Strain intensity factor

Fig. 3. Critical strain intensity factor versus entanglement density for various polymers (filled squares data taken from [13] open squares this study), a polystyrene b poly(methyl methacrylate) c poly(vinyl chloride) d polyamide 6 e polyoxymethylene f bisphenol-A polycarbonate g poly(ethylene terephthalate) h SAPA-A series i SAPA-R series.

Both Eqs. (11.1) and (11.2) account for the effect of transverse strain on plastic strain intensity factor characterized by the modified Poisson s ratio, V. In Eq. (11.1), this is accounted for by the ratio Sy/Sa, whereas in Eq. (11.2) the ratio Eg/E serves the same purpose as will be shown later. The modified Poisson s ratio in each case is intended to account for the different transverse contraction in the elastic-plastic condition as compared to the assumed elastic condition. Therefore this effect is primarily associated with the differences in variation in volume without any consideration given to the nonlinear stress-strain relationship in plasticity. Instead the approaches are based on an equation analogous to Hooke s law as obtained by Nadai. Gonyea uses expression (rule) due to Neuber to estimate the strain concentration effects through a correction factor, K, for various notches (characterized by the elastic stress concentration factor, Kj). Moulin and Roche obtain the same factor for a biaxial situation involving thermal shock problem and present a design curve for K, for alloy steels as a function of equivalent strain range. Similar results were obtained by Houtman for thermal shock in plates and cylinders and for cylinders fixed to a wall, which were discussed by Nickell. The problem of Poisson s effect in plasticity has been discussed in detail by Severud. Hubei... 

For a closing crack a different approach is required. Schapery 13) introduces a strain intensity factor to replace K in equation (14). The length d of the Dugdale zone is still given approximately by equation (15), but the apparent work of adhesion is now given approximately by... 

Step 2. After a contact time t, the material is fractured or fatigued and the mechanical properties determined. The measured properties will be a function of the test configuration, rate of testing, temperature, etc., and include the critical strain energy release rate Gic, the critical stress intensity factor K[c, the critical... 

Critical Stress Intensity Factor It has become common to use AT scc> the critical stress intensity factor, as a measure of the resistance of an alloy to s.c.c. Tests are performed on specimens which are precracked by a fatigue machine and must be of sufficient dimensions to ensure plane strain conditions. Recommendations on precracking and dimensions are given elsewhere . ... 

Fracture Mechanics Tests One problem of both sustained load and slow strain-rate tests is that they do not provide a means of predicting the behaviour of components containing defects (other than the inherent defect associated with the notch in a sustained load test). Fracture mechanics provides a basis for such tests (Section 8.9), and measurements of crack velocity as a function of stress intensity factor, K, are widely used. A typical graph of crack velocity as a function of K is shown in Fig. 8.48. Several regions may be seen on this curve. At low stress intensity factors no crack growth is... 

Fig. 8.52 Initial stress intensity factor and time to failure for a susceptible titanium alloy tested in a neutral aqueous environment under plane strain conditions...

Critical stress intensity factor Klc and critical strain energy release rate G1C quantify the stability of a polymer against the initiation and propagation of cracks. Stress intensity factor and energy release rate G, are not independent but they are related [76] by means of the appropriate modulus E. ... 

Materials Young s Modulus (GPa) Ultimate Tensile Strength (MPa) Critical Stress Intensity Factor K c (MN m- /2) Critical Strain Energy Release Rate, G c (J m-2)... 

K[c Critical stress intensity factor in mode I and plane strain conditions... 

Kic Mode I plane strain critical stress intensity factor (MPa m1/2)... 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

The values of the stress intensity factor (Klc) and of the strain energy release rate (Glc) of both crosslinked maleic and nadic oligomers are rather low and explain the poor mechanical properties of these materials. 

K Stress intensity factor (SIF) eo Reference strain rate for creep... 

The matrix fracture behavior can also be described by using stress intensity factors, K. This approach is more convenient than the /-integral in some cases particularly for short cracks and for fatigue.31,84 To apply this approach, it is first necessary to specify the contribution to the crack opening induced by the applied stress, as well as that provided by the bridging fibers. For a plane strain crack of length 2a in an infinite plate, the contribution due to the applied stress is85... 

The boundary layer approach is used to investigate the mode I plane strain fields near the crack. The symmetry of the problem allows consideration of only half the geometry (see Fig. 7), which consists of an initial blunted crack of radius n with traction-free surfaces along the crack. Along the boundary of the remote region at a distance R with R % 200rt, the mode I elastic field at stress intensity factor Ki is prescribed [8,22],... 

---