IMPACT FATIGUE ANALYSIS ON WELDED PIPELINES OF …

IMPACT FATIGUE ANALYSIS ON WELDED PIPELINES OF HYDROCARBON TRANSPORT

JOHAN ESTEBAN GARCIA PUENTES

UNIVERSIDAD DE LOS ANDES

FACULTY OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING

BOGOTÁ D.C., 2020

IMPACT FATIGUE ANALYSIS ON WELDED PIPELINES OF HYDROCARBON TRANSPORT

JOHAN ESTEBAN GARCIA PUENTES

MASTER’S DEGREE THESIS

JUAN PABLO CASAS RODIGUEZ Phd. ASSOCIATE PROFESSOR

ADVISOR

UNIVERSIDAD DE LOS ANDES FACULTY OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING BOGOTÁ D.C., 2020

Department of Mechanical Engineering . …………… … Impact Fatigue Analysis on Welded Pipelines of Hydrocarbon Transport

i

Acknowledgments

I want to thank my grandfather Reynaldo Puentes for constant support given to successfully

complete my master's degree.

Also, I would like to thank the administrative staff and laboratory technicians from department

of mechanical engineering of Universidad de los Andes because, without their help, it would not have been done this project satisfactorily.

I want to thank to my friend Andres Bautista for his advice and constant support during master's

studies.

Finally, I want to especially thank to Eng. Juan Carlos Garcia (Laboratory technician of

Mechanical Characterization of Materials) for sharing his knowledge, for his patience and guidance during project experimentation development.


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Abstract

Hydrodynamic forces, the falling of heavy objects from the surface, objects collide with the action

of sea waves (actually the most common), among others create an adverse environment to

submarine pipelines. Those forces are a combination of repetitive impact loads on pipes, generating a life reduction on material and final failure.

Studies of response on pipelines under repetitive action of dynamic forces are limited. For that

reason, the objective of this investigation is to determine the behavior of fatigue and fracture in

welded joints of pipelines under cyclic load and impact load conditions with the quasi-static and

dynamic material characterization of fracture toughness. This work focuses especially on the

analysis of repetitive low energy impacts loads which cause a progressive loss of carrying capacity in the pipes and final failure.

For that purpose, the experimentation was carried out, to estimate crack behavior response in a

base metal (BM) of API grade A steel (AISI 1020 steel) with a composition 0.22%wt of Carbon,

0.6%wt of manganese, 0.03%wt phosphorous, 0.03%wt of sulfur, 0.15%wt silicon. Furthermore,

the welded metal (WM) of joints and reparations were evaluated. Welding was done with the

Shielded metal arc welding (SMAW) technique using electrode E6011 (cellulose potassium shield)

as a root and electrode E7018 (low-hydrogen-potassium-iron-powder composition) as filling

welding.

The proposed experimentation is composed of quasi-static and dynamic characterization of

material through tests of crack mount opening displacement (CMOD) under plane strain condition

and unloading compliance, fatigue under sinusoidal constant load amplitude, impact fatigue crack

propagation (Dynamic CMOD) by drop weight test (DWT), and energy absorption analysis in

single edge notch bending (SENB) configuration followed by a metallographic and fractographic

inspection. Besides, an X-ray inspection test and uniaxial tensile test were performed as a

complement to the experimentation to validate the material meets the minimum requirements

given by the API 5L Specification for Line Pipe standard in terms of mechanical properties and

quality in the welding


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Results from experimentation shows welded metal material due to its heterogeneity presents

scattered values in comparison to base metal material. In the Fracture toughness test, WM show

mostly plastic behavior and reduction of load resistance compared with BM material. Moreover,

with the cycling load fatigue test and its data analysis with Paris Law were found WM

experimented higher propagation rates than BM which reflects on parameters C and m. Parameters in WM are about 1.5 – 2 times bigger than parameters in BM.

On the other hand, as of DWT, Base metal experiments a major life under low energy impact

fatigue that translates on lower crack growth rate compare to welded metal. Fatigue life reduction

was attributed to absorption energy capacity loss due to plastic deformation crack coalescence

processes. Furthermore, test proof relationship load amplitude and impact energy with material

life. Also, a clear dependence on the crack propagation rate with the material deformation was

found. That was evidenced in energy curves analysis when absorption energy becomes only in

deformation and cracking energy. According to tests results, impact fatigue has a greater growth

rate of crack propagation than other load conditions and has a high dependency on impact energy (potential energy used).

Furthermore, metallographic and fractographic inspection can determine a mechanism of crack

initiation, crack propagation, and final failure and component phases microstructure associates

with fracture. The ductile mechanism was predominant to cracking processes and perlite presence is associated with high crack growth rates.


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Table of Contents Acknowledgments ...............................................................................................................................i

Abstract ............................................................................................................................................. ii

List of Figures ................................................................................................................................... vi

List of Tables .................................................................................................................................. viii

1. Introduction ................................................................................................................................1

1.1. Objectives ...........................................................................................................................3

1.1.1. General Objective .........................................................................................................3

1.1.2. Specific Objectives .......................................................................................................4

2. Theoretical Background ...............................................................................................................5

2.1. Linear Elastic Fracture Mechanic (LEFM).............................................................................5

2.1.1. Energy Method.............................................................................................................5

2.1.2. Stress Intensity Factor ...................................................................................................7

2.2. Dynamic Fracture Mechanics ...............................................................................................8

2.2.1. Fatigue Generalities ......................................................................................................8

2.2.2. Fatigue Crack Propagation and Paris law........................................................................9

2.2.3. Impact Loading .......................................................................................................... 11

2.2.4. Low Energy Impact Fatigue ........................................................................................ 12

2.2.5. Dynamic Stress Intensity Factor (DSIF) ....................................................................... 13

3. Methodology............................................................................................................................. 15

3.1. Specimen Material ............................................................................................................. 15

3.2. Uniaxial Tensile Test ......................................................................................................... 16

3.3. Quasi-static Fracture Toughness Test .................................................................................. 17

3.3.1. Fracture Toughness Test on Linear-Elastic Plane-Strain ................................................ 17

3.3.2. Fracture Toughness Test with unloading compliance method......................................... 19

3.4. Dynamic Fracture Tests...................................................................................................... 20

3.4.1. Fatigue Crack Propagation Test ................................................................................... 21

3.4.2. Drop Weight Impact Fatigue Test ................................................................................ 22

3.5. Microstructural analysis and fractographic observations. ...................................................... 25

4. Results and Discussion .............................................................................................................. 26

4.1. X-ray inspection ................................................................................................................ 26

4.2. Mechanical Properties from Uniaxial Tensile Test ............................................................... 27


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4.3. Quasi-static Fracture Toughness ......................................................................................... 28

4.3.1. Fracture Toughness on Linear-Elastic Plane- Strain (5% Secant Method) ....................... 29

4.3.2. Quasi-static Fracture by unloading compliance ............................................................. 34

4.3.3. Ligament correction (W-a) for Quasi-static Fracture test Base Metal .............................. 41

4.3.4. Stress intensity factor validation .................................................................................. 43

4.4. Fatigue Crack Propagation.................................................................................................. 46

4.4.1. Fatigue Crack Propagation in Base Metal Samples........................................................ 46

4.4.2. Fatigue Crack Propagation in Welded Metal Samples ................................................... 50

4.5. Impact Fatigue Crack Propagation ...................................................................................... 55

4.5.1. Impact Fatigue in Base Metal Samples ......................................................................... 57

4.5.2. Impact Fatigue in Welded Metal Samples..................................................................... 62

4.5.3. Energy absorption analysis .......................................................................................... 67

4.5.4. Microstructural and fractographic analysis ................................................................... 70

5. Conclusions .............................................................................................................................. 75

6. References ................................................................................................................................ 77


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List of Figures Figure 1. (a) infinitesimal plate and (b) stress field element...................................................................6 Figure 2. Three modes of loading applied to crack growth. ...................................................................7 Figure 3. Constant amplitude fatigue crack growth under small-scale yielding conditions. It takes figure from T Anderson. Fracture mechanics, 2005, page 452. ........................................................................9 Figure 4. Crack growth rate (da/dN) vs ∆𝐾𝐾. ....................................................................................... 10 Figure 5. Impact load. ...................................................................................................................... 11 Figure 6. Ramp load......................................................................................................................... 12 Figure 7. Impact load stress pattern. .................................................................................................. 12 Figure 8. Schematic representation of welded plates and welding Process. .......................................... 16 Figure 9. Schematic illustrations of tensile specimen. ......................................................................... 16 Figure 10. Schematic dimensions of (a) SENB specimen and the locations where the (b) specimens were prepared (WM and BM). ................................................................................................................... 17 Figure 11. Schematic dimensions of (a) SENB specimen and the locations where the (b) specimens were prepared (WM and BM). ................................................................................................................... 18 Figure 12. Fracture toughness test configuration. ............................................................................... 19 Figure 13. Fatigue test configuration. ................................................................................................ 21 Figure 14. DWIT Configuration. ....................................................................................................... 22 Figure 15. a) The geometry of the pre-cracked three-point bend specimen subjected to dynamic loading and b) mode of the impact falling mass on a notched beam like mass-spring system.............................. 23 Figure 16. X-Ray test for a) welded plate and b) a cutting sample from usable sections. ....................... 26 Figure 17. Base metal tensile test curves............................................................................................ 27 Figure 18. Welded metal tensile test curves. ...................................................................................... 28 Figure 19. Experimental CTOA for a welded API A Steel. a) welded metal (WM) and base metal (BM) section. ............................................................................................................................................ 29 Figure 20. Method of determination critical charge, (a) regression on elastic loading (b) generation of 5% secant line. ....................................................................................................................................... 30 Figure 21. Probability graphs to different statistical distributions of SIF to BM, secant method. ............ 31 Figure 22. Confidence intervals summary of SIF to BM, secant method. ............................................. 32 Figure 23. Probability graphs to different statistical distributions of SIF to WM, secant method. ........... 33 Figure 24. Confidence intervals summary of SIF to WM, secant method. ............................................ 34 Figure 25. Load–CMOD curves for (a) BM and (b) WM. ................................................................... 35 Figure 26. Probability graphs to different statistical distributions of SIF to BM, CMOD. ...................... 36 Figure 27. Probability graphs to different statistical distributions of G to BM, CMOD. ......................... 37 Figure 28. probability graphs (a) SIF and (b) G for BM, CMOD. ........................................................ 38 Figure 29. Probability graphs to different statistical distributions of SIF for WM, CMOD..................... 39 Figure 30. Probability graphs to different statistical distributions of G to WM, CMOD. ........................ 40 Figure 31. probability graphs (a) SIF and (B) G for WM, CMOD........................................................ 41 Figure 32. Experimental CTOA for a welded API A Steel, ligament corrected. .................................... 41 Figure 33. (a) probability graph and (b) confidence intervals. ............................................................. 43 Figure 34. Constant-Amplitude Load Test. ........................................................................................ 46 Figure 35. Crack length versus number of cycles to Base Metal (BM). ................................................ 47


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Figure 36. Fatigue crack growth curve of base metal (BM). ................................................................ 48 Figure 37. Comparison of Fatigue crack grow curve of (a) base metal (BM) and (b) AISI 1020 steel (Kumar,1993). .................................................................................................................................. 49 Figure 38. Crack length versus number of cycles to Welded Metal (WM). ........................................... 51 Figure 39. Fatigue crack growth curve of welded metal (WM). ........................................................... 52 Figure 40. Fatigue crack growth curve (Zone II) welded metal (WM).................................................. 53 Figure 41. Impulse force in impact cycle to (a) BM and (b) WM. ........................................................ 55 Figure 42. Comparison between ASTM standard of stress intensity factor model and DSIF model correction to (a) impact number 1 of sample one (Kmax wave) and for (b) Kmax – cycle on 2.33 J of impact energy sample one, fatigue life. .............................................................................................. 56 Figure 43. advance of the crack under impact fatigue. BM Sample 1, energy level of 1.913 J. ............... 57 Figure 44. Crack length vs number of cycle curve to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J for BM. ............................................................................................................................................ 58 Figure 45. Propagation curves in BM to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples. ........................................................................................................................................... 59 Figure 46. Power fitting of each test to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples. ........................................................................................................................................... 60 Figure 47. Crack propagation curves under impact fatigue for BM (a) compilation of 3 tests and (b) Iguchi’s work. .................................................................................................................................. 61 Figure 48. advance of the crack under impact fatigue. WM Sample 1, energy level of 2.028 J. .............. 62 Figure 49. Crack length vs number of cycle curve to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to WM. ............................................................................................................................................ 63 Figure 50. Propagation curves in BM to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples. ........................................................................................................................................... 64 Figure 51. Power fitting of each test to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples. ........................................................................................................................................... 65 Figure 52. Crack propagation curves under impact fatigue for WM. .................................................... 66 Figure 53. (a) Force - maximum displacement curve and (b) force-displacement curve to BM. ............. 68 Figure 54. Force – displacement curve to WM. .................................................................................. 68 Figure 55. Energy curve to BM. ........................................................................................................ 69 Figure 56. Energy curve to WM. ....................................................................................................... 70 Figure 57. Metallographic inspection of (a) BM , (b) BM magnification were is found perlite (gray/black) and ferrite (beige/white), (c) and (d) represents HAZ with fine granular ferrite and perlite. (e) Transition zone between HAZ and WM, (f) magnification of transition zone, it can show carbon traces and perlite-ferrite structure. Finally (g) and (h) WM microstructure whit carbon traces.......................... 72 Figure 58. Fractographies taken in stereoscopy at x16 magnification. (a) and (b) are BM crack sample and (c) and (d) are WM sample.......................................................................................................... 73 Figure 59. SEM Fractographies (a) location of crack initiation and microvoids presence at that location in (b) BM and (c) WM. ......................................................................................................................... 73 Figure 60. Central part of WM sample where found combination of microvoids and cleavage............... 74 Figure 61. Final crack in WM, it found intergranular and cleavage presences....................................... 74


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List of Tables Table 1. Chemical composition and mechanical properties of steel samples. ........................................ 15 Table 2. Tensile data test for base metal (BM) ................................................................................... 27 Table 3. Tensile data test for welding metal (WM) ............................................................................. 28 Table 4. Summary table of the fracture toughness test of base metal .................................................... 30 Table 5. Summary table of the fracture toughness test of base metal .................................................... 33 Table 6. KIC and G values at critical CMOD of BM........................................................................... 36 Table 7. Goodness of fit Analysis for SIF and G of BM ...................................................................... 37 Table 8. KIC and G values at critical CMOD of WM.......................................................................... 38 Table 9. Goodness of fit Analysis for SIF and G of BM ...................................................................... 40 Table 10. Summary table of the fracture toughness test of base metal .................................................. 42 Table 11. Statistical analysis for SIF and G of BM. ............................................................................ 42 Table 12. Relative error to each method to determinate SIF for BM..................................................... 44 Table 13. Relative error to each method to validate SIF for WM ......................................................... 45 Table 14. Comparison of Paris law coefficients from literature with BM samples testing ...................... 50 Table 15. Comparison of Paris law coefficients from literature with WM samples testing ..................... 54


1

1. Introduction

Pipelines are essential in oil and gas transportation and distribution. It is a faster, safest, and most

convenient and economical way to transport hydrocarbons to high pressure for long distances in a

continuous way [1]. Pipelines are subject to different loads because of interaction with the

environment, especially offshore system pipes. Hydrodynamics loads, trawl loads and drop impact

objects from water waves, pullover of trawl gear in fishing activities, and falling objects coming

from surface platforms are creating hard conditions to submarine pipes [2-4], without mention

corrosion phenomena, overpressure in the flow system and erosion that are not analyzed at this work.

