. The fatigue data for a ductile cast iron are gi Cycles to Failure Stress Amplitude [MPa (ksi)] 248 (36.0) 236 (34.2) 224132 51 1 × 105 3 x 105 106
. The fatigue data for a ductile cast iron are gi Cycles to Failure Stress Amplitude [MPa (ksi)] 248 (36.0) 236 (34.2) 224132 51 1 × 105 3 x 105 106
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Cyclic Stresses (Fatigue): The S-N Curve**
4. The fatigue data for a ductile cast iron are given as follows:
| Stress Amplitude [MPa (ksi)] | Cycles to Failure |
|-----------------------------|-------------------|
| 248 (36.0) | \(1 \times 10^5\) |
| 236 (34.2) | \(3 \times 10^5\) |
| 224 (32.5) | \(1 \times 10^6\) |
| 213 (30.9) | \(3 \times 10^6\) |
| 201 (29.1) | \(1 \times 10^7\) |
| 193 (28.0) | \(3 \times 10^7\) |
| 193 (28.0) | \(1 \times 10^8\) |
| 193 (28.0) | \(3 \times 10^8\) |
**Tasks:**
(a) Make an S-N plot (stress amplitude versus logarithm cycles to failure) using these data.
(b) What is the fatigue limit for this alloy?
(c) Determine fatigue lifetimes at stress amplitudes of 230 MPa (33,500 psi) and 175 MPa (25,000 psi).
(d) Estimate fatigue strengths at \(2 \times 10^5\) and \(6 \times 10^6\) cycles.
**Explanation:**
An S-N curve (also known as a Wöhler curve) is a graph that shows how the stress amplitude of a material changes as the number of cycles to failure increases. Typically, the stress amplitude is plotted on the y-axis and the logarithm of the number of cycles to failure is plotted on the x-axis. The curve helps in understanding the fatigue characteristics of materials, allowing engineers to predict how long a material will last under cyclic stresses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf033eb0-5213-479e-b20c-cfd2190955a4%2F555a1f14-7d67-4b21-abb7-835c02035ff4%2Fjin4fjj_processed.png&w=3840&q=75)
Transcribed Image Text:**Cyclic Stresses (Fatigue): The S-N Curve**
4. The fatigue data for a ductile cast iron are given as follows:
| Stress Amplitude [MPa (ksi)] | Cycles to Failure |
|-----------------------------|-------------------|
| 248 (36.0) | \(1 \times 10^5\) |
| 236 (34.2) | \(3 \times 10^5\) |
| 224 (32.5) | \(1 \times 10^6\) |
| 213 (30.9) | \(3 \times 10^6\) |
| 201 (29.1) | \(1 \times 10^7\) |
| 193 (28.0) | \(3 \times 10^7\) |
| 193 (28.0) | \(1 \times 10^8\) |
| 193 (28.0) | \(3 \times 10^8\) |
**Tasks:**
(a) Make an S-N plot (stress amplitude versus logarithm cycles to failure) using these data.
(b) What is the fatigue limit for this alloy?
(c) Determine fatigue lifetimes at stress amplitudes of 230 MPa (33,500 psi) and 175 MPa (25,000 psi).
(d) Estimate fatigue strengths at \(2 \times 10^5\) and \(6 \times 10^6\) cycles.
**Explanation:**
An S-N curve (also known as a Wöhler curve) is a graph that shows how the stress amplitude of a material changes as the number of cycles to failure increases. Typically, the stress amplitude is plotted on the y-axis and the logarithm of the number of cycles to failure is plotted on the x-axis. The curve helps in understanding the fatigue characteristics of materials, allowing engineers to predict how long a material will last under cyclic stresses.
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