Rules of Thumb for Mechanical Engineers 2010 Part 15 ppt

340 Rules of Thumb for Mechanical Engineers Fast Fracture As stated earlier, fast fracture will occur when the stress intensity factor exceeds the fracture toughness. Fracture toughness is a material property that is dependent on tem- perature and component thickness. Figure 13 shows that decreasing temperature decreases the fracture toughness. This is due to the lower ductility at lower temperatures. Figure 14 shows that increasing thick- ness decreases the fracture toughness. This is because thin specimens are subject to plane stress, which allows much more yielding at the crack tip. As specimen thickness is in- -200 F ROOm Temperalure Tempemre Figure 13. Effect of decreasing temperature on fracture toughness. Plane e U $ I I I I I I 10 20 30 0 0 Thickness le), mm Figure 14. Effect of specimen thickness on fracture toughness p 41. (Reprinted with permission of John Wiley & Sons, Inc.) creased, it asymptotically approaches a minimum value. This is the value that is quoted as the fracture toughness. The actual fracture toughness for thin specimens may be somewhat greater than KIC. Figure 15 shows how fracture toughness varies with yield strength for aluminum, titanium, and steels. Note that for all three, alloys which had very high yield strengths had relatively low values of hcture toughness. Also, be- cause the stress intensity factor is a function of crack length to the .5 power, reducing the fracture toughness by a fac- tor of 2 will reduce the the critical crack size by a factor of 4. Therefore, a designer who considers specifying an alloy with a high yield strengh should realize he may be sig- nificantly reducing the critical crack size. In field service, this could result in sudden failures instead of components being replaced after cracks were discovered. Threshold Stress Intensity Factor If the stress intensity factor range does not exceed the threshold value, then a crack will not propagate. ASTM de- fines the threshold value to be where the crack growth per cycle(da/dn) drops below 3 x lW9 inches per cycle. Unlike fracture toughness, the threshold stress intensity factor, AK,, is dependent upon the R ratio. Threshold behavior is very important for components which must endure millions of cycles. In analysis, it can be used to make very conservative estimates. If the applied stress is known, a flaw size can be assumed, and the stress intensity factor can be calculated. As long as the threshold value exceeds AK, no crack growth can occur. If the stress MPa 240 200 160 120 E I 80 40 0 0 40 EO 120 160 200 240 280 320 360 Yield strength kri Figure 15. Fracture toughness versus yield strength for various classes of materials [18]. Fatigue 341 * 0. I 2 4 intensity factor range exceeds AK,, then more detailed analysis must be made to determine the number of cycles the component can be expected to last in service. Sometimes, after many parts have been released for field service, a problem will be discovered in the manufacturing process. The question is then raised, “Do we need to replace these parts immediately, or can we safely wait and replace them during the next overhaul?’ Obviously, the first approach is safer, but may be extremely costly. However, if the parts are left in service and fail, the consequences can be devas- tating. Therefore, any analysis which is done must err on the conservative side. In these instances, the stress intensity fac- tor is often calculated and compared to the A&. Estimates of threshold stress intensity factor. Testing to ob- tain AKth is quite time-consuming and, consequently, quite expensive. Cracks have to be propagated in a specimen, and then the load is slowly decreased until the crack stops propagating. Fortunately, there are some ranges available for different classes of materials at room temperature. These are shown in Figures 16 through 20. It may be nec- essary to adjust these values to use them at elevated tem- peratures, which may be done by scaling the threshold value based on the ratio of Young’s modulus. For example, a threshold value for steel is needed at: - I 8- i 1 6- An R ratio of .4 A temperature of 500 degrees From Figure 16, the minimum threshold stress intensity fac- tor is 4.0 at room temperature. If Young’s modulus is 25 x 106 at 500 degrees and 30 x lo6 at room temperature, the min- imum stress intensity factor at 500 degrees should be 4.0 x (25/30) = 3.33. R-ab Figure 17. Relationship between threshold stress in- tensity range and R ratio in aluminum alloys [lq. (With permission of Elsevier Science Ltd.) 342 Rules