The stress systems acting on a shaft must be clearly understood before the cause of a fracture in that shaft can be determined. Also, both ductile and brittle behavior under static loading or single overload, as well as the characteristic fracture surfaces produced by these types of behavior, must be clearly understood for proper analysis of shaft fractures Figure 1 shows simplified, two-dimensional, free-body diagrams illustrating the orientations of the normal-stress and shear-stress systems at any internal point in a shaft loaded in pure tension, torsion, and compression. Also, the single overload fracture behavior of both ductile and brittle materials is illustrated for each type of load T Elastic Elastic E lasti stress stress stress distribution distribution distribution a1s Tensile stress 3=Compressive stress mor: Maximum sheor stress Ductile Brittle Ductile Brittle Brittle Single-overlood fractures Single-overload fractures Single-overload fractures (a) Tension (b)Torsion (c)Compression Fig. 1 Free-body diagrams showing orientation of normal stresses and shear stresses in shaft and the single-overload fracture behavior of ductile and brittle materials.(a)Under simple tension.(b)Under torsion (c)Under compression loading. See text for discussion A free-body stress system may be considered to be a square of infinitely small dimensions. Tensile and compressive stresses act perpendicular to each other and to the sides of the square to stretch and squeeze the sides, respectively. The shear, or sliding, stresses act on the diagonals of the square, 45 to the normal stresses. The third-dimension radial stresses are ignored in this description. The effects of the shear and normal stresses on ductile and brittle materials under the three types of loads illustrated in Fig. I and under bending load are discussed belov Tension. Under tension loading, the tensile stresses, ol, are longitudinal, whereas the compressive-stress components, o3, are transverse to the shaft axis. The maximum-shear-stress components, tmax, are at 45 to the shaft axis(Fig. la) In a ductile material, shear stresses developed by tensile loading cause considerable deformation(elongation and necking before fracture, which originates near the center of the shaft and propagates toward the surface, ending with a conical shear lip usually about 45 to the shaft axis. However, in a brittle material, a fracture from a single tensile overlo roughly perpendicular to the direction of tensile stress, but involves little or no permanent deformation. The fracture surface is usually rough and crystalline in appearance The elastic-stress distribution in pure tension loading, in the absence of a stress concentration, is uniform across the section. Thus, fracture can originate at any point within the highly stressed volume Torsion. The stress system rotates 45 when a shaft is loaded in torsion( Fig. 1b). Both the tensile and compressive stresses are 45 to the shaft axis and remain mutually perpendicular. One shear-stress component is parallel with the shaft axis; the other is perpendicular to the shaft axis n a ductile material loaded to failure in torsion shear stresses cause considerable deformation before fracture. However this deformation is usually not obvious, because the shape of the shaft has not been changed. The distortion will be
The stress systems acting on a shaft must be clearly understood before the cause of a fracture in that shaft can be determined. Also, both ductile and brittle behavior under static loading or single overload, as well as the characteristic fracture surfaces produced by these types of behavior, must be clearly understood for proper analysis of shaft fractures. Figure 1 shows simplified, two-dimensional, free-body diagrams illustrating the orientations of the normal-stress and shear-stress systems at any internal point in a shaft loaded in pure tension, torsion, and compression. Also, the singleoverload fracture behavior of both ductile and brittle materials is illustrated for each type of load. Fig. 1 Free-body diagrams showing orientation of normal stresses and shear stresses in a shaft and the single-overload fracture behavior of ductile and brittle materials. (a) Under simple tension. (b) Under torsion. (c) Under compression loading. See text for discussion. A free-body stress system may be considered to be a square of infinitely small dimensions. Tensile and compressive stresses act perpendicular to each other and to the sides of the square to stretch and squeeze the sides, respectively. The shear, or sliding, stresses act on the diagonals