From those working conditions, pipes experiment significant reduction of mechanical properties

and material life, that translates on industry accidents [5]. Nevertheless, not only those conditions

can cause failure. Materials factors like, manufacturing defects, mechanical defects, steel grade

(chemical composition), geometrical factor (diameter, thickness), time of server and especially

type of welding and welding process, because it tends to form a weak and brittle (heat-affected zone) areas, that need to be analyzed and characterized to understand a failure phenomenon [5-7].

According to literature review, it found that dynamic and accidental loads of product to operational

environment are one of the most common causes of pipeline damage [8,9]. Many studies of the

North Sea, where pipeline system is heavily dense and has high port activity, relate several cases

of impact by anchor or heavy objects from the offshore platforms, ships, or vessels, which can

cause permanent damage on pipes or environmentally catastrophic accidents [5-10]. Incidents and

failures are classified by many databases, especially in Pipeline and Riser Loss of Containment

(PARLOC), which focus on the North Sea. PARLOC shows that impact load by external

interference (constant impact to pipelines) is the second cause of failure after internal and external

corrosion and corresponding to 6.51 x10-5 failures per km per year of which 35% corresponds to impacts by anchors, 10% to Ship Sinking and 55% to trawling and dropped objects [11,12].


2

Anchoring is a type load source most studied because it provokes severity damage on pipelines

integrity and catastrophic failure, but it is not a common cause of failure. Followed by studies to

impacts from dropped objects. For those cases are three types of dynamic loads [4], first is the

hooking load studied by Wei Y. This load caused by vertical displacement of pipe, when anchor

has dragged and come in contact with pipe with time duration of minutes [13]. From the same

action, another type of load known as pullover is generated and differs from before load because

the duration of load is just seconds.

Arabzadeth H, et al. and T Sriskandarajah in their research study the dynamic responses of pipeline

under trawling anchors and fishing trawl gears, through 3D simulation in nonlinear finite element

method (FEM) from characterization type, size, forces and contact mechanism between anchors

and pipelines [14,15]. The pipe on concrete structure has higher impact loads and greater

deformations compared to pipes rest on soil bed. The study concludes the location of the most

predominant failures are on girth welds and field joint which are impacted by anchor and suffer

buckling failure or loss of integrity itself

The last type of dynamic load is impact load and affect pipeline energy absorption capacity. This

load involves everything related to mass movement and contact between masses in a short time,

around milliseconds [16]. On operational conditions, pipelines are hit by dropped objects causing

elastic and plastic deformation, depending on mass, velocity, or in engineering terms, it depends

on pipes, geometry and impacts the energy that received [17]. Most previous studies focus on high

energy impacts that can cause accidental failures, those impacts are provoked by heavy objects

like anchor or Drop of cargo from ships, N Jones, et al., conducted an impact test by use of an

indenter with a constant impact velocity that hits specimens with different conditions, always

trying to simulate the simplest and fastest way to the pipeline fail.

That study conducted new works which try to replicate that results on different conditions like M.

Zeinoddini, et al. and E. Gücüyen, et al., that shows material fail on 70% of cases by the first

impact because deformation velocity is higher than striker velocity [8, 17–19]. Many other studies

focus on full-scale impact test and finite element simulation how is a case of L. Wang, et al. and

W Shen have analyzed the response of pipe under impact load and reduction in load carrying

capacity, considering defects in material by corrosion and/or internal pressure under different


3

scenarios [9,20]. Nonetheless, high energy impact scenarios rarely occurring, most cases of

impacts take place on low energy impacts loads, whichever reduce mechanical properties of pipes

under repetitive action and finally drive to failure [13, 17]. Objects hit pipes on repetitive way

come from surface operations and from hydrodynamic action, where water movement brings with

it particles, rocks, wastes and water mass that finally shocks to pipeline [21].

Analysis and modeling of pipeline responses under hydrodynamic action received attention from

many published researches. For complexity, studies carried out around the use of nonlinear FEM

as a case J. Chung, et al., analyzed three-dimensional pipe responses under impulse load in static

and dynamic conditions caused by dropping objects and hydrodynamic load [22, 23]. Furthermore,

Al-Warthan, et al., study axial a bending spans, provokes by anchor impacts loads in combination

of hydrodynamic forces by discrete element method [24]. Both authors focus on falling heavy

objects and reduction of mechanical properties by action on water wave but just to analyze this

effect at the moment of heavy object impact pipeline.

This work aims to perform an impact fatigue analysis on hydrocarbon transport pipelines by

combining experimentation tests, quasi-static and dynamic crack propagation tests. For that

purpose, toughness and impact crack propagation of base metal (AISI 1020 Steel) and welded

metal (E7018 and E6010) specimens were evaluated. Experimentation has done in single edge

notch configuration (three-point bending) and includes crack-resistant tests with loading and

unloading compliance method and crack propagation by cyclic loading in constant amplitude and

repetitive impact to evaluate Paris law and material resistance under dynamic conditions.

1.1. Objectives

According to the literature review of responses on pipelines under repetitive action impact forces of low energy, its following objectives were raised.

1.1.1. General Objective

Determine the behavior of fatigue and fracture in welded joints of pipelines under quasi-static,

cyclic load and impact load conditions.


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1.1.2. Specific Objectives • Characterize the pipe material and welding to analyze.

• Perform an experimental design for the analysis and characterization of fatigue by impact

on the material.

• Evaluate the results of the fatigue analysis by impact got experimentally to predict their

behavior in the material.


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2. Theoretical Background

This chapter exposes an overview of relevant linear elastic fracture mechanics (LEFM) theory to

analysis of welded pipeline integrity and effects of dynamic response of fatigue by impact or cyclic

loads. Chapter focus and describes stress intensity factor on quasi-static and dynamic fracture

toughness approaches.

As explained before, pipelines are subject to hard loading environment for that reason requires

high strength, toughness, and weldability [7]. However, despite that weld is the most common way

to joint pipe in transport lines and also is the preferential form of maintenance, welding process

tends to be a weak link rupture in pipeline [25]. Due to fracture analysis, gives tools necessary to

design and manufacturing pipes, because quantify the characteristic fracture under services

conditions.

2.1. Linear Elastic Fracture Mechanic (LEFM)

LEFM is the study of mechanical behavior of cracked material with the assumption that material

is linear elastic and is subject to a load. This study focuses on the irreversible process of crack

nucleation and cracks growth that possibly ends on a material rupture [26]. Two approaches make up the theory of LEFM energy balance method and stress intensity factor [27].

2.1.1. Energy Method

The energy balance is a Griffith theory based on the first law of thermodynamic and involves a

nonequilibrium system that reaches an equilibrium with losses of energy [28]. It supposes an initial

crack with initial potential energy (nonequilibrium state) and as the crack propagates the potential

energy decreases to reach the equilibrium (no energy changes) [26]. Energy balance for an

incremental crack area under equilibrium state is expressed how:

−𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

(1)


6

Where

U: Potential energy supplied by strain energy and external forces.

W: Work required to create new surfaces (surface energy).

In other words, as potential energy decreases, surface energy increased. But is too difficult to

measure stress fracture values, this theory evolves a new concept the energy release rate. Energy

release rate G is a measure of energy available for crack propagation [28], G is the energy per unit

area available for infinitesimal crack extension:

𝐺𝐺 = −𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

(2)

To define G suppose an infinitesimal plate with a crack length of 2a as a show in Figure 1, subject to tensile stress [27]. The expression got for that analogy is:

𝐺𝐺 = 𝜋𝜋𝜎𝜎2𝑎𝑎𝐸𝐸

(3)

Figure 1. (a) infinitesimal plate and (b) stress field element.

When G reaches a critical value Gc (G =Gc) crack becomes an unstable crack causing faster crack

propagation that results in an imminent failure. Therefore, it is said that the fracture failure occurs

and that value of Gc is the fracture toughness [28].


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2.1.2. Stress Intensity Factor

In fracture mechanics, stress intensity factor (SIF) is a parameter used to describe and predict the

stress field near to crack tip in a cracked material [29] where external forces cause stresses. This

parameter is an analogous criterion of critical G and is a fracture toughness parameter in a linear elastic material. SIF is defined as a driven force for fracture and is expressed by [30]:

𝐾𝐾 = 𝑘𝑘√2𝜋𝜋 (4)

Where k is a proportionality constant. K normally describes the different load modes (I, II, III) and

it denotes with mode [28]. Load modes refer to load applied direction to crack propagation. Mode

I, crack opening is by tensile loads. Mode II is by shear loads in the plane direction where stresses

and strain are anti-symmetrical to x-axis. Mode III is by shear loads in anti-plane direction [31]. Figure 2 shows a graphic description of load modes.

Figure 2. Three modes of loading applied to crack growth.

In mode I loading, the stress in x and y direction is equal and shear stress is zero

𝜎𝜎𝑥𝑥𝑥𝑥 = 𝜎𝜎𝑦𝑦𝑦𝑦 = 𝐾𝐾𝐼𝐼√2𝜋𝜋𝜋𝜋 (5)

𝐾𝐾𝐼𝐼 = 𝜎𝜎√2𝜋𝜋𝜋𝜋 (6)


8

K and G are analogous to each other and have a relationship with fracture behavior [30]. Consider

Equation (3) and Equation (6). If it can replace one in another, it can get the relationship between K and G to plane stress.

𝐺𝐺 = 𝐾𝐾𝐼𝐼2

𝐸𝐸 (7)

To plane strain:

𝐺𝐺 = 𝐾𝐾𝐼𝐼2(1−𝑣𝑣2)𝐸𝐸

(8)

2.2. Dynamic Fracture Mechanics

Dynamic fracture mechanics is the subfield of fracture mechanics which focuses on the study of

material behavior subjected to transient loadings where inertial forces, high strain rates and stress

waves become significant [32]. Inertia phenomena take importance when loading changes abruptly

or material presents a fast crack advance, also stress waves propagate through material and reflect

off free surface increasing crack growth rate [28].

2.2.1. Fatigue Generalities

All components, pipes, machines and any material exposed to loading fluctuation action and the

resultant stresses, they experiment reduction of mechanical properties and most times provokes an

anticipated failure [33]. This behavior knows as fatigue and is originated from live loads, dead weights, environmental circumstances, acceleration, dynamic response, and temperature changes.

Fatigue failure depends on local parameters of the affected zone like geometry, loading, material

type, imperfections, and service life. Those factors take on greater importance when analyzing

welding material because geometry and material are not homogenous also it appears residual

stresses [34]. Many of the heterogeneities in weld and heat-affected zone are because of many

properties were evaporated or calcined during the welding process and problems associated with

inclusions, high porosity in the welded area, loss, or lack of penetration, cavities and holes can be found [35].


9

There are many approaches to fatigue phenomena study, the most used are fatigue life prediction

and fatigue crack growth. This thesis focuses on Fatigue crack propagation approach that studies

the crack initiation, crack growth rate, and final failure with the assumption of material has an

initial crack and based in linear fracture mechanics [28].

Concepts to LEFM provide the theoretical foundation based on stress intensity factor (K) and it is

a critical value which assumed as a parameter of material will fail. Constant amplitude cyclic load

was studied for analysis fatigue where the plastic zone is too small to be negligible, the conditions

of crack tip depend on an elastic singularity zone defined by a SIF minimum and maximum (Kmin

and Kmax) as a show in Figure 3.

Figure 3. Constant amplitude fatigue crack growth under small-scale yielding conditions. It takes figure from T Anderson. Fracture mechanics, 2005, page 452.