of Thumb for Mechanical Engineers o 02 04 06 a) LO R-ntb Figure 19. Relationship between threshold stress in- tensity range and R ratio in nickel alloys [lq. (With per- mission of Elsevier Science Ltd.) o a2 0.0 0.6 a8 LO R-ntio Figure 20. Relationship between threshold stress in- tensity range and R ratio in titanium alloys [lq. (With per- mission of Elsevier Science Ltd.) Crack Propagation Calculations If the stress intensity factor is below the fracture tough- ness, and the range of the stress intensity factor is greater than the threshold value, the crack will grow in a stable man- ner. This is often referred to as “Subcritical crack growth.” Three approaches are commonly used to relate the crack growth rate to the stress intensity factor (C, indicates the material constant): Paris law [8]: This law assumes that the data can be fit as a straight line on a log-log plot. This usually gives a fair defini- tion of the curve. It usually does not model the crack growth rate well at low and high values of AK. Modified Paris law: This model seeks to overcome the limitations of the Paris law by using three sets of coefficients which are used over three ranges of stress intensity factors. Hyperbolic sine model: This model strives to use one relationship that is applicable over the entire range of stress intensity factors, and accurately models the crack growth rate at low and high values of AK. log - = C1 sinh (C2[log(AK) + C,]) + C4 (3 The analyst should realize that because cracks tend to grow at a continually increasing rate, most of the life oc- curs when the cracks are quite small. Therefore, it is im- portant to accurately model the crack growth rate at small values of AK, but usually not important at near-fracture val- ues. The exponent of the Paris law can be quite useful for determining the effect of a change in stress on crack growth life. Since AK is proportional to the applied stress range, The change in crack growth life may be estimated by: If the stress is increased 1096, and the Paris law exponent is 4, the crack growth rate will be increased by (1. which means it will grow 1.46 times faster. Therefore, the crack propagation life will be reduced by a factor of (U1.46) to 68% of its previous value. Crack growth under cyclic loading for a given material is dependent upon three variables: Fatigue 343 1. AK 2. R ratio (K~*/Kmm) 3. temperature The crack growth data is typically shown on a log-log plot, such as shown in Figure 21. The crack propagation rate increases with increased stress intensity factor range and higher R ratios. In the absence of more specific data, Barsom [9] rec- ommends using these rather conservative equations: Ferritic-pearlitic steels: da - (in./cycle) = 3.6 x lo-’’ (AK)”O0 dn Martensitic steels: da - (in. /cycle) = 6.6 x lo4 (AK)2.25 dn When the minimum stress intensity factor is negative, a value of 0 should be used to calculate AK. This is because crack propagation does not occur unless the crack is open at the tip. If the amount of compression is small (R > -3, then crack growth data at R = 0 (or .05) may be used with no significant loss in accuracy. If the amount of compres- sion is large, (R e -1), it may be wise to obtain data at the appropriate R ratio. Crack propagation at compressive R ra- tios is seldom done because the most commonly used test specimen, known as the compact tension (CT) specimen, can only be tested in tension. Estimation of K For a fairly uniform stress field, the analyst can estimate K quite easily. Common crack types are shown in Figure 22. Approximate values of p are: Austentitic stainless steels: P Crack mpe da - (in./cycle) = 3.0 x lo-‘’ (AK)3.25 dn 0.71 corner or surface cracks 1.00 center cracked panels 1.12 through cracks Stress intensity factor range, AK, ksi 6 These values will change when the crack approaches a free surface. Typically, this is not a significant effect until the crack is about 40% of the way through the section for corner and surface cracks. It is much more significant for center and through cracks because of the loss of mss-sec- tional area. 1 LTJ Q 0 \ 104 g z^ 2 10-6 +j 6 E 10-8 g .I- 2 5 rn Y 0 1 ~7 10-8 (a) Surface Crack (b) Corner Crack Figure 21. Increasing the R ratio increases the crack growth rate [14]. (Reprinted with permission of John Wiley & Sons, Inc.) (c) Center Cracked Panel (d) Edge Crack Figure 22. Common crack types. 