of the square, 45° to the normal stresses. The third-dimension radial stresses are ignored in this description. The effects of the shear and normal stresses on ductile and brittle materials under the three types of loads illustrated in Fig. 1 and under bending load are discussed below. Tension. Under tension loading, the tensile stresses, σ1, are longitudinal, whereas the compressive-stress components, σ3, are transverse to the shaft axis. The maximum-shear-stress components, τmax, are at 45° to the shaft axis (Fig. 1a). In a ductile material, shear stresses developed by tensile loading cause considerable deformation (elongation and necking) before fracture, which originates near the center of the shaft and propagates toward the surface, ending with a conical shear lip usually about 45° to the shaft axis. However, in a brittle material, a fracture from a single tensile overload is roughly perpendicular to the direction of tensile stress, but involves little or no permanent deformation. The fracture surface is usually rough and crystalline in appearance. The elastic-stress distribution in pure tension loading, in the absence of a stress concentration, is uniform across the section. Thus, fracture can originate at any point within the highly stressed volume. Torsion. The stress system rotates 45° when a shaft is loaded in torsion (Fig. 1b). Both the tensile and compressive stresses are 45° to the shaft axis and remain mutually perpendicular. One shear-stress component is parallel with the shaft axis; the other is perpendicular to the shaft axis. In a ductile material loaded to failure in torsion, shear stresses cause considerable deformation before fracture. However, this deformation is usually not obvious, because the shape of the shaft has not been changed. The distortion will be
obvious if there were axial grooves or lines on the shaft before twisting, or if the metal is hot etched to reveal grain-flow wisting. If a shaft loaded in torsion is assumed to consist of an infinite number of infinitely thin disks that slip slightly with respect to each other under the torsional stress, visualization of deformation is simplified Torsional single-overload fracture of a ductile material usually occurs on the transverse plane, perpendicular to the axis of the shaft In pure torsion, the final-fracture region is at the center of the shaft, the presence of slight bending will cause it to be off-center shaft axis. The resulting fracture surfaces usually have the shape of a spla hsile-stress component, which is now 45to the a brittle material in pure torsion will again fracture perpendicular to the ter The elastic-stress distribution in pure torsion is maximum at the surface and zero at the center of the shaft. Thus, in pure torsion, fracture normally originates at the surface, which is the region of highest stress stress,o3, is axial and the tensile stress, ol, is transverse. The shear stresses, Tmax, are 45 to the shaft axis, as theresa Compression. When a shaft is loaded in axial compression(Fig. Ic), the stress syste m rotates so during axial tension loading a ductile material overloaded in compression, shear stresses cause considerable deformation but usually do not result in fracture. The shaft is shortened and bulges laterally under the influence of shear stress. a brittle material loaded in pure ompression, if it does not buckle, again will fracture perpendicular to the maximum tensile-stress component. Because the tensile stress is transverse, the direction of brittle fracture is parallel to the shaft axis The elastic-stress distribution in pure compression loading, in the absence of a stress concentration, is uniform across the section. If fracture occurs, it will likely be in the longitudinal direction, because compression loading increases the shaft diameter and stretches the metal at the circumference Bending. When a shaft is stressed in bending, the convex surface is stressed in tension and has an elastic-stress distribution similar to that shown in Fig. 1(a). The concave surface is stressed in compression and has an elastic-stress distribution similar to that shown in Fig. 1(c). Approximately midway between the convex and concave surfaces is a neutral axis. where all stresses are zero Failures of shafts Revised by Donald J. ulpi, Metallurgical Consultant Fatigue failures Fatigue in shafts can generally be classified into three basic subdivisions: bending fatigue, torsional fatigue, and axial fatigue. Bending fatigue can result from these types of bending loads: unidirectional(one-way), reversed(two-way), and rotating. In