was taken to predict the stress redistribution due to fibre motion by the present authors7. Rather than using Darcy’s law, the radial strain due to fibre motion was represented by a radial creep strain. This approach is more appropriate when the fibre motion is a result of the slack in the wound cylinder rather than of the fibres moving through a liquid resin. As discussed elsewhere4, negligible stress relaxation was assumed during winding. Therefore, the analysis was applied to fully wound cylinders of 100 layers. An initial
68
COMPOSITES
MANUFACTURING
stress distribution in the wound cylinder was calculated using an elastic analysis and numerical simulations were performed for cylinders wound with winding tensions varying from 11.0 to 44.5 N. The compressive axial fibre stress was shown to increase upon relaxation of corn-pressive radial stress, the change increasing with the winding tension. This situation favours fibre buckling. The present paper describes the results of a study to relate the processing conditions to the occurrence of fibre waviness. Because resin flow and fibre migration are considered to be the major factors affecting fibre buckling, the effect of stress relaxation on fibre wrinkling was investigated. An analysis was performed to calculate the stress state within wound cylinders based on data obtained from filament winding experiments using graphite/epoxy prepreg tows. Comparison is provided with results from winding with dry graphite fibre. Although most analyses neglect resin flow during winding with prepreg tows, the present experimental results have shown clearly that significant stress relaxation occurs even at room temperature. Therefore, a stress relaxation analysis was performed to determine the stress development during winding. The results of the analysis and experiments were used to gain a better insight into the parameters that affect fibre wrinkling in thick, filament-wound structures.
ANALYSIS Formulation
During filament winding of thick cylinders, winding of each layer increases the stresses in the previously wound layers due to the winding tension. The compaction causes the fibres within the wound layers to move. The severity of the fibre migration will depend on the resin viscosity and the amount of slack in the wound cylinder. To determine the stress development during filament winding, the stresses accrued due to the application of the winding tension must be considered along with the stress relaxation due to the fibre movement. Suppose k layers have been wound on to a circular mandrel with inner and outer radii denoted by a, and b,, respectively, Figure 1. The inner and outer radii of the kth layer are denoted by ak and bk. The next (k + 1)th layer is wound under a winding tension T. The time required to wind each layer is dependent on the rotational speed of the mandrel, the width of the tow and the length of the mandrel. However, to simplify the analysis, it is assumed that each individual layer is wound instantaneously and between the winding of each subsequent layer there is a pause during which stress relaxation can occur. Therefore, the problem can be separated into two processes. The stresses due to the winding of each layer are considered to be elastically induced and they relax until the next layer is wound.
Volume 6 Number 2 1995
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
assumed to be a function of fibre volume fraction Vr, and given by K = K. exp [--Q( V’, - Vs,)]
(6)
where K. and cy are constants and V, is the initial fibre volume fraction. The fibre volume fraction changes due to radial displacement during stress relaxation Vf
VfO
=
(7)
1 +;+g The stresses induced by the radial creep satisfy the equilibrium equation
New Layer
Composite
aa,
Mandrel Figure
1
Three
components
for stress analysis
The elastic stresses due to winding are obtained from a plane stress solution for a cylindrically orthotropic ring. The ring is subject to external pressure due to the winding of the (k + 1)th layer and internal pressure due to the presence of the mandrel. The linear elastic winding analysis is described in detail in ref. 6. The resultant stresses and radial displacement after winding of the (k + 1)th layer are obtained by summing the initial values with those incurred by the winding of a new layer and those resulting from fibre motion occurring during the pause. Therefore, the total resultant stresses and radial displacement after winding the (k + 1)th layer are given by ($k+l) = $1 + &astic + a,(t) (k--1) = afl + aeglastlc + ao(t) "0 ,,(k+-1)
=
U(kl
+
Uelastic
+
(1) (-4
Note that all stresses, CT,are due to fibre motion and are time-dependent during the stress relaxation. The stressstrain relations are given by t, - f; = -‘T, - LJ,()-ffo (9) 4 Eo to = -00 - vor -CT, (10) E# 6 and the strain-displacement relations by au t, = (11) dr u Fg = (14 I Substituting equations (9)-( 12) into equation (8) results in the following equation for u: ~+~~-~~u=~-t~:(~o~~+l)
(13)
The other equation required for t’; is found by substituting equations (2) (4) (9) and (10) into equation (5):
u(t) (3)
where the superscript k denotes the values after winding the previous layer, elastic represents values obtained by the elastic winding analysis and the time-dependent values are obtained from the fibre motion analysis. Of course, immediately after a layer is wound, the values from the fibre motion analysis are zero. Therefore, the initial radial stress in the cylinder before the stress relaxation analysis is given by (+j = $’
+ &lstlc
(14) The mandrel is assumed to be much stiffer than the composite cylinder, so the radial displacement of the composite cylinder vanishes at its inner boundary. Also, the radial stress at the outer boundary is zero as no external pressure is applied. The boundary conditions necessary for the solution are u=o
(4)
As described in ref. 7, the radial strain resulting from the fibre motion is considered a creep strain and is denoted by 6:‘. Furthermore, the creep strain rate is assumed to be proportional to the total radiai stress: (5) Because the fibre migration will be less when the fibres are tightly packed, the proportionality parameter K is
COMPOSITES
ur = 0
at r = h,
(on the mandrel)
(15)
at r = hk+,
(on the outer cylinder)
(16)
Solving equations (9) and (10) for or and substituting equations (11) and (12) yields the boundary condition at the outer cylinder in a more useful form, in terms of u and $1
CT, = -au- E;+ v,o;u = 0 au >
(
The initial conditions
MANUFACTURING
at r = hk-,
(17)
for the stress relaxation are given
Volume
6 Number
2 1995
69
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
by
adjacent time steps as given by
E;= 0 u=o
at t=O
c
(18)
c
~i+l;j-t’lj=Kj(~~)j+~
att=O
-c;+l,j
At
(19) With the above boundary conditions and initial conditions, u(r, t) and E~(Y,t) can be determined from equations (11) and (12). However, because the equations cannot be solved analytically, an algorithm has been implemented to determine the solution numerically.
( %+l,j+l
+
rj+i
-
%+l,j-1
-
rj-1
+ F%+l,j J
>
%, j+l
-
ui, j-l
rj+i
-
rj-i
+FUi,j
J (21)
Numerical solution
where A = I$/(1 - u~~zQ), and i and j denote the time and radius steps, respectively8. The time step At = 1 s was used for these calculations. (cF)j are obtained from the elastic winding as given in equation (4), and the initial conditions eg,j and uo,j are given by equations (18) and (19). Because Ui+l,j is not known a priori, ey+t,j is calculated at each position, j = 1 to N, by letting Ui+l,j equal Ui, for an initial approximation. Equation (13) is used to calculate Ui+l, j. Representing the differential equation by an implicit finite difference equation at the point (i + l), equation (13) is written
A FORTRAN program was written to calculate the stress development during filament winding based on the elastic winding analysis and the stress relaxation equations detailed above. The partial differential equations, (13) and (14), can be solved using the finite difference method by approximating the derivatives with finite differences. This requires discretizing the problem by establishing a network of grid points through the radius of the cylinder and throughout the time of the simulation. Therefore, every value is evaluated at distinct radial positions for each time step. The nodal values are first determined using the elastic windin equations. When the first layer is wound, (a$l))j and (ge?I, )j are calculated for each point, denoted by the subscript j. n nodes are defined at equal increments through the thickness of the layer, with j = 1 at the mandrel/composite interface and j = n at the outer radius of the layer. For the winding of the (k + 1)th layer, the elastic stress and displacement values are calculated at each of the nodes throughout the first k layers and at n nodes within the new layer. Therefore, the number of nodes in the cylinder after (k + 1) layers have been wound is given by N=(n-l)(k+l)+l (20)
j
ui+l,
j+l
-
2ui+l,
[(rj+l
;
1 Ui+l,j+l +
‘j
(yj+l
c %+I, =
j +
%+l,
j-1
rj-l)]2
-
Ui+l,j-1
-
rj-l)
j+l
-
c Ei+l,
(rj+l
-
rj-1)
j-l
B -rjz”i+l~i
-bt$l,j Yj
where B = Eo/E, and C = q,B + 1. The boundary conditions, (15) and (17) written in terms of the nodal position are given by Ui,1 = 0
For the calculations detailed in this paper, y1= 5 points/ layer was used. Therefore, for a cylinder with 60 total layers, k = 59 and N = 241 total nodes. The behaviour during stress relaxation is calculated by converting equations (13) and (14) into approximate algebraic equations. A Crank-Nicolson representation of equation (14) is obtained by averaging each term at
Ui+l,N
rN
-
(23) %+l,N-1
+
urO”i+l,
N =
rN-l
c ‘%+l, N
(24)
TN
using a backward difference representation for du/dr at j = N. Solution of Ui+l j for j = 1 to N simultaneously is performed by solving the following set of N - 1 equations: -
-2 - B(Ar2)
r:
1 -
1 + &(Arz) B -2 -$(Ars)
&o)
1 1 +-(Ars)
0
0
0
0
0
0
0
0
4+
2r3
3
l -
70
0
2
21;
Car,)
-2-;(Arj) J
J
0
0
-1
1 + 2 (ArN)
0
0
0
0
0
0
0
MANUFACTURING
0
J
0
COMPOSITES
1 +$-(Ar)
Volume 6 Number 2 1995
1,2
%+1,3 . %+l, l
%+l.N
j
Effect of radial stress relaxation:
@+1,3
-2 6+1,2)
(Ar2)
(Ad2
cc;+,
E. A. Kempner and H. T. Hahn
2
r2 %+I,4
-
6+1,2)
(A,.)
