Issue34

B. Schramm et alii, Frattura ed Integrità Strutturale, 34 (2015) 280-289; DOI: 10.3221/IGF-ESIS.34.30 283 threshold value  K I,th of the subsequent material. If the gradation is oriented opposite, negative consequences for the prospective lifetime of the component are expected. With reaching the material transition the cyclic fracture toughness of the subsequent material might be exceeded resulting in the sudden failure of the structure. For further information about the influence of the gradation on the limits of stable fatigue crack growth see [4]. The change to a material with other fracture mechanical material properties is connected – besides the influence on the limits of fatigue crack growth – with a change in the crack growth rate da/dN [4, 5]. In the following, this influence is considered using principal crack growth rate curves of the materials M1 and M2 (Fig. 4). These curves have differences in the threshold value  K I,th , in the crack growth rate da/dN and in the cyclic fracture toughness  K IC . Material M1 possesses a smaller threshold value  K I,th , a higher crack growth rate da/dN and a smaller cyclic fracture toughness  K IC than material M2. At first, Fig. 4a considers a crack which grows within material M1. After some time the crack reaches the second material M2 leading to a change to the crack growth rate curve of M2 with the consequence of reaching the instability later as if the crack grows further within material M1. Besides the difference in the fracture mechanical limits a difference in the crack velocity can be observed: the velocity changes considerably at transition, so that the crack grows slower after reaching material M2. At the best, crack arrest occurs if the cyclic stress intensity factor  K I is smaller than the threshold value  K I,th,M2 of material M2. If the gradation is oriented opposite (Fig. 4b), i.g. the crack starts in material M2 and reaches the fracture mechanical worse material M1, the transition causes an increased crack growth rate da/dN and at the same time a reduced prospective life time. The worst imaginable case occurs if the cyclic stress intensity factor  K I is at transition already larger than the cyclic fracture toughness  K IC,M1 of material M1 leading to unstable crack growth and the immediate failure of the structure. a) b) Figure 4: Influence of the fracture mechanical material gradation on the crack velocity: a) transition from material M1 to M2, b) transition from material M2 to M1. These illustrations confirm that the fracture mechanical material gradation may have a grave impact on the fatigue behavior of components. However, they can’t clarify the influence on the occurring crack propagation direction. To make a statement on the crack propagation direction the TSSR-concept is developed. TSSR-concept for the prediction of crack propagation behavior in fracture mechanical graded structures The developed TSSR-concept enables the determination of the beginning of stable and unstable crack growth as well as the direction of the occurring crack propagation [4, 5]. In the following, the principal application is shown for a pure Mode I stress situation and an idealized sharp material transition. Fig. 5a shows a cracked structure consisting of the materials M1 and M2 and therefore of different fracture mechanical parameters, whereas the elastic parameters are the same for the entire structure. The cyclic load  (t) results in a pure Mode I stress situation at the crack tip. The gradation angle  M defines the position of the material transition in relation to