Strain Stress relaxation

Many designs incorporate the phenomenon of stress-relaxation. For example, in many products, when plastics are assembled they are placed into a permanently deflected condition, as for instance press fits, bolted assemblies, and some plastic springs. In time, with the strain kept constant the stress level will decrease, from the same internal molecular movement that produces creep. This gradual decay in stress at a constant strain (stress-relaxation) becomes important in applications such as preloaded bolts and springs where there is concern for retaining the load. The amount of relaxation can be measured by applying a fixed strain to a sample and then measuring the load with time. 

Because all tissues are viscoelastic this means that their mechanical properties are time dependent and their behavior is characterized both by properties of elastic solids and those of viscous liquids. The classic method to characterize a viscoelastic material is to observe the decay of the stress required to hold a sample at a fixed strain (stress relaxation) or by the increasing strain required to hold a sample at a fixed stress (creep) as diagrammed in Figure 7.1 and explained further in Figure 7.2. Viscoelastic materials undergo processes that both store (elastic) and dissipate (viscous)... 

As a result of the above process, the stress r° is built up. If at t = t we finish applying a strain, stress relaxation will take place, obeying... 

Fig. 4.5 Step-strain stress relaxation experiment (a) a constant strain Ao is applied at time t = 0 (e 0) and maintained for all times t > 0 (b) the stress relaxation a t) responding to the applied step strain.

Further detailed aspects of the viscoelastic behavior of amorphous copolymers that have been reported includes linear stress-relaxation behavior (49) and creep properties in the glass-transition region (50). Chen and co-workers (51) have also reported the large strain-stress relaxation and strain recovery of copolymers at temperatures above Tg, and found that the observed behavior could be rationalized in terms of various network models. 

In many applications (e.g., those involving an interference fit, such as pipe couplings, closures, and so on) we are concerned more with the decrease in stress with time at constant strain (stress relaxation), rather than with the increase in strain with time under constant stress (creep). 

The materials were studied in the form of thin films. Physical and mechanical properties were determined by DSC, torsion pendulum, stress strain, stress relaxation and water contact angle measurements. Transport properties were determined in alkaline solution. Evidence of the films microporosity is seen from ion and water sorption, sodium ion self-diffusion and electrolytic conductance measurements. The latter results for lower equivalent weight samples in concentrated NaOH solutions demonstrate that these materials are promising candidates as separators in advanced alkaline water electrolysis cells. 

Structural characterization of the polymers was obtained by FT-IR and NMR spectroscopy using a Nicolet MX-1 and Varian EM-390 spectrometer. The IR spectra for the oligomers and the copolymers were obtained from solution cast films on KBr discs. Dog-bone specimens were cut from the films for mechanical testing of the segmented copolymers. Mechanical measurements included stress-strain, stress relaxation, tensile hysteresis and permanent set behavior. All these tests were performed on an Instron. Model 1122 at room temperature. All stress-strain and hysteresis measurements were carried out at a strain rate of 200 per minute based on the initial sample length. 

Step-strain stress-relaxation measurements have been frequently used to determine Sr(X) for polymer melts > . Equation (6) shows that if separability of time and strain effects is possible for the melt under consideration, the stress after a step elongational strain can be factored into a time-dependent function, the linear shear relaxation modulus G(t), and a strain-dependent function, the nonlinear strain measure Sr(X). Also other types of experiment may be oerformed to obtain Sr(X), such as constant-strain-rate experiments "", creep under constant stress and constant-stretching-rate experiments but these methods require more involved analytical and/or numerical calculations. 

In addition to the normal stress differences and manifestations of non-Newtonian flow mentioned above, all the viscoelastic experiments described in Section C above (stress relaxation after sudden strain, stress relaxation after cessation of steady flow, creep, creep recovery, behavior in oscillating deformations, etc.) become much more complicated when deformations are large. A few examples will be shown in Chapter 2 and others in Chapters 13 and 17. 

Shape memorization is essentially a manner of strain or stress storage and release. The recovery stress of the T -SMPUs and T -SMPUUs should be eqiral to the deformation stress excluding its energetic part, the losses caused by unfixed strain, stress relaxation and decreasing modirlus. 

The breadth of the scope of nonlinear phenomena can be grasped in part by considering the various time-dependent probes of linear viscoelasticity cited in Table 3.3.2 sinusoidal oscillation, creep, constrained recoil, stress relaxation after step strain, stress relaxation after steady shearing, and stress growth after start-up of steady shearing. In the linear regime— that is, at small strains or small strain rates—the experimental results of any one of these probes (in simple shear, for example) can be used to predict results for any of the other probes, not only for simple shearing defor-... 

Uniaxial extension is an axi-symmetric deformation in which a tensile stress is appHed in one direction, we will call it the z-direction, while the free surfaces of the sample are under a uniform normal stress, usually one atmosphere of compression. The quantity measured is the net tensile stress t7g defined as (- a ), which is the applied axial stress minus that acting on the free surface. One could, in principle, carry out step-strain (stress relaxation) in extension, and if the tensile relaxation modulus (t,e) can be separated into time and strain-dependent contributions, a damping function could be determined as a function of strain. 

Figure 3.5. Calculated Ramp Strain Stress Relaxation Behavior of a Permanent Memory Material...

In addition, instruments can be operated in constant stress (creep) and constant strain (stress relaxation) modes. 

Stress-strain, stress relaxation and the energy loss during unload-reloading of PU were undertaken [2,4], The percent relaxation values in the case of DBDI based PU... 

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