Vindio 1.0 User's Manual

1. INTRODUCTION...................................................................................................................................................................................................................................................5

2. THEORETICAL-PRACTICAL FUNDAMENTALS2.1. Fracture-plastic collapse analysis of cracked components ..................................................................................6

2.2. Material tensile properties used in fracture-plastic collapse analyses .........................................8

2.3. Material fracture properties used in fracture-plastic collapse analyses ................................. 11

2.4. Failure assessment diagrams ....................................................................................................................................................................................... 13

2.5. Fatigue crack propagation ................................................................................................................................................................................................ 18

3. FRACTURE-PLASTIC COLLAPSE ANALYSIS FOLLOWING VINDIO 3.1. General overview ................................................................................................................................................................................................................................. 22

3.2. Material data ................................................................................................................................................................................................................................................. 23

3.2.1. Tensile properties .......................................................................................................................................................................................................... 233.2.1.1. Level 1 ....................................................................................................................................................................................................................... 233.2.1.2. Level 2 ....................................................................................................................................................................................................................... 253.2.1.3. Level 3 ....................................................................................................................................................................................................................... 27

3.2.2. Fracture properties .................................................................................................................................................................................................... 273.2.2.1. Format 1 ................................................................................................................................................................................................................ 283.2.2.2. Format 2 ................................................................................................................................................................................................................ 313.2.2.3. Format 3 ................................................................................................................................................................................................................ 32

3.3. Component and crack geometries .................................................................................................................................................................... 33

3.4. Acting loads .................................................................................................................................................................................................................................................... 42

4. CRACK PROPAGATION ANALYSIS FOLLOWING VINDIO ................................................................................ 44

5. TUTORIALS .................................................................................................................................................................................................................................................................. 455.1. Tutorial 1: assessment of an in-service component ........................................................................................................ 45

5.2. Tutorial 2: critical load search ...................................................................................................................................................................................... 57

5.3. Tutorial 3: crack size scanning .................................................................................................................................................................................... 67

5.4. Tutorial 4: crack propagation analysis ........................................................................................................................................................ 73

6. REFERENCES ............................................................................................................................................................................................................................................................ 78

Annex I. Glossary of symbols and acronyms ..................................................................................................................................................... 82

Annex II. ki and pl solutions .............................................................................................................................................................................................................. 85

5 1. Introduction

VINDIO is a software that allows fracture-plastic collapse analysis on cracked components to be made, as well as crack propagation calculations following the Paris law. In this manual, the user, who is supposed to have certain minimum knowledge on Fracture Mechanics and Plasticity, has a brief theoretical review about fracture-plastic collapse and fatigue assessments of structural components containing cracks, about the material parameters used in the analyses, and about the engineering tool used in VINDIO to determine if a given component is working under safe or unsafe conditions, which are the Failure Assessment Diagrams (FADs). Also, the different types of analyses that may be performed by using VINDIO are gathered and, finally, several tutorials are proposed in order the user becomes familiar with the capacities and the possibilities offered by the software.

Concerning the assessment procedure that supports the analyses, VINDIO is based on the FITNET FFS Procedure [1-3], which is an European procedure developed by the European Fitness-for-Service Network. Therefore, both the stress intensity factor solutions and the plastic collapse load solutions, the FAD expressions or the correlations between Charpy energy values and fracture toughness values (among others) have been mainly taken from such procedure. In those situations where other sources of analytical solutions or empirical correlations have been taken, it will explicitly be indicated in this manual.

Finally, it is important to notice that, given the FITNET FFS was developed for the assessment of metallic structures, VINDIO can be generally applied to this type of materials only. Its application to other kind of materials (possible in many cases) is left to the user’s judgment.

6

2.1. FRACTURE-PLASTIC COLLAPSE ANALYSIS OF CRACKED COMPONENTS

It is well known that the presence of a crack in a structural component subjected to loads produces a stress concentration in the crack tip, something that may lead to the final failure of the component. The different micromechanisms causing the failure depend on the material and the plasticity level occurring at the crack tip. Despite it is not the intention of this manual to describe the theoretical basis of the different situations that may occur in practice (for this purpose the reader is submitted to specialised literature, such as [4,5]), it is reminded here that, in a first approach, there are three possible mechanisms causing the final failure of a cracked component:

• Brittle fracture: associated to processes on which the plastic zone at the crack tip is small if compared to any other significant dimension (e.g., component thickness, length of re-manent ligament, etc). The analysis of this kind of situations is based on Linear Elastic Fracture Mechanics (LEFM), which proposes the following equation to establish fracture conditions (assuming Mode I of fracture [1,4,5]):

(1)

KI is the stress intensity factor, which defines the stress field at the crack tip under linear-elastic conditions and depends on a geometric factor (Y), the applied stress (σ) and the crack size (a). Most of the analytical solutions of KI (or Y) used in the software have been taken from [2]. KIc is the material fracture toughness [4,5].

• Ductile fracture: in this case, fracture is caused by ductile processes occurring in the crack tip and comprising the formation, growth and coalescence of microvoids in the plastic zone, which has larger dimensions than that existing in brittle situations. Following Elas-tic-Plastic Fracture Mechanics (EPFM), the stress field at the crack tip is defined by the J integral [1,4,5], whose value increases with crack stable propagation (thus, arising the JR or the J-Δa curve). Fracture require two simultaneous conditions:

(2)

2. Theoretical-practical fundamentals

7 2. THEORETiCAl-pRACTiCAl FUNDAMENTAlS ViNDiO USER´S MANUAl

(3)

Jap is the applied J, which is a curve that depends on both the applied load and the crack propagation considered, and JR (or J-Δa) is the material resistance curve, which is fitted through two material constants (A y n). As seen below, in certain occasions, a characteristic value (JIc) of the JR curve is considered, the fracture condition being:

(4)

In such case, the fracture analysis is analogous to that represented by equation (1), although representing elastic-plastic conditions. Therefore, it is not possible to consider the stable crack propagation occurring before the final fracture, the analysis being limited to fracture initiation.

Moreover, the J integral is composed by an elastic component (Je) and a plastic component (Jp). The former is related to KI following equation (5) [1,4,5]:

(5)

E´ being E in plane stress conditions and E/(1-ν2) in plane strain conditions (see Section 2.2). E and ν are, respectively, the Young´s modulus and the Poisson´s ratio.

• Finally, there are situations in which the crack does not act as a stress riser, the reduction of the load bearing capacity being associated to the reduction of the resistant section [1,4]. In such cases, with generalised plasticity, failure takes place when the applied load P equals the plastic collapse load PL:

(6)

8 ViNDiO USER´S MANUAl 2. THEORETiCAl-pRACTiCAl FUNDAMENTAlS

Most of the analytical solutions used for PL in VINDIO have been taken from [2], although in several occasions (explicitly indicated in Annex II) other sources have been considered.

In practice, it is not simple to distinguish in which of the previous situations the user is and, moreover, fracture and plastic collapse processes interact. Fortunately, the use of Failure Assessment Diagrams allows the analyses to be performed regardless of the type of failure taking place, which on the other hand is revealed by the location of the assessment point within the FAD (see Section 2.4).

2.2. MATERIAL TENSILE PROPERTIES USED IN FRACTURE-PLASTIC COLLAPSE ANALYSES

Material tensile properties constitute fundamental data for the fracture-plastic collapse analysis of cracked components. These properties are obtained by testing material specimens whose geometry and dimensions are defined following well known national or international standards (e.g., [6-8]). The specimens are then subjected to tensile loads until the final rupture. The testing machine used in a tensile test register the applied load, whereas an extensometer is also used to register the length increment occurring in the specimen. Therefore, during the test there is continuous register of both the applied load on the specimen (F) and the specimen length increment (Δl). Thus, it is obtained a load-displacement curve (F-Δl) that it is converted into the corresponding stress-strain (σ-ε) curve in engineering variables by using the following relations:

(7) (8)


A0 are l0, respectively, the specimen initial cross section and the initial length (or the extensometer initial gauge length).

There are two basic types of stress-strain curves in metals, depending on whether or not they present a yield plateau. Figures 1 and 2 present both types, as well as the definition of the main material tensile parameters, which are the following:

• The elastic modulus (or Young´s modulus), E: corresponding to the slope of the initial straight line of the stress-strain curve, which corresponds to the linear-elastic behaviour of the material.

• The yield stress, σy: in case the yield plateau exists, or the proof stress, σ0.2, in case there is no such plateau (continuous stress-strain curve), which correspond to the stress level causing a permanent strain of 0.2% (see Figure 2).

In those materials having yield plateau it is possible to distinguish between the upper yield stress (σy

upp) and the lower yield stress (σylow), as shown in Figure 3. Gene-

rally, as it is done in both VINDIO 1.0 and FITNET FFS, the value taken for assessment purposes is the lower yield stress, in order to take material properties that lead to conservative results. In those cases where there is no information on whether the available value represents the lower or the upper yield stress, it will be considered by defect that it represents the upper yield stress, the lower yield stress being estimated through equation (9):

(9)

• The ultimate tensile strength, σu: which is the maximum stress value of the stress-strain curve.

Finally, from a tensile test, it is possible to obtain a third curve when both the stress and the strain are represented in true variable (σv-εv), which differ from the engineering variables in the fact that they consider the specimens dimensions (cross section and length) existing


at each moment, and not the initial ones. Their definition and their relation with the engineering variables are gathered in the following expressions:

(10)

(11)

Figure 1. Stress-strain curve with yield plateau..

