Testing elastic modulus

In AFM, the relative approach of sample and tip is nonnally stopped after contact is reached. Flowever, the instrument may also be used as a nanoindenter, measuring the penetration deptli of the tip as it is pressed into the surface of the material under test. Infomiation such as the elastic modulus at a given point on the surface may be obtained in tliis way [114], altliough producing enough points to synthesize an elastic modulus image is very time consuming. 

As is true for macroscopic adhesion and mechanical testing experiments, nanoscale measurements do not a priori sense the intrinsic properties of surfaces or adhesive junctions. Instead, the measurements reflect a combination of interfacial chemistry (surface energy, covalent bonding), mechanics (elastic modulus, Poisson s ratio), and contact geometry (probe shape, radius). Furthermore, the probe/sample interaction may not only consist of elastic deformations, but may also include energy dissipation at the surface and/or in the bulk of the sample (or even within the measurement apparatus). Study of rate-dependent adhesion and mechanical properties is possible with both nanoindentation and... 

In a uniaxial tension test to determine the elastic modulus of the composite material, E, the stress and strain states will be assumed to be macroscopically uniform in consonance with the basic presumption that the composite material is macroscopically Isotropic and homogene-ous. However, on a microscopic scSeTBotFTfhe sfre and strain states will be nonuniform. In the uniaxial tension test,... 

Dynamic mechanical tests measure the response or deformation of a material to periodic or varying forces. Generally an applied force and its resulting deformation both vary sinusoidally with time. From such tests it is possible to obtain simultaneously an elastic modulus and mechanical damping, the latter of which gives the amount of energy dissipated as heat during the deformation of the material. 

Hard layer and soft layer combined together can reduce the intrinsic stress of the whole coating [17,18,22-27]. Samples 4, 5, and 6 have higher critical load than that of monolayer A and B. For Samples 5 and 6, no obvious crack occurs during the scratch test. Sample 5 has the highest hardness and reduced elastic modulus among the multilayer samples, and the interfaces in Sample 5 also contribute to scratch resistance. So it has the best micromechanical properties here. 

Figure 4 helps illustrate the terminology used for stress-strain testing. The slope of the initial straight-line portion of the curve is the elastic modulus of the material, In a tensile test this modulus is Young s modulus,... 

Since all practical methods of measuring the hardness of mbber involve measuring the resistance to indentation, hardness may be defined simply as resistance to indentation . Hardness is an expression of the elastic modulus of the mbber. More specifically, the load required to press a ball of given diameter to a given depth into the mbber is proportional to its elastic modulus. See Hardness Testing, Pusey and Jones Plastometer, Microhardness Testing. 

Tensile Modulus. Tensile samples were cut from the 0.125 in. plates of the compositions according to Standard ASTM D638-68, into the dogbone shape. Samples were tested on an Instron table model TM-S 1130 with environmental chamber. Samples were tested at temperatures of -30°C, 0°C. 22°C, 50°C, 80°C, 100°C and 130°C. Samples were held at test temperature for 20 minutes, clamped into the Instron grips and tested at a strain rate of 0.02 in./min. until failure. The elastic modulus was determined by ASTM D638-68. Second order polynomial equations were fitted to the data to obtain the elastic modulus as a function of temperature for each of the compositions. 

The elastic modulus (also called tensile modulus or modulus of elasticity) is the ratio of the applied stress to the strain it produces within the region where the relationship between stress and strain is linear. The ultimate tensile strength is equal to the force required to cause failure divided by the minimum cross-sectional area of the test sample. 

We will see in Section 5.4.2 that the elastic modulus of a unidirectional, continuous-fiber-reinforced composite depends on whether the composite is tested along the direction of fiber orientation (parallel) or normal to the fiber direction (transverse). In fact, the elastic modulus parallel to the fibers, Ei, is given by Eq. (1.62), whereas the transverse modulus, 2, is given by Eq. (1.63). Consider a composite material that consists of 40% (by volume) continuous, uniaxially aligned, glass fibers (Ef =16 GPa) in a polyester matrix (Em = 3 GPa). 

We have written Eq. (5.4) with variables grouped as they are in order to define two very important quantities. The first quantity in parentheses is called the modulus—or in this case, the tensile modulus, E, since a tensile force is being applied. The tensile modulus is sometimes called Young s modulus, elastic modulus, or modulus of elasticity, since it describes the elastic, or recoverable, response to the applied force, as represented by the springs. The second set of parentheses in Eq. (5.4) represents the tensile strain, which is indicated by the Greek lowercase epsilon, e. The strain is defined as the displacement, r — rp, relative to the initial position, rp, so that it is an indication of relative displacement and not absolute displacement. This allows comparisons to be made between tensile test performed at a variety of length scales. Equation (5.4) thus becomes... 

The modulus from a nanoindentation test is often reported in terms of a reduced elastic modulus, Er, to take into account the fact that at this size scale, the elastic response of the probe tip, E(, as well as the modulus of the test material, E, must be considered ... 

The tensile test is typically destructive that is, the sample is extended until it plasticly deforms or breaks, though this need not be the case if only elastic modulus determinations are desired. As described in the previous section, ductile materials past their yield point undergo plastic deformation and, in doing so, exhibit a reduction in the cross-sectional area in a phenomenon known as necking. 

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