Strained state

Considerable attention is given in the Institute to the application of the methods of acoustic emission and optical holography for engineering diagnostics of the service life and the stressed-strained state of welded metal structures. 

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. 

Osadchuk V.A. (1985) Stress-strain state and limiting equilibrium of shells with cuts. Naukova Dumka, Kiev (in Russian). 

X-ray Diffraction (XRD) is a powerful technique used to uniquely identify the crystalline phases present in materials and to measure the structural properties (strain state, grain size, epitaxy, phase composition, preferred orientation, and defect structure) of these phases. XRD is also used to determine the thickness of thin films and multilayers, and atomic arrangements in amorphous materials (including polymers) and at inter ces. 

XRD offers unparalleled accuracy in the measurement of atomic spacings and is the technique of choice for determining strain states in thin films. XRD is noncontact and nondestructive, which makes it ideal for in situ studies. The intensities measured with XRD can provide quantitative, accurate information on the atomic arrangements at interfaces (e.g., in multilayers). Materials composed of any element can be successfully studied with XRD, but XRD is most sensitive to high-Z elements, since the diffracted intensity from these is much lar r than from low-Z elements. As a consequence, the sensitivity of XRD depends on the material of interest. With lab-based equipment, surface sensitivities down to a thickness of -50 A are achievable, but synchrotron radiation (because of its higher intensity)... 

Thin-film XRD is important in many technological applications, because of its abilities to accurately determine strains and to uniquely identify the presence and composition of phases. In semiconduaor and optical materials applications, XRD is used to measure the strain state, orientation, and defects in epitaxial thin films, which affect the film s electronic and optical properties. For magnetic thin films, it is used to identify phases and to determine preferred orientations, since these can determine magnetic properties. In metallurgical applications, it is used to determine strains in surfiice layers and thin films, which influence their mechanical properties. For packaging materials, XRD can be used to investigate diffusion and phase formation at interfaces... 

To describe properties of solids in the nonlinear elastic strain state, a set of higher-order constitutive relations must be employed. In continuum elasticity theory, the notation typically employed differs from typical high pressure science notations. In the present section it is more appropriate to use conventional elasticity notation as far as possible. Accordingly, the following notation is employed for studies within the elastic range t = stress, t] = finite strain, with both taken positive in tension. 

In a uniaxial tension test to determine the elastic modulus of the composite material, E, the stress and strain states will be assumed to be macroscopically uniform in consonance with the basic presumption that the composite material is macroscopically Isotropic and homogene-ous. However, on a microscopic scSeTBotFTfhe sfre and strain states will be nonuniform. In the uniaxial tension test,... 

The basis for the determination of an upper bound on the apparent Young s modulus is the principle of minimum potential energy which can be stated as Let the displacements be specified over the surface of the body except where the corresponding traction is 2ero. Let e, Tjy, be any compatible state of strain that satisfies the specified displacement boundary conditions, l.e., an admissible-strain tieldr Let U be the strain energy of the strain state TetcTby use of the stress-strain relations... 

A real material whose behaviour can be modelled in this way initially undergoes irreversible deformation as the stress is applied. This eventually ceases, and the material then behaves effectively as an elastic solid. Release of the stress will cause a rapid return to a less strained state, corresponding to the spring component of the response, but part of the deformation, arising due to viscous flow in the dashpot will not disappear. 

Figure 8.31 shows central sections of two original SAXS patterns of PEE 1000/4394 in strained and relaxed state. In the strained state (Fig. 8.31a) a 6-point-diagram is detected. During relaxation (Fig. 8.31b) a well-separated 4-point-diagram is observed. Interpretation of the patterns is restricted to description and speculation. 

The two-network theory for a composite network of Gaussian chains was originally developed by Berry, Scanlan, and Watson (18) and then further developed by Flory ( 9). The composite network is made by introducing chemical cross-links in the isotropic and subsequently in a strained state. The Helmholtz elastic free energy of a composite network of Gaussian chains with affine motion of the junction points is given by the following expression ... 

After introduction of cross-links in the strained state, the composite network retracts, upon release, to a stress-free state-of-ease (J9 ) The amount of retraction is determined by the degree of strain during cross-linking and by the ratio >i/v2. The elastic properties relative to the state-of-ease are isotropic for a Gaussian composite network ( 8, 1 9,20). 

Figure 2. The principle of the two-network method for cross-linking in a state of simple extension. First network with modulus Gy is entirely due to chain entangling. Second network with modulus Gx is formed by cross-linking in the strained state. Both Gy and Gx can be calculated from the two-network theory.

A5. Chain disentangling prior to and after introduction of chemical cross-links in the strained state is negligible. 

Re A5. The experiment shows that no chain disentangling takes place after introduction of chemical cross-links in the strained state. Chain disentangling may take place prior to cross-linking if the relaxation period is long enough. 

Selective Quenching of Large-Scale Molecular Motions by Cross-Linking in the Strained State... 

The challenge is therefore to develop an experiment which allows an experimental separation of the contributions from chain entangling and cross-links. The Two-Network method developed by Ferry and coworkers (17,18) is such a method. Cross-linking of a linear polymer in the strained state creates a composite network in which the original network from chain entangling and the network created by cross-linking in the strained state have different reference states. We have simplified the Two-Network method by using such conditions that no molecular theory is needed (1,21). 

Table 1. Results from cross-linking in the strained state...

Transmission Electron IVOcroscopy of Semiconductor Nanostructures An Analysis of Composition and Strain State... 

Every cell actively underwinds its DNA with the aid of enzymatic processes (described below), and the resulting strained state represents a form of stored energy. Cells maintain DNA in an underwound state to facilitate its compaction by coiling. The underwinding of DNA is also important to enzymes of DNA metabolism that must bring about strand separation as part of their function. 

Ferry and co-workers (295) have obtained a value Me = 13000 for 1,2 polybutadiene by a new method which involves crosslinking the polymer in a strained state. The initial extension of the uncrosslinked sample, the recovery after... 

For the inflation method the test piece is held with a circular clamp and pressurized through a central hole. The biaxial strain state holds near the apex and optical methods can be used to find the radius of curvature and the extension of a grid drawn on the test piece. The nominal stress is then ... 

In principle, any of the low temperature tests can be used to study crystallisation effects by conditioning the test pieces at the low temperature for much longer times than is usual. In fact, most of the standard methods include a clause to the effect that the method can be used in this way. In the temperature retraction test, it is suggested that the greater degrees of applied elongation are used when the effects of crystallisation are to be considered, because crystallisation is more rapid in the strained state. 

Because antiozonants and waxes, which to be effective must form a surface bloom, are used to enhance ozone resistance it is usual to condition test pieces in the strained state before exposure. The usual conditioning period is between 48 and 96h and the test pieces should be kept in the dark and in an ozone-free atmosphere. For this treatment to be effective, the test piece surface must not of course be touched in the course of subsequent handling. Where specifications wish to specifically exclude compounds which rely on an adequate wax film for protection, the conditioning period is dispensed with. Hill and Jowett47 in a criticism of ozone test methods strongly make the point that the conditioning process should be relevant to service conditions if a discriminating evaluation of waxes is to be made. 

Lavochnik Yu.B., Beghishev V.P., Shadrin O.A., Stress-Strain State and Strength of Designs, Ural NTS, Sverdlovsk, 129 (1982) - in Russian. 

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