Residual Internal Stresses Determined Experimentally In Hollow Composite
Laminates
Dr.eng. Horatiu Teodorescu1, Prof.dr.eng. Sorin Vlase2, eng. Dorin Rosu3, dr.eng. Mihai Ulea4
1,2,4
Transilvania University of Brasov, Romania, Dept. of Mechanical Engineering
29 Eroilor Blvd., 500036-Brasov, Romania, [email protected]
3
Compozite Ltd. Brasov, Romania, 14A Plevnei street, 500187-Brasov, Romania
ABSTRACT
The paper presents an experimental destructive method to determine residual internal stresses introduced in hollow polymer
matrix composite structures during their manufacturing process. According to this method the shape variations of a hollow
structure resulted from the destructive process will be considered as a measure of residual internal stresses. The distribution
of residual internal stresses along the length of the specimens is presented.
KEY WORDS: residual internal stresses, radial cut method, hollow composite laminates
INTRODUCTION
A trustworthy and complete calculus to determine residual internal stresses introduced in hollow polymer matrix composite
structures during their manufacturing process is very difficult to accomplish. The mathematical description must consider
various factors of influence and material values which depend on temperature and time. Therefore, experimental methods to
determine residual internal stresses are still used. These methods are divided in destructive and non-destructive ones. All
destructive methods to determine residual internal stresses are based on the determination of shape changes of a composite
structure, changes caused by the balance state disturbance. This balance state is disturbed since the forces flux included at
the inner of the composite structure is interrupted by the destructive process. Structure’s shape changes (strains) resulted
from the destructive process will be interpreted as a measure of residual internal stresses. Determining the composite
structure’s shape changes, the values of these internal stresses can be computed. The most known destructive methods to
measure residual internal stresses introduced in the manufacturing process of a composite hollow structure are presented in
the paper [1].
MATERIAL AND METHOD
Regarding the experimental determination of residual internal stresses introduced in the manufacturing process of a composite
tubular structure, a method partial similar to that described by Aleong [2] has been used. The experiments were accomplished
on tubular specimens made at COMPOZITE Ltd. Brasov, Romania (fig. 1). The tubes material used during tests is a
compound based on glass-fabric reinforced polyester resin. The tube wall structure was manufactured very accurate in the
fabric winding process. Fabric strips (dimensions: 2000 x 250 mm) used in the winding process were cut in length and at 45°
from the production direction (fig. 2). The geometrical elements and wall structure of the specimens are presented in table 1.
Rings (25 mm length) have been cut from the left end (L), from middle (M) and from the right end (R) of the specimens used in
tests (fig. 3). In principle, the method of determination residual internal stresses consists in the disturbance of rings’ balance
state by cutting them on the generator, on radial direction and the determination of external surface strains resulted from the
cutting process [3]. Regarding the specimens made in the fabric winding process (pure circumferential winding), the highest
residual internal stresses take form on circumferential direction. The axial residual internal stresses may be neglected since
they are insignificant in comparison with the circumferential ones and does not act on main stress direction.
Thus, a uniaxial distribution of internal stresses is determined. The maximum value of this distribution of residual internal
stresses can be found in the outer surface ply of the ring, value which decreases in neutral fiber direction [5]. In case of ring’s
radial cut, the balance state of residual internal stresses is disturbed, stresses become free and deform the ring. A ring’s
widening means the existence in the ring before cutting, of tensile (compression) residual internal stresses at the inner (outer)
surface of the ring. A decrease of ring diameter after the cutting process signify the initial existence of compression (tensile)
residual internal stresses at the inner (outer) surface of the ring. Because of small differences regarding the diameters ratio
(de/di ≈ 1), the residual internal stresses at the inner of a tubular specimen present close values with those existent of its outer
surface since a symmetric distribution of stresses occurs. A method to compute the stresses σe existent at the outer surface of
the ring, is the string measure method [6]. According to this method, the residual internal stresses can be computed after,
beforehand, the string length sn, formed as a result of its radial cut, has been measured (fig. 4).
