Immediate elastic deformation

The Kohlrausch formula is well suitable to represent the creep at small stresses and strains. Do is then the compliance at f = 0, and is a measure of the immediate elastic deformation. The formula, however, fails when the creep behaviour is nonlinear this is, in general, the case with stresses occurring in practice. 

The second equation appears to be applicable to a number of glassy polymers, and also to other materials the exponent m is always about 3, so that creep can be described by two parameters, Do and to, while the immediate elastic deformation is also taken into account (Do). As a matter of fact, Do and to are temperature dependent. When the experimentally found creep curves are shifted along the horizontal axis and (slightly) along the vertical axis, they can be made to coincide... 

Immediate elastic deformation n. Recoverable deformation that is essentially independent of time, i.e., occurring in (a time approaching) zero time and recoverable in (a time approaching) zero time after removal of the applied load. 

Creep describes time-dependent permanent deformation of materials resulting from constant structural stress. The creep of polymers can be divided into two main stages primary creep and steady-state creep. The creep strain rate decreases with time in the primary creep and is constant in the steady-state creep. Strain recovery occurs with the removal of external load after a creep time. Therefore, the total strain (e) consists of three separate parts el, e2, and e3. The el and e2 are the immediate elastic deformation and delayed elastic deformation, respectively. The e3 is the Newtonian flow. It was found that the el and e2 decreased with increasing clay contenf indicating lower creep recovery with the addition of C20A. The creep compHance J, the ratio of strain and applied load, can be expressed as... 

The effect of applying a similar loading programme to a linear viscoelastic solid has several similarities (Figure 5.2(b)). In the most general case, the total strain e is the sum of three separate parts e, and ez. e and are often termed the immediate elastic deformation and the delayed elastic deformation respectively, ez is the Newtonian flow, that is that part of the deformation, which is identical with the deformation of a viscous liquid obeying Newton s law of viscosity. 

The design of load-bearing structures for service at room temperature is generally based on the yield strength or for some appHcations on the tensile strength. The metal is expected to behave essentially in an elastic manner, that is, the stmcture undergoes an elastic deformation immediately upon load apphcation and no further deformation occurs with time. When the load is removed, the stmcture returns to its original dimensions. 

The first consequence of the work assumption may be established immediately for elastic deformations. Consider an arbitrary finite smooth closed cycle of homogeneous deformation %(ti, f ) which lies entirely in the elastic... 

Likewise, the longer the duration of material stress or strain, the more time for viscous flow to occur. Finally, the greater the material stress or strain, the greater the likelihood of viscous flow and significant permanent deformation. For example, when a TP product is loaded or deformed beyond a certain point, the material comprising it yields and immediate or eventually fails. Conversely, as the temperature or the duration or magnitude of material stress or strain decreases, viscous flow becomes less likely and less significant as a contributor to the overall response of the material and the essentially instantaneous elastic deformation mechanism becomes predominant. 

The cross section of the collision region that the particle impacts with the Si surface with an incident angle of 45° at a speed of 2,100 m/s is shown in Fig. 16 [28]. As the particle impacts into the Si surface layer, the contact region of the Si surface layer transforms from crystal into amorphous phase immediately. The area of the depressed region and the thickness of the amorphous layer increase with the penetration depth of the particle (Figs. 16(a)-16(c)). After it reaches the deepest position, the particle then moves both upwards and rightwards, and some silicon atoms ahead of the particle are extruded out and result in a pileup of atoms. Then the released elastic deformation energy of the Si surface pushes... 

In order to simplify the discussion and keep the derivation of the formulae tractable, a fibre with a single orientation angle is considered. In a creep experiment the tensile deformation of the fibre is composed of an immediate elastic and a time-dependent elastic extension of the chain by the normal stress ocos20(f), represented by the first term in the equation, and of an immediate elastic, viscoelastic and plastic shear deformation of the domain by the shear stress, r =osin0(f)cos0(f), represented by the second term in Eq. 106. 

Note 6 Given that Q(D) is a polynomial of degree n + 1 if P(D) is also of degree n + 1 the material shows instantaneous elasticity if P(D) is of degree n, the material does not show instantaneous elasticity (i.e. elasticity immediately the deformation is applied.)... 

