Stress critical intensity factor

K,- = lG,. = fracture toughness (sometimes critical stress intensity factor). Usual units MN m ... 

This is the probability that failure will occur due to the propagation of one tip of the initial defect c under stress o, where is the critical stress intensity factor of the filler particle and a is the filler particle size. 

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... 

The critical stress intensity factor is sometimes referred to as the fracture... 

Example 2.20 A cylindrical vessel with an outside radius of 20 mm and an inside radius of 12 mm has a radial crack 3.5 mm deep on the outside surface. If the vessel is made from polystyrene which has a critical stress intensity factor of 1.0 MN calculate the maximum permissible pressure in this vessel. 

If the material has a critical stress intensity factor of 1.8 MN m and it is known that the moulding process produces defects 40 m long, estimate the maximum repeated tensile stress which could be applied to this material for at least 10 cycles without causing fatigue failure. 

A very wide sheet of grp which is known to contain intrinsic defects 1 mm long, is subjected to a fluctuating stress which varies from 0 to 80 MN/m. How many cycles would the sheet be expected to withstand if it is made from (a) chopped strand mat (CSM) and (b) woven roving (WR) reinforcement. The crack growth parameters C and n, and the critical stress intensity factors, Kc, for these materials are... 

The stress corrosion resistance of maraging steel has been evaluated both by the use of smooth specimens loaded to some fraction of the yield strength and taking the time to failure as an indication of resistance, and by the fracture mechanics approach which involves the use of specimens with a pre-existing crack. Using the latter approach it is possible to obtain crack propagation rates at known stress intensity factors (K) and to determine critical stress intensity factors (A iscc) below which a crack will not propagate (see Section 8.9). 

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 . ... 

I mpact strength Notch sensitivity Critical stress intensity factor... 

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. ... 

Polymer Network A/E = 1 [105] Glass transition temperature T/C Molecular mass of strands (experimental) Mc/kg moF1 Critical stress intensity factor (crack initiation) KIC/MPa ]/m Yield stress, taken from Fig. 9 [110] cry/MPa Half crack opening displacement w = Kfc/2E[Pg.347]

Several additional, non-microstructural, inputs are required for the fracture model (i) Particle critical stress intensity factor, KIc. Here, the value determined in a previous study (Klc = 0.285 MPa in )[3] was adopted for all four graphites studied. This value is significantly less than the bulk Klc of graphites (typically -0.8-1.2 MPa rn). However, as discussed in the previous section, when considering fracture occurring in volumes commensurate in size with the process zone a reduced value of Klc is appropriate (ii) the specimen volume, taken to be the stressed volume of the ASTM tensile test specimens specimen used to determine the tensile strength distributions and (iii) the specimen breadth, b, of a square section specimen. For cylindrical specimens, such as those used here, an equivalent breadth is calculated such that the specimen cross sectional area is identical, i.e.,... 

In a first testing series, the fracture behavior of the neat, fully crosslinked epoxy network was studied. A fully unstable crack propagation behavior was observed and the critical stress intensity factor, Kj (0.82 MPaxm ), and the critical energy release rate, Gj (0.28 kj/m ), were determined [87]. These are typical values for highly crosslinked epoxy networks prepared with DGEBPA and aromatic or cycloaliphatic diamines. 

Fig. 46. a Critical stress intensity factor, of solvent-modified and macroporous epoxy networks prepared via CIPS with various amounts of cyclohexane, b Fracture energy of sol-vent-modified and macroporous epoxy networks prepared via CIPS with various amounts of cyclohexane... 

Fig. 52. Critical stress intensity factor, Kj, and critical stress energy release rate, of solvent-modified, semi-porous, and macroporous epoxies prepared via kinetically controlled Cl PS with 1 wt % catalyst calculated from SENB tests...

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

Owen M.J. and Bishop, P.T. (1973). Critical stress intensity factors applied to glass reinforced polyester resin. J. Composite Mater. 7, 146-159. 

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)... 

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