Mechanism-based Strain Gradient Research Articles

Lower-order mechanism-based strain gradient plastic model considering stress gradient effect

Lower-order mechanism-based strain gradient plastic model considering stress gradient effect

Effect of grain boundary on scratch behavior of polycrystalline copper

The anisotropy in the elastoplastic response of crystalline solids influences substantially their scratch resistance at the microscale. While grain boundaries typically act as obstacles to the motion of dislocations at the grain level, the scratch behavior in the vicinity of the grain boundary is influenced by other factors such as crystallographic orientation and pile-up topography. We performed a systematic set of nano-scratch simulations using the mechanism-based strain gradient crystal plasticity to study the evolution of scratch force and depth near grain boundaries. To validate our model, we conducted a nano-scratch test on a polycrystalline copper sample and compared the scratch depth profile for a specific grain boundary with the simulated result, where a good qualitative agreement was achieved. Our simulations showed that the scratch depth, force, and hardness vary between the corresponding values for the individual constitutive grains, and the variation decreases by reducing the grain size. Additionally, we analyzed the scratch response in terms of the pile-up topography and subsurface stresses and distinguished different regimes when the indenter approaches and scratches across the boundary. Our findings offer a new direction to optimize the scratch resistance of polycrystalline metals by tailoring the size and orientation of grains near the surface. Additionally, it introduces scratching as a robust material characterization method.

Effect of stress/strain partition on the mechanical behavior of heterostructured laminates: A strain gradient plasticity modeling

Based on the structure of natural nacres, laminated metal materials have been successfully developed to possess desirable mechanical properties for diverse engineering applications. These heterostructured (HS) laminates consist of layers with different mechanical performances, resulting in asynchronous deformation and intricate stress/strain partitioning behavior. These distinctive phenomena are crucial in achieving the strength-ductility synergy of HS laminates. Nonetheless, further investigations are imperative to gain a comprehensive understanding of local stress and strain evolutions during deformation, and to thoroughly explore the influence of stress/strain partition on the mechanical behavior of the HS laminates. This study utilized the conventional mechanism-based strain gradient (CMSG) plasticity theory to conduct finite element simulations. The tensile deformation of HS laminate comprising nanostructured (NS) bronze and coarse-grained (CG) copper layers was simulated as a benchmark. The simulation results revealed the following: (1) Stress partition and stress transfer between the layers occur during deformation and are influenced by the layer thickness; (2) Both strain partition and strain banding exist in the HS laminates with relatively thinner layers, and the formation of dispersed strain bands is related to the plastic strain gradient; (3) Heterogeneous deformation promotes strain delocalization and strain hardening, consequently leading to improved uniform elongation. This study provides valuable insights into the significant effect of stress/strain partition on the strength-ductility synergy of HS laminates from the perspective of constitutive modeling.

The coupling effects of strain gradient and damage on Mode I crack tip stress fields

The cleavage fracture of metallic materials is determined by the crack tip stress field depending on plastic strain gradient and microstructural damage. The synergistic effects of strain gradient and damage on the stress fields near a Mode I crack tip in metallic materials are investigated using a modified conventional theory of mechanism-based strain gradient plasticity (CMSG). Besides preserving the essence of classical CMSG, a stress-dependent damage variable is introduced to characterize the effect of microstructural damage on the material's intrinsic length, elastic modulus and plastic yielding criterion. Based on the present theoretical model, it is found that the strain gradient and microstructural damage effects both are prominent in a small region near the Mode I crack tip, at which the damage evolution is determined by the strain gradient. Although the crack tip stress field with strain gradient and damage effects is lower than the existing ones influenced only by strain gradient, it is still significantly higher compared with the yielding strength of the material so that the cleavage fracture at the crack tip can be well explained. The damage-induced stress level reduction indicates that the stress concentration at the crack tip can be alleviated to inhibit the crack propagation. As a result, when the damage effect is considered, not only a larger external load is required to induce crack propagation but also the plastic region in front of the crack tip is enlarged, consequently leading to increases of fracture strength and energy dissipation in the material. The present research provides a more precise prediction of the crack tip stress distribution in metallic materials, which is helpful for better understanding the microscopic mechanism of the cleavage fracture phenomenon.

