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Numerical fracture mechanics as a practical failure investigatory tool: The outlook of cracked round bars

https://doi.org/10.1016/j.engfailanal.2021.105630Get rights and content

Highlights

  • The use of numerical fracture mechanics for failure investigations.

  • The importance of SIF data for small crack sizes.

  • The increase of corner point singularity due to a shoulder fillet.

  • The shoulder fillet has stronger effect on the SIFs around the corner points.

  • Lesser influence of the shoulder fillet on the SIFs around the deepest point of larger planar flaws.

Abstract

Many failure investigations related to the failed round bars/shafts for various applications have been reported in literature. The cracks were often initiated at the regions with a high stress concentration. However, numerical fracture mechanics was frequently not used in the failure investigations. Nowadays advancement of computational development on the interactive numerical techniques allows the analysts to more accessibly figure out the fracture phenomena when performing engineering analyses. In addition, the computational cost is no longer the issue of performing numerical fracture mechanics analyses. The stress intensity factors (SIFs) of a surface planar flaw at a stepped round bar are of practical interest, however, the SIF solutions along the flaw front were not yet documented in literature. Here, the practical abilities of the numerical fracture mechanics on the fracture analyses are demonstrated by evaluating a planar surface flaw at the shoulder fillet through numerical simulations by the finite element method (FEM) and the dual boundary element method (DBEM). The use of tetrahedral meshing of FEM is presented, and the concern of corner point singularity on a surface planar flaw is highlighted. The stress contours around the front of planar flaws that are hardly acknowledged in literature are also presented. The SIF behaviors of the semi-elliptical planar flaws are discussed. The SIF data for relatively small crack sizes are valuable to be used for judging a condition of crack size whether or not it would grow to a critical size.

Introduction

Nowadays, numerical techniques such as finite element method (FEM) and boundary element method (BEM) have become essential tools for a broad range of applications. The presence of cracks increases the period and effort expended for repair/maintenance. Since cracks cannot be eliminated, a procedure must be devised to quantify and predict the behaviour of cracked components/structures under service conditions. Systematic scientific procedures must be planned to characterize cracks and their effects. The prime characterization and prediction parameter is the stress intensity factor [1]. The stress intensity factor concept was introduced by Williams in 1957 [2].

Round bars/shafts are widely used in various structural and engineering components. A number of failure analyses associated with the failed round bars/shafts for various applications have been reported in literature. Sattari-Far [3] reported a fractured shaft of a plug screw feeder of a paper production plant due to a fatigue crack growth. The crack was initiated from a high stress concentration region, i.e. the threaded part of the shaft. Ost et al. [4] conducted a failure investigation of the connecting piston- and pump shafts due to the fatigue crack propagation at the bottom radius of the groove for the coupling bush. Ni et al. [5] studied the failure of boric acid pump shaft through material inspection, macro and micro observations. The crack was initiated at a high stress concentration region of the shaft. A combination of inappropriate processing, surface defects and inclusions was identified to be the main root cause of failure. Göksenli and Eryürek [6] reported a fatigue crack that was initiated at the keyway edge of an elevator drive shaft. Stress analysis around the cracked region by the finite element simulations was carried out. The effect of change in the curvature radius on stress distribution was noted. Zangeneh et al. [7] investigated a failure of an agitator shaft in a large vessel by the fracture surface examination and finite element method for stress analysis. Inadequate fillet radius size and improper surface finish at the shoulder of the shaft were known to be the main cause of the shaft failure. Han [8] performed the root cause analysis (RCA) of the failure of reduction gear input shaft connecting a diesel engine. The crack was present at the end of the keyway and propagated to the rotational direction. Poor design of the keyway was promoting the failure of the shaft. Zhao et al. [9] reported a fatigue crack growth in a vehicle drive shaft under cyclic stress amplitudes of less than the yielding strength of the material. The crack was observed to nucleate at the root fillet of the spline and propagated under high cycle fatigue. Vicente et al. [10] presented the failure analysis of a coupled shaft from a shredder machine. The failure analysis was performed by visual and microscopic inspection, tensile and hardness tests and theoretical stress calculations to determine the main root causes. The radial misalignment of the shaft was identified to cause combined torsion-bending cyclic loadings, leading to the failure of the shaft. Shuchao et al. [11] investigated multiple-origin fatigue fracture on the feed water pump shaft used in a HRSG (Heat Recovery Steam Generator) of 9F class gas turbine generator unit. The initial cracks were originated on stress concentration region of the matched lock nut. Roy et al. [12] conducted an investigation of torsional fatigue failure of a centrifugal pump shaft. The main root cause of the failed shaft was the insufficient size of the keyway width, causing over-tight fitting of the key within the keyway. The phenomenon was worsened by the sharp notch radius of the keyway, which in turn increased the stress concentration. Through analytical fatigue analysis and finite element modelling. Seifoor et al. [13] observed the effect of the fillet radius at the diameter change of the shaft. The fillet radius smaller than the recommended size potentially promotes a failure event.

