A cylindrical pressure vessel has an inner diameter of 150 mm and a wall thickness of 5 mm, an

step 1 In this question, they want us to find the pressure that acts on the spherical pressure vessel t

A cylindrical pressure vessel has an inner diameter of 150...

A cylindrical pressure vessel has an inner diameter of $150 \mathrm{~mm}$ and a wall thickness of $5 \mathrm{~mm}$, and it contains a pressure of $20 \mathrm{MPa}$. The safety factor against yielding must be at least $X_{o}=2$. Also, a leak-before-break criterion must be met, with a safety factor of at least $X_{a}=9$ on crack length, requiring $c_{c} \geq X_{a} t$. (a) Is the vessel safe if it is made from $300-\mathrm{M}$ steel ( $\left(300^{\circ} \mathrm{C}\right.$ temper)? (b) From ASTM A517-F steel? (c) What minimum fracture toughness is required for the material in this application? (d) What is the safety factor on $K$ relative to $K_{I c}$ due to the $X_{a}=9$ requirement?

A cylindrical pressure vessel has an inner diameter of $150 \mathrm{~mm}$ and a wall thickness of $5 \mathrm{~mm}$, and it contains a pressure of $20 \mathrm{MPa}$. The safety factor against yielding must be at least $X_{o}=2$. Also, a leak-before-break criterion must be met, with a safety factor of at least $X_{a}=9$ on crack length, requiring $c_{c} \geq X_{a} t$.
(a) Is the vessel safe if it is made from $300-\mathrm{M}$ steel ( $\left(300^{\circ} \mathrm{C}\right.$ temper)?
(b) From ASTM A517-F steel?
(c) What minimum fracture toughness is required for the material in this application?
(d) What is the safety factor on $K$ relative to $K_{I c}$ due to the $X_{a}=9$ requirement?

Key Concepts

Cylindrical Pressure Vessel Design

This concept involves the principles used to design vessels that contain pressurized fluids. It includes understanding how the geometry of a cylinder, such as its diameter and wall thickness, influences the internal stress distribution when subjected to internal pressures.

Hoop Stress Calculation

Hoop stress is a critical component in the analysis of pressure vessels. It is the circumferential stress experienced by the vessel wall due to internal pressure, and its calculation helps determine whether the material will yield or fail under operating conditions.

Yielding and Safety Factors

The yielding safety factor is a measure of the design margin used to ensure that stresses in the material remain below the yielding limit. This factor provides a buffer between the calculated operating stresses and the material's yield strength to promote safe operation.

Leak-Before-Break Criterion

The leak-before-break concept ensures that a structural component will exhibit detectable leakage before catastrophic failure occurs due to crack growth. It requires that cracks must reach a specified length threshold in a controlled manner, allowing for preventive measures to be taken before a complete failure.

Fracture Toughness

Fracture toughness is a material property that quantifies the ability of a material to resist crack propagation. It is a critical parameter in applications where crack initiation and growth could lead to sudden failure, ensuring that the material can absorb energy without fracturing.

Stress Intensity Factor (K) and Crack Propagation

The stress intensity factor defines the local stress state near a crack tip and is used in fracture mechanics to predict crack growth behavior. Comparing this factor with the material's fracture toughness helps engineers determine the safety margins against crack propagation.

Material Selection Based on Mechanical Properties

Selecting appropriate materials for high-pressure applications involves evaluating properties such as yield strength, fracture toughness, and resistance to crack propagation. Materials must be chosen so that their mechanical properties support both the yield safety factor and the leak-before-break criterion required for safe operation.

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