Stress-controlled experiment

We have developed the idea that we can describe linear viscoelastic materials by a sum of Maxwell models. These models are the most appropriate for describing the response of a body to an applied strain. The same ideas apply to a sum of Kelvin models, which are more appropriately applied to stress controlled experiments. A combination of these models enables us to predict the results of different experiments. If we were able to predict the form of the model from the chemical constituents of the system we could predict all the viscoelastic responses in shear. We know that when a strain is applied to a viscoelastic material the molecules and particles that form the system gradual diffuse to relax the applied strain. For example, consider a solution of polymer... 

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The viscosity obtained from the above equation in the linear region of a creep experiment can be used to extend the low-shear rate region of apparent viscosity versus shear rate data obtained in a flow experiment by about two decades (Giboreau et al., 1994 Rayment et al., 1998). The low shear rate region of about 10 -10 is often used for the characterization and differentiation of structures in polysaccharide systems through the use of stress controlled creep and non destructive oscillatory tests. The values of strain (y) from the creep experiment can be converted to shear rate from the expression y t) = y t)/t. 

Upon exceeding a critical stress, ductile surfaces deform plastically. Often in nanoindentation experiments under controlled load, the indenter moves in a... 

In the formulas, e t), e(t), a t) is respectively strain rate, strain and stress. C is the elastic wave velocity in pressure bar, 5060 m/s. is the elastic modulus of bar material, 200 Gpa. A, L is respectively cross-sectional area and length of specimen. The impact velocity of experiment was controlled within 2-6 m/s. Because the impact velocity of bullet is provided by high pressure gas, the impact speed of coal and limestone samples will vary slightly. 

The light-induced shape-memory functionality of the polymers is quantified by cyclic, photomechanical experiments luider stress-controlled and/or strain-controlled conditions. These cyclic experiments have been designed in analogy to those characterizing a thermally-induced SME. 

Fig. 16 Cyclic, photomechanical experiment. Tests performed with a grafted polymer (obtained by copolymerization of n-butylacrylate, hydroxyethyl methacrylate and ethyleneglycol-1-acrylate-2-CA with poly(propylene glycol)-dimethacrylate as crosslinker (10,2,1)) under stress-controlled conditions. Here Smax = 10%, T = 25°C is the temporarily fixed elongation, and gp is the remaining elongation after shape recovery. Taken from ref. [29]. Reprinted by permission from Macmillan Publishers Ltd, Copyright 2005. http //dx.doi.org/10.1038/nature03496...

The creation of the triple-shape capability for an AB polymer network system by a simple one-step process similar to a conventional dual-shape progranuning process was shown for networks based on PCL and PCHMA [24] (see Sect. 2.4). In these materials a stress-controlled cyclic, thermomechanical experiment was used to quantify the triple-shape effect. The sample was deformed at 150°C (liigh) to 50% (Ein) and subsequently cooled to —10°C (Tio ). The large temperature interval of around 160 K led to a strong reduction of the strain. When the sample was heated... 

Table 2 Impact of aqueous environment and drug loading with ethacridine lactate (EL) and enoxacine (EN) on key shape memory properties from stress-controlled experiments and on the thermal transition of an amorphous oLG tetrole derived SMP network. Modified from [30]. Copyright 2009, with permission from Elsevier...

Since most DMA experiments are run at very low strains ( 0.5% maximum) to stay well within a polymer s linear region, it has been reported that both the analyzers give the same results. However, when one gets to the nonlinear region, the difference becomes significant, as stress and strain are no longer linearly related. Stress control can be said to duplicate real-life conditions more accurately since most applications of polymers involve resisting a load. 

Rheological experiments were carried out on a stress-controlled rheometer type CVO-120 (Bohlin, Germany) with cone-plate geometry, cone-angle a = 1 , cone radius R = 20 mm. 

If we look at an S-N curve (figure 10.18), we can see that the number of cycles to failure strongly depends on the stress in the LCF regime. Small scatter in the stress-strain properties of different specimens (due to scatter in the material properties, for example) would cause large changes in the number of cycles to failure measured in the experiment. The scatter band would thus be rather wide. In this regime, strain-controlled experiments are more useful since, with a prescribed strain amplitude, the scatter of the stress amplitude is small. Furthermore, stress-controlled experiments would also cause more rapid failure due to the reduction in the cross section of the specimen caused by crack propagation ]113]. 

If a strain-controlled fatigue experiment is performed at a non-zero mean strain, cyclic relaxation may occur in addition to cyclic hardening or softening, with the mean stress decreasing over time (figure 10.31(a)). If, on the other hand, the experiment is stress-controlled at a non-zero mean stress, the hys-... 

Analyzers are available for both strain (displacement) and stress (force) control. On the one hand, under strain control, the probe is displaced and the resulting stress of the sample is measured by implementing a force balance transducer, which utilizes different shafts. The advantages of strain control include a better short-term response for materials of low viscosity, which allows experiments of stress relaxation to be performed with relative ease. On the other hand, under stress control a set force is applied while several other experimental conditions (temperature, frequency, or time) are varied. Although stress control analyses are... 

