Stress-strain rate effects

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

A review by Bird and Wiest [6] gives a more complete list of existing viscoelastic models. The upper convective model and the White-Metzner model are very similar with the exception that the White-Metzner model incorporates the strain rate effects of the relaxation time and the viscosity. Both models provide a first order approximation to flows, in which shear rate dependence and memory effects are important. However, both models predict zero second normal stress coefficients. The Giesekus model is molecular-based, non-linear in nature and describes thepower law region for viscosity andboth normal stress coefficients. The Phan-Thien Tanner models are based on network theory and give non-linear stresses. Both the Giesekus and Phan-Thien Tanner models have been successfully used to model complex flows. 

Fig. 15. The craze stress versus loading frequency in the case of a cyclic loading, in experimental conditions where hysteretic heating occurs in PMMA at the crack-tip. Note the increase of the craze stress due to strain rate effects at low frequencies, and the decrease of craze stress due to hysteretic heating above 100 Hz. From Refs. and courtesy of Society of Plastics Engineers Edn.

The second term on the right-hand side of Eq. (8.5) describes the increase in true yield stress with true strain rate. If the initial yield stress is measured in a tensile test, the low strain means there is no contribution from orientation hardening (see the next section), and there is insignificant heating. Consequently, the strain rate effect can be isolated. The initial yield stress was foimd, for HOPE at 20 °C, to vary with the true strain rate according to... 

Dynamic properties of soils are dependent on a number of factors, such as OCR, effective stress, void ratio, and saturation (Athanasopoulos and Richart, 1983a, 1983b Wu et al., 1984). The measurement of these dynamic properties is often influenced by strain rate effects (Isenhower and Stokoe, 1981). The strain rate effect of the measured variation of shear modulus with shear strain amplitude is shown in Figure 9.31. Laboratory... 

Traction depends heavily on the lubricant used, which has been shown to variously display elastic, non-Newtonian or Newtonian she u stress/strain rate beha viour depending upon the degree of sliding. (5). Traction coefficient is found to rise rapidly with increasing slide-roll ratio and then to fall at higher sliding due to combined non-Newtonian and thermal effects. An Importeuit practical characteristic for each lubricant at a given load and temperature is the maximum value of the traction coefficient reached. This is typically between 0.02 and 0.08. 

Longitudinai, mid-thickness stress-strain reiations for as-roiied plate. Strain rate effects on the stresses required for plastic deformation should be similar to that of other alloys such as Ti-8A1-1 Mo-1 V. 

Fig. 14 Effect of test temperature on the stress-strain rate curves for super Og.

They reported that Eq. 23.7 could be used successfully to describe uniaxial tension and compression behavior of various metal alloys. Equation 23.7 was later modified by McLellan (1969) to accommodate strain rate effects. McLellan interpreted the terms E, K, and ii of Eq. 23.7 as material functions with the function E representing viscoelastic behavior and functions if and W representing work-hardening characteristics. The terms E, K, and t/ were all described as functions of the strain rate (ds/dt) so that rigidity, stress, and plastic flow, respectively, were aU affected by variations in the strain rate. 

Tarantili, P.A., Andreopoulos, A.G., Galiotis, C. Retd-time micro-Rtiman measurements on stressed polyethylene fibers. 1. strain rate effects tmd molecular stress redistribution. Macromolecules 31, 6964-6976 (1998)... 

Out-Of-Gage Failures and Extraneous Stresses Slow Crack Growth, Strain Rate Effects and Test Environment Accurate Strain/Elongation Measurement... 

Fig. 6. The effect of rate of extension on the stress—strain curves of rayon fibers at 65% rh and 20°C. The numbers on the curves give the constant rates of...

Fig. 3. Effect of temperature and strain rate on stress—strain diagram of Ti—5% Al—2.5% Sn where A—E correspond to the strain rates 1.6x10, ...

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

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