Stress transient

The common civil engineering seismic testing techniques work on the principles of ultrasonic through transmission (UPV), transient stress wave propagation and reflection (Impact Echo), Ultrasonic Pulse Echo (UPE) and Spectral Analysis of Surface Waves (SASW). 

A problem obviously exists in trying to characterise anomalies in concrete due to the limitations of the individual techniques. Even a simple problem such as measurement of concrete thickness can result in misleading data if complementary measurements are not made In Fig. 7 and 8 the results of Impact Echo and SASW on concrete slabs are shown. The lE-result indicates a reflecting boundary at a depth corresponding to a frequency of transient stress wave reflection of 5.2 KHz. This is equivalent to a depth of 530 mm for a compression wave speed (Cp) of 3000 m/s, or 706 mm if Cp = 4000 m/s. Does the reflection come from a crack, void or back-side of a wall, and what is the true Cp ... 

Because the integral in Figure 10.5 reflects more than just a transient stress on the system (it also includes the cumulative contribution of unknown hand-written checks), this search for a useful indicator of system stress that could be used as a driving force for the estimation of future clearings was abandoned. 

However, if the rate of heat transfer is not infinite the thermal shock-induced stresses will gradually build up and after some time reach a peak value that will be a fraction of the value given by equation (15.10). The solution requires transient stress analysis such as those of Cheng (1951) and Manson (1966) with the assumption of the plate of Fig. 15.1 being infinite. Following Fu and Fleck (1998), the plate is initially held at temperature T0 and at time t= 0 its top and bottom faces (at /= H) are suddenly exposed to a convective medium of temperature T, . The surface heat flow is assumed to satisfy... 

The simplest theory of impact, known as stereomechanics, deals with the impact between rigid bodies using the impulse-momentum law. This approach yields a quick estimation of the velocity after collision and the corresponding kinetic energy loss. However, it does not yield transient stresses, collisional forces, impact duration, or collisional deformation of the colliding objects. Because of its simplicity, the stereomechanical impact theory has been extensively used in the treatment of collisional contributions in the particle momentum equations and in the particle velocity boundary conditions in connection with the computation of gas-solid flows. 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

J. A. van Aken and H. Janeschitz-Kriegl, Rheol. Acta, Simultaneous measurement of transient stress and flow birefringence in one sided compression (biaxial extension) of a polymer melt, Rheol. Acta, 20,419 (1981). 

The adhesive s thermal conductivity is important in minimizing transient stresses during cooling. This is why thinner bond thickness and adhesives or sealants with higher levels of thermal conductivity generally have better cryogenic properties. 

At elevated temperatures, creep deformation and transient stress redistribution between the fibers and matrix can have a significant influence on... 

In the latter case, the transient stress can be stated as well. The isothermal result for constant a is5... 

When the applied stress a is less than Su, creep of the matrix will commence after application of the load. During this creep, the matrix will relax and the stress on the fibers will increase. Therefore, further fiber failure will occur. In addition, the process of matrix creep will depend on the extent of prior fiber failure and, as mentioned previously, on the amount of matrix cracking. The details will be rather complicated. However, the question of whether steady-state creep or, perhaps, rupture will occur, or whether sufficient fibers will survive to provide an intact elastic specimen, can be answered by consideration of the stress in the fibers after the matrix has been assumed to relax completely. Clearly, when the matrix carries no stress, the fibers will at least fail to the extent that they do in a dry bundle. It is possible that a greater degree of fiber failure will be caused by the transient stresses during creep relaxation, but this effect has not yet been modeled. Instead, the dry bundle behavior will be used to provide an initial estimate of fiber failure in these circumstances. 

Polymers which arc not cross-linked to form infinite networks can behave elastically under transient stressing conditions. They cannot sustain prolonged loads, however, because the molecules can flow past each other to relieve the stress, and the shape of the article will be deformed by this creep process. [Alternatives to cross-linking are mentioned on pages 20 and. 315.]... 

The relaxation modulus G(t) is the value of the transient stress per unit strain in a step-strain experiment. This type of experiment may be achieved with modem rotary rheometers with a limited resolution in time (roughly 10 2 s). If one wishes to evaluate G(t) at shorter times, it is necessary to derive G(t) from the high frequency G (co) data by an inverse Carson-Laplace transform. 

No overshoot and linear limits in transient stress growth. Linear relaxation modulus in step shear strain. 

Lodge Meissner rule unsatisfied (2 slip parameters). Oscillations in transient stress growth. Negative relaxation modulus in large step shear strain. 

