Analysis mechanical

Dynamic-mechanical testing of cross-linked samples are often carried out with high precision on specimen strips in torsion mode, e.g., with a Rheo-metrics Dynamic Analyzer II (RDA) with a sample size of 28x10x2 mm. Here, temperature-and strain sweeps are performed in a displacement range from 0.01% to about 5% strain and a frequency range between 0.1 and 100 Hz. Dynamic mechanical testing of uncross-linked samples can be made, e.g., with a Rubber Process Analyzer RPA 2000 (Alpha Technologies) from 0.28% to 350% strain at various frequencies and elevated temperatures. 

Dynamic Mechanical Analysis (DMA) is concerned with the measurement of the mechanical properties (mechanical modulus or stiffness and damping) of a specimen as a function of temperature. DMA is a sensitive probe of molecular mobility within materials and is most commonly used to measure the glass transition temperature and other transitions in macromolecules, or to follow changes in mechanical properties brought about by chemical reactions. 

For this type of measurement the specimen is subjected to an oscillating stress, usually following a sinusoidal waveform  

The applied stress produces a corresponding deformation or strain (e) 

The strain is measured according to how the stress is applied e.g. compression, tension, bending, shear etc.). Strain is dimensionless, but often expressed as a %. 

For an elastic material, Hooke s law applies and the strain is proportional to the applied stress according to the relationship  

Polymers vary from liquids and soft rubbers to very hard and rigid solids. Many structural factors determine the nature of the mechanical behavior of such materials. In considering structure-property relationships, polymers may be classified into one of several regimes, shown in the volume-temperature plot (Fig. 23.1). 

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

DMA can be applied to a wide range of materials using the different sample fixture configurations and deformation modes (Table 23.1) [10,11]. This procedure can be used to evaluate by comparison to known materials (a) degree of phase separation in multicomponent systems (b) amount type, and dispersion of filler (c) degree of polymer crystallinity, (d) effects of certain pretreatment and (e) stiffness of polymer composites [8,11]. 

Finally, one of the most useful ways of measuring viscoelastic properties is dynamic mechanical analysis, or DMA. In this type of experiment, an oscillating stress is applied to the sample and the response is measured as a function of the frequency of the oscillation. By using different instruments this frequency can be varied over an enormous range. Actually, the sample is usually stretched a little bit and oscillated about this strain also, the stress necessary to produce an oscillatory strain of a given magnitude is the quantity usually measured. If the sample being oscillated happens to be perfectly elastic, so that its response is instantaneous, then the stress and strain would be completely in-phase. If a sinusoidal shear strain is imposed on the sample we have (Equation 13-72)  

In contrast, the shear required to produce sinusoidal strain in a Newtonian fluid would be 90° or TtH out of phase with the strain, as Equations 13-74 would indicate. 

This should immediately suggest to you that in a viscoelastic solid the applied stress and resnlting strain should be out of phase by some angle intermediate between 0 and Ttfl radians. In other words, in order to obtain a sinusoidally varying strain (Equation 13-75)  

A stress that is d out of phase wonld have to be applied (Equation 13-76)  

You could think about the experiment the other way around. An oscillating stress [r(r) = rQsin(of could be applied to the sample and the resulting strain would lag the stress by an amount 5 [y = y iniyot - (5)]. But mathematically you can write it either way, the strain lagging the stress by d or the stress leading the strain by 5. Everybody writes 

Once the molecular motions occurring in the glassy state have been characterised and assigned through dielectric relaxation, 13C and 2H NMR, it is interesting to investigate their effect on the dynamic mechanical response of Ar-Al-PA [60,61], 

The temperature dependence of tan S at 1 Hz in the glassy state for the various xTyl -y copolyamides [60] is shown in Fig. 89. Three secondary transitions y, P and co, in the order of increasing temperature, are clearly observed. 

The y transition observed from dynamic mechanical analysis at 1 Hz, is centred around - 150 °C. However, the temperature range available experimentally does not permit observation of the whole y relaxation. The temperature position is independent of the chemical composition of the xTy -y copolyamides. 

Furthermore, a quantitative analysis [60] performed on the loss compliance, J , shows that the intensity of the y transition is mostly determined by the amount of lactam-12 units and does not depend on the nature, iso- or fere-, of the phthalic acid. 

As the y transition observed by dielectric relaxation at 1 Hz occurs at the same temperature and the 13C NMR experiments show that the lactam-12 unit motions are also involved, it is very likely that the molecular motions 

DMA calculations are applied to data in the linear region of a stress-to-strain curve. The calculations are most suited for low-amplitude sinusoidal strain when the sinusoidal strain is out of phase with sinusoidal stress. Design considerations for djmamic mechanical applications use values for the stress, strain, phase angle, storage modulus, and loss modulus [14, 15, 17, 18]. 

