Fatigue, Fracture and Durability

Worked Engineering Derivation:

**Question:** Calculate alternating normal stress using max=130 MPa, min=-70 MPa. Using the explicit relationship for this simplified case, the arithmetic is `(130-(-70))/2`. The computed result is **100 MPa**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that entering peak-to-peak range as amplitude doubles the cyclic stress in the calculation. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate Goodman stress utilization using alternating=76 MPa, mean=38 MPa, Se=180 MPa, Sut=520 MPa. Using the explicit relationship for this simplified case, the arithmetic is `76/180+38/520`. The computed result is **0.4953 dimensionless**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that extrapolating a Goodman line to compressive mean stress or unconventional materials without evidence is unsound. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate fatigue notch concentration using Kt=2.2, q=0.7. Using the explicit relationship for this simplified case, the arithmetic is `1+0.7*(2.2-1)`. The computed result is **1.84 dimensionless**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that using Kt for static stress but forgetting Kf in alternating stress hides fatigue risk. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate Miner sum of two bins using n1=10000,N1=100000,n2=20000,N2=200000. Using the explicit relationship for this simplified case, the arithmetic is `10000/100000+20000/200000`. The computed result is **0.2 dimensionless**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that ignoring load sequence, corrosion or overload interactions can make a Miner estimate nonconservative. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.

Worked Engineering Derivation:

**Question:** Calculate distance accumulated in micro-slip using v=0.00001 m/s, t=12 h. Using the explicit relationship for this simplified case, the arithmetic is `0.00001*12*3600*1000`. The computed result is **432 mm**. This is a synthetic, rounded result; it is not a measured or independently certified design capacity. Recalculate with an independent calculator before passing it into a later sizing step. A result outside a plausible physical range is evidence that units or assumptions may be wrong, not automatically a new discovery. **Interpretation:** The number answers only the posed arithmetic question. A design release would require a defined allowable, actual load spectrum, material condition, geometric tolerances and a standard-appropriate assessment. The main danger in this particular lesson is that treating seal wear, corrosion and fatigue as unrelated independent hazards misses interactions. A responsible notebook records both the numerical output and the reason why the model is incomplete. For a learner, try replacing a primary load with 80% and 120% of its base value; check whether the response is linear, quadratic or more sensitive, and explain what happens to the corresponding margin.