Deciphering phase stress partition and its correlation to mechanical anisotropy of laser powder bed fusion AlSi10Mg

Laser powder bed fusion AlSi10Mg exhibits severe mechanical anisotropy, which hinders its applications in industrial field. In the present work, we investigated the mechanisms of anisotropy in the light of phase stress partition, using traditional crystal plasticity and mechanism-based strain gradient crystal plasticity models. Two representative volume elements of the Al-Si cellular structures, corresponding to 35 ℃ and 200 ℃ build platform temperatures, were built to assess the influences of Al matrix strength and strain gradient on phase stress partition and anisotropy. In addition, the maximum principal stress distribution of the Si-rich network was probed, based on which the potential damage sites and densities were evaluated. The results show that the anisotropic strength and damage both originate from the elongated Si-rich network. According to the comparison between the 35 ℃ and 200 ℃ materials, an increase in Al phase strength can change the phase stress partition and effectively mitigate the anisotropy degree. Moreover, it is revealed that the strain gradient tends to alleviate anisotropy and delay damage evolution. The findings of this work can pave the way to developing high-performance LPBF Al alloys with lower degrees of anisotropy.

On the size effect in scratch and wear response of single crystalline copper

Indentation hardness is a well-known material parameter for determining the resistance of a material to deformation. It is however known that indentation hardness alone cannot fully characterize anisotropic material strength in particular for single crystalline materials. Recently, it is shown that scratch hardness is a more suitable material property to characterize the wear response of crystalline materials. In this study, we use the mechanism-based strain gradient crystal plasticity to explore the size effect in the scratch behavior of single crystalline copper. Our simulations picture strong size effects in the scratch hardness value and pile-up magnitude. Interestingly, it shows that the degree and nature of size-dependency for these two parameters varies significantly and oppositely by the scratch direction. For instance, while [001] direction shows the highest degree of size effect in scratch hardness, it presents the lowest pile-up size effect. This opposite effect is explained in terms of the contribution of different slip systems to dislocation resistance and work hardening. We also show that scratch hardness, which takes into account both the size effect and crystallographic direction dependence, is an appropriate material property for wear characterization.

Structural modeling and mechanical research of carbon nanotube reinforced aluminum matrix composites using strain gradient theory

Carbon nanotube (CNT)-reinforced aluminum alloys (Al) are considered to be the ideal metal-matrix composites owing to their high strength and elastic moduli. However, they have low ductility. In addition, the inhomogeneity of the structure makes a strong strain gradient during deformation. In this research, a series of simulations under uniaxial tension and shear loading paths were conducted to investigate the mechanical properties of CNT/Al6061 composite. The novel multiple mechanism-based strain gradient models (MMSG) were proposed to study and analyze the correlation between microstructure evolution and macro mechanical responses. The interfacial bonding, grain size, and dislocation density were mainly considered during the simulation. The results of this study can be used to reveal the synergetic strength and ductility of all the structural microstructure, which also affects the strain partition and failure of different phases in CNT/Al6061 composites.

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

The particle/matrix interface of metal matrix composites (MMCs) can give rise to extra strength and then affect the local deformation behavior. This strengthening effect originates from the plastic strain gradients due to the incompatibility of plastic deformation between the particle and matrix. However, only limited researches utilized the strain gradient plasticity to study the damage evolution and fracture behavior, in which only one or two of the damage mechanisms (i.e., matrix damage, interface debonding, and particle fracture) was considered. In this work, all of these damage mechanisms were coupled into the finite element model under conventional theory of mechanism-based strain-gradient (CMSG) plasticity. Besides, a new numerical algorithm of geometrically necessary dislocations (GNDs) was proposed for a multi-scale model, and then this model was used to analyze the damage evolution and failure behavior of SiCp/AZ91 composite. The results show that the strengthening effects of plastic strain gradients can describe interface debonding, break the monotonicity of the effective plastic strain with the effective stress at the local area close to the particle/matrix interface, and give a more reasonable distribution of stress and plastic strain compared to the classical J2 flow theory. If the probability distribution of the interfacial strength is considered, the CMSG model has the potential capacity to capture the crack initiation in the matrix. When using the continuum damage mechanics approach to describe the fracture process based on the multi-scale model, the weakening exponent value should be considered.

An Improved Mechanism-Based Strain Gradient Plasticity Model and Its Application to Size Effect Under Complex Loading

The ingredient devices tend to be designed and fabricated with microscale, high accuracy, and complex geometry and are subjected to complex loading. Many experiments have proved that the size effect plays a significant role in designing and manufacturing an engineering component. This size effect is largely attributed to the grain size and the strain gradient. While the grain size effect was omitted in conventional strain gradient theories, an extended model that considers both effects of grain size and strain gradient has been proposed in the current work (denoted as GMSG). The proposed GMSG model has been implemented into the finite element method (denoted as GMSG-FEM) to investigate the size effect of copper wires under complex working conditions. The simulation results show that the hollow structure can improve the bearing capacity of the micro-wires under torsion. Among micro-wires with different cross-sections, the bearing capacity of the micro-wire with a circular section is the largest, followed by those with square and triangle sections. Complex loading also has an important influence on stress distribution. Based on the current study, it can be envisaged that the GMSG-FEM could be a useful tool in engineering applications where the size effect has to be considered.