Information on dynamic mechanical analysis and properties is found in Chap. 3, Properties, and Chap. 4, Processes.  

The viscoelastic properties of a polymeric material can be described by its reversible and irreversible responses to deformation. These can be identified most easily by dynamic mechanical analysis (DMA). Usually, the adhesive is placed between two parallel plates, one of which is oscillating sinusoidally, and the torque is measured. From the amplitude and the phase shift of the sinusoidal stress - strain curve, the elastic component, which is in phase, and the viscous component, which is 90° out of phase, can be derived [211, p. 158 if]. 

the viscoelastic properties are characterized by the storage modulus C (the elastic component of the modulus), the loss modulus G (the viscous component of the modulus), and tan d = O lO (the tangent of the phase shift between stress and strain), which are fimctions of the deformation rate and temperature. The method offers valuable information for the development and the application of adhesive tapes. 

The maximum of tan 5 as a function of temperature is generally identified as the (dynamically defined) glass transition temperature Tg, which is dependent on the deformation rate. Usually it changes by 6-7 °C per decade of frequency [219, p. 253]. 

A mixture of two compatible polymers with different Tg values exhibits a single Tg which is influenced by the Tg values and weight fractions of the two components. In many cases this Tg can be calculated approximately by the Fox equation (Eq. 1) [219, p. 277 ff] 

A mixture of partially compatible polymers exhibits the Tg of at least one pure component and a Tg, which is dependent on the mixture, according to Equation (1). 

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Reversibly fonned micelles have long been of interest as models for enzymes, since tliey provide an amphipatliic environment attractive to many substrates. Substrate binding (non-covalent), saturation kinetics and competitive inliibition are kinetic factors common to botli enzyme reaction mechanism analysis and micellar binding kinetics. 

Figure 5.22 Problem domain in the micro-mechanical analysis of the particulate polymer composite...

Crack Tip Stresses. The simplest case for fracture mechanics analysis is a linear elastic material where stress. O, is proportional to strain, S,... 

Other PDMS—sihca-based hybrids have been reported (16,17) and related to the ceramer hybrids (10—12,17). Using differential scanning calorimetry, dynamic mechanical analysis, and saxs, the microstmcture of these PDMS hybrids was determined to be microphase-separated, in that the polysiUcate domains (of ca 3 nm in diameter) behave as network cross-link junctions dispersed within the PDMS oligomer-rich phase. The distance between these... 

The volatile content of the treated paper is important because moisture acts as a temporary plasticizer to promote resin flow during early stages of pressing (9). Dynamic mechanical analysis of the treated paper is a very useful means to study the initial flow stages of a resin and the cure time required to complete cross-linking (10). 

Glass-transition temperatures are commonly determined by differential scanning calorimetry or dynamic mechanical analysis. Many reported values have been measured by dilatometric methods however, methods based on the torsional pendulum, strain gauge, and refractivity also give results which are ia good agreement. Vicat temperature and britde poiat yield only approximate transition temperature values but are useful because of the simplicity of measurement. The reported T values for a large number of polymers may be found ia References 5, 6, 12, and 13. 

The principal techniques for determining the microstmcture of phenoHc resins include mass spectroscopy, proton, and C-nmr spectroscopy, as well as gc, Ic, and gpc. The softening and curing processes of phenoHc resins are effectively studied by using thermal and mechanical techniques, such as tga, dsc, and dynamic mechanical analysis (dma). Infrared (ir) and electron spectroscopy are also employed. 

Dynamic mechanical analysis provides a useful technique to study the cure kinetics and high temperature mechanical properties of phenoHc resins. The volatile components of the resin do not affect the scan or limit the temperature range of the experiment. However, uncured samples must be... 

Thermal analysis iavolves techniques ia which a physical property of a material is measured agaiast temperature at the same time the material is exposed to a coatroUed temperature program. A wide range of thermal analysis techniques have been developed siace the commercial development of automated thermal equipment as Hsted ia Table 1. Of these the best known and most often used for polymers are thermogravimetry (tg), differential thermal analysis (dta), differential scanning calorimetry (dsc), and dynamic mechanical analysis (dma). 

Changes in heat capacity and measurement of T for blends have been used to determine components of copolymers and blends (126—129), although dynamic mechanical analysis has been found to give better resolution. Equations relating T of miscible blends and ratios of components have been developed from dsc techniques, eg, the Fox equation (eq. 1), where f the blend, or is the weight fraction of component 1 or 2,... 

