837:
741:: Features such as steps on a shaft, shoulders, and other abrupt changes in the cross-sectional area of components are often necessary for mounting elements like gears and bearings or for assembly considerations. While these features are essential for the functionality of the device, they introduce sharp transitions in geometry that become hotspots for stress concentration. Additionally, design elements like oil holes, grooves, keyways, splines, and screw threads also introduce discontinuities that further exacerbate stress concentration.
369:
713:: When designing mechanical components, it is generally presumed that the material used is consistent and homogeneous throughout. In practice, however, material inconsistencies such as internal cracks, blowholes, cavities in welds, air holes in metal parts, and non-metallic or foreign inclusions can occur. These defects act as discontinuities within the component, disrupting the uniform distribution of stress and thereby leading to stress concentration.
816:: Adjusting the hole shape, often transitioning from circular to elliptical, to minimize stress gradients. This must be checked for feasibility. One example is adding a fillet to internal corners. Another example is in a threaded component, where the force flow line is bent as it passes from shank portion to threaded portion; as a result, stress concentration takes place. To reduce this, a small undercut is made between the shank and threaded portions
747:: Imperfections on the surface of components, such as machining scratches, stamp marks, or inspection marks, can interrupt the smooth flow of stress across the surface, leading to localized increases in stress. These imperfections, although often small, can significantly impact the durability and performance of mechanical components by initiating stress concentration.
719:: Mechanical components are frequently subjected to forces that are concentrated at specific points or small areas. This localized application of force can result in disproportionately high pressures at these points, causing stress concentration. Typical instances include the interactions at the points of contact in meshing gear teeth, the interfaces between
207:
in metals, may also concentrate the stress. Inclusions on the surface of a component may be broken from machining during manufacture leading to microcracks that grow in service from cyclic loading. Internally, the failure of the interfaces around inclusions during loading may lead to static failure
827:
The optimal mitigation technique depends on the specific geometry, loading scenario, and manufacturing constraints. In general, a combination of methods is required for the best result. While there is no universal solution, careful analysis of the stress flow and parameterization of the model can
199:
Geometric discontinuities cause an object to experience a localised increase in stress. Examples of shapes that cause stress concentrations are sharp internal corners, holes, and sudden changes in the cross-sectional area of the object as well as unintentional damage such as nicks, scratches and
735:: Thermal stress occurs when different parts of a structure expand or contract at different rates due to variations in temperature. This differential in thermal expansion and contraction generates internal stresses, which can lead to areas of stress concentration within the structure.
796:: Introducing auxiliary holes in the high stress region to create a more gradual transition. The size and position of these holes must be optimized. Known as crack tip blunting, a counter-intuitive example of reducing one of the worst types of stress concentrations, a
607:
66:
is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as
31:
1148:
S. A. Meguid, “Finite element analysis of defence hole systems for the reduction of stress
Concentration in a uniaxially–loaded plate with coaxial holes,” Engineering Fracture Mechanics, vol. 25, no. 4, pp. 403-413,
856:
cracks growing from the high stress concentration caused by the use of punched rivet holes around the windows. The square passenger windows were also found to have higher stress concentrations than expected and were
360:
1130:
R. T. Fenner, “The boundary integral equation and boundary element method in engineering stress analysis”, The
Journal of Strain Analysis for Engineering Design IMechE, vol. 18, no. 4, pp. 199-205, 1983.
694:
As the radius of curvature approaches zero, such as at the tip of a sharp crack, the maximum stress approaches infinity and a stress concentration factor cannot therefore be used for a crack. Instead, the
1158:
G. S. Giare and R. Shabahang, “The reduction of stress concentration around the hole in an isotropic plate using composite material,” Engineering
Fracture Mechanics, vol. 32, no. 5, pp. 757-766, 1989.
184:
crack to initiate and slowly grow at a stress concentration leading to the failure of even ductile materials. Fatigue cracks always start at stress raisers, so removing such defects increases the
470:
365:
Note that the dimensionless stress concentration factor is a function of the geometry shape and independent of its size. These factors can be found in typical engineering reference materials.
766:
During the design phase, there are multiple approaches to estimating stress concentration factors. Several catalogs of stress concentration factors have been published. Perhaps most famous is
1167:
Z. Wu, “Optimal hole shape for minimum stress concentration using parameterized geometry models,” Structural and
Multidisciplinary Optimization, vol. 37, no. 6, pp. 625-634, Feb, 2009.
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a large hole at the end of the crack. The drilled hole, with its relatively large size, serves to increase the effective crack tip radius and thus reduce the stress concentration.
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276:
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118:
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196:
Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress.
435:
412:
994:
Tuplin WA. Gear-Tooth
Stresses at High Speed. Proceedings of the Institution of Mechanical Engineers. 1950;163(1):162-175. doi:10.1243/PIME_PROC_1950_163_020_02
176:
that will typically occur first at a stress concentration allowing a redistribution of stress and enabling the component to continue to carry load.
200:
cracks. High local stresses can cause objects to fail more quickly, so engineers typically design the geometry to minimize stress concentrations.
810:: Adding higher strength material around the hole, usually in the form of bonded rings or doublers. Composite reinforcements can reduce the SCF.
1139:
K. Rajaiah and A. J. Durelli, “Optimum hole shapes in finite plates under uni-axial load,” Applied
Mechanics, vol. 46(3), pp. 691-695, 1979.