_
(Ad2
2
I
= j+*
-
6++1, j-1)
2
-IA -(Arj)
0
where Arj = (rj+i - r,-,)/2. To evaluate the accuracy of the iteration, the differences between the approximated and the calculated values of u,+~,j are summed lu~~~Ss, - Ui+l,
(25)
0 (G+I,
error = 2
Cr~+,,3
jl
j=l
The solution is assumed to have converged if the error is less than a specified allowable error value. The allowable error used in these calculations was of the order of lo-t2 cm. If the solution has not converged, u~+~,i is used as the input for the next iteration. If acceptable error has been reached, the time step i can be incremented and the calculations continue from equation (21). The stress relaxation analysis continues for the time required to wind a given layer. The winding of subsequent layers are performed by adding the elastic stresses incurred during winding and repeating the stress relaxation analysis.
EXPERIMENTAL Filament winding was carried out on an Entec filament winder using both graphite/epoxy prepreg tows and dry graphite tows. Hercules 12 k, AS4/3501-6 prepreg and 12 k, AS4 dry fibres were used. The prepreg had a nominal fibre volume fraction of 61.0%. The prepreg tow was nominally 5.08mm wide and 0.25mm thick. The dry graphite tow was 3.18 mm wide and 0.41 mm thick. The tow was wound circumferentially on an aluminium mandrel over its 50.8 mm mid-section which was bounded by a pair of end plates. The mandrel was 57.7 mm in outside diameter, 3.4 mm thick and 203 mm long. The end plates were fitted on to the mandrel to prevent the wound tow from slipping. These end plates were machined out of transparent PlexiglasTM sheets to enable on-line monitoring of fibre buckling at an edge. Winding tension was applied using an American Sahm tensioner. The winding tensions used ranged from 13 to 34N. During each winding series the winding tension was kept constant throughout and a constant rotational speed of 10.5 revmin~’ was used for each cylinder. A full layer of winding required 9.85 revolutions for the prepreg and 20.0 revolutions for the dry
COMPOSITES
-) 2
---‘iCfF+,,
j
‘i
fibre. The test was only stopped if the tow being laid became crimped or flipped over. Cylinders of up to 60 layers were wound. CuriteTM process pressure sensors were used to measure the mandrel pressure. One sensor and a thermocouple were attached on the mandrel surface and an additional thermocouple was used to measure the ambient temperature. The sensors were 15 mm wide, 23 mm long, 0.3 mm thick and had a 1Omm diameter active area. Two types of sensors were used. The high pressure sensors had an operating range from 0.14 to 1.4 MPa and the low pressure sensors were designed for pressures up to 0.2 MPa. The thermocouple and pressure sensor wires were connected to an Omega 900 data acquisition system through a slip ring. The mandrel! sensor arrangement and the set-up used for these experiments are shown in ref. 6.
RESULTS
AND
DISCUSSION
Previously, filament winding was carried out using dry glass fibres to evaluate the elastic winding model typically used for dry winding6. The pressure at the mandrel/composite interface was measured during winding and compared with that from calculations using the winding model. The mandrel pressure was found to increase during the winding of only the first several layers. The maximum pressure was reached after about six layers and then stayed constant or even decreased slightly with subsequent winding. Because the radial modulus was not known, appropriate values were chosen by fitting the data to the numerical results. Calculations based on the elastic analysis exhibited a similar response to the experimental data when values for the radial modulus were chosen to be about 10 000 times less than the circumferential modulus. Radial modulus was found to increase with greater winding tensions. Similar experiments to those described in ref. 6 were performed using dry graphite fibre. The pressure during winding with dry fibre is shown in Figure 2. Due to the small size of the pressure sensors compared with the winding length, a stepwise increase in pressure occurred as additional layers were wound. Because the sensors were located midway between the end plates, the payout eye traversed to the end of the mandrel and back before an additional layer was wound. It took 20.0 revolutions
MANUFACTURING
Volume 6 Number 2 1995
71
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
Table 1 Effective composite properties Winding tension (N) Dry winding
Prepreg winding
Property
13.35
22.25
31.15
13.35
22.25
31.15
& @Pa) a 4 (MW
137.967 0.22 7.0 0.67 356 0 N/A
148.58 0.22 7.0 0.72 330 0 N/A
156.294 0.22 7.0 0.76 314 0 N/A
131.18 0.22 3.5 0.63 187 0.015 7000
132.741 0.22 28 0.64 185 0.015 7000
140.98 0.22 38 0.68 174 0.015 7000
Vf
Thickness (pm) K. ((MPa s)-‘) cl
0.7 -
-
g 0.6 .-
Experimental Simulation
z 0.6
%0.5-
;0.5
3 0.48 & 0.39 0.2’. 2 za 0.1 .0 ‘0
22.25 N
z 0.2 2 Htu 0.1
13.35 N
20 Time (min)
30
40
Figure 2 Experimental and calculated change in mandrel pressure with time for dry winding Table 2 Effective mandrel properties 68.95 0.33 25.4 28.80
Em @Pa)
2 (mm) b, W-4
to wind a complete layer; therefore, in this case, there was 114 s between sensor response of adjacent layers. The maximum pressure was reached after only about four layers were wound. The pressure then stayed nearly constant throughout the rest of winding. A total of 20 layers were wound. Also shown in Figure 2 are numerical results for change in mandrel pressure with time for each winding tension. The results were obtained by setting I& = 0 to neglect stress relaxation. The effective composite properties and mandrel properties used for the calculations are shown in Tables 1 and 2, respectively. Because radial modulus was not known a priori, it was varied until a reasonable fit was obtained. A radial modulus of 7.0 MPa was adequate for each winding tension. The mandrel pressure during winding with prepreg tows showed significant differences from the results obtained with dry fibre. Figure 3 shows mandrel pressure during winding with prepreg tows for winding tensions of 13.35, 22.25 and 31.15N. Although the resin in the prepreg has high viscosity at room temperature,
72
COMPOSITES
MANUFACTURING
Volume
13.35 N
2 0.4 12 & 0.3
-
10
Bottom Curve:
6 Number
-I
14 0
Figure
10
20
30 40 Time (min)
50
60
3 Mandrel pressure during prepreg winding
significant stress relaxation occurred during winding. While mandrel pressure was constant during the time between winding each layer with dry fibre, a large drop in mandrel pressure occurred when using prepreg tow. The pressure decrease was very rapid at first and slowly tapered off. The maximum mandrel pressure was reached after about three layers for winding at 13.35 and 12 layers at 3 1.15 N. After this point, the pressure decreased on the whole as the stress relaxation continued in the entire wound cylinder. Even though there was little pressure change during the winding of the last several layers, small pressure jumps were evident as each layer was wound. For each of the winding tensions used, the final mandrel pressure after winding 60 layers was approximately the same as the pressure after winding only the first layer. Following winding, each cylinder was left at room temperature for approximately 2 h. Mandrel pressure was continuously monitored during this storage period to measure any further change in pressure. Figure 4 shows mandrel pressure throughout the entire winding and storage at each winding tension. Very little stress relaxation was evident after winding. Finally, the cylinders were cured following the manufacturer’s suggested cure cycle. No augmented pressure was used during the cure. To examine the quality of the wound cylinder, the fully cured tube was cut in half to expose the inner cross-section. At the
2 1995
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
0.76 g 0.74
20.6 H P5 z 0.4 z kO.3
‘g 0.72 L a, 0.7 I
2 0.68 e
; 0.66
I
i? 0.64 0.62
4 xl
0
100
I
10
150
15
line (n-in) Figure
4
Mandrel
pressure
during
prepreg
winding
Figure
and storage
6
Change
in fibre
20
25
Winding
Tension
volume
fraction
with
30
winding
35
(N) tension
0
0.35..
