Question

A 1-in-diameter solid round bar has a groove 0.1-in deep with a 0.1-in radius machined into it. The bar is made of AISI 1020 CD steel and is subjected to a purely reversing torque of 1800 lbf • in. For theS-N curve of this material, let f = 0.9.

(a) Estimate the number of cycles to failure.

(b) If the bar is also placed in an environment with a temperature of 750°F, estimate the number of cycles to failure.

Answer 1

Obtain the value of tensile strength of 1020 CD steel from Table A-20, “Deterministic ASTM minimum tensile and yield strengths for Some Hot Rolled and Cold Drawn steel,” from the text book.

Ultimate Tensile Strength,

Calculate the diameter of bar passing through lower tip of grove.

Here, diameter of rod isand depth of groove is.

Substitute 1 in for and 0.1 in for

Calculate the ratio.

Here, radius of groove is and depth of groove is

Calculate the ratio.

Here, diameter of rod is.

Obtain the value of stress concentration factor of grooved round bar in torsion by using Table A-15, “Charts of Theoretical Stress Concentration Factors,” from the text book for corresponding values of and

Stress concentration factor,

Read the notch sensitivity value from Figure 6-21, “Notch sensitivity curves for materials in reversed torsion for notch radius,” corresponding to notch radius of 0.1in.

Notch sensitivity value,

Calculate the fatigue stress concentration factor.

Substitute 0.81 for and 1.4 for.

Calculate the maximum shear stress in the bar.

Here, torque is T.

Substitute 1.32 forfor and for

Calculate the endurance limit of the bar.

Since the ultimate tensile strength is less than, use the following relation to find the endurance limit.

Substitutefor

Obtain the following values from Table 6-2, “Parameters for Marin Surface Modification Factor,” for machined surface finish and units measured in kpsi.

and

Calculate the surface factor.

Substitutefor forand for

Calculate the size factor.

Since, the value of depth of groove lies in between and use the following expression for finding the size factor:

Substitute

Read the value of loading factor shown below the Table 6-3 from the text book.

Loading factor for torsion,

Generally temperature factor and reliability factor values are taken as follows:

Temperature factor,

Reliability factor,

Find the endurance strength by using Marin equation.

Substitute for 0.9 for 0.59 for 1 for 1 for and 34 kpsi for

Express the ultimate shear stress for pure reversing torsion.

Substitute 68 kpsi for

(a)

Calculate the constant a by using the following expression:

Here, fatigue strength fraction is.

Substitutefor for and for

Calculate the constant b by using the following expression:

Substitutefor for and for

Calculate the number of cycles to failure.

Substitute 105.9 forfor and for

Therefore, the number of cycles to failure is.

(b)

Bar is placed in an environment of, so effect of temperature on tensile strength has to be considered.

Obtain the value of temperature factor at by using Table 6-4, “Effect of Operating temperature on the tensile strength of steel,” from the text book.

Calculate the endurance strength by using Marin equation.

Substitute for 0.9 for 0.59 for 0.8995 for 1 for and 34 kpsi for

Calculate the constant a by using the following expression:

Here, fatigue strength fraction is.

Substitutefor for and for

Calculate the constant b by using the following expression:

Substitutefor for and for

Calculate the number of cycles to failure.

Substitute 117.6 forfor and for

Therefore, the number of cycles to failure is.