RUCHIR GAUR ID #: UM33770SCI42344
COURSE TITLE: FRACTURE MECHANICS
TO ANALYSE THE FATIGUE CRACK MECHANISM OF A FIXED PLATFORM ATLANTIC INTERNATIONAL UNIVERSITY HONOLULU, HAWAII WINTER 2016 6th January 2016
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Table of Contents Introduction
3
Description
4
Analysis
5
Actualisation
14
Recommendation
23
Conclusion
24
References
25
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Introduction The discussion in this paper explains the importance of the study of fractures in a structure. Not only the failure due to fracture costs money, it can cause loss of lives. The money is important but the loss of lives and injury is much more important. There are many reasons which can cause the failures such as loading understanding, environment, deficiencies in the design and construction. The study of design which is involved in the fracture is a special study of its own. This area of study is and has been of significant importance. (Victor, 2013) In this research paper, we will come across the important points of fracture analysis. Without the adequate understanding of fracture, there will be no point going further. We know that the strength of the structure can be increased by changing the microstructure. As a matter of fact, this causes the material to become brittle. This can lead to the formation of cracks without giving enough warning and the history shows that the large number of disasters have been caused because of this.
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Description Fracture mechanics mainly deals with the study of specialised branch of solid mechanics where it is assumed that a crack is present. In this study, relations which are quantitative are studied such as the crack length, the material’s resistance to the growth of crack and the level of the stress at which the crack increase. The main difficulty in designing the structures especially in high strength materials is that if the cracks are present, they can modify the local stresses to an extent that even the careful calculations of elastic stress analysis is considered insufficient. Once the crack reaches the length which is critical, it can increase catastrophically through the structure. This crack will propagate in spite of gross stress being less than would normally cause a failure in a tensile member. (David, 2010) In this research paper, the approaches which are used are analysis of fatigue and fracture mechanics approach. These approaches are based on BS7910 and API RP 2A standards. Based on these standards, fracture assessment was conducted and the fatigue life was predicted for the crack which already existed on a platform which was fixed.
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Analysis A “fracture� is something which involves a crack which increases by the loading. Fracture mechanics involves when the crack becomes criticial. In other words, when the crack prpogation gets to a significant length and the structure becomes from stable to unstable. We can describe fracture mecahnics with the equation below (David, 2010)
In the above equation, the stress intensity factor is used to forecast the state of the stress in the structure. The magnitude of the stress intensity factor (K) mainly depends on the size, location and the geometry of the crack. In polar coordinates it can be described as (David, 2010)
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In the above equation, stress intensity factor is defined by K. The unit of K is stress times length’s square root. We should know that a continuum which is three dimensional, if subjected
to
the
external
loads
will
deform.
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To understand the behaviour of the material, experiments need to be conducted. Figure below illustrates the tensile – compression loading of a bar which is tensile.
How the material will behave can be found mainly by strain time / stress time graphs. These graphs may illustrate linear, nonlinear, softening and hardening behaviour which is shown below
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At the time, when the material of the structure develops big cracks which can grow in size very quickly and become very dangerous to the structure, the averaging methods cannot be relied on. As a matter of fact, discontinuities should be taken into account. This local failure will result in a macroscopic crack, which might grow and result further in the failure of the whole structure. (Dr. Schreurs, 2012) In the early years, fractures were predicted by analysing the atomic bonds behaviour. It was shown by Griffith in 1921 that the behaviour of the existing crack should be given attention.
Fracture mechanics mainly focuses on a single crack. Various theoretical and experimental techniques have been and are still being developed to answer the questions such as •
Under any given load, whether the crack will increase?
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What will be the speed and direction of the crack, if it will increase? 9|Page
•
Whether the growth of the crack will stop?
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What will be the residual strength as a function of the crack length?
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What will be the frequency of the inspection?
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What kind of repair or replacement and when it must be done?
