PSI - Issue 18

Christoph Bleicher et al. / Procedia Structural Integrity 18 (2019) 46–62 Author name / Structural Integrity Procedia 00 (2019) 000–000

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2.5. Material stiffness During the strain-controlled fatigue tests, both the applied strain and the reacting force to achieve the total strain are measured. With these data, it is possible to determine the material’s stiffness, at least in the fatigue specimen’s test volume. As investigations on shrinkages in nodular cast iron and cast steel [Bleicher (2016), Sigl et al. (2003), Hardin et al. (2004), Blair et al. (2005), Hardin et al (2009) and Ol’khovik (2015)] show, a good correlation can be drawn between the material’s stiffness or the virtual Young’s modulus, E f , and the density ρ as described in Bleicher (2016). If a correlation between the material stiffness and the density is also valid for Dross, this is a possible means of transferring information coming from non-destructive test methods, such as X-ray (Bleicher (2016)) and ultrasonic testing (Kurz (2014) into a mechanical property, enabling a recalculation of a Dross-affected component with the local measured stiffness to assess the component’s lifetime. The material stiffness or the virtual Young’s modulus was determined with the help of the definition of the hyperbolic Young’s modulus, Fig. 10. This method determines the Young’s modulus using the ratio of strain to stress over the strain, which reduces influences of non-linearities in the material behaviour, especially at the beginning of the tensile test, where micro plasticising can take place, especially in nodular cast iron materials (Fang et al. (1995)). Plotting the strain to stress ratio over the strain results in a constant value for the strain to stress ratio, being the reciprocal of the Young’s modulus. For the determination of the virtual Young’s modulus in the fatigue tests, only the linear elastic part of the first half cycle is used. For the determination of the stress, the constant specimen cross section of 15 mm x 8 mm is used to determine the nominal stresses.

Fig. 10. Determinition of the hyperbolic Young’s modulus according to [27]

3. Materials and Methods 3.1. Sound material condition

The fatigue tests were evaluated, according to Ramberg et al. (1943) for the stress-strain curve, Equation (4), and according to Coffin (1954), Manson (1965), Basquin (1910) and Morrow (1965), for the strain-life curve, as the classical approach, Equation (5). The results are shown in Fig. 11 as the cyclic stress-strain curve and in Fig. 12 as the strain-life curve. ��� � ��� � ��� � � � � � ′ � � � � (4) ��� � ��� � ��� � � � � �2 � � � � � � �2 � � (5)