Unified model of nucleation and growth of fatigue cracks. Part 1. Use of force parameters of fracture mechanics of materials in the stage of crack nucleation

Abstract

According to the phenomenological model of nucleation of a fatigue macrocrack, the process is considered as a two-parameter process. The process is described by the local stress or strain range and a certain linear parameter of the material. We propose the corresponding parameters, namely, the local stress range At~. and the characteristic size d" of the prefracture zone. The formation of this zone is caused by the anomaly of the yield strength of the material in subsurface layers, the microstructure, the loading amplitude, the cyclic strain hardening, and the environment. The quantity d* is a constant of the material, which is independent of the geometry of notch and specimen. The boundary of the prefracture zone is considered as a macrobarrier that determines the growth of microstructuraliy short and physically small cracks. The moment when a physically small crack oversteps the boundary of the prefracture zone is defined by the quantitative criterion (ao= d* ) of the initial size a 0 of a macrocrack in the material. The proposed dependences of ( A~., At,.) and (d*, Ni) can be regarded as a basis for the determination of characteristics of resistance of the material to the nucleation of a fatigue macrocrack.Due to the rapid development of fracture mechanics, especially structural fracture mechanics, in the past ten years considerable progress has been made in understanding the phenomena of fatigue of metals. A detailed analysis of successes and failures concerning the solution of this problem is given in [1,2]. By summing our own data and literature data, we propose to consider fatigue of materials as a process that consists of the following main stages: 1) nucleation and growth of microstructurally short cracks, 2) growth of physically small cracks and formation of a macrocrack, and 3) growth of the macrocrack up to total fracture of the body.Within the framework of this approach, the endurance limit of the material is estimated by the maximum stresses for which a crack in the material does not grow, i.e., the crack is retarded by certain physical barriers (crack resistance of the material). These barriers are caused by the microstructure of the material (boundaries of grains and twins, sizes of pearlitic colonies and martensitic packs, etc.). Thus, the endurance limit is, to a great extent, connected with a certain linear parameter of the structure of the material, in particular, with the distance between structural barriers [2]. At the same time, it is necessary to take into account the following fact: if the microstructural barrier of the material is considered as the main factor for its endurance limit, then it is impossible to explain some experimental data. For example, there exist qualitatively opposite dependences of the fatigue limit t~ R of a smooth specimen and the fatigue threshold Kth of a cracked specimen on the grain size for the same material [3]. It is also known [4] that for a given loading amplitude, the growth rate of microstructuraily short and physically small cracks is greater than that ...

Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

“…Note: Numerator and denominator: values of ae for muiticycle fatigue (the number of cycles to failure N i is 105-107) and low-cycle fatigue (N i = 102-105 cycles) found experimentally in [2].…”

“…We establish the main dependences between the value of the range of local strains Ae* and the period N i prior to the nucleation of a fatigue macrocrack. Thus, by using the experimental quantity Ae*, we can estimate the period N i prior to the nucleation of a fatigue crack of length a i = ae for structural elements of a complicated geometry.As is known, the problem of fatigue fracture of materials is an actual problem of modern materials science and fracture mechanics of materials [ 1,2]. In solution of this problem, investigation of the nucleation of macrocracks near stress concentrators in structural elements plays an important role.…”

“…For this purpose, the force (stress), strain, and energetic parameters of the stress-strain state of the material are mainly used. The force approach to solution of the problem was earlier considered in [2]. Owing to the difficulty of calculations of stresses (force parameters) in the vicinity of various concentrators in structural elements during their service, especially with regard for elastoplastic strains of material and the action of the environment (working medium), it is necessary to search for the most simple approaches to solution of the problem.…”

“…As the period prior to the nucleation of a macrocrack N i, we take the number of loading cycles necessary for the crack to reach the value a 0 = d* and to have a formed self-similar elastoplastic zone in the vicinity of its tip [2]. The range of local (AOy) and maximum (AOy) stresses and the characteristic size d* were determined according to the recommendations given in [2,3]. We calculated the value of local strain At* by using the opening (relative displacement) of contour points of the specimen in the vicinity of the tip of the notch (Fig.…”

“…The instant of nucleation and length of a macrocrack were fixed with a KM-6 cathetometer with x 25 magnification and an MVT-71 optical microscope with • 400 magnification. As the period prior to the nucleation of a macrocrack N i, we take the number of loading cycles necessary for the crack to reach the value a 0 = d* and to have a formed self-similar elastoplastic zone in the vicinity of its tip [2]. The range of local (AOy) and maximum (AOy) stresses and the characteristic size d* were determined according to the recommendations given in [2,3].…”