\r\n\t2) The divergence between the levels of reliability required (twelve-9’s are not uncommon requirements) and the ability to identify or test failure modes that are increasingly unknown and unknowable \r\n\t3) The divergence between the vulnerability of critical systems and the amount of damage that an individual ‘bad actor’ is able to inflict.
\r\n
\r\n\t \r\n\tThe book examines pioneering work to address these challenges and to ensure the timely arrival of antifragile critical systems into a world that currently sees humanity at the edge of a precipice.
",isbn:"978-1-83969-461-5",printIsbn:"978-1-83969-460-8",pdfIsbn:"978-1-83969-462-2",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"78d284ad921e9677830ef0335b1f1276",bookSignature:"Prof. Darrell Mann",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10692.jpg",keywords:"Complex-Adaptive-Systems, Edge-of-Chaos, Antifragile, Holistic-Design, Human-Error, Irrationality, Scientific Laws, Evolutionary-S-Curves, Anticipatory-Failure-Determination, Edge Effect, Feedback-Loops, OODA-Loop",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 15th 2021",dateEndSecondStepPublish:"March 15th 2021",dateEndThirdStepPublish:"May 14th 2021",dateEndFourthStepPublish:"August 2nd 2021",dateEndFifthStepPublish:"October 1st 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"A pioneering innovation-methods researcher, an innovator with a $6B track-record, and a regular author on innovation-related topics. 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\n\t\t\t
1. Introduction
\n\t\t\t
The booming aerospace industry and high levels of competition has forced companies to constantly look for ways to optimize their machining processes. Cycle time, which is the time it takes to machine a certain part, has been a major concern at various Industries dealing with manufacturing of airframe parts and subassemblies. When trying to machine a part as quick as possible, spindle speed or metal removal rates are no longer the limiting factor; it is the chatter that occurs during the machining process. Chatter is defined as self-excited vibrations between the tool and the work piece. A tight surface tolerance is usually required of a machined part. These self-excited vibrations leave wave patterns inscribed on the part and threaten to ruin it, as its surface tolerances are not met. Money lost due to the destructive nature of chatter, ruining the tools, parts and possibly the machine, has driven a lot of research into determining mathematical equations for the modeling and prediction of chatter. It is well established that chatter is directly linked to the natural frequency of the cutting system, which includes the spindle, shaft, tool and hold combination.
\n\t\t\t
The first mention of chatter can be credited to Taylor [18], but it wasn’t until 1946 that Arnold [3] conducted the first comprehensive investigation into it. His experiments were conducted on the turning process. He theorized that the machine could be modelled as a simple oscillator, and that the force on the tool decreased as the speed of the tool increased with relation to the work piece. In his equations, the proportionality constant of the speed of the tool to the force was subtracted from the damping value of the machine; when the proportionality constant increases beyond the damping value of the machine, negative damping occurs causing chatter. This was later challenged by Gurney and Tobias who theorized the now widely accepted belief that chatter is caused by wave patterns traced onto the surface of the work piece by preceding tool passes [9]. The phase shift of the preceding wave to the wave currently being traced determines whether there is any amplification in the tool head movement. If there exists a phase shift between the two tool passes, then the uncut chip cross-sectional area is varied over the pass. The cutting force is dependent on the chips cross sectional area, and so, a varying cutting force is produced [19]. To perform calculations on this system, they modelled a grinding machine as a mass-spring system as opposed to an oscillating system. It had a single degree of freedom, making its calculations quite simple. The spring-mass system is also the widely used modelling theory for how a vibrating tool should be characterized today.
\n\t\t\t
Prior to 1961, the research papers published on the machining processes regarded them as steady state, discrete processes [8]. This erroneous idea led to the creation of machines that were overly heavy and thick walled. It was believed that this provided high damping to the forces on the tool tips that were thought to be static. To properly predict chatter, one must realize that machining is a continuous, dynamic process with tooltip forces that are in constant fluctuation. When performing calculations, the specific characteristics of each machine must also be taken into consideration. If one takes two identical tools, placed into two identical machines, and perform the same machining process on two identical parts, the lifespan of the tools will not be the same. The dynamics and response of each of the machines differs slightly due to structural imperfections, imbalances, etc. Therefore, calculations must always take the machine-tool dynamics into consideration [23]. The modes of the machines structure determine the frequency and the direction that the tool is going to vibrate at [11]. Rather than the previously used machine design philosophy of “where there’s vibration, add mass”, it was then stated that designers must investigate the mode-forms, weak points, bearing clearances, and self-inducing vibratory components of their machine design to try to reduce chatter [8, 15]. Certain researchers even further investigatedthe required number of structural modes to produce accurate results [6]. Since it is impractical to investigate an unlimited bandwidth of a signal, restrictions must be made. This has generally been restrained to one or two modes of vibration of the machine. Their study proves that using low order models, that only incorporate two modes, are sufficiently accurate to model the machines.
\n\t\t\t
In 1981, one of the first papers documenting the non-linearity of the vibratory system occurring during chatterwas published [20]. Self-excited chatter is a phenomenon that grows, but does not grow indefinitely. There is a point in time where the vibrations stabilize because of the tool jumping out of the cut. As the vibrations amplify, the tool head displacement increases. The displacement of the tool is not linear, but occurs in all three dimensions. When the force on the tool due to chatter causes displacement away from the work piece that exceeds the depth of cut, the tool will lose contact with the work piece. When this occurs, the work piece exerted forces on the tool all go to zero. The only forces acting on it now are the structural forces that want to keep the tool on its planned route. It is impossible for chatter to amplify further past this point, and so, this is where it stabilizes. Previous reports do not account for this stabilization. Their results are accurate up to this point, but then diverge from the experimentally obtained results. Tlusty’s investigation was then complemented by adding the behaviour of the tool after the onset of chatter [12]. The paper discusses the effects preceding passes of the tool have on the current state. It was generally accepted that wave patterns left on the work piece from a previous pass greatly effects the current pass, however, it is demonstrated that tool passes two or more turns prior to the current also have an effect. The phase difference and frequency of the waves etched into the surface of the prior turns interact with one another, and if the conditions are correct, interact in a critical way that produces increasing amplitude vibrations [10]. While Tlusty was able to theorize that chatter stabilizes at a certain point due to the tool leaving the work piece, [12] set off to prove this theory. They had the novel idea to turn the machine-work piece system into a circuit. Current was passed through the machine and into the work piece while turning. When chatter occurred, they noticed drops in current at the machine-tool contact point. This proves that an open circuit was being created, proving that the tool was losing contact with the work piece. They also sought out to prove why cutting becomes more stable at lower speeds. They believed that there was a resistive force caused by the tool moving forward along the cut. They found this resistive force to be inversely proportional to the cutting speed, and directly proportional to the relative velocity of the tool to the work piece. When this force was taken into account in their equations, it produces a wider region of stability while the spindle is at lower speeds. This resistive force was proven to be responsible for the large regions of stability at low spindle speeds, and is what diminishes at higher spindle speeds resulting in less stability. The majority of papers published prior to the 80’s examined chatter with reference to the turning and boring processes. Milling is plagued with the same issues of chatter, but its modelling becomes more complicated. Tlusty and Ismail [21] characterized the chatter in the milling process by examining the periodicity of the forces that occur at the tool that are not present in other processes. During the milling process, cutter teeth come into and out of contact with the work piece. It is on the surface of these teeth that the force is applied. The same number of teeth are not always in contact with the work piece, and each tooth may be removing a different amount of material at a time. This leads to widely varying forces at the tool tip, creating a more challenging system to model. Forced vibrations can be attributed to periodic forces that the machine is subjected to. This can include an imbalance on rotating parts, or forces the machine transfers to the tool while moving. Chatter must be isolated from this in experiments so that the observations and calculations can be kept specific to the chatter phenomenon.
