Conventional Mechanism-based Strain Gradient Plasticity Research Articles

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.

Mixed mode crack paths in terms of plastic stress intensity factors based on conventional and strain gradient plasticity

The effect of an initial mode II loading on subsequent mixed-mode crack path was investigated through experiments and computations for 34X and P2M steels, 7050 aluminum, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. An optical microscope and the drop potential method were used to determine the actual position of the crack tip on the curvilinear crack path monitoring and continuous measurements of the crack size were made along the path in the CTS specimen. In accordance with these experimental observations, the main feature of the initial mode II fracture is the crack growth on a curvilinear path. For subsequent mixed-mode crack propagation, the crack front continuously changes the shape and direction with each loading cycle. For a mode II loaded initial crack, the scenario becomes more complex because of the change in the propagation direction when a kinked crack is formed. The experimental data on crack growth for all tested materials are represented in terms of the elastic and new plastic stress intensity factors (SIFs). To this end, both the classical and the conventional mechanism-based strain-gradient plasticity (CMSGP) theories were employed. The material constitutive equation is implemented in a finite element code and the elastic and plastic fracture resistance parameters are calculated as a function of the position along the curvilinear crack path in all tested CTS specimens produced from 34X and P2M steels, 7050 aluminum and Ti-6Al-4V alloys. As a result of the finite element calculations, nonlinear amplitude factor solutions are determined across a wide range of material work hardening conditions, and the role of the Taylor’s intrinsic material length and both the coupled effect of these parameters are established. The potential of fundamental and practical applications of introduced fracture resistance parameters are discussed.

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.

Three-Dimensional Elastoplastic Contact Analysis of Rough Surface Considering a Micro-Scale Effect

Abstract The micro-surface asperity scale of grinding metal parts is within several microns. When two grinding surfaces are in contact, the unevenness of the plastic deformation of the asperities at the micro-scale leads to greater plastic hardening strength of the material. The results of the nano-indentation experiment conducted in this paper confirmed this phenomenon. Based on conventional mechanism-based strain gradient (CMSG) plasticity theory, the micro-scale plastic constitutive equation of materials is given and then is verified by the nano-indentation experiment. Finite element software abaqus and the user-defined element (UEL) subroutine are used to build three-dimensional rough surface elastoplastic contact models. By calculating the grinding rough surface contact in the macro-scale constitutive model based on J2 theory and in the CMSG plasticity constitutive model, the influence law of plastic micro-scale effect on contact performance is obtained.

Effect of crack curvature radius on the stress fields under nonlinear deformation

The influence of crack curvature radius and plastic properties of material on the crack tip fields is evaluated by conventional mechanism-based strain gradient (CMSG) plasticity theory, and classical plasticity theory. Stress fields in single edge tension specimen are investigated numerically for a wide range of the crack curvature radius variations. The strain hardening exponent varied from N=0.075 to N=0.4. The local areas of the influence of the crack tip curvature radius are established for the strain gradient plasticity and classical plasticity. The couple effects of material length scale parameter and plastic properties of material on crack tip fields are established for strain gradient plasticity. The boundaries of CMSG plasticity dominated zone are determined.

Strain-gradient effect on the crack tip dislocations density

In this study, the influence of a material’s plastic properties on the crack tip fields and dislocation density behavior is analytically and numerically analyzed using the conventional mechanism-based strain-gradient plasticity (CMSGP) theory established using the Taylor model. The material constitutive equation is implemented in a commercial finite element code by a user subroutine, and the crack tip fields are evaluated with novel parameters in the form of the intrinsic material length, characterizing the scale over which gradient effects become significant. As a consequence of the strain-gradient contribution, FE results show a significant increase in the magnitude of the stress fields of CMSGP when the material length parameter is considered. It is found that the density of geometrically necessary dislocations (GND) is large around the crack tip, but it rapidly decreases away from the crack tip. On the contrary, the density of statistically stored dislocations (SSD) is not as large as geometrically necessary dislocations around the crack tip, but it decreases much slower than GND away from the crack tip. A couple effect of material work hardening and the crack tip distance is identified.

Establishment of damage estimation rules for brittle fracture after cyclic plastic prestrain in steel

The microprocess of brittle fracture in steel is suggested to occur because microcracks appearing in the brittle layer at the grain boundary propagate driven by increased piled-up dislocation. Thus, loading plastic deformation, equivalent to the increase in dislocation, is directly connected to the increase in brittle fracture risk. Because of these mechanisms, prestraining means approaching the limits of the material, which could lead to deterioration of fracture toughness. For a lifetime evaluation of steel structure, it is important to generalize the effect of various cyclic prestrains.In this paper, material toughness changes when tensile and compression prestrain occur were investigated. A general three-point bending test was employed to evaluate fracture. Synthetic analysis using Conventional Mechanism-based Strain Gradient Plasticity (CMSGP) theory, in which dislocation density is used to determine the amount of material damage, was carried out as well as employing conventional macroscopic material damage consideration rules. The consistency of the simulation and the experimental results were supported by the Electron Back Scattered Diffraction Pattern (EBSD) observation. Additionally, critical stress was calculated, and the change in critical stress for prestrain conditions was investigated. Then, the mechanism of critical stress changes could be expressed by the yield point increase and dislocation density.

