Fig. 1 Lamina coordinate system
THE CHARACTERIZATION of engineering properties is a complex issue for fiber-reinforced composites due to their inherent anisotropy and inhomogeneity. In terms of mechanical proper-ties, advanced composite materials are evaluated by a number of specially designed test methods.
These test methods are mechanically simple in concept but extremely sensitive to specimen preparation and test-execution procedures. They include:
● Tensile tests
● Compression tests
● Shear tests
● Flexural tests
● Fracture tests
● Fatigue tests
These test methods are covered by standards de-veloped by ASTM, the International Standards Organization (ISO), and the Suppliers of Ad-vanced Composite Materials Association (SACMA).
This chapter is limited to tensile property test methods. Tensile testing of fiber-reinforced composite materials is performed for the pur-pose of determining uniaxial tensile strength, Young’s modulus, and Poisson’s ratio relative to principal material directions. The unidirectional lamina provides the basic building block of the multidirectional laminate. Therefore, character-ization of lamina material properties allows pre-dictions of the properties of laminates. In actual practice, considerable success has been demon-strated in predicting laminate effective modulus or Poisson’s ratio from ply properties. However, prediction of laminate strength properties from lamina strength data has proved more difficult, and therefore it is often necessary to resort to characterization of laminate strength properties.
Thus, basic tensile testing is divided into lamina
and laminate testing. There also are specimen differences between polymeric-matrix and metal-matrix composites that require separate discussions. Basic tensile-test methods for both polymeric-matrix and metal-matrix composites are confined to those materials that behave on the macroscale as orthotropic bodies.
Fundamentals of Tensile Testing of Composite Materials
Unlike homogeneous, isotropic materials, fi-ber-reinforced composites are characterized by properties that are direction-dependent. Ad-vanced composites, whether of the polymeric-matrix class or the metal-polymeric-matrix class, often are utilized in the form of a laminate. The lamina, or unidirectionally reinforced ply (Fig. 1), is the basic building block of the laminate. In order to perform engineering analysis, the heterogeneous lamina consisting of a fiber phase and a matrix phase is treated as a homogeneous, orthotropic material. In addition, laminate modeling as-sumes that plies are in a state of plane stress.
Stress-Strain Relationships for an Ortho-tropic Material. Development of stress-strain
relationships for an orthotropic material requires the definition of engineering constants. Using Fig. 1, the unidirectional material is orthotropic with respect to the x1-x2 axes. The stress-strain relationships for plane stress are of the forms
1 m12
where, in the usual manner, the normal stresses and strains in the x1and x2directions are denoted byr1,e1,r2, ande2, respectively, whereas the shear stress and strain are denoted by s12 and c12, respectively. In addition, E1, E2, and G12are the Young’s modulus parallel to the fibers, the Young’s modulus transverse to the fibers, and the shear modulus relative to the x1-x2plane, re-spectively. The major Poisson’s ratio, as deter-mined from contraction transverse to the fibers during a uniaxial test parallel to the fibers, is denoted by12. For laminates in which the mac-roscopic stress-strain relationships are ortho-tropic, Eq 1 is valid, with the subscripts 1 and 2 replaced by x and y, respectively.
Shear Coupling Phenomenon. Components of stress and strain can be transformed from one coordinate system to another. Thus, it is possible to establish the stress-strain relationship in any coordinate system. For the unidirectional com-posite in Fig. 1, the constitutive relationships relative to the x-y coordinate system can be writ-ten in the forms
1 m12 gx
Equations 2a, b, and c correspond to the stress-strain relationships of an anisotropic ma-terial subjected to plane stress. Of particular sig-nificance is the fact that the normal strains are coupled to the shear stress and the shear strain is coupled to the normal stresses. Such behavior is referred to as the “shear coupling
phenome-non” and requires the definition of two addi-tional elastic properties. In particular, the elastic constantsgx and gyare shear coupling coeffi-cients determined from uniaxial tensile tests in the x and y directions, respectively—i.e.,
cxy
g ⳱x (uniaxial tension in the x-direction) ex
(Eq 3a)
cxy
g ⳱y (uniaxial tension in the y-direction) ey
(Eq 3b) Symmetric Laminates and Laminate No-tation. As shown in Fig. 1, the principal mate-rial directions within each ply of a laminate are denoted by an x1-x2axis system. Laminate stack-ing sequences can be easily described for com-posites composed of layers of the same material with equal ply thickness by simply listing the ply orientations from the top of the laminate to the bottom. Thus, the notation [0⬚/90⬚/0⬚]
uniquely defines a three-layer laminate. The an-gle denotes the orientation of the principal ma-terial axis, x1, within each ply. If a ply were re-peated, a subscript would be used to denote the number of repeating plies. Thus, [0⬚/90⬚3/0⬚] in-dicates that the 90⬚ ply is repeated three times.
