Compressive strength and failure modes of boron fiber-magnesium matrix composit

Schuerch, H.

English

NASA Technical Reports Server

NASA CONTRACTOR 
REPORT 
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COMPRESSIVE STRENGTH OF 
BORON-METAL COMPOSITES 
by H. Schemb 
Prepared under Contract No. NASw-652 by 
ASTRO RESEARCH CORPORATION 
Santa Barbara, Calif. 
f OT 
NATIONAL AERONAUTiCS AND SPACE ADMINISTRATION l WASHINGTON, 0. C. l APRIL 1965 
https://ntrs.nasa.gov/search.jsp?R=19650010244 2020-03-17T00:42:45+00:00Z
TECH LIBRARY KAFB, NM 
NASA CR-202 
COMPRESSIVE STRENGTH OF BORON-METAL COMPOSITES 
By H. Schuerch 
Distribution of this report is provided in the interest of 
information exchange. Responsibility for the contents 
resides in the author or organization that prepared it. 
Prepared under Contract No. NASw-652 by 
ASTRO RESEARCH CORPORATION 
Santa Barbara, Calif. 
for 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
.~ 
For sole by the Office of Technical Services, Deportment of Commerce, 
Washington, D.C. 20230 -- Price $2.00 

TABLE OF CONTENTS 
LIST OF SYMBOLS 
SUMMARY 
I. INTRODUCTION 
II. COMPRESSIVE FAILURE IN UNIAXIAL LAMINATES 
A. Micro-Stability Failure 
B. Limits of Elastic Stability Failure ?, 
III. COMPRESSIVE STRENGTH OF BORON-MAGNESIUM 
COMPOSITES 
A. Experimental 
B. Analysis 
IV. CONCLUSIONS 
REFERENCES 
FIGURES 
iii 
Page 
V 
vii 
a 
10 
11 
12 
13 

