Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a ...wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.
This work reviews and critically discusses the current understanding of two scaling laws, which are ubiquitous in the modeling of monotonic plastic deformation in face-centered cubic metals. A ...compilation of the available data allows extending the domain of application of these scaling laws to cyclic deformation. The strengthening relation tells that the flow stress is proportional to the square root of the average dislocation density, whereas the similitude relation assumes that the flow stress is inversely proportional to the characteristic wavelength of dislocation patterns. The strengthening relation arises from short-range reactions of non-coplanar segments and applies all through the first three stages of the monotonic stress vs. strain curves. The value of the proportionality coefficient is calculated and simulated in good agreement with the bulk of experimental measurements published since the beginning of the 1960s. The physical origin of what is called similitude is not understood and the related coefficient is not predictable. Its value is determined from a review of the experimental literature. The generalization of these scaling laws to cyclic deformation is carried out on the base of a large collection of experimental results on single and polycrystals of various materials and on different microstructures. Surprisingly, for persistent slip bands (PSBs), both the strengthening and similitude coefficients appear to be more than two times smaller than the corresponding monotonic values, whereas their ratio is the same as in monotonic deformation. The similitude relation is also checked in cell structures and in labyrinth structures. Under low cyclic stresses, the strengthening coefficient is found even lower than in PSBs. A tentative explanation is proposed for the differences observed between cyclic and monotonic deformation. Finally, the influence of cross-slip on the temperature dependence of the saturation stress of PSBs is discussed in some detail. This works takes into account current discussions on the microstructural aspects of cyclic deformation and highlights further work that is required for fully understanding the physical origin of the two scaling laws.
A few issues related to the modeling of size effects in terms of geometrically necessary dislocations (GNDs) are critically discussed, viz. strain hardening, length scale dependence, types of GND ...arrays. Consequences are drawn regarding the continuum modeling of size effects in plasticity.
The first part of a dislocation-based constitutive formulation for strain hardening in face-centered cubic crystals is presented. This multiscale approach is based on the storage–recovery framework ...expanded at the scale of slip systems. A parameter-free formulation is established for the critical stress and the storage rate, taking advantage of recent results yielded by dislocation dynamics simulations. The storage rate of dislocations in the presence of forest obstacles is modeled for the first time at the level of dislocation intersections and reactions. The mean free path per slip system is found to be inversely proportional to the critical stress. It also depends on the number of active slip systems, which leads to an orientation dependence of stage II strain hardening in agreement with experimental data. The total storage rate is obtained by including three additional contributions, notably that of the self-interaction, which leads to a model for stage I hardening.
The mechanisms of dislocation intersection and strain hardening in fcc crystals are examined with emphasis on the process of junction formation and destruction. Large-scale 3D simulations of ...dislocation dynamics were performed yielding access for the first time to statistically averaged quantities. These simulations provide a parameter-free estimate of the dislocation microstructure strength and of its scaling law. It is shown that forest hardening is dominated by short-range elastic processes and is insensitive to the detail of the dislocation core structure.
The present work emphasises the potentialities of dislocation dynamics simulations for performing analyses of crystal plasticity and obtaining information that cannot be reached by experiment. As an ...example, a study is presented of parameters that are critical for modeling strain hardening in face-centred cubic crystals, the mesoscopic coefficients of interaction between non-coplanar slip systems.
Simulations of dislocation dynamics in single crystals of hcp zirconium are presented with emphasis on the hardening associated with prismatic slip at low temperature. Two original aspects of the ...simulation method are discussed, the treatment of the hcp lattice by an orthorhombic representation and the use of periodic boundary conditions. The mobility of screw and non-screw segments are defined in a phenomenological manner. Different investigations on the interactions between dislocations gliding in different prismatic planes show that no junction is formed between intersecting screw dislocations, which results in a rather small forest hardening at low temperature. This explains experimental observations of an initial deformation stage with a low strain hardening coefficient in zirconium or titanium crystals at low temperature.
We connected dislocation-based atomic-scale and continuum models of plasticity in crystalline solids through numerical simulations of dislocation intersections in face-centered cubic crystals. The ...results contradict the traditional assumption that strain hardening is governed by the formation of sessile junctions between dislocations. The interaction between two dislocations with collinear Burgers vectors gliding in intersecting slip planes was found to be by far the strongest of all reactions. Its properties were investigated and discussed using a multiscale approach.
A model for dynamic strain aging is proposed. It is written as a local constitutive formulation but can easily be extended to account for spatial interactions. The model is obtained by embedding ...accepted ‘slow’ time scale formulations for dislocation dynamics and aging kinetics in a multiple time scales dynamic system. Dislocation and solute dynamics are coupled at the ‘fast’ time scale pertaining to dynamic aging. Features of jerky flow described by standard models such as the negative strain rate sensitivity of the flow stress and critical strains for the occurrence of the Portevin-Le Chatelier effect are retrieved. In addition, negative strain rate sensitivity of the threshold stress for instability is predicted.
The orientation dependence of dynamic recovery in face-centered cubic crystals is investigated in relation to the critical annihilation distance of screw dislocations. The critical conditions for the ...onset of stage III are discussed in terms of a cross-slip mechanism that is locally modified by the interaction with a neighboring attractive screw dislocation. Two orientation domains are defined. From
1
¯
1
1
to the central region of the standard stereographic triangle, the attractive interaction stress enforces obtuse cross-slip, which inhibits dynamic recovery. The critical parameters for dynamic recovery are then derived using simple scaling laws. For other orientations, the interaction stress enhances cross-slip, which is treated using Escaig’s model. Numerical results are obtained using a single adjustable parameter. They are fully consistent with experimental data in copper and silver at 300
K. The discussion emphasizes the need for more precise information from atomic-scale modeling of the dynamic recovery process.
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