Any laminate in which the ply stacking se-quence below the midplane is a mirror image of the stacking sequence above the midplane is re-ferred to as a symmetric laminate. For a sym-metric laminate, such as a [0⬚/90⬚2/0⬚] plate, the notation can be abbreviated by using [0⬚/90⬚]s, where the subscript s denotes that the stacking sequence is repeated symmetrically. Angle-ply laminates are denoted by [0⬚/Ⳮ45⬚/ⳮ45⬚]s, which can be abbreviated as [0⬚/Ⳳ45⬚]s. For laminates with repeating sets of plies—e.g., [0⬚/
Ⳳ45⬚/0⬚/Ⳳ45⬚]s, the abbreviated notation is of the form [0⬚/Ⳳ45⬚]2s. If a symmetric laminate contains a ply that is split at the centerline, a bar is used to denote the split. Thus, the laminate [0⬚/90⬚/0⬚] can be abbreviated as [0⬚/ ⬚]90 s. For unsymmetric laminates, a subscript T is often used to denote total laminate. For example, the laminate [0⬚/90⬚] can be written as [0⬚/90⬚]T. This assures the reader that the laminate is in-deed unsymmetric and that a subscript s was not inadvertently omitted.
Balanced Laminates. Laminates in which each ply oriented at an angle ofⳭh (h ⬆ 0⬚ or 90⬚) also contains a ply at ⳮh are referred to as
Fig. 2 Schematic showing typical specimen-mounting method for determining single-filament tensile strength
balanced. Such composites are orthotropic rela-tive to the x-y coordinate of the laminate. Thus, Eq 1a, b, and c with the subscripts 1 and 2 re-placed by x and y, respectively, are applicable to balanced laminates.
Tensile Testing of
Single Filaments and Tows
Although emphasis in this chapter has been placed on tensile testing of laminates, other con-stituent materials are also tested. These include single filaments and tows (untwisted bundles of continuous filaments).
Single-filament tensile strength can be de-termined using ASTM D 3379 (Ref 1), which can be summarized as a random selection of sin-gle filaments made from the material to be tested. Filaments are centerline-mounted on spe-cial slotted tabs (Fig. 2). The tabs are gripped so that the test specimen is aligned axially in the jaws of a constant-speed movable-crosshead test machine. The filaments are then stressed to fail-ure at a constant strain rate. For this test method, filament cross-sectional areas are determined by planimeter measurements of a representative number of filament cross sections as displayed on highly magnified photomicrographs. Alter-native methods of area determination include the use of optical gages, an image-splitting micro-scope, or the linear weight-density method.
Tensile strength and Young’s modulus of elas-ticity are calculated from the load/elongation records and the cross-sectional area measure-ments. Note that a system compliance adjust-ment may be necessary for single-filaadjust-ment ten-sile modulus.
Tow tensile testing is carried out using ASTM D 4018 (Ref 2) or an equivalent test method. This is summarized as finding the ten-sile properties of continuous filament carbon and graphite yarns, strands, rovings, and tows by the tensile loading to failure of the resin-impreg-nated fiber forms. This technique loses accuracy as the filament count increases. Strain and Young’s modulus are measured by an extensom-eter.
The purpose of using impregnating resin is to provide the fiber forms, when cured, with enough mechanical strength to produce a rigid test specimen capable of sustaining uniform loading of the individual filaments in the speci-men.
To minimize the effect of the impregnating resin on the tensile properties of the fiber forms, the resin should be compatible with the fiber, the resin content in the cured specimen should be limited to the minimum amount required to pro-duce a useful test specimen, the individual fila-ments of the fiber forms should be well colli-mated, and the strain capability of the resin should be significantly greater than the strain ca-pability of the filaments.
ASTM D 4018 method I test specimens re-quire a special cast-resin end tab and grip design to prevent grip slippage under high loads. Al-ternative methods of specimen mounting to end tabs are acceptable, provided that test specimens maintain axial alignment on the test machine centerline and that they do not slip in the grips at high loads. ASTM D 4018 method II test specimens require no special gripping mecha-nisms. Standard rubber-faced jaws should be ad-equate.