344 Rules of Thumb for Mechanical Engineers Computer codes which calculate crack growth use two approaches: 1. The cycle-by-cycle approach is the simplest, but it can be excessively time-consuming for slow-growing cracks. With this method, the stress intensity factors and crack growth for one cycle is calculated. The crack length is then increased by this amount and the process is repeated until the desired crack length is reached or the fracture toughness is exceeded. 2. With the step method, the number of cycles to grow the crack a certain distance (or step) is calculated after the crack growth rate is determined. This method generally requires significantly fewer iterations than the cycle-by-cycle method. Care must be taken in se- lecting the step size. If the step is too large, accuracy can be lost. If the step is too small, too much computer time will be required. For initial crack sizes around .015 inches, .001 makes a good step size. Any engineer can write a simple computer code to per- form these iterations. All that is required is a stress inten- sity factor solution and a relationship between the stress in- tensity factor range and crack growth rate. For simple cases, the crack growth life can be calculat- ed by simple integration. For example: If da/dn = 2.0 x 10-12(~~)5 and K = 56.71 Solving for dn and integrating from initial crack size Ai and final crack size Af gives: (Af’.’ - 1 N= (-1.5) (2 x (50 fi .71) For an initial crack size of .015 inches and a final crack size of .050 inches, the crack growth life would be 153,733 cycles. Plastic &ne Size Because a crack is assumed to be infinitely sharp, the elas tic stresses are always infinite at the tip, but drop off very quickly. Yielding always occurs in the region ahead of the crack tip, which is referred to as the plastic zone. The size of the plastic zone under plane stress conditions can be es- timated by: 2 rp=-[-] 1AK 2n Qy Under plane strain, the plastic zone is approximately one- fourth as large. The plastic zone is important for a number of reasons: For LEFM calculations to be valid, the crack length should be at least 10 times the length of the plastic zone. Anyone testing to determine crack growth properties should realize that large and sudden changes in the loads can affect the plastic zone ahead of the crack and significantly alter the crack growth properties. It is possible with a single overload to significantly re- duce the crack growth rate, or even arrest the crack. This can occur because the overload causes additional yield- ing in front ofthe crack, which inhibits its future growth through the region. Keep in mind that during the single overload, the crack grew at a greater rate, so it is not cer- tain what the net effect of the overload will be. Creep Crack Growth Creep crack growth (dddt) occurs when a tensile stress is applied for an extended time at a high temperature. This process should not be confused with conventional creep, which is an inelastic straining of material over time. Creep crack growth can be detected by metallurgical investiga- tion of the crack surfaces: When cyclic crack growth dominates, the crack grows When creep crack growth dominates, the crack grows across the grains (transgranular). along the grain boundaries (intergranular). Several points should be made comparing creep and cyclic crack growth: The rate of creep crack growth is related to the steady- state K, while cyclic crack growth rate is based on AK. Creep crack growth is time dependent, while cyclic crack growth is not. The threshold value for creep crack growth is much higher than it is for cyclic crack growth. Temperature has a much greater influence on creep crack growth than on cyclic crack growth. Fatigue 345 INSPECTION TECHNIQUES Several inspection methods are available, each with its own positive and negative aspects. Fluorescent Penetrant Inspection (FPII With fluorescent penetrant inspection @PI), a fluorescent dye penetrant is smeared on a surface to be checked for cracks. The surface is then cleaned off and placed under a black light. Lines will be observed where the dye seeped into cracks. The advantages of this method are that it is sim- ple and requires no elaborate test apparatus. The disad- vantages are that it is applicable only to surface cracks, may only be used on a relatively smooth surface (rough surfaces will give many false indications of cracks), and is very op erator-dependant. The human observer is the weak link in this system. Studies show that crack detection capability varies widely from person to person. These studies also show that a given person’s capability will vary from one day to another. If the surface crack is in a residual compressive stress field, it will be very difficult to detect because the crack faces will be pressed tightly together. This