Creep retardation

Our data given here for ABS resins hold for other polymers as well since many exhibit similar values for fg9 the Poisson ratio, and the limiting stress. For example, the shift of four decades in PVC creep retardation time after annealing was obtained by Turner (13). The maximum excess entropy at Tg is similar for many polymers and some inorganic glasses (14). 

This does display the three elements of real behavior, an instantaneous elastic response, primary creep (retarded elastic response) and secondary creep (permanent deformation). However, the fit to real data is not good and again it is because real materials have behavior that is characterized by a spectrum of relaxation times. 

Due to the polymer nature of most structural engineering adhesives, their viscoelastic deformation behavior is strongly time- and temperature-dependent and associated to creep (retardation) under static or so-called dead load condition. 

While creep experiments apply a constant load to the sample and follow the increase of strain over time, the relaxation method applies a fixed strain to the specimen at the beginning of the test and records the decrease in stress over time caused by relaxation of the adhesive polymer. The basic difference in creep (retardation) testing versus relaxation testing is illustrated in Fig. 34.16. 

Comparison of input and response in creep (retardation) and relaxation tests... 

Use a Kelvin model for creep and show that the inflection point on the log scale plot corresponds to the creep retardation time t. Then the asymptotic time can be estimated at 3-5x even though the... 

PEI polymers exhibit minimal creep underload. Eor example, unreinforced Ultem 1000 maintains part dimensions over thousands of hours at room temperature at a loading of 34 N/mm (4930 psi). PEI resins are available with HDTs ranging to 220°C (Ultem 5000). PEI copolymers with siUcone mbber allow for flame-retardant, high temperature appHcations such as plenum wire coatings (Siltem). Reinforcement of PEI resins improves their temperature performance. Table 13 compares unreinforced and 20% glass-reinforced Ultem resins. 

The dashpot constant, rj2, for the Kelvin-Voigt element may be determined by selecting a time and corresponding strain from the creep curve in a region where the retarded elasticity dominates (i.e. the knee of the curve in Fig. 2.40) and substituting into equation (2.42). If this is done then r)2 = 3.7 X 10 MN.s/m ... 

The load or stress has another effect on the creep behavior of most plastics. The volume of isotropic or amorphous plastic increases as it is stretched unless it has a Poisson ratio of 0.50. At least part of this increase in volume manifests itself as an increase in free volume and a simultaneous decrease in viscosity. This decrease in turn shifts the retardation times to being shorter. 

The effect of a flame-retardant additive on the flexural modulus provides an indication of its effect on long-time creep. 

Note that the term y in Eqs. 2-15 and 2-16 has a different significance than that in Eq. 2-14. In the first equation it is based on a concept of relaxation and in the others on the basis of creep. In the literature, these terms are respectively referred to as a relaxation time and a retardation time, leading for infinite elements in the deformation models to complex quantities known as relaxation and retardation functions. One of the principal accomplishments of viscoelastic theory is the correlation of these quantities analytically so that creep deformation can be predicted from relaxation data and relaxation data from creep deformation data. 

Since the stress is constant, it follows that so also is the creep rate. The creep compliance at time t, 7, can be considered to consist of three terms, an instantaneous compliance, Jq, a term covering a variety of retardation processes, xj/it), and a viscous term, t/rj. These are related by ... 

Figures 5 and h show how the shape of the creep curve is modified by changes in the constants of the model. The values of the constants are given in Table I. Curve I is the same as shown in Figure 4, curve II shows onlv a small amount of viscous creep, and in curve 111, viscous flow is a prominent part of the total creep. The same data were used in Figures 5 and 6, but notice the dramatic, change in the shapes of the curves when a linear time scale is replaced by a logarithmic time scale. In the model, most of the recoverable creep occurs "Within about one decade of the retardation time.

A distribution obtained by the use of equation (13) is only a first approximation to the real distribution. The corresponding distribution of retardation times is designated as L(T). It may be estimated from the slope of a compliance curve D(0 or J(t), for tensile or shear creep, respectively, plotted on a logarithmic time scale according to the equation (for shear creep)-... 

To get accurate distributions of relaxation or retardation times, the expetimcntal data should cover about 10 or 15 decades of time. It is impossible to get experimental data covering such a great range of times at one temperature from a single type of experiment, such as creep or stress relaxation-t Therefore, master curves (discussed later) have been developed that cover the required time scales by combining data at different temperatures through the use of time-temperature superposition principles. 

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

If the Boltzmann superposition principle holds, the creep strain is directly proportional to the stress at any given time, f Similarly, the stress at any given lime is directly proportional to the strain in stress relaxation. That is. the creep compliance and the stress relaxation modulus arc independent of the stress and slrai . respectively. This is generally true for small stresses or strains, but the principle is not exact. If large loads are applied in creep experiments or large strains in stress relaxation, as can occur in practical structural applications, nonlinear effects come into play. One result is that the response (0 l,r relaxation times can also change, and so can ar... 

In order to obtain a general model of the creep and recovery functions we need to use a Kelvin model or a Kelvin kernel and retardation spectrum L. However, there are some additional subtleties that need to be accounted for. One of the features of a Maxwell model is that it possesses a high frequency limit to the shear modulus. This means there is an instantaneous response at all strains. The response of a simple Kelvin model is shown in Equation 4.80 ... 

Polyamide-imides are appreciated for good mechanical and electrical properties high service temperatures (up to 220°C with possible long service times at 260°C) rigidity good creep behaviour fatigue endurance low shrinkage and moisture uptake inherent flame retardancy chemical resistance usability down to -196°C. 

Note 5 The standard linear viscoelastic solid can be used to represent both creep and stress relaxation in materials in terms of single retardation and relaxation times, respectively. 

Note 5 The retardation spectrum (spectrum of retardation times) describing creep in polymers may be considered as arising from a group of Voigt-Kelvin elements in series. 

In principle a shifting rnle conld be applied, bnt the volnme retardation (physical ageing) is responsible for a gradual increase of the resistance against creep, so that the rate of creep gradually decreases. Creep curves at e.g. 20 °C thus proceed considerably less steep, and the real creep is therefore (fortunately ) much less than would follow from the T-log t shift (see MT 7.2.4). 

The first attempt to account for surface contamination in creeping flow of bubbles and drops was made by Frumkin and Levich (FI, L3) who assumed that the contaminant was soluble in the continuous phase and distributed over the interface. The form of the concentration distribution was controlled by one of three rate limiting steps (a) adsorption-desorption kinetics, (b) diffusion in the continuous phase, (c) surface diffusion in the interface. In all cases the terminal velocity was given by an equation identical to Eq. (3-20) where C, now called the retardation coefficient , is different for the three cases. The analysis has been extended by others (D6, D7, N2). 

Creep Force of a Projectile This force results from the gradual retardation of a projectile due to air resistance encountered during its flight. It has the effect of causing objects within the fuze, which are free to move, to move slowly (creep) forward toward the nose of the fuze... 

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