Crack Paths 2009

crack initiation angle at failure. Chen and Ozaki [9] tested V-notched specimens made

of an acrylic resin whereas Ayatollahi and Aliha [10] proposed a new test configuration

for mixed mode fracture and provided a complte set of experimental data from

diagonally loaded square cracked plate specimens made of P M M A .

The main aim of the first part of the present paper is to present a complete synthesis

based on the local S E Din order to discuss the capability of the volume-based strain

energy density approach to summarise data obtained under a large range of loading

conditions and very different geometrical parameters (notch radius, opening angle,

notch depth). Regardless of the mode mixity, the SED-based synthesis will result to be

satisfactory also in cases very close to pure modeII loading.

The second part of the paper deals with the analysis of fracture initiation direction

and early propagation. Very different fracture angles are documented, strongly

dependent on the mode I and mode II stress fields ahead of the notches. The angles are

summarised both for sharp and rounded notches. Dealing with sharp notches, two well

knowncriteria [11-12], the former due to Erdogan and Sih (1963), the latter due to Sih

(1974), are used to assess the initiation angle and to compare theoretical values and

experimental results. Particular attention is paid to show the influence on the fracture

angles of the non-singular stress term and the distance from the notch tip.

E X P E R I M E N TPARLO G R A PM :M MTAE S T EAD TL O WT E M P E R A T U R E

The material chosen for the experimental programme was polymethyl-methacrylate

(PMMA)tested at −60˚C, an amorphous glassy polymer that exhibits a non-linear

behaviour at room temperature and linear elastic up to fracture at −60˚C, even when

tested without cracks or notches. The experimental programme was performed both

with U- and V-notched specimens, varying the notch inclination, the notch angle and

the boundary conditions. The geometry of the specimens is shown in Fig.1. In all

specimens, the thickness, B, was 14 mm, the depth, W, was 28 mm, and the notch

length, a, was 14 mm.

Dealing with sharp notches [8], the notch root radius, R, was always less than 0.1

mm, ranging between 20 μ m and 72 μm. To achieve different mixed mode loadings,

two types of V-notched specimens were studied; beams with vertical notches, with

notch angles, 30˚, 60˚ and 90˚ (Fig. 1a), and beams with titled notches at 45˚, with notch

angles 30˚ and 60˚ (Fig. 1b) and 90˚ (Fig. 1c). Samples were loaded as shown in Fig. 1.

When loading beams with vertical notches, the position of the loading point was

modified; the distance from this point to the middle point, b, was 1 m mor 9 mm.When

loading beams with tilted notches, the position of the support was moved and the

horizontal distance to the centre of the specimen, m, was 9 m mor 18 mm.Notch angles

higher than 90˚ were not considered in this research.

Dealing with U-notches [6, 7] two different geometries were tested, as indicated in

Fig. 1; standard U-notched beams (Fig. 1d) and beams with a tilted U-notch (Fig. 1e), to

explore a larger range of mixed modes. For vertical U-notched beams (Fig. 1d), notches

with six different notch root radii, R, were tested; R = 0, 0.2, 0.3, 0.5, 1.0, 2.0 and 4.0

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