.
e
0.3 .0.25 0.2 --
I
I
I
‘0.15 0.1 .0.05.. 10
Figure
5
Change
15
in effective
20
25
Winding
Tension
layer
thickness
with
30
41t
15
(N)
winding
Figure
tension
winding conditions studied, no fibre ply waviness was evident. However, there were large intertow gaps due to poor consolidation. Consolidation would have been improved if the cylinder had been cured under pressure. However, external pressure would almost certainly have caused fibre wrinkling as the low resin viscosity causes the cylinder to become very compliant. The effective layer thickness was calculated for each cylinder by measuring the thickness after winding and dividing by the number of layers wound, Figure 5. Tighter winding was achieved with higher winding tensions, resulting in smaller effective layer thicknesses. Negligible difference was found in the thicknesses of prepreg wound cylinders before and after curing. Fibre volume fraction was calculated for each cylinder by dividing the total cross-sectional area of the fibres by the total cross-sectional area of one layer v, = 12 OOO*df(rev) f
10
35
(27)
where dr = 8 pm is the diameter of AS4 fibres, rev is the number of revolutions required to wind a layer, 1 is the length of the wound cylinder and t is the effective layer
COMPOSITES
7
Mandrel
pressure
20
25
Winding
Tension
after
first
layer
30
35
(N)
wound
thickness. Fibre volume fractions ranged from 0.63 to 0.68 for prepreg winding and 0.67 to 0.76 for dry winding, Figure 6. These values are higher than they should be considering the poor consolidation evident in the cured cylinders. The unexpectedly high values could have resulted from broken fibres which would result in less fibres per tow than expected. Figure 7 shows the initial mandrel pressure after the first layer was wound for each winding condition and the calculated expected pressure. The expected pressure is different for the prepreg tow than for the dry fibre due to the smaller tow width of the dry fibre. Large variation is evident between the actual and the expected mandrel pressures. This can be attributed to sensor and tow placement variability. The pressure sensor measurement will depend on tow coverage. In general, few gaps and laps occurred during winding. However, uneven tow placement sometimes occurred during the first layer of winding due to an uneven surface created by the wires and the sensor. Because several revolutions were needed for the tow to completely cover the sensor, uneven tow placement could have affected the measurements. As shown for the dry winding, numerical simulations
MANUFACTURING
Volume 6 Number 2 1995
73
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
0.7,
I
F 0.6.. H F 0.5 .I 0.4.B a’ 0.3..
T = 13.35 N
T = 13.35 N
-0.3.. Simulation
-0.4.. , -0.5, 0
0.2
0.4
0.6
0.6
1
0.6
1
0, 10
0
20
s
30
40
50
60
4
-0.1..
U
0
T = 22.25 N
Time (min) Figure 8 13.35N
Change
in mandrel
pressure
with
time,
winding
tension
=
zo.5
-0.2
z 0.4 Iz h 0.3
-0.3
0.4
0.6
T = 31.15 N
-0.1
T = 22.25 N
go.6
0.2
-0.4 ,I”‘.’ I
2 0.2 2 2l.0 0.1
0
I 012
0.4
0.6
0.8
i
Normalized Radius
0 10
0
20
30
40
50
60
Time (min) Figure 9 22.25 N
Change
in mandrel
pressure
with
time,
winding
tension
=
0.7 T = 31.15 N
20.6 PO.5 5CfJ0.4 % ; 0.3 3 0.2 2 Im 0.1 0
Simulation
10
0
20
30
40
50
60
Time (min) Figure 31.15N
10
Change
in mandrel
74
COMPOSITES
pressure
with
time,
MANUFACTURING
winding
tension
=
Figure 11 Radial with dry fibre
stress
distribution
after
winding
60-layer
cylinder
were performed using the algorithm developed earlier. The simulations were used to calculate the stress development during winding accounting for stress relaxation. Because the radial modulus E, and the creep parameters K0 and QI in equation (6) were not known a priori, they were varied until reasonable results were obtained. Although radial modulus will be different under various conditions, the creep values should be the same for all of the winding assuming the resin was at a uniform state for each experiment. To effectively relate the numerical results with the experimental results, many features need to correspond. The features used to fit the calculated results to the winding results were extent of relaxation between layers, maximum mandrel pressure reached during winding, number of layers to reach maximum pressure and pressure after winding. Figures 8-10 show the experimental and calculated values for the mandrel pressure throughout winding for each winding tension. Although the numerical results do not completely correspond with all of the features, considering the variability of the sensors, the trend of the data is approximated well
Volume 6 Number 2 1995
Effect of radial stress relaxation:
-0.2
.-
-0.3
..
-0.4
‘-
E. A. Kempner and H. T. Hahn
60% 5040.. 30 T
T = 13.35
T = 13.35
N
N
I I 1
-301 0
0.2
0.4
0.6
0.8
0
1 z tn -_ 8 g
Ti
-0.4
'-
m
5 E t?! P-
T = 22.25 N 0.2
0.4
0.6
3 1
0.8
50
0.4
0.6
0.8
60 50 40 30 20 10 0 -10 -20 -3OC
T = 22.25
0
.t
0
0.2
0.2
0.4
0.6
N
0.8
1
60T
1
0. -0.1
..
-0.2
'-
-0.3
'.