2.2.2. Fatigue Crack Propagation and Paris law Paris law is a semi-empirical approach used to describe growth and propagation models from

cyclic load process or fatigue [36]. This law states that crack growth depends on the stress intensity

factor K and additionally depends on the geometric parameters of the material analyzed. From the above described, the following functional relationship is formulated:

𝑑𝑑𝑎𝑎𝑑𝑑𝑑𝑑

= 𝑓𝑓(∆𝐾𝐾,𝑅𝑅) (9)

Where


10

∆𝐾𝐾 = 𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑘𝑘𝐾𝐾𝑘𝑘𝑘𝑘

𝑅𝑅 =𝐾𝐾𝐾𝐾𝑘𝑘𝑘𝑘𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾

𝑑𝑑𝐾𝐾𝑑𝑑𝑑𝑑

= 𝐶𝐶𝜋𝜋𝐾𝐾𝐶𝐶𝑘𝑘 𝑔𝑔𝜋𝜋𝑔𝑔𝑔𝑔𝑔𝑔ℎ 𝑝𝑝𝑝𝑝𝜋𝜋 𝐶𝐶𝑐𝑐𝐶𝐶𝑐𝑐𝑝𝑝

This law can be analyzed by log-log plot of da/dN vs ∆𝐾𝐾 as a show in Figure 4. This method

proposes 3 stages of crack propagation. The first stage, corresponding to regime A, includes the

slow and microscopic growth of the crack not visible to the naked eye. The second stage refers to

the Paris regime where load factors, geometry, and material properties affect the crack and its

propagation. And finally, the C regime, or last stage, includes the accelerated crack growth until

the failure of the material or unstable crack Region [37].

Figure 4. Crack growth rate (da/dN) vs ∆𝐾𝐾.

Region B or linear region is a Paris regime and is described by a power law:


= 𝐶𝐶∆𝐾𝐾𝑚𝑚 (10)

Where C and m are environmentally sensitive material constants determined experimentally. However, this equation has no physical basis, and it was derived from curve fitting.


11

2.2.3. Impact Loading

This loading is categorized as rapid loading characterizing by vibration motion and stress waves

moving into material [28]. Impact occurs when an object hits whatever material with an initial

velocity (v0) and dynamic impact force (time depend force, F (t)) [23]. Stress and strain in impact

material depend on the amount of energy that is absorbing and dissipating by deformation and

heat. Impact forces are represented by two types of impacts loads, triangular impulse loading and

ramp loading.

• Impulse Loading: is the maximum impact load for a triangular wave, the duration of this

load is about milliseconds as a show in Figure 5. This load is quantified by a term of impulse I of Newton’s second law that is an overall effect of a force acting over time.

𝑰𝑰 = ∫ 𝑭𝑭𝑭𝑭𝑭𝑭 = 𝒎𝒎𝒎𝒎𝒎𝒎−𝒎𝒎𝒎𝒎𝒎𝒎 (11)

This impact load is characterized by the object that impacts does not remain in contact with the

impacted material.

Figure 5. Impact load.

• Ramp loading: is similar to impulse load with the initial triangular shape until maximum

load but on that point, load remains constant. This occurs because object to hit material stays in

contact with it. Figure 6 shows the shape of ramp load.


12

Figure 6. Ramp load.

2.2.4. Low Energy Impact Fatigue

Repetition of impulse load on structural members and materials is named impact fatigue, that

fatigue behavior can cause failure of material [38]. Usually, impact fatigue divide in two types,

repeated impacted load and randomly repeated impact load. The typical stress wave is composed

of initial tensile impact stress which propagates throughout the material and interacting with crack

and defect of materials, followed to compressive stress and decaying stress vibration that depends

on stiffness and material damping capacity [39] as shown in Figure 7.

Figure 7. Impact load stress pattern.

Impact fatigue resistance depends on material strength level, impact energy level, loading rates, plasticity, and stress ratio (R=𝜎𝜎𝐾𝐾𝑘𝑘𝑘𝑘/𝜎𝜎max ). For this work, the stress ratio is zero because only

the impulse load was studied through the tests carried out (weight drop test), also other authors

such as H. Iguchi, et al. focus on the influence of R on crack propagation by impact fatigue[38].

Those tests analyzed notched specimens where crack initiation life is shorter than quasi-static and

standard fatigue due to notch acting as a stress concentrator and many researches attribute to plastic


13

deformation as the crack initiation mode [39] (On this thesis will corroborate that affirmation with

fractography analysis).

The analysis of crack propagation from impact fatigue follows the Paris law on linear region. The

relationship between power fitting differs from standard fatigue because crack growth rate da/dN it compares with maximum stress intensity factor and not with the difference ∆𝐾𝐾 [38]. Brown and

Srawley modified Paris law, this modification is shown below:


= 𝐶𝐶𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝑚𝑚 (12)

2.2.5. Dynamic Stress Intensity Factor (DSIF)

Dynamic fracture phenomena need to be analyzed as static and quasi-static loading with the

difference that it depends on material load-time response. On dynamic loading, load becomes a

wave that passes through the material and to increase with time to achieve a critical or maximum

value, then it oscillates and decreases depending on material geometry and properties, especially

strength and damping [28]. Besides these effects of inertia and kinetic energy take on greater relevance as the load lasts less time (Rapid loading) and changes stress field behavior [40].

On near tip, the stress field is characterized by propagation and interaction of load pulse with

existing cracks, producing a wave of stress (𝜎𝜎0) and strain that travels with velocity C1 toward the

crack [41]. Waves that pass through material are reflected, resulting in complex wave distribution,

affecting fracture toughness value, and making it dependent on stress waves magnitude that pass

through the crack tip region at a particular moment [28]. A mathematical definition of DSIF is

given by the following expression:[42]

𝐾𝐾𝐼𝐼(𝑔𝑔) = lim𝑟𝑟→0

√2𝜋𝜋𝜋𝜋𝜎𝜎0 (𝜋𝜋,𝜃𝜃 = 0,𝑔𝑔) (13)

Achebach and Freund deduced a solution for DSIF using Green’s functions [41] and that solution

is given for the following Equation:

𝐾𝐾𝐼𝐼 = 2𝜎𝜎0(1−𝑣𝑣)1/2

1−𝑣𝑣�𝐶𝐶1𝑡𝑡

𝜋𝜋 (14)

Where v is the Poisson ratio.


14

Parameters remaining constant except time for that reason is possible to say, DSIF is proportional

to √𝑔𝑔:

𝐾𝐾𝐼𝐼(𝑔𝑔) = 𝛼𝛼√𝑔𝑔 (15)

Introducing bending beams theory where stress is proportional to bending moment, DSIF is

proportional too. In addition, considering symmetric vibration modes it assumed the first mode is

predominant, the dynamic stress intensity factor is proportional to bending moment at specimen

mid-span and it can be expressed as a function of load-displacement (u (t)) of the beam [42].

𝐾𝐾𝐼𝐼(𝑔𝑔) = 𝐶𝐶𝐶𝐶(𝑔𝑔) (16)

Where C is a static stress intensity factor 𝐾𝐾𝐼𝐼


15

3. Methodology

This chapter exposes the material description of specimen and experimentation methodology that is used to analyze fatigue and fracture phenomena by impact loads.

3.1. Specimen Material

In this study was used API Grade A steel (AISI 1020 steel) with chemical composition and

minimum mechanical properties required for this material indicated in Table 1 form API 5L

standard and welded steel (same grade). For samples preparation, steel plates were welded by

shielded metal arc welding (SMAW) technique to simulate the action of pipeline reparation or

maintenance and it was ignored the aqueous medium and possible manufacturing or

corrosion/erosion defects in base metal (BM) due to the limitations in experimentation, process

shown in Figure 7 (b). AWS A5.1 E6011 was the electrode used for root welding where it provides

a high welding penetration. This electrode has a cellulose potassium shield, designed to high metal

solidification and AC/DC application. For filling welding AWS A5.1 E7018 electrode designed to

improve deposition rate, bead appearance for welding alternating current applications. This type

of electrode is a low-hydrogen-potassium-iron-powder coated carbon steel.

Table 1. Chemical composition and mechanical properties of steel samples.

Chemical composition

Carbon (C) Manganese, Mn Phosphorous, P Sulfur, S Silicon, Si

[%wt] [%wt] [%wt] [%wt] [%wt]

0.22 0.6 0.03 0.03 0.15

Minimum Mechanical properties required

Yield Strength [MPa] Tensile Strength, Ultimate [MPa] Elongation

294.74 394.72 0.365


16

To prepare samples, it made a bevel to the steel plates creating an angle of 60°, and plates was

welded with 1/8 in of separation (see Figure 8 (a)). Dimensions of plates are 150 mm of length per

42.1 mm of width per 4.75 mm of thickness to SENB configuration and 92 mm of width for tension

samples. A current between 55 A to 90 was used to weld Plates. Then for checking welding defects

like porosity and undermining, the X-Ray test to inspect Welded plates was used, as shown in

Figure 15, and chose a better section to make samples. Those sections are mechanized and

homogenized in its thickness to avoid stress concentrators in samples.

Figure 8. Schematic representation of welded plates and welding Process.

3.2. Uniaxial Tensile Test

It machined specimens with CNC for uniaxial tensile test (UTT), geometry shows in Figure 9. To

get the mechanical properties of BM and WM and do the verification of welding conditions was

done with this test. UTT was conducted at 20°C by universal testing machine (INTRON 5985) at

displacement control rate of 3 mm/min, clip gauge was used to measure the strain. The design of

the test and its development follow ASTM E8 [43].

Figure 9. Schematic illustrations of tensile specimen.


17

3.3. Quasi-static Fracture Toughness Test

This test has done according to ASTM standard E399 and E1820 [26, 27]. For the test samples, it

machined on SENB configuration as shown in Figure 10. Specimens dimensions are 81 mm of

length, 4.75 mm of thickness (B), and 18 mm of width (W), with spam (S) of 72 mm, each sample

has a notch machined with a 9 mm deep and 0.3 mm of width. Pre-crack was positioned in two

different samples of base metal (BM) and welded metal (WM) to compare the behavior of both.

This test divides into two sections, the first determination of stress intensity factor KIC and second

with method CMOD or unloading compliance method to evaluate the fracture crack propagation

[46].

For both tests, it is necessary to generate a fatigue pre-cracking about 0.5 mm-1.0 mm to each

specimen, for that purpose each sample was pre-fatigued with a load frequency of 2.5 Hz, load

amplitude to 3.5 kN, and 103 cycles. The relative initial crack oscillates between a0/W = 0.45 and

a0/W = 0.55.

Figure 10. Schematic dimensions of (a) SENB specimen and the locations where the (b) specimens were prepared (WM and BM).

3.3.1.Fracture Toughness Test on Linear-Elastic Plane-Strain

After pre-cracking fracture toughness test was done on INSTROM 5985 universal machine test

with a load cell of 100 kN. Test control was with displacement control rate of 3 mm/s and a

maximum load of 7 kN. After fracture test with the load-displacement curve, the analysis is done.

Three possible types of curves can get as shown in Figure 11 and depending on the type of curve

a critical load (PQ) is defined. The method used on this thesis to find PQ is the secant line method,

a) b)


18

which is determined 5% secant line (the line is traced from the origin with a slope equal to 95% of

the elastic line of the load-displacement curve) and finds P5 [44].

Figure 11. Schematic dimensions of (a) SENB specimen and the locations where the (b) specimens were prepared

(WM and BM).

From Figure 11 it can note that depending on the type of curve, PQ takes different values. In the

case of type I curve, PQ = P5 and different to the maximum load (Pmax), in that case, Pmax is

located on the plasticity zone and has subcritical crack growth. For a type II small amount of

unstable crack growth occurs until maximum load, in this case, PQ is different from P5 and Pmax.

And finally, with the behavior of the type III curve, the specimen fails until reaching P5, for that

reason PQ = Pmax [28]. One critical load is determined, and the initial crack length is measured

the stress intensity factor is found with the following equation:

𝐾𝐾𝐼𝐼𝐶𝐶 = 𝑃𝑃𝑃𝑃 .𝑆𝑆�𝐵𝐵𝐵𝐵𝑁𝑁𝑑𝑑3/2 𝑓𝑓 �𝑎𝑎

𝑑𝑑� (17)

With the relationship between SIF and G, the energy release rate is equivalent to:

𝐺𝐺 = 𝐾𝐾IC2�1−𝑣𝑣2�𝐸𝐸

(18)


19

3.3.2.Fracture Toughness Test with unloading compliance method

The second test was conducted in the same universal machine test. This test consists of a procedure

of cycles of load/unload sample and stops when the load drops to 80% of maximum load. This test

was correct or validate the previous test, especially if the material presents not linear elastic behavior with high plasticity, stress concentrators and invalid 𝐾𝐾IC determinations [29, 30]. A

displacement rate of 0.02 mm/s was loading procedure control used to have enough time to identify

crack advance. The CMOD was measured with a strain gauge installed on the inferior part of the

specimen. The test system is shown in Figure 12.

Figure 12. Fracture toughness test configuration.

Stress intensity factor and elastic part of J-integral for SENB were calculated by test data according

to ASTM E1820. Just to elastic part of J equivalent to energy release rate (G) [28] was studied, to

analyzes the fracture toughness into limitations of linear fracture mechanics. For that reason, is

convenient to divide a J-integral value into two components, plastic, and elastic as a show in

Equation (17).