\n\t\t\t
Once an accurate model of the milling process had been created, a reliable stability lobe can be constructed. Stability lobes plot the axial depth of cut vs. spindle speed. The resulting graph has a series of lobes that intersect each other at certain points. The area that is formed underneath the intersection of these lobes represents conditions that will produce stable machining. The area above these intersections represent unstable machining conditions. The concept of the stability lobe was first proposed by Tobias [24] As the mathematical modelling of the machining systems improved, so did the accuracy of the stability lobes. Prior to the paper by Tlusty et al. [22], most stability lobe calculations contained many simplifying assumptions, and therefore, were not very accurate; all teeth on the cutter were assumed to be oriented in the same direction, and also had a uniform pitch. They eliminated all of these assumptions and proved their math represented reality more accurately. A quarter of a centurylater, Mann et al. [14] discovered unstable regions in a stability lobe graph that existed underneath the stability boundary for the milling operation. They resemble islands in the fact that they are ovular areas contained within the stable regions, complicating the previously thought simple stability lobe model. It was found that stability lobes taken from modal parameters of the machine at rest (static) were not as accurate as the stability lobes produced from the dynamic modal properties. Zaghbani & Songmene [25] obtained these dynamic properties using operational modal analysis (OMA). OMA uses the autoregressive moving average method and least square complex exponential method to obtain these values, producing a dynamic stability lobe that more accurately represents stable cutting conditions. These stability lobes have proven to be an invaluable asset to machinists and machine programmers. They provide a quick and easy reference to choose machining parameters that should produce a chatter free cut [2].
\n\t\t\t
Tool wear is an often-overlooked factor that contributes to chatter. With the aid of more powerful computers this variable can now be included in simulations. The cutting tool is not indestructible and will change its shape while machining, and consequently affects the stability of the system and stability lobes [7]. As the tool becomes worn, its limits of stability increase. Therefore, the axial depth of cut can be increased while maintaining the same spindle speed that would have previously created chatter. The rate of wear was incorporated into the stability lobe calculations for the tools so that it was now also a function of wear. To verify their calculations, the tools were ground to certain stages of wear and then tested experimentally. They were found to be in strong agreement. Tool wear, however, is not something that machine shops want increased. Chatter increases the rates of tool wear, shortening their lifespan, and increasing the amount of money the shops must spend on new tools. Li et al. [13] determined that the coherence function of two crossed accelerations in the bending vibration of the tool shank approaches unity at the onset of chatter. A threshold needs to be set [16] and then detected using simple mechanism to alert the operator to change the machining conditions and avoid increased tool wear.
\n\t\t\t
In most of the previous stability prediction methods, a Frequency Response Function (FRF) is required to perform the calculations. FRF refers to how the machine’s structure reacts to vibration. It is required to do an impact test to acquire the system’s FRF [17]. In this case, an accelerometer is placed at the end of the top of the tool, and a hammer is used to strike the tool. The accelerometer will measure the displacement of the tool, telling the engineer how the machine reacts to vibration. This test gives crucial information about the machine, such as the damping of the structure and its natural frequencies. This method of obtaining information is impractical; because the FRF of the machine is always changing, it would require the impact test to be performed at all the different stages of machining. Also, having to do this interrupts the manufacturing processing and having machines sitting idle costs the company money. An offline method of obtaining this information could greatly benefit machining companies by eliminating the need for the impact test. Adetoro et al. [1] proposed that the machine, tool and work piece could be modelled using finite element analysis.A computer simulation would be able to predict the FRF during all phases of the machining process. As the part is machined and becomes thinner, its response to vibration changes dramatically. Previous research papers assume a constant FRF throughout the whole process for the sake of reducing computations. However, a constantly updated FRF would allow for accurate, real time stability calculations.
\n\t\t\t
To the authors’ best knowledge, the spindle decay/bearings wear over the service time and their effects on the system natural frequencies, and consequently change of the stability lobes, have not been investigated.The objective of the present study is to determine the natural frequencies/vibration characteristics ofmachine tool spindle systems by developing its Dynamic Stiffness Matrix (DSM) [4] and applying the proper boundary conditions. These results would then be compared to the experimental results obtained from testing a common cutting system to validate/tune the model developed. The Hamilton’s Principle is used to derive the differential equations governing the coupled Bending-Bending (B-B) vibration of a spinning beam, which are solved for harmonic oscillations. A MATLAB® code is developed to assemble the DSM element matrices for multiple components and applying the boundary conditions (BC). The machine spindles usually contain bearings, simulated by applying spring elements at said locations. The bearings are first modeled as Simply-Supported (S-S) frictionless pins. The S-Sboundary conditions are then replaced by linear spring elements to incorporate the flexibility of bearings into the DSM model. In comparison with the manufactures’ data on the spindle’s fundamental frequency, the bearing stiffness coefficients, K\n\t\t\t\t\n\t\t\t\t\tS\n\t\t\t\t, are then varied to achieve a Calibrated Dynamics Stiffness Matrix (CDSM) vibrational model. Once the non-spinning results are confirmed and the spindle model tuned to represent the real system, the formulation could then be extended to include varying rotational speeds and torsional degree-of-freedom (DOF) for further modeling purposes. The research outcomepresented in this Chapter is to be used in the next phase of the authors’ ongoing research to establish the relationship between the tool/system characteristics (incorporating spindle’s service time/age), and intended machining process, through the development of relevant Stability Lobes, to achieve the best results.
\n\t\t
\n\t\t
\n\t\t\t
2. Mathematical model
\n\t\t\t
Computer Numeric Control (CNC) machines are quite often found in industries where a great deal of machining occurs. These machines are generally 3-, 4- or 5-axis, depending on the number of degrees of freedom the device has. Having the tool translate in the X, Y and Z direction accounts for the first three degrees-of-freedom (DOF). Rotation about the spindle axes account for any further DOF. The spindle contains the motors that rotate the tools and all the mechanisms that hold the tool in place. Figure 1 displays a sample spindle configuration and a typical tool/holder configuration is shown in Figure 2.
\n\t\t\t
Figure 1.
Typical Spindle Configuration.
\n\t\t\t
Figure 2.
Typical Tool/Holder Configuration.
\n\t\t\t
In this section, following the assumptions made by Banerjee & Su [5], discarding torsional vibrations, neglecting the rotary ineriaand shear deformation effects, the development of the governing differential equations of motion for coupled Bending-Bending (B-B) vibratins of a spinning beam is first briefly discussed. Then, based on the general procedure presented by Banerjee [4], the development of Dynamic Stiffness Matrix (DSM) formulation of the problem is conciselypresented. Figure 3 shows the spinnning beam, represented by a cylinder in a right-handed rectangular Cartesian coordinates system. The beam length is L, mass per unit length is m=ρA, and the bending rigidities are EI\n\t\t\t\t\n\t\t\t\t\txx\n\t\t\t\t and EI\n\t\t\t\t\n\t\t\t\t\tyy\n\t\t\t\t. See Figure 4 for the Degrees-of-Freedom (DOF) of the system.
\n\t\t\t
Figure 3.
Spinning Beam.
\n\t\t\t
Figure 4.
