Modified Goodman Theory
Explain what the Modified Goodman Theory is.
Expand Hint
The modified Goodman theory is a method for predicting the fatigue failure of a material under cyclic loading.
Hint 2
In order to predict failure via the modified Goodman theory, the material’s endurance limit and ultimate tensile strength must be known.
The modified Goodman theory is a method for predicting the fatigue failure of a material under cyclic loading. It states that fatigue failure will occur whenever
$$$\frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_{ut}}\geq 1\:\:or\:\:\frac{\sigma_{max}}{S_y}\geq 1$$$
if
$$\sigma_m \geq 0$$
where:
- $$S_e$$ is the endurance limit (the max load level where a material can be cycled indefinitely without failure).
- $$S_{ut}$$ is the ultimate strength (max stress a material can withstand from being pulled before yielding).
- $$S_y$$ is the yield strength (the max load a material can withstand without deforming).
- $$\sigma_a$$ is the alternating stress (subtracting the max and min stress levels and dividing by 2)
- $$\sigma_m$$ is the mean stress (adding the max and min stress levels and dividing by 2)
- $$\sigma_{max}=\sigma_m+\sigma_a$$
- $$n$$ is the factor of safety
The modified Goodman theory can also be expressed with a factor of safety:
$$$\frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_{ut}}\geq \frac{1}{n}\:\:or\:\:\frac{\sigma_{max}}{S_y}\geq \frac{1}{n}$$$
if
$$\sigma_m \geq 0$$
.
The modified Goodman theory is a method for predicting the fatigue failure of a material under cyclic loading. It states that fatigue failure will occur whenever
$$$\frac{\sigma_a}{S_e}+\frac{\sigma_m}{S_{ut}}\geq 1\:\:or\:\:\frac{\sigma_{max}}{S_y}\geq 1$$$
Time Analysis
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