Table 1. Geometrical elements and wall structure of the specimens
Specimen
Specimen
Characteristics
type 1
type 2
Number of specimens
1
1
Type of matrix
Unsaturated Polyester resin
Type of fabric
EWR-500
EWR-500
+0,4
+0,4
Tube diameter [mm]
80
80
Length of the tube [mm]
100
100
Wall thickness [mm]
3,1 – 4
3,7 – 4
Number of plies
8
8
Plies thickness [mm]
0,38 – 0,5
0,45 – 0,62
Strip cutting angle to production
0 (in length)
45
direction [°]
Fabric winding angle to mandrel [°]
0
0
Fibers volume fraction [%]
35
35
-3
-3
Weight of specimen [kg]
160 · 10
150 · 10
Fig. 1. Various tube specimens made at Compozite Ltd, Brasov, Romania
Fabric strip
Fabric roll
Fabric roll width
Winding mandrel
Fabric roll length
Fig. 2. Cutting method of fabric strips [4]
Φ 80
L
M
R
100
Fig. 3. Rings cutting scheme to determine residual internal stresses in tubular composite structures
h
rn
re
αs
sn
Fig. 4. Scheme of string measuring method
Thus:
sn = bn
α 
360
sin  s  ,
π (360 − α s )
 2 
(2 π rn ) +
σe = E ⋅
(1)
(360 − αs ) h π
− (2 π re )

 t s 
1

360 1 −
arcsin 
 2 rn 
 180
.
2 π re
(2)
where:
bn [mm] – the circumference of neutral fiber;
sn [mm] – string length between the cutting edges of the neutral fiber;
αs [°] – string angle of neutral fiber between both ends of the ring;
σe [MPa] – residual internal stress at ring’s outer surface;
E [MPa] – Young modulus;
re [mm] – rings outer surface radius;
rn [mm] – ring’s neutral fiber radius;
h [mm] – tube specimen wall thickness;
ts [mm] – cutting width.
EXPERIMENTAL RESULTS
The experimental determinations of residual internal stresses introduced in tubular polymer matrix composite specimens
during their manufacturing process, according to the above mentioned method, are presented in table 2 and fig. 5.
Table 2. Experimental determination of residual internal stresses introduced
in the manufacturing process of tube specimens type 1 and 2
Specimen type 1 Specimen type 2
Tube specimen wall thickness, h [mm]
3,6
4
Ring’s outer surface radius, re [mm]
44
44,5
Ring’s neutral fiber radius, rn [mm]
42,2
42,5
Cutting width, ts [mm]
2
2
String angle of neutral fiber between both
3,39
3,5
ends of the ring, αs [°]
Circumference of neutral fiber, bn [mm]
265
267
String length between the cutting edges of
2,5
2,6
the neutral fiber, sn [mm]
Young modulus, E [MPa]
25000
14000
Residual internal stress, σe [MPa]
- 1,93
- 1,41
Specimen type 1
Specimen type 2
-0,5
-1
-2
-1,41
-1,5
-1,93
Residual internal stresses [MPa]
0
-2,5
Fig. 5. Distributions of residual internal stresses σe introduced in the manufacturing process of two types of tube specimens
CONCLUSIONS
As a result of experimental determinations of residual internal stresses introduced in specimens manufacturing process, the
following conclusions can be drawn:
•
•
•
•
the maximum value of residual internal stresses can be found in the outer plies of the tube specimens;
the residual internal stresses decrease in neutral fiber direction;
there were no differences between the residual internal stresses determined in left, middle and right rings of the
specimens;
the residual internal stresses can be influenced by temperature and humidity variations.
ACKNOWLEDGMENTS
The authors acknowledge the contribution of Compozite Ltd, Brasov, Romania at the accomplishment of the specimens for
this paper.
REFERENCES
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