-0.4
'-
-0.5
I 0
-301 0
T = 31.15 N 0.2
0.4
0.6
0.8
0.2
0.4
0.6
J 1
0.8
Normalized Radius
1
Normalized Radius Figure 12 Radial with prepreg tow
stress
distribution
after
winding
60-layer
cylinder
throughout the winding. The input values used for the calculations are shown in Table I. The usefulness of the model is dependent on the ability to choose appropriate input values. In order to use the simulation as a predictive tool, information on parameter values needs to be available from previous experimental work. In this work, however, the model has been used to provide further information about the experiments that could not be measured on-line. In this case, the desired information for evaluating the filament winding process is the stress state within the cylinders. Subsequently, the analytical model was used to calculate the stress distribution in the cylinders after winding. Figures II and 12 show the radial stress distribution for each winding tension after winding 60 layers for the dry winding and prepreg winding cases, respectively. The radial stress was generally uniform throughout the dry fibre wound cylinders and increased in magnitude with winding tension. However, due to stress relaxation in the prepreg wound cylinders, the radial stress in the inner portion of the cylinders was very
COMPOSITES
Figure cylinder
13 Circumferential with dry fibre
stress
distribution
after
winding
60-layer
small. The stress in the outer portion of the cylinders was similar to that found for dry winding. Because the radial stress provides lateral support for fibres under compressive loading, depending on the circumferential stresses, fibre buckling will be more likely to occur in the inner part of the cylinder. The circumferential stress distributions for dry winding and prepreg winding are shown in Figures 13 and 14. The circumferential stress has large discontinuities at the layer interfaces. Throughout most of the cylinders, negative circumferential stresses occur. For dry winding the negative stresses increased in magnitude with greater winding tensions. However, for prepreg winding the compressive stresses of greatest magnitude occurred at the smallest winding tension. In all cases, greater compressive stresses occurred for dry winding than for prepreg winding. To understand how the development of compressive fibre stresses is affected by winding tension and radial modulus, simulations were run at various winding conditions. Figure 15 shows maximum compressive stress occurring in a 60-layer cylinder calculated at various combinations of radial modulus and winding
MANUFACTURING
Volume 6 Number 2 1995
75
Effect of radial stress relaxation:
T A
60 50 40 30 20 10 0 -10 -20 -30
g 2 al
60 50 40
R
;;
3 5 i
10 0 -10
E
-30 -20
e
. ‘. ‘. ‘-
0I
T = 13.35
N
0.4
0.6
0.8
I I 1
0.4
0.6
0.8
1
0.2
1
0
;‘;
U
E. A. Kempner and H. T. Hahn
0.2
60 50 40
T = 31.15
CONCLUSIONS
N
-20 ‘. 0
0.2
0.4
0.6
0.8
1
Normalized Radius
Figure 14 Circumferential cylinder with prepreg tow
stress
distribution
after
winding
increase in stress as radial modulus decreased. Therefore, the compliance of the cylinder is the most significant factor affecting the development of compressive fibre stresses. For winding tensions of 22.25 and 3 1.15 N, the radial modulus determined for prepreg winding was signilicantly larger than for dry winding. Subsequently, much smaller compressive stresses occurred in those prepreg wound tubes. At the lowest winding tension, T = 13.35 N, the prepreg winding modulus was slightly lower than for dry winding, resulting in similar circumferential stress distributions. In general, greater radial stiffness is expected for prepreg winding than dry winding due to resistance provided by the resin. Also, higher winding tensions tend to increase the radial modulus by improving compaction of the cylinder. Yet, stiffness may be increased further by using other means to improve consolidation during winding.
60-layer
In this study, the effect of stress relaxation during filament winding was investigated. Cylinders were wound of approximately 12 mm thickness with pressure gauges at the mandrel/composite interface. Winding tensions ranged from 13 to 34 N. Results were compared from winding with graphite/epoxy prepreg tow and dry graphite tow. Despite high resin viscosity, significant stress relaxation was evident during prepreg winding while little relaxation, if any, occurred using dry fibre. An analytical model was developed to calculate change in stress due to relaxation during winding. Several parameters were not known beforehand and had to be inferred from the data. Stress distributions following winding were- calculated for each case. The radial stress in prepreg wound cylinders was found to relax nearly to zero in the inner part of the tubes. Compressive circumferential stresses occurred throughout each of the cylinders. However, they reached greater magnitudes in the dry wound cylinders due to very low radial moduli. No fibre wrinkling was evident in any of the wound cylinders.
ACKNOWLEDGEMENTS 10
20
Wizing Tension (N) Figure 15 ing tension
Maximum and radial
compressive modulus
circumferential
stress
W~SUS wind-
tension. The creep parameters found for prepreg winding were used, but compressive stresses were less than 2% smaller when K,, = 0 was used. The magnitude of compressive stresses increased approximately linearly with winding tension. However, there was an exponential
76
COMPOSITES
MANUFACTURING
The present paper is based on work supported by the Office of Naval Research under Grant NOOO14-92-J1846. Sincere appreciation is extended to Yapa D. S. Rajapakse, Scientific Officer.
REFERENCES 1
2
Tarnapol’skii, Y.M. and Beil’, A.I. in ‘Handbook of Composites, Vol. 4: Fabrication of Composites’ (Ed% A. Kelly and S.T. Mileikoj. Elsevier Science Publisher B.V., Amsterdam, 1983, Ch. II, p. 45 Lee, S.Y. and Springer, G.S. J. Compos. Muter. 1990, 24, 1270
Volume 6 Number 2 1995
Effect of radial stress relaxation: 3 4 5 6
Calms, E.P., Lee, S.Y. and Springer, G.S. J. Compos. Mater. 1990,24, 1299 Cai. Z., Gutowski. T.G. and Allen, S. J. Compos. Mater. 1992, 26, 1374 Spencer. BE. Ph.D. rhesis, The University of Nebraska-Lincoln, 1988 Hahn, H.T.. Kempner. E.A. and Lee. S.S. Comoosires Manufacturing 1993. 4(3), i47
COMPOSITES
7
8
E. A. Kempner and H. T. Hahn
Kempner, E.A. and Hahn, H.T. in ‘Composites Modeling and Processing Science, Proc. 9th Int. Conf. Composite Materials’, Woodhead Publishing Company. Cambridge and Univ. of Zaragoza, Spain, 1993, p. 462 Carnahan, B., Luther, H.A. and Wilkes, J.O. ‘Applied Numerical Methods’, John Wiley and Sons, Inc.. New York, 1969. p. 429
MANUFACTURING
Volume 6 Number 2 1995
77
Manujircturing
6 (199.5)
61-11
c 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0956-7143/95/$10.00
Effect of radial stress relaxation on fibre stress in filament winding of thick composites
Evan
A. Kempner”
University
of California
and
H. Thomas
at Los Angeles,
Hahn Los Angeles,
CA 90024-
7597,
USA
During filament winding of thick cylinders, fibre wrinkling often occurs which severely decreases compressive strength. To eliminate fibre wrinkling, appropriate processing conditions must be found. Fibre migration and stress relaxation due to resin flow are generally considered the most important factors affecting fibre buckling. Therefore, the effect of stress relaxation on fibre wrinkling during the filament winding process was investigated. To study the stress development during filament winding of thick cylinders, experiments were carried out using graphite/epoxy prepreg tows as well as dry graphite fibre. Cylinders of approximately 12 mm thickness were hoop wound on a 50.8 mm diameter aluminium mandrel. Winding tensions ranged from 13 to 34 N and winding speed was constant. A foil-type pressure sensor was applied on the mandrel to monitor the interface pressure throughout winding and storage of the cylinder. Significant stress relaxation was found to occur during winding with prepreg tow. Mandrel pressure increased over the winding of the first eight layers or so. However, between the winding of one layer and the next. mandrel pressure dropped quickly. Also, it began to decrease after reaching a maximum value. A stress relaxation analysis was carried out to determine the stress in the cylinders during winding. Several parameters were not known a priori and had to be inferred from the data. Stress distributions following winding were calculated for each case. The radial stress in prepreg wound cylinders was found to relax nearly to zero in the inner part of the tubes. Compressive circumferential stresses occurred throughout each of the cylinders. However, they reached greater magnitudes in the dry wound cylinders due to very low radial moduli. No fibre wrinkling was evident in any of the wound cylinders. (Keywords:
filament
winding;
thick
cylinders;
stress
relaxation
INTRODUCTION
analysis)
of fibre tows on the mandrel and to improve consolidation, a tensile force called the winding tension is applied to the fibre tows. The winding tension exerts radial pressure on the previously wound layers and compacts the cylinder. Compaction occurs because fibres are not tightly packed. The radial fibre motion associated with the compaction reduces the tension in the fibres and continued compaction could cause compressive stresses to develop. However, the very radial pressure that causes compaction also supports the fibres and helps prevent buckling. Thus, compressive axial fibre stress and compressive radial stress are the two competing mechanisms for fibre buckling. As the fibre tows are compacted, the resin is squeezed out. The rate of flow due to compaction will depend on the viscosity of the resin. In dry winding, resins of higher viscosity are used, and hence relatively little resin flow occurs during winding itself. However, during curing, the temperature rise causes a drop in the resin viscosity, and the resin can flow easily accompanied by fibre motion
Filament winding is the predominant manufacturing process for composite cylinders. While winding of thin cylinders is fairly straightforward, fabrication of thick cylinders often results in wavy fibre tows which are detrimental to the compressive strength. To effectively use thick, filament-wound cylinders in compressioncritical applications, proper processing conditions must be found to eliminate the occurrence of fibre wrinkling. Fibre wrinkling results from the development of compressive axial fibre stresses combined with high radial compliance in the filament winding process. This could occur during the winding and/or curing stage. During winding, continuous bands of resin-impregnated fibres are wrapped on to a rotating mandrel. The fibres could be impregnated on-line by pulling them through a liquid resin bath; this is called wet winding. Alternatively, during dry winding, fibres pre-impregnated with B-staged resin (prepregs) are used. For accurate placement
until
* To whom correspondence should be addressed
The stress development during winding has been studied by a number of investigators’-5. A comprehensive
COMPOSITES
cure sets in.
