Strain gradient plasticity with nonlinear evolutionary energetic higher order stresses

Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi‐static or dynamic response of shell structures. The mesh refinement indicators are based on equi‐distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the non‐linear explicit finite element code LS‐DYNA. This module provides element‐wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user‐specified tolerance. The FE model of a conventional deep drawing process is used as a numerical model, including both material and geometrical non‐linearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, cup height variation versus circumference angle, effective plastic strain in the deformed sheet and punch force. It is shown that the proposed indicators can identify finite elements which have high gradients of effective stress or effective plastic strain so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.

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 effective threshold for fatigue crack propagation: a plastic size effect?

Indentation size effect: an improved mechanistic model incorporating surface undulation and indenter tip irregularity

Constraint and size effects in confined layer plasticity

Modelling the constitutive behaviour of thin metal sheet using strain gradient theory

In this paper, formulation of elastic-plastic analysis of functionally graded (FG) spherical pressure vessels under internal pressure based on strain gradient plasticity is presented. The material properties are assumed to vary in a power law manner in the radial direction. A linear hardening rule for the material behavior in the plastic region is assumed. After deriving the governing differential equations, a closed form solution is obtained. At the first step, the obtained results were validated against other available results in the literature. Then the effects of changing the inner radius from a few micro-meters to one meter, FG power index and strain gradient coefficient on stress and plastic region size are studied based on classical and strain gradient theories. Also, the effect of internal pressure on the size of plastic region is studied.

Surface treatment processes, such as shot peening, are routinely used by several manufacturing industries (automotive, aerospace, medical, etc.) to impart compressive residual stresses onto the surface of metal components to increase damage tolerance and fatigue life. These compressive stresses are engineered into components to delay initiation of surface cracks and retard crack growth rate thereby improving fatigue life. In addition, the plastic deformation resulting from the shot peening process hardens the material increasing the yield strength and elastic stress range. For elastic material response, accurate fatigue life estimates that include credit for residual stresses are possible for complex geometries with complicated load histories. However, when a shot peened component is subjected to elevated temperatures or cyclic loading, thermal relaxation and cyclic plasticity, respectively, produce inelastic material response from which residual stresses may change continuously. When the material response is inelastic, taking full credit for compressive residual stresses in fatigue models would result in a nonconservative prediction. As a result, designers are reluctant to incorporate any compressive residual stresses into fatigue life predictions of turbine engine components, subject to elevated temperatures and inelastic loading conditions. This paper investigates relaxation of shot peened residual stresses in IN100 when subjected to applied stress profiles that produce large plastic strains and strain gradients in laboratory test samples. Model predictions supported by experiments results are presented to explain that redistribution of residual stress depth profiles are a function of geometry and applied stress/strain profile.

The Hall‐Petch relation in aluminium is discussed based on the strain gradient plasticity framework. The thermodynamically consistent gradient‐enhanced flow rules for bulk and grain boundaries are developed using the concepts of thermal activation energy and dislocation interaction mechanisms. It is assumed that the thermodynamic microstresses for bulk and grain boundaries have dissipative and energetic contributions, and in turn, both dissipative and energetic material length scale parameters are existent. Accordingly, two‐dimensional finite element simulations are performed to analyse characteristics of the Hall–Petch strengthening and the Hall–Petch constants. The proposed flow rules for the grain boundary are validated using the existing experimental data from literatures. An excellent agreement between the numerical results and the experimental measurements is obtained in the Hall–Petch plot. In addition, it is observed that the Hall–Petch constants do not remain unchanged but vary depending on the strain level.