𝐽𝐽 = 𝐽𝐽𝑒𝑒𝑒𝑒 + 𝐽𝐽𝑝𝑝𝑒𝑒 (19)

Sample SENB configuration

Fixtures support

Strain gauge

INSTROM 5985


20

The elastic component is equivalent to G, for that reason according to the relationship of stress

intensity factor and ASTM E1820 is defined by:

𝐽𝐽𝑒𝑒𝑒𝑒 = 𝐺𝐺 = 𝐾𝐾2�1−𝑣𝑣2�𝐸𝐸

(20)

Where stress intensity factor is given by

𝐾𝐾(𝑘𝑘) = 𝑃𝑃(𝑖𝑖)𝑆𝑆�𝐵𝐵𝐵𝐵𝑁𝑁𝑑𝑑3/2 𝑓𝑓 �𝑎𝑎(𝑖𝑖)

𝑑𝑑� (21)

f(a(i)/w) is a coefficient factor of stress intensity, this factor must formulate to each crack

propagation unlading sequence. ASTM standard provides coefficient factor. Depending on

measure displacement (Vm) or compliance unloading (Ci) can calculate instantaneous crack length

so it calculated by:

𝐶𝐶𝑘𝑘 = ∆𝑉𝑉𝑚𝑚∆𝑃𝑃

(22)

Crack length is given by the following expression

𝑎𝑎(𝑖𝑖)𝑑𝑑

= 0.999748− 3.950𝐶𝐶 + 2.982𝐶𝐶2 − 3.21408𝐶𝐶3 + 51.51564𝐶𝐶4 − 113.031𝐶𝐶5 (23)

Where

𝐶𝐶 = 1

��4𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝑆𝑆 +1�

(24)

3.4. Dynamic Fracture Tests

Fracture toughness was studied with the previous tests with assuming of quasi-static conditions,

but to analyze material response when that exposes different loads during operations where effects

of inertia forces and motions can affect the fracture behavior, therefore, it becomes necessary to

approach the study through dynamic fracture mechanics. For the present work, it was divided the

dynamic analysis into two tests, fatigue crack propagation and drop weight impact fatigue test. For

both tests use SENB samples according to ASTM E399 like quasi-static tests, geometry of

specimens is shown in Figure 10. Samples have a relative initial crack that oscillates between a0/W

= 0.45 and a0/W = 0.55, where crack length includes a pre-cracking procedure explained in

previous tests.


21

3.4.1. Fatigue Crack Propagation Test

Fatigue crack growth was done in BM and WM regions, using an MTS model 370 servo-hydraulic

testing machine with a load frame of 100 kN. This test analyzes the effect of several strain cycles

product by operational load story. The test was conducted in several steps with scheduled stops to

measure crack length through to use of high-quality camera IDS- UI-1540LE-M-GL with a

resolution of 1280 x 1024 pixels, optical area of 6.656 mm x 5.325 mm, and 25 frames per second.

The experimental assembly is shown in Figure 13. Testing was performed at ambient temperate

(18-20 °C approximately) under load control using a sinusoidal waveform of 10 Hz and stress ratio

of 0.1 (R=Kmax/Kmin =0.1) with a maximum load of 2.0 kN in BM and 1.5 kN in WM.

Figure 13. Fatigue test configuration.

To increase reliability and reduce testing errors, testing was repeated five times, subsequently from

measurements of crack length on each stop programmed was got a function that it relates crack

growths with the number of cycles (a vs Cycle). The function was derivate to get a crack growth

rate (da/dN) function, later new expression was plotted in terms of change of stress intensity factor

in the concordance of ASTM standard E647 [47]. Laboratory fatigue crack propagation results are summarized in an expression of Paris law.

Sample SENB

configuration

IDS Camera

Hydraulic Wedge Grips

Experimental assembly

MTS 370 model Actuator


22


= 𝐶𝐶∆𝐾𝐾𝑚𝑚 (25)

Where C and m are material constants and those determined in the experimentation (Graph of

da/dN - ΔK), to find the value ΔK to each cycle it follows the expression of ASTM E399, where f (a/w) is a factor coefficient of stress intensity and a is crack length by cycle, respectively.

∆𝐾𝐾 = ∆𝑃𝑃 𝑆𝑆�𝐵𝐵𝐵𝐵𝑁𝑁𝑑𝑑

𝑓𝑓 �𝑎𝑎𝑑𝑑� (26)

3.4.2. Drop Weight Impact Fatigue Test

This test studies the material responses under repetitive impulse loads and reduction of absorption

energy capacity that can cause a failure in structure or material, that failure named impact fatigue

[38]. An experimental assembly of three points bending with samples in SENB configuration was

used for the test (see Figure 14). The principle of Drop weight impact tester (DWIT) is the use of

potential energy products an impact mass in free fall. The energy becomes in kinetic energy which

pass-through material and generates a wave of elastic and plastic deformation. For that purpose, a 7075-aluminum impactor with 7.626 kg of mass was used.

Figure 14. DWIT Configuration.

Experimental assembly

Hammer

Load cells Laser Sensor

Compressed air line

Pistons


23

DWIT has three different sensors to collect data, the first one is 3 load cells of 5000 lbf either one,

other is a precision laser LDMS 90/40 with a measuring range of 40 mm and a resolution of 0.0004

mm, and finally has a laser sensor which records the distance and helps position the hammer on

the top [48]. DWIT and experimental assembly are shown in Figure 14.

Test was performed with three different impact heights 31.26 mm 27.11 mm and 25.57 or three

different energy levels 2.33 J, 2.03 J, and 1.91 J respectively. Crack growth is measure by high-

quality camera IDS- UI-1540LE-M-GL to each impact. Imagine analyzer (Adobe Premier to get

imagine frame by frame and Tracker to physics measure) was used to measure crack length.

Results are summarized on a graph of da/dN – ΔK. it should be noted that the stress ratio is cero

(R = Kmin / Kmax = 0) because the harmer does not keep in contact with the specimen after

impact load (Kmin = 0) therefore ΔK is equal to Kmax product by the impulsive load. Kmax is

determinate by Equation (21) where load P is the maximum load register by the sensor in each impact.

However, the formulation of the stress intensity factor proposed by ASTM standard (Equation 21)

has a gap to characterize the dynamics of the material response, because of the phenomena of

inertial effects and the propagation of the stress wave in the theory of dynamic fracture are not

take into account [49]. For this reason, F. Jiang et al. proposed a correction of standard formulation

in base of dynamic impact theory by Hopkinson pressure bar that analyzes dynamic response on the specimen using a spring-mass model [50] as shown in Figure 15.

Figure 15. a) The geometry of the pre-cracked three-point bend specimen subjected to dynamic loading and b)

mode of the impact falling mass on a notched beam like mass-spring system.


24

In base of Figure 15, it builds a system equation according to of Newton’s second law for an

undamped system where assume a k (a) (spring constant) as material stiffness and it is a function

of crack length also this formulation consider an equivalent mass (me) and spring displacement

(u(t)) [29].

𝐾𝐾𝑝𝑝�̈�𝐶(𝑔𝑔) + 𝑘𝑘(𝐾𝐾)𝐶𝐶(𝑔𝑔) = 𝑃𝑃(𝑔𝑔) (27)

Where 𝐶𝐶(0) = 0 𝐾𝐾𝑘𝑘𝑑𝑑 �̇�𝐶(0) = 0 are initial conditions, then the solution that Equation is from

authors is:

𝐶𝐶(𝑔𝑔) = 1𝜔𝜔𝑚𝑚𝑒𝑒 ∫ 𝑃𝑃(𝜏𝜏) 𝑠𝑠𝑘𝑘𝑘𝑘𝜔𝜔(𝑔𝑔 − 𝜏𝜏)1

0 (28)

Where natural frequency 𝜔𝜔 of prepacked specimen is defined by Williams, et al., [51] and is given

by:

𝜔𝜔 = �𝑘𝑘(𝑎𝑎)𝑚𝑚𝑒𝑒

(29)

Given the SENB configuration, less than 1 percent of the energy is in the second vibration mode,

so the material is subject to the conditions of the vibration mode. So, a cracked sample is

proportional to the bending moment in mid-span [52]. From this assumption, the dynamic stress

intensity factor (DSIF) is given by:

𝐾𝐾𝐼𝐼𝐼𝐼(𝑔𝑔) = 𝐶𝐶𝐶𝐶(𝑔𝑔) (30)

Where C is a proportionality constant and is equivalent to the quasi-static stress intensity factor

from ASTM formulation shows in Equation (21) (C = KIc). The stiffness of material in-plane

strain condition from F. Jiang, et al. is shown in the following formulation:

𝑘𝑘(𝐾𝐾) = 48𝐸𝐸𝐼𝐼(1−𝑣𝑣2 )𝑆𝑆3

/�1 + 6𝑑𝑑𝑆𝑆𝑉𝑉 �𝑎𝑎

𝑑𝑑�+ 12� 2

� 1012+11𝑣𝑣

� 𝑑𝑑.𝑆𝑆2�� (31)

Where v (a/W) is given by polynomial that can found on F. Jiang et al. study. Solving the integral of u (t) and replace of Equation (19) the DSIF is given by:

𝐾𝐾𝐼𝐼𝐼𝐼(𝑔𝑔) = 𝑃𝑃𝑆𝑆�𝐵𝐵𝐵𝐵𝑁𝑁𝑑𝑑3/2 𝑓𝑓 �𝑎𝑎(𝑖𝑖)

𝑑𝑑� (𝐶𝐶𝑔𝑔𝑠𝑠𝜔𝜔(𝑔𝑔)− 𝐶𝐶𝑔𝑔𝑠𝑠𝜔𝜔(𝑔𝑔 − 0.2)) 1

𝜔𝜔 (32)


25

To get parameters for DSIF in combination to filtered data from experimentation it uses MATLAB

a file was exported in .xls format where maximum load, DSIF, and mechanical measurements are summarized to analyze fatigue crack propagation curves and energy absorption capacity.

3.5. Microstructural analysis and fractographic observations.

To study and identify the morphology and composition of different regions close to notch

machined, specimens were polished and chemically attacked using 3% nital solution (solution of

nitric acid and alcohol). Different regions are easy to distinguish (BS, WM, HAZ) by optical

microscopy technique, using Olympus BX-51M metallographic microscope. Furthermore, after

impact test, samples were broken, and through fractographic analysis, it identified fracture

morphology and the mechanism of the crack initiation, crack propagation, and final fracture, using

stereoscope Olympus SZX-9 and scanning electron microscope (SEM) JEOL model JSM 6490-

LV. Further, crack length was measured, and it was made a composition test especially of welded

metal region.


26

4. Results and Discussion

This section shows the results from the experimentation program formulated in the previous

chapter and their respective analysis. Results are present on a way to make a comparison of a quasi-

static and dynamic mechanic and fracture properties between base metal (BM) and welded metal

(WM).

4.1. X-ray inspection

Before starting a mechanical test, an X-ray inspection test was done for welded plates, to show

imperfections such as porosity and undermining in welding. Figure 16 (a) shows one of the welded

plates where it can see two different weld beads, that have dissimilar densities, also it can observe

the measure lines, which denote the usable sections to cut and prepare samples. For example, the

end part of these plates has a lot of porosity and on the central part, it can see traces of undermining.

Those imperfections are not acceptable in field welding, because it can generate a weak section in

the pipeline for that reason must be discarded. After plates inspection, samples were cut from

usable sections. Figure 16 (b) shows a cut sample (without notch machined) with minimum imperfections that was used in mechanical testing.

a) b) Figure 16. X-Ray test for a) welded plate and b) a cutting sample from usable sections.


27

4.2. Mechanical Properties from Uniaxial Tensile Test

The curves obtained from uniaxial tensile test for BM are shown below in Figure 17. As it was

expected, BM behavior is homogenous with some differences of tensile strain that it oscillates

between 10 -13 % at rupture moment. Maximum stress is about 747 MPa with a standard deviation

of 5.8.

Figure 17. Base metal tensile test curves.

Table 2 summarizes the average mechanical properties. It was not found a significant dispersion

between samples. With this test was confirmed that base metal samples meet the minimum mechanical properties required by API 5L standard (those requirements show in Table 1).

Table 2. Tensile data test for base metal (BM)

Maximum load

[kN]

Yield strength

[MPa]

Ultimate strength

[MPa]

Elasticity

modulus [GPa]

Media 90.382 726.71 561.354 217.75

deviation 0.456 6.933 4.944 2.847

Figure 18 shows curves got from uniaxial tensile test on welded metal. Despite high welded

heterogeneity and a minimum amount of internal porosity traces, welded samples were accepted

from X-Ray inspection. Those minimal imperfections are the main reason for the difference seen

in the stress and strain curves. Most of the samples failed from microvoids generation close to

microporous, which acts as a stress concentrator. Sample # 2 was discharged from this test due to

its premature failure attributed to said micropores that can generate noise in the analysis.


28

Figure 18. Welded metal tensile test curves.

For the other welded samples, maximum stress oscillates between 630 MPa to 700 MPa. Table 3

summarizes average mechanical properties; it can see that maximum dispersion is found in

ultimate strength and depends on the welding defect that was previously explained. Sample # 4

had the best behavior since it failed by pure tension, unlike the other samples that failed due to

stress concentrators generating a ductile crack initiation, but intergranular fault is present between

the pores of the weld.

Table 3. Tensile data test for welding metal (WM)

Maximum load

[kN]

Yield strength

[MPa]

Ultimate strength

[MPa]

Elasticity modulus

[GPa]

Media 14,936 515,569 639,523 212,182

deviation 2.005 48.132 89.294 70.249

4.3. Quasi-static Fracture Toughness

This section includes the results of quasi-static tests on base metal (AISI 1020 steel) and welded

metal (E7018 and E6011). According to the previous chapter, testing program for quasi-static

fracture was divided into two parts. The first was determination of stress intensity factor KIC with

the secant method and the second with unloading compliance method, fracture toughness of BM, and WM was evaluated.


29

4.3.1. Fracture Toughness on Linear-Elastic Plane- Strain (5%

Secant Method)

Quasi-static test was done according to ASTM E399, as mentioned in chapter 3. Plane strain

conditions at the crack tip are predominant for testing. Load curves vs CMOD for BM and WM

samples are shown in Figure 19, those curves show an initial elastic material response follow to

load drop section product to sample cracking. Fracture Toughness was found by Five percent (5%)

secant method which consists to build a line from the origin with a slope equal 95% of the initial

elastic loading slope, then applying the procedure of section 3.3.1, the type curve identification

was done, and then defines the critical load (PQ) to evaluate critical stress intensity factor.