Figure 2. Continuous stress-strain curve (without yield plateau).


Figure 3. Definition of the lower yield stress and the upper yield stress in those materials having yield plateau.

VINDIO allows the tensile data to be inserted by three different ways, depending on the quality and detail of the material´s property data available. This leads to the three analysis levels (1, 2 and 3) described in Section 3.2.1.

2.3. MATERIAL FRACTURE PROPERTIES USED IN FRACTURE-PLASTIC COLLAPSE ANALYSES.

Together with the tensile properties, the fracture properties constitute fundamental data in fracture analyses.

As shown in Section 2.1, the fracture process may be caused by different micromechanisms depending on the magnitude of the plastic phenomena occurring at the crack tip. This makes that the fracture resistance data required for the analysis may be different: thus, in linear-elastic conditions, in which the plastic zone size is very small if compared to other relevant dimensions (e.g., component size, remanent ligament, etc), the fracture resistance considered is the fracture toughness, KIc. The resulting fracture analyses are limited to


fracture initiation, given that these situations corresponds to physical processes on which there is no stable crack propagation before the final fracture (or it is negligible).

In other occasions, associated to lager plastic zones, it is necessary to perform an elastic-plastic analysis of the fracture process. In such cases, the fracture parameter generally used is the J integral (also the CTOD, Crack Tip Opening Displacement) [1,4,5]. In the most general situation the material fracture toughness in terms of the J integral is actually a curve, JR or J-Δa, (Section 2.1), that allows the stable crack propagation occurring before the final failure to be calculated. The resulting analysis considers the whole material resistance capacity, providing more adjusted results than those obtained through elastic-plastic initiation analysis, given that the latest do not consider the additional material resistance developed during the stable crack propagation.

In certain occasions, the fracture test performed to determine the material JR curve do not develop stable crack propagation before the final failure, and the resulting characterisation parameter is a unique value named Jc. In other occasions, in which there is stable crack propagation, it is possible to define, from the JR curve (J-Δa), parameters such as J0.2 or JIc, which is obtained in the intersection between the JR curve and a straight line drawn at a Δa coordinate of 0.2 mm with a given slope defined in the standards [9]. From both Jc and JIc it is possible to derive fracture toughness parameters expressed in terms of stress intensity factor units:

(12)

(13)

In case of using KJc or KJIc it is important to notice that, despite they are obtained from a JR curve, the provide fracture initiation analyses (without the consideration of any stable crack propagation).

In any case, the obtainment of any of these fracture parameters (whether linear-elastic or elastic-plastic) must follow the conditions and procedures established in international standards (e.g., [9-13]).

Finally, the Charpy energy (Cν) [4,14,15], despite it does not represent a fracture toughness parameter, may be used to estimate the material fracture toughness. The resulting estimations


are generally very conservative and are expressed with stress intensity factor units (Kmat) and, then, providing fracture initiation analyses. The Charpy-Kmat correlations used in VINDIO are those gathered in the FITNET FFS Procedure, and are shown in Chapter 3, Section 3.2.2.

Exceptionally, in case the material works at temperatures corresponding to its fracture toughness Upper Shelf (ductile behaviour), it is possible to correlate the material Charpy energy with the material JR curve. The result, although conservative, allows ductile tearing analyses (stable crack propagation) to be performed.

With all this, the software allows the material fracture resistance properties to be inserted following three different formats (see Section 3.2.2).

2.4. FAILURE ASSESSMENT DIAGRAMS

In order to perform fracture-plastic collapse analyses, VINDIO uses Failure Assessment Diagrams (FADs), which allow very diverse situations to be analysed, from brittle fracture to plastic collapse, and represents the situation of the structural component being analysed through a point with coordinates (Kr, Lr).

In a fracture initiation analysis (without any stable crack propagation), Kr represents the situation of the structural component against fracture, and follows equation (14):

KI is the stress intensity factor and Kmat is the material fracture toughness, also expressed with stress intensity factor units (KIc, KJc, KJIc or Kmat estimations from Charpy values, Cν). The former is automatically defined by VINDIO by using the analytical solutions proposed in FITNET FFS [2] and once the user introduces the acting loads (or stresses) and defines the geometry of both the component and the crack being analysed. In case of using different solutions to those proposed by FITNET FFS, it will be explicitly commented in the information provided for each geometry, and also in Annex II of this manual. Concerning Kmat, there are three different formats to introduce fracture toughness data (see Section 3.2.2).

(14)


Lr, on the other hand, represents the situation of the structural component against plastic collapse, and follows equation (15):

P being the applied load and PL being the yield limit load, which is also automatically defined by VINDIO by using FITNET FFS [2] analytical solutions and once the user introduces the material tensile properties and the geometry of both the component and the crack being analysed. Also, in case of using different solutions to those proposed by FITNET FFS, it is explicitly mentioned in the information provided for each geometry, and also in Annex II of this manual.

In multiple occasions, the combination of component and crack being analysed presents two solutions for the yield limit load: the global yield limit load, which is associated to the overall yielding, and the local yield limit load, which corresponds to a local yielding of the ligament at the crack. For example, assuming a pipe containing an internal circumferential surface crack, the global limit load corresponds to the overall yielding of the section containing the crack (shading area in Figure 4), whereas the local limit load corresponds to that load causing the local yielding of the ligament at the circumferential crack (pointed in blue in Figure 4), which need not correspond to overall yielding, as the pipe may be able to sustain a load equal to the limit load with a fully penetrating defect.

Therefore, the global limit load, which considers larger amounts of yielded material, generates higher limit load values that those generated by the local limit load (they could be equal in limiting situations). Thus, the Lr values obtained through global solutions are lower or, in other words, local solutions provide more conservative results.

Once the FAD coordinates of the component have been defined, the situation of the resulting assessment point is analysed in relation to the Failure Assessment Line (FAL), which is defined from the material tensile properties and follows the general expression gathered in equation (16) [1]:

(16)

(15)


Generally, the higher the knowledge about the material stress-strain curve is, the lower is the conservatism of the analysis through more adjusted Failure Assessment Lines. (Section 3.2.1).

Figure 4. Pipe section containing an internal circumferential surface crack. Shading area related to global limit load, and pointed blue area related to local limit load.

When the assessment point, with coordinates (Kr,Lr), lies within the area defined by the FAL and the coordinate axes (point A, Figure 5), the component is considered to be in acceptable (safe) conditions, whereas if the component lies above the FAL (point C, Figure 5), the component is in unacceptable (unsafe) conditions. Failure conditions correspond to those situations on which the assessment point is located in the FAL (point B, Figure 5).


Figure 5. FAD assessment (initiation), showing the three possible situations in the component: A, acceptable; B, limiting (failure); C, unacceptable.

In case of performing ductile tearing analysis (with stable crack propagation before final failure), the FAL is identically defined, but the fracture (limiting) condition is defined through the corresponding tangent Kr-Lr curve, which is obtained by considering different stable crack propagation values. This is done, firstly, defining the Kmat(Δa) curve from the material JR (J(Δa)) curve, considering the relation between the stress intensity factor K and the J integral (equation (5)) [1,4,5]:

(17)

Secondly, different values of crack propagation are considered (Δa1, Δa2... Δan), leading to different pairs of (Kr, Lr) values:

(18)

(19)


Finally, the resulting points are represented in the FAD, defining the corresponding assessment line. If such line cuts the FAL, the situation of the component is considered to be acceptable; if it does not cut the FAL, the situation is unacceptable. The limiting condition is provided by the assessment line that is tangent to the FAL. Figure 6 [1] shows an example of this type of assessment:

Figure 6. FAD assessment (ductile tearing) showing the three possible situations in the component: A1, acceptable; B1, limiting (failure); C1, unacceptable.

Moreover, the tangent point corresponds to the stable crack propagations occurring before the final fracture.

Finally, the position of the assessment point (or tangent point, in case of tearing analysis) provides information about the predominant fracture mechanism. Following FITNET FFS [1], failures represented by assessment points above the Kr/Lr = 1.1 line (or in the area defined by Kr/Lr > 1.1) are fracture dominated, whereas failures represented by points located below the Kr/Lr = 0.4 line (Kr/Lr < 0.4) are plastic collapse dominated. In intermediate situations (0.4 < Kr/Lr <1.1) fracture and plastic collapse are competing failure mechanisms.


2.5. FATIGUE CRACK PROPAGATION

Fatigue is a phenomenon that comprises crack initiation and their subsequent subcritical propagation till final fracture, and it is caused by the action of variable stresses. Therefore, it may appear in those structures subjected to variable loading conditions.

Depending on the variable stress conditions, and also on the existence (or not) of previous defects, there are different fatigue analysis situations, as shown in Figure 7.

Figure 7. Categories of fatigue [16].

As shown in the figure, it is possible to distinguish between fatigue of uncracked components and fatigue of cracked components.

Fatigue of Uncracked Components takes place in those situations where there are no pre-existing cracks. Most of the life of the component is, therefore, occupied by the crack initiation process. This category of fatigue may be divided into High Cycle Fatigue and Low Cycle Fatigue.

In the former case, stresses are below the material yield stress. It is very common in rotary equipment (wheels, axes, etc) and it is analysed through a stress approach. The first significant

Fatigue

Fatigue of uncracked componentsThere are no pre-existing cracks. Final fracture is controlled by crack initiation.