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However, the software of advanced stress controlled instruments allows for running an experiment at variable strain amplitudes. In this operation mode, several iterative cycles have to be measured before the actual measurement. In these iterations, the applied torque is adjusted to produce the desired strain amplitude [27]. In contrast to the classical way of amplitude adjustment, new operating modes of stress controlled rheometers (termed Direct Strain Oscillation or Continuous Oscillation) use a feedback control to compare the current strain signal y(t) at time t to the desired pure sinusoidal signal yd t) = y o sin(control loop then adjusts the torque accordingly in order to minimize the difference Yd t + At) — y (t -I- At)I for the next step at t -I- At. This deformation control enables a stress controlled rheometer to mimic a strain controlled experiment [27]. This holds true even beyond the linear regime where nonlinear contributions to the strain wave are compensated for and are then transferred into the stress wave, as the control loop tries to make the appropriate adjustments to the torque within minimum time. 

LAOS measurements for two samples, a polyisoprene melt (abbreviated PI-84k, Mw = 84,000 g/mol, PDI = 1.04) and a 10 wt% solution of poly isobutylene (abbreviated PIB, Af = 1.1 xlO g/mol) in oligoisobutylene, were conducted on four different rheometers. The first two were separated motor transducer(SMT)-rheometers, namely the ARES-G2 (TA Instruments) and the ARES-LS (TA Instruments) with a IKFRTNl transducer. The DHR-3 (TA Instruments) and the MCR501 (Anton Paar) are in principle stress controlled instruments, but can be used for strain controlled experiments when using the deformation control feedback option (called continuous oscillation for DHR-3 and direct strain oscillation for MCR501). 

Merger D, Wilhelm M (2014) Intrinsic nonlineeuity from LAOStiain—experiments on various strain and stress-controlled rheometers a quantitative comparison. Rheol Acta 53(8) 621-634... 

Both controlled-angular displacement (strain-controlled) and controlled-torque (stress-controlled) rotational rheometers are used, with the former giving superior performance at high frequencies and the latter better precision at low frequencies. There have also recently appeared on the market instruments said to be capable of operating in both modes. Controlled torque instruments can also be used to make creep and creep recovery tests, which are described in the next section. In order to obtain a linear viscoelastic characterization that includes the terminal zone, it is sometimes useful to combine data from oscillatory flow with those from a creep experiment, and this is also discussed in the following section. Rheometrical methods are described in some detail in several books [3,8,9]... 

Since it is the long-time behavior that is closely related to molecular structure, this is the information that is most interesting in the present context. For example, the zero-shear viscosity describes behavior in the limit of zero frequency and is very sensitive to molecular weight. However, for a material whose longest relaxation time is quite large, neither step-strain nor oscillatory shear experiments are useful to probe the behavior at very long times or very low frequencies. The main problem is that the stress is so small that it is not possible to measure it precisely. It is in this region that creep measurements are most useful. This is because it is possible to make a very precise measurement of a displacement, and it is also possible to apply a very small controlled stress. Controlled-torque (controlled-stress) rheometers are available from several manufacturers. 

Concentrations of hydrostatic stresses ahead of and equivalent plastic strains at the local carbide crack tips arise in both mode I and mode II loadings as shown in [5] and [11] - [13]. They give rise to the assumption of localized void nucleation and growth in both failure modes (Fig. 12). These processes are known from experiment to control the failure process unaer mode I loading [1]. The results presented suggest a crack propagation by void nucleation, growth and coalescence as shown in Fig. 13. 

Thanks to their relatively lower viscosity, food and cosmetic products allow this type of behavior to be easily documented, when performing experiments with controlled stress rheometers. There are commercial versions of such instruments, essentially rotating systems (parallel disks or cone-and-plate), which have the capability to measure extremely small rotation rates (in the 10 rad/s, i.e., one revolution in 20 years ). Experiments performed in such conditions are called creep testing using controlled torques as low as 10 Nm with a resolution of 10 Nm. Figure 5.5 shows an example of the shear viscosity function (vs. shear stress) measured on a typical cosmetic product (body cream), using such a controlled stress rheometer. 

The Institute has many-year experience of investigations and developments in the field of NDT. These are, mainly, developments which allowed creation of a series of eddy current flaw detectors for various applications. The Institute has traditionally studied the physico-mechanical properties of materials, their stressed-strained state, fracture mechanics and developed on this basis the procedures and instruments which measure the properties and predict the behaviour of materials. Quite important are also developments of technologies and equipment for control of thickness and adhesion of thin protective coatings on various bases, corrosion control of underground pipelines by indirect method, acoustic emission control of hydrogen and corrosion cracking in structural materials, etc. 

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