Fracture critical stress

Temperature differences in solids generally lead to thermal stresses, which may cause cracking and failure if they exceed the critical fracture stress. Thermal shock results from rapid heat transfer at the surface of a solid (quenching or laser beam impact), which may cause failure owing to large local transient thermal stresses. 

Kozlov, G. V, Shetov, R. A., Mikitaev, A. K. (1987). Methods of Elasticity Modulus Measurement in Polymers Impact Tests, k sokomolek. Soed. 29(5), 1109-1110. Bartenev, G. M., Razumovskaya, I. V. (1960). The Theoretical Strength and Critical Fracture Stress of Solids. Doklady AN SSSR, 133(2), 341-344. 

Recently the experimental data and analysis by Bennett et at, [27] have added a new dimension to our discussion by exhibiting a temperature-reduced time dependence of the cohesive fracture energy, = Y (t/a.j.), and consequently a predicted time-dependent critical fracture stress of... 

Fig. 8 Tensile curves of cellulose II fibres measured at an RH of 65% (1) Fibre B, (2) Cor-denka EHM yarn, (3) Cordenka 700 tyre yarn, (4) Cordenka 660 tyre yarn and (5) Enka viscose textile yarn [26]. The solid circles represent the strength corrected for the reduced cross section at fracture. The dotted curve is the hyperbola fitted to the end points of the tensile curves 1,3 and 5. The dashed curve is the fracture envelope calculated with Eqs. 9,23 and 24 using a critical shear stress rb=0.22 GPa... 

In conclusion, the initiation of fracture in a polymer fibre preferably occurs in the domains in the tail of the orientation distribution. The reasons are (1) in these domains the local shear stress will exceed the critical shear stress first, (2) the release of the strain energy is most effectively brought about by fracture of these domains and (3) the Griffith length in these domains adopts its lowest value. 

Impurities and flaws have a detrimental effect on the fibre strength. Due to shear stress concentrations at structural irregularities and impurities, the ultimate debonding stress r0 ( rm) or the critical fracture strain / may be exceeded locally far sooner than in perfectly ordered domains. Thus, during the fracture process of real fibres the debonding from neighbouring chains occurs preferably in the most disoriented domains and presumably near impurities. At the same time, however, the chains in the rest of the fibre are kept under strain but remain bonded together up to fracture. 

So far we have employed in this discussion a critical shear stress as a criterion for fibre fracture. In Sect. 4 it will be shown that a critical shear strain or a maximum rotation of the chain axis is a more appropriate criterion when the time dependence of the strength is considered. 

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

The decrease in K, with crack depth for fracture of IG-11 graphite presents an interesting dilemma. The utility of fracture mechanics is that equivalent values of K should represent an equivalent crack tip mechanical state and a singular critical value of K should define the failure criterion. Recall Eq. 2 where K is defined as the first term of the series solution for the crack tip stress field, ay, normal to the crack plane. It was noted that this solution must be modified at the crack tip and at the far field. The maximum value of oy should be limited to and that the far field stress should decrease only to the applied stress at increasing distance from the crack tip. The nominal fracture stress for IG-11 specimens with artificial flaws ranged from 28 to 100% of aLTS. 

A special advantage of this method is that the high shear rate range becomes available. It appears that one can measure nu — n33 up to the critical shear stress, at which extrusion defect (melt-fracture) occurs. On the other hand, entrance effects can also be studied, when the windows are located sufficiently close to the entrance. With the aid of the stress-optical coefficient, the corresponding normal stress difference can be... 

---