Mode-I stress intensity factor

Mode I is opening loading: crack faces are pulled apart normal to the crack plane. Other basic modes are in-plane and out-of-plane shear. Under mixed loading, KI alone is insufficient; corresponding intensity factors and a suitable failure criterion are needed. The geometry factor and crack-length convention must match a validated solution; compare with toughness only within LEFM validity limits. Application: Understand how crack size, stress and geometry affect crack-tip loading. The numerical example For Y=1.12, σ=100 MPa and a=2 mm, KI≈8.9 MPa√m anchors the idea in a concrete measurement case.

At equal nominal stress, a longer crack raises the intensity of the elastic field near its tip. The square-root dependence follows from the asymptotic crack-tip solution in linear elasticity. Geometry factor Y captures boundary and shape effects, so use a value only for the matching configuration. The geometry factor and crack-length convention must match a validated solution; compare with toughness only within LEFM validity limits. The corresponding units are KI in Pa√m; σ in Pa; a in m; Y dimensionless. For Y=1.12, σ=100 MPa and a=2 mm, KI≈8.9 MPa√m. This checks that the reference quantities are compatible.

A critical comparison requires valid linear-elastic fracture mechanics and dimensions meeting the material property’s validity conditions. A large plastic zone can invalidate a K description. Elastic-plastic measures such as J-integral or CTOD may then be needed; this equation alone does not certify a safe design. The geometry factor and crack-length convention must match a validated solution; compare with toughness only within LEFM validity limits. Scope: This geometry relation belongs to linear-elastic fracture mechanics; Y is not universal and a must match the selected crack geometry. Comparison with KIC requires valid plane-strain and size conditions. Plastic zones, mixed modes and fatigue crack growth need additional models; this equation is not a safety assessment. A practical application is Understand how crack size, stress and geometry affect crack-tip loading.

Write the quantity and unit from the variable list next to every value: KI in Pa√m; σ in Pa; a in m; Y dimensionless. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For Y=1.12, σ=100 MPa and a=2 mm, KI≈8.9 MPa√m. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The geometry factor and crack-length convention must match a validated solution; compare with toughness only within LEFM validity limits.

The background states this starting condition: This geometry relation belongs to linear-elastic fracture mechanics; Y is not universal and a must match the selected. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The geometry factor and crack-length convention must match a validated solution; compare with toughness only within LEFM validity limits.