High cycle fatigue• > 10.000 cycles to fracture.• Stresses lower than yield stress.

Low cycle fatigue• < 10.000 cycles to fracture.• Stresses higher than yield stress.Fatigue of cracked components

There are pre-existing cracks. Final fracture is controlled by crack propagation.


approach was provided by Wöhler [17], who noticed that low stress variations could cause the failure of structural components, and proposed a tool that it is still widely used: the S-N curves. These curves provide a direct relation between the applied stress variation and the number of cycles to failure.

In the latest case the applied stresses caused by variable loading are higher than the material yield stress, with significant plasticity effects. It is typical in, for example, certain nuclear components and it is usually analysed through a strain approach.

Finally, Fatigue of Cracked Components corresponds to those situations where there is a pre-existing crack and, therefore, fatigue life is governed by the subcritical crack growth preceding the final fracture. Fatigue analysis, in such situations, intends to predict the crack evolution, determining (for example) the number of cycles before fracture, or the maximum allowable stress variation in the component that ensures a certain number of applied loading cycles. This type of fatigue is common in large structures (ships, bridges, etc) and, specially, in those containing welds.

VINDIO analyses fatigue crack propagation processes (Fatigue of Cracked Components), as explained in Chapter 4, and not fatigue crack initiation processes. Therefore, it does not cover the Fatigue of Uncracked Components.

There are many situations on which after the inspection of a given structure or component, or because of the anomalous behaviour observed on any of them, a crack (or several cracks) is detected. In such cases the fatigue approach that must be followed is necessarily different to the Fatigue of Uncracked Components. Because there is a pre-existing crack, the life of the structure (or component) is governed by the crack propagations (initiation has already occurred).

Large structures subjected to variable loads, and specially those containing welds (bridges, nuclear components, ship hulls...), usually have cracks. However, such cracks do not necessary jeopardise the structural integrity of the referred structures, which may continue their operation in perfectly safe conditions. The analysis of these situations requires considering not only the stress range, but also the crack size and the stress intensity factor. Paris [18] observed experimentally that the crack propagation rate


depends on the stress intensity factor variation, ΔK, and also on the material, following the well-known Paris law:

(20)

C and m being material constants and ΔK:

(21)

In this case, again, the fatigue process (and therefore constants C and m) depends on the average applied stress (or the R parameter [19]), the material microstructure, the loading frequency, the shape of the loading wave, the environment, and the temperature.

Figure 8 represents the propagation process of a given crack in a given component. Three zones may be distinguished: • Zone A: Slow crack propagation zone, which is associated to the material’s fatigue

crack propagation threshold, ΔKth. In case the applied stress intensity factor range (ΔK) is lower than such threshold, the crack does not propagate. This zone is mainly influenced by the microstructure of the material, the environment and the applied average stress.

• Zone B: The crack propagation follows the Paris law. In case the axes are represented in logarithmic scale, it results a straight line whose slope is, precisely, m. The influence of microstructure and average stress is much lower than in Zone A.

• Zone C: Accelerated crack propagation rate. Once the crack enters this zone, its growth progressively accelerates until it reaches its critical size and failure takes place. This latest moment is, actually, a fracture-plastic collapse problem.


Figure 8. Different zones in fatigue crack propagation behaviour.

Finally, it is important to notice that, given the Paris law is based on a linear-elastic parameter (KI), its application is limited to those situations on which plasticity phenomena at the crack tip have a limited size, that must necessarily be reduced when compared to other relevant dimensions (crack size, grain size, component dimensions...). There are situations on which the plastic zone size is comparable to other relevant dimensions (e.g., short cracks fatigue). In such cases it is necessary to consider fatigue crack propagation laws that take into account plasticity effects at the crack tip (e.g., using the J integral as the governing parameter). A detailed explanation about these cases may be found in literature (e.g., [19-21]).

22 3. Fracture-plastic collapse analysis following VINDIO

3. 3.1. GENERAL OVERVIEW

Performing fracture-plastic collapse assessments requires the user to enter data concerning the material mechanical properties, the geometry of both the component and the crack, and the loading conditions. Thus, in a Failure Assessment Diagram (FAD), the component is represented by an assessment point (or curve) whose situation on the proper FAD, determines whether or not the component operates under acceptable (safe) conditions. In this context, the user has three analysis routes for fracture-plastic collapse analyses following VINDIO, named ASSESSMENT, SEARCH and SCANNING:

• ASSESSMENT: all the analysis variables are known (material, geometry and loads), and then the result of the analysis is the determination of the component situations against fracture-plastic collapse (following the procedure explained in Section 2.4). The user will notice that the sequence followed for entering the data is, precisely, that mentioned above: as long as the material data have not been introduced, it is not possible to enter geometry data. Likewise, once the geometry has been introduced (both component and crack), it is possible to enter the acting loads (or stresses).

• SEARCH: in this case, it is not the objective to analyse a situation on which all the varia-bles are defined, but to determine, once two of the variables are known (e.g., material and geometry), the critical value of the third variable (e.g., the load), that is, that one providing an assessment point which lies exactly over the Failure Assessment Line (or, in case of ductile tearing analysis, that one providing a Kr-Lr curve that is tangent to the FAL).

• SCANNiNG: this type of analysis allows different values of a given variable to be conside-red, the rest of variables being fixed. More precisely, VINDIO 1.0 allows the results to be obtained for a given number (up to 10) of crack sizes or applied loads.

The different situations arising from VINDIO are shown in the tutorials gathered in Chapter 5. The software allows the user to choose the most convenient analysis route.

23 3. FRACTURE-plASTiC COllApSE ANAlYSiS FOllOWiNG ViNDiO ViNDiO USER´S MANUAl

Now, Section 3.2. describes the different possibilities provided by VINDIO concerning the treatment of material data, geometry and acting loads (or stresses), all of them being applicable to the above mentioned three analysis routes.

3.2. MATERIAL DATA

3.2.1. TENSILE PROPERTIES

VINDIO allows the tensile properties (Section 2.2) to be entered following three different levels:

• level 1: it just requires to know the material yield stress (or proof stress, depending on whether or not the tensile curve has a yield plateau) and the modulus of elasticity (E).

• level 2: it requires to know the yield stress (or proof stress), the ultimate tensile strength (σu), and the modulus of elasticity. It this level, the user has a database with the tensile properties of common steels and metallic alloys [1,2].

• level 3: it requires the whole stress-strain curve.

It is important to notice that, generally, the higher the knowledge about the tensile properties (that is, when going from Level 1 to Level 3), the higher the accuracy of the analysis is.

3.2.1.1. lEVEl 1

In this level the material properties considered in the analysis represent, due to the lack of knowledge, a lower bound of the actual ones.

In those materials having yield plateau, the stress level at which the plateau takes place is taken as the yield stress. In many occasions, it is possible to distinguish (within the yield plateau) between the upper yield stress (σy

upp) and the lower yield stress (σylow), as shown in

Section 2.2, where it was stated that the value that must be entered in VINDIO is the latest one in order to consider material parameters providing conservative results. Also, when the nature of the available yield stress (upper or lower) is unknown, it will be considered by

24 ViNDiO USER´S MANUAl 3. FRACTURE-plASTiC COllApSE ANAlYSiS FOllOWiNG ViNDiO

default that it represents the upper yield stress, and the value entered in the software will be an estimation of the lower yield stress provided by equation (9).

In those materials without yield plateau, the proof stress will be considered in the analysis, as explained in Section 2.2.

Following the formulation provided by the FITNET FFS Procedure [1-3], the equations defining the Level 1 Failure Assessment Line (FAL) in those materials exhibiting yield plateau are:

(22)

(23)

In case there is no yield plateau, the formulae corresponding to Level 1 analysis are:

(24)

(25)

where

(26)

The situation of the analysed component, defined by the position of the assessment point (with coordinates (Kr,Lr)) regarding the FAL, determines whether or not it is working under acceptable (safe) conditions (see Section 2.4).

In those situations on which, together with the yield (proof ) stress, Charpy correlations are used for the estimation of the fracture toughness, Level 1 of VINDIO 1.0 corresponds to FITNET FFS [1] Option 0.

Level 1 should only be used when there are not more available data. When such additional data are available, it is recommended to follow higher analysis levels (Level 2 or Level 3).


3.2.1.2. lEVEl 2

It is the minimum recommended analysis level. It also uses material properties (yield or proof stress, and ultimate tensile strength) that lead to a conservative estimation of the actual material resistance, but in this case the resulting conservatism is lower than that obtained through Level 1.

Following FITNET FFS formulation, the equations defining the FAD for those materials exhibiting yield plateau are:

(27)

(28)

(29)

(30)

where:

(31)

(32)

(33)

(34)


σyupp is the upper yield stress, whereas σy

low is the lower yield stress (see Section 2.2). As explained above, in case only the upper yield stress is known, the corresponding lower yield stress is estimated through equation (9).

For those materials that do not have yield plateau, the equations defining the FAD in Level 2 are:

(35)

(36)

(37)

where

(38)

(39)

(40)

In both cases (with and without yield plateau), the location of the assessment point regarding the Failure Assessment Line (FAL) determines the component situation against fracture-plastic collapse failure (see Section 2.4).

In those cases where both the yield (or proof) stress and the ultimate tensile strength are used together with fracture toughness (Kmat) values, Level 2 in VINDIO corresponds to FITNET FFS Procedure Option 1. To that end, it is additionally necessary to obtain Kmat from, at least, three toughness tests characterising fracture initiation (brittle or ductile, depending on the case).