Although fatigue crack growth leading to final fracture has been known to be a large part of failure events in industrial practices, the role of fracture mechanics in failure analysis remains relatively limited. Zerbst et al. [14] highlighted a basic discussion of possible contributions of fracture mechanics to failure analysis. Various aspects with some circumstantial information that may be helpful in understanding the prospects and limitations of fracture mechanics in failure investigations and the conditions of its applications were elaborated. They [14] also listed down a number of failure analysis questions which can be potentially answered by fracture mechanics. The linear elastic fracture mechanics (LEFM) concept has been widely used in practical engineering problems to evaluate the mechanical behavior of a cracked component.

Numerical fracture mechanics has emerged to play an important role on the development of linear elastic fracture mechanics and has become a practical tool to the structural engineering analysts. Kuna [15] stated that prevention and assessment of fracture and damage processes are crucially important in the dimensioning and development of engineering structures/components in order to ensure the safety, durability, and reliability. Any failures may have catastrophic implications for the human lives, ruined environment and economic/revenue losses. The fracture mechanical assessment of crack-like flaws and the analysis of the mechanical loading condition at cracks, notches, and similar defects under operational conditions are of paramount importance. The stress intensity factor solutions are needed for the calculation of the residual strength of cracked components and the evaluation of the critical crack sizes as particularly stated in the practice codes such as BS 7910 (for acceptability of flaws) and API 579-1/ASME FFS-1 (for fitness for service). Since more than a half-century, a number of methods for obtaining SIF solutions have been developed. Today, numerous commercial software packages are available, which offer not only standard methods of structural mechanics but also fracture mechanical options with latest innovations.

Computer graphics becomes a powerful supporting tool for visual problem solving, and its interactivity plays an important role in harnessing ingenuities. It is worth to highlight some early developments on the interactive graphical-numerical techniques that are considered among the pioneer works. The interactive computer graphic techniques should offer a highly efficient technique of creating three-dimensional model surfaces with the minimum digital input [16], [17], [18]. Based on experiences with the FEM application, Perucchio and Ingraffea [19] stated that the high cost of performing numerical analysis on three-dimensional models is mainly due to the effort needed in defining and checking the geometrical data, element topology, boundary conditions, material properties and loadings. The preprocessing feature must be considered as a combination of coding and input techniques which greatly relieve the users from the tedious portion of checking tasks while enhancing the creative aspects of designing and modelling. Wawrzynek and Ingraffea [20] added that by integrating aspects of finite element analysis, fracture mechanics, mesh generation, post-processing, computer graphics, and data base design, it may become possible to develop a powerful investigatory tool. As computational fracture mechanics becomes more well-developed, the integrated programming solutions essentially become a necessity. Further, Abel et al. [21], [22] early expected that the future developments of interactive graphics can be highly successful to resolve difficulties in the performance of engineering analyses, especially involving complex three-dimensional geometries. The establishment of the best effective and appropriate analysis methodologies would benefit engineers/designers to sensibly carry out design projects. Perucchio and Ingraffea [23] developed an analysis system for three-dimensional fracture mechanics based on an interactive computer graphic preprocessor and a linear-elastic boundary element code. The crack surface modeling and singularity representation were featured into the BEM application. The combined strength of BEM analysis and interactive preprocessing was demonstrated by the application of the integrated system to a variety of three-dimensional fracture mechanics problems.

Through advances of the numerical fracture mechanics by FEM and DBEM, it allows the designers/engineers to justify critical stages of cracked components/structures. The early use of finite element analysis to the calculation of stress intensity factors for two dimensional cracked bodies was reported in 1969 [24]. Wawrzynek and Ingraffea [25] overviewed numerous early efforts and developments of the FEM to address the singular crack-tip stress and strain fields. The existence of singularity effects around a three-dimensional corner point (where a crack front intersects a free surface) has received attentions from researchers. The initial concepts related to corner point singularities were introduced by Benthem [26], [27], Bažant and Estenssoro [28] and Pook [29]. Pook et al. [30] observed that some of the inconsistencies in dealing with the corner point singularities were the artefacts of finite element analyses due to the use of coarse meshing.