will make it difficult for the dye penetrant to seep into the crack. Magnetic Particle Inspection (MPI) Magnetic pallick inspection (MPU is similar to FPI, but it can be used only on ferrous metals. With this method, a liquid containing magnetic particles is applied to the sur- face being tested. A magnetic field is then produced in the component by induction or passing an electric component through it. Surface or near-surface cracks will disrupt the magnetic flux lines and cause the magnetic particles to collect around them. MPI is more reliable than FPI, espe- cially for detecting cracks in residual compression and cracks which are filled with foreign matter. These may block the dye penetrant from entering the crack, but the mag- netic field is still disrupted. MPI also has limited capabil- ity to detect cracks just below the surface. In general, MPI is superior to FPI and should be used when possible. Radiography Radiography utilizes penetrating radiation (typically x- rays) to detect cracks. The basic concept is that where less material exists, less radiation will be absorbed. The unab- sorbed radiation is measured after passing through the test article (Figure 23). Radiography is used to detect internal cracks or voids, but it is not good at detecting cracks ori- ented perpendicular to the radiation beam. This is because there is very little difference in the amount of absorbed ra- diation between parallel paths. It is also widely used to in- spect welds and determine whether two pieces have been joined together solidly or are merely attached at the surface (Figure 24). X-Rays 1 Film + More radiation is received here because there was less material along the path to abwrb the x-rays Figure 23. Radiographic inspection for cracks. 346 Rules of Thumb for Mechanical Engineers Bad Weld Good Weld Figure 24. Radiography is often used to inspect welds. Ultrasonic Inspection Ultrasonic inspection utilizes high-frequency sound waves which are reflected by discontinuities. The return sig- nal is measured and analyzed to detect cracks. A great deal of energy is reflected at both surfaces of the compo- nent. This creates two dead zones where acoustic reflections caused by mcks cannot be distinguished from those caused by the component surfaces. The return signal for an un- cracked component will look like Figure 25: Peak A rep- resents the echo from the front wall, and peak B represents the back wall echo. Crack A in Figure 26 would reflect a portion of the signal and cause another peakbetween A and B. Crack B would reflect some of the wave at an angle and, therefore, would not cause another peak. Its existence could be deduced, however, because the back wall echo would be significantly curtailed. Any increase in the return signal between these two peaks indicates a discontinuity in Wave Generator/Receiver ll Dead Zone -/ I Figure 26. Effect of crack orientation on detectability: (Aj crack reflects signal back to receiver; (6) crack de- flects signal, reducing back wall echo; (C) crack cannot be detected. A - (Front Wall Echo) the component. Crack C would be extremely difficult to de- tect, since it would have little effect on the return signal be- cause of its orientation. Ultrasonic inspection is very accurate and can be used to inspect thick sections. It is limited to detecting internal cracks away from specimen surfaces. It requires a flat sur- face through which to apply the ultrasonic energy. Refer- for oneof-a-kind inspections. For some materials, grain boundaries, precipitates, or other internal inhomogeneities reflect so much acoustic energy, that crack detection is ex- Return Signal B - (Back Wall Echo) I ence standards are required, making this method unusable Time Figure 25. Ultrasonic return signal for an uncracked component. tremely difficult. Fatigue 347 Eddy-Current Inspection ~ Eddycurrent inspection can be performed on materials that conduct electricity. This method is based on the prin- ciple that cracks distort the eddy-currents which occur in a sample when current is passed through a nearby coil. Both surface and near-surface cracks may be detected reliably. Perhaps the most important feature of eddy-current in- spection is that it can be automated. This improves accu- racy significantly, and reduces cost if the inspections will be done in volume. The negative aspects are that special ma- chinery and reference standards (showing the signals for cracked and uncracked parts) are necessary, making it im- practical for one-of-a-kind inspections. Evaluation of Failed Parts If a failure occurs, all relevant information