In this level, it is possible to use a database containing the typical tensile properties of a number of common materials.


3.2.1.3. lEVEl 3

This level defines the FAD from the material stress-strain curve, which requires its detailed definition including any significant detail (e.g., yield plateau). Thus, the analysis considers the material actual properties, not conservative estimations (as it happens in levels 1 and 2), and the final assessment results are the most accurate.

Following the formulation proposed in FITNET FFS, the FAD is defined through the following equations:

(42)

where εr is the strain corresponding to a given stress, σr, which is equal to Lr·σy

low, in case the material does have yield plateau, or Lr·σ0.2 in case the material does not have any yield plateau. In both cases, stresses and strains are defined in true variables (not engineering variables). As in previous levels, the location of the assessment point regarding the FAL, defines the situation of the component against failure (Section 2.4).

Finally in those situations where, together with the material stress-strain curve, fracture toughness values are considered in the analysis, Level 3 in VINDIO coincides with FITNET FFS Procedure Option 3. To that end, it is additionally necessary to obtain Kmat from, at least, three toughness tests characterising fracture initiation (brittle or ductile, depending on the case).

3.2.2. FRACTURE PROPERTIES

VINDIO presents three different ways for the entering of the material fracture properties and fracture-plastic collapse assessments. These ways, here called formats, depend on the available information, and are the following:

(41)


• Format 1: it correlates the Charpy energy (Cν) with the fracture toughness through the application of equations that depend on where the material is regarding its ductile to brittle transition zone (Upper Shelf, Transition Zone, Lower Shelf ) (see Section 3.2.2.1).

• Format 2: it expresses the fracture resistance in terms of stress intensity factor, allowing fracture initiation analyses (not ductile tearing) to be performed. In this format, it is pos-sible to use a database containing the typical fracture properties of a number of common materials [1,2].

• Format 3: it requires knowing the whole material J-∆a curve, allowing ductile tearing analyses to be performed.

3.2.2.1. FORMAT 1

In those situations where there are no data about the material fracture toughness, but there are data about the corresponding Charpy energy (Cν) value at the assessment temperature, it is possible to establish correlations between such energy and the fracture toughness. The correlation that must be used on each case depends on where the material is being used (brittle zone - Lower Shelf-, Transition Zone or, finally, ductile zone – Upper Shelf-) [1,4].

Many materials exhibit a fracture behaviour that depends on the working temperature: at low temperatures they are brittle, at high temperature they are ductile, and at intermediate temperatures they present a ductile-to-brittle transition behaviour. Charpy tests do not provide toughness values, but they can reproduce such transition behaviour, in such a way that if Charpy values are represented against temperature, the results would be similar to those shown in Figure 9.

Following the FITNET FFS Procedure, the brittle behaviour zone is defined as that one where ductile fracture represents less that 20% of the total fracture surface, and also where the Charpy energy is lower than 27 J; the ductile zone is that one where the 100% of the fracture surface is ductile; finally, the zone located between brittle and ductile zones is known as the Transition Zone.


The user will be able to perform fracture assessments through the correlations between Charpy values and the fracture toughness, following the formulae proposed in FITNET FFS [1]. Thus, in the brittle zone, the correlation between the Charpy energy (Cν) and the fracture toughness (Kmat) is:

(43)

where B is the thickness of the component being analysed (in mm). This expression is suitable for a wide variety of steels [1].

Figure 9. Charpy energy against test temperature graph, showing the fracture surfaces at the Lower Shelf (brittle) and the Upper Shelf (ductile).

In the Transition Zone, the toughness may be estimated by using equation (44):

(44)


T being the working temperature (in ºC), T27J being the temperature at which the Charpy energy is 27 J (in ºC), and measured in a standard 10 mm x 10 mm Charpy V specimen), and Pf being the probability of fracture toughness being lower than Kmat. This latest datum (Pf) must be defined by the user in order to account for the high scatter existing in the ductile-to-brittle transition zone for both Cν and Kmat values.

Finally, the correlation used in the ductile behaviour zone is the following:

(45)

where E is the elastic modulus and ν Poisson´s ratio. The applicability of equation (45) is limited to yield stress values between 170 and 1000 MPa and Upper Shelf energies (Cν) between 20 and 300 J [1]. The resulting assessment corresponds to an initiation analysis (not ductile tearing).

Once Kmat has been defined, it is possible to define the Kr coordinate to be used in the FAD, following the methodology outlined in Section 2.4.

The Charpy energy in the Upper Shelf also allows ductile tearing analyses to be performed by using the following correlation [1]:

(46)

where T is the working temperature (in ºC) and σy is the corresponding yield stress. The correlation has been proved to provide conservative estimate of the mean J-Δa curve for materials with yield stresses between 171 and 985 MPa, and Cν values in the range 20-300 J, corresponding to an overall probability level of 5%, and is applicable at temperatures from -100 to 300 ºC [1]. Once the JR curve (J-Δa) has been estimated, a ductile tearing analysis can be performed following the methodology gathered in Section 2.4.


3.2.2.2. FORMAT 2

Format 2 requires fracture resistance data obtained from fracture toughness tests, and allows fracture initiation analysis to be performed.

In those cases where linear-elastic fracture mechanics conditions are fulfilled, as well as plane strain conditions, the fracture resistance is KIc; when the fracture toughness expressed in stress intensity factor units is obtained from the J integral (elastic-plastic parameter), the fracture resistance is named KJc or KJIc, whose expressions have been previously gathered in equations (12) and (13), respectively (Section 2.3).

Moreover, VINDIO allows the fracture toughness within the ductile-to-brittle transition zone to be obtained through the Master Curve methodology, which requires the material transition temperature (T0) to be known. This temperature corresponds to a median toughness of 100 MPam1/2 for 25 mm thick specimens [1]:

where B is the component thickness (in mm), Pf is the probability of fracture toughness being lower than Kmat, and T is the working temperature (in ºC).

In this format, it is possible to use a database containing the typical fracture properties of a number of common materials [1,2].

Analogously to Format 1, once Kmat has been defined, Kr coordinate can be defined following the methodology outlined in Section 2.

3.2.2.3. FORMAT 3

It requires the whole material JR curve (J-∆a) to be known, which is defined through the material constants A and n, following equation (48) (Section 2.1):

(48)

(47)


The resulting analysis is a ductile tearing analysis that allows the stable crack propagation occurring before the final failure to be determined, following the methodology gathered in Section 2.4.


3.3. COMPONENT AND CRACK GEOMETRIES

VINDIO comprises a wide variety of both crack and component geometries which allow most of the practical situations to be covered.

Firstly, the user must select the type of component to be analysed between the following options: round bars, pipes/cylinders, plates, spheres, and fracture toughness specimens (CT and SENB). Once the component geometry has been selected, VINDIO 1.0 activates the button corresponding to the crack geometry. Finally, once the crack type has also been defined, it is possible to enter all the geometric dimensions (component and crack) that are necessary to complete the assessment.

The whole list of geometries considered in VINDIO (34 combinations) is gathered in Table 1.

1. ROUND BARS

1.1. Straight fronted crack 1.2. Fully circumferential crack


1. ROUND BARS (continued)

1.3. Semicircular surface crack 1.4. Embedded crack

2. PIPES OR CYLINDERS

2.1. Through thickness axial crack. 2.2. Finite axial surface crack (internal)


2. PIPES OR CYLINDERS (continued)

2.3. Extended axial surface crack (internal) 2.4. Finite axial surface crack (external)

2.5. Extended axial surface crack (external) 2.6. Finite axial crack (embedded)



2.7. Extended axial crack (embedded) 2.8. Through-thickness circumferential crack

2.9. Finite circumferential surface crack (internal)

2.10. Extended circumferential surface crack (internal)



2.11. Finite circumferential surface crack (external)

2.12. Extended circumferential surface crack (external)

2.13. Finite circumferential crack (embedded)

2.14. Extended circumferential crack (embedded)



2.15. Circumferential compound (through thickness + extended) crack

3. PLATES

3.1. Central through-thickness crack 3.2. Surface finite crack

39 3. FRACTURE-plASTiC COllApSE ANAlYSiS FOllOWiNG ViNDiO ViNDiO USER´S MANUAl 1.0

3. PLATES (continued)

3.3. Surface extended crack 3.4. Embedded finite crack

3.5. Embedded extended crack 3.6. Edge crack

3.7. Double edge crack 3.8. Corner crack



3.9. Corner crack at a hole (symmetric) 3.10. Corner crack at a hole (single)

4. SPHERES

4.1. Through-thickness equatorial crack 4.2. Surface finite crack (internal)


4. SPHERES (continued)

4.3. Surface finite crack (external)

5. FRACTURE TOUGHNESS SPECIMENS

5.1. CT specimen 5.2. SENB specimen

Tabla 1. List of geometries (component and crack) considered in VINDIO Cracks with * are available under request.


3.4. ACTING LOADS

Once the material mechanical properties are known (both tensile and fracture properties), and once the geometry of both the component and the crack has been defined, the last data defining whether or not the cracked component is under safe or unsafe conditions are the acting loads.

