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The stress intensity factor for a Mode I crack is written as K I. Where the units are either ksi√ in or MPa√ m. Image Source: USAF Damage Tolerant Design HandbookĪ term K, called the stress intensity factor, can be defined in the form: The stress intensity factor is a useful concept for characterizing the stress field near the crack tip.įor Mode I loading, the linear-elastic stresses in the direction of applied loading near an ideally sharp crack tip can be calculated as a function of the location with respect to the crack tip expressed in polar coordinates: The most prevalent method in use today is to calculate a stress intensity factor, as discussed in a later section. The plastic deformation causes blunting of the crack tip which increases the radius of curvature and brings the stresses back to finite levels.īecause of the stress singularity issues that arise when using the stress concentration approach, and because of the plastic zone that develops around the crack tip which renders the stress concentration approach invalid, other methods have been developed for characterizing the stresses near the tip of the crack.
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This region of plastic deformation is called the plastic zone and is discussed in a later section. Instead, the stress distributes over the surrounding material, resulting in plastic deformation in the material at some distance from the crack tip. This infinite stress is known as a stress singularity and is not physically possible.
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Where σ is the nominal stress and ρ is the radius of curvature of the ellipse, ρ = b 2/a.Īs the radius of the crack tip approaches zero, the theoretical stress approaches infinity. The theoretical value of stress at the tip of the ellipse is given by: As a simple example, consider the case of an elliptical crack in the center of an infinite plate: Image Source: Wikimedia Commons Stress Concentrations Around CracksĬracks act as stress risers and cause the stress in the part to spike near the tip of the crack. An understanding of fracture mechanics would have prevented these losses. The SS Schenectady split in two while sitting at dock. Approximately half of the cracks initiated at the corners of the square hatch covers which acted as stress risers. The Liberty ships all had a tendency to crack during cold weather and rough seas, and multiple ships were lost. The image below shows the SS Schenectady tanker, one of the World War II Liberty Ships and one of the most iconic fracture failures. A failure due to brittle fracture is rapid and catastrophic and provides little warning.Ignoring fracture mechanics can lead to failure of parts at loads below what is expected using a strength-of-materials approach.The intuition of many engineers to prefer higher strength materials can lead them down a dangerous path. Typically, as the strength of a material increases, fracture toughness decreases.Cracks can either pre-exist in a part, or they can develop due to high stress or fatigue. Cracks and crack-like flaws occur much more frequently than might be expected.
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Fracture mechanics is important to consider for several important reasons: