scholarly journals Gradient Damage Analysis of a Cylinder Under Torsion: Bifurcation and Size Effects

2021 ◽  
Vol 143 (2) ◽  
pp. 209-237
Author(s):  
Tianyi Li ◽  
Radhi Abdelmoula
Keyword(s):  
Size Effects ◽  
Damage Evolution ◽  
Asymptotic Methods ◽  
Finite Thickness ◽  
Damage Model ◽  
Rayleigh Quotient ◽  
Length Scale ◽  
Internal Length ◽  
Boundary Layer Problem ◽  
Damage Field

AbstractIn this work, an elastic-damage evolution analysis is carried out for a cylinder under torsion made of a material obeying a gradient damage model with softening. Both semi-analytical and asymptotic approaches are developed to analyze the elastic, axisymmetric and bifurcation stages. We show the existence of a fundamental branch where the damage field is asymmetric and localized within a finite thickness from the boundary. By minimizing a generalized Rayleigh quotient, the bifurcation time and modes are obtained as a function of the length scale $\epsilon =\ell /R$ ϵ = ℓ / R involving a material internal length and the cylinder radius. We will then focus on these size effects by assuming that $\epsilon $ ϵ is a small parameter in an asymptotic setting. After justification, specific spatial and temporal rescaled variables are introduced for the boundary layer problem. It is shown that the axisymmetric damage evolution and the bifurcation are governed by two universal functions independent of the length scale. The simulation results obtained by the semi-analytical approach are formally justified by the asymptotic methods.

Intrinsic and Extrinsic Size Effects in Plasticity by Dislocation Glide

2000 ◽  
Vol 653 ◽  
Author(s):  
J. Gil Sevillano
Keyword(s):  
Size Effects ◽  
Mixed Effects ◽  
Length Scale ◽  
Internal Length ◽  
Strain Gradients ◽  
Dislocation Glide ◽  
Spatial Gradients ◽  
Internal Length Scale ◽  
Plastic Process

AbstractA classification of size effects (SE) in plasticity is attempted. ”Intrinsic” SE are perceived when any internal length scale directly influencing some process or property interferes with the size of the material region where the process is going on or when two internal length scales directly affecting the same process or property interfere. ”Extrinsic” SE arise from the external imposition of spatial gradients in the plastic process or by the building up of internal gradients by the (externally induced) process itself. In dislocation-mediated plasticity plastic strain gradients are resolved by the storage of geometrically necessary dislocations (GND) leading to prominent size effects. Of course, mixed effects with intrinsic and extrinsic contributions can be found as well as superposed effects involving more than two characteristic lengths (i.e., size effects on size effects).The inclusion of both types of SE in continuum or crystallographic theories is commented.

scholarly journals Comparison of evolving gradient damage formulations with different activity functions

2021 ◽  
Vol 91 (2) ◽  
pp. 597-627
Author(s):  
Adam Wosatko
Keyword(s):  
Strain Softening ◽  
Damage Zone ◽  
Damage Model ◽  
Length Scale ◽  
Internal Length ◽  
Internal Length Scale ◽  
Damage Theory ◽  
Simulation Results ◽  
The Impact ◽  
Gradient Enhancement

AbstractIn the paper, two existing upgrades of the gradient damage model for the simulations of cracking in concrete are compared. The damage theory is made nonlocal via a gradient enhancement to overcome the mesh dependence of simulation results. The implicit gradient model with an averaging equation, where the internal length parameter is assumed as constant during the strain softening analysis, gives unrealistically broadened damage zones. The gradient enhancement of the scalar damage model can be improved via a function of an internal length scale, so an evolution of the gradient activity is postulated during the localization process. Two different modifications of the averaging equation and respective evolving gradient damage formulations are presented. Different activity functions are tested to see whether the formation of a too wide damage zone still occurs. Activating or localizing character of the gradient influence can be introduced and the impact of both approaches on the numerical results is shown in the paper. The aforementioned variants are implemented and examined using the benchmarks of tension in a bar and bending of a cantilever beam.

A micromechanics-based constitutive model for nanocrystalline shape memory alloys incorporating grain size effects

2021 ◽  
pp. 1045389X2110282
Author(s):  
Xiang Zhu ◽  
Guansuo Dui ◽  
Yicong Zheng
Keyword(s):  
Grain Size ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Size Effects ◽  
Boundary Phase ◽  
Length Scale ◽  
Internal Length ◽  
Length Scales ◽  
Size Dependent ◽  
Grain Size Effects

A micromechanics-based model is developed to capture the grain-size dependent superelasticity of nanocrystalline shape memory alloys (SMAs). Grain-size effects are incorporated in the proposed model through definition of dissipative length scale and energetic length scale parameters. In this paper, nanocrystalline SMAs are considered as two-phase composites consisting of the grain-core phase and the grain-boundary phase. Based on the Gibbs free energy including the spatial gradient of the martensite volume fraction, a new transformation function determining the evolution law for transformation strain is derived. Using micromechanical averaging techniques, the grain-size-dependent superelastic behavior of nanocrystalline SMAs can be described. The internal length scales are calibrated using experimental results from published literature. In addition, model validation is performed by comparing the model predictions with the corresponding experimental data on nanostructured NiTi polycrystalline SMA. Finally, effects of the internal length scales on the critical stresses for forward and reverse transformations, the hysteresis loop area (transformation dissipation energy), and the strain hardening are investigated.

scholarly journals A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Jelena Živković ◽  
Vladimir Dunić ◽  
Vladimir Milovanović ◽  
Ana Pavlović ◽  
Miroslav Živković
Keyword(s):  
Phase Field ◽  
Damage Evolution ◽  
Deformation Gradient ◽  
Damage Model ◽  
Steel Structures ◽  
Plasticity Model ◽  
Metal Plasticity ◽  
Damage And Fracture ◽  
Von Mises ◽  
Von Mises Plasticity

Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the ‘one element’ example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field.