The type of loads depends on the type of component and crack. For example, the assessment of a certain pipe may require the internal pressure to be defined, whereas this type of load has no sense in a round bar. Moreover, in those situations corresponding to complex stress fields the user can introduce the stress profile in the analysed section through the stress values existing in a number of points along such section, or through polynomial expressions. In any case, following the FITNET FFS [1], the stress state is reduced to a combination of membrane stress and bending stress by using equations (49) and (50):

(49)

(50)

σm being the membrane stress, σb being the bending stress, σ is the stress distribution along the analysed section, and t is the thickness of such section.

The user is also required to distinguish between primary and secondary stresses. The former are those that contribute to both fracture and plastic collapse and, therefore, they must be considered when calculating both Kr and Lr (see Section 2.4); the latest are those that do not contribute to plastic collapse and, therefore, they only affect the fracture process (and then, Kr). One of the most typical example of secondary stresses are the residual stresses caused by welding processes.


In FAD analysis, secondary stresses must be considered in the definition of Kr, but not in the definition of Lr, which is only affected by primary stresses. Thus, in case both primary and secondary stresses exist, Kr is defined by equation (51):

(51)

KIp being the stress intensity factor corresponding to the primary stresses, KI

s being the stress intensity factor associated to the secondary stresses, K being the material fracture toughness, and ρ being a parameter that takes into account the plasticity correction due to the interaction between primary and secondary stresses, which is calculated following the methodology proposed in the FITNET FFS [1] and gathered in [22-24]. Equation (51) is, therefore, a particularisation of equation (14) to those situations on which stresses of different nature do coexist.

The distinction between primary and secondary stresses is a matter of some judgement [1]. The primary stresses are generated by applied external loads such as pressure, deadweight or interaction from other components. Secondary stresses are generally generated as a result of internal mismatch caused by, for example, thermal gradients and welding processes. These stresses will be self-equilibrating (i.e., the net force and bending moment will be zero) [1]. In case the user is not sure about the nature (primary vs. secondary) of the stresses, it is recommended to consider them as primary stresses.

Although in general thermal and residual stresses are self-equilibrating and therefore classed as secondary stresses, there are situations where they can act as primary stresses. In this sense, the user is suggested to check the guidance and recommendations gathered in structural integrity assessments such as the FITNET FFS [1], with the aim of establishing adequate criteria for the classification of the different acting stresses.

44 ViNDiO USER´S MANUAl 4. CRACk pROpAGATiON ANAlYSiS FOllOWiNG ViNDiO

4. CRACK PROPAGATION ANALYSIS FOLLOWING VINDIO

VINDIO has a fourth analysis route, this time related to fatigue, which is named PROPAGATION and which completes the analysis routes gathered in VINDIO (together with ASSESSMENT, SEARCH and SCANNING). This route allows crack propagation analysis by using the Paris law to be performed. The unknown in the analysis will be, at the user’s election, the initial crack size, the final crack (critical or not), or the applied fatigue cycles.

The methodology of the analysis is simple, presents an analogous environment to that found in fracture-plastic collapse analyses, and it is based on both the Paris law (equation (20)) and the use of the same stress intensity factor and limit load solutions used in the analysis routes gathered in Section 3. In order the PROPAGATION analysis to be performed, the user must first identify the unknown, which is necessarily one of the three variables appearing during the Paris law integration: the number of fatigue cycles, the initial crack size and the final crack (which may be the critical one or not).

Once the unknown has been defined, the following step consists on the definition of the material mechanical properties, this time also including the material constants (C and m) of the corresponding Paris law and the material fatigue threshold, ΔKth. Concerning tensile and fracture properties, the user may choose between levels 1 to 3 (in case of tensile properties), and between formats 1 and 2 (in case of fracture properties), analogously to the indications given in Chapter 3. Here, it is important to notice that in case the fatigue process does not lead to the final fracture, it is not necessary to enter neither the tensile properties nor the fracture properties.

Therefore, the user must define two of the integration variables, the third one being the unknown of the analysis to be determined by the software. For example, once the initial crack and the critical crack are defined, VINDIO provides the number of cycles to fracture; analogously, once the final crack size and the number of applied cycles have been defined, VINDIO provides the initial crack size. Concerning the final crack size, in many practical situations it does coincide with the critical crack size (when fatigue leads to final failure). The user may indicate this circumstance directly, and then the software automatically determines such critical size through a SEARCH-type analysis (and then, by using the FAD methodology), without any further considerations provided by the user.

45 5. Tutorials

This chapter presents four tutorials whose objective is to familiarise the user with VINDIO en-vironment, as well as to the different possibilities offered by the software when performing the different types of analysis.

As shown above, VINDIO presents three analysis routes related to fracture-plastic collapse (ASSESSMENT, SEARCH and SCANNING) and one route related to fatigue (PROPAGATION). Each tutorial corresponds to one of these four routes.

5.1. TUTORIAL 1: ASSESSMENT OF AN IN-SERVICE COMPONENT

In this first tutorial a pipe containing an internal axial surface crack is going to be assessed. The initial data are gathered in Table 2.

MATERIAL GEOMETRY LOADS

σy 300 MPa

Pipe containing an internal axial surface crack

Internal pressure 8.2 MPa

σu 500 MPa

Material with yield plateau

E 200 GPa Pipe

Ri 100 mm

B 8.5 mm

W 2000 mm

KIC 50 MPa·m1/2 Crack

2c 4 mm

a 2 mm

Table 2. Initial data for Tutorial 1.

46 ViNDiO USER´S MANUAl 5. TUTORiAlS

It can be noticed that all the variables implied in the analysis are known, so the analysis consists on the assessment of the component against fracture-plastic collapse.

The first screen the user sees in VINDIO is shown in Figure 10, and allows choosing one of the different analysis routes provided by the software (ASSESSMENT, SEARCH, SCAN-NING, AND PROPAGATION). In this tutorial, the ASSESSMENT route must be chosen. After that, material data must be entered, firstly the tensile data and, secondly, fracture data. To do so, it is necessary to click on the button “Tensile data” (Figure 11).

Figure 10. Main (first) screen in VINDIO, whe-re the type of analysis must be selected.

Figure 11. ASSESSMENT analysis route main screen, where it is first necessary to enter the tensile data.

47 5. TUTORiAlS ViNDiO USER´S MANUAl

A new screen appears then, and the user may check that there are three possible analysis levels, depending on the available tensile data (see Section 3.2.1). In this tutorial, both the yield stress and the ultimate tensile strength are known, so Level 2 is the most adequate. The user must click on Level 2 and introduce the corresponding data, as shown in Figure 12, and without any need of using the database. Also, it must be indicated that the material does have a yield plateau.

Now the user must click on “Accept” (Figure 12) and VINDIO comes back to the ASSESSMENT route main screen, where the button “Fracture data” (see Figure 11) has automatically been activated. It can also be noticed that tensile data, which have been previously entered, do appear on the screen (Figure 13).

Moreover, the user may click on the top-right icon in Figure 14, and the FAD appears on the graph, given that its definition just requires the tensile data to be known.

Figure 12. Tensile data screen, where Level 2 has been selected.


Figure 13. Capture of the ASSESSMENT route main screen, where the tensile data appear once they have been previously entered.

Figure 14. Capture of the ASSESSMENT route main screen, showing the resulting FAD in Tutorial 1.

The user may click on the button “Fracture data”, and the screen shown in Figure 15 appears. It can be noticed that the user has to choose between three different formats. Because in this tutorial the fracture resistance is provided in terms of plain strain fracture toughness, KIc, Format 2 must be selected. In Figure 15 it can be checked that the corresponding fracture toughness value (50 MPa·m1/2) has been entered.


Now, the “Accept” button must be clicked, and VINDIO comes back to the ASSESSMENT route main screen. Analogously to what happened with the tensile data, the user may noti-ce that the previously entered fracture toughness value is now shown on the screen (Figure 16), and also that the button “Component geometry” has been activated.

Figure 15. Fracture data screen, where Format 2 has been selected.

Figure 16. Capture of the ASSESSMENT route main screen, showing the fracture data.

The button “Component geometry” must now be clicked, and the screen shown in Figure 17 appears. The user must choose the pipe, and the software automatically comes back to the ASSESSMENT main screen, where the component geometry is now shown (see Figure 18) and where the button “Crack geometry” has been activated. When clicking this button, it appears the screen shown in Figure 19, where the user must choose the option “Finite axial


surface crack (internal)” and, automatically, the software comes back to the ASSESSMENT main screen, where now the selected crack geometry does appear (Figure 20).

Figure 17. Component geometry screen, where the pipe has been chosen.

Figure 18. Caption of the ASSESSMENT main screen, showing the selected component geometry, and where the button “Crack geometry” is active.


Figure 19. Crack geometry screen for pipes, where the option “Finite axial surface crack (internal)” has been chosen.

Figure 20. Caption of the ASSESSMENT main screen, showing both the component and the crack geometries.

The user may notice that the button “Geometric parameters” (see Figure 11) is now active in the ASSESSMENT main screen. Therefore, this button must be clicked and the correspon-ding parameters must be entered in the screen shown in Figure 21 (which automatically appears when clicking the mentioned button).


Figure 21. Geometric parameters entered in Tutorial 1.

Once the different values have been entered, the button “Accept” must be clicked, and the software comes back to the ASSESSMENT main screen, where, as usually, the entered data do appear (Figure 22).

Figure 22. Caption of ASSESSMENT main screen, showing the entered geometric parameters.

