Failure criteria are derived for several modes of failure (in unaxial tensile or compressive loading, or biaxial combined tensile-compressive loading) in the case of closely woven plain fabric, coarsely-woven plain fabric, or roving glass cloth reinforcements. The shear strength in the interaction formula is replaced by an equation dealing with tensile or compressive strength in the direction making a 45 degree angle with one of the anisotropic axes, for the uniaxial failure criteria. The interaction formula is useful as the failure criterion in combined tension-compression biaxial failure for the case of closely woven plain fabric laminates, but poor agreement is obtained in the case of coarsely woven fabric laminates

Haga, O.

Hayashi, N.

Kasuya, K.

English

NASA Technical Reports Server

NASA TECHNICAL MEMORANDUM
NASA TM-88406
FAILURE CRITERION OF GLASS FABRIC REINFORCED PLASTIC LAMINATES
Osamu Haga, Noriyuki Hayashi and Kazuo Kasuya
Translation of "Glass cloth sekiso kyoka plastic no
hakai kijun" Japan Society of Materials Science, Journal,
Vol. 25, No. 273, June 1976, pp. 516-520
(NASA-TM-88%06) fAILURE CRITERION OF GLASS
FABRIC REINFORCED PLASIIC iAMI_ATES
(National Aeronautics and Space
Administra%ion) 11 p HC A02/_F A01 CSCL 11D
G3/2_
N86-23657
Unclas
06003
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON D.C. 20546 APRIL 1986
https://ntrs.nasa.gov/search.jsp?R=19860014186 2020-03-20T15:44:36+00:00Z
FAILURECRITERIONOFGLASSFABRICREINFORCEDPLASTICLAMINATES* /1_6
by Osamu Haga, Noriyuki Hayashi and Kazuo Kasuya
Tension, compression and combined tension-compression biaxial tests were performed on three
types of glass fabric reinforced plastic laminates, and the applicability of an interaction formula was
investigated. Based on these results a new combined tension-compression biaxial failure criterion
have been derived. The results obtained are as follows ;
(1) The interaction formula can be used practically as the uniaxial failure criterion of glass
fabric laminates when it is transformed into the equation containing tensile or compressive strength
in the direction having an angle of 45 degree to one of the anisotropic axes.
(2) In the case of closely woven plain fabrics, the interaction formula can be applied as the
combined tension-compression biaxial failure criterion, but in the case of coarsely-woven plain fabrics,
the calculated values do not agree well with the experimental results.
(?,) The values calculated according to the new combined tension-compression biaxial failure
criterion agree fairly with the experimental results. When this criterion is applied to the case of
uniaxial loading, tile formula becomes tile same as that of the uniaxial failure criterion _iven in (1).
,,Received Sep. 22, 1975)
i. Introduction
In general, there are unidirectional fiber reinforced plastics in which fiber is
arranged in one direction, laminated in which the unidirectional fibers are
laminated perpendicularly or obliquely and laminates which are laminated with
fabrics, such as glass cloth, containing a plastic matrix in continuous fiber
reinforced plastics. Many theoretical and experimental studies concerning yield
and failure of the former material by combined stress have been accomplished (Ref-
erence (i) to (4)) but there are few studies directly concerning glass cloth
laminate of the latter.
The strength characteristics of glass cloth laminates are different from those of
unidirectional reinforced plastic or its laminates; it seems to be from the in-
fluence of the wave condition of woven fabrics, woven conditions and twined condi-
tion of fiber. The authors are studying biaxial stress-failure criterion of
laminated reinforced plastics made of glass fiber and in this report, the results
of experimental studies concerning failure criterion under tension-compression
biaxial stress conditions are reported.
