white paper accurate fracture and fatigue crack growth

$: White paper accurate fracture and fatigue crack growth$
White Paper

Accurate Fracture and Fatigue Crack Growth Fitness for Service Assessments

Authors

Matt Rudas - Senior FE Analyst, Deacon Engineers

Jurrien de Vos - Principal, Deacon Engineers

All information within this document is copyright and the property of Deacon Engineers - © 2015 Web: http://deaconengineers.com.au

ACN 135 205 408

www.deaconengineers.com.au

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CONTENTS

Page

1. EXECUTIVE SUMMARY ........................................................................................ 3

2. OVERVIEW ............................................................................................................ 3

3. FITNESS-FOR-SERVICE ASSESSMENTS OF CRACK-LIKE FLAWS .................. 3

4. NUMERICAL MODELLING OF CRACK-LIKE OF FLAWS ..................................... 5

4.1 Flaw modelling using FEA ...................................................................................... 7

4.2 Flaw modelling using BEA ...................................................................................... 7

5. CASE STUDY – SAG MILL GIRTH GEAR ASSESSMENT USING BEASY ........... 7

5.1 Background ............................................................................................................ 7

5.2 Numerical model for SIF evaluation ........................................................................ 9

5.3 Fatigue crack propagation of flaw ......................................................................... 11

5.4 Outcomes of gear assessment ............................................................................. 13

6. CONCLUSION ..................................................................................................... 13

7. BIOGRAPHIES ..................................................................................................... 13

7.1 Jurrien de Vos, Principal ....................................................................................... 13

7.2 Matthew Rudas, Senior FE Analyst ...................................................................... 13

Deacon Engineers – March 2015 Page 2 of 13


1. EXECUTIVE SUMMARY This whitepaper discusses the application of numerical modelling for the calculation of fracture parameters for Fitness-For-Service assessments. The shortcomings of analytical solutions presented in assessment codes, and the requirements for high degrees of accuracy of calculated fracture parameters, are discussed. The main two solid mechanics numerical techniques are briefly outlined and two commercially available fracture mechanics and fatigue crack growth software packages are presented. Finally, the fracture mechanics component of a Fitness-For-Service assessment is presented as a case study. The case study is a cracked helical mill gear tooth and the assessment was carried out using BEASY Boundary Element Analysis software.

2. OVERVIEW The quality of Fitness-For-Service assessments involving crack-like flaws is highly dependent on the accuracy of calculated fracture parameters. Analytical solutions presented in fracture assessment codes are limited to a small number of idealized situations and extrapolation beyond the validity of the solutions is not recommended. Numerical analysis, using Boundary Element Analysis (BEA) or Finite Element Analysis (FEA) software, is essential for structures having complex geometries and loading histories not covered by the solutions in the codes. Three-dimensional models that include detailed flaw morphologies generate accurate inputs for crack growth law calculations that are extremely sensitive to input errors. This provides accurate predictions for remaining life and equipment de-rating figures and allows the establishment of safe inspection and monitoring regimes.

3. FITNESS-FOR-SERVICE ASSESSMENTS OF CRACK-LIKE FLAWS Fitness-For-Service (FFS) assessments are carried out on defective engineering assets with the aim of answering the following key questions:

• Can the asset continue to be operated in a defective state?

• If not, can the asset be re-rated to ensure continued safe operation?

• What repair and inspection strategy should be adopted?

More specifically, for structures containing crack-like flaws, an FFS can provide answers to the following questions:

• What are the reasons for initiation of the flaw?

• Is the flaw growing in size, and if so, at what rate?

• What is the required load reduction to prevent the flaw from growing?

• What is the required load reduction to achieve a particular rate of growth?

• What is the critical (failure) size of the flaw?

• What is the growth path of the flaw?

The successful FFS assessment of crack-like flaws is heavily dependent on the accuracy of the fracture input data, namely the stress intensity factors (SIF’s). Crack growth rates, for example, are calculated by raising the crack tip SIF range to the power of m, the crack



growth exponent. Depending on the selected crack growth law, m can take on values as high as 8, where an error of 10% in the calculated SIF range can result in an error factor of 2.3 on the crack growth rate.

Figure 1 – The Paris Law for fatigue crack growth. The SIF range at the crack tip is raised to the power of the crack growth exponent, m in order to calculate the crack growth increment for a single load cycle, da/dn.

SIF’s can be determined in two ways:

• By analytical solutions presented in FFS and fracture assessment codes and handbooks, or;

• By numerical modelling of the structure containing the crack.

Calculation of SIF’s by analytical solutions is done using idealized scenarios of structure and flaw geometry and applied loads. Calculations are generally performed according to the rules of applicable codes such as BS 7910 - Guide to methods for assessing the acceptability of flaws in metallic structures. Care needs to be taken to ensure that the limits of applicability of the codes are not exceeded - extrapolation outside of the limits is forbidden by the rules of the codes. Simplification of the actual scenarios to allow the use of the codes may lead to errors that are highly magnified, as shown earlier in the hypothetical error factor calculation. Also, any changes in the crack geometry as a result of load re-distribution by crack growth, are not taken into account.

For cases that fall outside of the validity of the solutions within codes, accurate determination of SIF values can only be made by numerical fracture mechanics modelling of the structure containing the crack.



Figure 2 – Example surface flaw definition from BS7910. Analytical solutions for SIF’s are presented for specific ratios of a, c, B and W, the plate width in the plane of the flaw.

Figure 3 – Fracture of gear teeth showing complex crack propagation paths. Hypoid gear tooth loads and stress redistribution due to crack growth makes this scenario difficult to accurately assess with analytical solutions.

