Today we will cover fatigue after a short refresher of stress based static failure and fracture mechanics.

Transcription

1 dec Today we will cover fatigue after a short refresher of stress based static failure and fracture mechanics. Non-destructive Testing Testing methods exist that can detect cracks or flaws in metallic parts without destroying them. These methods are called non-destructive testing (NDT). If the flaw size can be established in a part through NDT, and the stress state at the location of the crack is known through analysis or test, then an analysis can be performed to determine if the crack is close to the critical crack size for the particular stress state. The combination of analysis to determine the stress state and NDT to establish the maximum flaw size are critical components of fracture prevention programs. Two NDT techniques: X-radiography and ultrasonic testing.

2

3

4 Rotating Beam Fatigue Test

5 S-N Curve The Fatigue Strength, Sf(N), is the stress level that a material can endure for N cycles. The stress level at which the material can withstand aninfinite number of cycles is call the Endurance Limit. The Endurance Limit is observed as a horizontal line on the S-N curve. Non-ferrous materials exhibit no endurance limit. Representative S-N curves

6 The Endurance Limit for a material can be obtained from Wohler tests or from the Ultimate tensile strength fo the material as shown below. Se = 0.3 Sut Endurance Limit Multiplying factors (Marin Factors) The endurance limit is for test specimens in laboratory conditions such as perfect surfaces, room temperature and reversed bending loading. There are several factors that are known to result in differences between the endurance limits in test specimens and those found in machine elements.

7 Mean Stress Effects The S-N curve obtained from a rotating beam test has completely reversed stress states. Many stress histories will not have completely reversed stress states. Some definitions: Note that R=-1 for a completely reversed stress state with zero mean stress. The plot shows the fatigue strength of several steels as a function of mean stress for a constant number of cycles to failure. Note that a tensile mean stress results in a significantly lower fatigue strength for a given number of cycles to failure.

8 The data for the mean stress effects are modeled by several models such as the Goodman Line. Any combination of mean and alternating stress that lies on or below the Goodman line will have infinite life. Note that the fatigue stress concentration factor is applied only to the alternating component.

9 Fatigue Stress Concentration Factors Comparisons of fatigue test results for notched and un-notched specimens revealed that a reduced Kt was warranted for calculating the fatigue life for many materials. Notch Sensitivity Factor The notch sensitivity of a material is a measure of how sensitive a material is to notches or geometric discontinuities. Kf is normally used in fatigue calculations. It is convenient to think of Kf as a stress concentration factor reduced from Kt because of lessened sensitivity to notches. If notch sensitivity data is not available, it is conservative to use Kt in fatigue calculations. Example A 1.5-inch round bar has been machined from AISI 1050 colddrawn round bar. This part is to withstand a fluctuating tensile load varying from 0 to 16 kip. Because of the design of the ends and the fillet radius, a fatigue stress-concentration factor of 1.85 exists. The remaining Marin factors have been worked out, and are ka=0.797,

10 kb=kd=1, and kc= Find the factor of safety using the Goodman interaction line. Calculate Material Property: endurance limit: Calculate alternating and mean stresses: Comparing the stress values and the endurance limit, calculate the safety factor:

11 Finite Life Estimates How can the life of a part be estimated if the mean stress-alternating stress pair lie above the Goodman line?

12

13 Multi-axial Fluctuating Stress States Miner s Rule is the simplest and most widely used Cumulative Damage Law.

14

15 Quiz Problem