Degrees-of-Freedom (DOF) of the system
\n\t\t\t
At an arbitrary cross section, located at z from O, u and v are lateral displacements of a point P in the X and Y directions, respectively. The cross section is allowed to rotate or twist about the OZ axis. The position vector \n\t\t\t\t\tr\n\t\t\t\t of the point P after deformation is given by
\n\t\t\t
\n\t\t\t\t\n\n\t\t\tE1
\n\t\t\t
where \n\t\t\t\t\ti\n\t\t\t\t and \n\t\t\t\t\tj\n\t\t\t\t are unit vectors in the X and Y directions, respectively. The velocity of point P is given by
Using the Hamilton Principle in the usual notation state
\n\t\t\t
\n\t\t\t\t\n\t\t\t\n\t\t\tE5
\n\t\t\t
where \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tand \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t are the time intervals in the dynamic trajectory and \n\t\t\t\t\t\n\t\t\t\t\t\tδ\n\t\t\t\t\t\n\t\t\t\tis the variational operator. Substituting the kinetic and potential energies in the Hamilton Principle, collecting like terms and integrating by parts,leads to the following set of equations.
\n\t\t\t
\n\t\t\t\n\n\n\t\t\t\n\t\t\tE6
\n\t\t\t
\n\t\t\t\t\n\t\t\tE7
\n\t\t\t
The resulting loads are then found to be in the following forms, written for Shear forces as
where \n\t\t\t\t\t\n\t\t\t\t\t\tω\n\t\t\t\t\t\n\t\t\t\tfrequency of oscillation and \n\t\t\t\t\t\n\t\t\t\t\t\tU\n\t\t\t\t\t\n\t\t\t\tand \n\t\t\t\t\t\n\t\t\t\t\t\tV\n\t\t\t\t\t\n\t\t\t\tare the amplitudes of\n\t\t\t\t\t\n\t\t\t\t\t\tu and v\n\t\t\t\t\t\n\t\t\t\t. Substituting equations (10) into equations (6) and (7), they can be re-written as:
Introducing \n\t\t\t\t\t\n\t\t\t\t\t\tξ\n\t\t\t\t\t\t=\n\t\t\t\t\t\tz\n\t\t\t\t\t\t/\n\t\t\t\t\t\tL\n\t\t\t\t\t\n\t\t\t\tand\n\t\t\t\t\t\n\t\t\t\t\t\tD\n\t\t\t\t\t\t=\n\t\t\t\t\t\td\n\t\t\t\t\t\t/\n\t\t\t\t\t\tdξ\n\t\t\t\t\t\n\t\t\t\t, which are non-dimensional length and the differential operator into equations (11) and (12) leads to
The solution of the differential equation is sought in the form\n\t\t\t\t\t\n\t\t\t\t\t\tW\n\t\t\t\t\t\t=\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\trξ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, and when substituted into (15), leads to
From the above solutions of U and V, the corresponding bending rotation about X and Y axes,\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΘ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t and\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tΘ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, respectively, are given by
The frequency-dependent dynamic stiffness matrix (DSM) of the spinning beam, \n\t\t\t\t\t\n\t\t\t\t\t\tK\n\t\t\t\t\t\t(\n\t\t\t\t\t\tω\n\t\t\t\t\t\t)\n\t\t\t\t\t\n\t\t\t\t,can be derived by eliminating\n\t\t\t\t\t\n\t\t\t\t\t\tR\n\t\t\t\t\t\n\t\t\t\t. The force amplitude is related to the displacement vector by
Once the correctness and accuracy of the DSM code was established, a real machine spindle was then modeled, where the non-uniform spindle was idealized as a piecewise uniform (stepped) beam. Each step was modeled as a single continuous element and the above steps in the DSM formulation are repeated several times to determine the stiffness matrix for each element of the spindle. The element Dynamic Stiffness matrices are then assembled and the boundary conditions are applied. The system is simplified to contain 12 elements (13 nodes), as shown in Figure 5.
\n\t\t\t
Figure 5.
Simplified Spindle sections, with bearings modeled as simply-supported BC.
\n\t\t\t
It is assumed that the entire system is made from the same material and the properties of tooling steel were used for all section. It was also assumed that the system is simply supported at the locations of the bearings. The simply supported boundary conditions were then modified and replaced by linear spring elements (Figure 6); the spring stiffness values were varied in an attempt to achieve a fundamental frequency equivalent to the spindle system’s natural frequency reported by the manufacturer.
\n\t\t
\n\t\t
Figure 6.
Spindle model, with bearings modeled as linear spring elements(modified BC).
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\n\t\t\t
3. Numerical tests and experimental results
\n\t\t\t
\n\t\t\t\t
3.1. DSM results
\n\t\t\t\t
When the spindle was modeled using simply supported boundary conditions at the bearing locations, the fundamental natural frequency of the system was found to be just below 1400 Hz, i.e., higher than the nominal value provided by the manufacturer. The boundary conditions were then updated and the simple supports (bearings) were replaced by spring elements. The new spring-supported model was then updated/calibrated to achieve the spindle’s nominal fundamental natural frequency by varying spring stiffness values, Ks, all assumed to be identical. It was observed that as the spring stiffness value increase the natural frequency of the system increases. The natural frequency then levels out and reaches an asymptote as the springs start behaving more like simple supports at high values of spring stiffness. It was also found that at spring stiffness value of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tK\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t2.1\n\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t8\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t N/m the system achieves the natural frequency reported by the spindle manufacturer. This value of spring stiffness will be used for any further analysis of the system. These results are shown in Figure 7.
\n\t\t\t\t
Using the above results the natural frequency of the spindle was also found for multiple rotational speeds (Figure 8). It was observed that, as expected, as the spindle rotation speed increases the natural frequency of the system decreases. It was also found that the spindle critical spindle speed is \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t2.3\n\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t RPM which is well above the operating rotational speed of the spindle, i.e., 3\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t.\n\t\t\t\t\t\t\t5\n\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t4\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t RPM.
\n\t\t\t\t
Figure 7.
System Natural Frequency vs. Bearing Equivalent Spring Constant (in log scale).
\n\t\t\t
\n\t\t\t
Figure 8.
Spindle Natural Frequency vs. Spindle RPM.
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\n\t\t\t\t
3.2. Preliminary Experimental results
\n\t\t\t\t
The experimentally evaluated Frequency Response Function (FRF) data were collected for a machine over the period of twelve months. A 1-inch diameter blank tool with a 2-inch protrusion was used. A typical shrink fit tool holder was also used (See Figure 9). This type of holder was selected for its rigid contact surface with the tool. Therefore, any play in the whole system was going to be attributed to the spindle. The tested machine was used to produce typical machined parts and was not restricted to one type of cut. This was done to observe the spindle decay over time while operating under normal production conditions. The tool was placed in the spindle and the spindle was returned to its neutral position as shown in Figure 9. Acceleration transducers were placed in both the X and Y direction. The tool was struck with an impulse hammer in both the X and Y directions and corresponding bending natural frequencies were evaluated over the time. Figure 10 shows the bending natural frequencies of the non-spinning spindle vs. machine hours. As can be seen, system natural frequencies in both X and Y directions reduce with spindle’s life, which can be attributed to bearings decay. Further reseatrch is underway to analyze more spindles and to model the system decay by establishing a relationship between bearings stiffness, Ks, and machine hours. This, in turn, can be used to predict the optimum machining parameters as a function of spindle age.
\n\t\t\t\t
Figure 9.
Blank Tool (left) and Blank Tool in Spindle (middle and right).
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\n\t\t
\n\t\t
Figure 10.
Natural Frequency vs. Machine Hours.