unidirectional bending, the stress at any point fluctuates. Fluctuating stress refers to a change in magnitude without changing algebraic sign. In reversed bending and rotating bending, the stress at any point alternates. Alternating stress refers to cycling between two stresses of opposite algebraic sign, that is, tension (+ to compression(-)or compression to tension. Torsional fatigue can result from application of a fluctuating or an alternating twisting moment torque). Axial fatigue can result from application of alternating (tension-and-compression) loading or fluctuating tension-tension) loading. More complete information is available in the article"Fatigue Failures"in this Volume Unidirectional-Bending Fatigue. The axial location of the origin of a fatigue crack in a stationary cylindrical bar or shaft subjected to a fluctuating unidirectional-bending moment evenly distributed along the length will be determined by some minor stress raiser, such as a surface discontinuity. Beach marks(also called clamshell, conchoidal, and crack-arrest marks )of the form shown in Fig. 2(a)and(b)are indicative of a fatigue crack having a single origin at the point indicated by the arrow. The crack front, which formed the beach marks, is symmetrical relative to the origin and retains a concave form throughout. Both the single origin and the smallness of the final-fracture zone in Fig. 2(a) suggest that the nominal stress was low. The larger final-fracture zone in Fig. 2(b)suggests a higher nominal stress Thefileisdownloadedfromwww.bzfxw.com
obvious if there were axial grooves or lines on the shaft before twisting, or if the metal is hot etched to reveal grain-flow twisting. If a shaft loaded in torsion is assumed to consist of an infinite number of infinitely thin disks that slip slightly with respect to each other under the torsional stress, visualization of deformation is simplified. Torsional single-overload fracture of a ductile material usually occurs on the transverse plane, perpendicular to the axis of the shaft. In pure torsion, the final-fracture region is at the center of the shaft; the presence of slight bending will cause it to be off-center. A brittle material in pure torsion will again fracture perpendicular to the tensile-stress component, which is now 45° to the shaft axis. The resulting fracture surfaces usually have the shape of a spiral. The elastic-stress distribution in pure torsion is maximum at the surface and zero at the center of the shaft. Thus, in pure torsion, fracture normally originates at the surface, which is the region of highest stress. Compression. When a shaft is loaded in axial compression (Fig. 1c), the stress system rotates so that the compressive stress, σ3, is axial and the tensile stress, σ1, is transverse. The shear stresses, τmax, are 45° to the shaft axis, as they are during axial tension loading. In a ductile material overloaded in compression, shear stresses cause considerable deformation but usually do not result in fracture. The shaft is shortened and bulges laterally under the influence of shear stress. A brittle material loaded in pure compression, if it does not buckle, again will fracture perpendicular to the maximum tensile-stress component. Because the tensile stress is transverse, the direction of brittle fracture is parallel to the shaft axis. The elastic-stress distribution in pure compression loading, in the absence of a stress concentration, is uniform across the section. If fracture occurs, it will likely be in the longitudinal direction, because compression loading increases the shaft diameter and stretches the metal at the circumference. Bending. When a shaft is stressed in bending, the convex surface is stressed in tension and has an elastic-stress distribution similar to that shown in Fig. 1(a). The concave surface is stressed in compression and has an elastic-stress distribution similar to that shown in Fig. 1(c). Approximately midway between the convex and concave surfaces is a neutral axis, where all stresses are zero. Failures of Shafts Revised by Donald J. Wulpi, Metallurgical Consultant Fatigue Failures Fatigue in shafts can generally be classified into three basic subdivisions: bending fatigue, torsional fatigue, and axial fatigue. Bending fatigue can result from these types of bending loads: unidirectional (one-way), reversed (two-way), and rotating. In unidirectional bending, the stress at any point fluctuates. Fluctuating stress refers to a change in magnitude without changing algebraic sign. In reversed bending and rotating bending, the stress at any point