(a) (b)

Figure 19. Experimental CTOA for a welded API A Steel. a) welded metal (WM) and base metal (BM) section.

4.3.1.1. Fracture Toughness for Base Metal by 5% Secant Method.

BM samples show mostly elastic behavior followed by short plastic section until maximum load

as it can see in Figure 19 (b), plastic deformation continues after crack initiation and load decrees

with a high crack propagation rate. For the determination of stress intensity factor, uses a procedure

section 3.3.1., for illustrative purposes Figure 20 shows the method applied on sample number one

to determine PQ. The procedure includes analysis of slope in the elastic region of the load-

displacement curve (Figure 20 (a)) and determination of critical load by secant method (Figure 20 (b)).


30

(a) (b)

Figure 20. Method of determination critical charge, (a) regression on elastic loading (b) generation of 5% secant line.

The average critical load (PQ) value was 5.513 kN with a variation between 5.168 kN and 5.861

kN. Below, in Table 4, summarized results of samples tested.

Table 4. Summary table of the fracture toughness test of base metal

Sample BM S1 BM S2 BM S3 BM S4 BM S5 BM S6 BM S7 BM S8 BM S9

Maximum load [N] 6473,218 6140,063 6389,789 6201,812 5656,712 6156,266 6036,059 5798,387 5771,514

PQ [N] 5504 5359,972 5552 5861 5189 5355 5168 5392 5343

K [MPa.m0,5] 94,350 91,881 95,173 96,101 95,148 93,871 94,763 92,430 93,661

F(a/w) 2,731 2,731 2,731 2,612 2,921 2,793 2,921 2,731 2,793

The stress intensity factor to each sample was found using Equation 17. SIF was analyzed by

goodness of Fit test to different statistical distributions, using Minitab 18 software. Probability

graphs are shown in Figure 21, where it can see the fitting parameter has no significant changes

and SIF average is approximately 94 MPa.m1/2. However, to get more precise data, it chose the

distribution with the best fitting. The Weibull distribution has the best-fit line on the probability

graph with few scattered data and Anderson - Darling parameter of 1.086.

PQ


31

Figure 21. Probability graphs to different statistical distributions of SIF to BM, secant method.

Analysis with Weibull distribution determines the average value of SIF and its confidence interval.

A summary graph of the confidence intervals of the media, median, and standard deviation is

shown with its respective histogram in Figure 22. In accordance with results, it was analyzed that

the maximum average load of BM was 6.069 kN with a critical stress intensity factor of 94.136

MPa.m1/2


32

Figure 22. Confidence intervals summary of SIF to BM, secant method.

According to those results, SIF is found between 93.473 MPa.m1/2 and 94.803 MPa.m1/2 with a

95% reliability based on the tests carried out and a standard deviation of 1.354. Also, from testing,

it can be seen that during stable crack growth, values of displacement do not change significantly,

showing they have more capacity to absorb energy and have less amount of energy dissipation,

reflecting on less deformation compared with welded metal samples.

4.3.1.2. Fracture Toughness for Welded Metal by 5% Secant

Method.

WM samples on the contrary of base metal, show mostly plastic behavior until load drop, also

reflect a short elastic section as shown in Figure 20 (a). Plastic deformation continues during stable

crack growth. Ductile crack initiation and crack propagation predominate in welded metal.

However, compared to BS, WM has less load resistance which is reflected on the maximum load

that was 3.925 kN and oscillates between 3.6 kN to 4.2 kN. It applied same procedure of BM

samples to evaluate fracture toughness for the welded zone, results summarized in Table 5.


33


Sample WS1 WS2 WS3 WS4 WS5 WS6 WS7

Maximum load [N] 3928,3801 4044,7886 3600,0169 4164,5283 4215,6597 3582,6065 3940,1382

PQ [N] 3596,1047 3727,1238 3598,0861 3907,0862 3773,0537 3525,2230 3525,2230

K [MPa. m0,5] 65,9402 68,3426 65,9765 71,6425 69,1848 64,6405 64,6405

F(a/w) 2,9214 2,9214 2,9214 2,9214 2,9214 2,9214 2,9214

For the analysis, it was done goodness of Fit test and it was determined that normal distribution

has the best fitting. As a show in Figure 23, Anderson-darling parameter dispersion is insignificant

and gives a SIF value with no important changes. It was chosen for normal distribution because it

is easy to use and have the same value of media to log-normal distribution (both distributions have

the lowest parameter value) that corresponds to 67,195 MPa.m1/2

Figure 23. Probability graphs to different statistical distributions of SIF to WM, secant method.

The average stress intensity factor for welded metal (ASW E6011 and ASW E7018) was 67.195

MPa.m1/2 with values between 65.626 MPa m1/2 to 68,767 MPa.m1/2, that corresponds to

confidence interval of 95% as a show on Figure 24 on summarize table. From the results, it can

conclude that welded metal has less resistance to fracture than the base metal. WM has less

capacity for storing energy, therefore energy excess is dissipated in elastic and plastic deformation

and heat. On the other hand, it can see the maximum load registered is about 1 kN less than BM,

demonstrating a clear reduction in its mechanical properties product to the welding process.


34

Figure 24. Confidence intervals summary of SIF to WM, secant method.

Furthermore, with the relationship between SIF and energy release rate is possible to determine

this fracture parameter with average KIC. For this test, the critical energy release rate (G) under

steady crack growth was 284.63 kJ/m2 for WM. This value was found with the relation between

SIF and G shows in Equation 19. The energy release rate represents the available energy to

increment crack extension, which was evaluated in the elastic loading section where the material has a capacity to absorb energy and does not lose it in plastic deformation or friction losses.

4.3.2. Quasi-static Fracture by unloading compliance

The unloading compliance test was done according to the procedure presented in section 3.3.2

based on ASTM E1820. This method consists to measure load - CMOD curve from load and

unload cycles. This test is especially used to analyze material with high plasticity and/or under

influence of residual loads. CMOD curves was got for BM and WM and are shown in Figure 25.

In accordance with those curves can be identified 2 different regions, first was an elastic-plastic

region when load almost reaches maximum load (this zone is much more pronounced on WM

samples) and finally a small crack propagation region until the load drops of 80% of the maximum

load (this region was not taken in care for analysis).


35

The equivalent crack length a(i) was predicted by Equation 23. It should be clarified, the length is

an assumed crack length for the method and depends on material compliance (real crack length

remains constant until load drops). Then the stress intensity factor and energy release rate were

found and corroborates and/ or correct (if it is the case) the critical KIC determined in the secant

method.

Figure 25. Load–CMOD curves for (a) BM and (b) WM.

In term of G is an easy way to explain how the material was gradually losing absorption energy capacity, and it prepares to fail. The measure of G in this test corresponds to critical G.

4.3.2.1. Fracture Toughness for Base Metal by Unloading

Compliance Method

The results of the Unloading compliance test for base metal are shown in Table 6. The equivalent

crack length a (i) was predicted by Equation 23 in a base of crack mount opening displacement

measure by the strain gauge, also it recalls the real crack length remains constant until the load

drop and cracks propagation region was discharged. On the other hand, with Equation 21, K(i)

values were found (see table 6), those values were computed on an average value that corresponds

to critical SIF (KIC). Furthermore, with the relation between K(i) and G(i) (Equation 20) was found the value of G(i) and the average values of G correspond to critical energy release rate GC.


36

Table 6. KIC and G values at critical CMOD of BM.

From this test, it is possible to get more points of K(i) of BM to each loading-unloading cycle

before reaching the maximum load. The numbers of points of K depend on material plasticity. The

statistical distribution functions analysis with Minitab 18 software are shown below in Figure 26.

Figure 26. Probability graphs to different statistical distributions of SIF to BM, CMOD.

Also, Same as the secant method, it was done a statistical analysis where it found that critical SIF

and GC follow a normal distribution with the Anderson-darling parameter of 0.817 and 0.801

correspondingly, as shown in Figure 26-27. According to probability graphs, it can be appreciated

that the average value of SIF is approximately 95 MPa.m1/2and G is 410 kJ/m2 for BM samples.

However, those values were corroborated and corrected with a specific analysis of normal

distribution.

Samplea [mm] 9,891 9,888 9,756 9,823 9,764 9,890 9,889 9,944 9,792 9,917 9,967 9,843 9,952 9,952

G [KJ/m^2] 395,611 396,711 414,979 423,102 383,823 404,913 399,491 391,002 382,029 397,551 423,969 438,922 452,193 455,571K [Mpa.m0,5] 89,843 90,093 94,241 96,086 87,166 91,955 90,724 88,796 86,758 90,283 96,283 99,679 102,693 103,460

Samplea [mm] 9,760 9,803 9,847 9,933 9,792 9,829 9,776 9,995 9,907 9,937

G [KJ/m^2] 380,496 404,306 408,730 431,442 403,341 443,831 434,759 422,959 419,292 428,117K [Mpa.m0,5] 86,410 91,817 92,822 97,980 91,598 100,794 98,733 96,054 95,221 97,225

4

5 6 7

1 2 3


37

Figure 27. Probability graphs to different statistical distributions of G to BM, CMOD.

By means of normal distribution analysis can determine average critical values of G at pre-crack

length. G for BM oscillates into confidence interval of 95 % between 405.504 kJ/m2 to 422.591

kJ/m2, and stress intensity factor between 92.423 MPa.m1/2 to96.269 MPa.m1/2, values shown in

Table 7.

Table 7. Goodness of fit Analysis for SIF and G of BM

The average value for stress intensity factor (KIC) is 94.346 MPa.m1/2. This value is too close to

the initial value of the previous test (5% secant method, section 4.3.1.1), confirming KIC found

was the right value. Furthermore, critical G corresponds to 414 422.591 kJ/m2. Additionally, the

Error Error

Estimation Standard Lower upper Estimation Standard Lower upper

Media(MTTF) 94,3459 0,981155 92,4229 96,269 414,048 4,35889 405,504 422,591Standard Desviation 4,70545 0,693781 3,52451 6,28209 21,3541 3,0822 16,0924 28,3362

Median 94,3459 0,981155 92,4229 96,269 414,048 4,35889 405,504 422,591

Critical G Distribution: Normal

Anderson-Darling0,801

KICDistribution: Normal


Confidence Interval de 95,0%

Goodness of Fit



38

probability graphs are shown in Figure 27 with their respective fitting, in a complement of table 7

as support of data obtained.

Figure 28. probability graphs (a) SIF and (b) G for BM, CMOD.

4.3.2.2. Fracture Toughness for welded Metal by Unloading

Compliance Method

For WM, it was done a similar analysis to BM samples. From the test, it can be seen that material

has a lower fracture toughness value. However, it can identify, material has a ductile crack

initiation which was corroborated by fractographic analysis of dynamic tests. Table 8 below shows

the points analyzed to determine the value of KIC and GC for weld metal.

Table 8. KIC and G values at critical CMOD of WM.

a [mm] G [KJ/m^2] K [Mpa,m0,5] a [mm] G [KJ/m^2] K [Mpa,m0,5] a [mm] G [KJ/m^2] K [Mpa,m0,5] a [mm] G [KJ/m^2] K [Mpa,m0,5]9,7178 302,5813 68,7159 9,7264 301,4337 68,4553 9,7230 267,7805 60,8127 9,7003 275,9656 62,67159,7424 312,0191 70,8592 9,7528 296,3073 67,2911 9,7332 269,9306 61,3010 9,7492 274,3519 62,30509,7652 301,1181 68,3836 9,8167 297,2265 67,4999 9,8076 273,2342 62,0512 9,8067 271,1805 61,58489,7664 290,7228 66,0229 9,8273 308,7622 70,1196 9,8205 272,3664 61,8541 9,8119 289,1215 65,65929,8270 275,6837 62,6075 9,8555 307,8018 69,9015 9,8347 266,5558 60,5346 9,8220 271,0294 61,55059,8475 298,8877 67,8771 9,9149 310,6342 70,5447 9,8578 275,3399 62,5294 9,8689 290,9811 66,08159,8705 319,2335 72,4976 9,9213 312,7329 71,0213 9,8792 288,8042 65,5871 9,8940 283,8739 64,46759,8936 311,8214 70,8143 9,9218 308,9763 70,1682 9,8855 279,1476 63,3941 9,9368 274,1716 62,26419,8958 317,4292 72,0879 9,9451 311,2491 70,6844 9,9800 281,0948 63,83649,9017 305,9375 69,4781 9,9605 314,5888 71,44289,9294 278,0081 63,1354 9,9649 305,2647 69,32539,9412 274,5638 62,35329,9689 324,7270 73,74529,9729 312,4910 70,96649,9800 323,5836 73,48559,9845 305,5188 69,38309,9973 298,4253 67,7721

WM S1 WM S2 WM S4 WM S5


39

The quantity of points depends on material plasticity and the number of cyclic loading-unloading.

Sample 3 was deleted because presents a different behavior concerning other samples tested. The

equivalent crack length a(i) was predicted by Equation 23 and with Equation 21, values of K(i)

can be found. Furthermore, G(i) is determined using Equation 20 (See procedure of section 3.3.2).

From the statistical analysis shown in Figure 29, it can determine that the best distribution for SIF

by CMOD method was a Weibull distribution with an Anderson-darling parameter value of 1.257.

From probability graph can see the SIF fit perfectly between 66 MPa.m1/2 and 72 MPa.m1/2. The

average value is close to 67 MPa.m1/2 that was corroborated to Weibull distribution media analysis.

