Determination of Storage and Loss Moduli of MultiComponent Elastomers on the Universal Nano+Micro Materials Tester UNMT
1. Test model
The storage and loss moduli were derived experimentally from the dynamic penetration experiments. Complex modulus can be determined from the force single degree of freedom oscillator model via contact mechanics expression:

(1)

where m, k, c and F_{0} are oscillator mass, stiffness, damping, and amplitude of sinusoidal force, respectively. Solution of the Eq. 1 for the displacement amplitude X_{0} can be expressed as:

(2) 
here, w is a cyclic frequency (rad/s). Interacting contact stiffness k_{cont} and damping c_{cont} can be derived in the following way:

(3) 

(4) 
where, j is a phase shift angle between force and displacement, and k_{inst} is a force sensor stiffness. Utilizing contact mechanics equations:

(5) 
Adding relationship between elastic penetration depth h_{cont} , indenter radius R_{i} and elastic contact area A_{cont} storage modulus could be expressed in the following way:

(6) 
Storage modulus E’, loss modulus E’’, and complex modulus E have the following relationships:

(7) 

(8) 
A multicomponent tire sample mounted in a metallurgical sample holder was tested. The test was performed on the Universal Nano+Micro Tester model UNMT1 (Fig.1), with the tire sample attached to a force sensor, and a 1 mm diameter stainless steel ball attached to a linear reciprocating drive with a LVDT displacement sensor and oscillating with a 200μm amplitude (Fig.2). Force and displacement signals were recorded for 4 seconds at frequencies of 5, 10, 15, 20, 25, and 30Hz at several locations across the sample with 1.5 mm increments. Values of storage, loss, and complex moduli were derived according to the equations 6, 7, and 8.
Figure 1. Nano+Micro Tester UNMT1 
Figure 2. Test setup 
3. Test results
The following differences in moduli across the sample were observed:
three regions of different elastic moduli were distinguished, the softest in the vicinity of “A” and “B”, middlerange in vicinity of locations “C” and “D” (the closest to the metal cords), the hardest (stiffest) in the locations “E” and “F”;
storage modulus was found to be the lowest of 198MPa ±0.5MPa at the location “A” and the highest of 227MPa ±0.5MP at the locations “E” and “F”; positions “C” and “D” had 213 and 215MPa, respectively;
in contrast, the loss modulus was the highest at the middle locations “C” and “D” (228 and 230 + 0.5MPa, respectively), lowest at “E” and “F” (165MPa and 170MPa ±0.5MPa, respectively);
the complex modulus changes from 301MPa and 302MPa at the locations “A” and “B” to the highest 312 and 315 ±0.5MPa at the middle locations “C” and “D”, then drops to 281MPa and 282 ±0.5MPa at the locations “E” and “F”.
4. Conclusions
The Universal Nano+Micro Materials Tester UNMT1 has excellent performance in determining the storage and loss moduli across multilayered elastomers at different local test points.
The UNMT can perform local dynamic tests on various sample sizes and shapes (servocontrol of displacement allows for precision multipositioning on nonflat rough surfaces), with automatic mapping (both the indenter and test sample can be moved and positioned in any direction with 1 μm increments; easyattachable Optical Microscope module helps in positioning on target surface areas), in either X or Y or Z directions (Linear Reciprocating Drives are easilyexchangeable modules) on both micro and nano scales (the MicroHead and NanoHead are easilyexchangeable modules, with various dynamic indenters). UNMT is an ideal tool for quantitative mechanical characterization of complex materials.