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The Mode I critical stress intensity factor, , is the most often used engineering design parameter in fracture mechanics and hence must be understood if we are to design fracture tolerant materials used in bridges, buildings, aircraft, or even bells. Polishing cannot detect a crack.
The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . [1] When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the ...
In this case, the material's fracture toughness is given by the critical stress intensity factor K Ic. [2] Approach
where E is the Young's modulus, ν is Poisson's ratio, and K I is the stress intensity factor in mode I. Irwin also showed that the strain energy release rate of a planar crack in a linear elastic body can be expressed in terms of the mode I, mode II (sliding mode), and mode III (tearing mode) stress intensity factors for the most general ...
The stress intensity range can be calculated from the maximum and minimum stress intensity for a cycle Δ K = K max − K min {\displaystyle \Delta K=K_{\text{max}}-K_{\text{min}}} A geometry factor β {\displaystyle \beta } is used to relate the far field stress σ {\displaystyle \sigma } to the crack tip stress intensity using
The energy release rate is directly related to the stress intensity factor associated with a given two-dimensional loading mode (Mode-I, Mode-II, or Mode-III) when the crack grows straight ahead. [3] This is applicable to cracks under plane stress, plane strain, and antiplane shear.
As part of this work, Irwin defined the fundamental concept of a Stress Intensity Factor and the critical plane-strain stress intensity factor (KIC) which is a material property. He was involved in the development of several standards and led several committees for the American Society for Testing and Materials (ASTM).
Where plane stress is dominant in low thickness samples increasing the critical stress intensity. As your thickness increases the critical stress intensity will decrease and eventually plateau. This behavior is caused by the transitioning from the plane stress to plain strain conditions as the thickness increases.