Various fields of engineering and science are heavily involved in answering these questions. Hence, we can say that fracture mechanics is itself a much specialised branch with its own theory and terminology. The cracks are detected by various experimental techniques which range from cheap to very expensive. These experiments are performed not only to detect the cracks but to determine the accurate geometry and loading conditions. (Dr. Schreurs, 2012)
In which way a crack will propagate is studied in fracture mechanics. There are mainly five different types of fractures which are discussed below: 10 | P a g e
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Fracture by shear
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Cleavage fracture
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Fracture by Fatigue
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Crazing
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De - adhesion
Fracture by shear - Shearing occurs when the material which is crystalline is subjected to load. Because of this loading, the dislocations starts and move through the lattice. At the same time, the number of dislocations increases. In this phenomenon, the internal structure is changed permanently; hence the deformation is permanent which is like plastic. These dislocations coalesce at the grain boundaries and gather to form a void. By time, these voids grow and form a macroscopic crack which can result in the failure of the structure. As these cracks are caused by the shear stresses, this mechanism is known as shearing. Dough like structures are formed with some dimples on the fractured surfaces. This indicates the loading on the crack. (Dr. Schreurs, 2012) Figure below illustrates this
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Cleavage fracture – When the deformation at the tip is restricted, the crack can travel through the grains by splitting the bonds. This phenomenon is known as trans -granular cleavage. The propagation is known as inter-granular cleavage when the crack propagates along the boundaries of grain. This type of crack is observed in the materials which are very weak and / or have badly damaged grain boundaries. This type of crack can also result by the environmental factors such as high temperatures or hydrogen. Figures below illustrate this
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Fracture by fatigue – Cyclic loading is responsible for the tip of the crack to travel short distance. This crack keeps on travelling with each cycle. However, the stress shouldn’t be very high so that it cause a sudden global fracture. As the propagation of the crack is very small in each cycle, we need a very large number of cycles to cause a total failure. (Dr. Schreurs, 2012)
Figure below illustrates the macroscopic and microscopic fatigue crack surfaces.
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Crazing – If the material is polymer, small voids can initiate when the critical loads exceeds. These crazes can grow locally leading to a major failure. I some cases, these crazes spread over a larger area and is known as stress whitening as of the refracted light. This is the reason of it being white coloured in appearance. (Dr. Schreurs, 2012) Figure below illustrates this
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. De – adhesion – The bonding between atoms of different materials is known as adhesion. However, the bonding between atoms of one and the same material is known as cohesion. The adhesion of the layer to the substrate is calculated by the chemical bond strength and is significantly influenced by the stresses and any damage in the layer which is on the surface. The strength of the adhesion can be determined by the normal strength which is at the maximum. (Dr. Schreurs, 2012)
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Actualisation A study was done by Yongquing Ye and Chaohe Chen where fracture assessment was conducted and the fatigue life for existing crack was predicted on the offshore platform. Offshore platform which is fixed is a welded structure. These platforms are constantly bombarded by the seawater which is highly corrosive in nature and constantly changing environment load which is very hard to predict. Due to this, the platform will suffer many damages including cracks and corrosion. These damages will impact on the performance of the fixed platform. Recently, in Public republic of China (PRC), various platforms have reached their design life and have been detected with cracks. Predicting the fracture analysis and fatigue life has become a problem in PRC. A good example is of CNOOC (China National Offshore Oil Corporation) where these platforms have been servicing for many years and have appeared to have cracks. (Ye & Chen, 2015) As we have seen that these platforms are welded structures, the failure which is mainly occurred because of welded joints which reached fatigue. This mainly happens in the area which is jointed to minimise the energy losses. However, the tubular joint failure is mainly because of external repeated load. To study the strength of the fatigue and the remaining life of the joint which is tubular and is core of the structure, a thorough fracture study and the rate with which the crack propagates should be performed. Once the safety of these cracks is correctly performed, the life of these platforms can be extended. (Ye & Chen, 2015) First we will calculate the stress of Hot Spot for the platform which contains the cracks. Here we will use Morrison’s equation which is
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Using this equation, we will calculate the sea load which is mainly acting on the leg of the platform. Here the acceleration and the velocity of the water particles can be calculated by the wave models theory. Stokes theory of fifth order may provide the accurate data which can be relied upon. The first variable which is at the end of the equation on the right hand side is the force known as drag force which is analysed by the calculations. This calculation is based on the assumption that the fluid is viscous and steadily uniform which can by -pass the cylinder. In the above equation, the second variable is inertia and is obtained from the analysis of the flow which is not steady and is only theoretical. Satisfactory results can be obtained from Morrison’s equation only if the ratio of the wavelength to the diameter is more than 5. This method is currently the main method for the calculations of force which waves exerts on a small structure. (Ye & Chen, 2015) The stress calculations of tubular joints are more difficult in comparison to the specimen of the plate. Therefore during the estimation of the fatigue of the tubular joint, difficulty is encountered in selecting the stress and also the stress definition. Significant research and studies are being done all over the world in order to analyse the selection of stress and stress design. (Ye & Chen, 2015). Hot spot stress is the biggest geometrical stress and it considered