4. NUMERICAL MODELLING OF CRACK-LIKE OF FLAWS Fracture parameters can be obtained numerically by commercially available software based on FEA and BEA. Solid mechanics FEA involves discretization of the volume of a structure into finite elements in order to generate an approximate solution for displacements, stresses and strains. Generally, as the number of elements increases, the error of the solution decreases. By using a different mathematical approach to FEA, BEA only requires that the surface of the model is discretized into boundary elements.

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Both methods have their strengths and weaknesses, and both are more suited to certain applications than others. However, when used correctly, both methods have been proven over time to accurately determine SIF’s for use in crack growth studies and FFS assessments.

Figure 4 – FEA ANSYS model of rotating equipment with girth gear.

Figure 5 – BEA BEASY model of helical girth gear segment.



4.1 Flaw modelling using FEA Commercially available packages such as Abaqus are able to calculate two- and three-dimensional SIF’s in a quasi-static fracture model using contour integrals. Solution dependant two- and three-dimensional crack growth is modelled using the extended finite element method (XFEM), where re-meshing of the model by the user is not required.

Figure 6 – Abaqus surface crack mesh and stress results.

4.2 Flaw modelling using BEA Commercially available packages such as BEASY are able to calculate two- and three-dimensional SIF’s using both crack tip opening displacement (COD) and the J-integral. BEASY uses the Dual Boundary Element Method for crack elements, which means that only one of the crack faces needs to be modelled by the user, with the other being generated automatically. Automatic two- and three-dimensional crack growth is also supported by the software.

5. CASE STUDY – SAG MILL GIRTH GEAR ASSESSMENT USING BEASY 5.1 Background

The girth gear on a semi-autogenous grinding (SAG) ball mill used in the mineral processing industry was found to contain a large crack, originating from the face of one of the helical gear teeth. Several attempts to repair the crack were made by excavating the surface of the gear tooth in the vicinity of the crack, however the crack continued to propagate. With a scheduled maintenance shut of the mill due some months away, the plant operator commissioned an FFS assessment with the aim of investigating the possibility of avoiding a costly, unscheduled shut to carry out weld repairs of the gear tooth. The flow of work for the assessment of the flaw is shown below in Figure 7.



Figure 7 – Mill gear assessment workflow.



Figure 8 – Mill girth gear showing excavated tooth face. The crack breakthrough edges spanned the width of the excavation.

5.2 Numerical model for SIF evaluation In this instance, the BEA fracture and fatigue crack growth module of BEASY software was used for the assessment. The helical gear geometry, tooth face excavation and non-planar flaw geometry were modelled in full detail in BEASY. SIF values were calculated using the J-contour integral at each mesh point along the crack front.

Figure 9 – BEASY element mesh showing excavation on tooth face.



Figure 10 – Cutaway BEASY mesh showing the crack originating at the base of the excavation.

Figure 11 – Scaled deflection image showing opening of the crack under load.



Figure 12 – Automatically generated BEASY internal points forming circular contour paths for evaluation of the J-integral at each element along the crack front.

Figure 13 – BEASY mode I SIF results along the crack front for the first crack growth step.

5.3 Fatigue crack propagation of flaw The automatic crack growth capabilities of BEASY were used to calculate the growth rate and path of the crack. A two stage crack growth law, in accordance with the requirements of BS 7910 for steels in air, was adopted for the crack propagation study. Material properties were taken from the BEASY database for the appropriate material, as follows:

• Ultimate stress

• Yield stress

• Part-through and plane-strain fracture toughness

• Threshold stress intensity factor range at R = 0



• Crack growth rate coefficient

• Crack growth rate exponent

Figure 14 - Cutaway BEASY mesh showing the crack after several growth steps. BEASY automatically meshed the crack and component breakthrough surfaces during crack growth.

Figure 15 – BEASY graph of average crack size on the crack front for 5 growth increments.



5.4 Outcomes of gear assessment Initially, the results of the BEASY SIF calculations were used to provide the plant operator with a reduced load magnitude, in order to eliminate propagation of the crack. The amount by which the load was required to be reduced was not feasible from a process perspective, therefore a fatigue crack growth study was carried out.

The crack growth calculations indicated the statistical probabilities of the crack reaching a critical size prior the planned maintenance shut. In this instance, the most likely rate of crack growth was low enough to allow the plant operator to continue running the mill. An NDT monitoring regime was put in place to ensure the growth rate did not exceed the predictions made using the fatigue crack growth software.

The FFS assessment enabled the plant operator to avoid a costly, unscheduled repair to the gear.

6. CONCLUSION Analytical solutions for fracture parameters presented in FFS and flaw assessment codes are often unable to be applied to structures with complex geometries, loading histories and flaw morphologies. Simplifying the assessments to enable the use of analytical solutions can lead to large errors in predicted safe operating lives of defective engineering assets. In these situations, accurate fracture parameters can only be obtained by numerical analysis of the flawed structure.

7. BIOGRAPHIES 7.1 Jurrien de Vos, Principal

Jurrien de Vos founded Deacon Engineers in Perth, Western Australia in 2009. Since then Deacon Engineers has expanded its offices across Australia. Jurrien has had many years’ experience in the design and failure investigation of gearing and tyres for rotating equipment. He has extensive experience with failure of elements in rolling contact from his time with Hofmann Engineering and RCR Tomlinson.

7.2 Matthew Rudas, Senior FE Analyst Deacon Engineers’ specialist FEA and BEA analyst is Matt Rudas who holds a PhD in fracture mechanics from the University of Western Australia. He has extensive experience in FEA and BEA, computer aided engineering, mechanical design, fracture, fatigue and dynamic stress analysis. He is experienced in laboratory and real world experimental fatigue and stress analysis and strain measurement. His postgraduate research focused on modelling crack growth in bi-material composites using BEA.