The return of shear deformation after elimination of an external stress at a moment tj is also plotted in Fig. 23 (curve d). This diagram shows the flow processes before and after discharge using Eq. (36) as well as a pure elastic deformation = o/G0 and a irreversible flow according to Eq. (41). The elastical deformation yei disappears immediately after discharge. 

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

The usual way in which the deformation changes with time, has been dealt with in 6.1. The best representation appeared to be a Maxwell element with a Kelvin-Voigt element in series the deformation is then composed of three components an immediate elastic strain, which recovers spontaneously after removal of the load, a delayed elastic strain which gradually recovers, and a permanent strain. Moreover, we noticed that a single retardation time (a single Kelvin-Voigt element) is not sufficient we need to introduce a spectrum ... 

In a typical indentation experiment the indenter is pressed onto the surface under investigation and the load is successively increased up to a certain maximum load. In the so-called compliance approach both load and indenter displacement are recorded and plotted as a load-displacement curve, the so-called compliance curve. If the experiment is exclusively run in the compressive load regime, the curve is also referred to as the load-penetration curve. Upon loading, elastic deformations occur succeeded by plastic ones. Upon releasing the imposed stress, elastic strain recovers immediately. 

After arriving at the maximum pressing force, pressure is released. If as shown in Fig. 8.1, compaction is performed by a punch in a die, the direction of travel of the piston reverses and, when no expansion of the densified body occurs, the pressing force should drop to zero immediately (vertical line). In reality, there is always a more or less pronounced spring-back which is caused by the expansion of compressed gas and the relaxation of elastic deformation. As mentioned before, this effect becomes more pronounced with increasing speed of densification until, at a certain compression rate, the compacted body disintegrates partially or totally upon depressurization. Therefore, it is often necessary to find an optimal compromise between densification speed (= capacity) and product integrity (= quality). 

Elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress. Elastic strain is also called elastic deformation. The applied stresses cause the atoms in a crystal to move from their equilibrium position. All the atoms are displaced the same amount and still maintain their relative geometry. When the stresses are removed, all the atoms return to their original positions and no permanent deformation occurs. 

Physiological disturbances are such factors as consumption of metabolic substrates or tissue damage, while the psychological disturbance factors are those related to, for example, anxiety about work or inadequate social support. Changes in the state variables of the worker are defined by the model as responses. A response is an effect of the dose caused by exposure. For example, hand exertion can cause elastic deformation of tendons and changes in tissue composition and/or shape, which in turn may result in hand discomfort. The dose-response time relationship implies that the effect of a dose can be immediate or the response may be delayed for a long periods of time. 

Reports Immediate elastic recovery % permanent deformation... 

In the Kelvin or Voigt model the spring and dashpot elements are connected in parallel, as shown in Figure 3.13a. This model roughly approximates the behavior of rubber. When the load is applied at zero time, the elastic deformation cannot occur immediately because the rate of flow is limited by the dashpot. Displacements continue until the strain equals the elastic deformation of the spring and it resists further movement. On removal of the load the spring recovers the displacement by reversing the... 

According to ASTM D1474 the Knoop hardness number is measured with the pyramidal Knoop diamond. According to ISO 2815 the Buchholz instrument is used. This method cannot detect elastic deformation of the coating that disappears immediately after the load is removed. 

The two extreme cases of mechanical behavior can be reproduced very well by mechanical models. A compressed Hookean spring can serve as a model for the energy-elastic body under load (Figure 11-11). On releasing the load, the compressed spring immediately returns to its original position. The relationship between the shear stress (021) = Oe, the shear modulus Ge, and the elastic deformation ye is given by Hooke s law [Equation (11-1)] ... 

A constant load (stress So) is applied and as a result the whole body will stretch. However, the spring caimot respond immediately as it is coimected to the dash-pot in a rigid manner. Therefore, there will be a retarded but final elastic deformation (damped). On removal of the load, the deformation will reverse, still retarded (time-dependent). The strain y is identical in both elements, but the stress is divided between them. This is shown in Figure 4-14. 

The second model (Figure 4.15d) describes the complicated viscoelastic behaviour of bitumen. Upon application of stress, the model immediately presents elastic deformation and continues to deform at a non-linear rate. Thus, for a given temperature, if a constant stress (oi) is applied, the strain (e) after time (t) could be calculated using the Burgers model by the following equation ... 

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