MANUFACTURING
Volume 6 Number 2 1995
67
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
discussion on the stress development at various stages of the filament winding process is given by Tamapol’skii and Beil”. One of the difficulties with the stress analysis is that the effective stress-strain behaviour in the radial direction is non-linear. Tamapol’skii and Beil” presented results based on linear, piecewise linear and non-linear elastic analyses, Cai et ~1.~used a piecewise linear elastic analysis while Springer and co-workers233 as well as Spencer’ used a linear elastic analysis based on an effective radial modulus. Since these investigators (except Tamapol’skii and Beil”) were interested in modelling the whole filament winding process, no experimental correlation was provided for the stressesdue to winding only. As the initial phase of the current research, the stress development was investigated6 during winding of dry glass fibres on a circular mandrel of 58 mm diameter. The wound composite cylinders were about 25 mm thick and contained more than 100 layers. A linear elastic analysis was used and an effective radial modulus was found by fitting the prediction to the experimentally measured pressure at the mandrel surface. The ratio of the hoop modulus to the inferred radial modulus was of the order of 104, indicating a much higher anisotropy than discussed by Tarnapol’skii and Beil”. From the theory-experiment correlation it was concluded that the axial fibre stress was compressive, although small in magnitude, throughout most of the cylinder thicknes8. The compressive nature of the fibre stress was also pointed out elsewhere’. While the small elastic compressive stresses resulting from winding are unlikely to cause fibre buckling, any fibre motion through the viscous resin may change the state of stress further to favour fibre buckling. The change of stress resulting from fibre motion has been studied by the same investigators mentioned earlier2-5. In all cases, Darcy’s law was used in one form or another to represent the resin flow. During winding with prepreg tows, however, the effect of resin flow is typically neglected due to the relatively high viscosity resins used. In ref. 4, the stress development due to winding and curing was assumed to be one of two limiting cases. In one case, resin flow completes during the winding operation. This would occur when using very low viscosity resins as in wet winding. In this situation the stresses due to fibre motion are very important during winding. However, for dry winding, resin flow was assumed to be negligible because winding. time will be much greater than the flow time. In this case, the material was considered as an elastic material during winding. An alternative approach was taken to predict the stress redistribution due to fibre motion by the present authors7. Rather than using Darcy’s law, the radial strain due to fibre motion was represented by a radial creep strain. This approach is more appropriate when the fibre motion is a result of the slack in the wound cylinder rather than of the fibres moving through a liquid resin. As discussed elsewhere4, negligible stress relaxation was assumed during winding. Therefore, the analysis was applied to fully wound cylinders of 100 layers. An initial
68
COMPOSITES
MANUFACTURING
stress distribution in the wound cylinder was calculated using an elastic analysis and numerical simulations were performed for cylinders wound with winding tensions varying from 11.0 to 44.5 N. The compressive axial fibre stress was shown to increase upon relaxation of corn-pressive radial stress, the change increasing with the winding tension. This situation favours fibre buckling. The present paper describes the results of a study to relate the processing conditions to the occurrence of fibre waviness. Because resin flow and fibre migration are considered to be the major factors affecting fibre buckling, the effect of stress relaxation on fibre wrinkling was investigated. An analysis was performed to calculate the stress state within wound cylinders based on data obtained from filament winding experiments using graphite/epoxy prepreg tows. Comparison is provided with results from winding with dry graphite fibre. Although most analyses neglect resin flow during winding with prepreg tows, the present experimental results have shown clearly that significant stress relaxation occurs even at room temperature. Therefore, a stress relaxation analysis was performed to determine the stress development during winding. The results of the analysis and experiments were used to gain a better insight into the parameters that affect fibre wrinkling in thick, filament-wound structures.
ANALYSIS Formulation
During filament winding of thick cylinders, winding of each layer increases the stresses in the previously wound layers due to the winding tension. The compaction causes the fibres within the wound layers to move. The severity of the fibre migration will depend on the resin viscosity and the amount of slack in the wound cylinder. To determine the stress development during filament winding, the stresses accrued due to the application of the winding tension must be considered along with the stress relaxation due to the fibre movement. Suppose k layers have been wound on to a circular mandrel with inner and outer radii denoted by a, and b,, respectively, Figure 1. The inner and outer radii of the kth layer are denoted by ak and bk. The next (k + 1)th layer is wound under a winding tension T. The time required to wind each layer is dependent on the rotational speed of the mandrel, the width of the tow and the length of the mandrel. However, to simplify the analysis, it is assumed that each individual layer is wound instantaneously and between the winding of each subsequent layer there is a pause during which stress relaxation can occur. Therefore, the problem can be separated into two processes. The stresses due to the winding of each layer are considered to be elastically induced and they relax until the next layer is wound.
Volume 6 Number 2 1995
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
assumed to be a function of fibre volume fraction Vr, and given by K = K. exp [--Q( V’, - Vs,)]
(6)
where K. and cy are constants and V, is the initial fibre volume fraction. The fibre volume fraction changes due to radial displacement during stress relaxation Vf
VfO
=
(7)
1 +;+g The stresses induced by the radial creep satisfy the equilibrium equation
New Layer
Composite
aa,
Mandrel Figure
1
Three
components
for stress analysis
The elastic stresses due to winding are obtained from a plane stress solution for a cylindrically orthotropic ring. The ring is subject to external pressure due to the winding of the (k + 1)th layer and internal pressure due to the presence of the mandrel. The linear elastic winding analysis is described in detail in ref. 6. The resultant stresses and radial displacement after winding of the (k + 1)th layer are obtained by summing the initial values with those incurred by the winding of a new layer and those resulting from fibre motion occurring during the pause. Therefore, the total resultant stresses and radial displacement after winding the (k + 1)th layer are given by ($k+l) = $1 + &astic + a,(t) (k--1) = afl + aeglastlc + ao(t) "0 ,,(k+-1)
=
U(kl
+
Uelastic
+
(1) (-4
Note that all stresses, CT,are due to fibre motion and are time-dependent during the stress relaxation. The stressstrain relations are given by t, - f; = -‘T, - LJ,()-ffo (9) 4 Eo to = -00 - vor -CT, (10) E# 6 and the strain-displacement relations by au t, = (11) dr u Fg = (14 I Substituting equations (9)-( 12) into equation (8) results in the following equation for u: ~+~~-~~u=~-t~:(~o~~+l)
(13)
The other equation required for t’; is found by substituting equations (2) (4) (9) and (10) into equation (5):
u(t) (3)
where the superscript k denotes the values after winding the previous layer, elastic represents values obtained by the elastic winding analysis and the time-dependent values are obtained from the fibre motion analysis. Of course, immediately after a layer is wound, the values from the fibre motion analysis are zero. Therefore, the initial radial stress in the cylinder before the stress relaxation analysis is given by (+j = $’
+ &lstlc
(14) The mandrel is assumed to be much stiffer than the composite cylinder, so the radial displacement of the composite cylinder vanishes at its inner boundary. Also, the radial stress at the outer boundary is zero as no external pressure is applied. The boundary conditions necessary for the solution are u=o
(4)
As described in ref. 7, the radial strain resulting from the fibre motion is considered a creep strain and is denoted by 6:‘. Furthermore, the creep strain rate is assumed to be proportional to the total radiai stress: (5) Because the fibre migration will be less when the fibres are tightly packed, the proportionality parameter K is
COMPOSITES
ur = 0
at r = h,
(on the mandrel)
(15)
at r = hk+,
(on the outer cylinder)
(16)
Solving equations (9) and (10) for or and substituting equations (11) and (12) yields the boundary condition at the outer cylinder in a more useful form, in terms of u and $1
CT, = -au- E;+ v,o;u = 0 au >
(
The initial conditions
MANUFACTURING
at r = hk-,
(17)
for the stress relaxation are given
Volume
6 Number
2 1995
69
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
by
adjacent time steps as given by
E;= 0 u=o
at t=O
c
(18)
c
~i+l;j-t’lj=Kj(~~)j+~
att=O
-c;+l,j
At
(19) With the above boundary conditions and initial conditions, u(r, t) and E~(Y,t) can be determined from equations (11) and (12). However, because the equations cannot be solved analytically, an algorithm has been implemented to determine the solution numerically.