All the data related to the material and geometry has been entered. The last set of data to be entered is that related to the acting loads. The user may notice that the ASSESSMENT main screen present two tabs for this purpose (see Section 11). One of them corresponds to the primary loads; the other corresponds to the secondary loads. In this tutorial, the only acting load is the internal pressure, which is a primary load (see Section 3.4), so only the button “Primary loads” must be clicked. When clicking in such button, it appears the screen shown in Figure 23. The user can now enter the internal pressure (8.2 MPa) and click the button “Accept”, coming back to the ASSESSMENT main screen, where the acting load is now shown (see Figure 24).


Figure 23. Screen showing how the acting pressure is entered in the software.

Figure 24. Caption of ASSESSMENT main screen, showing the acting load (pressure, primary load).

At this point, all the data required to perform an ASSESSMENT analysis have been entered and, therefore, it is possible to determine the component situation against failure in a FAD. To do so, the user just needs to click on the corresponding icon, which is a calculator placed at the right of the ASSESSMENT main screen (Figure 11), that it is activated once the material, geometry and loading data are known.

When clicking on the calculator icon, a new screen appears (Figure 25) allowing the as-sessment to be better described or refined. More precisely, the user may indicate on which point of the crack front is the assessment performed (point A vs. point B), which limit load must be chosen (global vs. local, as explained in Section 2.4), and whether or not the internal pressure acts on the crack surfaces.


In this tutorial, point A, global limit load and the pressure acting on the crack surfaces have been selected (Figure 25). Here, it is important to notice that in all these cases, both options may be selected, the FAD presenting a specific assessment point for each resulting combination.

Figure 25. Assessment refinement.

When clicking on “Accept” in Figure 25, the FAD appears (Figure 26) and the component situa-tion against failure can be checked. In this case, the assessment point (green) lies within the safe area. Also, the software provides the corresponding Reserve Factor (RF), which is defined by the following relation (see Figure 26) [23]:

(52)


Once the ASSESSMENT has been finished, the user may now check what would happen in case the acting pressure increases to 40 MPa. To do so, it is enough to click on the button “Primary loads” and enter the new acting internal pressure. Once done, the user must click on “Accept” and the software comes back to the ASSESSMENT main screen, where the new pressure does appear (Figure 27) and where the user must click on the calculator icon, kee-ping the same conditions of the previous assessment (point A, global limit load and the pressure acting on the crack surfaces point). The assessment point (red) is now located wi-thin the unsafe area, as shown in Figure 28.

Figure 26. FAD result of the component being analysed (green point), which is in acceptable (safe) conditions.


Figure 27. Caption of ASSESSMENT main screen, showing the new acting pressure.

Figure 28. FAD assessment of the component being analysed when the pressure increases to 40 MPa. The assessment point (red) lies within the unacceptable (unsafe) area.

57 5. TUTORiAlS ViNDiO USER´S MANUAl 57

5.2. TUTORIAL 2: CRITICAL LOAD SEARCH

This second tutorial shows how to calculate the critical load in a plate containing a surface finite crack (SEARCH route). The initial data are shown in Table 3:


σy 450 MPa

Plate containing a surface finite crack

Tensile ¿?

σu 700 MPa

Material without yield plateau

E 200 GPa PlateW 150 mm

B 25 mm

JA= 2n= 0.65J units = KN/m Crack

2c 80 mm

a 10 mm

a/2c 0.125


As done in Tutorial 1, the user must first select the analysis route to be followed. In this case it is intended to determine a critical parameter (critical load), so the route to be selected is SEARCH (Figure 29).

Figure 29. Main (first) screen in VINDIO, where the type of analysis (SEARCH) must be selected


Then, the user must choose the critical parameter to be determined. In this case, it is the critical load, so the corresponding button (“Loads”) must be clicked (Figure 30).

Figure 30. Selection of the critical parameter.

Once the parameter to be determined has been defined, the SEARCH main screen does appear. It may be notice that it is equal to that used in the ASSESSMENT route. Therefore, the user must first introduce the tensile data by clicking on the corresponding button. Figure 31 shows the data to be entered (in agreement with Table 3), following Format 2. Once finished this action, the user must click on “Accept” and the software comes back to the main screen.

Figure 31.Tensile data screen, where Level 2 has been selected.


Now it’s time to enter the fracture properties, by clicking on the button “Fracture data”. In this tutorial the whole JR curve is provided (ductile tearing analysis), so Format 3 must be followed (Figure 32). Once the corresponding button has been clicked, the screen shown in Figure 33 does appear, and coefficients A and n (see Section 3.2.2) can be entered. It can also be observed that both plane strain conditions and a Poisson ratio of 0.3 (standard value for steels) have been entered.

Figure 32. Fracture data screen, where Format 3 has been selected.

Figure 33. Definition of JR cur-ve through A and n coefficients.


Now, if the user clicks on “Calculate” (once A and n have been introduced), both the JR curve (J-Δa) and the K-Δa curve appear on the right side of the screen (see Figure 33). By clicking on “Accept” the software returns to the SEARCH main screen.

Analogously to Tutorial 1, the next step consists on the introduction of both the component and the crack geometry. In this case, it is a plate containing a surface finite crack, the corres-ponding captures being shown in figures 34 and 35.

Once the type of component and crack have been selected, the screen shows in Figure 36 does appear, on which the different dimensions associated to this tutorial (see Table 3) can be directly entered.

After clicking in “Accept” the software returns to the main screen, whose aspect at that mo-ment is shown in Figure 37.

The last variables to be defined are the loads. To do so, the button “Primary loads” must be clicked, and a new screen asks the user to define the unknown load (within those available for the geometry being analysed). In this case, the load “F” must be selected, given that it is the unknown in Tutorial 2 (see Figure 38).

Figure 34. Component geometry screen, where the plate has been chosen.


Figure 35. Crack geometry screen for plates, where the option “Surface finite crack” has been chosen.



Figure 37. SEARCH route main screen.

Figure 38. Selection of the unknown load. Here, it must be chosen between the tensile load and the bending moment (the pressure not being available for this geometry).

After selecting the unknown, another screen appears on which the user may enter the rest of the loads acting in the component (which must be known). In this case, there is no need to enter any additional load, so the user must click on “Accept” (Figure 39).


Figure 39. Additional loads input (if any).

At this moment, the calculator icon is activated, given that the problem being analysed is completely defined (see Figure 40). By clicking on such icon, VINDIO requires the user to define both the point on which the assessment must be performed (point A, in this case) and the type of limit load to be considered (local limit load, in this case, as a conservative assumption), as shown in Figure 41.

Figure 40. SEARCH main screen, with the calculator icon being active.


Figure 41. Definition of the assessment point and the type of limit load.

By clicking in “Continue”, it may be observed how VINDIO proceeds to determine the critical load through an iterative process. When the iteration finishes, the critical load is defined (as long as the iteration is occurring, the load appears in red, whereas it appears in grey once the iteration is complete). Figure 42 shows the final result, which provides a critical load of 519.1 kN, with a corresponding stable crack propagation of 2.25 mm before the final failure.


Figure 42. Final solution of the SEARCH performed in Tutorial 2.

In case the user does not know which the worst combination is, it is possible to perform simultaneously the resulting four analyses (points A and B, combined with global and lo-cal limit loads). To do so, it is necessary to click on “Both” in the selection process shown in Figure 43, and the corresponding FAD will present the four searches (Figure 44), only one of them (the critical one) being tangent to the FAL. It can be noticed that in this case the critical situation corresponds to the combination of point B and local limit load, leading to a critical load of 330.44 kN. The colour code shown in the screen allows the four combi-nations to be identified.


Figure 43. Simultaneous selection of the four combinations.

Figure 44. Result of the simultaneous analysis of points A and B, combined with local and global limit loads.


5.3. TUTORIAL 3: CRACK SIZE SCANNING

This third tutorial presents an example of the SCANNING analysis route on which the results obtained for different crack sizes (from 4 mm up to 20 mm) are presented. The initial data are gathered in Table 4.


σy 500 MPaRound bar containing a fully circumferential crack Tensile (N)

Bending (N·mm)

125000

5175000


E 210 GPa Bar R 40 mm

Cν 6 J Crack a 4 mm-20 mm


As done in previous tutorials, the user must first select the analysis route to be followed. In this case it is intended to determine the situation of the component when it contains a crack with variable length, so it a SCANNING analysis route must be chosen, as shown in Figure 45.

Figure 45. Main (first) screen in VINDIO, where the type of analysis must be selected (SCAN-NING).


Once the SCANNING route has been selected the screen shown in Figure 46 does appear, where the user must select the variable on which the SCANNING process is going to be per-formed. In this case, the button “Crack size” must be clicked.

Figure 46. Selection of the type of variable on which the SCANNING process is performed

Once the variable has been selected, the software shows the SCANNING main screen, which is totally analogous to that shown in ASSESSMENT and SEARCH analysis routes. As done in pre-vious tutorials, the user must first click on “Tensile data”, and such data are introduced as shown in Figure 47. A similar process must be followed for fracture data (Figure 48). Given the initial data, Level 1 (in tensile data) and Format 1 (in fracture data) must be selected. Also, given that the material has a low Charpy energy (6 J), the material has a significantly brittle behaviour, so the corresponding Toughness-Charpy correlation must be selected.



Figure 48. Fracture data screen, where Format 1 (Lower Shelf ) has been selected.

The user must now click on “Accept” and the software comes back to the SCANNING main screen, where the fracture toughness estimation obtained through the Charpy-toughness correlation is now shown on it (Figure 49).