A new model for permanent flexural deflection of cantilever MEMS actuator by conventional mechanism-based strain gradient plasticity framework

In two past decades, there are so many works representing to elastic behaviors of cantilever MEMS actuators in the micro and nanoscales for various loading conditions and geometries. However, there are little efforts available for the permanent plastic behavior of the MEMS structures and actuators. In addition, the most size—dependent plasticity considerations based on gradient models have been limited to primary concepts on material modeling or microstructural evolution as compared with structural analyses. In this paper, a conventional mechanism-based strain gradient (CMSG) plasticity theory is applied to investigate permanent behavior of the cantilever micro-beam actuators, by determining the effect of length scale on flexural displacement. If the beam is scaled to micron size, mechanical behavior follows from material dimension or length scale. While the model consisted of a multiple plastic work hardening, its kinematics is established on the Euler–Bernoulli hypothesis. The deflection of cantilever MEMS actuator is determined for different cases of the loading and length scales, compared with other relevant theoretical and experimental observations. Also, the effect of the elastic medium of the environmental foundation is considered for the actuator, dedicatedly.

Size-dependent plastic buckling behavior of micro-beam structures by using conventional mechanism-based strain gradient plasticity

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

Strain gradient plasticity analysis of elasto-plastic contact between rough surfaces

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J2 isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J2 isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J2 isotropic plasticity analysis, furthermore, bounded by the two.

Effect of Strain-gradient Plasticity in Engineering Fracture Assessments

This study implements the conventional mechanism-based strain gradient plasticity (CMSG) in the engineering fracture assessment of structural steels, to estimate both the near-tip opening displacements and the probability of brittle fracture. The CMSG theory recognizes the dependence of the material hardening on both the strain and its gradient, for plastic deformations occurring at micron or sub-micron levels, through a material length scale. The CMSG presents a more realistic description of the stress, strain and displacement field in the immediate vicinity of the crack tip, than does the classical plasticity. This study therefore examines the near-tip opening displacement, commonly used in the assessment for ductile fracture in structural steels. This study also integrates the CMSG theory in calculating the microscopic crack driving force in a cleavage fracture assessment framework, namely the Weibull stress approach. The accuracy of the scalar Weibull stress relies significantly on the gradient- dependent, near-tip stress field, which subsequently impinges on the failure probability estimated using the Weibull stresses.

The correlation between the internal material length scale and the microstructure in nanoindentation experiments and simulations using the conventional mechanism-based strain gradient plasticity theory

In the present work a new equation to determine the internal material length scale for strain gradient plasticity theories from two independent experiments (uniaxial and nanoindentation tests) is introduced. The applicability of the presented equation is verified for conventional grained as well as for ultrafine-grained copper and brass with different amounts of prestraining. A significant decrease of the experimentally determined internal material length scale is found for increasing dislocation densities due to prestraining. Conventional mechanism strain gradient plasticity theory is used for simulating the indentation response, using experimentally determined material input data as the yield stress, the work-hardening behavior and the internal material length scale. The work-hardening behavior and the yield stress were taken from the uniaxial experiments, whereas the internal material length scale was calculated using the yield stress from the uniaxial experiment, the macroscopic hardness H0 and the length scale parameter h* following from the nanoindentation experiment. A good agreement between the measured and calculated load–displacement curve and the hardness is found independent of the material and the microstructure.

The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.

Finite element modelling for materials with size effect

This paper involves the formulation of the C0 finite elements incorporating the conventional mechanism-based strain gradient plasticity theory. Higher-order variables and consequently higher-order continuity conditions are not required allowing the direct applications of conventional plasticity algorithms in the existing finite element package. Implementation of the model whether analytically or computationally is efficient and straightforward as the strain gradient effect is confined in the material constitutive relation. The accuracy of the proposed elements in simulating the response of materials with strong size effect is verified through several numerical examples. The approach is applicable and valid to any materials with non-uniform plastic deformation larger than about 100 nm onwards. The proposed model becomes imperative when the deformation is less than 10 µm as classical plasticity is unable to describe the phenomenon comprehensively at this low level of deformation.

Numerical simulation of indentation with size effect

Indentation size effect (ISE), whereby the strength of materials is observed to increase significantly with decreasing indentation depths has been reported in several experimental studies. In the present study, a series of nanoindentation experiments with maximum indentation depths varying from 400 to 3400 nm are carefully designed and implemented to study the indentation size effect on copper and Al7075. 3-D finite element analyses incorporating the conventional mechanism-based strain gradient (CMSG) plasticity theory which requires only C 0 solid elements are performed to simulate the indentation size effect. In order to circumvent the ambiguity associated with various methods to evaluate indentation hardness, the indentation size effect is investigated at the more fundamental level by considering changes to the load–displacement curve. The finite element results incorporating the CMSG plasticity theory are found to be in good agreement with experimental results at all levels of indentation depth conducted in the present study.