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Combining Thermal Autofrettage with Various Other Processes
Published in Uday S Dixit, Seikh Mustafa Kamal, Rajkumar Shufen, Autofrettage Processes, 2019
Uday S. Dixit, Seikh Mustafa Kamal, Rajkumar Shufen
The fatigue life of the shrink-fitted thermally autofrettaged is estimated numerically using Paris’ law (Paris and Erdogan, 1963). Paris’ law is a power law expression that relates the stress intensity factor range to the crack growth rate during a state of cyclic loading. Mathematically, it is expressed as: dldN=AΔKIm,
Optimal prognostic maintenance policy for railway track systems using rolling contact fatigue data
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
Many models have so far been developed to describe the crack growth process, e.g. Paris’ law (also known as the Paris-Erdogan law). The Paris’ law is a power-function used to predict crack evolution for structures subject to fatigue stresses. The Paris’ law equation is given as follows (Paris and Erdogan, 1963): () dadN=C(ΔK)m,
A stochastic model for damage evolution of mode II delamination fatigue of composite wind turbine blades
Published in Jaap Bakker, Dan M. Frangopol, Klaas van Breugel, Life-Cycle of Engineering Systems, 2017
Fatigue damage can weaken the resistance properties of the materials by cyclically loading on specific parts in long time and delamination is one of major failure for composite blades. The delamination fatigue crack propagation study needs to develop a proper model adopting the rate of fatigue crack growth under cyclic loadings. In order to find crack threshold and crack growth propagation, a widely used method known as Paris law is often used to construct the relationship between the fatigue crack growth rate and strain energy release rate ΔGII. The crack growth propagation in Paris law can be divided into three stages, crack initiation stage, subcritical crack propagation stage and critical crack propagation stage, as shown in Figure 2 (Al-Khudairi et al. 2015). With fatigue crack propagation under repeated loading, the structures easily reach the first stage of the failure process. Thus, the life of a structure can be predicted by using the Paris law model.
Fatigue crack propagation simulation of vertical centrifugal pump runner using the extended finite element method
Published in Mechanics of Advanced Materials and Structures, 2023
Xiaocui Chen, Yukun Cui, Yuan Zheng, Yuquan Zhang
Several studies have been conducted on the fatigue behavior of stainless steel, which is commonly utilized in hydraulic infrastructure [8, 9]. The fatigue failure procedure of ductile metals such as stainless steel can be separated into two stages: crack initiation and crack propagation [10, 11]. Crack propagation in such materials is triggered by crack tip plasticity [12–15], which relies on the plastic properties and crack driving force, stress intensity range ΔK, and cyclic J integral. Fatigue crack growth rate (FCGR) definitely plays an important role in fatigue crack propagation and FCGR is usually determined experimentally. Paris and research engineers at the Boeing Airplane Company [16] examined the factors influencing the growth of fatigue cracks and proposed an equation describing the relationship between the crack growth rate, da/dN, and stress intensity factor range, ΔK. The equation was later termed “Paris law” and is widely used to predict the cracking path during engineering fatigue safety assessment.
Probability-based surface deterioration assessment of bridge pylon and state updating using inspected crack length distribution
Published in Structure and Infrastructure Engineering, 2023
Mingyang Zhang, Xin Ruan, Yue Li, Baiyong Fu
Paris’ law is widely used to predict the crack propagation in metal materials (Han, Yang, & Frangopol, 2019; Kim & Frangopol, 2018; Kim, Ge, & Frangopol, 2019) owing to the well-understood phenomenon of metal fatigue. However, owing to the quasi-brittle nature of concrete, the fatigue mechanism in concrete differs from that in metals. Slowik et al. (1996) proposed a fatigue crack propagation law for concrete materials subjected to cyclic loading by modifying Paris’ law. Based on the model proposed by Slowik et al. (1996), for simplicity without accounting for the overload, the ratio of the crack length increment to the increment in the cyclic stress can be expressed as: where a denotes crack length; N indicates the number of cycles; C refers to the material parameters. m, n, and p denote constant coefficients determined through an optimization process using experimental data (Slowik et al., 1996); denotes the maximum stress intensity factor in a cycle; is the maximum stress intensity factor ever reached by the structure in its past loading history; denotes the fracture toughness; denotes the stress intensity factor range, which can be calculated as follows: where S indicates the stress range; Y(a) represents the geometry function.
Modelling of the fatigue cracking resistance of grid reinforced asphalt concrete by coupling fast BEM and FEM
Published in Road Materials and Pavement Design, 2023
A. Dansou, S. Mouhoubi, C. Chazallon, M. Bonnet
Suitable criteria for crack propagation are still being debated, especially for 3D configurations. A simple criterion for fatigue crack growth is the Paris law, see Paris and Erdogan (1963). Many other propagation criteria are proposed, see e.g. Mi and Aliabadi (1994), Bouchard et al. (2003), Ma (2005), Sun and Jin (2012) and Recho (2013). Paris postulated that sub-critical crack growth under fatigue loading can be predicted in terms of the ranges of stress intensity factors (SIFs) in the same way that thresholds on SIFs or energy release rate characterise brittle fracture. Abundant experimental evidence supports the view that the crack growth rate can be correlated with the cyclic variation in the SIFs, e.g. through where s is the arc length coordinate along the crack front, N is the current number of loading cycles, is the fatigue crack advancement rate per cycle, is the SIF range for the current cycle, while A and m are parameters that depend on the material, environment, frequency, temperature and stress ratio.