Transcription of Chapter 9
1 Design for Strength and Endurance Chapter 9. Chapter 9. Fluctuating Load Analysis Screen Titles Fluctuating Stresses Generic Stress-Time Behavior Stress-Time Relations Modified Goodman Diagram Mean/Fluctuating Stress Diagram Soderberg Failure Theory Goodman Failure Theory Gerber Failure Theory Sample Problem 1. Problem 1 Solution Torsional Fatigue Combined Loading Modes Sample Problem 2. Problem 2 Solution Cumulative Fatigue Damage Palmgren-Minor Theory Sample Problem 3. Problem 3 Solution Mason's Modification Review Exercise Off Line Exercise _____. Fluctuating Load Analysis - 189 - Zorowski 2002.
2 Design for Strength and Endurance Chapter 9. _____. Fluctuating Load Analysis - 190 - Zorowski 2002. Design for Strength and Endurance Chapter 9. 1. Title page 2. Page Index Chapter 9 continues the study of the fatigue Listed on this page are all the individual pages in analysis and behavior of mechanical parts. Chapter 9 with the exception of the exercise Attention is now directed to elements subjected problems. Each page title is hyperlinked to its to general fluctuating loads as contrasted to specific page and can be accessed by clicking complete reversed stress states treated in on the title.
3 It is suggested that the reader first Chapter 8. The presentation begins with proceed through all pages sequentially. Clicking defining generic parameters to represent on the text button at the bottom of the page fluctuating loads. General fatigue failure under provides a pop up window with the text for that fluctuating normal stress loading is then page. The text page is closed by clicking on the discussed and three specific failure theories are x in the top right corner of the frame. Clicking on introduced together with fatigue under the index button returns the presentation to the fluctuating torsional stresses.
4 A method of page index of Chapter 9. fatigue analysis for combined stress states is also covered. The Chapter concludes with two methods of determining the effects of cumulative fatigue damage due to multiple loads applied for different durations of cyclic application. Several exercise problems and extended sample problems are included to demonstrate the application of the subject content. _____. Fluctuating Load Analysis - 191 - Zorowski 2002. Design for Strength and Endurance Chapter 9. 3. Fluctuating Stresses 4. Generic Stress Time Behavior Chapter 8 considered the fatigue behavior of Depicted in the figure is an idealized general mechanical elements subjected to complete fluctuating stress versus time behavior curve.
5 Reversed stress states in which the stress level Although this is represented as a smooth varied from some specific negative value to the sinusoidal function the parameters that will be same positive value and then repeated this used to generalize its description will be the behavior continuously. This Chapter will deal same irrespective of the specific shape of the with repeated stress states that may vary from curve provided it is periodic in behavior. In other zero to some specific value and then back to words the shape could be saw tooth or a square zero continuously or even more generally from wave, it would still be characterized for fatigue some minimum value to a different numeric analysis in the same way.
6 The four parameters positive value and then back to the minimum used to define the curves characteristics for the value repeatedly. In this instance the variation fatigue discussions and analyses to follow are its will possess some mean value of stress that will maximum value, sigma max, its minimum value, lie between the minimum and maximum value of sigma min, its mean value, sigma m and its the applied stress state. alternating value about the mean, sigma a. _____. Fluctuating Load Analysis - 192 - Zorowski 2002. Design for Strength and Endurance Chapter 9. 5. Stress Time Relations Of primary interest in the developments to follow are the mean stress and the alternating stress components.
7 The mean stress is of course just the average of the two extreme values or one half the sum of the maximum and minimum values. The alternating stress, which is sometimes referred to as the stress amplitude, is simply one half the difference between the maximum and minimum values. Of occasional value is the stress ratio, R, defined as the minimum stress divided by the maximum stress and the amplitude ratio, A, which is the alternating component divided by the mean component. _____. Fluctuating Load Analysis - 193 - Zorowski 2002. Design for Strength and Endurance Chapter 9. 6. Modified Goodman Diagram Fatigue failure behavior from experiments failure increases as indicated by the third set of conducted under different combinations of red and green dots.
8 Thus the area enclosed by fluctuating normal stress loading states are the red boundary in the first quadrant proposes conveniently presented and described on a states of stress for which fatigue failure will not Modified Goodman Diagram . In this occur. Experimental results have verified that representation the mean stress is plotted on the this is a good approximation for defining fatigue horizontal axis and all other stresses are plotted behavior under a general fluctuating state of vertically with tension to the right and up. A 45- stress. degree line from the origin in the first quadrant represents the mean stress of an applied stress state.
9 When the mean stress is zero fatigue failure is represented by plus and minus the endurance stress on the vertical axis. This is indicated by the red dot at the origin and the green dot on the vertical axis. A green dot on the negative vertical axis is not shown due to space limitations. Now consider the case where the mean stress plus the stress amplitude are equal to the yield stress of the material. This is illustrated by the second set of red and green dots. Assuming that yielding is considered as undesirable, that is equivalent to failure , then lines drawn from the second set of green dots to the positive and negative endurance limits on the vertical axes corresponds to a proposed criteria for defining fatigue failure for a generalized fluctuating stress loading.
10 The failure boundary is completed by extending the line from the upper green dot on the maximum stress line to the value of the yield stress on the mean stress line and from that point to the lower green dot on the minimum stress line. Note that when the mean stress is equal to the yield stress no alternating stress is necessary to produce yielding. However, as the mean stress decreases the corresponding value of alternating stress required to define fatigue _____. Fluctuating Load Analysis - 194 - Zorowski 2002. Design for Strength and Endurance Chapter 9. 7. Mean/Fluctuating Stress Diagram 8.
