International Journal of Plasticity最新文献

Coherent twin boundaries (CTBs) are internal planar defects that offer a promising pathway for designing advanced metallic materials with superior strength-ductility synergy. However, incorporating nanoscale CTBs into additive manufacturing (AM) microstructures is highly challenging without severe plastic deformation. Here, by utilizing the intrinsic cellular structures in AM alloys, we for the first time achieved a high density of multi-scale annealing twins in a laser powder bed fusion (LPBF) Ni₃₅Co₃₅Cr₂₅Ti₃Al₂ medium-entropy alloy. These multi-scale annealing twins, together with nanoprecipitates and dislocations, resulted in gigapascal strength (∼1.4 GPa) and substantial tensile ductility (∼25 %). We reveal that the AM-induced cellular structures, decorated with entangled dislocations and Ti segregation at the cellular boundaries, facilitate the abundant nucleation of multi-scale annealing twins through interactions with migrating recrystallization boundaries. Additionally, the cellular precipitation networks enhance the thermal stability of nanoscale annealing twins. Frequent dislocation-TB interactions during deformation contribute to superior strain hardenability and thus good ductility. Synergized multiple strengthening mechanisms, i.e., boundary strengthening, precipitation strengthening, and dislocation strengthening, are responsible for the excellent strength. Our present findings advance the design of AM microstructures by harnessing the beneficial effects of cellular structures and provide valuable guidance for developing alloys with exceptional mechanical properties.

This study primarily aims to develop a robust modeling approach to capture the complex material behavior of CP-Ti, appeared by high anisotropy, differential hardening due to anisotropy evolution, and flow behavior sensitive to strain rate and temperature, using artificial neural networks (ANNs). Plasticity is characterized by uniaxial tension and in-plane biaxial tension tests at temperatures of 0 °C and 20 °C with strain rates of 0.001 /s and 0.01 /s, and the results are used to calibrate the non-quadratic anisotropic Yld2000–3d yield function with respect to the plastic work. In order to predict the intricate plastic deformation with the temperature and strain rate effects, two distinct ANN models are developed; one to capture the strain hardening behavior and the other to predict the anisotropic parameters in the chosen yield function. The developed ANN models predict an unseen dataset well, which is intermediate testing conditions at a temperature of 10 °C and strain rate of 0.005 /s. The ANN models, being computationally stable and adhering to conventional constitutive equations, are implemented into a user material subroutine for the ductile fracture characterization of CP-Ti sheet using the hybrid experimental-numerical analysis. The favorable agreement between experimental data and numerical predictions, particularly using the ANN models with evolving anisotropic material parameters for the Yld2000–3d yield function, underscores the significance of the differential hardening effect on the ductile fracture behavior and highlights the capabilities of ANN models to capture the complex plastic behavior of CP-Ti. The key parameters including stress triaxiality, Lode angle parameter, and equivalent plastic strain at the fracture location are extracted from the simulations, enabling the calibration of ductile fracture models, namely Johnson-Cook, Hosford-Coulomb, and Lou-2014, and construction of fracture envelopes.

This paper combines energy decomposition and an extended gradient damage (EGD) model to develop an anisotropic fracture framework with decoupling of tensile and shear cohesive laws. By introducing the shear-normal decomposition in the energy form, the driving force of the damage variable is established within the framework of the EGD model, which is then capable of capturing the traction-separation of potential crack surfaces in both shear and normal directions. The intrinsic correspondence between the cohesive law and the damage evolution enables the accurate prediction of anisotropic fracture behavior in the mixed form of Mode I and Mode II. Furthermore, the proposed model also addresses the damage unloading issue, which still remains a challenge in classic phase field theory or non-local damage theory. A number of numerical examples are presented as validation. Some cutting-edge benchmarks, such as complex mixed-mode fracture and perfect shear fracture, are well reproduced.