alternates. Alternating stress refers to cycling between two stresses of opposite algebraic sign, that is, tension (+) to compression (-) or compression to tension. Torsional fatigue can result from application of a fluctuating or an alternating twisting moment (torque). Axial fatigue can result from application of alternating (tension-and-compression) loading or fluctuating (tension-tension) loading. More complete information is available in the article “Fatigue Failures” in this Volume. Unidirectional-Bending Fatigue. The axial location of the origin of a fatigue crack in a stationary cylindrical bar or shaft subjected to a fluctuating unidirectional-bending moment evenly distributed along the length will be determined by some minor stress raiser, such as a surface discontinuity. Beach marks (also called clamshell, conchoidal, and crack-arrest marks) of the form shown in Fig. 2(a) and (b) are indicative of a fatigue crack having a single origin at the point indicated by the arrow. The crack front, which formed the beach marks, is symmetrical relative to the origin and retains a concave form throughout. Both the single origin and the smallness of the final-fracture zone in Fig. 2(a) suggest that the nominal stress was low. The larger final-fracture zone in Fig. 2(b) suggests a higher nominal stress. The file is downloaded from www.bzfxw.com
Low nominal High nominal stress stress No stress concentration (d) (e) Moderote stress concentration g (]) Severe stress concentration Fig 2 Fatigue marks produced from single origins at low and high nominal stresses and from multiple origins at high nominal stresses. Fatigue marks are typical for a uniformly loaded shaft subjected to unidirectional bending. Arrows indicate crack origins; final fracture zones are shaded Figure 2(c)shows a typical fatigue crack originating as several individual that ultimately merged to form a single crack front. Such multiple origins are usually indicative of high nominal Radial steps(ratchet marks)are present between crack origins igures 2(d),(e), and (f) show typical fatigue beach marks that result when a change in section in a uniformly loaded shaft provides a moderate stress concentration. With a low nominal stress, the crack front changes from concave to convex before rapture(Fig. 2d). At higher nominal stresses, the crack front flattens and may not become convex before final fracture(Fig. 2e and f) change in section in a uniformly loaded shaft that produces a severe stress concentration will lead to a pattern of beach marks such as that shown in Fig. 2(g),(h), or () An example of a severe stress concentration is a small-radius fillet at the junction of a shoulder and a smaller-diameter portion of a shaft or at the bottom of a keyway. Such a fillet usually results in the contour of the fracture surface being convex with respect to the smaller-section side The crack-front pattern shown in Fig. 2(g) was produced by a low nominal stress. The crack front in Fig. 2(h) developed more rapidly because of a higher stress in the peripheral zone. Multiple crack origins, high nominal stress, and unidirectional bending usually produce the beach-mark pattern shown in Fig. 20 Example 1: Unidirectional-Bending Fatigue Failure of an A6 Tool Steel Shaft. The shaft shown in Fig 3 was part of a clamping device on a tooling assembly used for bending 5.7-cm(2.25-in. )outer-diameter tubing on an 86-cm(3. 375-in) radius. The assembly contained two of these shafts, both of which failed simultaneously and were sent to the laborator for examination. The maximum clamping force on the assembly was 54, 430 kg(120,000 lb). The material specified for the shafts was a free-machining grade of A6 tool steel
Fig. 2 Fatigue marks produced from single origins at low and high nominal stresses and from multiple origins at high nominal stresses. Fatigue marks are typical for a uniformly loaded shaft subjected to unidirectional bending. Arrows indicate crack origins; finalfracture zones are shaded. Figure 2(c) shows a typical fatigue crack originating as several individual cracks that ultimately merged to form a single crack front. Such multiple origins are usually indicative of high nominal stress. Radial steps (ratchet marks) are present between crack origins. Figures 2(d), (e), and (f) show typical fatigue beach marks that result when a change in section in a uniformly loaded shaft provides a moderate stress concentration. With a low nominal stress, the crack front changes from concave to convex before rapture (Fig. 2d). At higher nominal stresses, the crack front flattens and may not become