Rubber elasticity indentation

Stress/strain relationships are commonly studied in tension, compression, shear or indentation. Because in theory all stress/strain relationships except those at breaking point are a function of elastic modulus, it can be questioned as to why so many modes of test are required. The answer is partly because some tests have persisted by tradition, partly because certain tests are very convenient for particular geometry of specimens and partly because at high strains the physics of rubber elasticity is even now not fully understood so that exact relationships between the various moduli are not known. A practical extension of the third reason is that it is logical to test using the mode of deformation to be found in practice. 

By determining its resistance to a rigid indentor to which a force is applied, the hardness measurement is obtained, giving the measure of the elastic modulus of the rubber. Hardness may be regarded as depending simply on Young s modulus, as the cured rubber is perfectly elastic. Indentation involves deformation in tension, shear, and compression. 

It is customary to characterize the modulus, stiffness, or hardness of rubbers by measuring their elastic indentation by a rigid die of prescribed size and shape under specified loading conditions. Various nonlinear scales are employed to derive a value of hardness from such measurements (Soden, 1952). Corresponding values of shear modulus G for two common hardness scales are given in Figure 1.18. 

In principle, as in metals it is possible to measure indentation magnitude after unloading or under load whereas the latter method is preferred for plastics and in the case of elastomers unavoidable due to the rubber-elastic redeformation. 

As the rubber hardness is a measurement of almost completely elastic deformation, it can be related to elastic modulus. Most rubber hardness tests measure the depth of penetration of an inden-tor under either a fixed weight or a spring load, and when rubber is assumed to be an elastic isotropic medium, the indentation obtained at small deformation depends on the elastic modulus, the... 

The apparently simple process of indentation involves deformations in tension, shear and compression but, as in the case of a perfectly elastic rubber the moduli controlling these are closely related, it is convenient to regard hardness as depending simply on Young s modulus. Approximate relationships for various geometries of indentor have been given in Section 1 and will be further considered, where appropriate, for the standard methods in later sections. 

The measured hardness decreases with time of load application because rubbers are not perfectly elastic, hence results at different times will not be in agreement. Furthermore, the effect will be material dependent. The effect of time was investigated in some detail for Shore A58 several decades ago by filming both the durometer on a stand and the stopwatch. This work demonstrated the considerable creep that occurs and concluded that manual measurements should be taken at 30 sec. Measurements were also made with a dead load tester which showed less creep than the Shore because the load is constant and not increasing with indentation. 

Fig. 42. Depth variation of the elastic modulus for rubber, two different polyurethanes, PVC and PS as a function of the indentation depth. Bars demonstrate the range of elastic bulk modulus variation for a specific material. Reproduced from [415]...

Microhardness, therefore, appears to be an elastic-plastic rather elusive parameter (Marsh, 1964). Microhardness as a property is, in fact, a complex combination of other properties elastic modulus, yield strength and strain hardening capacity. One way to differentiate between the reversible and irreversible components of contact deformation is to measure the elastic recovery during unloading of the indenter (Stilwell Tabor, 1961). Extreme cases of depth recovery are best described by soft metals, where it is negligible, and fully elastic rubber, where it is complete. 

The standard test method for measuring the durometer hardness of rubbers according to ASTM D2240-05 [6] is based on the penetration of a specified indentor forced into the material under specified conditions. The indentation hardness is inversely related to the penetration and is dependent on the elastic modulus and viscoelastic behaviour of the material. This method is an empirical test intended primarily for control purposes. No simple relationship exists between indentation hardness determined by this method and any fundamental property of the material tested. 

Let us consider further the theoretical estimation of the value, according to the two methods and compare these results with the ones obtained experimentally. The first method simulates the interfecial layer in the polymer composites as a result of the interaction of two fiactals - the polymer matrix and the nanofiller surface. In this case there is a sole linear seale /, which defines the interpenetration distance of the fiactals. Since the nanofiller elasticity modulus is essentially higher than the corresponding parameter for rubber (in this case - by 11 times, see Fig. 1.1), then the indicated interaction reduces to nanofiller indentation in the polymer matrix and then / = / ... 

PU two-part sealants cure to a durable rubber consistency with high elasticity, abrasion/indentation resistance and bonding strength over a wide range of temperatures. 

This consideration already shows that hardness is a complex material property because the elastic and plastic properties of the material play a role. In materials that are not linear-elastic and can deform with large elastic deformations, there is no simple relation between hardness and the yield strength. This is illustrated by rubber, which cannot be indented permanently, resulting in an infinite hardness. 

Microprobing technique applied here is sensitive to the depth distribution of the elastic properties and can provide insight on buried details of the surface distribution of different polymer phases. As demonstrated in Figure 4, elastic modulus for the rubber phase shows the presence of hard PS surface underneath of compliant material. The elastic modulus depth profile shows a large variation at a very low indentation depth (below 20 nm) caused, mainly, by the instability of the first mechanical contact as discussed in our previous papers [12-14]. In the range of indentation depths from 20 to 150 nm, a gradual decrease of elastic modulus is observed that can be related to either surface hardening phenomena or rate dependent (viscoelastic) contribution. At intermediate indentation depth, a stable, virtually constant value of the elastic modulus is recorded. 

By combining optimal cantilever parameters and experimental conditions one can obtain reliable force distance data which is appropriate for further contact mechanics analysis for a wide selection of polymeric materials. Both Sneddon s and Hertzian models of elastic contact give consistent results in the range of indentation depth up to 100 nm. Close correlation is observed between elastic moduli determined by SFM in compression mode (approaching cycle) and measured values for bulk materials. As shown, for elastic materials force-distance curves can be used for evaluation of tensile elastic moduli from retracing cycle. For rubber material, the latest is in a good agreement with measuremente in compression mode. 

This property may indicate the rubber like nature of the matrix the indenter stress is probably distributed to other parts of the shell and stored as elastic energy which is released when the indenter is raised. ... 

---