Tensile Testing of Laminates
The basic physics of most tensile test methods are very similar: a prismatic coupon with a straight-sided gage section is gripped at the ends and loaded in uniaxial tension. The principal dif-ferences between these tensile test coupons are the coupon cross section and the load-introduc-tion method. The cross secload-introduc-tion of the coupon may be rectangular, round, or tubular; it may be straight-sided for the entire length (a “straight-sided” coupon) or width- or diameter-tapered from the ends into the gage section (often called
“dogbone” or “bow-tie” specimens). Straight-sided coupons may use tabbed load application points. This section briefly discusses the most common tensile test methods that have been standardized for fiber-reinforced composite ma-terials. Reference 3 includes a more detailed
dis-Fig. 3 Specimen for tensile testing of composites as defined in ASTM D 3039. Lg⳱ gage length; LT⳱ tab length;
h ⳱ tab bevel angle; W ⳱ width. Note: the gage length is com-monly 125 to 150 mm (5 to 6 in.).
cussion and briefly reviews several nonstandard methods as well.
By changing the coupon configuration, many of the tensile test methods are able to evaluate different material configurations, including uni-directional laminates, woven materials, and gen-eral laminates. However, some coupon/material configuration combinations are less sensitive to specimen preparation and testing variations than others. Perhaps the most dramatic example of this is the unidirectional coupon. Fiber versus load axis misalignment in a 0⬚ unidirectional coupon, which can occur due to either specimen preparation or testing problems or both, can re-duce strength as much as 30% due to an initial 1⬚ misalignment. Furthermore, bonded end tabs intended to minimize load-introduction prob-lems in high-strength unidirectional materials can actually cause premature coupon failure (even in nonunidirectional coupons) if not ap-plied and used properly. Because of these and similar issues, tensile testing is subject to a great deal of “art” in order to obtain legitimate data.
Alternatives to problematic tests, such as the unidirectional tensile test, are often available, and careful attention must be paid to the test specification for recommendations. Reference 1 is also an excellent resource for test optimization suggestions.
In-Plane Tensile Test Methods
Straight-sided coupon tensile tests include:
● ASTM D 3039/D 3039M, “Standard Test Method for Tensile Properties of Polymer-Matrix Composites”
● ISO 527, “Plastics—Determination of Ten-sile Properties”
● SACMA SRM 4, “Tensile Properties of Ori-ented Fiber-Resin Composites”
● SACMA SRM 9, “Tensile Properties of Ori-ented Cross-Plied Fiber-Resin Composites”
ASTM D 3039/D 3039M, originally released in 1971 and updated several times since then, is the original standard test method for straight-sided rectangular coupons (Fig. 3). It is still the most commonly used in-plane tension method.
ISO 527 parts 4 and 5 and the two SACMA tensile test methods, SRM 4 and SRM 9, are substantially based on ASTM D 3039 and as a result, are quite similar. Care should be taken, however, not to substitute one method for an-other, because subtle differences between them do exist. In general, the ASTM standard offers
better control of testing details that may cause variability, as discussed subsequently. For this reason, it is the preferred method.
In each of the previous test methods, a tensile stress is applied to the specimen through a me-chanical shear interface at the ends of the cou-pon, normally by either wedge or hydraulic grips. The material response is measured in the gage section of the coupon by either strain gages or extensometers, subsequently determining the elastic material properties.
If used, end tabs are intended to distribute the load from the grips into the specimen with a minimum of stress concentration. A schematic example of an appropriate failure mode of a multidirectional laminate using a tabbed tensile coupon is shown in Fig. 4. Because the straight-sided specimen provides no geometric stress-concentrated region, such as would be found in a specimen with a reduced-width gage section, failure often occurs at or near the ends of the tabs or grips. While this failure mode is not nec-essarily invalid, care must be taken when eval-uating the data to guard against unrealistically low strengths resulting from poorly performing tabs or overly aggressive gripping.
Design of end tabs remains somewhat of an art, and an improperly designed tab interface will produce low coupon strengths. For this rea-son, a standard tab design has not been man-dated by ASTM, although unbeveled 90⬚ tabs are preferred. Recent comparisons confirm that the success of a tab design is more dependent on the use of a sufficiently ductile adhesive than on the tab angle. An unbeveled tab applied with a ductile adhesive will outperform a tapered tab that has been applied with an insufficiently duc-tile adhesive. Therefore, adhesive selection is most critical to bonded tab use. Furthermore, the use of a softer tab material is usually preferred when testing high-modulus materials (such as fiber-glass tabs on a graphite-reinforced speci-men).
The simplest way to avoid bonded tab prob-lems is to not use them. Many laminates (mostly
Fig. 4 Typical tension failure of multidirectional laminate using a tabbed coupon
nonunidirectional) can be successfully tested without tabs, or with friction rather than bonded tabs. Flame-sprayed unserrated grips have also been successfully used in tensile testing without tabs.
