PSI - Issue 13

Josef Květoň et al. / Procedia Structural Integrity 13 (2018) 1367 – 1372 Josef Kveˇtonˇ / Structural Integrity Procedia 00 (2018) 000–000

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4

0.25 mm/s

0.35 m/s

0.74 m/s

1.00 m/s

2.40 m/s

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25

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0 . 0 0.50 1.00 1.50 strenth multiplier m load [kN]

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damage:

vertical displacement of loading point [mm]

0

1

Fig. 1. Influence of fracture material properties on load–displacement response and crack pattern.

The reason to impose this is that cracking occurring in this area in the late stages influences the final crack pattern. Material parameters of discrete model were set to following values: elastic meso-level parameters E 0 = 40 GPa, α = 0 . 273, fracture parameters for reference simulation (mean value for random distribution of material properties) f t = 3 . 12MPa and G f = 20 N / m 2 .

3.1. Scaling of material fracture parameters

Firstly, the basic influence of constitutive law was investigated. The strength and fracture energy are scaled similarly to application of spatial material randomness, but constant field is considered: h ( x ) = m , where m is strength multiplier. From load displacement curves in Fig.1, one can observe that the value of the peak load for quasi-static rates is largely influenced, whereas the e ff ect for other loading rates is substantially lower, especially for loading velocity 0 . 35 m / s. Larger di ff erences in response curves for higher loading velocities are caused by cracking in the area of applied load. For low loading rates, no such cracking is present and the force is predominantly generated by accelerating the mass of elastic material and it is therefore not a ff ected by fracture parameters. In the same figure, the crack patterns are plotted at the end of each simulation. We can observe the change of the crack pattern with increasing rate. For quasi-static loading, the crack propagates in the horizontal direction and with an increasing rate, the inclination angle grows up to the vertical direction. With further increase of loading velocity, multiple cracking occurs. Comparing crack patterns for di ff erent scaling parameter m used in calculations, it can be seen that for any sim ulated loading rate, the crack pattern changes with the change of material properties in such a way that for weaker material, the greater inclination angle of crack direction is obtained and crack branching occurs at lower loading velocity than for stronger material.

3.2. Application of rate dependent constitutive law

As has been shown in Fig. 1, the numerical model predicts cracking in the area of applied load, which does not occur in the experimental study, see Ozˇbolt et al. (2015). Furthermore the model does not su ffi ciently capture the