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\n\t\t\t
4. Conclusion
\n\t\t\t
The effects of spindle system’s vibrational behavior on the stability lobes, and as a result on the Chatter behavior of machine tools have been established. It has been observed that the service life changes the vibrational behavior of spindles, i.e., reduced natural frequency over the time. An analytical model of a multi-segment spinning spindle, based on the Dynamic Stiffness Matrix (DSM) formulation and exact within the limits of the Euler-Bernoulli beam bending theory, was developed. The beam exhibits coupled Bending-Bending (B-B) vibration and, as expected, its natural frequencies are found to decrease with increasing spinning speed. The bearings were included in the model using two different models; rigid, simply-supported,frictionless pins and flexible linear spring elements. The linear spring element stiffness, Ks, was then calibrated so that the fundamental frequency of the system matched the nominal data provided by the manufacturer. This step is vital to the next phase of the authors’ ongoing research, where the bearing wear would be modeled in terms of spindle’s service time/age, to investigate the consequent effects on the stability lobes and, in turn, on themachine Chatter.
\n\t\t
\n\t
Acknowledgments
\n\t\t\t
The authors wish to acknowledge the support provided by Ryerson University and Natural Science and Engineering Research Council of Canada (NSERC).
\n\t\t
\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/39838.pdf",chapterXML:"https://mts.intechopen.com/source/xml/39838.xml",downloadPdfUrl:"/chapter/pdf-download/39838",previewPdfUrl:"/chapter/pdf-preview/39838",totalDownloads:2464,totalViews:199,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,dateSubmitted:"March 8th 2012",dateReviewed:"July 6th 2012",datePrePublished:null,datePublished:"October 2nd 2012",dateFinished:"October 5th 2012",readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/39838",risUrl:"/chapter/ris/39838",book:{slug:"advances-in-vibration-engineering-and-structural-dynamics"},signatures:"Seyed M. Hashemi and Omar Gaber",authors:[{id:"19621",title:"Prof.",name:"Seyed M.",middleName:"M.",surname:"Hashemi",fullName:"Seyed M. Hashemi",slug:"seyed-m.-hashemi",email:"smhashem@ryerson.ca",position:null,institution:null},{id:"159513",title:"Mr.",name:"Omar",middleName:null,surname:"Gaber",fullName:"Omar Gaber",slug:"omar-gaber",email:"ogaber@ryerson.ca",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Mathematical model",level:"1"},{id:"sec_3",title:"3. Numerical tests and experimental results",level:"1"},{id:"sec_3_2",title:"3.1. DSM results",level:"2"},{id:"sec_4_2",title:"3.2. Preliminary Experimental results",level:"2"},{id:"sec_6",title:"4. Conclusion",level:"1"},{id:"sec_7",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAdetoro\n\t\t\t\t\t\t\tO. B. \n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tWen\n\t\t\t\t\t\t\tP. H.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSim\n\t\t\t\t\t\t\tW. 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S.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tNee\n\t\t\t\t\t\t\tA. Y. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1997\n\t\t\t\t\tTool Wear and Chatter Detection using the Coherence Function of Two Crossed Accelerations.\n\t\t\t\t\tInternational Journal of Machine Tools and Manufacture\n\t\t\t\t\t37\n\t\t\t\t\t4\n\t\t\t\t\tApril\n\t\t\t\t\t425\n\t\t\t\t\t435\n\t\t\t\t\t0890-6955\n\t\t\t\t\n\t\t\t'},{id:"B14",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMann\n\t\t\t\t\t\t\tB. P.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tEdes\n\t\t\t\t\t\t\tB. T.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tEasly\n\t\t\t\t\t\t\tS. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYoung\n\t\t\t\t\t\t\tK. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMa\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008\n\t\t\t\t\tChatter Vibration and Surface Location Error Prediction for Helical End Mills.\n\t\t\t\t\tInternational Journal of Machine Tools and Manufacture\n\t\t\t\t\t48\n\t\t\t\t\t3-4\n\t\t\t\t\tMarch\n\t\t\t\t\t350\n\t\t\t\t\t361\n\t\t\t\t\t0890-6955\n\t\t\t\t\n\t\t\t'},{id:"B15",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPeng\n\t\t\t\t\t\t\tZ. K.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJackson\n\t\t\t\t\t\t\tM. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGuo\n\t\t\t\t\t\t\tL. Z.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tParkin\n\t\t\t\t\t\t\tR. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMeng\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2010\n\t\t\t\t\tEffects of Bearing Clearance on the Chatter Stability of Milling Process.\n\t\t\t\t\tNonlinear Analysis: Real World Applications\n\t\t\t\t\t11\n\t\t\t\t\t5\n\t\t\t\t\tOctober\n\t\t\t\t\t3577\n\t\t\t\t\t3589\n\t\t\t\t\t1468-1218\n\t\t\t\t\n\t\t\t'},{id:"B16",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRahman\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIto\n\t\t\t\t\t\t\tY.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1986\n\t\t\t\t\tDetection of the Onset of Chatter Vibration.\n\t\t\t\t\tJournal of Sound and Vibration\n\t\t\t\t\t109\n\t\t\t\t\t2\n\t\t\t\t\tSeptember\n\t\t\t\t\t193\n\t\t\t\t\t205\n\t\t\t\t\t0002-2460X\n\t\t\t\t\n\t\t\t'},{id:"B17",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSolis\n\t\t\t\t\t\t\tE.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPeres\n\t\t\t\t\t\t\tC. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJimenez\n\t\t\t\t\t\t\tJ. E.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAlique\n\t\t\t\t\t\t\tJ. R.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMonje\n\t\t\t\t\t\t\tJ. C.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2004A New Analytical-Experimental Method for the Identification of Stability Lobes in High-Speed Milling.\n\t\t\t\t\tInternational Journal of Machine Tools and Manufacture\n\t\t\t\t\t44\n\t\t\t\t\t15\n\t\t\t\t\tDecember)1591\n\t\t\t\t\t1597\n\t\t\t\t\t0890-6955\n\t\t\t\t\n\t\t\t'},{id:"B18",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTaylor\n\t\t\t\t\t\t\tF. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1907\n\t\t\t\t\tOn the Art of Cutting Metal.\n\t\t\t\t\tTrans. ASME\n\t\t\t\t\t28\n\t\t\t\t\t31\n\t\t\t\t\t350\n\t\t\t\t\n\t\t\t'},{id:"B19",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tShabana\n\t\t\t\t\t\t\tA.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tThomas\n\t\t\t\t\t\t\tB.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1987\n\t\t\t\t\tChatter Vibration of Flexible Multibody Machine Tool Mechanisms.\n\t\t\t\t\tMechanical Machine Theory\n\t\t\t\t\t22\n\t\t\t\t\t4\n\t\t\t\t\t359\n\t\t\t\t\t369\n\t\t\t\t\t0009-4114X\n\t\t\t\t\n\t\t\t'},{id:"B20",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTlusty\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIsmail\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1981\n\t\t\t\t\tBasic Non-Linearity in Machining Chatter.\n\t\t\t\t\tCIRP Annals- Manufacturing Technology\n\t\t\t\t\t30\n\t\t\t\t\t1\n\t\t\t\t\t299\n\t\t\t\t\t304\n\t\t\t\t\t0007-8506\n\t\t\t\t\n\t\t\t'},{id:"B21",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTlusty\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIsmail\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1983\n\t\t\t\t\tSpecial Aspects if Chatter in Milling.\n\t\t\t\t\tJournal of Vibration, Acoustics, Stress, and Reliability in Design\n\t\t\t\t\t105\n\t\t\t\t\t1\n\t\t\t\t\tJanuary\n\t\t\t\t\t24\n\t\t\t\t\t32\n\t\t\t\t\t0739-3717\n\t\t\t\t\n\t\t\t'},{id:"B22",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTlusty\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZaton\n\t\t\t\t\t\t\tW.