convex before final fracture (Fig. 2e and f). A change in section in a uniformly loaded shaft that produces a severe stress concentration will lead to a pattern of beach marks such as that shown in Fig. 2(g), (h), or (j). An example of a severe stress concentration is a small-radius fillet at the junction of a shoulder and a smaller-diameter portion of a shaft or at the bottom of a keyway. Such a fillet usually results in the contour of the fracture surface being convex with respect to the smaller-section side. The crack-front pattern shown in Fig. 2(g) was produced by a low nominal stress. The crack front in Fig. 2(h) developed more rapidly because of a higher stress in the peripheral zone. Multiple crack origins, high nominal stress, and unidirectional bending usually produce the beach-mark pattern shown in Fig. 2(j). Example 1: Unidirectional-Bending Fatigue Failure of an A6 Tool Steel Shaft. The shaft shown in Fig. 3 was part of a clamping device on a tooling assembly used for bending 5.7-cm (2.25-in.) outer-diameter tubing on an 8.6-cm (3.375-in.) radius. The assembly contained two of these shafts, both of which failed simultaneously and were sent to the laboratory for examination. The maximum clamping force on the assembly was 54,430 kg (120,000 lb). The material specified for the shafts was a free-machining grade of A6 tool steel
A6 tool steel Rockwell C 48 Fracture 3.75 diam lg 0 15 2. 25 diam 32R 0.00R1 (min) (max) Fracture Original design Improved design Section A-A View B Fig3 A6 tool steel tube-bending-machine shaft that failed by fatigue fracture. Section A- A: Original and improved designs for fillet in failure region. Dimensions are in inches. View B: Fracture surface showing regions of fatigue-crack propagation and final fracture The shafts were subjected to a tensile stress imposed by the clamping force and a bending stress resulting from the nature of the operation. Unidirectional-bending stresses were imposed on one shaft when a right-hand bend was made in the tubing and on the other shaft when a left-hand bend was made. Approximately 45 right-hand and 45 left-hand bends were made per hour on the machine; the total number of bends made before the shafts failed was not known. The tensile stress on the shafts was also cyclic, because the clamping force was removed after each bend was made Investigation. Analysis of the steel, using wet chemical and spectroscopic techniques, showed that the composition was within specifications. The average hardness of the steel was 48 HRC. A 1.3-cm(0.505-in )diam tensile specimen removed from the center of one of the shafts failed in a brittle manner at a tensile stress of 1572 MPa(228 ksi) The microstructure of the steel was fine, dispersed, tempered martensite with elongated stringers of manganese sulfide Also present were spheroidized white particles that were identified as high-alloy complex carbides(MC)corresponding Thefileisdownloadedfromwww.bzfxw.com
Fig. 3 A6 tool steel tube-bending-machine shaft that failed by fatigue fracture. Section AA: Original and improved designs for fillet in failure region. Dimensions are in inches. View B: Fracture surface showing regions of fatigue-crack propagation and final fracture The shafts were subjected to a tensile stress imposed by the clamping force and a bending stress resulting from the nature of the operation. Unidirectional-bending stresses were imposed on one shaft when a right-hand bend was made in the tubing and on the other shaft when a left-hand bend was made. Approximately 45 right-hand and 45 left-hand bends were made per hour on the machine; the total number of bends made before the shafts failed was not known. The tensile stress on the shafts was also cyclic, because the clamping force was removed after each bend was made. Investigation. Analysis of the steel, using wet chemical and spectroscopic techniques, showed that the composition was within specifications. The average hardness of the steel was 48 HRC. A 1.3-cm (0.505-in.) diam tensile specimen removed from the center of one of the shafts failed in a brittle manner at a tensile stress of 1572 MPa (228 ksi). The microstructure of the steel was fine, dispersed, tempered martensite with elongated stringers of manganese sulfide. Also present were spheroidized white particles that were identified as high-alloy complex carbides (M6C) corresponding The file is downloaded from www.bzfxw.com
