Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
bartleby

Concept explainers

Question
Book Icon
Chapter 11, Problem 11.12P

(a)

To determine

The predicted crack length at fracture.

(a)

Expert Solution
Check Mark

Answer to Problem 11.12P

The predicted crack length at fracture is 0.026 m .

Explanation of Solution

Given:

The critical stress intensity factor is 60 MPam1/2 .

The minimum detectable crack length is 0.20×103 m .

Stress range is 300MPa .

Mean stress is 150 MPa .

Concept used:

Write the expression for stress intensity range.

  Kmax=Yσmax(πaf)1/2 …… (1)

Here, Kmax is the max stress intensity range, af is the crack length at fracture, Y is the geometrical factor and σmax is the maximum stress..

For internal cracks the value of geometrical factor is 1.0 .

Calculation:

Substitute 1.0 for Y , 300MPa for σmax and 60MPam1/2 for Kmax in equation (1).

  60MPam1/2=(1.0)(200MPa)(π a f)1/2(π a f)1/2=0.2 m1/2πaf=0.04maf=0.013 m

Calculate the critical length of failure.

  2a=2(0.013 m)=0.026 m

Conclusion:

Thus, the predicted crack length at fracture is 0.026 m .

(b)

To determine

Lifetime of part based upon fatigue crack propagation.

(b)

Expert Solution
Check Mark

Answer to Problem 11.12P

Lifetime of part based upon fatigue crack propagation is 2.21×104 cycles .

Explanation of Solution

Given:

Rate of crack growth is dadN=1×1013(ΔK)6 .

Concept used:

Write the expression for the number of crack propagation cycle to failure.

  Nf=1(n2+1)(1AΔσnπ n/2)(af( n/2)+1ai( n/2)+1) …… (2)

Here, Nf is the number of crack propagation cycle to failure, n is the slope of plot between log(dadN) versus log(ΔK) , Δσ is the stress range, A is the constant and ai is the initial detectable crack length.

Write the expression for crack growth rate.

  dadN=1×1013(ΔK)6

Take log on both sides.

  log(dadN)=log(1×1013)+6log(ΔK)

The above expression represents a straight line with slope 6 . Thus, the slope of plot between log(dadN) versus log(ΔK) is 6 .

Calculation:

Substitute 1×104 m for ai , 6 for n , 300MPa for Δσ , 0.013 m for af and 1×1013 MPam for A in equation (2).

  Nf=1( 6 2 +1)(1 ( 1× 10 13 ) ( 200 ) 6 π 6/2 )( ( 0.013 ) ( 6/2 )+1 ( 1× 10 4 ) ( 6/2 )+1)Nf=13+1(1 2.26× 10 3 )( ( 0.013 ) ( 6/2 )+1 ( 1× 10 4 ) ( 6/2 )+1)Nf=12(1 2.26× 10 3 )(1× 108)Nf=2.21×104 cycles

Conclusion:

Thus, the Lifetime of part based upon fatigue crack propagation is 2.21×104 cycles .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A thin plate of a ceramic material with E = 225 GPa is loaded in tension, developing a stress of 450 MPa. Is the specimen likely to fail if the most severe flaw present is an internal crack oriented perpendicular to the load axis that has a total length 0.25 mm and a crack tip radius of curvature equal to 1 μm?
3. A steel specimen is tested in tension. The specimen is 1.0 in. wide by 0.25 in. thick in the test region. By monitoring the load dial of the testing machine, it was found that the specimen yielded at a load of 12.5 kips and fractured at 17.5 kips. а. Determine the tensile stresses at yield and at fracture. b. Estimate how much increase in length would occur at 60% of the yield stress in a 2-in. gauge length
2- What is the largest size (mm) internal through crack that a thick plate of aluminium alloy 7075-T651 can support at an applied stress of (a) three-quarters of the yield strength and (b) one-half of the yield strength? Assume Y = 1. for 7075-T651, KỊC = 24.2 MPa ym and oYS = 495 MPa.
Knowledge Booster
Background pattern image
Civil Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Materials Science And Engineering Properties
Civil Engineering
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Cengage Learning