* Received Sept. 22, 1975
** Official member, The engineering dept. of Chiba University, Yayoi-cho, Chiba
*** The engineering dept. of Chiba University, Yayoi-cho, Chiba
**** Numbers in margin indicate foreign pagination.
OlimNAL PAGE IS
OF POOR QUALIFY
2. Failure Criterion
2.1. Failure criterion of uniaxial tension and uniaxial compression
There is a report which tried to make tension failure criterion of glass cloth
laminate reinforced plastic from the characteristics of the content materials
(Reference (5)) but it seems to be difficult to generalize for
glass cloth laminates with differently woven cloth because the report does not
consider the influence of the weave. I[owever, it would be very difficult to consider
the influence of weave on strength. Thus the authors adopted a criterion which is
a little modified from the Interaction formula (Reference (6)) proposed by Norris
by considering the strength of composite mater:ial including the influence
of weave as the base. For the coordinate system shown in Fig.l, the stress O-'(o)
in the X direction with angle 0 against the anisotropic axis L can be written
as equation (i) by applying the coordinate conversion rule to the interaction
formula.
According to equation (I), when _is close to 45 °, the stress does not match the
actual measured value thus an equation which uses the tensile strength or compres-
sive strength F45 o at G =45 ° instead of the shear strength SLT is conducted, i.e.,
= 45 ° is applied to the equation (I) and solve SLT then apply it to equation
(i) again. 1
/_ ,_2 "2!,n')_ (2)
"(O)=l/(t'-"'2>( F,' _)+,_,,, ,
1177
In the case that two materials which have the same strength are laid up in dif-
ferent ply orientation, equation (2) can be simplified as shown below by applying
FL=Fr=F.
From equation (2) or (2)', if tensile or compressive strength in the direction of
the anisotropic axis and the direction of 45 ° from the axis is given, the failure
strength of the arbitrary angle between the axis can be calculated.
¥
/
Fig. 1, Coordinate system of the glass fabric
reinforced plastic laminates.
ORIG_AL PAGE m
oe eooe
2.2 Tension-compression combination biaxial failure criterion
The previous report (Reference (7)) studied the failure mode of the biaxial test
results and the failure criterion was conducted from the results. In this report,
the authors revised them and assumed that failure occurs under the following con-
ditions.
(i) The condition in which ox or _y reaches uniaxial tensile strength ot(0) or
uniaxial compressive strength Oc(0) expressed in equation (2), i.e.
_=_,_0) or _,=_(0) (3)
(2) The condition in which the shear stress TLT reaches the shear strength SLT of
the composite material. Since this study deals with tension-compression combination
biaxial case, the relationships between Ox and Oy when failure occurs is as follows.
SLr (4)
(3) By considering the influence of both perpendicular stress against the aniso-
tropic axis L and T, and the shear stress, the combined stress which is from
_,=_T_ (Reference (8)) was considered when a e reaches the uniaxial tensile
strength _,(_> or theuniaxiai compression strength %_) in the direction which
corresponds to the direction of tan p=_/= , the following equations can be obtained
where _ and _,_. is the combined stress against the other orientation axis L and
T and their directions are BL and BT and Ox/ Oy is written as -$.
_ _ =(y /l 2 m 2
_,L--)'_L2+rLr 2 *V +--_--
_L =tan -I rmr =tan-Z-(_'+ l)h'L
o"L _p_2_ m 2
_r = tan-1 rcr (_+ l)lm
_=tan-i _
r _O.z 2 _ 12
From equation (2), (5) and (6)
(5)
(6)
c%- /l_+_r or _= /. p-
V _- V _'+--_r
(7)
_,c2_) and %(at) are the values obtained by applying B L and gT of equation (9)
to equation (5). The authors assumed that failure occurs at the minimum stress of
equations (3), (4) and (7).
3. Test method
Three types of woven glass cloth were used. Fig.2 shows the weave of the glass
cloth. (I) is a fabric with a little twisted wide roving cloth. (2) is a closely
woven fabric with thin fiber. (3) is a fabric with the same thin fiber as (2) but
is coarsely woven. In this report these fabrics (I), (2) and (3) are called
3
"Roving glass cloth", "Close plain wovenglass cloth" and "Coarse plain woven glass
cloth". The test specimens used non-saturated polyester as a matrix resin and were
prepared by hand layup method. B.P.O 1.5 wt%was used as a hardener and the hardening
condition was 90 °C for 4 hours. The specimenswere laid up keeping 90 degrees of
the ply orientation of each ply so that the strength of the laminates in the two
directions is the same.
|_ _-ir*,ina mlls_ c!n'h
• b _ t m
qtl-t_q'_q1,_t,q
.....
' C]_e pllin ,,e',en _[:lss c],_lh <_ Coarse p!ain ,,_oven i_'.ass cloth
Fi_ 2. Types of g_nss f_bric.
Y 7
t !
--.._
- ----- _6o ---- !
k_
(o)
Y T
_,.,,- k,-- 4s -_
(_! Uni_xi.nl tensLnn nnd bi_xiM l_nsion-compves
sion test specimen
!b) L'niaxial rnmpressif_n test spncimen
Fig. 3, Dimensions o[ test specimen.
/ 1.__88
The dimensions of the specimens and the coordinates of the anisotropic axis are shown
in Fig.3. (a) is the specimen for uniaxial tension test and combined biaxial test
and (b) is the specimen for uniaxial compression. The dimensions of the specimen
for the uniaxial test were determined as shown in Fig.3(b) after verifying that
buckling failure does not occur in the preliminary tests.
The details of the tension-compression biaxial test equipment have been described in
the previous report (Reference (7)).
4
4. Test results and considerations
Fig.4 (a) to (c) and Fig.5(a) to (c) show the relationships between the orientation
angle _ which is the angle betweenone anisotropic axis and the direction of applied
tensioner compressionand failure stress. All of the test specimens were prepared
to have equal strength in the elastic axis, thus the equation (2)' was applied.
In the compression tests, the test results show large scatter thus 4 to 5 of the
specimenswere tested and the figure shows the maximumand the minimumstress.
The calculation and the test results seemto match well and in the case of compression,
the failure stress of the specimenswhich have low fiber content and of the roving
cloth is not influenced by the ply orientation angle _ and the failure stress was
almost constant. Thus it was found that the equation (2)' matches the actual re-
sults well for uniaxial failure criterion. In general, the test methods for equation
(2)' (or Equation(2)) have not been established and shear strength of which measure-
ment stress is scattered is not included. Thus the equation is expressed only with
tensile strength or compressive strength which are easy to obtain by test so it is
practical.
From the equation (2) or (2)', physical meaning of failure can not be obtained. The
failure mechanismof glass cloth laminates differs from tension or compression fail-
ure of uniaxial reinforced plastic. The failure criterion having physical meaning
seemsto be expressed with various unique factors of glass fiber fabric besides fiber
content and layer strength such as tension, compression and shear in the fiber
matrix. Therefore, it would be difficult to conduct such a criterion.
For tension-compression biaxial criterion when the interaction formula, mentioned
in the previous report (Reference (7)) using Ft for tensile strength, Fr for comp-
ressive strength and SLT for shear strength was applied to the coarse plain woven
glass cloth laminates, the result did not match the test results well. As can be
found from equation (i), the uniaxial strength has discrepancy with a different
value by considering the condition of uniaxial tension as a special case of combined
biaxial tension or a special case of combination of tension and compression. But
the interaction formula is a very simple formula so it is convenient in practical use.
3O
• -- = 45 %_V_
{_ :_,. o---Vf :35 %
_20
(_) i ; ]
4O
E" e---Vf =45 "/.
E o---Vf = 35 %
-- "9-:
[,o
1" (b) I I 1
4O
• - -- Vf =45 %
o__. Vf =35 o/.
'0
',c,)
, i [ t_
0 15 3o 45
Orientc_tion ong_e e (o)
i it ; "i i_,_ <,_[_,;,_li_nn _l" _;r,i_:,:!3[ fai',ure
_,._, Ir_r _lniaxi:d t_'n._i!c load.