about the event should be recorded as quickly as possible. Seemingly minor details may help pinpoint the cause of the failure. If a tur- bine wheel fails when power is being increased or de- creased, it may indicate that thermal gradients are respon- sible. Any failed parts that can be retrieved should be handled with extreme care. The parts should not be cleaned until they have been examined thoroughly, because surface debris may yield important clues. Paint on a cracked sur- face might indicate that the crack occurred during the man- ufacturing process, and was present when the component was placed into service. Oxidation on a cracked surface may indicate how long that surface was exposed to the envi- ronment. Important regions should be photographed for fu- ture reference. From the primary crack (the one responsi- ble for failure), attempts should be made to determine: Crack origin (there may be more than one) Critical crack size Crack growth rate (if striations are present) The critical crack size and crack growth rates may be used to make rough estimates of the loads present. Sec- ondary cracks (ones not responsible for failure) may also be used for this purpose. The surfaces of the primary crack are often too damaged for meaningful evaluation after failure. Secondary cracks, whose surfaces are more pro- tected, may be more useful for post-failure examination. Examining the microstructure of the component, includ- ing regions not near the fracture surface, can indicate what conditions it was subjected to during operation. The microstructure of some materials changes when they are subjected to high temperatures. Armed with this knowledge, it might be possible to determine that the operating tem- perature exceeded a certajn level. Small specimens may be (a) Tension (b) Bending Figure 27. Failure surfaces of round bars subjected to (A) tensile loading and (B) bending. (a) Notched (b) Unnotched Figure 28. Failure surfaces of notched and unnotched rectangular bars. cut from a failed component and tested to determine if the material properties are within specifications. Keep in mind that different regions of the same component can have sig- nificantly different properties. The fracture surface may also indicate the type of load. Figure 27 shows failure surfaces for round bars subjected to tensile loading and to bending. In bending, there is a ten- dency to initiate cracks at the top and bottom, since the stresses will be highest at these two locations. Figure 28 compares the cross-section of notched and unnotched rec- tangular bars. The notch creates a local area of high stress, and multiple cracks tend to initiate in this region. Eventu- ally, these cracks generally coalesce into a single large crack. For cases of uniform stress, the tendency is towards a single crack. 348 Rules of Thumb for Mechanical Engineers NONMETAUIC MATERIALS .m - .050- .m - .010 - This chapter has focused on metals, which are widely used for structural components. A few comments will be made about plastics, composites, and ceramics as well. The Properties of plastics vary greatly, but the same method- ology that is used for metals can often be used for plastics. Dr. Grandt has done numerous experiments on poly- methylmethacrylate and polycarbonate [ 101. His research indicates that crack growth in these plastic materials can be related to the stress intensity factor, just as it is in metals. Composites are being used more frequently for structural components. Fatigue of composite materials is a very com- plicated subject, which will not be dealt with in this book. Complications in fatigue analysis arise because: =:: . . . The material is not homogeneous. Residual stresses are present due to the difference in thermal expansion coefficients between the fibers and matrix materials. Once cracks initiate, the fibers often act as barriers to crack growth. Compd to metals, fatigue strengths are generally high- er (relative to their ultimate strengths) for composites under uniaxial tensile loading (R > 0). The opposite is true when cornpressive or fully reversed (R c - 1)loading is applied [ 1 13. Inspection of composites is diEcult because crachng is more likely to occur internally than it is for metals. Ceramics offer strength, light weight, and outstanding temperature resistance, but have been shunned in the past due to their brittleness. A great deal of effort is currently being expended to develop ceramics with improved tough- ness. If we assume that ceramic materials have no ductil- ity, then some simple analysis can be done. When ceram- ic components are