Threshold strain

When environmental stress cracking tests are carried out to detect the time to onset of crazing, results are generally obtained as a function of applied strain, and possibly also of temperature. There is then an apparent threshold strain below which crazing does not occur for a very long time. A discussion of how this data can be treated has been given by Wright [18]. 

Figure 16-6. Threshold strain. L = limiting threshold strain...

Figure 16-7. Relation between crack size and strain (diagrammatic). T is the threshold strain curve A, average crack length curve B, average crack length with coalescence of cracks ...

Sahimi and Arbabi (1993) considered the fracture properties of an elastic network where each bond has a fixed spring constant (k) but the critical or threshold strain or the bond-length Oc is randomly distributed following the distribution... 

Figure 2 shows the general stress-strain behaviour coupled to aperture changes. A threshold strain (e ) defines the initiation of fracture aperture. A strain corresponding to failure is indicated (ci). Failure is achieved when the normal stress reaches the tensile strength (o,). e , ei and o, are model parameters. 

Rubbers having main chain unsaturation can undergo ozone cracking when test pieces are exposed to atmospheric traces of ozone at an elongation above a characteristic threshold strain [63]. For most diene rubbers this strain is typically around 5% in the absence of any protective agent, although under dynamic strain conditions it can be reduced to less than 1%. Antiozonant materials are added to rise the threshold strain above the maximum strain encountered in service life or alternatively, as is usually the case in dynamically strained applications, to reduce the rate of crack growth. 

These abrupt transitions with a director reorientation of 90° [51] were found to have a characteristic threshold strain and show qualitative similarities to predictions from a model based on rubber elasticity... 

Here, A is the greater of the axial stiffnesses An and A22 for the sublaminate and e is the applied strain. By comparing the difference in energies to Gic, the SERR required to cause Mode I failure of the resin, it is possible to approximately predict the threshold strain below which propagation of a delamination will not occur. 

Figure 4.12 Comparison of (a) buckling strains and (b) threshold strains for first four interfaces of [45/0/-45/90]4s and [(45/—45/45/—45)2/(90/0/90/0)2ls laminates. A 30 mm diameter delamination is assumed at each interface in turn and material properties are defined in Table 4.4.

Threshold strain for zero growth- VID large damage... 

Pore pressure as a function of cyclic shear strain illustrating a threshold strain of about 0.01%, below which no excess pore pressure are developed. (After Dobry, R. et al.. Prediction ofPorewater Pressure Buildup and Liquefaction of Sands during Earthquakes by the Cyclic Strain Method, NBS Building Science Series 138, U.S. Department of Commerce, National Bureau of Standards, 1982.)... 

Fig. 16 Stress-strain curves for N-NC4 gels with different Rmo (wt%). The numerical values indicate / h20- Th h20 value for the as-prepared NC4 gel is 689 wt%. A dashed line illustrates the failure envelope obtained by connecting the rupture points. The arrows represent the threshold strain points (Ct) above which the strain-hardening occurs. /, II, and III indicate the distinct stages of tensile deformation. Reprinted from Haraguchi and Li [54], Copyright 2009, with permission of Wiley...

Although ozone exists in only very small quantities in the atmosphere, it is important because less than 1 pphm (part per hundred million) can severely attack non-resistant rubbers in the strained condition. Indeed, ozone attack can be the major factor as regards lifetime when exposed to the atmosphere. The effect of ozone is to produce clearly visible and mechanically very damaging cracking of the rubber surface. It only attacks rubber in the strained condition, although with the less resistant rubbers the threshold strain for attack may be very low. Rubbers with unsaturated (C=C) bonds in the main chain have very poor ozone resistance. 

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