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to be more reasonable in comparison to the notch stress. There are few reasons which suggest that Hot spot stress is more reasonable for fatigue analysis which are •
The quality of welding and the defects which are caused by initial welding lead to the unstable value of maximum notch stress
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The various experiments and researches have illustrated that hot spot stress is very stable at the weld toe of the structure
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The maximum notch stress is greatly affected by the quality of the weld, shape and any defects which were present initially which makes it very difficult to perform the accurate calculations by using a method known as three dimensional finite element method. However, the hot spot stress is mainly dependent on the geometry of tubular node
•
As per the mechanics of fracture, notch stress only effects the formation of the cracks which were initially present. Its effect on the growth of the crack is negligible. Hot spot stress is mainly responsible on the crack’s growth stage which is very important for the fatigue life
In case of fixed platform, the location of hot spots is generally between the pipe (which is welded) and the branch pipes. We need to calculate the tubular joint hot spot stress where the tubular joint is suffering the axial stress. Axial stress occurs when the structure is exposed to the bending in the inner and outer surface at the same time, generally the following equation is used (Ye & Chen, 2015)
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However, this method is conservative as using the axial stress in plane and out of plane bending stress are at the maximum which doesn’t consider the defects which are on the intersecting lines. Therefore the more accurate method is to use the following equation
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So that we can maximise the hot spot stress magnitude, the two phases must be selected to achieve the stress. The stress concentration factor is calculated by dividing the maximum principal stress on the struts by the main nominal stress on the strut. It is calculated by the following equation
If we want to calculate the stress of the welded tubular joint, we can achieve this by calculating stress concentration factor and the nominal stress. Following table illustrates crack assessments. (Ye & Chen, 2015)
Here
Assessment of the fracture 20 | P a g e
As per standard BS7910, any fracture is assessed by analysing the crack plane which has three levels. To decide which level should be selected depends on the type of materials used, available data and finally the conservatism which is required. The three levels are described below •
The first level is a basic assessment where there is not much information available of the properties of the material and the stresses on the material. In this type of assessment, the methods which are applied are very conservatively. (Ye & Chen, 2015)
•
The second level is a general assessment. The details which are required in this level is more than level one. This method uses two different methods i.e. 2A and 2B in order to assess the failure. (Ye & Chen, 2015)
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To assess the ductile materials, third type of method is used which is known as tearing resistance assessment. Figure below illustrates the Failure Assessment Diagram (FAD)
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The failure assessment of the second level deals with the interaction which is between the structures of the yielding which are minor with the plastic yield. Figure above illustrates FAD. This graph includes the failure assessment curve and the vertical line ( Lr =Lr max). (Ye & Chen, 2015) As we know that appearances of the cracks are mainly in welds (toe), the second level 2A failure assessment diagram should be better.
The materials which show the discontinuity of yield in the curve which is of stress and strain. This means a curve which is not increasing monotonically. (Ye & Chen, 2015). In other
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words we can say that there is no confidence in the continuities. In the calculations, the value of Lr = 1.0 should be applied. The other option is to use level 2B. In case it is not possible to calculate the value of level 2B, the value of Lr = 1.0 should be assumed. (Ye & Chen, 2015) In the crack assessment, various methods are used. However, this paper will deal with level 2A assessment. Following is the assessment
To calculate the load ratio Lr, we use Here sigma y is the strength which is known as yield and is lower and sigma ref is the reference to the stress. While carrying out the analysis of the failure, it is very important to calculate the reference stress for the structure or component which is flawed. (Ye & Chen, 2015) There are three types of collapse which can be identified by the assessment: •
Collapse which is local – this is the collapse of the ligament which is next to the flaw which is being analysed
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The failure of the net section – this is the failure of the structural section
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Gross section collapse – this type of collapse happens when the collapse is away from the section which has flaw
(Ye & Chen, 2015) Figure below illustrates the fatigue assessment flowchart and the table 3 and 4 illustrates the crack assessment results for crack A and crack assessment and fatigue for crack B respectively.
