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Many structural components and devices in combustion and automotive engineering undergo highly intensive cyclic thermal and mechanical loading during their operation, which leads to low cycle (LCF) or thermomechanical (TMF) fatigue crack growth. This behavior is often characterized by large scale plastic deformations and creep around the crack, so that concepts of linear-elastic fracture mechanics fail. The finite element software ProCrackPlast has been developed at TU Bergakademie Freiberg for the automated simulation of fatigue crack growth in arbitrarily loaded three-dimensional components with large scale plastic deformations, in particular under cyclic thermomechanical loading. ProCrackPlast consists of a bundle of Python routines, which manage finite element pre-processing, crack analysis, and post-processing in combination with the commercial software Abaqus . ProCrackPlast is based on a crack growth procedure which adaptively updates the crack size in finite increments. Crack growth is controlled by the cyclic crack tip opening displacement \(\varDelta \)CTOD, which is considered as the appropriate fracture-mechanical parameter in case of large scale yielding. The three-dimensional \(\varDelta \)CTOD concept and its effective numerical calculation by means of special crack-tip elements are introduced at first. Next, the program structure, the underlying numerical algorithms and calculation schemes of ProCrackPlast are outlined in detail, which capture the plastic deformation history along with the moving crack. In all simulations, a viscoplastic cyclic material law is used within a large strain setting. The numerical performance of this software is studied for a single edge notch tension (SENT) specimen under isothermal cyclic loading and compared to common finite element techniques for fatigue crack simulation. The capability of this software is featured in two application examples showing crack growth under mixed-mode LCF and TMF in a typical austenite cast steel, Ni-Resist. In combination with a crack growth law identified in terms of \(\varDelta \)CTOD for a specific material, the tool ProCrackPlast is able to predict the crack evolution in a 3D component for a given thermomechanical loading scenario.
Nowadays, hot parts in combustion and automotive components like vessels, piping, turbo-chargers, exhaust pipes, etc., undergo highly intensive cyclic thermal and mechanical loading during their service phase, which leads to isothermal (LCF) or thermomechanical (TMF) fatigue crack growth. This failure behavior is accompanied by large scale plastic deformations and creep around the crack. Thus, established finite element (FEM) or boundary element simulation tools for 3D fatigue crack growth such as FRANC3D (Fracture 2016), ZenCrack (Zentech 2019), AdapCrack (Schllmann et al. 2003), CrackTracer (Dhondt 2016), ProCrack (Rabold et al. 2013; Rabold and Kuna 2014) or BEASY (CM 2011), are not suitable, since they are based on linear elastic fracture mechanics. Therefore, the current procedure in practice with detected defects often consists of a prophylactic, cost-intensive replacement of the entire part. To resolve this issue, there is high demand for a pragmatic FEM-based crack growth simulation software to predict and assess lifetime and safety of three-dimensional structural components under complex thermomechanical loading conditions, if the intensity and extend of inelastically deformed zones cannot be neglected. This is the motivation for the presented research results.
Among the numerical simulation tools, the so-called Extended Finite Element Method (X-FEM) (Fries and Belytschko 2010; Mos et al. 2002) has been established in the last decades, which avoids the repeated remeshing of the structure by extending the shape functions of the cracked elements. The additional shape functions reflect the displacement jump across the crack faces and the singular crack tip fields. However, the method is limited to linear elasticity. Despite its attractions, applications of X-FEM to large scale yielding (LSY) fracture problems or LCF/TMF are difficult, since the required local crack-tip fields for enhancement are not known. Therefore, the X-FEM does not allow to calculate the fracture parameter CTOD with required accuracy.
In recent years, the phase field method has been developed to address fracture mechanics problems as well, see e. g. Ambati et al. (2015) and Keip et al. (2016). This approach considers the damage state of the material as an order parameter and is able to simulate crack propagation by minimizing an energy functional. However, this technique requires extremely fine meshes and needs further improvement to solve complex engineering problems as 3D LCF/TMF in irreversible materials.
