THE PENNSYLVANIA STATE UNIVERSITY

SCHREYER HONORS COLLEGE

DEPARTMENT OF ENGINEERING SCIENCE AND MECHANICS

EVALUATION OF THE CRITERIA FOR CRACK PROPAGATION

IN THE PRESENCE OF HIGH SURFACE STRESSES

KATELYN J. SMITH

Spring 2010

A thesis

submitted in partial fulfillment

of the requirements

for a baccalaureate degree

in Engineering Science

with honors in Engineering Science

Reviewed and approved* by the following:

Albert E. Segall

Professor of Engineering Science and Mechanics

Thesis Supervisor

Christine B. Masters

Assistant Professor and Undergraduate Program

Coordinator of Engineering Science and Mechanics

Honors Adviser

Judith A. Todd

P. B. Breneman Department Head Chair

Professor, Department of Engineering Science and Mechanics

* Signatures are on file in the Schreyer Honors College and Engineering Science

and Mechanics Office.

i

ABSTRACT

The petrochemical industry is largely dependent on the continuous operation of

equipment to turn the maximum profit. Thus, there exists an intricate balance between the

financial gains of the business and the structural integrity of the equipment. Numerous standards

are therefore used to establish an appropriate degree of conservatism in the design process to

ensure safe and reliable long-term operation.

The standard under evaluation in this thesis research is the API 579-1/ASME FFS-1. The

present methods for determining critical crack dimensions in this standard compare a calculated

stress intensity value from the surface and depth locations with the material fracture toughness. In

cases where high, residual stresses exist on the surface, this treatment may result in an overly

conservative estimation of the likelihood of crack propagation due to the rapidly diminishing

stresses as the crack face moves away from any high surface stresses. Since over-conservatism

can be problematic, the goal of this project is to evaluate the critical crack assessment in the

presence of a stress field that diminishes rapidly in the through-thickness direction.

Through the use of finite element analysis and other analytical tools, the depth and

surface locations of a semi-elliptical surface crack were examined in terms of stress intensity

solutions. A comparison between the standard and the finite element analysis confirmed that the

critical crack-like flaw assessment provides an additional degree of conservatism at the depth

location of the flaw; this inherent conservatism is equivalent to a safety factor of approximately

1.375 or higher for the cases reviewed. The surface location was unable to be properly assessed

due to inconsistencies in the mesh applied at this location. Thus, further modeling work is

necessary to accurately evaluate the level of conservatism at the surface location of the semi-

elliptical crack.

ii

TABLE OF CONTENTS

LIST OF FIGURES ............................................................................................................... vi

LIST OF TABLES ................................................................................................................. vii

ACKNOWLEDGEMENTS ................................................................................................... viii

Chapter 1 Introduction .......................................................................................................... 1

1.1Equitment Evaluation ................................................................................................ 1 1.2 Objectives................................................................................................................. 2

Chapter 2 Background .......................................................................................................... 3

2.1 Pressure Vessel Stress Assessment ........................................................................... 3 2.1.1 Characterization of Stress .............................................................................. 3

2.1.2 Origin of Stresses in Pressure Vessels ........................................................... 5 2.1.3 Stress Intensity Factor.................................................................................... 5

2.2 API 579-1/ASME FFS-1Standard ............................................................................ 7 2.2.1 Backgound of the API 579-1/ASME FFS-1Standard..................................... 8

2.2.2 Critcal Crack Calculation in the API 579-1/ASME FFS-1Standard .............. 9 2.3 Weight Function Application ................................................................................... 14

Chapter 3 Modeling .............................................................................................................. 17

3.1 Finite Element Analysis ........................................................................................... 17 3.2 Model Design ........................................................................................................... 18

3.2.1 Crack Construction ........................................................................................ 20

3.2.2 Loading Specifications .................................................................................. 21

3.2.3 Material Selection .......................................................................................... 21 3.2.4 Additional Model Construction Parameters ................................................... 22

Chapter 4 Results .................................................................................................................. 23

4.1 Finite Element Analysis Results ............................................................................... 23 4.2 Analytical Work ....................................................................................................... 26

4.2.1 API 579-1/ ASME FFS-1Analysis ................................................................. 26

4.2.2 Weight Function Comparison ........................................................................ 29

Chapter 5 Summary and Dicussions ..................................................................................... 31

5.1 Dicussions ................................................................................................................ 31 5.1.1 Depth Stress Intensity Factor ......................................................................... 32

5.1.2 Surface Stress Intensity Factor ....................................................................... 33

iii

5.2 Summary .................................................................................................................. 34

Chapter 6 Conclusions .......................................................................................................... 36

Chapter 7 Future Work ......................................................................................................... 38

7.1 Modeling Work ........................................................................................................ 38 7.2 Analytical Work ....................................................................................................... 39

References.............................................................................................................................. 40

Appendix A Overview of the Assessment Procedure ............................................................ 42

Appendix B Stress Distributions ............................................................................................ 43

Appendix C Weight Function Calculations ............................................................................ 45

iv

LIST OF FIGURES

Figure 2-1: A three-dimensional semi-elliptical external crack ............................................ 6

Figure 2-2: Geometry with an external axial crack of semi-elliptical shape ........................... 7

Figure 2-3: Failure Regions on the Failure Assessment Diagram. ......................................... 9

Figure 2-4: Schematic Overview of the FAD Procedure ........................................................ 13

Figure 3-1: Cut-Away View of Modeled Crack and Boundary Conditions. .......................... 22

Figure 4-1: View of Model 2 Undeformed Stressed State .................................................... 24

Figure 4-2: View of Model 1 Deformed Stressed State ......................................................... 25

Figure 4-3: ABAQUS/CAE Stress Linearization Through-Thickness for Load 1 .................. 27

Figure 4-4: ABAQUS/CAE Stress Linearization Through-Thickness for Load 2 .................. 27

Figure 4-5: Polynomial Fit to Stress Normal to Crack for Load 1 .......................................... 28

Figure 4-6: Polynomial Fit to Stress Normal to Crack for Load 2 .......................................... 28

v

LIST OF TABLES

Table 3-1: Dimensions of ABAQUS/CAE Model for Semi-elliptical Crack Growth. ........... 18

Table 4-1: Stress Intensity Values for ABAQUS/CAE Model. ............................................. 24

Table 4-2: Linear Approximation of Stress Intensity Values for ABAQUS/CAE Model ...... 26

Table 4-3: Stress Intensity Values from API 579-1/ASME FFS-1Standard. ..............