Figure 11.14 Reduced shear stress (transient stress divided by steady-state stress) plotted...

Two liquid crystalline polybenzylglutamate solutions, adjusted to the same Newtonian viscosity, have been investigated Theologically. The steady state shear properties and the transient behaviour are measured. For the same kind of polymer, the dynamic moduli upon cessation of flow can either increase or decrease with time. This change in dynamic moduli shows a similar dependency on shear rate as the final portion of the stress relaxation but no absolute correlation exists between them. By comparing the transient stress during a stepwise increase in shear rate with that during flow reversal the flow—induced anisotropy of the material is studied. 

Consider imposing a step strain of magnitude 7 at time t = 0 (see Fig. 7.20). If the material between the plates is a perfectly elastic solid, the stress will jump up to its equilibrium value Gj given by Hooke s law [Eq. (7.98)] and stay there as long as the strain is applied. On the other hand, if the material is a Newtonian liquid, the transient stress response from the jump in strain will be a spike that instantaneously decays to zero. For viscoelastic materials, the stress after such a step strain can have some general time dependence a(t). The stress relaxation modulus G(t) is defined as the ratio of the stress remaining at time t (after a step strain was applied at time t = 0) and the magnitude of this step strain 7 ... 

We consider the material to be in a visco-elastic state. A transient stress distribution will therefore occur after each change of the applied stress and/or temperature profile. Only very small local deformations and, thus, short times are necessary to adjust local stresses to the general continuity condition. After the transition, the whole specimen will creep in tension under the action of a radial distribution of axial stresses o(r) which assures, respecting the creep rate equation, an equal creep rate for the whole specimen. From the viewpoint of continuum mechanics, a chemically homogeneous specimen with a radial temperature gradient is indeed a "graded material" inasmuch as each coaxial shell offers a different resistance to the applied stress and has a different time constant for relaxation. We may speak of a "thermally graded material". 

A third source of stress waves derives from the expansion of any gases (CO, CN, N2, CH3 etc.) produced by thermal or photochemical decomposition within the substrate [104]. This factor, for instance, has been invoked to account for the transient stresses of about 0.1 MPa detected in the UV irradiation of polyimide below the ablation threshold [106]. In the case of doped PMMA, irradiation with 150-ps pulses at 1064 nm, Hare et al. [104] estimate that at the ablation threshold, the thermoelastic mechanism and the expansion of the decomposition products contribute about equally to the generated pressure. For specifically designed polymers that upon irradiation form a high enough concentration of volatile products, the generated pressure has been suggested to be the primary cause of material ejection [68-69]. 

Experimental verification of Eqs 7.94 indicated that the scaling relationships are valid, but the shape of experimental transient stress curves, after step-change of shear rate, did not agree with Doi-Ohta s theory [Takahashi et al., 1994]. Similar conclusions were reported for PA-66 blends with 25 wt% PET [Guenther and Baird, 1996]. For steady shear flow the agreement was poor, even when the strain-rate dependence of the component viscosities was incorporated. Similarly, the... 

Solid oxide fuel cells (SOFCs) involve structures composed of multiple ceramic layers, or interleaved layers of ceramic membranes and metal interconnects. To eliminate premature mixing of fuel and air gases or leaking of these gases from interior regions of the structure, the interfaces of adjacent layers are sealed with a glass or ceramic seal. These seals must withstand the high-temperature environment of the SOFC over its lifetime. Therefore these materials must be thermally matched with the adjacent layers to minimize transient stress risers and eliminate the potential for consequent seal failure. 

On detailed analysis of the transient stress signatures, certain numerical discrepancies were noted [Gu et al., 1993 Gu and Jamieson, 1994a] between the experimental increments in Leslie viscosities 8as and Sas versus the Brochard prediction. Specifically, for the side-chain LCP, assuming an oblate conformation, the theory [Eiqs. (1.55)] predicts that both 8as and Sas should be positive, whereas we found [Gu et al., 1993 Gu and Jamieson, 1994a] that Sas < 0 and Sas > 0. Also, the magnitude and signs of these viscosity increments were found to be strictly inconsistent with... 

A drop-type impingement can also lead to purely mechanical damage and deformation on such parts where a liquid-filled gap, in this case between parts of a canned motor pump made of steel 1.4408, is submitted to transient stressing in the axial direction with simultaneous oscillating radial movement without contact between the metal surfaces. 

Frequent shutdowns and restarts can lead to the accumulation of transient stresses in equipment that may lead to premature failure. 

---