Cleavage, dislocation emission, and shielding for cracks under general loading

The enhancement of toughness at low temperatures in fine grained low carbon steel was studied, basing on a shielding theory due to dislocations and grain boundaries. Fully annealed low carbon steel was subjected to an accumulative roll bonding (ARB) process for grain refining. The grain size perpendicular to the normal direction was found to be approximately 200 nm after the ARB process. The fracture toughness of low carbon steel ARB applied was measured at 77 K by four-point bending, comparing with the fracture toughness of those without the ARB process. It was found that the value of fracture toughness at 77 K was increased by grain refining due to the ARB, indicating that the ARB process enhances toughness at low temperatures as reported in interstitial free steel and phosphorus doped interstitial free steel. It also deduces that the brittle-ductile transition (BDT) temperature shifted to a lower temperature. The enhancement of toughness and the decrease of the BDT temperature due to grain refining cannot be explained completely by the dislocation pile-up model of dislocations at grain boundaries. Quasi-two-dimensional simulations of dislocation dynamics, taking into account of crack tip shielding due to dislocations, were performed to investigate the effect of a dislocation source spacing along a crack front on the BDT. The simulation indicated that the BDT temperature is decreased by decreasing the dislocation source spacing. In addition to the simulation, the authors suggest a new concept of accommodating stress intensity at the crack tip due to grain boundaries to explain the enhancement of toughness and the decrease of the BDT temperature in fine grained materials.

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“…23,24) The crack extension force in the plane strain condition under a simple mode I stress field is given by: …”

Section: Resultsmentioning

confidence: 99%

Fracture Toughness Enhanced by Grain Boundary Shielding in Submicron-Grained Low Carbon Steel

2008

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“…0Ao OAr (19) be satisfied. The resulting functions A, B, C, obtained so as to require r to vanish as A 0--" 0% are…”

Section: Form Of a Combined Tension-shear Constitutive Lawmentioning

confidence: 95%

“…(13). The latter condition requires that the Maxwell reciprocal relation (17), (18), (19)and (20) as (22) % and this reduces to a potential introduced by Needleman [29] when p = q.…”

Section: Form Of a Combined Tension-shear Constitutive Lawmentioning

confidence: 99%

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Sun

Beltz

Rice

1993

Materials Science and Engineering: A

140

108

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The normal stress distribution across a slip plane has the effect of reducing the critical loading required for dislocation emission from a crack tip. The reduction by normal stresses was found to be very significant for Si, based on properties estimated for it using density functional theory, to be large for Fe as modeled by the embedded atom method (EAM), and to be smaller in AI, Ni and ordered Ni3A1, estimated using the EAM. The general dependence over a wide range on parameters characterizing the tension-shear coupling was also determined. In the context of a Peierls model for dislocation nucleation at a crack tip (J. R. Rice, J. Mech. Phys. Solids, 40 (1992) 239), our approach was to search for onset of the dislocation nucleation instability based on the numerical solution of the system of non-linear integral equations describing an incipient dislocation. The incipient dislocation consists of a distribution of sliding and opening displacements along a slip plane emanating from the crack tip; these displacements are related to the shear and tensile stresses across the slip plane by constitutive relations based on the atomic models mentioned. Results from the atomic models are used to parametrize constitutive relations involving a Frenkel sinusoidal dependence of shear stress on sliding displacement at any fixed opening displacement, and a Rose-Ferrante-Smith universal binding form of dependence of tensile stress on opening displacement at any fixed shear displacement. These relations then enter the system of integral equations, solved numerically, which describe the elasticity solution for a non-uniform distribution of sliding and opening along the slip plane. The results show that tension-shear coupling will often significantly reduce the loading for dislocation emission from the value estimated on the basis of an unstable stacking energy Yu~ determined with neglect of such coupling, in a shear-only type analysis. For the EAM models of the metals considered, a simple and approximate method to account for the tension effects is to use a modified quantity yo iu*~, which is an unstable stacking energy for lattice planes which are constrained to a fixed opening A0*, corresponding to that for vanishing normal stress at the unstable shear equilibrium position. Moreover, it is found that the normal stress effect can be described well in these cases by replacing the unstable stacking energy 7u~ in the shear-only model by a tension softened ~' u~(q~), which depends on the phase angle ~p of the combined tension-shear loading along the slip plane according to the stress intensity factors of the elastic singular solution. The same simple procedures for accounting for tension effects on nucleation are less suitable for lattices with strong coupling such as Si.

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“…17,18) The concept of stress accommodation is termed as 'dislocation shielding', which has been independently suggested by Thomson and Weertman. 19,20) It was experimentally confirmed by transmission election microscopy and photoelasticity in silicon single crystals.…”

Section: Introductionmentioning

confidence: 99%

Brittle-Ductile Transition in Low Carbon Steel Deformed by the Accumulative Roll Bonding Process

et al. 2009

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Brittle-ductile transition (BDT) behaviour was investigated in low carbon steel deformed by an accumulative roll-bonding (ARB) process. The temperature dependence of its fracture toughness was measured by conducting four-point bending tests at various temperatures and strain rates. The fracture toughness increased while the BDT temperature decreased in the specimens deformed by the ARB process. Arrhenius plots between the BDT temperatures and the strain rates indicated that the activation energy for the BDT did not change due to the deformation with the ARB process. It was deduced that the decrease in the BDT temperature by grain refining was not due to the increase in the dislocation mobility controlled by short-range obstacles. Molecular dynamics simulations revealed that moving dislocations were impinged against grain boundaries, creating a shielding field, and were reemitted from there with increasing strain. Grain refining led to an increase in the fracture toughness at low temperatures and a decrease in the BDT temperature. In the present paper, the roles of grain boundaries have been discussed in order to explain the enhancement in the fracture toughness of fine-grained materials at low temperatures, and the decrease in the BDT temperature.

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Cleavage, dislocation emission, and shielding for cracks under general loading

Cited by 438 publications

References 22 publications

Fracture Toughness Enhanced by Grain Boundary Shielding in Submicron-Grained Low Carbon Steel

Fracture Toughness Enhanced by Grain Boundary Shielding in Submicron-Grained Low Carbon Steel

Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip

Brittle-Ductile Transition in Low Carbon Steel Deformed by the Accumulative Roll Bonding Process

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