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Research Papers

Crack Growth Resistance in Metallic Alloys: The Role of Isotropic Versus Kinematic Hardening

[+] Author and Article Information
Emilio Martínez-Pañeda

Department of Engineering,
Cambridge University,
Cambridge CB2 1PZ, UK
e-mail: mail@empaneda.com

Norman A. Fleck

Department of Engineering,
Cambridge University,
Cambridge CB2 1PZ, UK

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 19, 2018; final manuscript received June 24, 2018; published online July 17, 2018. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 85(11), 111002 (Jul 17, 2018) (6 pages) Paper No: JAM-18-1299; doi: 10.1115/1.4040696 History: Received May 19, 2018; Revised June 24, 2018

The sensitivity of crack growth resistance to the choice of isotropic or kinematic hardening is investigated. Monotonic mode I crack advance under small scale yielding conditions is modeled via a cohesive zone formulation endowed with a traction–separation law. R-curves are computed for materials that exhibit linear or power law hardening. Kinematic hardening leads to an enhanced crack growth resistance relative to isotropic hardening. Moreover, kinematic hardening requires greater crack extension to achieve the steady-state. These differences are traced to the nonproportional loading of material elements near the crack tip as the crack advances. The sensitivity of the R-curve to the cohesive zone properties and to the level of material strain hardening is explored for both isotropic and kinematic hardening.

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References

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Figures

Grahic Jump Location
Fig. 1

Uniaxial stress strain response for (a) cyclic loading ofa nonlinear hardening solid with N = 0.2 and (b) half-cycle forlinear and nonlinear hardening. Material properties: σ0/E = 0.003.

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Fig. 2

Schematic representation of the cohesive zone model for fracture

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Fig. 3

Cohesive traction T–separation δ law characterizing the fracture process

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Fig. 4

Finite element mesh and configuration of the boundary layer

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Fig. 5

Crack growth resistance curves for linear isotropic and kinematic hardening plasticity and different hardening levels. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, ν = 0.3, and σ̂=3.5σ0.

Grahic Jump Location
Fig. 6

Crack growth resistance curves for power law isotropic and kinematic hardening plasticity and different levels of the cohesive strength. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, ν = 0.3, and N = 0.1.

Grahic Jump Location
Fig. 7

Steady-state toughness as a function of the cohesive strength for isotropic and kinematic hardening at different N levels. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, and ν = 0.3.

Grahic Jump Location
Fig. 8

Crack extension at steady-state as a function of the cohesive strength for isotropic and kinematic hardening at different N levels. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, and ν = 0.3.

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Fig. 9

Log–log representation of the relation between thecrack extension at steady-state and the steady-state fracture toughness for isotropic and kinematic hardening at different N levels. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, and ν = 0.3.

Grahic Jump Location
Fig. 10

Schematic insight into the effect of isotropic or kinematic hardening on a material point ahead of the initial crack (r = 2R0); (a) active plastic zone and evolution path, and (b) stress state on the π-plane. Material properties: δ1/δc = 0.15, δ2/δc = 0.5, σ0/E = 0.003, ν = 0.3, σ̂/σY = 3.7, and N = 0.1.

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