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tIsmail\n\t\t\t\t\t\t\tF.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1983Stability Lobes in Milling. CIRP Annals- Manufacturing Technology\n\t\t\t\t\t32\n\t\t\t\t\t1\n\t\t\t\t\t309\n\t\t\t\t\t313\n\t\t\t\t\t0007-8506\n\t\t\t\t\n\t\t\t'},{id:"B23",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTobias\n\t\t\t\t\t\t\tS. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tAndrew\n\t\t\t\t\t\t\tC.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1962\n\t\t\t\t\tVibration in Horizontal Milling.\n\t\t\t\t\tInternational Journal of Machine Tool Design Research\n\t\t\t\t\t2\n\t\t\t\t\t4\n\t\t\t\t\tOctober-December\n\t\t\t\t\t369\n\t\t\t\t\t378\n\t\t\t\t\t0890-6955\n\t\t\t\t\n\t\t\t'},{id:"B24",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTobias\n\t\t\t\t\t\t\tS. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1965\n\t\t\t\t\tMachine Tool Vibration. Blackie and Sons Ltd.\n\t\t\t\t\tLondon, Glasgow\n\t\t\t\t\n\t\t\t'},{id:"B25",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZaghbani\n\t\t\t\t\t\t\tI.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSongmene\n\t\t\t\t\t\t\tV.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2009\n\t\t\t\t\tEstimation of Machine-Tool Dynamic Parameters During Machining Operation Through Operational Modal Analysis.\n\t\t\t\t\tInternational Journal of Machine Tools and Manufacture\n\t\t\t\t\t49\n\t\t\t\t\t12-13\n\t\t\t\t\tOctober\n\t\t\t\t\t947\n\t\t\t\t\t957\n\t\t\t\t\t0890-6955\n\t\t\t\t\n\t\t\t'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Seyed M. Hashemi",address:"smhashem@ryerson.ca",affiliation:'
Department of Aerospace Eng., Ryerson University, Toronto (ON), Canada
Department of Aerospace Eng., Ryerson University, Toronto (ON), Canada
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1. Introduction
Stress corrosion cracking (SCC) in chemical, petrochemical, and power plant industries is an insidious form of corrosion, which causes a lot of financial losses and human damages [1, 2, 3, 4, 5]. This phenomenon is associated with a combination of tensile stress, environment, and some metallurgical conditions as described in Figure 1.
Figure 1.
The essential requirements for SCC.
During stress corrosion cracking, the metal or alloy is virtually unattacked over most of its surface, while fine and branch cracks progress through the bulk of material [6]. It is shown in Figure 2. This cracking phenomenon has serious consequences since it can occur under stresses much lower than design stresses and lead the equipment and structures to premature failures [7, 8, 9, 10, 11].
Figure 2.
Crack development in carbon steel exposed to nitrate solution.
Stress corrosion cracking starts from corrosion sites at the material surfaces and progresses into a brittle manner. The process of cracking is not strictly a mechanical process, as the corrosivity of the environment strongly affects the fracture mode. Both intergranular and transgranular stress corrosion cracking are observed. Intergranular cracking proceeds along grain boundaries, while transgranular cracking advances without apparent preference for boundaries [12]. An example of stress corrosion cracking in which the crack has progressed in both intergranular and transgranular paths is shown in Figure 3. The development mode of cracking depends on the composition and microstructure of the material and environment.
Figure 3.
Intergranular and transgranular stress corrosion cracking of the AISI 316L stainless steel at polythionic acid environment [8].
In this chapter, the conditions for the occurrence of SCC are first introduced. Then, the stress corrosion cracking mechanism for various materials in conditions that are susceptible is discussed in detail. The design of industrial structures and components is usually based on tensile properties, which have many disadvantages. So, the science of fracture mechanics applies in the situations prone to SCC because of the inevitability of manufacturing and service defects in materials and for considering the role of such imperfections. Methods of prevention based on corrosion science and empirical data are presented. Finally, practical examples are given to better understand the issue.
2. Requirements for SCC
Not all metal-environment combinations are susceptible to cracking. In other words, the environment for occurrences of SCC for each metal or alloys is specific. Also, the resources of stress for each case of failure may be different.
2.1 Materials
2.1.1 Stainless steels
Austenitic stainless steels suffer from SCC in chlorides, caustic, and polythionic acid. When austenitic stainless steels with sufficient carbon content (more than 0.03 wt.%) are heated in the range of 415–850°C, their microstructure becomes susceptible to precipitation of chromium carbides (M23C6) along grain boundaries known as sensitization [9, 12, 13]. Formation of Cr-rich carbides along grain boundaries may drastically deplete free chromium content in the area adjacent to the grain boundaries and render them susceptible to rapid preferential dissolution. Sensitized steels are most susceptible; the stress corrosion cracking of nonsensitized steels is also observed [14, 15]. Dissolution of grain boundaries in some corrosive environments aside from tensile stress led these types of materials to SCC.
2.1.2 Copper and copper alloys
Seasonal cracking of brass in the rainy season in an ammoniacal environment is another classical example of SCC. This was first identified on the brass cartridge used by the British Army in India. Since it is usually identified during the rainy season, it is also called seasonal cracking [12]. Alpha brass is an alloy of Cu-Zn. It can crack either intergranularly or transgranularly in nontarnishing ammonia solutions, depending on its zinc content [16, 17, 18]. Transgranular stress corrosion cracking, TGSCC, is observed in alloys with 20 or 30% Zn but not in alloys with 0.5 or 10% Zn [19, 20]. Stress corrosion cracking of Cu-Zn and Cu-A1 alloys in cuprous ammonia solutions can only occur when the parting limits for dealloying are exceeded. The parting limits are about 14 and 18 a/o for Cu-A1 and Cu-Zn, respectively [21]. Cu-A1 and Cu-Ga alloys have shown similar behaviors [19, 22].
2.1.3 Aluminum and aluminum alloys
Aluminum and all its alloys can fail by cracking along grain boundaries when simultaneously exposed to specific environments and stresses of sufficient magnitude [23, 24]. Of eight series of aluminum alloys, 2xxx, 5xxx, and 7xxx aluminum alloys are susceptible to SCC. Among them, 7xxx series aluminum alloys have a specific application in aerospace, military, and structural industries due to superior mechanical properties. In these high-strength 7xxx aluminum alloys, SCC plays a vital factor of consideration, as these failures are catastrophic during the service [25].
2.1.4 Carbon steels
Carbon and low alloy steels have shown SCC in a wide range of environments that tend to form a protective passive or oxide film [26, 27, 28, 29, 30]. The environments that would passivate carbon steels have been found to cause SCC, including strong caustic solutions, phosphates, nitrates, carbonates, ethanol, and high-temperature water. The problems are important for both economic and safety reasons, due to the extensive use of carbon steels [31]. For example, nitrate cracking in an ammonium nitrate plant caused by catastrophic failures and a lot of financial losses. Caustic cracking of steam-generating boilers made of low alloy steels was a serious problem, which led an ammonia plant to repeated emergency shutdowns.
