Crack opening tip displacement

One way of looking at the fracture characteristics of a ductile material is by measuring the amount of plasticity at a crack tip prior to crack propagation (Fig. 8.84). One test which measures this is the crack-tip opening displacement (CTOD), 5. Wells has found that 6 can be related to the strain energy release rate, G, by the formula ... 

Fig. 8.85 The variation of crack tip opening displacement with temperature...

We obtained full field solutions for an axial crack on the ID surface of a pipe under plane strain conditions. The pipe has an outside diameter of 40.64 cm and a wall thickness h = 9.52 mm. The depth of the axial crack is a = 1.9 mm (a/h = 0.2) (Fig. 2). In the absence of hydrogen, we assume a finite crack-tip opening displacement (CTOD), ha = 2 pm. 

Figure 3. Evolution of normalized NILS hydrogen concentration C, IC vs. normalized distance R lb ahead of the crack tip for crack size r/ = 1.9 mm (a) near crack tip solution, (b) solution over the entire uncracked ligament. The parameter b denotes the crack tip opening displacement which varies with time as the hydrogen pressure increases toward its final value of 15 MPa over 1 sec. The parameter C =2.659x10 H atoms/m ( = 3.142x10 H atoms per solvent atoms) denotes the hydrogen concentration on the inner wall-surface and crack faces in equilibrium with the hydrogen gas.

Figure 4. Plot of the full-field solution for the normalized hydrostatic stress

Figure 5. Description of (a) boundary conditions for the elastoplastic problem and (b) initial and boundary conditions for the hydrogen diffusion problem at the blunting crack tip in the MBL formulation. The parameter bCl denotes the crack tip opening displacement in the absence of hydrogen. The parameter C, (P) denotes NILS hydrogen concentration on the crack face in equilibrium with hydrogen gas pressure P. and / is hydrogen flux.

Figure 6. Normalized NILS hydrogen concentration CL / C at steady state vs. normalized distance R/b from the crack tip for the full-field (crack depth wh=0.2) and MBL (domain size L=h-a) solutions under zero hydrogen flux conditions on the OD surface and remote boundary, respectively. The parameter b denotes the crack tip opening displacement for each case. The inset shows the concentrations near the crack tip.

The crack-opening displacement (COD) at any point along the crack is defined as twice the displacement of the crack surface at that location, i.e., COD = 2v -r, 0). The quantity crack-tip-opening displacement (CTOD), however, is given a special designation as the opening displacement at the actual crack tip, which is assumed to be correctly located at a distance x = -Vy from the effective crack tip based on Irwin s approximation. As such, from Eqns. (3.28), (3.37), and (3.49), one obtains ... 

Fig. 5.12 Crack tip opening displacement (8j) versus stable crack growth (Aa). the numbers indicate tool...

Fig. 5.26 Crack tip opening displacement in friction stir welded 5051-T5 Al in both the nugget and heat-affected zone (HAZ) compared to the base material. RW repair weld PW, production weld. Source Ref 72...

Fracture Toughness by Crack Tip Opening Displacement (CTOD)... 

Wells [11] first proposed the crack opening displacement as a measure of fracture toughness for tough metals such as the structural steels where LEFM is not valid. The concept became a standard in 1979 in the form of British Standard (BS) 5762 [12], which is now-superseded by BS 7448 Part 1. 1991. Method of determination of Afi. critical CTOD and critical J values of metallic materials [13], More recently. ASTM E1290-9,3, Crack-tip opening displacement (CTOD) fracture toughness measurement [14] was issued. It is stated that this method may be used to characterize the toughness of materials that arc (a) too ductile or fail the size conditions to be tested for or (b) likely to produce unstable crack extension that would invalidate Ji tests in accordance with the requirements of ASTM E81.3 [15]. 

ASTM El290. 1993. Crack-tip opening displacement (CTOD) fracture toughness measurement. 

Analysis also gives crack tip opening displacement 8q (Fig. 9.8), the height of the thick end of the yielded zone, as... 

The crack growth condition of Eq. (9.15) can be used A craze fails when its opening displacement reaches a critical value. Flowever, this does not explain the failure mechanism. It could be by failure of the entanglement network in the craze fibrils. Crazes in some polymers fail at their midplanes, and in other polymers at the bulk-craze interface. For viscoelastic materials, in which both the craze stress and the Young s modulus vary with the strain rate, Eq. (9.19) predicts that the crack tip opening displacement is no longer proportional to the stress intensity factor. Figure 9.11 shows that... 

Si mm crack-tip-opening displacement in mode 1 (the index 1 is only used in the case of geometry independence)... 

Critical crack-tip-opening displacement [87Gre, 86Hof] ... 

Available results show that proportionality crmstants jS, s and are material-dependent They also indicate that specimen dimensions required for acquiring fracture mechanics values ruider impact loading are maintained for 6 = 4 mm and a/W > 0.2 in the LEFM concept the MC and ST /-integral estimation methods and in the CTOD concept, if the notch part of critical crack-tip-opening displacement is used. 

When yielding causes large departures from linearity in the force-displacement curve, such that valid Kiq data cannot be obtained, it is still possible to make geometry-independent measurements of the fracture resistance of the material, using the methods of elastic-plastic fracture mechanics. These usually require additional information to determine whether non-linearity is due to crack tip plasticity alone, or to a combination of plasticity and crack growth. Several different approaches have been developed, of which we will discuss onfy two the crack tip opening displacement (CTOD) and /-integral methods. 

Compact tension tests on PMMA specimens give a value of 325 J m" for Gic at 23°C, for a crosshead speed of 5 mm min". The critical crack tip opening displacement 8, determined using an optical interferometry technique, is 4.2 m. Calculate the surface stress acting on the craze formed ahead of the crack tip. 

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