Issue 41

A.S. Chernyatin et alii, Frattura ed Integrità Strutturale, 41 (2017) 293-298; DOI: 10.3221/IGF-ESIS.41.39 294 F ATIGUE CRACK PROPAGATION UNDER CYCLIC LOADING AND RESIDUAL STRESS Crack propagation low he method is based on the modified Forman expression which includes the nonsingular T-stress        max 1 m T c C q dl K K dN K (1) where    max min K K K is the stress intensity factor (SIF) range and  min max R K K is the SIF ratio. The correction function q T can be represented taking into account the T-stress as follows [3]           1 T C T Y T q e (2) The constants C , m , C T , as well as the critical stress intensity factor K c and yield strength σ Y are the properties of the material. It should be noted that in this case, the SIF ratio varies along the crack front (here, it is not a characteristic of external loads) due to the effect of the residual stress (RS). Since, the fatigue crack increment occurs when load is increased to maximum values at the cycle, the T- stress in Eq. (2) should be determined as T max . Therefore, Eq. (1) becomes         max max , m dl C K T K dN (3) Numerical simulation of three-dimensional planar cracks can be constructed as a gradual process of crack increments (after finite number of the cycles Δ N ) in a limited set of the crack front points, the position of which will be characterized by a dimensionless local coordinate s that runs along the crack front from one external points to other. An infinitely small value dN can be replaced by a finite cycle increment Δ N and dl replaced by Δ l in Eq. (1). So, the crack increment at the current crack front configuration (after N cycles) can be calculated according to the follow equation                    max max , , , , , m l N s C K N s T N s K N s N (4) For the successful solution of the crack propagation problem under the action of residual stresses and taking into account the constraint along the crack front by means implementation of Eq. (4), the principle of remeshing procedure of finite elements in the vicinity of the crack front is proposed. Adaptive parametric finite elements model with varying crack configuration The parametric finite element model (FE-model) of crack area in the form of a prismatic region is developed in ANSYS software. The model includes the regions with different structures of the element mesh and its sizes. Embedding the crack volume into the FE-model is carried out by means of the macro "Crack" which contains the following features [7]: - configuration of the crack front as a line can be arbitrary, but must have smoothness; - an mapped mesh of the singular elements is created along the crack front. - crack front may pass through several geometric volumes. It is especially convenient for modeling of cracks intersection. Numerical procedure of the SIF and T-stress determination The elastic crack-tip displacement and stress fields of mode I crack can be represented as follows [8] T