LIST OF SYMBOLS 
f 
F 
E 
E: 
k 
& 
P 
Subscripts: 
C 
cr 
SYm 
antis 
m 
f 
Y 
ult 
stress 
stress at failure 
Young's modulus 
tangent modulus 
shear modulus 
tangent shear modulus 
fiber packing density 
Poisson's ratio 
strain 
specific weight 
composite 
crippling 
symmetrical 
antisymmetrical 
matrix 
fiber 
yield 
ultimate 
V 
I I, ,,,,,,,, 11, . I ,I .I ,111. m-.-m,,. I . ..-~.I Im.--m..----1 . -.,,- . ..--.--.- - ..-..--__ -._ _-. -.-.. 
SUMMARY 
The compressive strength and failure mechanisms of an idealized 
composite material are analyzed. 
A method of predicting, theoretically, the compressive strength 
and failure modes of an idealized composite material is developed. 
The method is applied to a boron fiber/magnesium matrix composite 
and predicted strength values are compared to experimental data. 
vii 
I. INTRODUCTION * 
High modulus, high strength and lightweight filaments such as 
those made from quasi-amorphous boron (Refs. l-3 ) have recently 
become available for consideration in the design and construction 
of advanced space structures. This provides the challenge to the 
structural designer to utilize the intrinsic mechanical properties 
of these materials to the fullest possible extent. It is necessary, 
however, to avoid misapplication caused by indiscriminate enthusi- 
asm for the remarkable order-of-magnitude improvements in basic 
mechanical properties of these fibers compared to the more con- 
ventional materials of construction. Guidance in the search for 
fruitful avenues of development and structural design application 
can be derived from a careful study of the possibilities and limita- 
tions inherent in these new materials of construction. 
For this purpose, it is necessary to provide some theoretical 
and experimental foundation in predicting the useful mechanical 
properties of filament composite materials from the known properties 
of its individual constituents. Considerable work has been published 
by several authors predicting elastic composite properties from those 
of the constituents (Refs. 4 , 5). A more difficult, but equally 
important task is to predict mechanical strength. The difficulty is 
primarily due to the fact that mechanical strength is a property 
This report is one phase of a study on Boron filament composite materials 
for space structures. 
which is strongly affected by "accidents" such as premature modes of 
failure, micro-flaws, dislocation mobility (or the lack thereof), 
aging, manner of conducting the tests, etc. 
In this study, an attempt is made to isolate the uniaxial com- 
pressive failure mechanisms of a simplified model for a composite 
material and to predict its ultimate compressive strength based 
solely upon the elastic and elasto-plastic properties of the constitu- 
ents, and upon the geometry of the micro-structure in the composite 
material. Such predictions, supported by experimental evidence, can 
form the basis for generalized application studies such as presented 
in Refs. 6 and 7. These, in turn, will identify areas of worth- 
while application and, ultimately, allow a realistic judgement re- 
garding the relative cost effectiveness of new and necessarily 
expensive high performance composites as compared to alternate, 
more conventional methods and materials of construction. 
2 
II'. COMPRESSIVE FAILURE IN UNIAXIAL LAMINATES 
A. Micro-Stability Failure 
A strongly idealized "two-dimensional" model of a uniaxial 
composite material as shown in Figure 1 will be considered. This 
model consists of alternating layers of a relatively soft matrix and 
a hard, load-carrying skeleton which is representative of a fiber re- 
inforcement. We will assume that the skeletal constituent material 
is columnated, Hookean, and has unlimited compressive strength. We 
will further assume that the matrix has elasto-plastic properties 
and that its Young's modulus is small compared to that of the skeleton. 
The material will be subject to uniaxial compressive loading parallel 
to the direction of the reinforcement. Possible modes of materials 
failure, then, are those where the skeletal material will cripple 
elastically under applied axial loading (micro-stability failure). 
For this idealized material, there are two possible micro- 
stability failure modes as shown in Figure 2. The first forms a 
pattern symmetrical to mid-planes through the matrix layers (Fig. 2a). 
This case represents a condition analogous to the well known case of 
the column on an elastic foundation (Refs. 8, 9). Disregarding 
Poisson's ratio effects in the matrix yields the crippling stress 
F 
crSpl 1 (1) 
3 
where the packing density d= Wf is the volumetric ratio 
Wf + wm 
of skeleton material to total composite material. 
The second failure mode forms an antisymmetrical pattern 
as shown in Figure 2b. Here the matrix is primarily subject to 
shearing deformation. Considering only the contributions of axial 
skeletal stiffness and shear stiffness of the matrix, the method of 
minimum potential energy yields a crippling stress 
F = cr Gm antis 1 -0c 
(2) 
Note that, subject to the limitations inherent i;n the underlying 
assumptions, the two crippling stresses are independent of the over- 
all sample dimensions and dependent only of the micro-structure and 
constituent elastic materials properties characterized by o( and 
