Mechanical property measurement deformation under load

The principles of strength of materials are applied to the design of structures to assure that the elements of the structures will operate reliably under a known set of loads. Thus the field encompasses both the calculation of the strength and deformation of members and the measurement of the mechanical properties of engineering materials. 

In principle, the mechanical properties of particles can be determined by measuring their deformation under a mechanical load. This may be realised on single particles or a population. Mechanical characterisation of single particles is relatively difficult, particularly when their sizes are in the micro or nano ranges. The basis of many techniques for mechanical characterisation of single particles is micromanipulation. This can be... 

To quantify the mechanical properties of the shells from these measurements, we use the analytical solution obtained by Reissner as a starting point [22,23], This result describes the deformation of shallow spherical caps under point like loads. It is a special case of the more general solution found by Koiter for the deformation of a thin elastic shell under point like loads at the poles [24], Al-... 

As we saw in the preceding discussion, several mechanical parameters can be derived from stress-strain tests. Two of these parameters are of particular significance from a design viewpoint. These are strength and stiffness. For some applications, the ultimate tensile strength is the useful parameter, but most polymer products are loaded well below their breaking points. Indeed, some polymers deform excessively before rupture and this makes them unsuitable for use. Therefore, for most polymer applications, stiffness (resistance to deformation under applied load) is the parameter of prime importance. Modulus is a measure of stiffness. We will now consider how various structural and environmental factors affect modulus in particular and other mechanical properties in general. 

Transition temperatures that characterize the stmcture and behavior of polymers have already been dealt with some length. From a practical point of view, limiting temperatures for use is also of interest. One should differentiate between a statistical value derived from use data without material damage and a standard test under prescribed conditions, namely, heat distortion or deflection. In the latter, the temperature is measured wherein the samples undergo a definite deformation under a defined load (usually 264 psi). This temperature is taken to be an upper limit for use of the material without the danger of warping. This value obviously depends on the load (inversely affected). Thermal endurance can also be expressed by time and temperature data that affect mechanical and electrical properties. Data verify that for most polymers, the upper limiting useful temperature is rather low (60 -85 C),... 

The third complication is that the measured force - position curve relates to the distance from sample support to probe support. There are several compliant objects in series here. These are the cantilever, the tip, the tip-surface contact region, and the rest of the sample. The softest of these objects is the cantilever, and it deforms the most. However, the sample will also deform under the load applied by the tip. If the sample is soft, its mechanical properties will affect the results. These are elastic properties if the deflections are small, plastic properties if the local forces are large. 

In any given material, the relaxation modulus will reflect the response of the material on different timescales. To make a measurement, materials are deformed under a periodic load with frequency w. Then, G and G are measured across a wide range of frequencies (typically three to four decades). Measurements of G and G" can be used to characterize the mechanical properties of soft materials, including polymer networks and colloidal systems. The technique is also known as mechanical spectroscopy. In a viscoelastic material, the elastic modulus will cross over the viscous modulus at the transition point from viscous to elastic bulk behavior and indicates a possible sol-gel transition or the onset of rubbery behavior in a polymer network. 

Another mechanical property that may be important to consider is hardness, which is a measure of a material s resistance to localized plastic deformation (e.g., a small dent or a scratch). Early hardness tests were based on natmal minerals with a scale constructed solely on the ability of one material to scratch another that was softer. A qualitative and somewhat arbitrary hardness indexing scheme was devised, termed the Mohs scale, which ranged from 1 on the soft end for talc to 10 for diamond. Quantitative hardness techniques have been developed over the years in which a small indenter is forced into the surface of a material to be tested under controlled conditions of load and rate of application. The depth or size of the resulting indentation is measured and related to a hardness number the softer the material, the larger and deeper the indentation, and the lower the hardness index number. Measured hardnesses are only relative (rather than absolute), and care should be exercised when comparing values determined by different techniques. 

The storage modulus provides a measure of the effective stiffness of the material under dynamic loading conditions. The mechanical damping indicates the amount of energy dissipated as heat during the deformation of the material. Both properties are strongly dependent on frequency and temperature. 

Viscoelastic characteristics of polymers may be measured by either static or dynamic mechanical tests. The most common static methods are by measurement of creep, the time-dependent deformation of a polymer sample under constant load, or stress relaxation, the time-dependent load required to maintain a polymer sample at a constant extent of deformation. The results of such tests are expressed as the time-dependent parameters, creep compliance J t) (instantaneous strain/stress) and stress relaxation modulus Git) (instantaneous stress/strain) respectively. The more important of these, from the point of view of adhesive joints, is creep compliance (see also Pressure-sensitive adhesives - adhesion properties). Typical curves of creep and creep recovery for an uncross-Unked rubber (approximated by a three-parameter model) and a cross-linked rubber (approximated by a Voigt element) are shown in Fig. 2. 

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