2.1.5 Titanium alloys
Stress corrosion cracking may be a problem whenever certain high-strength titanium alloys are exposed to aqueous and certain solvent environments [32, 33, 34, 35, 36]. For the first time, SCC of titanium was reported by Kiefer and Harple who describe the cracking phenomena with commercially pure titanium in red fuming nitric acid [37]. Hot salt cracking of titanium alloys was reported in turbine blades that operate at high temperature in the mid-1950s. The subject became very active in the early 1960s because of the SCC problem connected to these alloys in a transportation program [38].The first known report of stress corrosion cracking of titanium alloys in room temperature aqueous environments was that of Brown. He found that titanium alloys, 8% aluminum–1% molybdenum–1% vanadium alloy (Ti, 8–1–1), were susceptible to SCC in seawater [38].
2.2 Environments
Another requirement for SCC to occur is a corrosive environment. The environments for SCC are specific because not all environments promote SCC. For those alloys that develop a protective film, an aggressive ion is required to promote SCC. The aggressive media to passive layer of stainless steels are chlorides, caustic, and polythionic acid. The austenitic stainless steel series 300 is more susceptible in an environment containing chlorides. Chlorides will not cause SCC unless an aqueous phase is present. It appears that stress corrosion cracking in austenitic stainless steels in the presence of chlorides proceeds transgranularly and usually occurs at temperature above 70°C [39, 40]. Cases of SCC due to chlorides have been experienced at ambient temperatures on parts that were subjected to heavy machining [41, 42]. Caustic embrittlement or stress corrosion cracking in caustic environment is another serious problem in austenitic stainless steels and causes many explosions and other types of failures in steam boiler and super heater components [9, 43, 44, 45]. Caustic cracking failures frequently originate in a welding area, which is intergranular, and a very concentrated caustic solution is usually necessary [40]. Polythionic acid is another environment, which causes SCC in austenitic stainless steels. Sulfur in feed gas in chemical and petrochemical plants led to formation of polythionic acid (H2SxO6, x = 2–5), which aside from moisture also induced intergranular stress corrosion cracking in austenitic stainless steels [46, 47]. Well-known specific environments for the stress corrosion cracking in Al alloys include water vapor, aqueous solutions, organic liquids, and liquid metals [48]. The SCC of Ti alloys in aqueous chloride and methanolic chloride environments at ambient temperatures has been widely reported [49]. The summary of environments that cause SCC in mostly used alloys is presented in Table 1.
Metal
Environment
Al alloys
NaCl-H2O2 solutions
NaCl solutions
Seawater
Copper alloys
Ammonia vapor and solutions
Amines
Water or water vapor
Gold alloys
FeCl3 solutions
Acetic acid-salt solutions
Inconel
Caustic soda solutions
Lead
Lead acetate solutions
Magnesium alloys
NaCl-Na2CrO4 solutions
Rural and coastal atmospheres
Seawater
Distilled water
Nickel
Fused caustic soda
Steels
NaOH solutions
NaOH-Na2SiO4 solutions
Calcium, ammonium, and sodium nitrite solutions
Mixed acids (H2SO4-HNO3)
Acidic H2S solutions
Seawater
Carbonate-bicarbonate solutions
Stainless steels
Acidic chloride solutions
NaCl-H2O2 solutions
Seawater
H2S
NaOH-H2S solutions
Condensing steam from chloride waters
Titanium alloys
Red fuming nitric acid
Seawater
Methanol-HCl
Table 1.
Summary of some environments caused by SCC on different alloys.
The stress in the form of tensile (not compressive) plays a key role in the SCC fracture processes. In fact, SCC would never have occurred in the absence of stress. The required tensile stresses may be in the form of directly applied stresses, thermal, in the form of residual stresses, or a combination of all [8, 50]:
σ=σapplied+σthermal+σresidualE1
For SCC to occur alone by applied stress, it must have a very high magnitude. The welding and mechanical residual stresses are the main sources of stress attributed to the stress corrosion cracking. The welding residual stress is produced as a result of nonuniform temperature changes during welding operation and can be calculated from thermal strain vectors.
The thermal strain vector, Δεth, is formulated by a temperature-dependent differential expansion coefficient (°/c) as follows [2]:
Δεth=αΔTE2
in which Δεth is the variation of strain, α is the thermal expansion of material, and ΔT is the temperature change.
The operational thermal stress can also be calculated from Eq. 2. Mechanical workings such as cold deformation and forming, machining, and grinding are the other sources, which introduce residual stresses [8, 51].
3. Stress corrosion cracking mechanism
Extensive investigations have been devoted to find mechanisms of SCC for different materials and environments. An SCC failure illustrates the combined effects of mechanical, physical, and chemical/electrochemical factors causing the separation of metal bonds at the crack tip, thereby advancing the crack. Three mechanisms for SCC have been proposed through the investigations [52]:
3.1 Pre-existing active path mechanism
This model supposes that there are pre-existing paths in an alloy that is susceptible to anodic dissolution. Because of precipitation or solute segregation of impurities like sulfur, phosphorus, and chromium carbides, the electrochemical properties of the matrix and segregates are changed. The area adjacent to the grain boundaries is depleted from one or more alloying elements, and so under such conditions, localized galvanic cells are created (Figure 4). Since precipitation or segregation is generally anodic to the matrix of the grains, dissolution under an anodic reaction occurs and provides active path for localized corrosions [53]. Also, the removal of the protective film at the pre-existing crack tips by plastic deformation would facilitate the onset of localized corrosion.
Figure 4.
Galvanic cell mechanism [52].
3.2 Strain-generated active path mechanisms
This mechanism has been extensively studied in stress corrosion cracking of alpha brass in ammoniacal environment and also proposed for caustic cracking of boiler steel. The model is based on the idea of a strain-induced rupture of the protective film, and so plastic strains play a main role in failure processes [52, 55]. The theory assumes the existence of a passivation film on a metal surface. The passivation film protects the underlying metal against corrosive agents. The passivation film is ruptured by plastic strain due to mechanical workings. After the film is ruptured, the bare metal is exposed to the corrosive environment. The processes of disruptive strain (disruption of protective film) and film formation (due to repassivation) have occurred and alternate with each other. The crack propagates when the rate of rupture of oxide film is higher than the rate of repassivation of the film [52]. The mechanism is shown in Figure 5.
Figure 5.
Strain-generated active path mechanisms. (A) Film rupture model and (B) slip-step dissolution model [52].
3.3 Adsorption-related phenomenon
This model is based on the effects of environmental species on interatomic bond strength. The theoretical fracture stress required to separate two layers of atoms of spacing b is given by [56].
σf=Eγsb1/2E3
where E is the Young modulus, γ is the surface energy, and b is the spacing between atoms.
This theory implies that if surface energy is reduced, then σf will also be reduced. In corrosive environments, aggressive agents are present and they are absorbed at the crack tips, the surface energy is effectively lowered, and fracture takes place in stress much lower than design stress [52].
4. Application of fracture mechanics
The design of steel structure and component based on tensile properties has many disadvantages that do not take into account the role of imperfections. Fracture mechanic introduces another material characteristic, namely, fracture toughness, KIC, which considered the role of cracks and imperfection in the form of cracks in designs. In its simplest form [57].
KIC=σπaE4
where σ is the design stress and a is the size of an existing crack.
According to this equation, fracture occurs when stress intensity factor, Kt, on the crack tip is equal to KIC. This applies for the propagation of cracks due to mechanical loadings. For the structure parts exposed to corrosive environments, the situation is quietly different. The corrosive agents caused a significant drop in the load capacity and the fracture toughness of the metals. This is typically shown in Figure 6. As outlined in the diagram, designs of structures in the corrosive environment based on KIc led the component to failure in a short period of time. Therefore, in these situations, KIc should be replaced with KIscc, which is the threshold value for SCC [12]. This means that in the corrosive environment, the load capacity must be significantly lower than the clean environments. The use of fracture mechanics for high-strength low alloy steels is responsive, but for austenitic steels with branch cracks, the subject should be treated with caution [12].
