Constraint estimation schemes for semi-elliptical surface cracks under tensile and bending loads
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Date
2017-08-01
Authors
Rizman Hariz Abdul Latiff
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Abstract
A three-dimensional constraint estimation scheme was examined for surface cracked plates with semi-elliptical surface cracks under tensile and bending loads. Detailed finite element models were developed to elucidate the crack tip constraint along the crack front of a semi-elliptical surface crack. The finite element models were characterized with a non-hardening elastic-perfectly plastic material with a hardening exponent of 𝑛=∞. Crack tip constraint along the semi-elliptical crack front was found to be significantly affected by the type of loading applied to the surface cracked plat.
Under bending loads, T-stress varied between positive values near the deepest point of the semi-elliptical crack front and negative values near the free surface. A reduction of the relative crack depth, 𝑎/𝑡 caused the T-stress along the crack front to become negative. T-stress was found to be predominantly negative along the semi-elliptical crack front under tensile loads, while being largely unaffected by 𝑎/𝑡. Crack tip constraint along the semi-elliptical crack front was investigated by comparing the crack tip asymptotic stress fields to the Prandtl field solutions for plane strain conditions and Sham & Hancock’s crack tip solutions for plane stress conditions. Crack tip constraint loss along the crack front was shown to be significantly affected by the T-stresses developed along the crack front, which was driven by the loading type. At the free surface, the crack tip fields did not achieve the full plane stress state as a result of the corner singularity field effects. A constraint estimation scheme for the stresses ahead of the crack tip, at 𝜃=0, was proposed for 𝜎𝜃𝜃 and 𝜎𝑚 along the semi-elliptical surface cracks under bending and tensile loads.
The constraint estimation scheme for 𝜎𝜃𝜃 and 𝜎𝑚 ahead of the crack tip was developed via application of the 𝐽-Δ𝜎 approach to semi-elliptical surface cracks. The 𝐽-Δ𝜎 approach was found to be able to estimate the in-plane and out-of-plane crack tip constraint loss along the semi-elliptical crack front by characterising the 𝜎𝜃𝜃 and 𝜎𝑚 against a dimensionless 𝐽/𝑧𝜎𝑜 parameter.