Stress-Strain-Time Behaviour

When a polymer mass is stressed, the resultant deformation Dtotai iriay be 

It will be noticed that, given sufficient time, will reach a constant value whilst Dvisc continues to increase with time. On release of stress will eventually disappear but visc will remain constant. 

One of the most important conclusions from this is that since both the viscous and the high elastic components of deformation depend on both time and temperature, the total deformation will depend on time and temperature. Since this fact has been shown to be an important factor affecting many polymer properties it is proposed to consider the background to this in greater detail in the following section. 

It is thus seen that the simple relationship I total = OE + I HE visc 

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Hobbs, D. W. (1970). Stress-Strain-Time Behaviour of a Number of Coal Measure Rocks. International Journal of Rock Mechanics and Mining Sciences, 7, 149. doi 10.1016/0148-9062(70)90009-4... 

These equations should fully describe the stress-strain-time relationship for the materials over the full range of response. However, the range over which such linear behaviour is observed is invariably limited. Usually large stresses and strains or short times cause deviations from Equations 1.4 or 1.5. 

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. 

Sulphur concrete (without additives) will typically have a near-linear stress-strain curve up to failure, which occurs explosively at a strain usually between 0.0005 and 0.002. The peak stress varies from 20 to 70 MPa depending on the mix design. Sulphur concrete is thus a strong but brittle concrete material the brittleness need not necessarily be a grave disadvantage cast iron was used for a long period of time as a construction material. Any modification to the stress-strain behaviour should be evaluated carefully to see whether the modification is potentially useful. Two different approaches have been used to modify stress-strain behaviour. The modifications are (a) polymerization of the binder 04, j>, 17) and (b) use of the thermodynamically stable orthorhombic sulphur as the binder with alteration of the bond behaviour (3, 18). The matrices of both types of concrete are thus "modified" sulphur. 

The properties of a material must dictate the applications in which it will best perform its intended use. All materials made to date with polymerized sulphur show time-dependent stress-strain behaviour. The reversion to the brittle behaviour of orthorhombic sulphur is inevitable as the sulphur transforms from the metastable polymeric forms to the thermodynamically stable crystalline structure. The time-span involved of at most 15 months (to date) would indicate that no such materials should be used in applications dependent on the strain softening behaviour. Design should not be based on the stress-strain relationships observed at an age of a few days. Since the strength of these materials is maintained, however, uses based on strength as the only mechanical criterion would be reasonable. 

Sulphur concretes have undergone substantial development in the last six years. Recent effort has been directed towards improved durability and less brittle stress-strain behaviour has been achieved. A technology has been developed to produce a material (Sudicrete) with the same stress strain behaviour after three years as that observed soon after casting. Other materials show a consistent reversion to brittle behaviour with time. Nevertheless, there is considerable room for improvement in mix design. 

Fig. 7 a and b. Scheme of the thermomechanical behaviour of a well phase-separated thermoelasto-plastic. Stress-strain (or time) curves. Plots of heat effects versus time. First loading (ABC) and unloading (CD) cycle. Second loading (AC) and unloading (CD) cycle. The yielding point occurs at B. AD indicates the residual deformation after the first cycle. AB on the dQ/dT-time curve is the endo-effect resulting from the initial small-strain deformation AB U9)... 

Very important phenomena in polymer behaviour, such as viscoelasticity, stress, strain, volume and enthalpy relaxation, ageing, etc., are characterised by time-dependence of the polymer properties. 

In the category of deformation properties the phenomena of stress-strain behaviour, modulus and yield, stress relaxation and creep have been discussed already in Chap. 13. Here we want to give special attention to the long-term deformation properties. For a good design we need sufficiently reliable creep data (or stress-strain curves as a function of time and temperature). 

Al-Saidi LF, Mortensen K, Almdal K (2003) Environmental stress cracking resistance behaviour of polycarbonate in different chemicals by determination of the time-dependence of stress at constant strains. Polym Degradat Stabil 82(3) 451—461... 

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