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It has to be noted that for the flaws which are embedded, the stress intensity factor value (K1) which has been determined will vary at the front of the crack. We note that the maximum value of K1 will be at the location at the maximum depth (known as surface breaking flaws) or at the location which is nearest to the surface (known as embedded flaws). It was found that in these two cases, the angle which is along the perimeter was equal to pi divided by two. But this doesn’t happen always as the location of the point of maximum K1 around the crack can be affected by many other factors such as (a) flaw aspect ratio (b) stress concentrations at the surface (c) thermal shock and (d) stress variation of the residual. (Ye & Chen, 2015)
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Recommendation If cracking happens in the welded joint or next to it, the repair can be made by welding. It is very important that the cracked material is removed so that a deep penetration repair can be made. If before the repair, it is found that the required repaired life is more than the original achieved life, the cyclic stress levels should be reduced especially near the area of the repair. Other option is to improve the fatigue strength which can be achieved by performing the post repair for example the grinding of weld toe. In order to reduce the cyclic stress levels, additional materials can be added by welding or doing the local redesign so that the stresses concentrations can be reduced. (David, 2010) A welded repair may be practical where the fatigue cracking starts in plain material and is aloof from any welds. It will definitely have a reduced fatigue life. To overcome this issue, the attention is required to improve the fatigue strength and / or cyclic stress at the starting crack position. (David, 2010) I would strongly recommend that when there are embedded flaws and the surface breaks, the stress intensity factor shall be calculated at the various points along the front of the crack. In order to make sure that conservatism is still there, while performing the assessment of the fracture, the maximum value of fracture ratio should be used which is calculated around the front of the crack. I would also recommend using finite element method so that the stress concentration factor at the crack or the area near the crack can be calculated.
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Conclusion In this research paper, fracture analysis has been calculated on the mechanics of fracture which has been applied to the tubular joint which was already known (crack A and B). Based on this following are the conclusions •
It was found that A crack is sound when the assessment of second level was performed under one hundred years extreme loading which was 200Mpa.
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It was found that the important size of A crack is 11.868 mm in the one hundered years of extreme loading which is 200Mpa
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The analysis is based on one hundred years of wave conditions which were extreme and the results are on the conservative side
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B crack has been found to be safe at level 2 assessment in one hundred years extreme loading which 300 Mpa
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It was found that the important size of crack A is 13.005 mm in the one hundered years of extreme loading which is 300 Mpa
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Crack B has a fatigue life of sixteen years in per one hundred years of extreme loading conditions which is 300 Mpa
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The analysis is based on one hundred years of wave conditions which were extreme and the results are conservative
(Ye & Chen, 2015)
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References 1. Ye, Y., & Chen, C. (2015). Research on fatigue crack assessment for fixed
platform. Journal of Coastal Research, Special Issue, No. 73 577-583. Retrieved from http://www.jcronline.org/doi/abs/10.2112/SI73-100.1?journalCode=coas 2. Roylance, D. (June 2010). Introduction to Fracture Mechanics. Department of
Materials Science and Engineering. Massachusetts Institute of Technology. Cambridge, MA 02139 Retrieved from http://ocw.mit.edu/courses/materialsscience-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/frac.pdf 3. Dr. Schreurs, P. (September 6, 2012). Fracture Mechanics. Retrieved from
http://www.ce.berkeley.edu/~paulmont/241/fracture.pdf 4. Victor, E.S. (May 01, 2013). What is Fracture Mechanics? University of Colorado,
Boulder, CO 80309-0428. Retrieved from http://civil.colorado.edu/~saouma/Lecture-Notes/lecfrac.pdf
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