Figure 29. Probability graphs to different statistical distributions of SIF for WM, CMOD.

Same as SIF and G were evaluated by the goodness of fit test and have similar behavior where

Weibull distribution was the best fit. Figure 30 shows a fitting analysis. In concordance of

probability graphs, it can seem that a better fit was achieved. The average value of G is close to 275 kJ/m2


40

Figure 30. Probability graphs to different statistical distributions of G to WM, CMOD.

As of Weibull distribution analysis can determine that critical G for WM oscillates into a

confidence interval of 95% between 266.424 kJ/m2 and 281.265 kJ/m2, and stress intensity factor

to 65.51184 MPa.m1/2 and 68.0214 MPa.m1/2. The Average was 273.744 kJ/m2 for G and 66.758

MPa.m1/2 for SIF. The value from the previous test (5% secant method) of critical G and KIC was

281 kJ/m2 and 67 MPa.m1/2 respectively, those values are within the range found with the unloading compliance test. Table 9 summarize confidence intervals to SIF and critical G.

Table 9. Goodness of fit Analysis for SIF and G of BM

Probability graphs shown in a way of compliment of table 9 and support of data obtained, those

graphs show in figure 31.

Error Error

Estimation Standard Lower upper Estimation Standard Lower upper

Media(MTTF) 66,7582 0,638482 65,5184 68,0214 273,744 3,78547 266,424 281,265Standard Desviation 4,27718 0,461915 3,46124 5,28546 32,0858 2,65847 27,2763 37,7432

Median 67,3452 0,61449 66,1515 68,5604 277,343 3,74984 270,09 284,79

Confidence Interval de 95,0% Confidence Interval de 95,0%

Goodness of FitKIC Critical G

Distribution: Weibull Distribution: Weibull

Anderson-Darling Anderson-Darling1,257 0,839


41

Figure 31. probability graphs (a) SIF and (B) G for WM, CMOD.

4.3.3. Ligament correction (W-a) for Quasi-static Fracture test

Base Metal

To corroborate the data obtained for 5% secant method, it was done a quasi-static test with the

secant method analysis. With the guideline of ASTM E399, a check was performed of ligament

according to KIC got by the previous test. Follow the relation between yield stress and Young

Module (𝜎𝜎𝑦𝑦𝑦𝑦/𝐸𝐸) for substantially less than the minimum recommended ligament [44], it used

base metal value got from the tensile test. Relation got was 0.0083341 equivalent to the minimum

ligament of 19 mm according to number 7.1.3 of the standard.

Figure 32. Experimental CTOA for a welded API A Steel, ligament corrected.


42

In accordance with ligament value, it was designed a new sample with height (W) of 40 mm, span

(S) of 160 mm, thickness (B) of 10 mm, and initial crack (a) = 18 mm – 20 mm (machined notch

and prefatigated crack), corroborating ligament (W-a) is around 20 mm – 22 mm. Four samples

with those dimensions were tested, results shown in Figure 32. Table 10 summarizes data obtained

from experimentation and KIC calculated.


Sample BM S1 BM S2 BM S3 BM S4 Maximum load[N] 28186.920 25582,310 22488.473 24830.109

PQ [N] 24064.656 23894,400 19890.973 24189.125 K [Mpa.m0.5] 97.144 96,456 93.090 92.930

F(a/w) 2.018 2,018 2.340 1.921

For analysis of SIF was done a goodness-of-fit test, without significant variation of its statistical

parameters. To ease of calculations and due to the low amount of data, it was chosen the normal

distribution, analysis, and confidence interval shown below in Table 11. Media value for KIC was

94.905 MPa.m1/2 between of confidence interval 93.0316 MPa.m1/2 to 96.7782 MPa.m1/2. In

comparison of value for base metal for before the tests (ligament correction), 94.136 of secant

method and 94.346 of unloading compliance, the difference is minimum. Those values present a

relative error compared to ligament corrected of 0.8249 % and 0.6035% respectively, which it shows small size and ligament do not generate affectation of SIF determination.

Table 11. Statistical analysis for SIF and G of BM.

The probability graph and confidence intervals graph is shown in Figure 33 as support results

obtained in table 11.

ErrorEstimation Standard Lower upper

Media(MTTF) 94,9049 0,955794 93,0316 96,7782Standard Desviation 1,91159 0,675849 0,955981 3,82243

Median 94,9049 0,955794 93,0316 96,7782

KICDistribution: Normal




43

Figure 33. (a) probability graph and (b) confidence intervals.

4.3.4. Stress intensity factor validation

With literature review of fracture toughness in metals focus on steel AISI 1020 and welds

evaluation of electrodes E7016, E7018, and E6011 used on the oil and gas industry, the validation of the data got in the experimentation was carried out.

4.3.4.1. Stress intensity factor validation for base metal

Research studies of Ariel E. Matusevich et al. (Determinación de la tenacidad a la fractura del

material de un gasoducto) and H. M. Ledbetter (Physical Properties Data Compilations Relevant

to Energy Storage: Mechanical Properties Data on Alloys for Use in Flywheels), it found values

for stress intensity factor comparable to the data got in this thesis. First one by using ASTM E23

standard Charpy impact test, it determined energy CVN values, and with Rolfe, Novak-Barsom

correlation converts those values on KIC, whose values range from 88.7 MPa.m1/2 to 91.1 MPa.m1/2

but those values are influenced by inertial effects [53].

On other hand, H. M. Ledbetter gives a value of SIF directly from experimentation in the base of

ASTM E399 standard. Experimentation was done with compact tension specimens under the

supervision of the Office of Standard Reference Data (OSRD) and National Bureau of Standards


44

of United States, also publication based on metallic materials handbook and manufacturer reviews.

The value registered is 95.1 MPa.m1/2 with a standard deviation of 7 and uncertainty of 7.4 [54].

To validate KIC, it used Ledbetter publication due to his study is the standard guideline for US

metallurgical industry and it doesn’t depend on empirical correlations. Relative error from base

metal SIF was analyzed for all tested done based on 95.1 MPa.m1/2. It found error does not exceed

2%, CMOD has more precision than the secant method but samples with ligament corrected have a less experimental error. Table 12 shown relative errors to each experiment.

Table 12. Relative error to each method to determinate SIF for BM.

Test Stress Intensity

factor KIC Experimental

Error

[MPa.m0.5] [%]

Method of secant 94.1358 1.0139 CMOD 94.3459 0.7930

Method of secant (Ligament corrected) 94.9188 0.1905

H. M. Ledbetter validation 95.1 -

Through comparison, it is possible to affirm that KIC found from experimentation on this study

effectively represent the value of SIF for base metal Material (AISI 1020 steel), also with a

verification hypothesis test, can build a confidence interval between 93.460 MPa.m1/2 to 95.474

MPa.m1/2, and standard deviation of 0.405.

4.3.4.2. Stress intensity factor validation for welded metal

To validate the stress intensity factor of the welded metal region, this thesis was based on various

studies of welding SMAW fracture toughness because of welded heterogeneity. Studies analyze

SIF through compact tensile (CT), and single edge notch bending (SENB) method, with samples

with different size. From studies, it made a comparison with weld bead in the middle orientation,

like used on this project.

Herrera D., et al., and Sumardiyant D. have based their analysis on the API 5L pipeline. The first

author compares longitudinal submerged arc-welding (SAW) with shield metal arc weld (SMAW),

the study used electrode E7018 and it found to SMAW, stress intensity factor was 75.4 ± 3.22


45

MPa.m1/2 [55]. The other research studies welded with electrode E70XX (various electrodes from

13 to 20) and E6013 use the impact Charpy energy test to get fracture toughness value, KIC found from the experimentation was 65.1 ± 5.6 MPa.m1/2 (1.9 J/mm2).

Sieurin H., et al. on their study “fracture toughness of a welded duplex stainless steel”, which

evaluated results was got with J-integral calculations and correlations to Charpy impact value with

stress intensity factor. Research analyzes 2 different thickness, 30 mm and 50 mm, values it KIC

found 68 ± 2 MPa.m1/2 and 65 MPa.m1/2 to 74 MPa.m1/2 respectively [56].

To have another reference due to the dispersion of the enclosed data between different authors, it

used to report of United States Steel Corp Monroeville Research Lab, wrote by Sovak J. F., et al.

where it was analyzed various fracture toughness tests giving a criterion to predict the fracture

behavior of weldments and found values between 60.2 MPa.m1/2 to 74.58 MPa.m1/2 [57]. Below is

a comparative table (Table 13) between KIC found by this thesis experimentation and research

studies consulted.

Table 13. Relative error to each method to validate SIF for WM

As it can see in the table 13 value of SIF got by the experimentation program, approximately 67

MPa.m1/2adjusts values from Sieurin H., et al., Sumardiyant D and Sovak J. F., et al. studies with

4% of maximum relative error and is close to value got by Herrera D., et al. with an error of 11%

(actually that was a maximum error found). With those values, it can be concluded that the SIF

value determined by the experimentation carried out on this thesis is within the values got by other

studies mentioned before, and KIC got is valid.

Error experimental Error experimentalMethod of secant CMOD

Lower Upper Media [%] [%]Herrera D., et al. 72.18 78.62 75.4 10.881 11.462

Sumardiyant D 59.5 70.7 65.1 3.219 2.547Sieurin H., et al. 30 mm 66 70 68 1.183 1.826Sieurin H., et al. 50 mm 65 74 69.5 3.316 3.945

Sovak J. F., et al. 60.2 74.58 67.39 0.289 0.938

Thesis Experimentation

Method of secant 65.168 69.223 67.196CMOD 65.512 68.021 66.758

Factor de intensidad de esfuerzo KIC[Mpa,m0.5]SIF Study


46

4.4. Fatigue Crack Propagation

Fatigue crack propagation test was done according to the procedure explained in chapter 3 based

on ASTM E647. To this test, a sinusoidal wave constant load amplitude of 2.5 kN to BM and 1.5

kN to WM was used, with stress relation of R = 0.1, representation of cycles shown in Figure 34.

From those loads amplitudes, it was reached almost 105 cycles. Crack length was measured on

stages, first at 3000 cycles and rest each 1000 cycles, an HD camera, and an image processing

program were used. To build a propagation curve was necessarily done an exponential curve fitting

in function of crack length and number of cycles, then function fitting was derived to formulate

the rate of crack growth function (da/dN). The range of stress intensity factor (∆𝐾𝐾) was obtained

by Equation 26 in function of Load range (∆𝑃𝑃) and crack length measure at a certain point

according to ASTM standard.

Figure 34. Constant-Amplitude Load Test.

The crack growth rates (a) at different fatigue cycles (N) from testing were computed, and it got

the relationship of a, in function of number of cycles, a (N). Data were analyzed with Matlab on

curve fitting app, using an exponential fitting of 2 coefficients to generate a better curve function

approximation, also it used the weight method of LAR for data with less outliners/anomalies in

data (every data point is as important as one other). The coefficient of determination of that approximation was between 0.94 to 0.99 which corroborates that the adjustment was adequate.

4.4.1. Fatigue Crack Propagation in Base Metal Samples

Crack length for base metal was measure with an HD camera and image processing program as

explained before. Using Matlab, it was correlated crack length with the number of cycles with a

curve fitting (a (N)), crack length (a) versus N curves for BM shown in Figure 35. It can see the

numbers of cycles average is around of 5x104, many of the curves have a good fitting on crack


47

growth stage, and have minimal differences with values that remain constant (no propagation

stage), for each sample, curve fitting function shows at figure legend.

Figure 35. Crack length versus number of cycles to Base Metal (BM).

In base of each fitting (a (N)) it got a derivate function da/dN to build crack propagation power

function better known as Paris law. Paris law correlates crack growth rate with the range of

toughness measure, in this case with the difference between maximum and minimum stress

intensity factor corresponding to load and unload SIF on each cycle. Figure 36 shows the

propagation curves of BM of where it can be identified two regions, first a threshold region

between ΔK of 20 MPa.m1/2 and 30 MPa.m1/2, and second, was a propagation region or Paris’

regimen between ΔK of 30 MPa.m1/2 and 80 MPa.m1/2.BM had a low crack growth rate because

material is able to resist almost 3x104 to 4x104 cycles before to start propagation process and 1x104 to 3x104 cycles on crack propagation stage before overload fracture.


48

Figure 36. Fatigue crack growth curve of base metal (BM).

From Figure 36 it can see threshold zone corresponds to da/dN of 1x10-9 m/cycle and the transition

zone between 1x10-8 and 1x10-9 m/cycle, in analogy to the literature of fatigue limit, every ΔK

below to relating da/dN less than 1x10-9 m/cycle correspond a non-propagation zone [58]. Zone II

or propagation zone corresponds to da/dN between 1x10-6 to 1x10-8 m/cycle. Unstable zone

corresponds to da/dN higher than 1x10-6 m/cycle but it cannot record the crack advance data

because filming tools have not capacity to recorder high-velocity images and untestable crack can

no permit to stop machine test without overload generating. For this thesis, the study focusses on

analysis, of Paris regimen or propagation zone.

Analysis of data gives for base metal has Paris law parameters corresponding to C=4.12x10-12 and

m coefficient of 2.6. Shown below in Figure 37 a comparison of Paris regime of fatigue crack

propagation curves between this thesis and Raghuvir Kumar and S. B. Singh research “A Study of Fatigue Crack Growth IS-1020 Steel under Constant-Amplitude Loading” [59].


49

Figure 37. Comparison of Fatigue crack grow curve of (a) base metal (BM) and (b) AISI 1020 steel (Kumar,1993).