In a similar fashion. Thermally Stimulated Current spectrometry (TSC) makes use of an appHed d-c potential that acts as the stress to orient dipoles. The temperature is then lowered to trap these dipoles, and small electrical currents are measured during heating as the dipoles relax. The resulting relaxation maps have been related to G and G" curves obtained by dynamic mechanical analysis (244—246). This technique, long carried out only in laboratory-built instmments, is available as a commercial TSC spectrometer from Thermold Partners L.P., formerly Solomat Instmments (247). 

Table 9. ASTM Standards on Dynamic Mechanical Analysis...

Thermal Properties. Spider dragline silk was thermally stable to about 230°C based on thermal gravimetric analysis (tga) (33). Two thermal transitions were observed by dynamic mechanical analysis (dma), one at —75° C, presumed to represent localized mobiUty in the noncrystalline regions of the silk fiber, and the other at 210°C, indicative of a partial melt or a glass transition. Data from thermal studies on B. mori silkworm cocoon silk indicate a glass-transition temperature, T, of 175°C and stability to around 250°C (37). The T for wild silkworm cocoon silks were slightly higher, from 160 to 210°C. 

The thermal glass-transition temperatures of poly(vinyl acetal)s can be determined by dynamic mechanical analysis, differential scanning calorimetry, and nmr techniques (31). The thermal glass-transition temperature of poly(vinyl acetal) resins prepared from aliphatic aldehydes can be estimated from empirical relationships such as equation 1 where OH and OAc are the weight percent of vinyl alcohol and vinyl acetate units and C is the number of carbons in the chain derived from the aldehyde. The symbols with subscripts are the corresponding values for a standard (s) resin with known parameters (32). The formula accurately predicts that resin T increases as vinyl alcohol content increases, and decreases as vinyl acetate content and aldehyde carbon chain length increases. 

A partial answer to the first question has been provided by a theoretical treatment (1,2) that examines the conditions under which a matrix crack will deflect along the iaterface betweea the matrix and the reinforcement. This fracture—mechanics analysis links the condition for crack deflection to both the relative fracture resistance of the iaterface and the bridge and to the relative elastic mismatch between the reinforcement and the matrix. The calculations iadicate that, for any elastic mismatch, iaterface failure will occur whea the fracture resistance of the bridge is at least four times greater than that of the iaterface. For specific degrees of elastic mismatch, this coaditioa can be a conservative lower estimate. This condition provides a guide for iaterfacial desiga of ceramic matrix composites. 

Shock isolation is also possible usiag the dampiag characteristics of FZ elastomer. Dynamic mechanical analysis iadicates multiple transitions and a broad dampiag peak. This dampiag can be enhanced usiag formulatioas containing both siUca and carbon black fillers. 

Mechanical analysis. This includes detailed analysis of the bearing temperatures, lube, and seal oil systems and other mechanical subsystems. 

Fracture mechanics analysis requires the determination of the mode I stress intensity factor for a surface crack having a circular section profile. Here the circular section flaw will be approximated by a semi-elliptical flaw. 

E. P. Kennedy, Fracture Mechanics Analysis of Extruded Graphite, Extended Abstracts and Program-lb Biennial Conference on Carbon, Pub American Carbon Society, 1985, pp 287 288. 

Conversely, processes which convert carbons to sfp- carbons are more favorable for five-membered than for six-membered rings. This can be illustrated by the data for acetolysis of cyclopentyl versus cyclohexyl tosylate. The former proceeds with an enthalpy of activation about 3kcal/mol less than the latter." A molecular mechanics analysis found that the difference was largely accounted for by the relief of torsional strain in the cyclopentyl case." Notice that there is an angle-strain effect which is operating in the opposite direction, since there will be some resistance to the expansion of the bond angle at the reaction center to 120° in the cyclopentyl ring. 

In dynamic mechanical analysis of plastics, the material is subjected to a sinusoidal variation of stress and the strain is recorded so that 1, 2 and S can be determined. The classical variation of these parameters is illustrated in Fig. 2.55. 

For brittle failures we may use the fracture mechanics analysis introduced in the previous sections. From equations (2.96) and (2.99) we may write... 

Functional groups Glassing point temperature (Tg) K Thermo- mechanic analysis (TMK), K... 

Besides the thermodynamic modelings, the statistical mechanical analysis has also been used to study the high-pressure hexagonal phase of PE. Priest [73-75] re-... 

The dynamic mechanical analysis of the ternary blends with 75 25 PVC-ENR bl6nd showed single Tg at all levels of XNBR concentrations, which indicates the miscibility of the system. In the 50 50 PVC-ENR blend, when the concentration of XNBR increased, the blend becomes progressively miscible. 

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

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