Figure 49. Caption of SCANNING main screen, showing the fracture toughness estimation.

In the next step, the geometry must be defined. To do so, the user must, firstly, select the geometry of the component (round bar), as shown in Figure 50, and secondly, select the geometry of the crack (Figure 51). Finally, the different geometric parameters are entered as shown in Figure 52.


Figure 50. Component geometry screen, where the round bar has been chosen.

Figure 51. Crack geometry screen for round bars, where the option “Fully circumferential crack” has been chosen.



In order to complete the definition of the problem being analysed, once the software is again on the SCANNING main screen, the user must define the acting loads. Therefore, the button “Primary loads” must be clicked, and the screen shown in Figure 53 does appear, where the corresponding data have already been entered.

Figure 53. Screen showing the acting loads in Tutorial 3.


The user may finish now the analysis by clicking on the corresponding icon (calculator), and the results shown in Figure 54 appear on the screen (both graphically and tabulated). It can be noticed that the solution comprises ten assessment points, and also that the critical situa-tion corresponds to a 9.2 mm crack.

Figure 54. Results of the SCANNING analysis performed in Tutorial 3.


5.4. TUTORIAL 4: CRACK PROPAGATION ANALYSIS

This fourth and last tutorial presents a crack PROPAGATION analysis, whose main data are gathered in Table 5. As shown in the table, it is intended to determine the final crack size after the application of 106 load cycles.

MATERIAL GEOMETRY Loads

σy 500 MPa

Round bar containing a semicircular surface crack

Bendingstress

+/- 110 MPa

σu --


E 200 GPa Bar r 100 mm

KIC 50 MPa √mCrack

ainitial 12.5 mm

Paris law: afinal ¿?

da/dN m/cycle

ΔKth 9 MPa √m

C 1.21e-12

m 3.46

N 1000000


Firstly, as shown in Figure 55, it is necessary to select the PROPAGATION analysis route.


Figure 55. Main (first) screen in VINDIO 1.0, where the type of analysis must be selected (PROPAGATION).

Then, the screen shown in Figure 56 does appear, on which it is necessary to define the pa-rameter to be calculated (the unknown). There are different options: a) Number of cycles until a certain crack size is reached (such crack size being, or not, the critical one); b) Crack size after the application of a certain number of cycles, and; c) Initial crack size that has lead to a given final crack size (critical or not) after the application of a certain number of cycles. In this tutorial, the user must select the second option (Figure 56).


Figure 56. Selection of the unknown in Tutorial 4.

Once the unknown has been selected, the user must click on “Accept” and VINDIO comes back to the PROPAGATION main screen shown in Figure 57.

Figure 57. PROPAGATION analysis route main screen.


Now the user must enter the tensile data (Figure 58), as it was done in previous tutorials, selecting Level 1.


After clicking on “Accept” and coming back to the PROPAGATION main screen, the fracture data must be entered. In case of PROPAGATION analysis, fracture data include the material constants defining the Paris law. Figure 59 shows the corresponding screen.


Figure 59. Fracture (Format 2) and fatigue data entered in Tutorial 4.

Figures 60 to 62 show how the geometric data (component and crack) must be entered.

Figure 60. Component geometry screen, where the round bar has been chosen.


Figure 61. Crack geometry screen for round bars, where the option “Semi-circular surface crack” has been chosen.


Finally, it is necessary to enter the acting loads (Figure 63). In this case, the acting loads are provided as bending stresses varying from + 110MPa to -110 MPa.


Figure 63. Acting loads entered in Tutorial 4.

Once almost all the data that are needed to define the propagation process have been en-tered, the user may click on the calculation icon (Figure 64). At that moment, the software requires the user to enter the last datum: the number of applied cycles, as shown in Figure 65. After clicking in “Accept”, the software performs the corresponding calculations until the solution is found, as shown in Figure 66. The figure shows both the crack size evolution and the corresponding final value.

80 ViNDiO USER´S MANUAl 5. TUTORiAlS80

Figure 64. PROPAGATION route main screen and calculator icon.

Figure 65. Number of applied cycles entered in Tutorial 4.


Figure 66. Final result obtained in the PROPAGATION analysis.

82 6. References

[1] FITNET Fitness-for-Service (FFS) Procedure - Volume I, Editors: M. Kocak, S. Webster, J.J. Jano-sch, R.A. Ainsworth, R. Koers, ISBN 978-3-940923-00-4, GKSS Research Centre, Geesthacht, Ale-mania, 2008.

[2] FITNET Fitness-for-Service (FFS) Annex - Volume II, Editors: M. Kocak, I. Hadley, S. Szavai, Y. Tkach, N. Taylor, ISBN 978-3-940923-01-1, GKSS Research Centre, Geesthacht, Alemania, 2008

[3] FITNET Fitness-for-Service (FFS) Case Studies and Tutorials – Volume III, Editors: M. Kocak, A. Laukkanen, F. Gutiérrez-Solana, S. Cicero, I. Hadley, ISBN 978-3-940923-02-8, en imprenta.

[4] Anderson T. L., Fracture Mechanics: Fundamentals and Applications, 2nd Edition, CRC Press, Boca Raton, 1995.

[5] Broek, D., Elementary Engineering Fracture Mechanics, 3rd Edition, Martinus Nijhoff, The Hague, 1982.

[6] UNE-EN 10002-1:2002, Materiales metálicos. Ensayos de tracción. Parte 1: Método de ensayo a temperatura ambiente, AENOR, 2002.

[7] ASTM E8/E8M-08, Standard Test Methods for Tension Testing of Metallic Materials, ASTM In-ternational, 2008.

[8] ASTM D638-08, Standard Test Method for Tensile Properties of Plastics, ASTM International, 2008.

[9] ASTM E1820-08a, Standard Test Method for Measurement of Fracture Toughness, ASTM In-ternational, 2008.

[10] ASTM E399-09, Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials, ASTM International, 2009.

[11] ASTM E1737-96, Test Method for J-Integral Characterization of Fracture Toughness, ASTM International, 1996.

83 6. REFERENCES ViNDiO USER´S MANUAl

[12] ASTM E1290-08, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Frac-ture Toughness Measurement, ASTM International, 2008.

[13] ESIS P1-92: ESIS Recommendation for Determining the Fracture Resistance of Ductile Mate-rials, European Structural Integrity Society, 1992.

[14] ISO 148-1: 2006, Metallic materials - Charpy pendulum impact test - Part 1: Test method, 2006.

[15] ASTM E23 - 07ae1, Standard Test Methods for Notched Bar Impact Testing of Metallic Materi-als, 2007.

[16] Ashby, MF., Jones, DRH., Engineering Materials 1: An Introduction to their Properties and Applications, 2nd Edition, Ed. Butterworth Heinemann, 1996

[17] Wöhler, A., Zeitschrift Für Bauwesen, Vol. 10, 1860, p. 583

[18] Paris, PC., Gomez, MP., Anderson, WP., The Trend in Engineering, Vol. 13, 1961, pp. 9-13

[19] Suresh, S., Fatigue of Materials, 2nd Edition, Cambridge Solid State Science Series, Cam-bridge University Press, 2006

[20] Bannantine, JA., Fundamentals of Metal Fatigue Analysis, Prentice Hall, 1989

[21] Stephens, RI. et al., Metal Fatigue in Engineering, Wiley-Interscience, 2000

[22] SINTAP: Structural Integrity Assessment Procedure for European Industry. SINTAP BRITE-EURAM Project BRPR-CT 95-0024, 1999

[23] BS7910: 2005, Guide on Methods for Assessing the Acceptability of Flaws in Metallic Struc-tures, BSi, London, 2005

[24] R6: Assessment of the Integrity of Structures Containing Defects. British Energy Generation, Report R6, Revision 4, 2009

84 ViNDiO USER´S MANUAl 6. REFERENCES

[25] Thomson, K.D., Sheppard, S.D., Stress Intensity Factors of Shafts Subjected to Torsion and Axial Loading, Engineering Fracture Mechanics, Vol. 42, 1992, pp. 1019-1034

[26] Daoud, O.E.K., Cartwright, D.J., Strain Energy Release Rates for Straight Fronted Edge Crack in a Circular Bar Subjected to Bending, Engineering Fracture Mechanics, Vol. 19, 1984, pp. 7011-707

[27] Akhurst, K.N., Ewing, D.J.F., The Failure Assessment of a Shaft Containing a Chordal Crack, TPRD/L/MT0010/M82, 1982

[28] Zahoor, A., Closed Form Expressions for Fracture Mechanics Analysis of Cracked Pipes, ASME-J, Pressure Vessel Technology, Vol. 107, 1985, pp. 203-205

[29] Kastner, W., Röhrich, E., Schmitt, W., Steinbuch, R., Critical Crack Sizes in Ductile Piping, Inter-national Journal of Pressure Vessels and Piping, Vol. 9, 1981, pp. 197-219

[30] Zahor, A., Ductile Fracture Mechanics Methodology for Complex Cracks in Nuclear Piping, Nuclear Engineering and Design, Vol. 106, 1988, pp. 243-256

[31] Willoughby, A.A., Davey, T.G., Plastic Collapse at Part Wall Flaws in Plates, In: R.P.Wei, ed. Fracture Mechanics: Perspectives and Directions, Proceedings 20th National Symposium (ISBN 0803112505), Bethlehem, PA, 1987. ASTM. STP 1020, pp. 390-409, 1987

85 Annex i. Glossary of symbols and acronyms

This annex gathers a brief definition of the different symbols and acronyms used in both this user´s manual and VINDIO:

a Crack size.