( %+l,j+l
+
rj+i
-
%+l,j-1
-
rj-1
+ F%+l,j J
>
%, j+l
-
ui, j-l
rj+i
-
rj-i
+FUi,j
J (21)
Numerical solution
where A = I$/(1 - u~~zQ), and i and j denote the time and radius steps, respectively8. The time step At = 1 s was used for these calculations. (cF)j are obtained from the elastic winding as given in equation (4), and the initial conditions eg,j and uo,j are given by equations (18) and (19). Because Ui+l,j is not known a priori, ey+t,j is calculated at each position, j = 1 to N, by letting Ui+l,j equal Ui, for an initial approximation. Equation (13) is used to calculate Ui+l, j. Representing the differential equation by an implicit finite difference equation at the point (i + l), equation (13) is written
A FORTRAN program was written to calculate the stress development during filament winding based on the elastic winding analysis and the stress relaxation equations detailed above. The partial differential equations, (13) and (14), can be solved using the finite difference method by approximating the derivatives with finite differences. This requires discretizing the problem by establishing a network of grid points through the radius of the cylinder and throughout the time of the simulation. Therefore, every value is evaluated at distinct radial positions for each time step. The nodal values are first determined using the elastic windin equations. When the first layer is wound, (a$l))j and (ge?I, )j are calculated for each point, denoted by the subscript j. n nodes are defined at equal increments through the thickness of the layer, with j = 1 at the mandrel/composite interface and j = n at the outer radius of the layer. For the winding of the (k + 1)th layer, the elastic stress and displacement values are calculated at each of the nodes throughout the first k layers and at n nodes within the new layer. Therefore, the number of nodes in the cylinder after (k + 1) layers have been wound is given by N=(n-l)(k+l)+l (20)
j
ui+l,
j+l
-
2ui+l,
[(rj+l
;
1 Ui+l,j+l +
‘j
(yj+l
c %+I, =
j +
%+l,
j-1
rj-l)]2
-
Ui+l,j-1
-
rj-l)
j+l
-
c Ei+l,
(rj+l
-
rj-1)
j-l
B -rjz”i+l~i
-bt$l,j Yj
where B = Eo/E, and C = q,B + 1. The boundary conditions, (15) and (17) written in terms of the nodal position are given by Ui,1 = 0
For the calculations detailed in this paper, y1= 5 points/ layer was used. Therefore, for a cylinder with 60 total layers, k = 59 and N = 241 total nodes. The behaviour during stress relaxation is calculated by converting equations (13) and (14) into approximate algebraic equations. A Crank-Nicolson representation of equation (14) is obtained by averaging each term at
Ui+l,N
rN
-
(23) %+l,N-1
+
urO”i+l,
N =
rN-l
c ‘%+l, N
(24)
TN
using a backward difference representation for du/dr at j = N. Solution of Ui+l j for j = 1 to N simultaneously is performed by solving the following set of N - 1 equations: -
-2 - B(Ar2)
r:
1 -
1 + &(Arz) B -2 -$(Ars)
&o)
1 1 +-(Ars)
0
0
0
0
0
0
0
0
4+
2r3
3
l -
70
0
2
21;
Car,)
-2-;(Arj) J
J
0
0
-1
1 + 2 (ArN)
0
0
0
0
0
0
0
MANUFACTURING
0
J
0
COMPOSITES
1 +$-(Ar)
Volume 6 Number 2 1995
1,2
%+1,3 . %+l, l
%+l.N
j
Effect of radial stress relaxation:
@+1,3
-2 6+1,2)
(Ar2)
(Ad2
cc;+,
E. A. Kempner and H. T. Hahn
2
r2 %+I,4
-
6+1,2)
(A,.)
_
(Ad2
2
I
= j+*
-
6++1, j-1)
2
-IA -(Arj)
0
where Arj = (rj+i - r,-,)/2. To evaluate the accuracy of the iteration, the differences between the approximated and the calculated values of u,+~,j are summed lu~~~Ss, - Ui+l,
(25)
0 (G+I,
error = 2
Cr~+,,3
jl
j=l
The solution is assumed to have converged if the error is less than a specified allowable error value. The allowable error used in these calculations was of the order of lo-t2 cm. If the solution has not converged, u~+~,i is used as the input for the next iteration. If acceptable error has been reached, the time step i can be incremented and the calculations continue from equation (21). The stress relaxation analysis continues for the time required to wind a given layer. The winding of subsequent layers are performed by adding the elastic stresses incurred during winding and repeating the stress relaxation analysis.
EXPERIMENTAL Filament winding was carried out on an Entec filament winder using both graphite/epoxy prepreg tows and dry graphite tows. Hercules 12 k, AS4/3501-6 prepreg and 12 k, AS4 dry fibres were used. The prepreg had a nominal fibre volume fraction of 61.0%. The prepreg tow was nominally 5.08mm wide and 0.25mm thick. The dry graphite tow was 3.18 mm wide and 0.41 mm thick. The tow was wound circumferentially on an aluminium mandrel over its 50.8 mm mid-section which was bounded by a pair of end plates. The mandrel was 57.7 mm in outside diameter, 3.4 mm thick and 203 mm long. The end plates were fitted on to the mandrel to prevent the wound tow from slipping. These end plates were machined out of transparent PlexiglasTM sheets to enable on-line monitoring of fibre buckling at an edge. Winding tension was applied using an American Sahm tensioner. The winding tensions used ranged from 13 to 34N. During each winding series the winding tension was kept constant throughout and a constant rotational speed of 10.5 revmin~’ was used for each cylinder. A full layer of winding required 9.85 revolutions for the prepreg and 20.0 revolutions for the dry
COMPOSITES
-) 2
---‘iCfF+,,
j
‘i
fibre. The test was only stopped if the tow being laid became crimped or flipped over. Cylinders of up to 60 layers were wound. CuriteTM process pressure sensors were used to measure the mandrel pressure. One sensor and a thermocouple were attached on the mandrel surface and an additional thermocouple was used to measure the ambient temperature. The sensors were 15 mm wide, 23 mm long, 0.3 mm thick and had a 1Omm diameter active area. Two types of sensors were used. The high pressure sensors had an operating range from 0.14 to 1.4 MPa and the low pressure sensors were designed for pressures up to 0.2 MPa. The thermocouple and pressure sensor wires were connected to an Omega 900 data acquisition system through a slip ring. The mandrel! sensor arrangement and the set-up used for these experiments are shown in ref. 6.