manufactured, they always have some flaws in them. Since their ductility is assumed to be neg- ligible, no subcritical crack growth can occur. If the load is increased to the point that the stress intensity factor at one of these inherent defects exceeds the fracture toughness, fast fracture will occur. At a given stress level, a certain per- centage of ceramic components will fail immediately, while the rest will not fail no matter how many times the load is applied. This makes the standard S-N curves that are used Probability of Failure I I I I I I I 55 80 65 70 75 80 Figure 29. Typical probability of failure versus stress plot. to calculate lives for metals useless. Instead, a probabilis- tic method is applied. The probability ofsurvival (POS) is plotted against strength (Figure 29). Since larger compo- nents have more material, and therefore a greater probability of containing a large flaw, failure must be narmalized to ac- count for size. In test specimens, the failures are general- ly classified as either surface (failures orighting at the sur- face) or volume (failures originating internally). Separate Weibull curves are calculated for each type of failure. When this information is used to calculate the life of a com- ponent, its total probability of survival is the product of its POS for surface and volume flaws: A positive aspect of the lack of ductility in ceramics is that they can be "proof-tested." Because an applied load to a component with no ductility will do no damage unless it causes fast fracture, parts can be tested at a load equal to the highest load (multiplied by an appropriate safety fac- tor) that they will experience in service. Those that survive should not fail in service unless they are subjected to an even greater load. This means that if the specimens in Figure 29 are subjected to a stress of 60 ksi, the three weakest spec- imens would fail, but those remaining would be undamaged. This approach should not be used with metals, because they undergo subcritical crack growth. Fatigue 349 FATIGUE TESTING Fatigue testing can be difficult and can yield misleading data if not done correctly. Numerous small companies spe- cialize in generating fatigue data, and their services might be useful to those without proper facilities or experience. Companies that decide to generate their own fatigue data should carefully review the pertinent ASTM guidelines: 1. Low Cycle Fatigue (ASTM Standard E606-80). 2. High Cycle Fatigue (ASTM Standard EA.66-82). 3. Statistical Analysis of Linear or Linearized Stress-Life and Strain-Life Fatigue Data (ASTM Standard E739-91) 4. Plane-Strain Fracture Toughness Test Method (ASTM 5. Fatigue Crack Growth and Threshold Crack Growth 6. Creep Crack Growth Test Method (ASTM Standard 7. Surface Fatigue Crack Growth Test Method (ASTM Standard E399-90). Test Method(ASTM Standard E647-91). E 1457-92). Standard E740-88). It is particularly important to exercise care when testing to determine AI&. High loads are required to initiate a crack for testing purposes. If these loads are not reduced gradu- ally after initiation but before taking measurements to de- termine A&, the tests may show the threshold value to be much higher than it actually is. Obviously, this could have very serious consequences. Every effort should be made to keep the test specimens as similar to the actual hardware as possible. Seemingly unimportant details, such as how a surface is machined, may induce residual stresses or create small cracks which dras- tically alter the fatigue life. Figure 30 shows how the sur- face factor (q) is related to tensile strength and machining operations [12]. If it is necessary to use test data based on specimens with a different surface finish than actual com- ponents, the calculated life should be corrected: Cf (actual hardware) Cf (test specimens) Nactual= Ncalculated x Figure 30. Surface factors for various machining opera- tions [13]. (Reprinted with pemim'on ofPmfice-Ha//, /nc.) where: Nactual = actual life of component: Ncalculated = calculated life based on test specimen data Environmental Efl ects Fatigue can be accelerated significantly by aggressive en- vironments. This is especially true when the loads are ap- plied and maintained for long periods of time. These effects are difficult to quantify. The best rule is to attempt to sim- ulate environmental conditions during fatigue testing as closely as possible. Aggressive environments may include everything from salt air for carrier-based aircrail to nuclear radiation for electrical generating plants. [...]