(Ef/Em, Gm) respectively. 
The stability analysis is made by assuming perfectly elastic 
properties of the two composite constituents. Subject to the limi- 
tations of small deformation analysis, the results can also be 
applied to the case where the matrix has exceeded the yield point 
due to axial compressive strains. This requires replacing the trans- 
verse Young's modulus and shear modulus of the matrix material with 
the appropriate tangent moduli, corresponding to the particular axial 
compressive matrix strain in the material. The crucial assumption 
made here is that the material retains isotropy of its elastic 
properties in the post-yielded state. 
Equating the two crippling stresses given in 
and (2) yields an expression for the boundary between 
domains as follows: 
Equations (1) 
the two failure 
-1 ?-I 
Ef/Em = (1 +/ym) 2 (1 -d) 0f (1 + Em/Ef vr] (3) 
The failure domains according to Equation (3) are shown in Figure 3 
for a Poisson's ratio of Am = .5 (plastic) and .3 (elastic). 
This graph shows, that for reasonably high packing densities o( > .2 
and modulus ratios, Ef/~m>5, the ant' isymmetrical crippling mode 
will prevail. For this case, then, the compressive failure stress, 
Fcult ' can be determined solely from the effective (tangent) shear 
modulus zrn and the packing density b( by the relation given in 
Equation 2. As discussed below, in most cases the stability failure 
will take place at strain levels exceeding the yield point of the 
matrix material. Thus the point of failure will be determined by: 
F 
Cult = O(EEf + (1 -@f,* = $s) 
-o( (4) 
5 
Here f m* is the stress carried in the matrix at failure and Em (E) 
is the tangent shear modulus of the matrix material as a function 
of axial strain & . A graphical interpretation of Equation (4) 
is shown in Figure 4. 
B. Limits of Elastic Stability Failure 
Failure may take place in the fully elastic range or in a 
range where the matrix material has reached an elasto-plastic state. 
Let the composite modulus (Ref. 5) for a perfectly columnated 
composite: 
EC = O(Ef + (1 -o() im (5) 
then, as seen from Figure 4, elastic failure will take place if 
> EC = Gm (6) 
E 
mY 
(I- 4) 
where E mY and E m Y 
are the tangent shear modulus and com- 
pressive strain at the matrix yield point respectively. 
From Equations (5) and (6) we obtain as a criterion for 
elastic crippling 
(7) 
For the case /LI 
mY = .3 and for several values of o(, the relation- 
ship between Erny and Ef/Em is shown in Figure 5. 
The location of a number of candidate composite constituents 
are shown in Figure 5. Mechanical properties that have been assumed 
for this.purpose are listed below. Data have been obtained from 
References 10 and 11. 
c 
Skeleton: 
Boron 
S-Glass 
Matrix: 
Titanium 
Aluminum 
Magnesium 
Epoxy 
Ef' lo6 psi 
60 
12 
E m, lo6 psi &MY 
16 .75% 
10.2 .3 % 
6.5 .2 % 
I 5 2.5 % 
Note that of the several composites considered only the Boron-Epoxy 
combination has sufficiently high yield strain and modulus ratio to 
exhibit elastic crippling. Thus, in composites using metallic matrix 
materials, anelastic crippling may be expected to limit the ultimate 
compressive strength. 
This analysis also shows, that considerable improvements in 
compressive strength are available with matrix materials of moderate 
shear moduli and relatively high yield strains. 
7 
III. COMPRESSIVE STRENGTH OF BORON-MAGNESIUM COMPOSITES 
A. Experimental 
Composite materials samples have been prepared from boron 
fibers produced at ASTRO RESEARCH CORPORATION by infiltration with 
magnesium melts in a process similar to that described for boron- 
aluminum composite materials in previous work (Ref. 2 ). Figure 6 
shows a side view, and Figure 7 shows a cross-section micrograph of 
a typical sample. Two test samples were subject to compression loads 
in increments of approximately 30,000 psi and at average loading 
rates of approximately 1000 psi/set. In both cases, total failure 
was observed at compressive strains of approximately -7% to .8%. 
The failure appearance was that of a simultaneous crumbling of the 
test specimen along its total free length. A top view of the sample 
after complete failure is shown in Figure 8. 
A third sample was subject to 3-point bending tests in the 
apparatus shown in Figure 9. Here, the failure appeared localized 
at the point of maximum stress and essentially without permanent 
deformation. Observation of the fracture appearance did not establish 
whether it was initiated at the compression or the tension side of 
the specimen. 
Properties of the three samples and their experimentally 
determined failure stresses are as follows: 
Test Sample 
-.---.--- -- - -- 
Packing Density -- _ -.z>--- - 
Length/Diameter (in) - _~~_ - 
Y Specific Weight lbs/in3 
Type of Loading 
F c,Lt ultimate composite 
stress, 103 psi 
Ultimate Fiber Stress- lo3 psi 
- - _-- 
Few Specific Strength of 
P Composite, lo6 psi 
.52 -71 
.80/.13 .98/.25 
,085 .093 . 085 1 
Compr. Compr. Bending 1 
188 
342 
2.21 
- 
#2 
349 
486 
3.75 
For the purpose of comparison, the specific strength values 
for a number of typical isot.ropic high grade structural materials 
are given below. 
F 
103=pZi 
P 
lb&in3 
L/+ 
lo6 in 
High Strength Alloy Steel 300 . 285 1.05 
Aluminum Alloy 75 010 -75 
Titanium 200 l 15 1.33 
Berillium 90 .066 1.35 