RESULTS
AND
DISCUSSION
Previously, filament winding was carried out using dry glass fibres to evaluate the elastic winding model typically used for dry winding6. The pressure at the mandrel/composite interface was measured during winding and compared with that from calculations using the winding model. The mandrel pressure was found to increase during the winding of only the first several layers. The maximum pressure was reached after about six layers and then stayed constant or even decreased slightly with subsequent winding. Because the radial modulus was not known, appropriate values were chosen by fitting the data to the numerical results. Calculations based on the elastic analysis exhibited a similar response to the experimental data when values for the radial modulus were chosen to be about 10 000 times less than the circumferential modulus. Radial modulus was found to increase with greater winding tensions. Similar experiments to those described in ref. 6 were performed using dry graphite fibre. The pressure during winding with dry fibre is shown in Figure 2. Due to the small size of the pressure sensors compared with the winding length, a stepwise increase in pressure occurred as additional layers were wound. Because the sensors were located midway between the end plates, the payout eye traversed to the end of the mandrel and back before an additional layer was wound. It took 20.0 revolutions
MANUFACTURING
Volume 6 Number 2 1995
71
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
Table 1 Effective composite properties Winding tension (N) Dry winding
Prepreg winding
Property
13.35
22.25
31.15
13.35
22.25
31.15
& @Pa) a 4 (MW
137.967 0.22 7.0 0.67 356 0 N/A
148.58 0.22 7.0 0.72 330 0 N/A
156.294 0.22 7.0 0.76 314 0 N/A
131.18 0.22 3.5 0.63 187 0.015 7000
132.741 0.22 28 0.64 185 0.015 7000
140.98 0.22 38 0.68 174 0.015 7000
Vf
Thickness (pm) K. ((MPa s)-‘) cl
0.7 -
-
g 0.6 .-
Experimental Simulation
z 0.6
%0.5-
;0.5
3 0.48 & 0.39 0.2’. 2 za 0.1 .0 ‘0
22.25 N
z 0.2 2 Htu 0.1
13.35 N
20 Time (min)
30
40
Figure 2 Experimental and calculated change in mandrel pressure with time for dry winding Table 2 Effective mandrel properties 68.95 0.33 25.4 28.80
Em @Pa)
2 (mm) b, W-4
to wind a complete layer; therefore, in this case, there was 114 s between sensor response of adjacent layers. The maximum pressure was reached after only about four layers were wound. The pressure then stayed nearly constant throughout the rest of winding. A total of 20 layers were wound. Also shown in Figure 2 are numerical results for change in mandrel pressure with time for each winding tension. The results were obtained by setting I& = 0 to neglect stress relaxation. The effective composite properties and mandrel properties used for the calculations are shown in Tables 1 and 2, respectively. Because radial modulus was not known a priori, it was varied until a reasonable fit was obtained. A radial modulus of 7.0 MPa was adequate for each winding tension. The mandrel pressure during winding with prepreg tows showed significant differences from the results obtained with dry fibre. Figure 3 shows mandrel pressure during winding with prepreg tows for winding tensions of 13.35, 22.25 and 31.15N. Although the resin in the prepreg has high viscosity at room temperature,
72
COMPOSITES
MANUFACTURING
Volume
13.35 N
2 0.4 12 & 0.3
-
10
Bottom Curve:
6 Number
-I
14 0
Figure
10
20
30 40 Time (min)
50
60
3 Mandrel pressure during prepreg winding
significant stress relaxation occurred during winding. While mandrel pressure was constant during the time between winding each layer with dry fibre, a large drop in mandrel pressure occurred when using prepreg tow. The pressure decrease was very rapid at first and slowly tapered off. The maximum mandrel pressure was reached after about three layers for winding at 13.35 and 12 layers at 3 1.15 N. After this point, the pressure decreased on the whole as the stress relaxation continued in the entire wound cylinder. Even though there was little pressure change during the winding of the last several layers, small pressure jumps were evident as each layer was wound. For each of the winding tensions used, the final mandrel pressure after winding 60 layers was approximately the same as the pressure after winding only the first layer. Following winding, each cylinder was left at room temperature for approximately 2 h. Mandrel pressure was continuously monitored during this storage period to measure any further change in pressure. Figure 4 shows mandrel pressure throughout the entire winding and storage at each winding tension. Very little stress relaxation was evident after winding. Finally, the cylinders were cured following the manufacturer’s suggested cure cycle. No augmented pressure was used during the cure. To examine the quality of the wound cylinder, the fully cured tube was cut in half to expose the inner cross-section. At the
2 1995
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
0.76 g 0.74
20.6 H P5 z 0.4 z kO.3
‘g 0.72 L a, 0.7 I
2 0.68 e
; 0.66
I
i? 0.64 0.62
4 xl
0
100
I
10
150
15
line (n-in) Figure
4
Mandrel
pressure
during
prepreg
winding
Figure
and storage
6
Change
in fibre
20
25
Winding
Tension
volume
fraction
with
30
winding
35
(N) tension
0
0.35..
.
e
0.3 .0.25 0.2 --
I
I
I
‘0.15 0.1 .0.05.. 10
Figure
5
Change
15
in effective
20
25
Winding
Tension
layer
thickness
with
30
41t
15
(N)
winding
Figure
tension
winding conditions studied, no fibre ply waviness was evident. However, there were large intertow gaps due to poor consolidation. Consolidation would have been improved if the cylinder had been cured under pressure. However, external pressure would almost certainly have caused fibre wrinkling as the low resin viscosity causes the cylinder to become very compliant. The effective layer thickness was calculated for each cylinder by measuring the thickness after winding and dividing by the number of layers wound, Figure 5. Tighter winding was achieved with higher winding tensions, resulting in smaller effective layer thicknesses. Negligible difference was found in the thicknesses of prepreg wound cylinders before and after curing. Fibre volume fraction was calculated for each cylinder by dividing the total cross-sectional area of the fibres by the total cross-sectional area of one layer v, = 12 OOO*df(rev) f
10
35
(27)
where dr = 8 pm is the diameter of AS4 fibres, rev is the number of revolutions required to wind a layer, 1 is the length of the wound cylinder and t is the effective layer
COMPOSITES
7
Mandrel
pressure
20
25
Winding
Tension
after
first
layer
30
35
(N)
wound
thickness. Fibre volume fractions ranged from 0.63 to 0.68 for prepreg winding and 0.67 to 0.76 for dry winding, Figure 6. These values are higher than they should be considering the poor consolidation evident in the cured cylinders. The unexpectedly high values could have resulted from broken fibres which would result in less fibres per tow than expected. Figure 7 shows the initial mandrel pressure after the first layer was wound for each winding condition and the calculated expected pressure. The expected pressure is different for the prepreg tow than for the dry fibre due to the smaller tow width of the dry fibre. Large variation is evident between the actual and the expected mandrel pressures. This can be attributed to sensor and tow placement variability. The pressure sensor measurement will depend on tow coverage. In general, few gaps and laps occurred during winding. However, uneven tow placement sometimes occurred during the first layer of winding due to an uneven surface created by the wires and the sensor. Because several revolutions were needed for the tow to completely cover the sensor, uneven tow placement could have affected the measurements. As shown for the dry winding, numerical simulations
MANUFACTURING
Volume 6 Number 2 1995
73
Effect of radial stress relaxation:
E. A. Kempner and H. T. Hahn
0.7,
I
F 0.6.. H F 0.5 .I 0.4.B a’ 0.3..
T = 13.35 N
T = 13.35 N
-0.3.. Simulation
-0.4.. , -0.5, 0
0.2
0.4
0.6
0.6
1
0.6
1
0, 10
0
20
s
30
40
50
60
4
-0.1..
U
0
T = 22.25 N
Time (min) Figure 8 13.35N
Change
in mandrel
pressure
with
time,
winding
tension
=
zo.5
-0.2
z 0.4 Iz h 0.3
-0.3
0.4
0.6
T = 31.15 N
-0.1
T = 22.25 N
go.6
0.2
-0.4 ,I”‘.’ I
2 0.2 2 2l.0 0.1
0
I 012
0.4
0.6
0.8
i
Normalized Radius
0 10
0
20
30
40
50
60
Time (min) Figure 9 22.25 N
Change
in mandrel
pressure
with
time,
winding
tension
=
0.7 T = 31.15 N
20.6 PO.5 5CfJ0.4 % ; 0.3 3 0.2 2 Im 0.1 0
Simulation
10
0
20
30
40
50
60
Time (min) Figure 31.15N
10
Change
in mandrel
74
COMPOSITES
pressure
with
time,
MANUFACTURING
winding
tension
=
Figure 11 Radial with dry fibre
stress
distribution
after
winding
60-layer
cylinder
were performed using the algorithm developed earlier. The simulations were used to calculate the stress development during winding accounting for stress relaxation. Because the radial modulus E, and the creep parameters K0 and QI in equation (6) were not known a priori, they were varied until reasonable results were obtained. Although radial modulus will be different under various conditions, the creep values should be the same for all of the winding assuming the resin was at a uniform state for each experiment. To effectively relate the numerical results with the experimental results, many features need to correspond. The features used to fit the calculated results to the winding results were extent of relaxation between layers, maximum mandrel pressure reached during winding, number of layers to reach maximum pressure and pressure after winding. Figures 8-10 show the experimental and calculated values for the mandrel pressure throughout winding for each winding tension. Although the numerical results do not completely correspond with all of the features, considering the variability of the sensors, the trend of the data is approximated well
Volume 6 Number 2 1995
Effect of radial stress relaxation:
-0.2
.-
-0.3
..