RETRACTED: Contact analysis between rough surfaces considering the size-affected deformation behaviour of multi-scale asperities

Contact parameters such as the real contact area of rough surfaces depend on the interaction between asperities and the characteristic scale in which they remain. The high-stress deformation mechanism of the local contact spots exhibits size-dependent behaviour when the size of the asperities reaches a certain scale because of the scale effect. This causes deviations in the contact analysis, which can affect several tribological properties of the structural interface such as interface stiffness, fretting wear, and contact resistance. In this study, the deformation process affected by the scale effect is analysed using a finite element method that employs a conventional mechanism-based strain gradient plasticity (CMSGP) constitutive theory, whereas a full-scale elastoplastic contact model is developed for asperities at different size levels. Next, the contact analysis of rough surfaces is performed using the multi-scale contact theory proposed by Jackson and Streator (JS) considering this individual asperity model. The proposed model is validated using comparison with the refined finite element simulation analysis of rough surface contact that employs the CMSGP theory; further, the effect of morphology features on contact behaviour is discussed. The research results are conducive to the tribological design of small-size engineering interfaces.

Cohesive zone modelling of hydrogen assisted fatigue crack growth: The role of trapping

We investigate the influence of microstructural traps in hydrogen-assisted fatigue crack growth. To this end, a new formulation combining multi-trap stress-assisted diffusion, mechanism-based strain gradient plasticity and a hydrogen- and fatigue-dependent cohesive zone model is presented and numerically implemented. The results show that the ratio of loading frequency to effective diffusivity governs fatigue crack growth behaviour. Increasing the density of beneficial traps, not involved in the fracture process, results in lower fatigue crack growth rates. The combinations of loading frequency and carbide trap densities that minimise embrittlement susceptibility are identified, providing the foundation for a rational design of hydrogen-resistant alloys.

Inversion of dislocation densities under mixed mode fracture

Mixed-mode crack growth is here investigated through experiments and computations for 34X and P2M steels, 7050 aluminium, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. In this study, we use the mechanism-based strain gradient (MSG) plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on local stress distributions. The constitutive relations are based on Taylor’s dislocation model, which allows to gain insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIFs) are evaluated as a function of the intrinsic material length. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress–strain state are determined. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. Dislocation densities, stress fields and nonlinear SIF solutions are determined for experimental curvilinear crack paths by taking into account the transition from the initial Mode II crack to the mixed-mode fracture.

Experimental and numerical investigations of micro-meso damage evolution for a WC/Co-type tool material

Commercial Co/WC/diamond composites with 90vol.% Co also belong to hard metals and, as a kind of tool materials, are very useful. Their deformation behavior can be both ductile and quasi-brittle, determined by the diamond portion and local morphology. Another characteristic is that submicron-sized WC particles, possessing non-negligible strengthening influence due to the size effect, cannot be fully present in a representative microstructure. This work emphasizes the local damage evolutions’ dependence on microstructural features. Rice&Tracey damage and cohesive zone model describe the ductile and quasi-brittle damage behavior. The mechanism-based strain gradient plasticity takes the size effect of submicron-sized WC particles into consideration. Both real and artificial microstructures are used. Besides homogeneous boundary conditions (BCs), the periodic BCs are also applied in a 2D damage simulation. This work proves that FE models with two phases, the homogenized Co-WC matrix and diamond particles, can correctly predict damage evolution. FE results show that the WC phase has a higher mean stress value than the diamond phase, which is proved by the nano-indentation test. From FE simulation results, local hot spots appear in the matrix closed to sharp diamond corners/edges and crossing regions of shear bands. The experimental and numerical results are compared on micro and macro scales. For the local strain distribution and the damage development, numerical predictions match the reality well, even in morphological details. Furthermore, since the published data about WC-Co type tool materials with Co>50vol.% are rare, the obtained knowledge in this work also contributes to the data collection.

Understanding the effects of annealing temperature on the mechanical properties of layers in FAI-rich perovskite solar cells

This paper uses a combination of experiments and theory to study the effects of annealing temperature on the mechanical properties of hybrid organic–inorganic perovskites (HOIPs). We examined the mechanical (hardness and Young’s modulus), microstructural, and surface topography properties of the HOIP film at different annealing temperatures ranging from 80 to 170 °C. A mechanism-based strain gradient (MSG) theory is used to explain indentation size effects in films at different annealing temperatures. Intrinsic film yield strengths and hardness values (deduced from the MSG theory) are then shown to exhibit a Hall–Petch dependence on the inverse square root of the average grain size. The implications of the results are then discussed for the design of mechanically robust perovskite solar cells.