Aliabadi [31] reported the historical developments of the BEM for fracture mechanics in detail. It was mentioned that the applications of the boundary element method (BEM) to fracture mechanics problems have been started since 1970s. The main characteristic of BEM conceptually lies in the fact that an analytical approach towards the solution is taken by the implementation of weighting functions called fundamental solutions, which satisfy the governing equation. In most cases, only the boundary surfaces need to be discretized into elements to enclose the solid domain [19], [31]. The use of dual integral equations was first presented by Watson [32] for two-dimensional problems in which the displacement equation and its normal derivative were used. Next, Portela, et al. [33] proposed a formulation for two-dimensional problems based on the displacement and traction equations applied on the crack boundaries. Early work on the dual boundary element equations for 3D fracture analysis was presented by Gray et al. [34]. Later, Mi and Aliabadi [35] and Cisilino and Aliabadi [36] demonstrated the applications of the DBEM to evaluate three-dimensional crack problems.

A number of experimental studies [37], [38], [39], [40], [41], [42], [43] stated that during the early crack growth (i.e. small crack), the crack tends to have a semi-circular/elliptical front. In particular, Lorentzen et al. [41] reported that cracks in round bars are generally present as small surface planar flaws which are often nearly of semi-elliptical shapes. The opening mode SIF solutions for a surface crack in smooth round bars by FEM have been extensively reported in literature such as those in [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]. However, only few stress intensity factor solutions of a surface crack at a notched round bar by FEM were reported in literature [42], [51], [52], [54], [56]. Though, most SIF solutions were presented for larger ratios of the crack depth over cylinder diameter, and only a few works reported the SIFs at the corner points. With nowadays advancement of computational development on FEM, the modelling of small semi-elliptical surface cracks has become possible, and the improvement in the SIF calculations was noted [58]. Meanwhile, the analyses on the cracked round bars by the DBEM codes that presented the SIFs at the crack front and the corner points have been reported in literature [59], [60], [61], [62], [63], [64], [65].

The advancement of the interactive graphical features may help the analysts visualize the fracture phenomena in more details. In a stepped round bar design, the shoulder fillet radius needs to be properly sized to avoid interference with the fillet of the coupling component. The SIF solutions along the front of a surface crack at a stepped round bar were not yet documented in literature. In this paper, the practical abilities of the numerical fracture mechanics on the fracture investigations are demonstrated by evaluating a planar surface flaw at the shoulder fillet. The stress intensity factors on the front of a semi-elliptical planar flaw at the smooth and stepped round bars are presented and discussed. The use of tetrahedral meshing of FEM is presented, and the concern of corner point singularity on a surface planar flaw is highlighted. The stress contours around the front of planar flaws that were hardly acknowledged in literature are also presented. The finite element simulations are carried out by using ANSYS® 2019. Meanwhile, the dual-boundary element software package of BEASY® is used for the boundary element simulations. The BEASY® software uses the DBEM which was developed by Mi & Aliabadi [35].

Section snippets

Numerical modelling

For all cases, the Poisson’s ratio υ = 0.3 is used in all models, and the J-integral method is used to evaluate the stress intensity factors. The stress intensity factors along the crack front are presented in the form of the normalized values K/Ko, in which Ko is defined asKo=σπwhere σ is any applied tensile stress. Meshing and modelling parameters used in FEM and DBEM are presented in Fig. 1a and b.

The finite element models for the smooth [58] and stepped round bars are developed using ANSYS®

Results and discussion

To show the accurateness of FEM and DBEM for fracture mechanics analyses, the opening mode SIFs of a semi-elliptical surface crack (perpendicular to the cylinder axis) are compared with the published results [44], [52], [57]. For this purpose, the ratios of the crack depth over cylinder diameter a/d = 0.1 and 0.2 are chosen. As can be seen from Fig. 2, the SIFs for the points away from the corner points obtained by FEM and DBEM are shown to be in good agreements. Meanwhile, the SIFs around the

Conclusions

The computations of stress intensity factors of a semi-elliptical surface planar flaw at smooth and stepped round bars under tension were demonstrated by the use of FEM and DBEM. Some remarks may be fairly drawn from the findings as follows:

  • The SIF solutions for relatively small crack sizes were valuable to be used for judging a condition of crack size whether or not it would grow to a critical size.

  • The use of numerical fracture mechanics for failure investigations is highly encouraged.

  • The use

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors wish to thank the Ministry of Higher Education, Malaysia for the initial financial support through the High Impact Research Grant (UM.C/625/1/HIR/MOHE/ENG/33).

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