... not justified Whether the strain data is 354 Rules o Thumb for Mechanical Engineers f 0.1% accurate or 3% accurate probably will not change the decision to approve the part for service Although there are a wide variety of parameters that can be measured and an even wider variety of sensor technologies to perform those measurements (all with varying degrees of vendor literature available), there are a... “Interpretationof Fatigue Strengthsfor Combined Stresses,” presented at The American Society of Mechanical Engineers, New York, Nov 28-30,1956 6 Muralidharan, U and Manson, S S., “A Modified Universal Slopes Equation for the Estimation of Fatigue Characteristics of Metals,” Journal of Engineering Materials and Technology,Volume 110, Jan 1988, pp 55-58 Limit the report to your areas of expertise ff... can never raise the sen- 356 Rules o Thumb for Mechanical Engineers f sor temperatureabove that of t e highest temperature body h in the environment If a l of the environment exists withl in a temperature band that is a subset of the accuracy requirementsof the measurement, radiation emns can be summarily dismissed Conduction errors are present where the mounting mechanism for the sensor connects the... to mount the open end of a tube at the sensing location and route the other end of the tube to a separately 380 Rules of Thumb for Mechanical Engineers mounted transducer Due to this consideration, the renaainder of this section concentrates on tube mounting design considerations Pressure transducers can be chosen as stock vendor supplies that simply meet the requirementsin terms of accuracy, frequency... with high partic- 362 Rules of Thumb for Mechanical Engineers ulate count (soot, rust, etc.) then a 0.010-inch diameter orifice would impede pressure pulse propagation and/or would plug completely Not only is static pressure port diameter a consideration, but changes in that port diameter along its length close to the opening to the flow field can also be a source of error It is a good rule of thumb not... 1)M2]v(Y-I) where y is the ratio of specific heats (# c $ and equals 1.4 for air at 15 C M is the mach number See Table 1for tabular form of this equation The most common method of measuring Pt is to place a small tube (pressure probe) within the fluid at the point of interest and use the tube to guide pressure pulses back t o an externally mounted pressure transducer Error sources for this arrangement include... counseling, the chances for obtaining poor data are relatively high It is beyond the scope of this chapter to go through the finer points of gauge application, especially with the excellent vendor literature available However, some common failure points in gauge application include the areas of improper cleanliness of the part (and the hands of t e gauge applicationtechnician), improper part surh face finish,... Reprintecl bypmjssion~) Instrumentation 361 Pressure Gradient y E P r e Displacementof s ; 8o r I 0' 1 I I I 1 6 I 2 3 4 5 Ratio of Length of Sensing Elementto Diameter of Support (b) Figure 6 Total pressure probe errors of pressure gradient displacement due to sensing tube length [l] (Courtesy of instrument Society of America Reprinted by permission.) StaticlCavity Pressure Measurement While it is... half-shielded total temperature probe Approximate Relationships A= Clearancefor sensor (typically 0.001 - 0.003 inches loose) B= Defined by structural needs (typically 5.5A) D= 2A* E= 2A* F= 9A G= 1.5A Sect AA-AA equally spaced,TYP Figure 3 Parametric design: multiflow direction total temperature probe 358 Rules of Thumb for Mechanical Engineers _ ~ _ ~ _ _ _ _ _ _ _ _ ~ Surface Temperature Measurement... discrete length of w r The emf generated by each section is a function of ie the thermal emf coefficient of each material and the temperature gradient through which it passes Therefore: 32F +J""' 750'F EAL 750°F 500°F +I,,,Ecu 70°F 359 of which have sensing elements whose resistance changes in a repeatable way with temperature RTDs are usually constructed of platinum wire, while thermistors are of integrated . generally coalesce into a single large crack. For cases of uniform stress, the tendency is towards a single crack. 348 Rules of Thumb for Mechanical Engineers NONMETAUIC MATERIALS .m - .050-. Figure 23. Radiographic inspection for cracks. 346 Rules of Thumb for Mechanical Engineers Bad Weld Good Weld Figure 24. Radiography is often used to inspect welds. Ultrasonic. include everything from salt air for carrier-based aircrail to nuclear radiation for electrical generating plants. 350 Rules of Thumb for Mechanical Engineers Because fatigue analysis