Notch root

The criteria (Eqs. 11 and 12) are similar and are derived from studies on materials that are elastic at initiation of crazing, while more ductile materials like polycarbonate show a more pronounced sensitivity to the hydrostatic tension. This has been found experimentally by Ishikawa and coworkers [1, 27] for notched specimens of polycarbonate. Crazing appears ahead of the notch root, at the intersection of well-developed shear bands. From a slip fine field analysis, the tip of the plastic zone corresponds to the location of the maximum hydrostatic stress. This has been confirmed by Lai and Van der Giessen [8] with a more realistic material constitutive law. Therefore, Ishikawa and coworkers [1,27] suggested the use of a criterion for initiation based on a critical hydrostatic stress. Such a stress state condition can be expressed by Eq. 11 with erg = 0 and I r = B°/A°. Thus, the criterion (Eq. 11) can be considered general enough to describe craze initiation in many glassy polymers. For the case of polycarbonate, a similar criterion is proposed in [28] as... 

Figure 7, Temperature dependence of failure stresses in Instron three-point bend tests on Vs inch notched Izod bars cut from (a) extruded polycarbonate sheet and (b) compression molded block polymer B. Crosshead rate = 0,02 inch /min. Span = 2 inches, o = net section stress = force/net cross-section at notch root, O, Craze initiation , ductile failure X, brittle failure ...

The mechanism for craze nucleation and growth describai here is essentially possible in semicrystalline polymers since the criterion is only related with a stress field due to plastic constraint. Therefore, the size and geometry of a local plastic zone at the notch root is responsible for the formation of crazes (sometimes named internal crazes by the authors). 

Figure 13 also shows a series of microphotographs of microtomed sections of notched PE in which much finer sphcrulites arc dispersed. The processes involved in craze nucleation and growth are fundamentally similar to those of PP, but a craze bundle in PE is composed of smaller individual crazes in length. As the load is increased, a concentrated craze line extends into the interior of the specimen a long the midplane. A crack initiates within this craze line and propagates stably with decreasing the applied load. Unlike PP. final fracture in PE is ductile. A higher magnification view of Fig. 13c is shown in Fig. 14. The damage zone near the notch root is composed...

Figures 32 and 33 shows the variation of the ratio of distance x from the notch root to the position of a brittle crack nucleus to the radius of the notch root q with temperature for PAs and PEEK, respectively. The position of crack nuclei was measured...

Consequently, the expansion of the plastic zone below the notch root induces the increase of the maximum bending moment even though the sample fractures in a brittle way. 

For a brittle glassy polymer like PMMA, the results for both sharp and blunted cracks are reproducible and show negligible scattering. The sharp cracks give a lower estimation of the toughness but this is not only related to a notch root effect. In the case of a blunt crack with notch radius of 250 micrometers, stress induced birefringence related to plasticity is observed... 

Figure 7. Bright-field micrographs of thin sections of the whitened zone. The U-notch root is at the bottom. The scale bar represents 50 pm. (a) Specimen RH15, Section A. (b) Specimen RF15, Section A.

Munisso, M.C., Yano, S., Zhu, W.L., and Pezzotti, G. (2008) Spatially resolved piezo-spectroscopic characterization for the validation of theoretical models of notch-root fields in ceramics. Continuum Mech. Thermodyn., 20 (3), 123—132. 

R. Damani, R. Gstrein, and R. Danzer, Critical Notch Root Radius in SENB-S Fracture Toughness Testing, J. Eur. Ceram. Soc., 16, 695-702, (1996). 

Figure Sa. Effect of physical aging at 40°C on distance from notch root to craze.

The latter can be determined experimentally if the response is in the form of LEFM or when plasticity is confined to yielding only at the notch root. 

Argon and Cohen 2003). However, if plasticity prevails at the notch root, the local strain rate there will be strongly accentuated and would be... 

Dynamic fracture toughness, Kimpact-response curve and the time-to-fracture was 6.2MN/m for PSZ and 1.7MN/m for Si3N4. The effects of the notch-root radius on static and dynamic fracture toughness were also evaluated. The specimens were blunt-notched with radii p = 25, 50, 100 and 150 pm. They were tested by instmmented CIT, applying the impact-response... 

Fig. 1.77 Apparent dynamic and static fracture toughness, Kp, as a function of the notch root radius p a for PSZ b for Si3N4 [32]. With kind permission of Professor Toshiro Kobayashi...

The effect of the notch-root radius on the apparent dynamic fracture toughness, K(j, is shown in Fig. 1.77. Kdynamic fracture toughness. A similar notch-radius effect is observed for AI2O3. Note that the static fracture toughness of Si3N4 increases at first, but then becomes constant (Fig. 1.77b). 

The critical strain-energy release rate, Gp, in the specimen with notch-root radius, p, is indicated in Fig. 1.78 for both static and dynamic ceramic fracture. The linear relation of the lines in Fig. 1.78 are based on the Williams relation... 

The ceramic specimens mentioned above, tested by dynamic loading, namely impact testing, are notched as is usual during the performance of such tests. During conventional impact testing, the radius at the notch-root is significant, since it affects the outcomes. For metals, the dimensions of the specimens and the notches are standard. A standard CIT specimen consists of a bar of metal or other material (ceramics included), 55 x 10 x 10 mm having a notch machined across one of... 

Fig. 2.10 Effect of V-notch root radii on the Kjc values a for Si3N4, and b for Y-PSZ ceramics [17]. With kind permission of Elsevier...

Analysis of the data of the fractured specimens reveals that a fracture crack propagated from the points where additional stress concentrations were present. This confirms the assumption that the fracture of a loaded ceramic specimen starts from a small crack ahead of a machined notch root. It is beheved that is influenced more by the sharpness of the notch root, rather than by its shape. The data in Table 2.1 are from three to four-point flexure tests performed on several monolithic ceramics. Table 2.2 shows the Kic values at RT and high temperatures attained by the SEVNB method for these notched specimens. 

Fig. 3.1-115 Notched bar impact energy as a function of test temperature of various types of stainless steels (DVM samples dimension lOx 10x55 mm, notch depth 3mm, notch root radius 1 mm)...

FIG. 10—The frequency independence of CF life for blunt notch specimens of A517 steel, freely corroding in aqueous 3.5 % NaCI as a function of notch root strain range [4e[. (Initiation here is In fact crack formation plus early growth to a 1-mm depth.)... 

This test method parallels the use of F 519, specimen Type le in specimen design and concept. The steel specimen has been modified to have a lower hardness of 51 1 HRC, and the notch root radius is 20-mil instead of 9-mil in order to reduce the stress concentration. The modifications were made with the intent of making the specimen less sensitive because the application was lower hardness fasteners (33-44 HRC) for automotive applications as compared to the higher hardness (45-52 HRC) steel used in aerospace apphcations. 

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