Couple analysis of DIC and FEM to quantify strain fields and crack-flank displacements in structural materials under cyclic mixed-mode I/II fracture

Mixed mode cyclic fracture under multiaxial stress-strain state is critical for the generation of appropriate damage tolerance methodologies. To this end the elaborated approach is dedicated to full range of mixed mode loading for elastic-plastic plane problem. In this study, the digital image correlation (DIC) experimental results are represented as contours as well as radial strain distributions in the local system of coordinate centered at the current crack tip position along curvilinear crack path. As a complement to the DIC measurement, finite element (FE) modelling of the displacement and strain fields around the crack tip in the compact tension shear (CTS) specimen was performed in order to reproduce experimental mixed mode loading conditions. In this study, for comparison aim we used the conventional mechanism-based strain gradient (CMSG) and classical Hutchinson–Rice–Rosengren (HRR) plasticity theories to evaluate the coupled effect of the material plastic properties and the mode mixity on the crack tip behaviour. The new material model is implemented in a commercial finite element software package ANSYS 2021R1 using a user subroutine. The intention with this work was to complement the DIC measurements as well as acquire more detailed information about the local strain ahead of the crack tip and the crack opening. From a sensitivity analysis it has been established that the DIC value depends significantly from the location along the crack direction of the pair of points selected before and behind the crack tip. As a result of the FE calculations of strain distributions, the effects of both the fracture mode and the material properties are determined.

Crack root radius effect on stress fields under nonlinear

The influence of crack root radius and plastic material properties on the crack tip fields was evaluated by strain gradient plasticity theory, and classical plasticity theory. A conventional mechanism-based strain gradient (CMSG) plasticity theory was used in the study. The stress fields in single edge tension specimen are investigated numerically for a wide range of the crack tip radius variations. Five values of the crack tip curvature radius ρ = 0 (mathematical notch); ρ = 25 nm, ρ = 30 nm, ρ = 60 nm and ρ = 100 nm were investigated. The strain hardening exponent varied from N = 0.075 to N = 0.4. A stress analysis by CMSG plasticity was performed for two values of the Taylor’s length parameter l = 1μm and l = 10μm. The boundaries of the local areas, where the influence of the crack tip radius is realized were determined for both HRR and CMSG plasticity. The sizes of the dominance area of the strain gradient plasticity were established and their approximation equations were presented. The influence of the plastic properties and the Taylor’s length scale parameter on the stress fields in the vicinity of rhe crack tip was estimated for the strain gradient plasticity.

Study on damage evolution beneath spherical indenter through experiments and mechanism-based strain gradient crystal plastic simulations

Damage evolution of AA7075-T6 rolling plate with 2 mm thickness under highly compressive stress state, which is generated by spherical indentation, is studied through experiments and simulations. On the cross section of spherical deformation region, micro voids induced by crush of MgZn2 particles are observed by scanning electron microscopy (SEM) and some special characteristics are revealed including ductile tearing of the brittle particle, huddling between neighboring voids and an in-void crack, but no clue of void closure under such heavy compression. Through Electron Back-Scattered Diffraction (EBSD), strain gradient around void was found quite high (70 mm−1) and much higher than the theoretical strain gradient induced by spherical indentation (1.8 mm−1), which will result in a significant hardening effect and preventing the further shrink and closure of micro void. More insights are provided through mechanism-based strain gradient crystal plastic simulations which couples a polycrystalline, full-scale model, and a single crystal submodel. Simulation results verify the elevated strain gradient around microvoid and find strain gradient varies dramatically along the small range of void edge, which is validated by nanoindentation test around the edge of voids. Microvoid evolution controlled by strain gradient shows strong anisotropy on different cross sections. For the void at position D focused in present paper, its area on section perpendicular to Y axis (SecY) increases at the early stage of indentation, despite the compressive stress state. Influence of the orientations of adjacent grains is also studied. Void areas on SecZ and SecY are found more sensitive to the change of orientation of adjacent grain, however, the volume variation show much less sensitivity.

2021 Timoshenko Medal Acceptance Speech

2021 Timoshenko Medal Acceptance Speech

Mode I and mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity

In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress–strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor’s dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress–strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.

A mechanism-based gradient damage model for metallic fracture

A new gradient-based formulation for predicting fracture in elastic–plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material deformation is characterised by a mechanism-based strain gradient constitutive model. This non-local plastic-damage formulation is numerically implemented and used to simulate fracture in several paradigmatic boundary value problems. The case studies aim at shedding light into the role of the plastic and fracture length scales. It is found that the role of plastic strain gradients is twofold. When dealing with sharp defects like cracks, plastic strain gradients elevate local stresses and facilitate fracture. However, in the presence of non-sharp defects failure is driven by the localisation of plastic flow, which is delayed due to the additional work hardening introduced by plastic strain gradients.