The stability and durability of rocks in cold regions are significantly impacted by the degradation of mechanical properties caused by freeze–thaw (F–T) environment. In this work, we shall propose a rational multiscale nonlinear constitutive model based on thermodynamics, micromechanics, and fractional calculus theory to describe the complete deformation and failure process of F–T rocks under triaxial compression. The F–T rocks at the mesoscale are regarded as consisting of porous matrix and cracks, while porous matrix is composed of the micropores and elastic solid grains at the microscale. According to experimental observations, we assume the F–T action mainly causes micropores growth and cracks opening, and mechanical damage is resulted from the initiation and propagation of cracks. In this context, the effects of F–T and mechanical damage on effective elastic properties of rocks can be quantitatively analyzed by using the two-step Mori–Tanaka (M-T) homogenization method. After subtly deriving the total free energy function of F–T rocks under compression, we systematically develop specific criteria for describing open cracks closure deformation, mechanical damage evolution and frictional sliding induced plastic distortion. Note that to correctly capture the plastic deformation characteristics, the non-orthogonal flow rule based on fractional differential calculations is employed. Following that, analytical analyses and numerical implementation of the proposed model are conducted. The performance of the model is evaluated by the simulations with experimental data on two kinds of F–T rocks, and discussions on parameters sensitivity and effects of fractional order are followed.

A comprehensive investigation was conducted on the stress-strain responses and microstructural evolutions of 9Cr3Co3WCu martensitic steel at 650 ℃ subjected to low cycle fatigue tests, strain-controlled creep-fatigue tests (SNCFTs), and hybrid stress-strain-controlled creep-fatigue tests (HSSCFTs). The creep strain accumulation per cycle in HSSCFTs exhibited three stages: an initial decrease in the early cycles, followed by a prolonged period of steady increase, culminating in a rapid increase prior to fracture. In contrast, the creep strain accumulation in SNCFTs showed a consistent decreasing trend throughout the test. Through the employment of advanced characterization techniques, the evolution of dislocation density exhibited a decreasing rate in all cases, and a fracture morphology characterized by a large size of creep voids was observed in HSSCFTs. Consequently, a dislocation-based viscoplastic constitutive model was developed, incorporating a relaxation parameter, a slip deformation resistance model and a dislocation density evolution model interacting with the grain boundary. The proposed model demonstrated excellent congruences under fatigue, creep, creep-fatigue, and multi-step creep- fatigue tests between experimental and simulated results, thereby confirming its capability to comprehensively capture cyclic deformation under various loading modes.

In this study, the mechanical behavior and deformation mechanism of an extruded Mg–1.2 wt.%Y rod under tension and compression along the extrusion direction (ED) were systematically investigated through experiments and crystal plasticity simulations. A double-peak strain hardening behavior comprising five distinct stages was observed under compression along the ED. The five stages are as follows: a fast drop in the strain hardening rate (stage I), steady increase in the strain hardening rate (stage II), gradual decrease in the hardening rate (stage III), second increase in the strain hardening rate (stage IV), and rapid decrease in the strain hardening rate (stage V). This unique strain hardening behavior led to an ultimate compressive strength of up to 539 MPa at a high strain of 0.4. Crystal plastic simulations using an elastic viscoplastic self-consistent model revealed a high activity and a long process of {10$\overline{1}$2} twinning in a strain range of 0–0.35 under compression along the ED. The twinning behavior examined via electron backscattering diffraction indicated that the {10$\overline{1}$2} twinning was activated in both grains with relatively high and very low Schmid factors. Subsequently, the mechanism for the presence of this double-peak strain hardening was established and, finally, the significance of this double-peak strain hardening for strengthening Mg alloys was discussed.

The geometric and distributive properties of voids significantly influence anisotropic coalescence behaviour. However, this problem has received little attention owing to the complexity of considering all the properties in the current analytical framework of limit analysis. To address this issue, this study proposes an analytical framework based on an elliptic coordinate system, including the determination of the ligament zone, characterization of plastic flow, and derivation of the void coalescence criterion, for porous materials with various geometric and distributive properties, including size, shape, spacing, and orientation. This framework is motivated by our observations that the evolution of the void geometry and surrounding plastic flow can be well characterized by the grid of the elliptic coordinate system. Subsequently, an analytical function is proposed to determine the ligament zone and coalescence direction with various void properties. A hollow nonaxisymmetric cylindrical unit cell is proposed to describe this ligament zone, and the corresponding trial velocity field is derived by extending the previous Gurson-like velocity field into the elliptic cylindrical coordinate system. The rationality of the field is validated by comparing its equivalent strain rate field with numerical simulations. Finally, a coalescence criterion is derived via the limit analysis of the proposed unit cell undergoing internal necking. Two heuristic adjustments are formulated for the overflow phenomenon in the rigid zone and outer ligament zones. Numerical assessments with various void properties confirm the accuracy of the analytical model. The coalescence criterion can predict the independent and coupling effects of geometric and distributive properties on anisotropic void coalescence. This study provides possible solutions to future plasticity problems of ellipsoidal inclusions.

