The phrase "as a function of the crack" is correct and usable in written English.
It can be used in contexts related to mathematics, engineering, or materials science, where a variable or outcome is dependent on the characteristics of a crack.
Example: "The stress distribution in the material changes as a function of the crack length."
Alternatives: "in relation to the crack" or "depending on the crack".
It is well known that in analyses of plain concrete members using smeared crack models, the constitutive behaviour of cracked concrete has to be defined as a function of the crack bandwidth so that the results are not significantly affected by the adopted mesh discretization.
Measured velocities in Sample AJG02 were compared with velocities calculated as a function of the crack density parameter.
The procedure yields the fracture toughness of the composite as a function of the crack length.
The first corrective term of the outer expansion can be straightforwardly expressed as a function of the crack length.
The crack opening width is established as a function of the crack tip opening displacement and the residual flexural strength of SFRC beams.
For thin cracks, the effective elastic constants are formulated as a function of the crack density parameter (O'Connell and Budiansky 1974).
The crack number density (hereafter referred to as crack density) for each diagonal component of α ij is expressed as a function of the initial crack density at a reference stress state, ( varepsilon_{i}^{0} ), and the average initial crack aspect ratio, ( a_{i}^{0} ), at this reference stress state.
Figure 5A plots the failure strain as a function of the relative crack size, for a wide range of values of χ.
An analytical model was developed to predict the surface crack growth and the resulting interface crack driving force as a function of the pre-crack morphology.
The second surrogate model is trained using planar crack growth simulation to calculate the stress intensity factor as a function of crack size, crack orientation, and load magnitude for use in planar crack growth analysis.
The J-integrals were obtained for both left and right crack tips and the phase angles were evaluated as a function of the distance to the crack tip.