A Resistant section.

A Material constant in JR curve (equation (48)).

A0 Initial section in a tensile specimen.

B Specimen thickness, used in equations (43), (44) and (47).

c Half crack length for surface or embedded cracks.

C Material constant in Paris law (equation (20)).

Cν Charpy energy.

E Young´s (elastic) modulus.

E´ Elastic modulus corrected for constraint conditions: E´=E for plane stress; E´= E/(1-ν2) for plane strain

f(lr) Function of Lr defining the FAL in a FAD (equation (16)).

F Applied load in a tensile test.

J J integral, a parameter defining the stress state in a crack tip under elastic-plastic conditions.

Jap Applied J in a cracked component when it is subjected to a certain load.

86 ViNDiO USER´S MANUAl ANNEX i. GlOSSARY OF SYMBOlS AND ACRONYMS

Jc Material fracture toughness in terms of J integral, used in initiation analysis. This term only applies where stable crack propagation is lower than 0.2 mm.

Je Elastic component of J integral (equation (5)).

JR Characteristic toughness in units of J for ductile tearing analysis.

Jic IInitiation of ductile crack extension for quasi-static loading rates (kN/m2).

J0.2 Resistance to crack extension expressed in terms of J at 0.2 mm crack extension offset to the blunting line.

J-Δa Idem to JR.

ki Stress intensity factor, a parameter defining the stress state in a crack tip under linear-elastic conditions

kiC Plane strain fracture toughness.

kip Stress intensity factor due to primary stresses.

kis Stress intensity factor due to secondary stresses.

kJc Stress intensity factor (MPam1/2) calculated from Jc (equation (12)).

kJic Stress intensity factor (MPam1/2) calculated from JIc (equation (13)).

kmat Material toughness measured by stress intensity factor. It may be KIc, KJc, KJIc or values obtained from Charpy-toughness correlations (equations (43), (44) or (45), depending on the case).

kmat(Δa) Characteristic toughness in units of stress intensity factor for ductile tearing analy-sis. It is obtained from JR (J-Δa) (equation (17)).

87 ANNEX i. GlOSSARY OF SYMBOlS AND ACRONYMS ViNDiO USER´S MANUAl

kr Fracture ratio of applied elastic KI to Kmat (equation (14)).

kr(Δai) Fracture ratio of applied elastic KI(a0+Δai)) to Kmat(Δai), used in a ductile tearing FAD analysis.

l Length measured by an extensometer in a tensile test .

l0 Initial length measured by an extensometer in a tensile test .

lr Load ratio of applied load, P, to limit load PL (equation (15)).

lrmax Maximum permitted value of Lr (equations (26), (34) or (40), depending o the case).

lr(Δai) Load ratio of applied load (P) to limit load (PL(a0+Δai)), used in a ductile tearing FAD analysis (equation (19)).

m Material constant in Paris law (equation (20)).

n Material constant in the JR curve (equation (48)).

N Strain hardening exponent, estimated from equations (33) or (39), depending on the case.

p Applied load.

pf Probability of Kmat being less than estimated (equations (44) and (47)).

pl Limit load.

t Thickness of structural section.

T Temperature.

T0 Reference Temperature (ºC), corresponding to a median toughness of 100 MPam1/2 for 25 mm specimens (equation (47))


T27J Temperature (ºC) for energies of 27 J measured in a standard 10 mm x 10 mm Charpy V specimen(equation 44)).

Y Geometric factor used in the stress intensity factor (equation (1)).

Δa Crack extension.

Δl Length increment measured by an extensometer in a tensile test.

Δk Stress intensity factor range.

Δkth Fatigue threshold, value of ΔK below which it is considered there is no fatigue crack propagation.

Δε Lower yield or Lüder´s strain (equation (32)).

ε Engineering strain, obtained as the ratio of length increment to the initial length (equation (8)).

εmax Strain under maximum load in a tensile test.

εr True strain corresponding to a given true stress, σr, which is equal to Lr·σylow, in

case the material does have yield plateau, or Lr·σ0.2 in case the material does not have any yield plateau.

εR Strain at rupture in a tensile test.

εv True strain, obtained as the ratio between the length increment Δl to the actual length, l (equation (11)).

λ Parameter used in the FAD definition, following Level 2 and in those materials with yield plateau (equation (31)).

μ Parameter used in the FAD definition, following Level 2 and in those materials without yield plateau (equation (38)).

89 ANNEX i. GlOSSARY OF SYMBOlS AND ACRONYMS ViNDiO USER´S MANUAl

ν Poisson´s ratio.

ρ Plasticity correction factor (equation (51)).

σ Engineering stress, obtained as the ratio between the applied load F and the initial section A0 (equation (7)).

σ Acting stress.

σb Linearized bending stress (equation (50)).

σm Linearized membrane stress (equation (49)).

σr Reference stress (Lr·σyinf or Lr·σ0.2, depending on the case), which is associated to a

reference strain εr in the stress-strain curve.

σu Ultimate tensile strength.

σv True stress, obtained as the ratio between the applied load F and the actual section A (equation (10)).

σy Yield stress.

σylow Lower yield stress.

σysup Upper yield stress.

σ0.2 0.2% proof strength.

CT Compact Tension specimen.

CTOD Crack Tip Opening Displacement.

FAD Failure Assessment Diagram.


FAl Failure Assessment Line . FFS Fitness-for-Service.

RF Reserve Factor (equation (52)).

lEFM Linear-Elastic Fracture Mechanics.

EpFM Elastic-Plastic Fracture Mechanics.

SENB Single Edge Notched Bending specimen.

91 Annex ii. KI and pl solutions

This annex gathers, for each combination of component and crack geometry, the sources consulted for KI and PL solutions. As it may be noticed, most of the solutions have been taken from FITNET FFS Procedure [2], although there are several ones that have been obtained from other documents.

1. ROUND BARS

1.1. Straight fronted crack 1.2. Fully circumferential crack

KI: [25,26] KI: [2]

PL: [27] PL: [23]

92 ViNDiO USER´S MANUAl ANNEX ii. ki AND pl SOlUTiONS

1. ROUND BARS (continued)

1.3. Semicircular surface crack 1.4. Embedded crack

KI: [2] KI: Obtained by numerical simulationby Inesco Ingenieros

PL: [23] PL: Obtained by numerical simulationby Inesco Ingenieros

2. PIPES OR CYLINDERS

2.1. Through thickness axial crack 2.2. Finite axial surface crack (internal)

KI: [2] KI: [2]

PL: [2] PL: [2]

93 ANNEX ii. ki AND pl SOlUTiONS ViNDiO USER´S MANUAl


2.3. Extended axial surface crack (internal) 2.4. Finite axial surface crack (external)

KI: [2] KI: [2]

PL: [2] PL: [2]

2.5. Extended axial surface crack (external) 2.6. Finite axial crack (embedded)

KI: [2] KI: Obtained by numerical simulationby Inesco Ingenieros

PL: [2] PL: Obtained by numerical simulationby Inesco Ingenieros



2.7. Extended axial crack (embedded) 2.8. Through-thickness circumferential crack

KI: Obtained by numerical simulationby Inesco Ingenieros KI: [28]

PL: Obtained by numerical simulationby Inesco Ingenieros PL: [29]

2.9. Finite circumferential surface crack (internal)

2.10. Extended circumferential surface crack (internal)

KI: [2] KI: [2]

PL: [23] PL: [23]



2.11. Finite circumferential surface crack (external)

2.12. Extended circumferential surface crack (external)

KI: [2] KI: [2]

PL: [30] PL: [23]

2.13. Finite circumferential crack (embedded)

2.14. Extended circumferential crack (embedded)

KI: Obtained by numerical simulationby Inesco Ingenieros

KI: Obtained by numerical simulationby Inesco Ingenieros

PL: Obtained by numerical simulationby Inesco Ingenieros

PL: Obtained by numerical simulationby Inesco Ingenieros



2.15. Circumferential compound (through thickness + extended) crack

KI: [30]

PL: [30]

3. PLATES

3.1. Central through-thickness crack 3.2. Surface finite crack

KI: [2] KI: [2]

PL: [23] PL: [2]



3.3. Surface extended crack 3.4. Embedded finite crack

KI: [2] KI: [2]

PL: [2] PL: [2]

3.5. Embedded extended crack 3.6. Edge crack

KI: [2] KI: [2]

PL: [2] PL: [23]



3.7. Double edge crack 3.8. Corner crack

KI: [2] KI: [2]

PL: [2] PL: [23,31]

3.9. Corner crack at a hole (symmetric) 3.10. Corner crack at a hole (single)

KI: [2] KI: [2]

PL: [23,31] PL: [23,31]


4. SPHERES

4.1.Through-thickness equatorial crack 4.2. Surface finite crack (internal)

KI: [2] KI: Obtained by numerical simulation by Inesco Ingenieros

PL: [2] PL: Obtained by numerical simulation by Inesco Ingenieros

4.3. Surface finite crack (external)

KI: Obtained by numerical simulation by Inesco Ingenieros

PL: Obtained by numerical simulation by Inesco Ingenieros


5. FRACTURE TOUGHNESS SPECIMENS

5.1. CT specimen 5.2. SENB specimen

KI: [10]

PL: [4]

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Vindio 1.0 User's Manual