Figure 6.
Effects of corrosive environment on fracture toughness [12].
5. Prevention
Since the exact mechanism of SCC has not been completely understood, prevention methods are either general or empirical in nature. Appropriate strategy should be done in order to minimize this problem to ensure not only the safety of human life but also the safety of cost. The following general methods are recommended to overcome the SCC problems [12, 52, 58, 59]:
Lowering the tensile stress in the welded component using post weld heat treatment. The post weld heat treatment reduced or eliminated residual stress on surface and through the bulk of material. Plan and low alloy steels may be a stress relief at 1100–1200°F. The range of residual stress relief temperature for austenitic stainless steels is from 1500 to 1700°F. Reduction of tensile stresses by shot peening is also recommended. Shot peening introduces surface compressive stresses.
Eliminating aggressive agents from the environment by, for example, degasification, demineralization, or distillation.
Changing the alloy is one possible solution if neither the environment nor stress can be changed. For example, it is a common practice to use Inconel (raising the nickel content) when typ. 304 stainless steel is not satisfactory.
Applying cathodic protection: impressed current cathodic protection system has been successfully used to prevent SCC of steels.
Adding inhibitors to the system if feasible: high concentrations of phosphate have been successfully used.
Coatings are sometimes used, and they depend on keeping the environment away from the metal.
6. Failure case studies
6.1 Case 1: stress corrosion cracking of a circulation water heater tube sheet [8]
After only 3 years’ service of a circulation water heater (heat exchanger), it has been shown to sever leakage and has led a methanol plant to emergency shutdown. An on-site investigation revealed extensive cracking initiated at weld area and through the tube sheet holes as it is shown in Figure 7.
Figure 7.
Failed area (a) cracks extending in the weld joint of tube sheet to plugs and (b) branched cracks in the surface of the tube sheet and through the holes [8].
6.1.1 Material and environment
The circulation water heater is a vertical U-type heat exchanger made of austenitic stainless steels. The equipment used to decline reforms gas temperature in a methanol plant. The hot reformed gas at approximately 385°C entered the tubes and is cooled down to 168°C by exchanging the heat with processed water in the shell. The gases that flow through the tubes are mainly CO2, CO, H2, CH4, and N2 and at a pressure of 3.9 MPa. At the shell cooling process, water flows with about 6 MPa pressure.
6.1.2 Cause
Deposits had formed on top of the tube sheet due to shutdown errors. AISI 316L materials overheated in service because of the insulation role of the deposits. Material sensitization occurs since overheating. The presence of sulfur in the process gas aside from moisture formed polythionic acid during shutdowns. Residual stress produced by heavy machining and welding aside from operational thermal stress provided tensile stress, which is needed for SCC. Stress corrosion cracking is induced by polythionic acid. Concentrated water with other aggressive agents such as caustic and chlorides leaked through the cracks aid the failures.
6.1.3 Prevention
Cleaning of the shell by demineralized water after each shut down in order to prevent the forming of insulating deposits above the tube sheet
Reduction of sulfur in feeding gas
Reduction of caustic and chlorides in processed water
6.2 Case 2: failure of an austenitic stainless steel tubes in a gas-fired steam heater [9]
Carryover of caustic soda (NaOH) in the steam path caused catastrophic failure of superheater stainless steel tubes in a gas-fired heater and led to an unexpected shutdown after just 5 months of continuous service following the start of production. The failure areas are shown in Figure 8. Three types of cracks are identified in various regions of the tube: circumferential cracks adjacent to the seam weld, circumferential cracks at the ribbon of the seam weld, and longitudinal cracks on the U-bend. The path of cracks was complex on the surface or in the bulk metal; all had nucleated from inside the tubes. A visual inspection revealed a white deposit, high in sodium, around the cracks on the surface of the tubes.
Figure 8.
(a and b) Circumferential cracks adjacent to the seam weld, (c and d) circumferential cracks at the ribbon of seam weld, and (e) longitudinal cracks on the U-bend [9].
6.2.1 Material and environment
The superheater tube material was made of AISI 304H austenitic stainless steel material.
The gas-fired steam heater (FH) generates high-pressure (HP) steam for turbines for the processing of methanol. Demineralized water for the boiler and subsequent steam path is prepared in the water treatment unit. Caustic soda is injected to demineralized water for pH control. The water is transferred to the preheat exchangers, is converted to saturated high-pressure steam at 325°C and 119 MPa, and is sent to the FH. Through the FH tubes, saturated steam converted to supersaturate steam at a temperature of 505°C and pressure of 119 MPa.
6.2.2 Cause
The main cause of crack initiation was the increase of pH due to the rise of caustic concentration in condensed drops. Sensitized austenite grains caused by chromium carbide depletion adjacent to the grain boundaries were attacked by concentrated caustic in the HAZ metal and U-bend area and led the heater to the caustic SCC failure.
6.2.3 Prevention
Using A335 Grade P9, a low alloy steel tube shows higher resistance to SCC than AISI 304H stainless steel
Proper discharge of the tubes during shutdowns to prevent the formation of the concentrated deposits of caustic through the tubes
6.3 Case 3: failures of brass condenser tubes [60]
After a general overhaul of a thermal power plant in Serbia in November 2014, failure of hundreds of brass condenser tubes occurred during the hydrostatic test. Also, it was noted that some backing plates had fallen off from the tubes before this test. Fracture is observed only in condenser tubes of brass, as can be seen in Figure 9.
Figure 9.
Failure of brass condenser tubes near joining location with backing plate.
6.3.1 Material and environment
The failed tube material of the condenser was made of brass CuZn28Sn1 (admiralty brass). The cooling water (roughly filtered river water) flows through the tubes, while the hot steam flows around the tubes.
6.3.2 Cause
Analysis of fracture surfaces using scanning electron microscopy (SEM) has shown the brittle transgranular fracture due to the occurrence of SCC. The condenser tubes are made of brass CuZn28Sn1. Ammonia and other nitrogen compounds in the cooling water through the tubes were found. These compounds are specific agents that cause stress corrosion cracking (SCC) in brass. In the joining region of condenser tubes to backing plates, there are residual tensile stresses. During the floods in May 2014, there was an increase in the concentration of ammonia and other nitrogen compounds in the river cooling water flowing through the condenser tubes. Failure of brass condenser tubes occurred due to SCC, because the necessary conditions for the SCC occurrence were fulfilled.
6.3.3 Prevention
The risk of SCC in brass condenser tubes can be reduced if specific substances responsible for SCC occurrence are removed, as much as possible. This can be achieved by cleaning and drying the tubes immediately after the operation delay of the power plant.
Another way to reduce the risk of SCC occurrence in condenser tubes is the replacement of existing tubes (made of brass CuZn28Sn1, very susceptible to SCC) with tubes made of alloys of greater resistance to SCC, such as copper-nickel alloys or Bi-brass alloys [61].
7. Conclusion
Stress corrosion cracking is one of the main causes of unforeseen and dangerous destruction of industrial plants. The sensitized material, certain environments, and stress are three factors necessary for the occurrence of these types of failures. The environment prone to the cracking for each metal or alloy is specific because not all environments promote the SCC. Austenitic stainless steels suffer from SCC in chlorides, caustic, and polythionic acid. Copper alloys corrode in ammonia-containing environments. Well-known specific environments for the stress corrosion cracking in Al alloys include water vapor, aqueous solutions, organic liquids, and liquid metals. The SCC of Ti alloys in aqueous chloride and methanolic chloride environments has been widely reported. The tensile stress plays a key role in the stress corrosion cracking phenomenon. The required tensile stresses may be in the form of directly applied stresses, thermal, in the form of residual stresses, or a combination of all.
If one of these three components does not exist, this type of corrosion will not occur. Therefore, the solving methods should be based on the elimination of one of these three factors. Corrosive environment modification, the stress in the form of compression, and using proper material are three general proposed methods of prevention.
\n',keywords:"stress corrosion cracking, environments, materials, mechanisms, fracture mechanic",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/63441.pdf",chapterXML:"https://mts.intechopen.com/source/xml/63441.xml",downloadPdfUrl:"/chapter/pdf-download/63441",previewPdfUrl:"/chapter/pdf-preview/63441",totalDownloads:716,totalViews:0,totalCrossrefCites:2,dateSubmitted:"March 21st 2018",dateReviewed:"August 9th 2018",datePrePublished:"September 27th 2019",datePublished:"December 18th 2019",dateFinished:"September 7th 2018",readingETA:"0",abstract:"Stress corrosion cracking (SCC) is the formation and growth of crack through materials subjected to tensile stress and a specific corrosive medium. It can lead to unexpected sudden failure of normally ductile metals. Metal-environment combinations susceptible to cracking are specific. This means that all environments do not cause SCC on all of the alloys. Additionally, the environments that cause this kind of cracking have little corrosion effect on the alloy in normal conditions. In certain states, unwanted environmental and metallurgical changes have occurred and provide the metal-environment combination sensitive to SCC. The SCC sites on the metal surfaces may not be visible by visual inspection, while metal parts are being filled with microscopic cracks. These invisible cracks progress rapidly and lead the component and structures to catastrophic failures. In this chapter, the incidence of SCC on important industrial alloys from the chemical, metallurgical, and mechanical point of view is discussed.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/63441",risUrl:"/chapter/ris/63441",signatures:"Alireza Khalifeh",book:{id:"7369",title:"Failure Analysis",subtitle:null,fullTitle:"Failure Analysis",slug:"failure-analysis",publishedDate:"December 18th 2019",bookSignature:"Zheng-Ming Huang and Sayed Hemeda",coverURL:"https://cdn.intechopen.com/books/images_new/7369.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"196101",title:"Dr.",name:"Zheng-Ming",middleName:null,surname:"Huang",slug:"zheng-ming-huang",fullName:"Zheng-Ming Huang"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"251415",title:"Ph.D. Student",name:"Alireza",middleName:null,surname:"Khalifeh",fullName:"Alireza Khalifeh",slug:"alireza-khalifeh",email:"areza1006@gmail.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Requirements for SCC",level:"1"},{id:"sec_2_2",title:"2.1 Materials",level:"2"},{id:"sec_2_3",title:"2.1.1 Stainless steels",level:"3"},{id:"sec_3_3",title:"2.1.2 Copper and copper alloys",level:"3"},{id:"sec_4_3",title:"2.1.3 Aluminum and aluminum alloys",level:"3"},{id:"sec_5_3",title:"2.1.4 Carbon steels",level:"3"},{id:"sec_6_3",title:"2.1.5 Titanium alloys",level:"3"},{id:"sec_8_2",title:"2.2 Environments",level:"2"},{id:"sec_9_2",title:"2.3 Stress",level:"2"},{id:"sec_11",title:"3. Stress corrosion cracking mechanism",level:"1"},{id:"sec_11_2",title:"3.1 Pre-existing active path mechanism",level:"2"},{id:"sec_12_2",title:"3.2 Strain-generated active path mechanisms",level:"2"},{id:"sec_13_2",title:"3.3 Adsorption-related phenomenon",level:"2"},{id:"sec_15",title:"4. Application of fracture mechanics",level:"1"},{id:"sec_16",title:"5. Prevention",level:"1"},{id:"sec_17",title:"6. Failure case studies",level:"1"},{id:"sec_17_2",title:"6.1 Case 1: stress corrosion cracking of a circulation water heater tube sheet [8]",level:"2"},{id:"sec_17_3",title:"6.1.1 Material and environment",level:"3"},{id:"sec_18_3",title:"6.1.2 Cause",level:"3"},{id:"sec_19_3",title:"6.1.3 Prevention",level:"3"},{id:"sec_21_2",title:"6.2 Case 2: failure of an austenitic stainless steel tubes in a gas-fired steam heater [9]",level:"2"},{id:"sec_21_3",title:"6.2.1 Material and environment",level:"3"},{id:"sec_22_3",title:"6.2.2 Cause",level:"3"},{id:"sec_23_3",title:"6.2.3 Prevention",level:"3"},{id:"sec_25_2",title:"6.3 Case 3: failures of brass condenser tubes [60]",level:"2"},{id:"sec_25_3",title:"6.3.1 Material and environment",level:"3"},{id:"sec_26_3",title:"6.3.2 Cause",level:"3"},{id:"sec_27_3",title:"6.3.3 Prevention",level:"3"},{id:"sec_30",title:"7. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Abedi SS, Abdolmaleki A, Adibi N. 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Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran
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The correct diagnosis and effective treatment of H. pylori gastric infection are essential in controlling this condition. The available diagnostic methods have advantages and limitations related to factors such as age of patients, technical difficulty level, costs and extensive accessibility in hospitals. The eradication therapy of H. pylori infection is still a challenge for gastroenterologists. One of the main causes of failure in H. pylori eradication is antibiotic resistance. Biopsy cultures are the most widely used methods among the antimicrobial susceptibility tests. In case of a negative culture, H. pylori can be clearly recognised in histological sections. The sensitivity and specificity of histology for the diagnosis depend on clinical settings, density of colonisation and the experience of the histopathologist. 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CSIC affiliated authors can also take advantage of a central Open Access fund (amounting to 10,000 EUR) to cover up to 50% of the rest of the OAPF until it expires. Effective for chapters accepted from January 1, 2020.
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Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
The Claremont Colleges are pledging funds via the Knowledge Unlatched program to ensure academics can publish Open Access content more easily.
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The University of Surrey is pledging funds via the Knowledge Unlatched program to ensure academics can publish Open Access content more easily.
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Virginia Polytechnic Institute and State University
Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
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CSIC affiliated authors can also take advantage of a central Open Access fund (amounting to 10,000 EUR) to cover up to 50% of the rest of the OAPF until it expires. Effective for chapters accepted from January 1, 2020.
Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
Corresponding authors will receive a 25% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters. A 20% discount for publishing a long-form monographs, 25% for compacts and 23% for short-form monographs.
The Claremont Colleges are pledging funds via the Knowledge Unlatched program to ensure academics can publish Open Access content more easily.
\n\n
Corresponding authors will receive a 15% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters or monograph publications. To use the discount you will need to verify your institutional email address. These discounts are valid from 2020 to 2022.
The University of Massachusetts, Amherst is pledging funds via the Knowledge Unlatched program to ensure academics can publish Open Access content more easily.
\n\n
Corresponding authors will receive a 10% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters or monograph publications. To use the discount you will need to verify your institutional email address. These discounts are valid from 2020 to 2022.
The University of Surrey is pledging funds via the Knowledge Unlatched program to ensure academics can publish Open Access content more easily.
\n\n
Corresponding authors will receive a 10% discount on their Open Access Publication Fees (OAPF) for Open Access book chapters or monograph publications. To use the discount you will need to verify your institutional email address. These discounts are valid from 2020 to 2022.
\n\n
\n\t
Virginia Polytechnic Institute and State University
Important: You must be a member or grantee of the above listed institutions in order to apply for their Open Access publication funds.
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