Stress Intensity Factor

In fracture mechanics, stress intensity factor (SIF) is used to describe the stress field around the tip of a crack in a material.  It quantifies the stress concentration at the crack tip and is a key factor in determining whether the crack will propagate and cause failure.

Three Primary Modes of Loading

• Mode I  (\(K_1\))  -  Tensile or opening mode, where the crack surfaces are pulled apart.
• Mode II  (\(K_2\))  -  Shear or sliding mode (in-plane shear), where the crack surfaces slide past each other in a direction perpendicular to the crack front.
• Mode III  (\(K_3\))  -  Tear or anti-plane shear mode (out-of-plane shear), where the crack surfaces slide past each other in a direction parallel to the crack front.

These stress intensity factors are crucial in predicting the behavior of cracks in materials under different loading conditions.  They are often used in fracture mechanics equations, such as the Griffith criterion for crack propagation and the Irwin's stress criterion.

The calculation of stress intensity factors involves complex mathematical and numerical methods, including analytical solutions for simple geometries and numerical simulations for more complex cases. Understanding stress intensity factors is essential for engineers and researchers involved in the design and analysis of structures to prevent catastrophic failures due to crack propagation.

 

Mode I - Stress Intensity Factor formula
\( K_1 \;=\; Y_I \; \sigma \; \sqrt{ \pi \; a } \)
Symbol	English	Metric
\( K_1 \) = Stress Intensity Factor for Mode I Loading	\(lbf-ft\)	\(J\)
\( Y_I \) = Geometric Factor (Stress Intensity Factor Coefficient)	\( dimensionless \)	\( dimensionless \)
\( \sigma \)  (Greek symbol sigma) = Applied Stress	\(lbf \;/\; in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( a \) = Crack Size (Half Length of the Crack)	\(in\)	\( mm \)

   

Mode II - Stress Intensity Factor formula
\( K_2 \;=\; Y_{II} \; \tau \; \sqrt{ \pi \; a } \)
Symbol	English	Metric
\( K_2 \) = Stress Intensity Factor for Mode I Loading	\(lbf-ft\)	\(J\)
\( Y_{II} \) = Geometric Factor (Stress Intensity Factor Coefficient for Mode II)	\( dimensionless \)	\( dimensionless \)
\( \tau \)  (Greek symbol tau) = Applied Shear Stress	\(lbf \;/\; in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( a \) = Crack Size (Half Length of the Crack)	\(in\)	\( mm \)

  

Mode III - Stress Intensity Factor formula
\( K_3 \;=\; Y_{III} \; \tau \; \sqrt{ \pi \; a } \)
Symbol	English	Metric
\( K_3 \) = Stress Intensity Factor for Mode I Loading	\(lbf-ft\)	\(J\)
\( Y_{III} \) = Geometric Factor (Stress Intensity Factor Coefficient for Mode III)	\( dimensionless \)	\( dimensionless \)
\( \tau \)  (Greek symbol tau) = Applied Shear Stress	\(lbf \;/\; in^2\)	\(Pa\)
\(\large{ \pi }\) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( a \) = Crack Size (Half Length of the Crack)	\(in\)	\( mm \)