Magnesium 30 -065 .46 
t 
B. Analysis 
For the case of a boron/magnesium composite, the anelastic 
crippling failure has been evaluated according to the shear crippling 
theory for the simplified composite model discussed in Section II. 
Figure10 shows the post-yielding shear modulus Gm of magnesium in 
function of normal strain, computed from stress-strain curves given 
in Reference 10. Also in Figure10 is shown the scaled stress-strain 
curve for the boron/magnesium composite, for two typical packing 
densities . It can be seen that the matrix material will exceed 
the yield point at stress levels of approximately 25% to 30% of the 
ultimate strength of the composite. 
Ultimate composite stress Fcult and strain,& ult, at failure 
are plotted in function of packing density in Figure 11. Experi- 
mental values obtained from the three samples are also shown. In 
view of the relatively crude analysis and the very limited experi- 
mental data, the correlation obtained between theoretical prediction 
and experimental data appears remarkable and, perhaps, fortuitous, 
Nevertheless, some hope is generated that the approach outlined in 
this report may bear fruit in identifying the critical composite 
materials parameters and in providing analytical tools for quantita- 
tive prediction of significantly improved mechanical properties. 
10 
IV. CONCLUSIONS 
Metal matrix-boron fiber composite materials can be made that 
exhibit specific strength values considerably above those available 
in monolithic materials. Limited test data indicate that anelastic 
micro-stability failure analysis yields theoretical strength pre- 
dictions which are reproduced in experiments. The high modulus 
of the reinforcing boron fiber allows the design of very efficient 
compression resistant structural elements (such as truss columns), 
which can exploit the available high specific strength of the 
composite materials. 
An important characteristic of these materials is the fact 
that yielding in the ductile matrix will occur at small fractions 
of the ultimate failure stress. As a consequence, the use of their 
high stress level capacity in applications requiring repeated load- 
ing has to be viewed with care, "Single shot" missile applications 
would appear to constitute first contenders for practical applica- 
tions, until the fatigue characteristics of those materials are 
well established. 
Finally, the use of a castable metallic matrix allows a design 
freedom at attachment and interface structures which is not available 
with.the more conventional glass-resin fiber composites. It can be 
expected, therefore, that the boron-metal composite materials will 
find practical applications in areas formerly reserved to conventional 
metal construction. 
11 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
REFERENCES 
Talley, C. P., et al: "Boron Reinforcements for Structural 
Composites", ASD-TDR-62-257, March 15, 1962. 
Witucki, R. M.: "Boron Filaments", NASA CR-96, September 1964. 
Berry, J.: "Preliminary Mechanical Properties of High Modulus 
Filaments" (U), General Electric Company, February 1964 (Confidential 
Rosen, B. W., Dow, N. F., Hashin, Z.: "Mechanical Properties 
of Fibrous Composites", NASA CR-31, April 1964. 
Tsai, S. W.: "Structural Behavior of Composite Materials", 
NASA CR-71, July 1964. 
Micks, W. R,: "A Review and Evaluation of Filament-Composite 
Materials" (U), Memorandum RM-4168-PR, The RAND Corporation, 
October 1964 (Confidential). 
Dow, N. F., Rosen, B. W.: "Evaluations of Filament-Reinforced 
Composites for Aerospace Structural Applications," Annual Report, 
Contract NASw-817, October 1964. 
Timoshenko, S.: "Theory of Elastic Stability", McGraw-Hill, 
New York, 1936. 
Pfluger, A.: "Stabilitaets Probleme der Elastostatik", Springer- 
Berlin, 1950. 
10. "Materials Manual", Aerophysics Development Corporation, 
1957. 
11. "Metals Handbook", Vol. I, Am, Sot. Metals, 1961. 
12 
E BE 
Em, Grn 
t 
\ \ 
\ 
Figure 1 
Idealized Composite Geometry 
FCRANTIS 
/ 1111111 
4 SYMMETRICAL 
(TRANSVERSE) 
b) ANTISYMMETRICAL 
(SHEAR) 
Figure 2 
Micro-Stability Failure Modes 
13 
! 
I- 
I 
1 ANTISYMMETRIC (SHEAR) BUCKLING 
YMMETRIC (TRANSVER 
I I I I I 
IO IO.0 b 1000 
MODULUS RATIO Ef E,,, / 
Figure 3 
Micro-Stability Failure Domains 
4 
ELASTIC CRIPPLING FAILURE 
b 
ANELASTIC CRIPPLING FAILURE 
YIELD 
Figure 4 
Composite Stress-Strain Limits 
15 
IO 
CC= -\ -0 \ \ ’ \ \ \ 
ANELASTIC 
@BORON /TITANIUM 
ELASTIC 
\ \ \ P  
aeoRoN /ALUMI NUM 
I BoRoN/MAGNESl UM 
03 0oRoNf EPOXY 
Anelastic and Elastic Shear Crippling Failure Domains 
IO 100 
Et/E - m  
Figure 5 
16 
Figure 6 
B/Mg Compression Test 
Sample - Side View 
Figure 8 
B/Mg Compression Test 
Sample - Top View After 
Failure 
Figure 7 
B/Mg Comprksion Test 
Sample - &= .71 - 
Partial Cross-section 
Microphotograph 10 x 
Linear Magnification 
Figure 9 
3-Point Bending Test 
Set-up 
17 
600 
20( 
I 
.004 .Ol 
Figure 10 
--T* 
MAG 
A .oos 
Tangent Shear Modulus for Magnesium and Composite Stress vs Strain 
2oc 
1.0 
.S 
.8 
.? 
.6 
* 
fm 
‘\ \ 
7 
THEORETICAL 
LEGEND t 
$COMPRESSlON TEST 
A SENDING TEST 
.I .2 .3 .4 .5 .6 .7 .0 .S 
Figure 11 o(+ 
B/Mg Composite - Predicted and Experimental Compressive Strength vs Packing Density 


Compressive strength of boron-metal composites

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