Raghuvir Kumar and S. B. Singh found that coefficient for same steel class are C=2.96x10—12 and

m= 2.93, test was done at a frequency of 10 Hz under 23 kN on cyclic loading with a stress ratio

of 0.1 to 0.4 [59-60]. Also, it found other studies from those authors where with constant amplitude

test in SEN (Single-edged Notched) samples with an initial crack of 6 mm and different loading

cycles, fatigue coefficients are C=2.09x10-12 and m= 3.21 [61]. From “Atlas of fatigue curves” by

Howard Boyer, it found m parameter oscillates between 2.6 to 3.73 for steels and C between 1x10-

12 to 1x10-7. Other literature was consulted, and it was found on “Mechanical Properties of

Materials” by David Roylance, the parameters of crack propagation C and m curve for metals

oscillates between C=1x10-10 to1x10-12 and m = 2 to 4[62-63].


50

The relation of crack growth rate with ΔK determined by power function is valid for steel that was

analyzed on this thesis project, coefficient C and m are into the range found on literature for ferrite

perlite steel and more specific ASIS or SAE 1020 steel. A comparison table (Table14) summarizes

coefficients publishing by different authors with current steel (yellow color).

Table 14. Comparison of Paris law coefficients from literature with BM samples testing

Author Publishing C m

Kumar R. and Singh S. A Study of Fatigue Crack

Growth IS-1020 Steel under Constant-Amplitude Loading

2.96x10-12 2.93

Kumar R. and Singh S.

Experimental observations of fatigue crack growth in IS-1020 steel under constant

amplitude loading

2.09x10-12 3.21

D. Roylance Mechanical Properties of Materials 1x10-11-1x10-12 2-4

R. I. Stephens et al. Metal Fatigue in Engineering 3.6x10-10-6.9x10-12 3

Prashant Kumar Elements of Fracture Mechanics 6.8 x10-12 3

SAE 1020 Steel, fatigue samples testing 4.1172x10-12 2.6046

4.4.2.Fatigue Crack Propagation in Welded Metal Samples

For welded metal was done the same procedure. Crack (a) versus number of cycles (N) curves for

WM are shown in Figure 38. It can observe fatigue life on samples is very different from each

other, especially sample 1 and sample 2 which have a short fatigue life compared to the other 3

samples. Samples 3-5 have a most uniform behavior with a number of cycles average of 5x104.

Differences on welding samples are common due to internal heterogeneity and possible

imperfections as has been clarifying on this thesis study.


51

Figure 38. Crack length versus number of cycles to Welded Metal (WM).

As it can see from graphs, the life of materials has a close relationship with initial crack length, for

small values of crack length, material experiment more resistance under fatigue condition than

high initial crack length. Before affirmation translates that material has major fatigue life if it

presents a low initial crack length, furthermore it evidenced that small changes on crack length

produce a greater change on fatigue life, that was a case of those test were initial crack correspond

9 ± 0.5 mm, the deviation is produced by the machined process, those changes translate on

reduction fatigue life on 104 cycles without mention scattered reflected on welding samples product to heterogeneity in materials.

Welded metal samples are analyzed to make a comparison with fatigue parameter and propagation

curves of BM. Figure 39 shows fatigue crack propagation curve of WM, where two zones are

identified. First is threshold zone, and it oscillates on ΔK between 20 MPa.m1/2 and 25 MPa.m1/2,

and propagation zone between of ΔK 30 MPa.m1/2 and 65 MPa.m1/2 too close to the critical stress


52

intensity factor. However, the transition zone between threshold and Paris regime is 1x10-7 to 1x10-

8 m/cycle which makes a clear difference with the base metal samples, this means that WM samples experiment more cycles in microstructural crack propagation and have less fatigue life.

Figure 39. Fatigue crack growth curve of welded metal (WM).

WM experiments a high crack growth rates in propagation zone 1x10-4 to 1x10-6 m/cycle with the

same range of intensity stress of BM, which shows that its propagation rate is 102 times higher

than BM, and possibly has a shorter unstable zone. From the propagation curve, it was got material

coefficients, C = 8.826x10-12 and m= 3.1732. Paris regime (zone II) for WM, it is shown in figure

40.


53

Figure 40. Fatigue crack growth curve (Zone II) welded metal (WM).

To validate curves and fatigue parameters, various authors were consulted. From M. Beltrão, et al,

the research compares values of C those values oscillate between 1.33x10-9 and 6.111x10-14. and

m values between 2 and 4.59, where author explains that changes depend on microstructure and

composition in steels that he compared (high strength steel API grade X)[64]. D. Bowman on his

study found crack growth parameters of m = 2.4 -5.8 and C = 2.9662 x10-14 (value converted to

ksi.in1/2 to MPa.m1/2), this study was done under high fatigue cycle, using load control of 22 kN [65].


54

According to T. Lassen research it evidenced values of C = 12.6 x10-12 – 13.5 x10-12 and m = 2.6

from SMAW welding (E7018) using in offshore platforms with 8 Hz of frequency and R=0.5 [66].

Other studies was consulted and gives values to C = 6.98 x10-12 and 1.5 x10-12 and m = 3.65 and

3.2 to welding with electrode E7018 [67-68]. Following comparison table 15 summarized the

results of coefficient and compare authors parameters.

Table 15. Comparison of Paris law coefficients from literature with WM samples testing

Author Publishing C m

M., Beltrão, et al

Fatigue crack propagation in API 5L X-70 pipeline steel longitudinal welded joints

under constant and variable amplitudes

1.33x10-9 - 6.111x10-14 2-4.59

D. Bowman Fatigue Behavior of Steel Butt Welds Containing

Artificial Discontinuities. 2.9662 x10-14 2.4 -5.8

T. Lassen The effect of the welding

process on the fatigue crack growth

12.6 x10-12 – 13.5 x10-12 2.6

P. Singh, et al Fatigue studies on carbon steel piping materials and

components: Indian PHWRs 6.98 x10-12 3.65

J. Otegui Growth and coalescence of

fatigue cracks at weld toes in steel

1.5 x10-12 3.2

Welded Metal, Electrode E7018, fatigue samples testing 8.8265x10-12 3.1731

Through table 15 it can be stated that the values got for the coefficients C and m are within the

range for this type of welding with some small dispersions of the values shown. High exponent m

makes to denotes the reason of WM has a higher crack propagation rate than BM samples, even if

both have a coefficient C of the order of 10-12. This behavior although reflected in Figure 35 and

Figure 37 where crack propagation of BM is around 20x104 - 30x104 cycles in comparison to

10x104 cycles of WM. Additionally, the welded metal samples reflect a more plastic behavior than

the base metal when subjected to fatigue, therefore their load capacity is reduced by that action.


55

4.5. Impact Fatigue Crack Propagation

Impact fatigue consists of repetitive impact loads or impulsive loads. Those loads have a triangular

waveform load with a short duration around milliseconds. This impulse is a wave to transmit to

material span, but due to material and environment damping, load and deformation wave decays

to magnitudes become cero [24]. Figure 41 shows various measurements for impact load in

different impact fatigue tests on BM and WM. Note that by increasing the number of impacts on

the material, the measured force decreases, because test is controlled by displacement control or

height control (energy level), for that reason impact force is a function of material stiffness, that

decreases as the crack grows [69].

Figure 41. Impulse force in impact cycle to (a) BM and (b) WM.

Impact fatigue test was conducted by DWIT on different energy levels (1.913 J, 2.028 J, and

2.342). From number of cycles in each energy level, a minimum change of impact energy affects

drastically material life, especially BM samples. For BM under 3 energy impact levels proposed

in the experimental procedure, it went from resisting 190 to 40 impacts. However, WM shows a

bit different behavior because energy level does not affect drastically material life in comparison

to BM. Material life reduction was only of 10 to 15 impacts less (from 46 to 30 impacts) form low

to high energy impact levels, but plastic deformation starts almost immediately, that implies

material loses the capacity to absorb energy, causing premature crack coalesce (around 20 to 25

impacts, depends on energy which material was impacted and possible micro defects in welding)

and rapid crack growth and final fracture.


56

Data from those tests are presented in the form of da/dN – Kmax curves. Where Kmax is a

maximum dynamic stress intensity factor (DSIF) or maximum KID that it was corrected by the

assumption of sample behaves like mass-spring model and inertial effects affect the measurements.

Correction of the stress intensity factor was done by formulation showed in section 3.4.2, and

Equation. 32. Correction was applied for each impact, since this generates a crack growth in the crack propagation stage, using MATLAB.

Figure 43 shows Kmax determined by ASTM standard and the mas-spring correction model. Note

the difference of the maximum value of dynamic stress intensity factor between suiting ASTM

quasi-static standard and correction applied. Standard reflects a value of Kmax close to critical

stress intensity factor determined on the quasi-static test (almost 95 MPa.m0.5) which can indicate

material is on crack propagation stage and is too close to failure. However, with the correction of

equation 32, the inertial effect is included on the calculated force determination, reducing its value

and therefore reduces the value of Kmax indicating material is not on the propagation stage but is

in the microcracks coalescing state in the threshold region.

(a) (b)

Figure 42. Comparison between ASTM standard of stress intensity factor model and DSIF model correction to (a) impact number 1 of sample one (Kmax wave) and for (b) Kmax – cycle on 2.33 J of impact energy sample one,

fatigue life.

t [s]


57

4.5.1. Impact Fatigue in Base Metal Samples

Crack length was measured with an HD camera and image processing program. To determinate

crack growth rate, an exponential or potential curve fitting where crack length is in function of

cycle (a (N)) were generated to each sample and finally, function is derived(da/dN), similar

procedure to fatigue in constant amplitude test, with the difference, of each impact was recorded.

Crack growth photo recorded for base metal sample 1, on the test with an impact energy level of

1.913 J shows below in Figure 43.

Figure 43. advance of the crack under impact fatigue. BM Sample 1, energy level of 1.913 J.


58

Previous images show the relevant changes in the advance of the crack. With data analysis, Crack

length versus number of impacts curves were done. Then the following figure shows those curves for base metal to each energy level, for every sample. Curve fitting function shows at figure legend.

Figure 44. Crack length vs number of cycle curve to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J for BM.

By means of fitting curves, da/dN function was obtained. Crack growth rate has plotted a graph in

function of maximum DSIF that was calculated previously by equation 32 (see formulation on chapter 3, section 3.4.2).


59

From propagation curves in Figure 45, is identified three regions. The first region is a threshold or

crack nucleation, second is a crack propagation region, and finally unstable crack (Kmax > KIC)

[28]. In a second region was evaluated the propagation rate with a power function fitting called

Paris law with modification because Kmin = 0 [38]. Crack propagation curve for each test was

plotted below.

Figure 45. Propagation curves in BM to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples.

For BM crack propagation curve shows in Figure 46 and it was identified threshold and

propagation regions where threshold is close to the critical value of stress intensity factor between

75 MPa.m1/2 - 80 MPa.m1/2. It can appreciate region II, crack growth is very high, and it comprises

between 1x10-4 m/cycle and 1x10-3 m/cycle or 0.1 mm/cycle to 1 mm/cycle. The explanation of

that behavior is material has a great capacity to absorb energy until crack initiation and start

propagation, since once the crack is nucleated, the material life is significantly reduced reaching in few impacts a stage of unstable crack growth and final failure.


60

Paris law was evaluated in region two to each test, with a power curve fitting with equation 33

shape it found parameters C and m. The results are shown in figure 46.


= 𝐶𝐶𝐾𝐾𝐼𝐼𝐼𝐼(𝑚𝑚𝑎𝑎𝑥𝑥)𝑚𝑚 = 𝐶𝐶𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝑚𝑚 (33)

(a) (b) (c)

Figure 46. Power fitting of each test to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples.

Analysis of propagation graphs (Figure 46) gives for base metal has Paris law parameters

corresponding to C=2.49x10-13 and m coefficient of 4.48 for the test with an impact energy of

1.913 J. Parameters C=7.4075x10-15 and m coefficient of 5.379 for the test with an impact energy

of 2.028 J and C=1.7936x10-15 and m coefficient of 5.623 for the test with an impact energy of

2.342 J. Coefficients C are between 1.8 x10-13 to 3 x10-15 and m to close to 5.2, in comparison

with fatigue under constant amplitude this exponent is too high and makes to increase crack growth

rate in a more accelerated way. To define a unique parameter for BM, all 3 tests were plotted on

the same graph and a single curve fit was got, Figure 47 (a) shows propagation results to BM.

In accord with Figure 47 (a), with curve fit of 3 tests with respective repetitions it was determined

that Paris law parameters for base metal corresponding to C = 3.282x10-13 and m coefficient of

4.474. Those parameters are compared with Iguchi’s work, where C=2.37x10-11 and m=2.9 [38].

In comparison with Iguchi’s study, this research found parameter C is under the range, but m is


61

considerably higher around 1.5 times than Iguchi result which translates into a faster crack growth

rate for BM in this study. The difference between material life lies in the number of impact cycles

and impact energy on each study. Iguchi’s work was designed for analyzing high cycle loading

with 105 to 106 impact load cycles where impact energy is too small in comparison with thesis

experimentation.

Figure 47. Crack propagation curves under impact fatigue for BM (a) compilation of 3 tests and (b) Iguchi’s work.

Changes in impact energy provoke changes on crack growth rate where high impact energy

translates on high crack growth rates. Look at Figure 47 (a) small changes in impact energy makes

propagation points have small changes on their slope. Also, it was identified, that load amplitude

and load ratio of experimentation are extrinsically property of threshold material, and can affect

the threshold and crack propagation behavior [28]. The load effect at near-threshold was attributed to crack closure and dislocation behavior [70-71].