to the double carbides Fe, Mo2C and Fe Cr2C. Microscopic examination of the edge of the fracture surface at 100 and 1000x revealed some nonmetallic oxide-sulfide segregation Visual examination of the fracture surface revealed both a smooth area and a coarse, granular area(View B, Fig. 3). The dull, smooth area is typical of some fatigue fractures and resulted as the crack was opened and closed by the bending stress. Beach marks on the smooth area of the fracture surface also indicate fatigue fracture. The coarse. bright crystalline-appearing area is the final-fracture zone. The smooth-textured fatigue zone is relatively large compared with the crystalline-textured final-fracture zone, which indicates that the shaft was subjected to a low overstress. The final fracture surface at bottom shows that a one-way bending load was involved The fatigue crack was initiated in a 0.25-mm(0.010-in )radius fillet at a change in section( "Original design, Section A A, Fig. 3). Cracking was nucleated by a nonmetallic inclusion that intersected the surface at a critical location in the fillet Conclusions. The shafts fractured in fatigue as the result of a low-overstress, high-cycle unidirectional-bending load. The small radius of the fillet at the change in section resulted in a stress concentration that, in conjunction with the oxide fide inclusion that intersected the surface of the fillet initiated a crack Corrective Measures. New shafts were made with a 2.4-mm(0.09-in )radius fillet at the critical change in section (Improved design, Section A-A, Fig. 3). The larger-radius fillet minimized stress concentration in this region and prevented recurrence of failure Reversed-Bending Fatigue. When the applied bending moment is reversing (alternating), all points in the shaft are subjected alternately to tension stress and compression stress, while the points on one side of the plane of bending are in tension, the points on the opposite side are in compression. If the bending moment is of the same magnitude in either direction, two cracks of approximately equal length usually develop from origins diametrically opposite each other and often in the same transverse plane. If the bending moment is greater in one direction than in the other, the two cracks will differ in length Figure 4 shows typical fatigue marks on the fracture surface of a stationary(nonrotating) shaft subjected to a reversing bending moment evenly distributed along its length. The crack origins(arrows) are shown diametrically opposite each other. but sometimes e slightly displaced by minor stress raisers. The pattern shown in Fig. 4(a) is typical of that for a single-diameter shaft with no stress concentration. The bending moment is equal in both directions (b) Fig. 4 Typical fatigue marks on the fracture surface of a uniformly loaded nonrotating shaft subjected to reversed-bending stresses.(a) No stress concentration.(b) Moderate tress concentration.(c) severe stress concentration. Arrows indicate crack origins; shaded areas are final-fracture zones A large-radius fillet at a change in shaft diameter imposes a moderate stress concentration. Figure 4(b) shows the pattern on the surface of a fracture through such a fillet. A small-radius fillet at a change in diameter results in a severe stress concentration. Figure 4(c)shows the typical pattern on the surface of a fracture through a small-radius fillet. The reason for the fatigue-pattern changes is that the fatigue crack propagates faster in more severe stress concentrations at each end than in the interior Under the above loading conditions, each crack is subjected alternately to tensile and compressive stresses, with the result that the surfaces of the crack are forced into contact with one another during the compression cycle, and rubbing occurs Rubbing may sometimes be sufficient to obliterate many of the characteristic marks, and the crack surfaces may become dull Rotating-Bending Fatigue. The essential difference between a stationary shaft and a rotating shaft subjected to the same bending moment is that in a stationary shaft the tensile stress is confined to a portion of the periphery only. In a rotating shaft, every point on the periphery sustains a tensile stress, then a compressive stress, once every revolution. The relative magnitude of the stresses at different locations is determined by conditions of balance or imbalance imposed on the shaft Another important difference introduced by rotation is asymmetrical development of the crack front from a single origin There is a marked tendency of the crack front to extend preferentially in a direction opposite to that of rotation. The crack
