Elastoplastic crack analysis for pressure-sensitive dilatant materials ? Part I: Higher-order solutions and two-parameter characterization

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The problem of a plane strain crack lying along an interface between a rigid substrate and an elasticplastic material has been studied. The elastic-plastic material exhibits pressure-sensitive yielding and plastic volumetric deformation. Two-term expansions of the asymptotic solutions for both closed frictionless and open crack-tip models have been obtained. The Mises effective stress in the interfacial crack-tip fields is a decreasing function of the pressure-sensitivity in both open and closed-crack tip models. The variable-separable solution exists for most pressure-sensitive materials and the limit values for existence of the variable-separable solution vary with the strain-hardening exponents. The governing equations become singular as the pressure-sensitivity limit is approached. Strength of the leading stress singularity is equal 1/(n + 1) for both crack-tip models, regardless of the pressure-sensitivity. The second-order fields have been solved as an additional eigenvalue problem and the elasticity terms do not enter the second-order solutions as n/> 2. The second exponents for the closed crack model are negative for the weak strain hardening, whereas the negative second-order eigenvalue in the open crack model slightly grows with the pressure-sensitivity. The second-order solutions are of significance in characterising the crack-tip fields. The leading-order solution contains the dominant mode I components for both open and closed crack-tip models when the materials do not have substantial strain hardening. The second-order solutions are generally mode-mixed and depend significantly on the pressure-sensitivity.

Section: C~ \ 2a~mentioning

confidence: 99%

Section: C~ \ 2a~mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Elastoplastic crack analysis for pressure-sensitive dilatant materials-Part II: Interface cracks

Yuan

1995

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“…Achenbach, Kanninen and Popelar [4], Ponte Castaneda [5], Ponte Castarleda and Mataga [6], t3stlund and Gudmundson [7] and Yuan, Yuan and Schwalbe [8,9] generalized those investigations for a dynamic crack propagation including the plastic reloading region on the crack surfaces for a mixed mode loading situation. Studies concerning pressure-sensitive materials using the HRR-field theory were performed by Li and Pan [10], Li [11] and Yuan and Lin [12]. Bigoni and Radi [13,14] advanced the before mentioned investigation [7-9] for pressure-sensitive materials.…”

mentioning

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Asymptotic crack tip fields for pressure-sensitive materials and dynamic crack growth under plane stress conditions

Herrmann

Potthast

1996

For the mathematical description of the yield behaviour of elastic-plastic materials the von Mises yield criterion proves to be suitable for the interpretation of the stress and strain curves of metals. However, many materials exhibit a pressure-sensitive yielding. These material properties are not adopted in the von Mises yield criterion. Hence a generalization of the yield criterion is necessary to examine pressure-sensitive materials. In this contribution, a generalization of the von Mises yield criterion is used to investigate the crack tip fields of pressure-sensitive materials like porous metals and certain polymers [1,2]. This extension, which includes a share of the hydrostatic stresses, leads to the so-called Drucker-Prager yield criterion. The factor ~ in this yield criterion is the measure of the pressure-sensitivity and describes the strength of the influence of the hydrostatic stresses on the yield process.A first asymptotic analysis of stress and displacement fields for dynamic crack problems in elastic-plastic solids was performed by Amazigo and Hutchinson [3] by assuming the validity of the J2-flow theory. Achenbach, Kanninen and Popelar [4], Ponte Castaneda [5], Ponte Castarleda and Mataga [6], t3stlund and Gudmundson [7] and Yuan, Yuan and Schwalbe [8,9] generalized those investigations for a dynamic crack propagation including the plastic reloading region on the crack surfaces for a mixed mode loading situation. Studies concerning pressure-sensitive materials using the HRR-field theory were performed by Li and Pan [10], Li [11] and Yuan and Lin [12]. Bigoni and Radi [13,14] advanced the before mentioned investigation [7-9] for pressure-sensitive materials. However, that analysis was restricted to quasistatic crack extension as well as mode I loading.In this paper, the asymptotic stress and velocity crack tip fields for fast running cracks in an elastic-plastic, pressure-sensitive material are determined. The behavior of the singularity exponent s of the stress-singularity was examined for different pressure-sensitivity parameters kt, crack-tip velocities v and hardening coefficients a. The hardening coefficient t~ describes the relation between the shear and the tangent shear modulus. The assumption of homogeneous, isotropic material behaviour showing linear hardening was used. Further, the incremental theory was applied and stationary crack growth under plane stress conditions has been adopted.

Analysis of elastoplastic sharp notches

Yuan

Lin

1994

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In this paper the elastoplastic solutions with higher-order terms for apex V-notches in power-law hardening materials have been discussed. Two-term expansions of the plane strain and the plane stress solutions have been obtained. It has been shown that the leading-order singularity approaches the value for a crack when the notch angle is not too large. In plane strain cases the elasticity does not enter the second-order solutions when the notch opening angle is too small. For a large notch angle, the two-term expansions of the plane strain near-tip fields are described by a single amplitude parameter. The plane stress solutions generally contain the elasticity terms. The boundary layer formulations based on the small-strain plasticity theory confirm that a dominance zone exists ahead of the notch tip. Finite element results give good agreement to the asymptotic solutions under both plane strain and plane stress conditions. The second-order terms cannot improve the predictions significantly. The near-tip fields are dominated by a single parameter. Finite element calculations under the finite strain J2-flow plasticity theory revealed that the finite strains can only affect local characterization of the asymptotic solution.The asymptotic solution has a large dominance zone around the notch tip. For an apex notch bounded to a rigid substrate the leading-order singularity falls with the notch angle significantly more slowly than in the homogeneous material. It vanishes at the notch angle about 135 ° for all power-hardening exponents. The elasticity effects enter the second-order solutions when the notch angle becomes large enough. The tip fields are characterized by the hydrostatic stress and the shear stress ahead of the notch.