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602:{\displaystyle \sigma _{\max }=\sigma _{0}\left(1+2{\cfrac {a}{b}}\right)=\sigma \left(1+2{\sqrt {\cfrac {a}{\rho }}}\right)}
1200:
1195:
836:
820:
120:, which is the ratio of the highest stress to the nominal far field stress. For a circular hole in an infinite plate,
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Stress concentrations can be mitigated through techniques that smoothen the flow of stress around a discontinuity:
824:: Using materials with properties that vary gradually can reduce the SCF compared to a sudden change in material.
707:
Stress concentration can arise due to various factors. The following are the main causes of stress concentration:
775:
696:
154:
1018:"A performance comparison between cooled and uncooled infrared detectors for thermoelastic stress analysis"
180:
materials will typically fail at the stress concentration. However, repeated low level loading may cause a
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The sharp corner at the brick has acted as a stress concentrator within the concrete causing it to crack
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is the radius of curvature of the elliptical hole. For circular holes in an infinite plate where
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Persson, B.N.J. Surface
Roughness-Induced Stress Concentration. Tribol Lett 71, 66 (2023).
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96:
83:. Stress concentrations may also occur from accidental damage such as nicks and scratches.
756:
43:
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experienced a number of catastrophic failures that were eventually found to be due to
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17:
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A focus point of stress on the margins of an implant, where metal meets bone, of an
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There are experimental methods for measuring stress concentration factors including
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Location in an object where stress is far greater than the surrounding region
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which defines the scaling of the stress field around a crack tip, is used.
877:
849:
797:
464:, the stress at the ends of the major axes is given by Inglis' equation:
158:
177:
165:
355:{\displaystyle K_{t}={\frac {\sigma _{\max }}{\sigma _{\text{nom}}}}}
372:
Stress concentration around an elliptical hole in a plate in tension
835:
801:
367:
153:. The stress concentration factor should not be confused with the
68:
29:
828:
point designers toward an effective stress reduction strategy.
86:
The degree of concentration of a discontinuity under typically
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are commonly used in design today. Other methods include the
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in cold and stressful conditions in winter storms in the
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759:, thermoelastic stress analysis, brittle coatings or
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161:on the stresses in the region around a crack tip.
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860:Brittle fractures at the corners of hatches in
1058:ESDU64001: Guide to stress concentration data
786:Limiting the effects of stress concentrations
8:
90:loads can be expressed as a non-dimensional
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913:
168:materials, large loads can cause localised
1022:Quantitative InfraRed Thermography Journal
1005:https://doi.org/10.1007/s11249-023-01741-4
880:is very likely to be the point of failure.
305:of the gross cross-section and defined as
157:, which is used to define the effect of a
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381:elastic stress distribution around a hole
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1108:Peterson's Stress Concentration Factors
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62:) is a location in an object where the
770:by Peterson, first published in 1953.
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658:, the stress concentration factor is
251:, is the ratio of the highest stress
7:
1028:(2). Taylor & Francis: 207–221.
298:{\displaystyle \sigma _{\text{nom}}}
1083:Stress Concentration Design Factors
922:Fatigue of Structures and Materials
768:Stress Concentration Design Factors
391:. In an elliptical hole of length
203:Material discontinuities, such as
25:
1016:Rajic, Nik; Street, Neil (2014).
900:"Stress Concentrations at Holes"
945:Shigley, Joseph Edward (1977).
751:Methods for determining factors
271:{\displaystyle \sigma _{\max }}
1081:Peterson, Rudolf Earl (1953).
976:"Stresses At Elliptical Holes"
949:(Third ed.). McGraw-Hill.
703:Causes of Stress Concentration
379:derived the equations for the
1:
947:Mechanical Engineering Design
821:Functionally Graded Materials
387:occurs in the area of lowest
1035:10.1080/17686733.2014.962835
757:photoelastic stress analysis
963:stress at round-tip notches
723:, and the contact zones in
457:{\displaystyle \sigma _{0}}
437:, under a far-field stress
222:stress concentration factor
216:Stress concentration factor
92:stress concentration factor
1217:
1106:Pilkey, Walter D. (1999).
1085:. John Wiley & Sons.
739:Geometric Discontinuities
924:. Springer. p. 90.
38:are denser near the hole
1181:When Metal Lets Us Down
1110:(2nd ed.). Wiley.
776:boundary element method
697:stress intensity factor
684:{\displaystyle K_{t}=3}
155:stress intensity factor
146:{\displaystyle K_{t}=3}
920:Schijve, Jaap (2001).
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857:redesigned.
192:Description
36:force lines
1190:Categories
981:2020-03-13
885:References
414:and width
205:inclusions
1044:137607813
875:implanted
620:ρ
586:ρ
548:σ
489:σ
476:σ
446:σ
377:E. Kirsch
342:σ
332:σ
287:σ
260:σ
34:Internal
1060:. ESDU.
878:orthosis
850:aircraft
832:Examples
800:, is to
174:yielding
854:fatigue
182:fatigue
178:Brittle
166:ductile
88:tensile
81:fillets
77:notches
73:grooves
1114:
1089:
1064:
1042:
928:
612:where
64:stress
1149:1986.
1040:S2CID
802:drill
798:crack
385:notch
159:crack
69:holes
54:or a
1112:ISBN
1087:ISBN
1062:ISBN
926:ISBN
845:The
778:and
220:The
164:For
79:and
46:, a
1030:doi
763:.
691:.
480:max
346:nom
336:max
291:nom
264:max
208:by
172:or
58:or
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317:K
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