TY - JOUR

T1 - The mode III full-field solution in elastic materials with strain gradient effects

AU - Zhang, L.

AU - Huang, Y.

AU - Chen, J. Y.

AU - Hwang, K. C.

N1 - Funding Information:
Y.H. and K.C.H. appreciate helpful discussions with Drs. J.W. Hutchinson, C.F. Shih, and W. Yang. Y.H. acknowledges the support from the US National Science Foundation (Grant #INT-94-23964 and #CMS-96-10491). L.Z. and K.C.H. acknowledge the support from China National Natural Science Foundation and China State Commission of Education.

PY - 1998

Y1 - 1998

N2 - The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r-3/2 singularity near the crack tip, and are significantly larger than the classical KIII field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical KIII field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical KIII field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.

AB - The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r-3/2 singularity near the crack tip, and are significantly larger than the classical KIII field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical KIII field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical KIII field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.

KW - Full-field solution

KW - Strain gradient effects

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U2 - 10.1023/A:1007552621307

DO - 10.1023/A:1007552621307

M3 - Article

AN - SCOPUS:0009107948

VL - 92

SP - 325

EP - 348

JO - International Journal of Fracture

JF - International Journal of Fracture

SN - 0376-9429

IS - 4

ER -