For the assessment of high cycle fatigue crack growth, the cyclic stress intensity concept has been established for decades in the frame of linear elastic fracture mechanics (LEFM). In case of low cycle fatigue (LCF) with plasticity at room temperature and/or creep at high homologous temperatures, global fracture mechanics parameters J or \(C^*\) are traditionally used or derived quantities. They can be determined from path-independent contour integrals, and most commercial FE programs offer this function. The disadvantage is that the validity of path independence, which is necessary for a reliable numerical evaluation, imposes very restrictive conditions on the material laws and on the loading scenario (e.g. monotonic loading, steady-state creep for the case of \(C^*\)), which are not fulfilled for large scale yielding (LSY) and under TMF conditions. The application of the cyclic J-integral \(\varDelta J\) as advocated by Beesley et al. (2015), Ochensberger and Kolednik (2015), Dowling and Iyyer (1987), Tanaka (1983) and Wthrich (1982) is also problematic since there is usually no global, location-independent load reversal point for a thermally stressed component, which would be necessary to determine \(\varDelta J\). Its numerical calculation (Muhamad Azmi et al. 2017; Vormwald 2016) requires a relatively elaborate evaluation methodology in 2D and is hardly applicable to creep fatigue and TMF. For 2D cracks under mode I, Metzger et al. (2015) have shown that \(\varDelta J\) and the cyclic crack tip opening \(\varDelta \)CTOD are equivalent quantities for describing crack propagation in isothermal LCF.
An alternative to the above mentioned global fracture parameters is the application of local loading parameters like the crack-tip opening displacement CTOD, which retain their physical validity under more general conditions. Numerous experimental studies (Laird and Smith 1962; Pelloux 1970; Chowdhury and Sehitoglu 2016) and numerical simulations of cyclic crack tip plasticity (Pippan et al. 2011; Tvergaard 2004) have shown that crack propagation in ductile metals under fatigue loading results directly from the irreversible deformation processes that occur at the crack tip. The \(\varDelta \)CTOD is a measure of these local plastic deformations. Many investigations at room temperature (Pelloux 1970; Ktari et al. 2014; Antunes et al. 2017; Vasco-Olmo et al. 2020) and at high temperatures (Kiyak et al. 2008; Schweizer 2013) have found a correlation between the measured crack propagation rate \(\textrmda/ \textrmdN\) and the experimentally or numerically determined \(\varDelta \)CTOD in the following form:
Although the \(\varDelta \)CTOD concept has a convincing physical meaning, its application to fatigue crack growth (CG) in engineering structures is rarely found in the literature. One reason for this lies in the difficulty to determine the CTOD by experimental measurements or by numerical computations with sufficient accuracy. Please note that the value of \(\varDelta \)CTOD has the same order of magnitude as the crack growth rate per cycle itself, i.e. values of a few micrometers, which even may dramatically vary during crack growth. In last decades, the digital image correlation technique (DIC) has been advanced so far that the CTOD can be measured with high resolution on a propagating crack, see exemplarily (Sutton et al. 2007; Vasco-Olmo et al. 2019). Unfortunately, the method is restricted to the surface of the body and primarily to laboratory samples.
The calculation of CTOD requires very fine FE discretizations and a flexible control of the element size at the crack tip in dependence on the solution variables. Therefore, most numerical studies in literature consider only 2D mode I problems and use a fine mesh of regular isoparametric elements along the prospective straight crack path. The crack propagation is numerically driven by the node release technique, which is controlled by a global quantity like \(\varDelta K_\textrmeff\) and not a local physical variable. Another ambiguous issue is the proper definition of CTOD. Most researchers determine CTOD from the vertical displacement of the first node (Antunes et al. 2017, 2018a, b; Tinoco et al. 2019) or the second node (Pommier 2002) behind the crack tip, or use the 45\(^\circ \)-secant intersection method with the crack profile, see e. g. Kiyak et al. (2008) and Kuna (2013). Many numerical issues have been addressed in numerous investigations of this kind, as there are: convergence studies regarding the influence of mesh refinement, required numbers of load cycles to stabilize solution, influence of crack face contact (called plasticity induced crack closure), etc. Here, we refer to a selection of representative papers by Solanki et al. (2004), Antunes et al. (2017, 2018a, 2018b), Cochran et al. (2011) and Jiang et al. (2005).
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