Creep Analysis of Cr-Mo Steels Using a Dislocation Based Constitutive Modelling

2004 ◽  
Vol 449-452 ◽  
pp. 117-120 ◽  
Author(s):  
Hyoung Seop Kim ◽  
Min Hong Seo ◽  
Sun Ig Hong ◽  
Sung Ho Kim ◽  
Woo Seog Ryu
Keyword(s):  
Kinetic Equation ◽  
Dislocation Density ◽  
Metal Forming ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Creep Behaviour ◽  
Constitutive Modelling ◽  
Internal Variables ◽  
Dislocation Glide ◽  
Creep Analysis

In order to analyze the creep behaviour of Cr-Mo steels, an elasto-viscoplastic constitutive model based on dislocation density considerations is described. A combination of a kinetic equation, which describes the mechanical response of a material at a given microstructure in terms of dislocation glide, and evolution equations for internal variables characterising the microstructure provide the constitutive equations of the model. Microstructural features of the material are implemented in the constitutive equation. The internal variables are associated with the total dislocation density. The model has a modular structure and can be adjusted to describe a particular type of materials behaviour and metal forming processes. In this paper, the predicted creep behaviour of Cr-Mo steels is compared with the experimental results.

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

MRS Advances ◽  
2016 ◽  
Vol 1 (24) ◽  
pp. 1791-1796 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Slip System ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Structure Evolution ◽  
Internal Variables ◽  
Plastic Shear ◽  
Continuum Dislocation Dynamics ◽  
Dynamics Simulations

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

Strain-Rate Sensitive Constitutive Modeling of Anisotropic Visco-Hyperelastic Materials

2012 ◽  
Author(s):  
Sahand Ahsanizadeh ◽  
LePing Li
Keyword(s):  
Strain Rate ◽  
Evolution Equations ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Internal Variables ◽  
Current Configuration ◽  
Hyperelastic Materials ◽  
History Of ◽  
Viscoelastic Constitutive Model

Integral-based formulations of viscoelasticity have been widely used to describe the mechanical behavior of soft biological tissues and polymers. However, it is suggested that they are not suitable to be used under high strain rates. On the other hand, strain-rate sensitive models with an explicit dependence on the strain-rate have been developed for a certain class of materials. They predict the viscoelastic behavior during ramp loading more accurately while fail to account for the relaxation response. In order to overcome these drawbacks, a viscoelastic constitutive model has been proposed in this study based on the concept of internal variables. While the behavior of elastic materials is uniquely determined by the current state of deformation or external variables, the mechanical response of inelastic materials are regulated also by internal variables. The internal variables are associated with the dissipative mechanisms in the material and along with the evolution equations introduce the effect of history of the deformation to the current configuration. The current study employs short-term and long-term internal variables to account for the viscoelastic response during loading and relaxation respectively.

scholarly journals A dislocation density-based model for the work hardening and softening behaviors upon stress reversal

2021 ◽  
Vol 21 (2) ◽  
Author(s):  
Paulina Lisiecka-Graca ◽  
Krzysztof Bzowski ◽  
Janusz Majta ◽  
Krzysztof Muszka
Keyword(s):  
Dislocation Density ◽  
Electron Backscatter Diffraction ◽  
Microstructural Analysis ◽  
Back Stress ◽  
Carbon Steels ◽  
Internal Variables ◽  
Low Carbon ◽  
Average Dislocation Density ◽  
Calculation Results ◽  
Mechanical Behaviours

AbstractThe mechanical behaviours of microalloyed and low-carbon steels under strain reversal were modelled based on the average dislocation density taking into account its allocation between the cell walls and cell interiors. The proposed model reflects the effects of the dislocations displacement, generation of new dislocations and their annihilation during the metal-forming processes. The back stress is assumed as one of the internal variables. The value of the initial dislocation density was calculated using two different computational methods, i.e. the first one based on the dislocation density tensor and the second one based on the strain gradient model. The proposed methods of calculating the dislocation density were subjected to a comparative analysis. For the microstructural analysis, the high-resolution electron backscatter diffraction (EBSD) microscopy was utilized. The calculation results were compared with the results of forward/reverse torsion tests. As a result, good effectiveness of the applied computational methodology was demonstrated. Finally, the analysis of dislocation distributions as an effect of the strain path change was performed.

A Dislocation Density Based Constitutive Model for Cyclic Deformation

1996 ◽  
Vol 118 (4) ◽  
pp. 441-447 ◽  
Author(s):  
Y. Estrin ◽  
H. Braasch ◽  
Y. Brechet
Keyword(s):  
Cyclic Loading ◽  
Dislocation Density ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Cyclic Deformation ◽  
Internal Variables ◽  
Density Evolution ◽  
Alloy 800H ◽  
Material Response ◽  
Dislocation Densities

A new constitutive model describing material response to cyclic loading is presented. The model includes dislocation densities as internal variables characterizing the microstructural state of the material. In the formulation of the constitutive equations, the dislocation density evolution resulting from interactions between dislocations in channel-like dislocation patterns is considered. The capabilities of the model are demonstrated for INCONEL 738 LC and Alloy 800H.

Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

2014 ◽  
Vol 1651 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Evolution Equations ◽  
Continuum Theory ◽  
Orientation Distribution ◽  
Line Length ◽  
Second Order ◽  
Dislocation Dynamics ◽  
Alignment Tensor ◽  
Length Changes ◽  
Edge Dislocations

ABSTRACTIn the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

scholarly journals Dislocation dynamics modelling of the creep behaviour of particle-strengthened materials

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210083
Author(s):  
F. X. liu ◽  
A. C. F Cocks ◽  
E. Tarleton
Keyword(s):  
Elevated Temperatures ◽  
Creep Behaviour ◽  
Particle Interaction ◽  
Three Dimensional ◽  
Cross Slip ◽  
Dislocation Dynamics ◽  
Dislocation Slip ◽  
Fundamental Particle ◽  
Dislocation Glide ◽  
Time Scale Separation

Plastic deformation in crystalline materials occurs through dislocation slip and strengthening is achieved with obstacles that hinder the motion of dislocations. At relatively low temperatures, dislocations bypass the particles by Orowan looping, particle shearing, cross-slip or a combination of these mechanisms. At elevated temperatures, atomic diffusivity becomes appreciable, so that dislocations can bypass the particles by climb processes. Climb plays a crucial role in the long-term durability or creep resistance of many structural materials, particularly under extreme conditions of load, temperature and radiation. Here we systematically examine dislocation-particle interaction mechanisms. The analysis is based on three-dimensional discrete dislocation dynamics simulations incorporating impenetrable particles, elastic interactions, dislocation self-climb, cross-slip and glide. The core diffusion dominated dislocation self-climb process is modelled based on a variational principle for the evolution of microstructures, and is coupled with dislocation glide and cross-slip by an adaptive time-stepping scheme to bridge the time scale separation. The stress field caused by particles is implemented based on the particle–matrix mismatch. This model is helpful for understanding the fundamental particle bypass mechanisms and clarifying the effects of dislocation glide, climb and cross-slip on creep deformation.

Anisotropic Creep Behaviour of Bridgman Notch Specimens

2005 ◽  
Vol 219 (3) ◽  
pp. 163-175 ◽  
Author(s):  
T H Hyde ◽  
I A Jones ◽  
S Peravali ◽  
W Sun ◽  
J G Wang ◽  
...  
Keyword(s):  
Cross Section ◽  
Bulk Material ◽  
Creep Behaviour ◽  
Practical Application ◽  
Material Anisotropy ◽  
Yield Model ◽  
Anisotropic Parameter ◽  
Creep Analysis ◽  
Minimum Cross Section ◽  
Anisotropic Creep

A series of finite element anisotropic creep analyses of a Bridgman notch specimen have been performed. The anisotropic creep analysis is based on Hill's anisotropic yield model and the Norton creep law. An anisotropic parameter, p, is defined in order to quantify the degree of bulk material anisotropy which exists in a weld metal. The effects of p and the Norton stress exponent, n, on the stationary-state stresses, at the minimum cross-section of the notch, are presented. The material constants were chosen to include the practical range for engineering materials. Indications of the practical application of anisotropic analyses to welds are given.

On the Modeling of Evolving Elastic and Plastic Anisotropy in the Finite Strain Regime – Application to Deep Drawing Processes

2012 ◽  
Vol 504-506 ◽  
pp. 679-684 ◽  
Author(s):  
Ivaylo N. Vladimirov ◽  
Michael P. Pietryga ◽  
Vivian Tini ◽  
Stefanie Reese
Keyword(s):  
Deep Drawing ◽  
Evolution Equations ◽  
Finite Strain ◽  
Kinematic Hardening ◽  
Plastic Anisotropy ◽  
Material Model ◽  
Internal Variables ◽  
Time Step ◽  
Finite Element Software ◽  
Structure Tensors

In this work, we discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been used for the simulation of the phenomenon of earing during cylindrical deep drawing.

Influence of the Applied Load on the Creep Behaviour of Tin-Silver-Copper Solder

2019 ◽  
Author(s):  
Delfim F. Soares ◽  
Pedro E. Ribeiro ◽  
Pauline Capela ◽  
Daniel A. Barros ◽  
Maria F. Cerqueira ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Applied Load ◽  
Printed Circuit Boards ◽  
Creep Behaviour ◽  
Creep Tests ◽  
Dislocation Glide ◽  
Pcb Assembly ◽  
Creep Mechanisms ◽  
Solder Joint Fatigue

Abstract During the life cycle of an electronic printed circuit boards (PCBs), the cold solder joints formation between the component and PCB are a failure mode that happen commonly. This phenomenon is related to solder joint fatigue and is attributed mainly to the mismatch of the coefficients of thermal expansion (CTE) of component-solder-PCB assembly. With today’s solder joint thickness decreasing and increasing working temperatures, among others, the stresses and strains due to temperature changes are growing, leading to limited fatigue life of the products. In this way, once as fatigue life decreases with increasing plastic strain, it is important to study creep occurrence, especially during thermal cycles. In this work, a dynamic mechanical analyser (DMA) was used to study the influence of different applied load and temperature on the creep behaviour of the solder during a sequence of cycles. For these tests, different SAC405 alloy samples were produced, all in the same processing conditions. Creep tests were made on three-point-bending clamp configuration, isothermally at 303, 323 and 348 K, under three separate applied load of 3, 5 and 9 MPa. The results show that creep rate has an important decrease from the 1st to the following applied creep cycles. This behaviour occurs for all the tested loads and temperatures. Results, also, show that the main creep mechanisms changes, from a diffusion base type, for low load and different temperatures, to a dislocation glide-climb type for an applied load of 9 MPa and temperatures from 303 to 348 K. Experimental determined n exponent for the tested conditions allows the correlation between creep mechanisms and experimental parameters (applied load and temperature).

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