Other important factors that affect tension testing results include control of specimen prep-aration, specimen design tolerances, control of conditioning and moisture content variability, control of test machine-induced misalignment and bending, consistent measurement of thick-ness, appropriate selection of transducers and calibration of instrumentation, documentation and description of failure modes, definition of elastic property calculation details, and data re-porting guidelines. These factors are described in detail by ASTM D 3039/D 3039M.
Limitations of the straight-sided coupon tensile methods are described subsequently.
Bonded Tabs. The stress field near the termi-nation of a bonded tab is significantly three-di-mensional, and critical stresses tend to peak at this location. Much research has been done on minimizing peak stresses, but it is impossible to make general recommendations that are appro-priate for all materials and configurations. Fur-thermore, improperly designed tabs can signifi-cantly degrade results. As a result, tabless or tabbed configurations that use unbonded tabs are becoming more popular, when the resulting fail-ure mode is appropriate.
Specimen Design. There are, particularly within ASTM D 3039, a number of coupon de-sign options included in the standard, which are needed to cover the wide range of materials sys-tems and lay-up configurations within the scope of the test method. Great care should be taken to ensure that an appropriate geometry is chosen for the material being tested.
Specimen Preparation. Specimen preparation plays a crucial role in test results. While this is true for most composite mechanical tests, it is particularly important for unidirectional tests, and unidirectional tensile tests are no exception.
Fiber alignment, control of coupon taper, and specimen machining (while maintaining align-ment) are the most critical steps of specimen preparation. For very low strain-to-failure
ma-terials systems or test configurations, like the 90⬚
unidirectional test, flatness is also particularly important. Edge machining techniques (avoid-ing machin(avoid-ing-induced damage) and edge sur-face finishes are also particularly critical to strength results from the 90⬚ unidirectional test.
Unidirectional Testing. All the elements that make tensile testing subject to error are exacer-bated in the unidirectional case, particularly in the 0⬚ direction. This has led to the increased use of a much less sensitive [90/0]ns-type laminate coupon (also known as the “crossply” coupon) from which unidirectional properties can be eas-ily derived (Ref 4). Properly tested crossply cou-pons often produce results equivalent to the best attainable unidirectional data. While unidirec-tional testing is still performed, and in certain cases may be preferred or required, a straight-sided, tabless, [90/0]ns-type coupon is now gen-erally believed to be the lowest cost, most reli-able configuration for lamina tensile testing of unidirectional materials. This straight-sided tab-less configuration also works equally well for nonunidirectional material forms and for other general laminates. Another advantage is that, unlike with 0⬚ unidirectional specimens, [90/
0]ns-type coupon failures do not usually mask indicators of improper testing/specimen prepa-ration practices.
Width tapered coupon tensile tests are standardized in ASTM D 638, “Standard Test Method for Tensile Properties of Plastics.” The test, developed for and limited to use with plas-tics, uses a flat, width-tapered tensile coupon with a straight-sided gage section. Several ge-ometries are allowed, depending on the material being tested. Figure 5 shows a schematic of one general configuration. Despite its heritage, this coupon has also been evaluated and applied to composite materials. The coupon taper is ac-complished by a large cylindrical radius between the wide gripping area at each end and the nar-rower gage section, resulting in a shape that jus-tifies the nickname of the “dogbone” coupon.
The taper makes the specimen particularly un-suited for testing of 0⬚ unidirectional materials, because only about half of the gripped fibers are continuous throughout the gage section. This
Fig. 6 Stress concentration adjacent to a hole in a composite laminate subjected to uniaxial loading
Fig. 5 Schematic of typical ASTM D 638 test specimen geometry. W, width; Wc, width at center; WO, width overall; T, thickness;
R, radius at fillet; RO, outer radius; G, gage length; L, length; LO, length overall; D, distance between grips
usually results in failure by splitting at the ra-dius, due to inability of the matrix to shear the load from terminated fibers into the gage sec-tion.
While the ASTM D 638 coupon configuration has been successfully used for fabric-reinforced composites and with general nonunidirectional laminates, some materials systems remain sen-sitive to the stress concentration at the radius.
For its intended use with plastics, the coupon is molded to shape. Likewise, discontinuous fiber composites can be molded to the required ge-ometry. To ensure valid results, care must be
For its intended use with plastics, the coupon is molded to shape. Likewise, discontinuous fiber composites can be molded to the required ge-ometry. To ensure valid results, care must be