The yield strength of nanocrystalline metals is an emphasis for designing and fabricating more reliable and cost-effective devices for application in aircraft and renewable energy systems. Grain size is a major influence factor affecting the variation of yield strength. Both Hall-Petch strengthening and inverse Hall-Petch softening, which focus on the variation of grain size, have always been the main areas of interest. Determining the critical grain size between Hall-Petch strengthening and inverse Hall-Petch softening is a challenge. In this study, a yield criterion for nanocrystalline metals is proposed by considering the dominant mechanism of plasticity yielding, which encompasses both Hall-Petch strengthening and inverse Hall-Petch softening. Subsequently, a new theoretical model for the grain size effect on yield strength is established based on the proposed criterion, which considers the grain size effect on Young's modulus, grain interior energy, and grain boundary energy. Further, taking the grain boundary migration into account to modify the established inverse Hall-Petch model. The established model accurately captures the quantitative relationships between elastic deformation energy and the dominant yielding mechanism, leading to the precise determination of the yield strength of three exemplary metals (bcc, fcc, hcp) across a wide range of grain sizes. In addition, the critical grain size between Hall-Petch strengthening and inverse Hall-Petch softening can be effectively predicted by the established model. By incorporating more detailed considerations and introducing a reference point to effectively capture experimental errors, this work achieves higher prediction accuracy compared to other existing theoretical models. In light of the established model, the analysis of influencing factors is conducted, indicating that the effect of grain boundary migration energy is greater than that of grain boundary energy. This work contributes to a deeper understanding of the plastic deformation mechanism of nanocrystalline metals and provides a new avenue and theoretical guidance for designing more high-strength systems.

The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite of the long term research and many material models proposed in literature, accurate modeling and prediction of this complex phenomenon still remain a challenging task.

In this work, we present a novel approach using deep symbolic regression (DSR) to generate material models describing the Mullins effect in the context of nearly incompressible hyperelastic materials. The two step framework first identifies a strain energy function describing the primary loading. Subsequently, a damage function characterizing the softening behavior under cyclic loading is identified. The efficiency of the proposed approach is demonstrated through benchmark tests using the generalized the Mooney–Rivlin and the Ogden–Roxburgh model. The generalizability and robustness of the presented framework are thoroughly studied. In addition, the proposed methodology is extensively validated on a temperature-dependent data set, which demonstrates its versatile and reliable performance.

Multilayered structures of dissimilar titanium alloys can achieve excellent fracture ductility and strength, while their fatigue characteristics especially dislocation networks and twin formation are rarely reported. Heterogeneous microstructures are observed in the multilayered TC4/TB8 alloys, including fine acicular α grains, continuous α layer at prior β grain boundaries (α_GB) and β matrix on the TB8 layer, together with equiaxed α grains on the TC4 layer. High-cycle fatigue (HCF) and low-cycle fatigue (LCF) tests show that the initial fatigue damage appears at the α_GB/β matrix interfaces on the TB8 layer instead of the boned TC4/TB8 interfaces. Since the stress concentration induced by dislocation pile-up is prone to micro-void formation and crack propagation at the α_GB/β interfaces. For LCF, the α_GB/β interfaces can not only act as impenetrable barriers and sources of lattice dislocations, but also allow the dislocations cross boundaries during cyclic tension and compression because of the high boundary energy. The formation characteristic of deformation twins that is beneficial for the plastic deformation of α grains in TC4 layer during cyclic strain is investigated. Furthermore, the hexagonal dislocation networks are also found within the equiaxed α grains of TC4 layer after LCF, and the role between interface barrier and slip direction in the formation mechanism is analyzed.