I
ORIGINAL PAGE IS
oF POORQUALIFY
Here, the authors applied the interaction formula to the close plain woven glass
cloth laminates and the roving glass woven laminates. Fig.6 (a) to (d) show compar-
ison of the calculation results and test results. As shown in the figure, both
match pretty well. Thus it seems to be able to be used as failure criterion for /19
close plain woven glass cloth and roving glass cloth of which fibers are woven closely.
ORIGINAL PAGE 1_
OF POOR Q4JAL_ _'Y
E I---Vf= 3S%
E t-'- Vf = 25 %
.... Cal.
O
o
U (O) l J f ,
'O3_''0 I--- Vf=42%
_t20 _--
'_ • 6.
t
E
o ,(b)
I I I
E I - - - Vf = 40 %
E
•._ _ -- - Vf = 34 %
--I ...Mean
'o
..c;
E"
20
T .
o ! (") t ,
L
O 15 30 /-5
Or,entatlc, n eng!e 0 (_
1 i', F . ;: ,, , ,,,,I
b: : • .... '
to, /, 'i:'T "'
C'lt, r:,;, ']'_' 'I i T: " rlr.! : -_11;:
-2C. •.....o" I
o-... 15" !
----'------- / ......30" !
"%.2-", _""-_ -c,,_ 2
(°) , \* s \ , _'.
-ZO • .... O"
e... 15"
• '- 30" I
?
-30 40
• .... 01
_ I ..... 30'
._._'_. _. i_°: ?,'
\-b,\\\
, ,_._L____L__,_
-30 ..................
• .....O" ,
15"
30'
_-20 ....
E •
,_ '\\
-18
\',
\/, "_
(d}
: I
1C, 23 30
:a. h; {'_n,_" r]:,i:: wo.,,,n _:_s< ,-:_1!1. ',r ]:_ 13_
2r_d :-_, r_'sp_'ct]'.e]y
!c), ,4 E_'.L:;1 _!,_ss cloth. I't" :_ 45i7 _._t S-,%.
r,,_t, ec: [,, el:.
t:i_ G rl_e cr_mparisnn of calcula[ed ",'alues bv
interaction formula with the experimental
results ',ruder }_ia:,:in]. [ondx_.
The comparison of calculation results of equations (3), (4) and (7) which were
conducted as new failure criteria and the test results is shown in Fig.7(a) to (c)o
In the case of the coarse plain woven glass cloth, the calculation results and the
test results match well but in the case of the roving glass cloth and the close
plain woven glass cloth which have wide weave or close weave the results did not
match well, It may be from the interactive influence of the stress components o L
and o in the L and T direction in the case that 0 = 0 °. When compressive strength
r
is low, this tendency occurred more. Compressive stress reduces in order with the
coarse plain woven glass cloth, the close plain woven glass cloth and the roving
glass cloth and this coincides with the order of weave roughness, and thickness of
the fiber, i.e., the order of weave of the fiber which composes the fabrics. Thus it
seems that the fabric with larger weave has larger mutual interference of o _ and o °
r"
Equation (4) which expresses failure by shear stress in all of the cases coincided
well with the test results. Under pure shear stress condition between the anisotropic
axis (for example, the place where 0 = 45 ° and _ = -i in Fig.8(a)), shear failure
occurs easily at 1/3 of tensile strength and about i/2 of compressive strength in
fiber direction for the roving glass cloth and the close plain woven glass cloth
Therefore, it should be _iven enough attention.
The trend from equation (7) which expresses mutual interference of the perpendicular
stress and the shear stress seems to match with the test results and in this case.
also mutual influence of the components of the perpendicular stress in the L and T
d ir ec tion. /20
-3°[ ....... 0
1_ll----ll------_ l _"""l_
jlI,, _ • ..... 3_
|_, , ® • _ I .....• :I.{d,
-_o[- x',, \, i
(o_ II I I
-30 i ..._t--L.___,,,_....L__
5. Conclusions
Tension, compression and tension-compression biaxial tests were performed on three
types of glass fiber fabric reinforced plastic laminates and the applicability of
the generally used interaction formula was studied. Based on the results, new
tension-compression combination biaxial failure criteria were conducted. The
following conclusions were obtained.