An improved nonlinear damage model of rocks considering initial damage and damage evolution

2020 ◽  
Vol 29 (7) ◽  
pp. 1117-1137 ◽  
Author(s):  
Wenlin Feng ◽  
Chunsheng Qiao ◽  
Shuangjian Niu ◽  
Zhao Yang ◽  
Tan Wang
Keyword(s):  
Damage Evolution ◽  
Least Squares Method ◽  
Damage Model ◽  
Creep Damage ◽  
Secondary Creep ◽  
Nonlinear Creep ◽  
Creep Failure ◽  
Initial Damage ◽  
Nonlinear Damage Model ◽  
Creep Damage Model

The experimental results show that the creep properties of the rocks are affected by the initial damage, and the damage evolution also has a significant impact on the time-dependent properties of the rocks during the creep. However, the effects of the initial damage and the damage evolution are seldom considered in the current study of the rocks' creep models. In this paper, a new nonlinear creep damage model is proposed based on the multistage creep test results of the sandstones with different damage degrees. The new nonlinear creep damage model is improved based on the Nishihara model. The influences of the initial damage and the damage evolution on the components in the Nishihara model are considered. The creep damage model can not only describe the changes in three creep stages, namely, the primary creep, the secondary creep, and the tertiary creep, but also reflect the influence of the initial damage and the damage evolution on creep failure. The nonlinear least squares method is used to determine the parameters in the nonlinear creep damage model. The consistency between the experimental data and the predicted results indicates the applicability of the nonlinear damage model to accurately predict the creep deformation of the rocks with initial damage.

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

2016 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
Amin Zaami ◽  
Ali Shokuhfar
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Strain Gradient ◽  
Stress Concentration Factor ◽  
Size Effects ◽  
Crack Tip ◽  
Length Scale ◽  
State Variables ◽  
Dependent Model ◽  
Homogeneous Strain

In this study, a scale-dependent model is employed to investigate the size effects of copper on the behavior of the crack-tip. This model includes the homogeneous and non-homogeneous strain hardening based on the wavelet interpretation of size effect. Introducing additional micro/nano structural considerations together with decreasing grain size, different size effects can be obtained. As the size dependency is not taken into account in conventional plasticity, an enhanced theory which is related to the strain gradient introduces a length scale will give more realistic representations of state variables near the crack-tip. Accordingly, the contribution of geometrically necessary dislocations (GNDs) activity on strengthening and stress concentration factor is identified in the crack-tip. Finally, the affected zone which is dominated by presence of GNDs is identified

Damage Evolution and Failure Modeling in Unidirectional Graphite/Epoxy Composite

2001 ◽  
Author(s):  
G. P. Tandon ◽  
R. Y. Kim
Keyword(s):  
Damage Evolution ◽  
Failure Modes ◽  
Epoxy Composite ◽  
Damage Model ◽  
Tensile Loading ◽  
Unidirectional Composite ◽  
Concentric Cylinder ◽  
Failure Modeling ◽  
Stress Levels

Abstract A study is conducted to examine and predict the micromechanical failure modes in a unidirectional composite when subjected to tensile loading parallel to the fibers. Experimental observations are made at some selected stress levels to identify the initiation and growth of micro damage during loading. The axisymmetric damage model of a concentric cylinder is then utilized to postulate and analyze some failure scenarios.

Ductile Damage Model Based On Void Growth Analysis for Application to Ductile Crack Growth Simulation

2021 ◽  
Author(s):  
Takehisa Yamada ◽  
Mitsuru Ohata
Keyword(s):  
Crack Growth ◽  
Void Growth ◽  
Damage Evolution ◽  
Damage Model ◽  
Crack Growth Resistance ◽  
Growth Behavior ◽  
Ductile Crack ◽  
Growth Simulation ◽  
Crack Growth Simulation ◽  
Ductile Crack Growth

Abstract The aim of this study is to propose damage model on the basis of the mechanism for ductile fracture related to void growth and to confirm the applicability of the proposed model to ductile crack growth simulation for steel. To figure out void growth behavior, elasto-plastic finite element analyses using unit cell model with an initial void were methodically performed. From the results of those analyses, it was evident that the relationships between normalized void volume fraction and normalized strain by each critical value corresponding to crack initiation were independent of stress-strain relationship of material and stress triaxiality state. Based on this characteristic associated with void growth, damage evolution law was derived. Then, using the damage evolution law, simple and phenomenological ductile damage model reflecting void growth behavior and ductility of material was proposed. To confirm the validation and application of proposed damage model, the damage model was implemented in finite element models and ductile crack growth resistance was simulated for cracked components were performed. Then, the simulated results were compared with experimental ones and it was found that the proposed damage model could accurately predict ductile crack growth resistance and was applicable to ductile crack growth simulation.

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