PSI - Issue 42

Sarim Waseem et al. / Procedia Structural Integrity 42 (2022) 1692–1699 Waseem et al. / Structural Integrity Procedia 00 (2019) 000–000

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A staggered solution scheme is used in the context of finite element method (see Miehe et al. (2010)), which are not unconditionally stable, and tend to be preferred over monolithic schemes in terms of computation time. In staggered schemes, both the phase field and displacement field are solved separately based on field values from the previous increment for each. This sets a requirement for a maximum increment size, which if exceeded, can influence and divert crack paths.

3. Numerical results

Two boundary value problems are considered to demonstrate two di ff erent aspects of the formulation, with the first being measurable overload e ff ects and the other being the crack propagation in complex geometries. The former is demonstrated through a single edge notched mode-I specimen and a 3-point bending test with stop holes is considered for crack path prediction.

3.1. Overload and crack retardation

Initially a single edge notched mode-I specimen is studied for the illustration of crack retardation phenomenon due to the overloads (see Fig. 1 for the loading and the mesh). The process parameters are tabulated in Table 1. An oscillating displacement is applied to the upper edge of the specimen. 8087 elements are used for the mesh which gets finer along the predicted crack path.

Fig. 1. Single edge notched mode-I specimen with loading and the mesh.

Table 1. Material Parameters Young’s Modulus(MPa)

Poisson’s Ratio

Length Scale(mm)

Fracture Toughness(N / mm)

Threshold Fatigue Damage α T

210,000

0.3

335.6

0.01

2.7

The crack pattern that emerged is consistent with preceding studies. The crack growth with cycles is visualized in Fig. 2. Furthermore, an overload is introduced in the 118 th cycle, recording the crack growth against di ff erent overload ratios. For that single cycle, its contribution to crack growth is neglected to be able to better understand the overload contribution to the crack growth rate. The results are illustrated also in the Fig. 2. Higher overloads are observed to produce greater crack retardation e ff ects, which is consistent with the experimental literature (see e.g. Jones (1973)). While of course a more realistic representation of overload and crack growth could be demonstrated through cycles in the order of 10 6 to demonstrate high cycle fatigue results, due to computational limitations, the