PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 103–114 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

112 10

2



u



.

(58)

  E t *

01

2

02 u and 03 u , are found by replacing of  with the stresses in the lower crack arm and

The strain energy densities,

the un-cracked beam portion in (58), respectively.

6 0.2 10     1/sec, curve 2 – at

6 0.4 10     1/sec and

Fig. 6. Variation of the strain energy release rate with m (curve 1 – at

6 0.6 10     1/sec).

curve 3 – at

The strain energy release rates found by (56) match these determined by using (51) which represents a verification of the analysis developed in this paper. 3. Numerical results The effects of temperature, loading conditions and material inhomogeneity on the longitudinal fracture are studied numerically. For this purpose, calculations of the strain energy release rate are carried-out by applying the solutions of the strain energy release rate derived in the previous section of this paper. The following data are used: 0.020  b m, 0.030  h m, 0.600  l m, 0.7  i  where 1, 2, ..., 9  i and 2 0  M Nm. The variation of the strain energy release rate with time is depicted in Fig. 4 at three S T T / 1 ratios. It should be noted that the strain energy release rate and time in Fig. 4 are presented in non-dimensional form by applying the formulae   G G E b I N  /  and    1 / I I N t tE  , respectively. The curves in Fig. 4 indicate that increase of S T T / 1 ratio induces increase of the strain energy release rate. The influence of the parameters,  and n , on the strain energy release rate is shown in Fig. 5. It can be