Effects of anisotropic hardening on crack propagation in porous-ductile materials

Radi, Enrico; Bigoni, Davide

doi:10.1016/0022-5096(96)00037-3

Cited by 7 publications

(10 citation statements)

References 41 publications

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“…Equations (12)(13)(14) can be substituted into (9) and (10) to obtain, together with (8), a system of six PDEs for the six unknowns functions O'3r , o"30 , v3, O~3r , Ol30, and ae. The PDEs system can be reduced to a system of ODEs when a solution is sought of the separable variable form T~, To, w, At, Ao, T~ and the field singularity s become the unknowns of the problem (the present asymptotic problem is homogeneous and thus the amplitude factor B remains undetermined).…”

Section: Field Equationsmentioning

confidence: 99%

“…The deformation, stress, and back stress rates, (12)(13)(14) may be written in terms of fields (31), and these expressions can be substituted into the constitutive equation (36) and (37). Therefore, at first order, (36) gives …”

Section: Pure Kinematic Hardening Limitmentioning

confidence: 99%

“…Despite the importance of employing an anisotropic hardening law to model the Bauschinger effect, which is commonly exhibited by ductile metals and alloys, the only available asymptotic solution for crack propagation in a material characterized by the J2-flow theory with mixed isotropic/kinematic hardening is due to Zhang et al [14], who analyzed mode I propagation. These results can be obtained as a particular case of a porous elastoplastic solid analyzed by the authors in [13], to which the interested reader is referred. However, an asymptotic solution for mode III is still lacking; this is obtained in the present paper.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of linear isotropic hardening, Ponte Castafieda [8] was successful in generalizing the asymptotic analysis of Amazigo and Hutchinson [9] by including plastic reloading on crack flanks. Inspired by his solving technique, the authors have obtained solutions for fracture propagation in materials characterized by pressure-sensitive yielding with isotropic hardening [10][11][12] and, quite recently, with anisotropic hardening [13]. Despite the importance of employing an anisotropic hardening law to model the Bauschinger effect, which is commonly exhibited by ductile metals and alloys, the only available asymptotic solution for crack propagation in a material characterized by the J2-flow theory with mixed isotropic/kinematic hardening is due to Zhang et al [14], who analyzed mode I propagation.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic solution for mode III crack growth in J 2-elastoplasticity with mixed isotropic-kinematic strain hardening

Bigoni

Radi

1996

Int J Fract

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Mode III fracture propagation is analyzed in a J2-flow theory elastoplastic material characterized by a mixed isotropic/kinematic law of hardening. The asymptotic stress, back stress and velocity fields are determined under small-strain, steady-state, fracture propagation conditions. The increase in the hardening anisotropy is shown to be connected with a decrease in the thickness of the elastic sector in the crack wake and with an increase of the strength of the singularity. A second order analytical solution for the crack fields is finally proposed for the limiting case of pure kinematic hardening. It is shown that the singular terms of this solution correspond to fully plastic fields (without any elastic unloading sector), which formally are identical to the leading order terms of a crack steadily propagating in an elastic medium with shear modulus equal to the plastic tangent modulus in shear.

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Section: Field Equationsmentioning

confidence: 99%

Section: Pure Kinematic Hardening Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic solution for mode III crack growth in J 2-elastoplasticity with mixed isotropic-kinematic strain hardening

Bigoni

Radi

1996

Int J Fract

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“…Here X(), W(), and Z() are functions of . Now we substitute Equation 41into (40) and compare the coefficients of the most singular terms with 1=r ln jR=rj. Then we obtain the governing equation for X() as…”

Section: Centered Fan Sectormentioning

confidence: 99%

Untitled

Chang

Kim

Pan

1997

International Journal of Fracture

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Quasi-statically growing crack-tip fields in elastic perfectly plastic pressure-sensitive materials under plane strain conditions are investigated in this paper. The materials are assumed to follow the Drucker-Prager yield criterion and the normality flow rule. The asymptotic mode I crack-tip fields are assumed to follow the five-sector assembly of Drugan et al. (1982) for Mises materials. The crack-tip sectors, in turns, from the front of the crack tip are a constant stress sector, a centered fan sector, a non-singular plastic sector, an elastic sector and finally a trailing non-singular plastic sector bordering the crack face. The results of the asymptotic analysis show that as the pressure sensitivity increases, the plastic deformation shifts to the front of the tip, the angular span of the elastic unloading sector increases, and the angular span of the trailing non-singular plastic sector bordering the crack surface decreases. As the pressure sensitivity increases to about 0:6, the angular span of the trailing non-singular plastic sector almost vanishes. The effects of the border conditions between the centered fan sector and the first non-singular plastic sector on the solutions of the crack-tip fields for both Mises and pressure-sensitive materials are investigated in details.

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Effect of porosity and tension–compression asymmetry on the Bauschinger effect in porous sintered steels

Deng

Piotrowski

Williams

et al. 2005

International Journal of Fatigue

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Effects of anisotropic hardening on crack propagation in porous-ductile materials

Cited by 7 publications

References 41 publications

Asymptotic solution for mode III crack growth in J 2-elastoplasticity with mixed isotropic-kinematic strain hardening

Asymptotic solution for mode III crack growth in J 2-elastoplasticity with mixed isotropic-kinematic strain hardening

Untitled

Effect of porosity and tension–compression asymmetry on the Bauschinger effect in porous sintered steels

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