to the double carbides Fe4Mo2C and Fe4Cr2C. Microscopic examination of the edge of the fracture surface at 100 and 1000× revealed some nonmetallic oxide-sulfide segregation. Visual examination of the fracture surface revealed both a smooth area and a coarse, granular area (View B, Fig. 3). The dull, smooth area is typical of some fatigue fractures and resulted as the crack was opened and closed by the bending stress. Beach marks on the smooth area of the fracture surface also indicate fatigue fracture. The coarse, bright, crystalline-appearing area is the final-fracture zone. The smooth-textured fatigue zone is relatively large compared with the crystalline-textured final-fracture zone, which indicates that the shaft was subjected to a low overstress. The finalfracture surface at bottom shows that a one-way bending load was involved. The fatigue crack was initiated in a 0.25-mm (0.010-in.) radius fillet at a change in section (“Original design,” Section AA, Fig. 3). Cracking was nucleated by a nonmetallic inclusion that intersected the surface at a critical location in the fillet. Conclusions. The shafts fractured in fatigue as the result of a low-overstress, high-cycle unidirectional-bending load. The small radius of the fillet at the change in section resulted in a stress concentration that, in conjunction with the oxidesulfide inclusion that intersected the surface of the fillet, initiated a crack. Corrective Measures. New shafts were made with a 2.4-mm (0.09-in.) radius fillet at the critical change in section (“Improved design,” Section A-A, Fig. 3). The larger-radius fillet minimized stress concentration in this region and prevented recurrence of failure. Reversed-Bending Fatigue. When the applied bending moment is reversing (alternating), all points in the shaft are subjected alternately to tension stress and compression stress; while the points on one side of the plane of bending are in tension, the points on the opposite side are in compression. If the bending moment is of the same magnitude in either direction, two cracks of approximately equal length usually develop from origins diametrically opposite each other and often in the same transverse plane. If the bending moment is greater in one direction than in the other, the two cracks will differ in length. Figure 4 shows typical fatigue marks on the fracture surface of a stationary (nonrotating) shaft subjected to a reversing bending moment evenly distributed along its length. The crack origins (arrows) are shown diametrically opposite each other, but sometimes they are slightly displaced by minor stress raisers. The pattern shown in Fig. 4(a) is typical of that for a single-diameter shaft with no stress concentration. The bending moment is equal in both directions. Fig. 4 Typical fatigue marks on the fracture surface of a uniformly loaded nonrotating shaft subjected to reversed-bending stresses. (a) No stress concentration. (b) Moderate stress concentration. (c) Severe stress concentration. Arrows indicate crack origins; shaded areas are final-fracture zones. A large-radius fillet at a change in shaft diameter imposes a moderate stress concentration. Figure 4(b) shows the pattern on the surface of a fracture through such a fillet. A small-radius fillet at a change in diameter results in a severe stress concentration. Figure 4(c) shows the typical pattern on the surface of a fracture through a small-radius fillet. The reason for the fatigue-pattern changes is that the fatigue crack propagates faster in more severe stress concentrations at each end than in the interior. Under the above loading conditions, each crack is subjected alternately to tensile and compressive stresses, with the result that the surfaces of the crack are forced into contact with one another during the compression cycle, and rubbing occurs. Rubbing may sometimes be sufficient to obliterate many of the characteristic marks, and the crack surfaces may become dull or polished. Rotating-Bending Fatigue. The essential difference between a stationary shaft and a rotating shaft subjected to the same bending moment is that in a stationary shaft the tensile stress is confined to a portion of the periphery only. In a rotating shaft, every point on the periphery sustains a tensile stress, then a compressive stress, once every revolution. The relative magnitude of the stresses at different locations is determined by conditions of balance or imbalance imposed on the shaft. Another important difference introduced by rotation is asymmetrical development of the crack front from a single origin. There is a marked tendency of the crack front to extend preferentially in a direction opposite to that of rotation. The crack