The simulation of machining of soft metals at the 100 microns-few mm length-scale requires capturing complex flow physics induced by the high ductility and polycrystalline aggregate nature of these metals. This work presents a remeshing and mesh-to-mesh transfer approach that can successfully simulate complex flows including highly sinuous flow with surface folding in polycrystalline aggregate cutting. The meshing scheme is both graded and adaptive, with the ability to automatically refine regions such as self-contacts. Notably, the presence of microstructure makes these simulations far more complex than their homogeneous counterparts, with several additional constraints on the remeshing algorithm. The approach is general, with no limitations on rake angle, grain-size, or friction coefficient, and does not use an artificial, predefined separation layer. The scheme accurately tracks individual grains and allows grain splitting in a manner consistent with imaging experiments. The plastic strain field, cutting-force evolution, and deformed grain shape from several annealed-copper cutting simulations are presented, representing a range of rake angles and friction coefficients as high as 0.5. The simulations accurately capture the thick chips, high cutting force, and highly undulating streaklines of flow that characterize sinuous flow, as well as the experimental observation that the sinuous flow is suppressed on using a high rake-angle for the cutting. Moreover, in grains that are split between the chip and residual surface, we can accurately capture the extreme grain stretching that is observed prior to splitting in imaging experiments. Remeshing also provides a way to accurately capture the residual surface plastic strains and strain gradients. The latter are particularly steep, with the strain falling from a value greater than 10 to 2 within a distance of 30 microns. The use of remeshing has numerous advantages over a predefined separation layer, including the fact that one can parametrically explore the effect of variables like the extent of yield stress inhomogeneity on the flow pattern with no limitations. Interestingly, the technique allows us to find the actual line of material separation in such cutting processes: As opposed to a horizontal line, this is typically an undulating curve with a deviation of about 0.06 of the undeformed chip thickness on either side of the horizontal. This fraction increases with the extent of sinuous flow. A simple, pseudograin model with spatial inhomogeneity in flow stress is used to represent the microstructure in the present work, but the present scheme can easily be used with more complex microstructural models as well.

Computational modeling of size-dependent superelasticity of shape memory alloys

Materials containing heterogeneous nanostructures hold great promise for achieving superior mechanical properties. However, the strengthening effect due to plastically inhomogeneous deformation in heterogeneous nanostructures has not been clearly understood. Here, we investigate a prototypical heterogeneous nanostructured material of gradient nanotwinned (GNT) Cu to unravel the origin of its extra strength arising from gradient nanotwin structures relative to uniform nanotwin counterparts. We measure the back and effective stresses of GNT Cu with different nanotwin thickness gradients and compare them with those of homogeneous nanotwinned Cu with different uniform nanotwin thicknesses. We find that the extra strength of GNT Cu is caused predominantly by the extra back stress resulting from nanotwin thickness gradient, while the effective stress is almost independent of the gradient structures. The combined experiment and strain gradient plasticity modeling show that an increasing structural gradient in GNT Cu produces an increasing plastic strain gradient, thereby raising the extra back stress. The plastic strain gradient is accommodated by the accumulation of geometrically necessary dislocations inside an unusual type of heterogeneous dislocation structure in the form of bundles of concentrated dislocations. Such a heterogeneous dislocation structure produces microscale internal stresses leading to the extra back stress in GNT Cu. Altogether, this work establishes a fundamental connection between the gradient structure and extra strength in GNT Cu through the mechanistic linkages of plastic strain gradient, heterogeneous dislocation structure, microscale internal stress, and extra back stress. Broadly, this work exemplifies a general approach to unraveling the strengthening mechanisms in heterogeneous nanostructured materials.

Bauschinger and size effects in thin-film plasticity

In a remarkable series of experiments, Elssner et al. (1994) and Korn et al. (2002) observed cleavage cracking along a bimaterial interface between Nb and sapphire. The stress required for cleavage cracking is around the theoretical strength of the material. Classical plasticity models fall short to reach such a high stress level. We use the conventional theory of mechanism-based strain gradient plasticity (Huang et al., 2004) to investigate the stress field around the tip of an interface crack between Nb and sapphire. The tensile stress at a distance of 0.1 µm to the interface crack tip reaches 13.3σY ,w hereσY is the yield stress of Nb. This stress is nearly 4 times of that predicted by classical plasticity theory (3.6σY ) at the same distance to the crack tip, and is high enough to trigger cleavage cracking in materials and interfaces. This is consistent with Elssner et al.'s (1994) and Korn et al.'s (2002) experimental observations.

Recent experiments have shown that the microscale material behavior is very different from that of bulk materials, and displays strong size effects when the characteristic length associated with the deformation is on the order of microns. Conventional continuum theories, however, can not predict this size dependence because they do not have an intrinsic length in their constitutive models. A new continuum theory, namely the strain gradient theory, has been proposed to investigate the deformation of solids at the microscale. For materials undergoing plastic deformation, the basis of strain gradient theory is the dislocation theory in materials science, and strain gradient plasticity has agreed remarkably well with experiments. For elastic materials with microstructures, it has also been established that the material behavior can be represented by an elastic strain gradient theory. A general approach to investigate fracture of materials with strain gradient effects is established. Both the near-tip asymptotic fields and the elastic full-field solutions are obtained in closed form. Due to stain gradient effects, stresses ahead of a crack tip are significantly higher than those in the classical K field. The plastic zone size surronunding a crack tip is estimated by elastic near-tip fields, as well as by the Dugdale model. It is established that the plastic zone is, in general, much more round and larger than that estimated from the classical K field.