62

Look at Figure 47 that shows a comparison with different impact energy levels, threshold region

moves between 78 MPa.m1/2 – 85 MPa.m1/2 as the impact energy increases and if it compares with

Iguchi work that has different impact energy and longer material life, threshold locate in 10

MPa.m1/2, but it was necessary to emphasize that the load and energy applied by Iguchi are much

lower than the one applied in this work. For this comparison, it can assume that load conditions

affect drastically crack growth and threshold behavior. Therefore, higher impact energy in zone I

(crack nucleation zone) of the crack propagation curve will result in a threshold closer to the KIC

and a higher crack growth rate in zone II, since the applied load is directly proportional to the stress

intensity factor.

4.5.2. Impact Fatigue in Welded Metal Samples

For WM the crack propagation under impact fatigue was also analyzed with similar procedure to

BM. Image recorded to crack propagation test under impact fatigue for WM shows below in Figure

48. As shown in Figure 48 propagation stage does not start until 25 impacts for all samples tested,

also it can see a plastic deformation producing by impact test it most pronounced than BM test

which means WM has a high tendency of premature failure with few impacts on propagation stage.

Figure 48. advance of the crack under impact fatigue. WM Sample 1, energy level of 2.028 J.


63

Previous images show the relevant changes in the advance of the crack. With data analysis Crack

length versus number of impacts curves was done. With fitting curves, a function of crack length

was determined and with respective derivate to build a crack propagation curve. Curve fitting is

shown below.

Figure 49. Crack length vs number of cycle curve to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to WM.

Figure 50 shows crack growth propagation curve under three different energy levels. It was

identified 2 regions like BM, Threshold region and propagation region. For WM crack propagation

curves were identified threshold regions move into stress intensity factor values between 42


64

MPa.m1/2 - 55 MPa.m1/2. It can appreciate region II of the curve where crack growth is very high,

and it comprises between 5x10-4 m/cycle and 1x10-3 m/cycle or 0.5 mm/cycle to 1 mm/cycle. In

comparison to base metal, the propagation zone for welded metal is short, without mention critical

SIF is 55 MPa.m1/2 less than BM, which is interpreted as a greater crack propagation at a lower

fracture toughness.

Figure 50. Propagation curves in BM to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples.

Paris law was evaluated in region two to each test, results shown in Figure 51. Analysis of

propagation graphs gives Paris law parameters for welded metal corresponding to C=2.7409x10-7

and m coefficient of 1.786 for test with impact energy of 1.913 J. Parameters C=1.78113x10-7 and

m coefficient of 1.943 for test with impact energy of 2.028 J and C=2.0642x10-7 and m coefficient of 1.911 for test with impact energy of 2.342 J.


65

Figure 51. Power fitting of each test to impact energy of (a) 1.913 J, (b) 2.028 J, (c) 2.342 J to BM samples.

Coefficients C are between 1.7 x10-7 to 3 x10-7 and m too close to 1.8, in comparison with base

metal, parameter C denotes a high propagation rate with C 1x108 higher than BM, m exponent is

into parameters and makes propagation rate does not drive into early unstable crack propagation.

To define a unique parameter for WM, all 3 tests were plotted on the same graph and a single curve

fit was got, Figure 52 shows propagation results to WM.


66

Figure 52. Crack propagation curves under impact fatigue for WM.

From the analysis of Paris law, it found of coefficients are C = 6.1703x10-7 and m = 1.6393. Results

from those samples show that WM has less resistance to impact fatigue life, because of capacity

of absorption energy loss in plastic deformation. This behavior reflects an on the number of

impacts that welded metal resist which is clear few than base metal under the same impact energy

levels, also crack propagation is shorter than BM. To compare C coefficient indicates that WM has a high crack propagation rate under a less SIF.


67

4.5.3. Energy absorption analysis

Impact response of material can be analyzed by energy balance. Impact energy in this case

potential energy, most of that coverts in kinetic energy and elastic deformation energy when

impactor reaches a material but like all real process that involves conversion energy in work

(deformation work for this study) is an irreversible process for that reason part of energy loses in

heat way [72]. Equation 34 describes the conversion energy process in elastic behavior.

𝐸𝐸𝑖𝑖𝑚𝑚𝑝𝑝𝑎𝑎𝑖𝑖𝑡𝑡 = 𝐾𝐾𝑔𝑔ℎ = 12𝐾𝐾𝑉𝑉2 + 𝑊𝑊𝑑𝑑𝑒𝑒𝑑𝑑 +𝑄𝑄 (34)

However, if it adds for that energy balance the effects of plastic deformation and cracking

propagation of material that becomes of new losses of that impact energy. Also, part of

deformation energy becomes in absorption energy and recovery energy. The absorption energy is

real deformation energy that storage on material and provokes real deformation. Recover energy

as its name says it is the energy used by the material to recover its original form [73]. Following it shows a new energy balance that includes those concepts where D represents energy losses.

𝐸𝐸𝑖𝑖𝑚𝑚𝑝𝑝𝑎𝑎𝑖𝑖𝑡𝑡 = 12𝐾𝐾𝑉𝑉2 + 𝐸𝐸𝑎𝑎𝑎𝑎𝑦𝑦 + 𝐸𝐸𝑟𝑟𝑒𝑒𝑖𝑖 +𝐷𝐷 (35)

It is known that the area under the curve of the force-displacement graph represents a type of

energy. Figure 53 shows a comparison between force - maximum displacement curve and force-

displacement curve, of BM sample at different impacts. The first one represents total deformation

energy and the second one represented absorption energy. It can see from the end value of

displacement of second curve that material tries to recover the original form.


68

Figure 53. (a) Force - maximum displacement curve and (b) force-displacement curve to BM.

With repetitive impact, energy capacity absorption decrease, especially where material starts a

plastic deformation because capacity of material to recover, it loses in each impact cycle, due to

material begins to have a permanent deformation, also crack nucleation and crack propagation help to decrease absorption capacity because of an increasing amount of energy it uses to crack growth.

This behavior is most predominant on wedded metal as shown in Figure 54, where permanent

deformation is measured with displacement, note that displacement on welded metal sample is

around 1.7 times bigger than base metal, it is a clear indication of material absorb energy but it

was dissipated on early plastic deformation. Furthermore, as shown on force-displacement curves

to each impact, displacement moves as the material lose its ability to resist load, which results in

the loss of energy absorption capacity.

Figure 54. Force – displacement curve to WM.


69

On unstable crack stage, material loses all capacity of absorption and energy becomes on

deformation energy only and propagation energy, added other energy losses on energy balance.

Figure 55 shows an energy quantification of deformation energy, absorption energy, recover

energy, and decrees the amount of energy of the material.

In base metal Approximately 1 J loses into Kinetical energy, heat loses, plastic deformation energy

and when starting a crack growing, energy loss also in crack propagation. From Figure 55 it can

see that the top of the curve represents the total amount of energy deformation, the absorbed energy

is representing by the final part of the curve, and finally recover energy is the difference between

deformation and absorbed energy. It should be remembered that the measurement of energy was

made with a level of energy of 1.9 J for BM.

Figure 55. Energy curve to BM.

For WM absorption energy is less because the material presents a major ductile-plastic

deformation in comparison to BM. As a show on figure 56, deformation energy represents 0.1 J

more than BM, which emphasizes what was said previously, material experiences a greater plastic

deformation, that translates on less availed recovery energy just amount of 0.2 J to 0.15 until crack

propagation stage, that’s a clear difference to BM recovery energy (Figure 56) that varies between

0.5 J to 0.3 J until crack propagation stage. During crack propagation a final failure amount of

energy decrees on slow way on BM samples with 50 to 30 impacts before to material failure. That

is occurs on different way on welded metal samples, where that stage is too short just to 15 to 10 impacts before to final failure.

Ener

gy [J

]

Absorbed Energy

Recover Energy

Total deformation Energy


70

Figure 56. Energy curve to WM.

4.5.4. Microstructural and fractographic analysis

This section shows metallographic observation of welded metal samples to identify BM, HAZ and

WM sections and fractographic inspection of BM and WM samples to identify mechanism to crack

nucleation, crack propagation and final failure.

4.5.4.1. Metallographic inspection With Metallographic inspection can easily identify a BM, HAZ and WM zone also is possible to

identify a fusion zone. From the examination, It found ferrite (beige color) structure with is

associate of strength of material [74] and found grained perlite structure. Perlite was found along

the crack zone; some studies correlate perlite (black color) presence with ductile and high crack

growth rates and depend on carbon concentration of steels. Additionally, it found cementite traces that have brittle behavior and reduces load capacity of material.

From HAZ it found very fined granular traces of ferrite and perlite associate to toughens decrease

[75]. From WM it found a local region rich in carbon and some impurities (corroborated to Sem).

Metallographic inspection shows in Figure 57.


71

(a) (b)

Perlite

Ferrite

Perlite

Ferrite

(c) (d)

(e) (f)

HAZ

Ferrite

Perlite

HAZ

HAZ to WM

HAZ

WM


72

Figure 57. Metallographic inspection of (a) BM , (b) BM magnification were is found perlite (gray/black) and ferrite (beige/white), (c) and (d) represents HAZ with fine granular ferrite and perlite. (e) Transition zone between

HAZ and WM, (f) magnification of transition zone, it can show carbon traces and perlite-ferrite structure. Finally (g) and (h) WM microstructure whit carbon traces.

4.5.4.2. Fractographic inspection Fractographic observations were also made of crack growth under impact fatigue loading. From

Figure 58 (b) BM sample reflects shear lips (red lines) formed on the outer edges with possibly

caused by shear stresses, lines are on crack direction, and center chevron V marks. The direction

of V is opposite to crack propagation (black lines) signal of ductile fracture. In the center also can

see retched marks (blue lines) from changes in surface’s level.

Furthermore, welded metal was analyzed, Figure 58 (d). WM sample shows shear lips (red lines)

on the outer edges but a possible fibrous zone is evidenced in the center but, final crack zone

exhibits a possible intergranular cracking (blue dark lines) because it does not show visible plastic

deformation and its very granular appear that reflect the light, also presents some pours that act

like stress concentrators (blue light lines). That shows a fragilization of material under impact load.

(g) (h)

Carbon traces

Carbon traces


73

Figure 58. Fractographies taken in stereoscopy at x16 magnification. (a) and (b) are BM crack sample and (c) and

(d) are WM sample.

SEM fractographic analysis was realized. For BM and Welded metal microstructure at crack

initiation reflects highly presence of microvoids at as shown in Figure 59, which confirms the last

assumption of crack initiation, which is by microvoids nucleation, indicating that crack nucleation

and initiation is by the ductile mechanism.

Figure 59. SEM Fractographies (a) location of crack initiation and microvoids presence at that location in (b) BM and (c) WM.

(a) (b)

(d) (c)


74

By observation of central part of WM, it shows a transition of ductile zone to brittle zone, because

it can see cleavage structure in a combination of microvoids reflected in Figure 60. This shows

that impact fatigue weakens the material by embrittlement process. That was a contrary behavior

of BM that shows a microvoid structure indicating ductile propagation. Also, in outer edges was

found microvoids presences indicating plastic deformation and ductile cracking in that zone.

Figure 60. Central part of WM sample where found combination of microvoids and cleavage.

Finally, at the end of the crack in BM can show a microvoids presences some kind of cleavage

indicating brittle-ductile combination fracture but in WM all final zone has a cleavage structure

and presence of intergranular fracture, indicating brittle final fracture as a show in Figure 61.

Figure 61. Final crack in WM, it found intergranular and cleavage presences.


75

5. Conclusions

On this work analyzes base metal of API grade A steel (AISI 1020 and welded metal with SMAW

technique (E6010 and E7018), under different loads conditions, where base metal steel shows a

major resistance than WM. Nonetheless, imperfection and defects reduce considerably resistance

of welded metal because it becomes on weak part of metal union as knowing by literature. Finally,

experimentation shows, the plasticity behavior of WM reduces the capacity to carrying load, since

the material focuses on plastic deformation and therefore in energetic terms the material increases

its deformation energy on irreversibly way and loses its capacity to absorb energy, weakening the

material much faster than in an elastic process which leads to the early fracture.

On the other hand, material life under dynamic load has a direct relationship with load amplitude

and impact energy, since from fatigue impact test was proof than small changes on impact energy

affect drastically material life, especially on BM steel also at high energy and high load conditions

make to move threshold zone close to critical stress intensity factor generating that crack grow rate

increase considerably.

Continuing with the dynamic behavior of material, BM under fatigue constant amplitude load has

a very low crack growth rate in comparison with the same material, when was exposed to repetitive

impact loading. Contrary behavior was found in WM to has almost similar performance in constant

amplitude load fatigue and impact fatigue with changes of stress intensity factor of threshold zone

affected by impact energy and loading conditions. In impact fatigue, BM has a longer life than

WM, that is because a high plastic deformation in WM causes it too quickly loses in its capacity

of the material to resist load and absorption energy, even though WM had a lower crack

propagation rate.

Concerning energy, it was analyzed and conclude that 1J of energy lose y heat and friction losses

and the par of energy remaining is used to do work which corresponds in this case in deformation

and cracking processes. Moreover, It was identified that Absorption energy is a component of

deformation energy and corresponds to real plastic and elastic deformation energy, and its value

decreases as the material deforms plastically and loses its load capacity. When crack is nucleated,


76

and starts to propagate, the material loses the capacity to absorb energy because the available

energy is used to crack propagation. Other component of deformation energy (recovery energy) tends to disappear went material cannot recover the original form due to plastic deformation.

It was analyzed impact fatigue failure mechanisms, and it was found from the fractographic

analysis that crack initiation is because of microvoids nucleation indicating ductile cracking

initiation. Also, mechanism of crack propagation and final failure changes, showing ductile-brittle

propagation on WM and ductile propagation in BM and brittle final fracture especially in WM,

phenomenon helped by the welding defects. From this study is possible to conclude that with

impact fatigue it has a greater growth rate of crack propagation than other load conditions and highly has a dependency on impact energy.


77

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