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Plane strain conditions give the lowest fracture toughness value which is a material property. 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 ...
Fracture mechanics is the field of mechanics concerned with the study of the propagation of ... For the special case of plane strain deformation ... is low, one knows ...
The fracture toughness and the critical strain energy release rate for plane stress are related by = where is the Young's modulus. If an initial crack size is known, then a critical stress can be determined using the strain energy release rate criterion.
where is the fracture toughness, ′ = / for plane strain and ′ = for plane stress. The critical stress intensity factor for plane stress is often written as K c {\displaystyle K_{\rm {c}}} . Examples
The chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes. This means that cases involving multiple out-of-phase load inputs, or crack closure can be treated with high ...
where is the plane strain toughness, is a constant that incorporates the stress state, is the tensile flow stress at fracture, is the tensile fracture strain, and is the radius of crack tip. In a low yield strength material, the crack tip can be blunted easily and larger crack tip radius is formed.
Figure 7.1 Plane stress state in a continuum. In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 ...
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.