(i) The interaction formula which is transformed into the formula for tensile or
compressive strength instead of shear strength in the direction of 45 ° to one of
the anisotropic axis can be used as an uniaxial failure criterion for glass cloth
laminates.
(2) The interaction formula can be applied to closely woven plain fabric laminates
as a tension-compression combination biaxial failure criterion but for coarsely
woven plain fabric laminate, the formula does not agree with the test results.
(3) The authors studied the failure modes and a new tension-compression combination
biaxial failure criterion was conducted. The tendency of calculation results and
the test results coincided and when this criterion is applied to the case of uniaxial
loading, the formula is the same as the formula used for tension or compression
strength instead of shear strength in the direction of 45 ° to the anisotropic axis.
At last, the authors cordially thank Professor Hidekatsu Shiratori and Assistant
Professor Kozo Ikegami of the Precision Engineering Institute of Tokyo Technical
College for their assistance throughout this study.
Lecture given at the 24th science council of the Japan Material Society on May 20,
1975)
References
(i) Koichi Ohira : Kyudai Kogaku Shuho, 42,454 (1969)
(2) Kozo Kawada : Zairyo, 20,881 (1971)
(3) Puppo, A.H. and H.A. Evensen, AIAA Journal, i0, 468(1972)
(4) Wu, E.M. and J.K.Scheublein, ASTM STP, 546, 188 (1974)
(5) Sadao Amijima and Harunori Konami : Zairyo, 22, 1017 (1973)
(6) Norris, C.B. : Forest Products Laboratory Report, 1816 (1962)
(7) Osamu Haga, Noriyuki Hayashi and Kazuo Kasuya : Zairyo, 24, 776 (1975)
(8) Hidekatsu Shiratori, Kozo Ikegami and Toshio Hattori : Zairyo, 22, 1802 (1973)
!. R¢lWtWt No.
NASA TM- 88406
4. Tlt|o e_d S*_bNtll
ORIGINAL Pf_GE I$
2 C_t_,mNt A_ceool_ Nqk
FAILURE CRITERION OF GLASS FABRIC REINFORCED
PLASTIC LAMINATES
7. Av,k,_,)
Osamu Haga, NOriyuki Hayashi and Kazuo Kasuya
t. Per(o,,_,r,g O,tlt_tQtio_ N_o end Add,oss
SCZTRAN
Box 5456
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12. S_le:,no Alon_T Ne,-o end Ad_rou
_tlona_ Aerouautlcl and Spice Adm.{.niit:etion
Washington. D,C. _0546
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Translation of "Glass cloth sekiso kyoka plastic no hakai kijun",
Japan Society of Materials Science, Journal, Vol. 25, No. 273,
June 1976, pp. 516-520 (A76-41242).
I_ Abutrtct "
Failure criteria are derived for several modes of failure (in unaxial
tensile or compressive loading, or biaxial combined tensile-compressive
loading) in the case of closely woven plain fabric, coarsely-woven plain
fabric, or roving glass cloth reinforcements. The shear strength in the
interaction formula is replaced by an equation dealing with tensile or
compressive strength in the direction making a 45 degree angle with one of
the anisotropic axes, for the uniaxial failure criteria. The interaction
formula is useful as the failure criterion in combined tension-compression
biaxial failure for the case of closely woven plain fabric laminates,
but poor agreement is ogtained in the case of coarsely woven fabric
laminates.
17. K_t Verde (Sete_le4 _ Aut.INn,r(_j_
19. 5cc_,_r C|elsig, (_l I_1|
• Uucluaif£_ Unclm_lLf_,_ I


Failure criterion of glass fabric reinforced plastic laminates

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