ISSN:
1573-2673
Keywords:
Fracture
;
finite elements
;
viscoplasticity
;
constraint
;
crack growth
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract A finite element analysis is presented for quasi-statically steady crack growth in an elastic-viscoplastic material under Mode I, plane strain and small scale yielding conditions. The effects of material rate-sensitivity on the fields in the vicinity of the moving crack tip are examined. Our analysis employs a modified boundary layer formulation whereby the remote tractions are given by the first two-terms of elastic asymptotic stress field, characterized by K Iand T. When the physical coordinates are scaled by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-Hcaca% WFlbWaaSbaaSqaaGqaaiaa+fdaaeqaaOGaai4laiabeo8aZnaaBaaa% leaacaaIWaaabeaakiaacMcadaahaaWcbeqaaiaaikdaaaaaaa!3ECA!\[(K_1 /\sigma _0 )^2 \], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaacaaIWaaabeaaaaa!3A07!\[\sigma _0 \] is the tensile yield stress, the near-tip fields over a wide range of stress triaxialities are members of a family of self-similar solutions parameterized by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-rfaca% WFVaGaeq4Wdm3aaSbaaSqaaiaa-bdaaeqaaaaa!3B8E!\[T/\sigma _0 \]. Members of this family are found to collapse into a single near-tip distribution when the physical coordinates are normalized by a characteristic length L g, which is a significant fraction of the plastic zone length directly ahead of the crack tip. This distribution depends only on the relative crack speed given by the dimensionless number % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-zfaca% WFVaGaa8hkaiaa-XeadaWgaaWcbaGaa83zaaqabaacciGccuGFiiIZ% gaGaamaaBaaaleaacaaIWaaabeaakiaacMcaaaa!3EB2!\[V/(L_g \dot \in _0 )\] where V is the crack speed and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGGaciqb-HGioB% aacaWaaSbaaSqaaiaaicdaaeqaaaaa!39D6!\[\dot \in _0 \] is the material's viscoplastic strain rate at a reference stress. Near-tip field distributions are obtained for several values of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-zfaca% WFVaGaa8hkaiaa-XeadaWgaaWcbaGaa83zaaqabaacciGccuGFiiIZ% gaGaamaaBaaaleaacaaIWaaabeaakiaacMcaaaa!3EB2!\[V/(L_g \dot \in _0 )\] and material strain rate sensitivity, m. Our results show that strong material rate sensitivity and high crack speed elevate the stress level ahead of the moving crack tip.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00034658
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