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Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding
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1988
Year
EngineeringMultiscale MechanicsMechanical EngineeringCrack TipFracture ModelingStructural MaterialsMechanics ModelingElasticity (Physics)MechanicsStressstrain AnalysisDeformation ModelingMaterials ScienceStrain LocalizationMechanical BehaviorElastic-plastic AnalysisSolid MechanicsMaterial MechanicsPlasticityFull-field Numerical SolutionsMechanical PropertiesPart I—small ScaleApplied PhysicsNumerical MethodCrack FormationDynamic Crack PropagationMechanics Of MaterialsFracture MechanicsBimaterial Interfaces
The study concerns cracks at elastic‑plastic interfaces, with σ0 as the reference yield stress and L as the crack length. The article presents results for loading that induces only small‑scale yielding at the crack tip, with subsequent work to address fully plastic behavior. The authors solve interface crack problems numerically using a small‑strain J2‑deformation theory with power‑.
Full-field numerical solutions for a crack which lies along the interface of an elastic-plastic medium and a rigid substrate are presented. The solutions are obtained using a small strain version of the J2-deformation theory with power-law strain hardening. In the present article, results for loading causing only small scale yielding at the crack tip are described; in subsequent articles the mathematical structure of the crack-tip fields under small scale yielding and results for contained yielding and fully plastic behavior will be presented. We find that although the near-tip fields do not appear to have a separable singular form, of the HRR-type fields as in homogeneous media, they do, however, bear interesting similarities to certain mixed-mode HRR fields. Under small scale yielding, where the remote elastic fields are specified by a complex stress-concentration vector Q = |Q|eiφ with φ being the phase angle between the two in-plane stress modes, we find that the plastic fields are members of a family parameterized by a new phase angle ξ, ≡ φ + εln(QQ/σ02L), and the fields nearly scale with the well-defined energy release rate as evaluated by the J-integral. Here σ0 is the reference yield stress and L is the total crack length (or a relevant length of the crack geometry). Numerical procedures appropriate for solving a general class of interface crack problems are also presented. A description of a numerical method for extracting the mixed mode stress intensities for cracks at interfaces and in homogeneous isotropic or anisotropic media, is included.