-0.4
‘-
E. A. Kempner and H. T. Hahn
60% 5040.. 30 T
T = 13.35
T = 13.35
N
N
I I 1
-301 0
0.2
0.4
0.6
0.8
0
1 z tn -_ 8 g
Ti
-0.4
'-
m
5 E t?! P-
T = 22.25 N 0.2
0.4
0.6
3 1
0.8
50
0.4
0.6
0.8
60 50 40 30 20 10 0 -10 -20 -3OC
T = 22.25
0
.t
0
0.2
0.2
0.4
0.6
N
0.8
1
60T
1
0. -0.1
..
-0.2
'-
-0.3
'.
-0.4
'-
-0.5
I 0
-301 0
T = 31.15 N 0.2
0.4
0.6
0.8
0.2
0.4
0.6
J 1
0.8
Normalized Radius
1
Normalized Radius Figure 12 Radial with prepreg tow
stress
distribution
after
winding
60-layer
cylinder
throughout the winding. The input values used for the calculations are shown in Table I. The usefulness of the model is dependent on the ability to choose appropriate input values. In order to use the simulation as a predictive tool, information on parameter values needs to be available from previous experimental work. In this work, however, the model has been used to provide further information about the experiments that could not be measured on-line. In this case, the desired information for evaluating the filament winding process is the stress state within the cylinders. Subsequently, the analytical model was used to calculate the stress distribution in the cylinders after winding. Figures II and 12 show the radial stress distribution for each winding tension after winding 60 layers for the dry winding and prepreg winding cases, respectively. The radial stress was generally uniform throughout the dry fibre wound cylinders and increased in magnitude with winding tension. However, due to stress relaxation in the prepreg wound cylinders, the radial stress in the inner portion of the cylinders was very
COMPOSITES
Figure cylinder
13 Circumferential with dry fibre
stress
distribution
after
winding
60-layer
small. The stress in the outer portion of the cylinders was similar to that found for dry winding. Because the radial stress provides lateral support for fibres under compressive loading, depending on the circumferential stresses, fibre buckling will be more likely to occur in the inner part of the cylinder. The circumferential stress distributions for dry winding and prepreg winding are shown in Figures 13 and 14. The circumferential stress has large discontinuities at the layer interfaces. Throughout most of the cylinders, negative circumferential stresses occur. For dry winding the negative stresses increased in magnitude with greater winding tensions. However, for prepreg winding the compressive stresses of greatest magnitude occurred at the smallest winding tension. In all cases, greater compressive stresses occurred for dry winding than for prepreg winding. To understand how the development of compressive fibre stresses is affected by winding tension and radial modulus, simulations were run at various winding conditions. Figure 15 shows maximum compressive stress occurring in a 60-layer cylinder calculated at various combinations of radial modulus and winding
MANUFACTURING
Volume 6 Number 2 1995
75
Effect of radial stress relaxation:
T A
60 50 40 30 20 10 0 -10 -20 -30
g 2 al
60 50 40
R
;;
3 5 i
10 0 -10
E
-30 -20
e
. ‘. ‘. ‘-
0I
T = 13.35
N
0.4
0.6
0.8
I I 1
0.4
0.6
0.8
1
0.2
1
0
;‘;
U
E. A. Kempner and H. T. Hahn
0.2
60 50 40
T = 31.15
CONCLUSIONS
N
-20 ‘. 0
0.2
0.4
0.6
0.8
1
Normalized Radius
Figure 14 Circumferential cylinder with prepreg tow
stress
distribution
after
winding
increase in stress as radial modulus decreased. Therefore, the compliance of the cylinder is the most significant factor affecting the development of compressive fibre stresses. For winding tensions of 22.25 and 3 1.15 N, the radial modulus determined for prepreg winding was signilicantly larger than for dry winding. Subsequently, much smaller compressive stresses occurred in those prepreg wound tubes. At the lowest winding tension, T = 13.35 N, the prepreg winding modulus was slightly lower than for dry winding, resulting in similar circumferential stress distributions. In general, greater radial stiffness is expected for prepreg winding than dry winding due to resistance provided by the resin. Also, higher winding tensions tend to increase the radial modulus by improving compaction of the cylinder. Yet, stiffness may be increased further by using other means to improve consolidation during winding.
60-layer
In this study, the effect of stress relaxation during filament winding was investigated. Cylinders were wound of approximately 12 mm thickness with pressure gauges at the mandrel/composite interface. Winding tensions ranged from 13 to 34 N. Results were compared from winding with graphite/epoxy prepreg tow and dry graphite tow. Despite high resin viscosity, significant stress relaxation was evident during prepreg winding while little relaxation, if any, occurred using dry fibre. An analytical model was developed to calculate change in stress due to relaxation during winding. Several parameters were not known beforehand and had to be inferred from the data. Stress distributions following winding were- calculated for each case. The radial stress in prepreg wound cylinders was found to relax nearly to zero in the inner part of the tubes. Compressive circumferential stresses occurred throughout each of the cylinders. However, they reached greater magnitudes in the dry wound cylinders due to very low radial moduli. No fibre wrinkling was evident in any of the wound cylinders.
ACKNOWLEDGEMENTS 10
20
Wizing Tension (N) Figure 15 ing tension
Maximum and radial
compressive modulus
circumferential
stress
W~SUS wind-
tension. The creep parameters found for prepreg winding were used, but compressive stresses were less than 2% smaller when K,, = 0 was used. The magnitude of compressive stresses increased approximately linearly with winding tension. However, there was an exponential
76
COMPOSITES
MANUFACTURING
The present paper is based on work supported by the Office of Naval Research under Grant NOOO14-92-J1846. Sincere appreciation is extended to Yapa D. S. Rajapakse, Scientific Officer.
REFERENCES 1
2
Tarnapol’skii, Y.M. and Beil’, A.I. in ‘Handbook of Composites, Vol. 4: Fabrication of Composites’ (Ed% A. Kelly and S.T. Mileikoj. Elsevier Science Publisher B.V., Amsterdam, 1983, Ch. II, p. 45 Lee, S.Y. and Springer, G.S. J. Compos. Muter. 1990, 24, 1270
Volume 6 Number 2 1995
Effect of radial stress relaxation: 3 4 5 6
Calms, E.P., Lee, S.Y. and Springer, G.S. J. Compos. Mater. 1990,24, 1299 Cai. Z., Gutowski. T.G. and Allen, S. J. Compos. Mater. 1992, 26, 1374 Spencer. BE. Ph.D. rhesis, The University of Nebraska-Lincoln, 1988 Hahn, H.T.. Kempner. E.A. and Lee. S.S. Comoosires Manufacturing 1993. 4(3), i47
COMPOSITES
7
8
E. A. Kempner and H. T. Hahn
Kempner, E.A. and Hahn, H.T. in ‘Composites Modeling and Processing Science, Proc. 9th Int. Conf. Composite Materials’, Woodhead Publishing Company. Cambridge and Univ. of Zaragoza, Spain, 1993, p. 462 Carnahan, B., Luther, H.A. and Wilkes, J.O. ‘Applied Numerical Methods’, John Wiley and Sons, Inc.. New York, 1969. p. 429
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